Tag Archives: Statistical Mechanics

A Maximum Entropy Principle for inferring the Distribution of 3D Plasmoids [HEAP]

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http://arxiv.org/abs/1702.05782


The Principle of Maximum Entropy, a powerful and general method for inferring the distribution function given a set of constraints, is applied to deduce the overall distribution of plasmoids (flux ropes/tubes). The analysis is undertaken for the general 3D case, with mass, total flux and (3D) velocity serving as the variables of interest, on account of their physical and observational relevance. The distribution functions for the mass, width, total flux and helicity exhibit a power-law behavior with exponents of $-4/3$, $-2$, $-3$ and $-2$ respectively for small values, whilst all of them display an exponential falloff for large values. In contrast, the velocity distribution, as a function of $v = |{\bf v}|$, is shown to be flat for $v \rightarrow 0$, and becomes a power law with an exponent of $-7/3$ for $v \rightarrow \infty$. Most of these results exhibit a high degree of universality, as they are nearly independent of the free parameters. A preliminary comparison of our results with the observational evidence is presented, and some of the ensuing space and astrophysical implications are discussed.

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M. Lingam, L. Comisso and A. Bhattacharjee
Tue, 21 Feb 17
25/70

Comments: 15 pages, 6 figures

Statistical mechanics of gravitating gas like galaxy [GA]

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http://arxiv.org/abs/1702.05429


The most probable state of an infinite self-gravitating gas in the dynamical equilibrium is defined by “gravitational haziness”, a parameter representing many-body effects and like the temperature in the case of thermal equilibrium. A kinetic equation for the distribution function of gas particles in the phase space is derived from a concept of statistical equipartition of the virial among subsystems. Its solution, an analog of the Maxwell-Boltzmann weight, is found in the limit of thick “gravitational haziness” (the high-temperature expansion) where the gravitational potential follows the Lane-Emden equation. A more general equation for arbitrary “gravitational haziness” is conjectured as a special property of the kinetic equation. The first law of a “hazydynamics” (thermodynamics) states that the total mass of an astronomical stellar collection is the sum of the Archimedes displaced mass and an excess “gobbled” mass determined by the “gravitational haziness” and history.

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A. Kashuba
Mon, 20 Feb 17
2/37

Comments: 5 pages

Kinetic theory of fermions in curved spacetime [CL]

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http://arxiv.org/abs/1701.08844


We build a statistical description of fermions, taking into account the spin degree of freedom in addition to the momentum of particles, and we detail its use in the context of the kinetic theory of gases of fermions particles. We show that the one-particle distribution function needed to write a Liouville equation is a spinor valued operator. The degrees of freedom of this function are covariantly described by an intensity function and by a polarisation vector which are parallel transported by free streaming. Collisions are described on the microscopic level and lead to a Boltzmann equation for this operator. We apply our formalism to the case of weak interactions, which at low energies can be considered as a contact interaction between fermions, allowing us to discuss the structure of the collision term for a few typical weak-interaction mediated reactions. In particular we find for massive particles that a dipolar distribution of velocities in the interacting species is necessary to generate linear polarisation, as opposed to the case of photons for which linear polarisation is generated from the quadrupolar distribution of velocities.

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C. Fidler and C. Pitrou
Wed, 1 Feb 17
11/67

Comments: 47 pages, 1 figure

Isotropic-Nematic Phase Transitions in Gravitational Systems [GA]

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http://arxiv.org/abs/1701.03271


We examine dense self-gravitating stellar systems dominated by a central potential, such as nuclear star clusters hosting a central supermassive black hole. Different dynamical properties of these systems evolve on vastly different timescales. In particular, the orbital-plane orientations are typically driven into internal thermodynamic equilibrium by vector resonant relaxation before the orbital eccentricities or semimajor axes relax. We show that the statistical mechanics of such systems exhibit a striking resemblance to liquid crystals, with analogous ordered-nematic and disordered-isotropic phases. The ordered phase consists of bodies orbiting in a disk in both directions, with the disk thickness depending on temperature, while the disordered phase corresponds to a nearly isotropic distribution of the orbit normals. We show that below a critical value of the total angular momentum, the system undergoes a first-order phase transition between the ordered and disordered phases. At the critical point the phase transition becomes second-order while for higher angular momenta there is a smooth crossover. We also find metastable equilibria containing two identical disks with mutual inclinations between $90^{\circ}$ and $180^\circ$.

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Z. Roupas, B. Kocsis and S. Tremaine
Fri, 13 Jan 17
32/44

Comments: 33 pages, 23 figures

Formation and relaxation of quasi-stationary states in particle systems with power law interactions [CL]

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http://arxiv.org/abs/1701.01865


We explore the formation and relaxation of so-called quasi-stationary states (QSS) for particle distributions in three dimensions interacting via an attractive radial pair potential $V(r \rightarrow \infty) \sim 1/r^\gamma$ with $\gamma > 0$, and either a soft-core or hard-core regularization at small $r$. In the first part of the paper we generalize, for any spatial dimension $d \geq 2$, Chandrasekhar’s approach for the case of gravity to obtain analytic estimates of the rate of collisional relaxation due to two body collisions. The resultant relaxation rates indicate an essential qualitative difference depending on the integrability of the pair force at large distances: for $\gamma >d-1$ the rate diverges in the large particle number $N$ (mean field) limit, unless a sufficiently large soft core is present; for $\gamma < d-1$, on the other hand, the rate vanishes in the same limit even in the absence of any regularization. In the second part of the paper we compare our analytical predictions with the results of extensive parallel numerical simulations in $d=3$, for a range of different exponents $\gamma$ and soft cores leading to the formation of QSS. We find, just as for the previously well studied case of gravity (which we also revisit), excellent agreement between the parametric dependence of the observed relaxation times and our analytic predictions. Further, as in the case of gravity, we find that the results indicate that, when large impact factors dominate, the appropriate cut-off is the size of the system (rather than, for example, the mean inter-particle distance). Our results provide strong evidence that the existence of QSS is robust only for long-range interactions with a large distance behavior $\gamma < d-1$; for $\gamma \geq d-1$ the existence of such states will be conditioned strongly on the short range properties of the interaction.

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B. Marcos, A. Gabrielli and M. Joyce
Tue, 10 Jan 17
16/75

Comments: 21 pages, 11 figures, submitted to PRE

Dynamical system modeling fermionic limit [CL]

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http://arxiv.org/abs/1612.05442


The existence of multiple radial solutions to the elliptic equation modeling fermionic cloud of interacting particles is proved for the limiting Planck constant and intermediate values of mass parameters. It is achieved by considering the related nonautonomous dynamical system for which the passage to the limit can be established due to the continuity of the solutions with respect to the parameter going to zero.

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D. Bors and R. Stanczy
Mon, 19 Dec 16
46/54

Comments: 12 pages, 2 figures

Thermodynamics of gravitational clustering phenomena: $N$-body self-gravitating gas on the sphere $\mathbb{S}^{3}\subset\mathbb{R}^{4}$ [CL]

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http://arxiv.org/abs/1610.02112


This work is devoted to the thermodynamics of gravitational clustering, a collective phenomenon with a great relevance in the $N$-body cosmological problem. We study a classical self-gravitating gas of identical non-relativistic particles defined on the sphere $\mathbb{S}^{3}\subset \mathbb{R}^{4}$ by considering gravitational interaction that corresponds to this geometric space. The analysis is performed within microcanonical description of an isolated Hamiltonian system by combining continuum approximation and steepest descend method. According to numerical solution of resulting equations, the gravitational clustering can be associated with two microcanonical phase transitions. A first phase transition with a continuous character is associated with breakdown of $SO(4)$ symmetry of this model. The second one is the gravitational collapse, whose continuous or discontinuous character crucially depends on the regularization of short-range divergence of gravitation potential. We also derive the thermodynamic limit of this model system, the astrophysical counterpart of Gibbs-Duhem relation, the order parameters that characterize its phase transitions and the equation of state. Other interesting behavior is the existence of states with negative heat capacities, which appear when the effects of gravitation turn dominant for energies sufficiently low. Finally, we comment the relevance of some of these results in the study of astrophysical and cosmological situations. Special interest deserves the gravitational modification of the equation of state due to the local inhomogeneities of matter distribution. Although this feature is systematically neglected in studies about Universe expansion, the same one is able to mimic an effect that is attributed to the dark energy: a negative pressure.

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F. Tello-Ortiz and L. Velazquez
Mon, 10 Oct 16
16/51

Comments: To appear in J. Stat. Mech.: Theo. Exp

Entanglement Growth after a Global Quench in Free Scalar Field Theory [CL]

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http://arxiv.org/abs/1609.00872


We compute the entanglement and R\’enyi entropy growth after a global quench in various dimensions in free scalar field theory. We study two types of quenches: a boundary state quench and a global mass quench. Both of these quenches are investigated for a strip geometry in 1, 2, and 3 spatial dimensions, and for a spherical geometry in 2 and 3 spatial dimensions. We compare the numerical results for massless free scalars in these geometries with the predictions of the analytical quasiparticle model based on EPR pairs, and find excellent agreement in the limit of large region sizes. At subleading order in the region size, we observe an anomalous logarithmic growth of entanglement coming from the zero mode of the scalar.

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J. Cotler, M. Hertzberg, M. Mezei, et. al.
Tue, 6 Sep 16
68/74

Comments: 32 pages, 9 figures

Quantum statistics of classical particles derived from the condition of free diffusion coefficient [CL]

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http://arxiv.org/abs/1608.08655


We derive an equation for the current of particles in energy space; particles are subject to a mean field effective potential that may represent quantum effects. From the assumption that non-interacting particles imply a free diffusion coefficient in energy space we derive Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein statistics. Other new statistics are associated to a free diffusion coefficient; their thermodynamic properties are analyzed using the grand partition function. A negative relation between pressure and energy density for low temperatures can be derived, suggesting a possible connection with cosmological dark energy models.

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M. Hoyuelos and P. Sisterna
Thu, 1 Sep 16
52/74

Comments: 7 pages, 1 figure

Jets or vortices – what flows are generated by an inverse turbulent cascade? [CL]

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http://arxiv.org/abs/1608.04628


An inverse cascade – energy transfer to progressively larger scales – is a salient feature of two-dimensional turbulence. If the cascade reaches the system scale, it creates a coherent flow expected to have the largest available scale and conform with the symmetries of the domain. In a doubly periodic rectangle, the mean flow with zero total momentum was therefore believed to be unidirectional, with two jets along the short side; while for an aspect ratio close to unity, a vortex dipole was expected. Using direct numerical simulations, we show that in fact neither the box symmetry is respected nor the largest scale is realized: the flow is never purely unidirectional since the inverse cascade produces coherent vortices, whose number and relative motion are determined by the aspect ratio. This spontaneous symmetry breaking is closely related to the hierarchy of averaging times. Long-time averaging restores translational invariance due to vortex wandering along one direction, and gives jets whose profile, however, can be deduced neither from the largest-available-scale argument, nor from the often employed maximum-entropy principle or quasi-linear approximation.

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A. Frishman, J. Laurie and G. Falkovich
Wed, 17 Aug 16
6/48

Comments: N/A

Theory of complex fluids in the warm-dense-matter regime, and application to phase-transitions in liquid carbon [CL]

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http://arxiv.org/abs/1607.07511


Using data from recent laser-shock experiments and related density-functional molecular-dynamics simulations on carbon, we demonstrate that the ionic structures predicted within the neutral-pseudo-atom approach for a complex liquid in the warm-dense matter regime are in good agreement with available data, even where transient covalent bonding dominates ionic correlations. Evidence for an unusual phase transition of a liquid $\to$ vapor with an abrupt decrease in ionization occurring simultaneously is presented. Here a covalently-bonded metallic-liquid, i.e., carbon of density 1.0 g/cm$^3$, transits to a disordered mono-atomic fluid at 7 eV. Other transitions where the mean ionization $Z$ drops abruptly are also uncovered

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M. Dharma-wardana
Wed, 27 Jul 16
64/69

Comments: 4 pages, three figures, Revtex

Truncated $γ$-exponential models for tidal stellar systems [GA]

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http://arxiv.org/abs/1607.03774


We introduce a parametric family of models to characterize the properties of astrophysical systems in a quasi-stationary evolution under the incidence evaporation. We start from an one-particle distribution $f_{\gamma}\left(\mathbf{q},\mathbf{p}|\beta,\varepsilon_{s}\right)$ that considers an appropriate deformation of Maxwell-Boltzmann form with inverse temperature $\beta$, in particular, a power-law truncation at the scape energy $\varepsilon_{s}$ with exponent $\gamma>0$. This deformation is implemented using a generalized $\gamma$-exponential function obtained from the \emph{fractional integration} of ordinary exponential. As shown in this work, this proposal generalizes models of tidal stellar systems that predict particles distributions with \emph{isothermal cores and polytropic haloes}, e.g.: Michie-King models. We perform the analysis of thermodynamic features of these models and their associated distribution profiles. A nontrivial consequence of this study is that profiles with isothermal cores and polytropic haloes are only obtained for low energies whenever deformation parameter $\gamma<\gamma_{c}\simeq 2.13$.

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Y. Gomez-Leyton and L. Velazquez
Thu, 14 Jul 16
39/72

Comments: N/A

Duration of classicality in highly degenerate interacting Bosonic systems [CL]

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http://arxiv.org/abs/1607.00949


We study sets of oscillators that have high quantum occupancy and that interact by exchanging quanta. It is shown by analytical arguments and numerical simulation that such systems obey classical equations of motion only on time scales of order their relaxation time $\tau$ and not longer than that. The results are relevant to the cosmology of axions and axion-like particles.

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P. Sikivie and E. Todarello
Tue, 5 Jul 16
66/80

Comments: 5 pages, 3 figures

Secular diffusion in discrete self-gravitating tepid discs III. Resonant thickening in the tightly wound limit [GA]

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http://arxiv.org/abs/1605.03384


The secular thickening of a discrete self-gravitating galactic disc is investigated using the inhomogeneous multi-component Balescu-Lenard equation. The thick WKB limit for the diffusion and drift coefficients is found using the epicyclic approximation, while assuming that only radially tightly wound transient spirals are sustained by the disc. This yields a simple double quadrature for the drift and diffusion coefficients, providing a clear understanding of the positions of maximum vertical orbital diffusion within the disc induced by the effects of a finite number of particles. When applied to a tepid stable tapered disc, the Balescu-Lenard formalism predicts the formation of ridges of resonant orbits towards larger vertical actions, as found in direct numerical simulations, but over-estimates the timescale involved in their appearance. Swing amplication is likely needed to resolve this discrepancy, as demonstrated in the case of razor-thin discs. The joint evolution of a population of giant molecular clouds within the disc may accelerate the secular disc’s thickening induced by finite${-N}$ effects, but the observed number of clouds in the Milky Way does not seem to be sufficient to explain its thick disc.

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J. Fouvry, C. Pichon and P. Chavanis
Thu, 12 May 16
39/59

Comments: 18 pages, 14 figures, submitted to A&A

Photophoresis on particles hotter or colder than the ambient gas in the free molecular flow [CL]

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http://arxiv.org/abs/1605.01022


Aerosol particles experience significant photophoretic forces at low pressure. Previous work assumed the average particle temperature to be very close to the gas temperature. This might not always be the case. If the particle temperature or the thermal radiation field differs significantly from the gas temperature (optically thin gases), given approximations overestimate the photophoretic force by an order of magnitude on average with maximum errors up to more than three magnitudes. We therefore developed a new general approximation which on average only differs by 1 % from the true value.

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C. Loesche, G. Wurm, T. Jankowski, et. al.
Wed, 4 May 16
9/44

Comments: 11 pages

Theory of Thomson scattering in inhomogeneous media [CL]

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http://arxiv.org/abs/1604.08260


Thomson scattering of laser light is one of the most fundamental diagnostics of plasma density, temperature and magnetic fields. It relies on the assumption that the properties in the probed volume are homogeneous and constant during the probing time. On the other hand, laboratory plasmas are seldom uniform and homogeneous on the temporal and spatial dimensions over which data is collected. This is partic- ularly true for laser-produced high-energy-density matter, which often exhibits steep gradients in temperature, density and pressure, on a scale determined by the laser focus. Here, we discuss the modification of the cross section for Thomson scattering in fully-ionized media exhibiting steep spatial inhomogeneities and/or fast temporal fluctuations. We show that the predicted Thomson scattering spectra are greatly altered compared to the uniform case, and may even lead to violations of detailed balance. Therefore, careful interpretation of the spectra is necessary for spatially or temporally inhomogeneous systems.

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P. Kozlowski, B. Crowley, D. Gericke, et. al.
Fri, 29 Apr 16
35/57

Comments: 18 pages, 4 figures. Publication with corrected referencing for submitted article: this http URL

Relative information entropy in cosmology: The problem of information entanglement [CL]

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http://arxiv.org/abs/1604.06947


The necessary information to distinguish a local inhomogeneous mass density field from its spatial average on a compact domain of the universe can be measured by relative information entropy. The Kullback-Leibler (KL) formula arises very naturally in this context, however, it provides a very complicated way to compute the mutual information between spatially separated but causally connected regions of the universe in a realistic, inhomogeneous model. To circumvent this issue, by considering a parametric extension of the KL measure, we develop a simple model to describe the mutual information which is entangled via the gravitational field equations. We show that the Tsallis relative entropy can be a good approximation in the case of small inhomogeneities, and for measuring the independent relative information inside the domain, we propose the R\’enyi relative entropy formula.

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V. Czinner and F. Mena
Tue, 26 Apr 16
58/61

Comments: 6 pages, 3 figures, to appear in Phys. Lett. B

Functional integral approach to the kinetic theory of inhomogeneous systems [GA]

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http://arxiv.org/abs/1604.02338


We present a derivation of the kinetic equation describing the secular evolution of spatially inhomogeneous systems with long-range interactions, the so-called inhomogeneous Landau equation, by relying on a functional integral formalism. We start from the BBGKY hierarchy derived from the Liouville equation. At the order ${1/N}$, where $N$ is the number of particles, the evolution of the system is characterised by its 1-body distribution function and its 2-body correlation function. Introducing associated auxiliary fields, the evolution of these quantities may be rewritten as a traditional functional integral. By functionally integrating over the 2-body autocorrelation, one obtains a new constraint connecting the 1-body DF and the auxiliary fields. When inverted, this constraint allows us to obtain the closed non-linear kinetic equation satisfied by the 1-body distribution function. This derivation provides an alternative to previous methods, either based on the direct resolution of the truncated BBGKY hierarchy or on the Klimontovich equation. It may turn out to be fruitful to derive more accurate kinetic equations, e.g., accounting for collective effects, or higher order correlation terms.

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J. Fouvry, P. Chavanis and C. Pichon
Mon, 11 Apr 16
43/52

Comments: 13 pages, accepted for publication in Physica A

The effect of $^{22}$Ne diffusion in the evolution and pulsational properties of white dwarfs with solar metallicity progenitors [SSA]

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http://arxiv.org/abs/1604.01744


Because of the large neutron excess of $^{22}$Ne, this isotope rapidly sediments in the interior of the white dwarfs. This process releases an additional amount of energy, thus delaying the cooling times of the white dwarf. This influences the ages of different stellar populations derived using white dwarf cosmochronology. Furthermore, the overabundance of $^{22}$Ne in the inner regions of the star, modifies the Brunt-V\”ais\”al\”a frequency, thus altering the pulsational properties of these stars. In this work, we discuss the impact of $^{22}$Ne sedimentation in white dwarfs resulting from Solar metallicity progenitors ($Z=0.02$). We performed evolutionary calculations of white dwarfs of masses $0.528$, $0.576$, $0.657$ and $0.833$ M$_{\sun}$, derived from full evolutionary computations of their progenitor stars, starting at the Zero Age Main Sequence all the way through central hydrogen and helium burning, thermally-pulsing AGB and post-AGB phases. Our computations show that at low luminosities ($\log(L/L_{\sun})\la -4.25$), $^{22}$Ne sedimentation delays the cooling of white dwarfs with Solar metallicity progenitors by about 1~Gyr. Additionally, we studied the consequences of $^{22}$Ne sedimentation on the pulsational properties of ZZ~Ceti white dwarfs. We find that $^{22}$Ne sedimentation induces differences in the periods of these stars larger than the present observational uncertainties, particularly in more massive white dwarfs.

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M. Camisassa, L. Althaus, A. Corsico, et. al.
Thu, 7 Apr 16
21/51

Comments: Accepted for publication in ApJ. 8 pages, 6 figures

Discriminating Topology in Galaxy Distributions using Network Analysis [CEA]

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http://arxiv.org/abs/1603.02285


(abridged) The large-scale distribution of galaxies is generally analyzed using the two-point correlation function. However, this statistic does not capture the topology of the distribution, and it is necessary to resort to higher order correlations to break degeneracies. We demonstrate that an alternate approach using network analysis can discriminate between topologically different distributions that have similar two-point correlations. We investigate two galaxy point distributions, one produced by a cosmological simulation and the other by a L\’evy walk. For the cosmological simulation, we adopt the redshift $z = 0.58$ slice from Illustris (Vogelsberger et al. 2014A) and select galaxies with stellar masses greater than $10^8$$M_\odot$. The two point correlation function of these simulated galaxies follows a single power-law, $\xi(r) \sim r^{-1.5}$. Then, we generate L\’evy walks matching the correlation function and abundance with the simulated galaxies. We find that, while the two simulated galaxy point distributions have the same abundance and two point correlation function, their spatial distributions are very different; most prominently, \emph{filamentary structures}, absent in L\’evy fractals. To quantify these missing topologies, we adopt network analysis tools and measure diameter, giant component, and transitivity from networks built by a conventional friends-of-friends recipe with various linking lengths. Unlike the abundance and two point correlation function, these network quantities reveal a clear separation between the two simulated distributions; therefore, the galaxy distribution simulated by Illustris is not a L\’evy fractal quantitatively. We find that the described network quantities offer an efficient tool for discriminating topologies and for comparing observed and theoretical distributions.

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S. Hong, B. Coutinho, A. Dey, et. al.
Wed, 9 Mar 16
12/71

Comments: 11 pages, 5 figures, submitted to MNRAS on 12/15/2015, now fully reviewed for publication; more information about our network analyses can be found at this https URL

Jeans instability criterion from the viewpoint of non-gaussian statistics [CEA]

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http://arxiv.org/abs/1603.00296


In this Letter we have derived the Jeans length in the context of the Kaniadakis statistics. We have compared this result with the Jeans length obtained in the non-extensive Tsallis statistics and discussed the main differences between these two models. We have also obtained the kappa-sound velocity. Finally, we have applied the results obtained here to analyze an astrophysical system.

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E. Abreu, J. Neto, E. Barboza, et. al.
Wed, 2 Mar 16
15/65

Comments: 6 pages, 3 figures

Is the Hypothesis About a Low Entropy Initial State of the Universe Necessary for Explaining the Arrow of Time? [CEA]

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http://arxiv.org/abs/1602.05601


According to statistical mechanics, micro-states of an isolated physical system (say, a gas in a box) at time $t_0$ in a given macro-state of less-than-maximal entropy typically evolve in such a way that the entropy at time $t$ increases with $|t-t_0|$ in both time directions. In order to account for the observed entropy increase in only one time direction, the thermodynamic arrow of time, one usually appeals to the hypothesis that the initial state of the universe was one of very low entropy. In certain recent models of cosmology, however, no hypothesis about the initial state of the universe is invoked. We discuss how the emergence of a thermodynamic arrow of time in such models can nevertheless be compatible with the above-mentioned consequence of statistical mechanics, appearances to the contrary notwithstanding.

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S. Goldstein, R. Tumulka and N. Zanghi
Fri, 19 Feb 16
33/50

Comments: 13 pages LaTeX, 3 figures

Practical Introduction to Clustering Data [CL]

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http://arxiv.org/abs/1602.05124


Data clustering is an approach to seek for structure in sets of complex data, i.e., sets of “objects”. The main objective is to identify groups of objects which are similar to each other, e.g., for classification. Here, an introduction to clustering is given and three basic approaches are introduced: the k-means algorithm, neighbour-based clustering, and an agglomerative clustering method. For all cases, C source code examples are given, allowing for an easy implementation.

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A. Hartmann
Wed, 17 Feb 16
30/55

Comments: 22 pages. All source code in anc directory included. Section 8.5.6 of book: A.K. Hartmann, Big Practical Guide to Computer Simulations, World-Scientifc, Singapore (2015)

Current issues in finite-$T$ density-functional theory and Warm-Correlated Matter [CL]

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http://arxiv.org/abs/1602.04734


Finite-temperature DFT has become of topical interest, partly due to the increasing ability to create novel states of warm-correlated matter (WCM). Warm-dense matter (WDM), ultra-fast matter (UFM), and high-energy density matter (HEDM) may all be regard as subclasses of WCM. Strong electron-electron, ion-ion and electron-ion correlation effects and partial degeneracies are found in these systems where the electron temperature $T_e$ is comparable to the electron Fermi energy $E_F$. Thus many electrons are in continuum states which are partially occupied. The ion subsystem may be solid, liquid or plasma, with many states of ionization with ionic charge $Z_j$. Quasi-equilibria with the ion temperature $T_i\ne T_e$ are common. The ion subsystem in WCM can no longer be treated as a passive “external potential”, as is customary in $T=0$ density functional theory (DFT) dominated by solid-state theory or quantum chemistry. Hohenberg-Kohn-Mermin theory can be adapted for treating these systems if suitable finite-$T$ exchange-correlation functionals can be constructed. They are functionals of both the one-body electron density $n_e$ and the one-body ion densities $\rho_j$. Here $j$ counts many species of nuclei or charge states. Many basic questions arise in trying to implement DFT for WCM. In this review current developments and concerns in finite-$T$ DFT, especially in the context of non-relativistic warm-dense matter and ultra-fast matter will be presented.

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M. Dharma-wardana
Tue, 16 Feb 16
57/71

Comments: Presented at the DFT16 meeting in Debrecen, Hungary, September 2015, held on the 50th anniversary of Kohn-Sham Theory, 9 pages, 3 figures

Gravitation Field Dynamics in Jeans Theory [CL]

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http://arxiv.org/abs/1602.01041


Closed system of time equations for nonrelativistic gravitation field and hydrodynamic medium was obtained by taking into account binary correlations of the field, which is the generalization of Jeans theory. Distribution function of the systemwas built on the basis of the Bogolyubov reduced description method. Calculations were carried out up to the first order of a perturbation theory in interaction. Adiabatic and enthropic types of perturbations were corrected and two new types of perturbations were found.

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A. Stupka
Wed, 3 Feb 16
12/54

Comments: Time equations; Jeans theory; Bogolyubov reduced description method; perturbation types. this http URL

Attractor non-equilibrium stationary states in perturbed long-range interacting systems [CL]

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http://arxiv.org/abs/1601.03644


Isolated long-range interacting particle systems appear generically to relax to non-equilibrium states (“quasi-stationary states” or QSS) which are stationary in the thermodynamic limit. A fundamental open question concerns the “robustness” of these states when the system is not isolated. In this paper we explore, using both analytical and numerical approaches to a paradigmatic one dimensional model, the effect of a simple class of perturbations. We call them “internal local perturbations” in that the particle energies are perturbed at collisions in a way which depends only on the local properties. Our central finding is that the effect of the perturbations is to drive all the very different QSS we consider towards a unique QSS. The latter is thus independent of the initial conditions of the system, but determined instead by both the long-range forces and the details of the perturbations applied. Thus in the presence of such a perturbation the long-range system evolves to a unique non-equilibrium stationary state, completely different to its state in absence of the perturbation, and it remains in this state when the perturbation is removed. We argue that this result may be generic for long-range interacting systems subject to perturbations which are dependent on the local properties (e.g. spatial density or velocity distribution) of the system itself.

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M. Joyce, J. Morand and P. Viot
Thu, 21 Jan 16
43/52

Comments: 16 pages, 12 figures

Classical particle scattering for power-law two-body potentials [CL]

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http://arxiv.org/abs/1601.00064


We present a rigorous study of the classical scattering for anytwo-body inter-particle potential of the form $v(r)=g/r^\gamma$, with$\gamma\textgreater{}0$, for repulsive ($g\textgreater{}0$) and attractive ($g\textless{}0$)interactions. We give a derivation of the complete power series of thedeflection angle in terms of the impact factor for the weak scatteringregime (large impact factors) as well as the asymptotic expressionsfor the hard scattering regime (small impact factors). We see a verydifferent qualitative and quantitative behavior depending whether theinteraction is repulsive or attractive. In the latter case, thefamilies of trajectories depend also strongly on the value of$\gamma$. We also study carefully the modifications of the resultswhen a regularization is introduced in the potential at small scales.We check and illustrate all the results with the exact integration ofthe equations of motion.

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D. Chiron and B. Marcos
Tue, 5 Jan 16
35/104

Comments: 23 pages, 17 figures

Black hole thermodynamics in finite time [CL]

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http://arxiv.org/abs/1601.00353


Finite-time thermodynamics provides the means to revisit ideal thermodynamic equilibrium processes in the light of reality and investigate the energetic “price of haste”, i.e. the consequences of carrying out a process in finite time, when perfect equilibrium cannot be awaited due to economic reasons or the nature of the process. Employing the formalism of geometric thermodynamics, a lower bound on the energy dissipated during a process is derived from the thermodynamic length of that process. The notion of length is hereby defined via a metric structure on the space of equilibrium thermodynamics, spanned by a set of thermodynamic variables describing the system. Since the aim of finite-time thermodynamics is to obtain realistic limitations on idealized scenarios, it is a useful tool to reassess the efficiency of thermodynamic processes. We examine its implications for black hole thermodynamics, in particular scenarios inspired by the Penrose process, a thought experiment by which work can be extracted from a rotating black hole. We consider a Kerr black hole which, by some mechanism, is losing mass and angular momentum. Thermodynamically speaking, such a process is described in the equilibrium phase space of the black hole, but in reality, it is neither reversible nor infinitely slow. We thus calculate the dissipated energy due to non-ideal finite-time effects.

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C. Gruber
Tue, 5 Jan 16
78/104

Comments: 4 pages, 2 figures, Proceedings of the 14th Marcel Grossmann Meeting

Poiseuille flow in curved spaces [CL]

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http://arxiv.org/abs/1512.02982


We investigate Poiseuille channel flow through intrinsically curved (campylotic) media, equipped with localized metric perturbations (campylons). To this end, we study the flux of a fluid driven through the curved channel in dependence of the spatial deformation, characterized by the campylon parameters (amplitude, range and density). We find that the flux depends only on a specific combination of campylon parameters, which we identify as the average campylon strength, and derive a universal flux law for the Poiseuille flow. For the purpose of this study, we have improved and validated our recently developed lattice Boltzmann model in curved space by considerably reducing discrete lattice effects.

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J. Debus, M. Mendoza, S. Succi, et. al.
Fri, 11 Dec 15
23/71

Comments: N/A

Trapping scaling for bifurcations in Vlasov systems [CL]

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http://arxiv.org/abs/1511.07645


We study non oscillating bifurcations of non homogeneous steady states of the Vlasov equation, a situation occurring in galactic models, or for Bernstein-Greene-Kruskal modes in plasma physics. We show that resonances are strongly suppressed, leading to very different phenomena with respect to the homogeneous case. Through an unstable manifold expansion, we show that the dynamics is very sensitive to the initial perturbation: the instability may saturate at small amplitude -generalizing the “trapping scaling” of plasma physics- or may grow to produce a large scale modification of the system. These analytical findings are illustrated and extended by direct numerical simulations with a cosine interaction potential.

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J. Barre, D. Metivier and Y. Yamaguchi
Wed, 25 Nov 15
56/74

Comments: 8 pages, 2 figures. Movies illustrating the numerical simulations available upon request

Thermodynamic optimization of a Penrose process: an engineers' approach to black hole thermodynamics [CL]

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http://arxiv.org/abs/1511.06801


In this work we present a new view on the thermodynamics of black holes introducing effects of irreversibility by employing thermodynamic optimization and finite-time thermodynamics. These questions are of importance both in physics and in engineering, combining standard thermodynamics with optimal control theory in order to find optimal protocols and bounds for realistic processes without assuming anything about the microphysics involved. We find general bounds on the maximum work and the efficiency of thermodynamic processes involving black holes that can be derived exclusively from the knowledge of thermodynamic relations at equilibrium. Since these new bounds consider the finite duration of the processes, they are more realistic and stringent than their reversible counterparts. To illustrate our arguments, we consider in detail the thermodynamic optimization of a Penrose process, i.e. the problem of finding the least dissipative process extracting all the angular momentum from a Kerr black hole in finite time. We discuss the relevance of our results for real astrophysical phenomena, for the comparison with laboratory black holes analogues and for other theoretical aspects of black hole thermodynamics.

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A. Bravetti, C. Gruber and C. Lopez-Monsalvo
Tue, 24 Nov 15
84/85

Comments: 12 pages, 4 figures. Comments are welcome!

Explaining the stellar initial mass function with the theory of spatial networks [SSA]

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http://arxiv.org/abs/1511.05200


The distributions of stars and prestellar cores by mass (initial and dense core mass functions, IMF/DCMF) stay among the key factors regulating star formation and are subject of detailed theoretical and observational studies. Results from numerical simulations of star formation qualitatively resemble an observed mass function, a scale free power law with a sharp decline at low masses. However, most analytic IMF theories critically depend on the empirically chosen input spectrum of mass fluctuations which evolve into dense cores and, subsequently, stars. Here we propose a new approach exploiting the techniques from the field of network science. We represent a system of dense cores accreting gas from the surrounding diffuse interstellar medium (ISM) as a spatial network growing by preferential attachment and assume that the ISM density has a self-similar fractal distribution following the Kolmogorov turbulence theory. As opposed to gravoturbulent fragmentation theories, we consider the dense core growth and demonstrate that the power law core mass function emerges independently of the initial distribution of density fluctuations by mass. Our model yields a power law solely defined by the fractal dimensionalities of the ISM and accreting gas. With a proper choice of the low mass cut-off, it reproduces observations over three decades in mass. We also rule out a low mass star dominated “bottom-heavy” IMF in a single star forming region.

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A. Klishin and I. Chilingarian
Wed, 18 Nov 15
54/61

Comments: submitted to ApJ, 7 pages, 5 figures

Analysis of Jeans instability from Boltzmann equation [CEA]

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http://arxiv.org/abs/1508.07324


The dynamics of self-gravitating fluids is analyzed within the framework of a collisionless Boltzmann equation in the presence of gravitational fields and Poisson equation. The equilibrium distribution function takes into account the expansion of the Universe and a pressureless fluid in the matter dominated Universe. Without invoking Jeans “swindle” a dispersion relation is obtained by considering small perturbations of the equilibrium values of the distribution function and gravitational potential. The collapse criterion — which happens in an unstable region where the solution grows exponentially with time — is determined from the dispersion relation. The collapse criterion in a static Universe occurs when the wavenumber $k$ is smaller than the Jeans wavenumber $k_J$, which was the solution found by Jeans. For an expanding Universe it is shown that this criterion is $k\leq\sqrt{7/6}\,k_J$. As a consequence the ratio of the mass contained in a sphere of diameter equal to the wavelength $\lambda=2\pi/k$ to the Jeans mass in an expanding Universe is smaller than the one in a static Universe.

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G. Kremer
Tue, 1 Sep 15
51/82

Comments: 4 pages, 1 figure

Complexity Induced Sporadic Localized Multifractal Antiscreening in Gravitational Evolution at Large Scales [CL]

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http://arxiv.org/abs/1508.07261


It has been suggested that antiscreening effects due to the running of the gravitational constant G might provide a partial solution to the dark matter mystery. It has also been hypothesized that renormalization group scaling transformations at large scales might supply the theoretical explanation. In this letter, we demonstrate that multifractal coarse-graining scaling effects due to classical fluctuations in the IR with consecutive symmetry breakings in gravitational evolution and induced running of the gravitational constant with fractal structures at larger scales may provide the plausible explanation of the observed results of weak lensing observations and beyond. The sporadic and localized antiscreening due to the running of the gravitational constant can also provide the backbone for the cosmic evolution and large scale structure formation. Our interpretation of this interesting finding is that such effects are the result of the complexity phenomenon involving the evolution of large-scale multifractal structures and accompanying fluctuations, not the conventional arguments suggesting quantum gravity being the primary cause. We also suggest that the running of the cosmological constant due to such stochastic complexity evolution may provide a key to the understanding of the observed cosmic acceleration.

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T. Chang
Mon, 31 Aug 15
35/63

Comments: 16 pages

Thermal radiation and blackbody radiation drag of a large-sized perfectly black particle moving with relativistic velocity [HEAP]

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http://arxiv.org/abs/1508.04455


We have developed a self-consistent description of the radiation heat transfer and dynamics of large perfectly black spherical bodies with sizes much greater than the characteristic wavelength of radiation moving in a photon gas with relativistic velocity. The results can be important in astrophysics.

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A. Kyasov and G. Dedkov
Thu, 20 Aug 15
32/55

Comments: 10 pages, 1 figure

The nonextensive parameter for the astrophysical systems in an external rotating field [CL]

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http://arxiv.org/abs/1508.02290


Based on the q-kinetic theory in nonextensive statistics, we study the nonextensive q-parameter for the astrophysical systems in an external rotating field. We exactly obtained the equation of the q-parameter for the rotating self-gravitating system. We show that the q-parameter is not only related to the temperature gradient and the gravitational acceleration of the system, but also depends on the inertial centrifugal acceleration and the angular velocity of the rotation, and so the rotation introduces the nonextensivity. This equation of the q-parameter is also applicable to the rotating space plasmas, where an exact expression is presented. We take the Sun, Jupiter and Saturn as examples to illustrate the nonextensive effect introduced by the rotation.

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H. Yu and J. Du
Tue, 11 Aug 15
43/57

Comments: 8 pages, 39 references

Crossing Statistics of Anisotropic Stochastic Surface [CL]

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http://arxiv.org/abs/1508.01409


We use crossing statistics and its generalization to determine the anisotropic direction imposed on a stochastic fields in $(2+1)$Dimension. This approach enables us to examine not only the rotational invariance of morphology but also we can determine the Gaussianity of underlying stochastic field in various dimensions. Theoretical prediction of up-crossing statistics (crossing with positive slope at a given threshold $\alpha$ of height fluctuation), $\nu^+_{\diamond}(\alpha)$, and generalized roughness function, $N^{\diamond}_{tot}(q)$, for correlation length ($\xi_{\diamond}$) and/with scaling exponent ($\gamma_{\diamond}$) anisotropies are calculated. The strategy to examine the anisotropy nature and to determine its direction is as follows: we consider a set of normal axes, and sign them $||$ (parallel) and $ \bot$ (normal) with respect to unknown anisotropic direction. Then we determine $\nu_{\diamond}^+ (\alpha)$ and $N^{\diamond}_{tot}(q)$ in both directions. The directional dependency of difference between computed results in mentioned directions are clarify. Finally we systematically recognize the anisotropy direction at $3\sigma$ confidence interval using P-value approach. In order to distinguish between nature of anisotropies, after applying a typical method in determining the scaling exponents in both mentioned directions with respect to the recognized anisotropy direction using up-crossing statistics, the kind and the ratio of correlation length anisotropy are specified. Our algorithm can be mounted with a simple software on various instruments for surface analysis, such as AFM, STM and etc.

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M. Nezhadhaghighi, S. Movahed, T. Yasseri, et. al.
Fri, 7 Aug 15
35/51

Comments: 14 pages and 11 figures

Anomalous scaling in magnetohydrodynamic turbulence: Effects of anisotropy and compressibility in the kinematic approximation [CL]

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http://arxiv.org/abs/1507.08516


The field theoretic renormalization group and the operator product expansion are applied to the model of passive vector (magnetic) field advected by a random turbulent velocity field. The latter is governed by the Navier–Stokes equation for compressible fluid, subject to external random force with the covariance $\propto \delta(t-t’) k^{4-d-y}$, where $d$ is the dimension of space and $y$ is an arbitrary exponent. From physics viewpoints, the model describes magnetohydrodynamic turbulence in the so-called kinematic approximation, where the effects of the magnetic field on the dynamics of the fluid are neglected. The original stochastic problem is reformulated as a multiplicatively renormalizable field theoretic model; the corresponding renormalization group equations possess an infrared attractive fixed point. It is shown that various correlation functions of the magnetic field and its powers demonstrate anomalous scaling behavior in the inertial-convective range already for small values of~$y$. The corresponding anomalous exponents, identified with scaling (critical) dimensions of certain composite fields (“operators” in the quantum-field terminology), can be systematically calculated as series in $y$. The practical calculation is performed in the leading one-loop approximation, including exponents in anisotropic contributions. It should be emphasized that, in contrast to Gaussian ensembles with finite correlation time, the model and the perturbation theory presented here are manifestly Galilean covariant.

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N. Antonov and M. Kostenko
Fri, 31 Jul 15
14/59

Comments: 14 pages, LaTeX source, two EPS figures. arXiv admin note: text overlap with arXiv:1410.1262

Secular diffusion in discrete self-gravitating tepid discs II: accounting for swing amplification via the matrix method [GA]

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http://arxiv.org/abs/1507.06887


The secular evolution of an infinitely thin tepid isolated galactic disc made of a finite number of particles is investigated using the inhomogeneous Balescu-Lenard equation expressed in terms of angle-action variables. The matrix method is implemented numerically in order to model the induced gravitational polarization. Special care is taken to account for the amplification of potential fluctuations of mutually resonant orbits and the unwinding of the induced swing amplified transients. Quantitative comparisons with ${N-}$body simulations yield consistent scalings with the number of particles and with the self-gravity of the disc: the fewer particles and the colder the disc, the faster the secular evolution. Secular evolution is driven by resonances, but does not depend on the initial phases of the disc. For a Mestel disc with ${Q \sim 1.5}$, the polarization cloud around each star boosts up its secular effect by a factor of the order of a thousand or more, promoting accordingly the dynamical relevance of self-induced collisional secular evolution. The position and shape of the induced resonant ridge are found to be in very good agreement with the prediction of the Balescu-Lenard equation, which scales with the square of the susceptibility of the disc.
In astrophysics, the inhomogeneous Balescu-Lenard equation may describe the secular diffusion of giant molecular clouds in galactic discs, the secular migration and segregation of planetesimals in proto-planetary discs, or even the long-term evolution of population of stars within the Galactic centre. It could be used as a valuable check of the accuracy of ${N-}$body integrators over secular timescales.

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J. Fouvry, C. Pichon, J. Magorrian, et. al.
Mon, 27 Jul 15
37/40

Comments: 21 pages, 19 figures

Formation of H2-He Substellar Bodies in Cold Conditions: Gravitational Stability of Binary Mixtures in a Phase Transition [GA]

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http://arxiv.org/abs/1507.04604


Molecular clouds consist typically of 3/4 H2, 1/4 He and traces of heavier elements. In an earlier work we showed that at very low temperatures and high densities, H2 can be in a phase transition leading to the formation of ice clumps as large as comets, or even planets. However, He has very different chemical properties and no phase transition is expected before H2 in dense ISM conditions. The gravitational stability of fluid mixtures has been studied before, but not including a phase transition.
We study the gravitational stability of binary fluid mixtures with special emphasis if one component is in a phase transition. The results are aimed at applications in molecular cloud conditions.
We study the gravitational stability of van der Waals fluid mixtures using linearised analysis and examine virial equilibrium conditions using the Lennard-Jones inter-molecular potential. Then, combining the Lennard-Jones and gravitational potentials, the non-linear dynamics of fluid mixtures are studied using the molecular dynamics code LAMMPS.
Besides the classical ideal-gas Jeans instability criterion, a fluid mixture is always gravitationally unstable if it is in a phase transition. In unstable situations the species can separate: in some conditions He precipitates faster than H2, while in other conditions the converse occurs. Also, for an initial gas phase collapse the geometry is essential: contrary to spherical or filamentary collapses, sheet-like collapses starting below 15 K allow to easily reach H2 condensation conditions because then it is the fastest, and both the increase of heating and opacity are limited.
Depending on density, temperature and mass, either rocky H2 planetoids, or gaseous He planetoids form. H2 planetoids are favoured by high density, low temperature and low mass, while He planetoids need more mass and can form at temperature well above the critical one.

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A. Fuglistaler and D. Pfenniger
Fri, 17 Jul 15
5/54

Comments: 20 pages, 28 figures, submitted to A&A. Find simulation videos here: this https URL

Exponentiating Higgs [CL]

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http://arxiv.org/abs/1506.05761


The scalar models with exponential interaction, introduced in arXiv:1506.00987, include theories with $\langle \phi(x)\rangle\neq0$. Here, we first consider the theory obtained by normal ordering the exponential of the integrated potential $\int d^Dx\mu^D \exp(-\alpha\phi)$, rather than of $V(\phi)$ itself. This corresponds to fill-in the vacuum of the free scalar theory coupled to the external source with the scalar modes. Next, we show that such a regularization prescription, that we are able to implement in the path-integral formulation, also cures some classical potentials which may be unbounded below. We focus on $V(\phi)=m^4\big(e^{-\phi/m}-e^{\phi/m}\big)$, whose regularized partition function $$ W_R[J]={}_J\langle 0| :e^{-\int d^4xV(\phi)}:|0\rangle_J $$ leads to the exact result $$ \langle\phi(x)\rangle=2m \ , $$ in agreement with the experimental data. Another test is that, while the $(2N+1)$-point function is non-trivial, the full propagator is the free one, so that $m^2$ also corresponds to the pole of the propagator. Such an investigation suggests a natural way to get the lagrangian of the Standard Model, with a different Higgs lagrangian, that may be tested in future experiments at LHC.

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M. Matone
Wed, 24 Jun 15
20/54

Comments: 9 pages. Relevant additions. Typos corrected

Universal structure of two and three dimensional self-gravitating systems in the quasi-equilibrium state [CL]

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http://arxiv.org/abs/1505.02014


We study a universal structure of two and three dimensional self-gravitating systems in the quasi-equilibrium state. It is shown numerically that the two dimensional self-gravitating system in the quasi-equilibrium state has the same kind of density profile as the three dimensional one. We develop a phenomenological model to describe this universal structure by using a special Langevin equation with a distinctive random noise to self-gravitating systems. We find that the density profile derived theoretically is consistent well with results of observations and simulations.

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T. Tashiro
Mon, 11 May 15
16/44

Comments: N/A

Secular diffusion in discrete self-gravitating tepid discs I : analytic solution in the tightly wound limit [GA]

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http://arxiv.org/abs/1504.05028


The secular evolution of an infinitely thin tepid isolated galactic disc made of a finite number of particles is described using the inhomogeneous Balescu-Lenard equation. Assuming that only tightly wound transient spirals are present in the disc, a WKB approximation provides a simple and tractable quadrature for the corresponding drift and diffusion coefficients. It provides insight into the physical processes at work during the secular diffusion of a self-gravitating discrete disc and makes quantitative predictions on the initial variations of the distribution function in action space.
When applied to the secular evolution of an isolated stationary self-gravitating Mestel disc, this formalism predicts initially the importance of the corotation resonance in the inner regions of the disc leading to a regime involving radial migration and heating. It predicts in particular the formation of a “ridge like” feature in action space, in agreement with simulations, but over-estimates the timescale involved in its appearance. Swing amplification is likely to resolve this discrepancy.
In astrophysics, the inhomogeneous Balescu-Lenard equation and its WKB limit may also describe the secular diffusion of giant molecular clouds in galactic discs, the secular migration and segregation of planetesimals in proto-planetary discs, or even the long-term evolution of population of stars within the Galactic center.

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J. Fouvry, C. Pichon and P. Chavanis
Tue, 21 Apr 15
25/69

Comments: 22 pages, 12 figures

Features of the fractional diffusion-advection equation [SSA]

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http://arxiv.org/abs/1504.02999


We advance an exact, explicit form for the solutions to the fractional diffusion-advection equation. Numerical analysis of this equation shows that its solutions resemble power-laws.

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M. Rocca, A. Plastino, A. Plastino, et. al.
Tue, 14 Apr 15
6/87

Comments: 17 pages. 9 figures. arXiv admin note: substantial text overlap with arXiv:1412.0255

A New Blackbody Radiation Law Based on Fractional Calculus and its Application to NASA COBE Data [CL]

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http://arxiv.org/abs/1503.06010


By applying fractional calculus to the equation proposed by M. Planck in 1900, we obtain a new blackbody radiation law described by a Mittag-Leffler (ML) function. We have analyzed NASA COBE data by means of a non-extensive formula with a parameter $(q-1)$, a formula proposed by Ertik et al. with a fractional parameter $(\alpha-1)$, and our new formula including a parameter $(p-1)$, as well as the Bose-Einstein distribution with a dimensionless chemical potential $\mu$. It can be said that one role of the fractional parameter $(p-1)$ is almost the same as that of chemical potential $(\mu)$ as well as that of the parameter $(q-1)$ in the non-extensive approach.

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M. Biyajima, T. Mizoguchi and N. Suzuki
Mon, 23 Mar 15
24/46

Comments: N/A

Sub-stellar fragmentation in self-gravitating fluids with a major phase transition [GA]

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http://arxiv.org/abs/1503.04788


The existence of sub-stellar cold H2 globules in planetary nebulae and the mere existence of comets suggest that the physics of cold interstellar gas might be much richer than usually envisioned.
We study the case of a cold gaseous medium in ISM conditions which is subject to a gas-liquid/solid phase transition.
First the equilibrium of such fluids is studied using the virial theorem and linear stability analysis. Then the non-linear dynamics is studied by using simulations in order to characterize the expected formation of solid bodies analogous to comets. The simulations are run with a state of the art molecular dynamics code (LAMMPS). The long-range gravitational forces can be taken into account together with short-range molecular forces with finite limited computational resources by using super-molecules, provided the right scaling is followed.
The concept of super-molecule is tested with simulations, allowing to correctly satisfy the ideal gas Jeans instability criterion for one-phase fluids. The simulations show that fluids presenting a phase transition are gravitationally unstable as well, independent of the strength of the gravitational potential, producing two distinct kinds of sub-stellar bodies, those dominated by gravity (“planetoids”) and those dominated by molecular attractive force (“comets”).
Observations, formal analysis and computer simulations suggest the possibility of the formation of sub-stellar H2 clumps in cold molecular clouds due to the combination of phase transition and gravity. Fluids in a phase transition are gravitationally unstable, independent of the strength of the gravitational potential. Small H2 clumps may form even at relatively high temperatures, up to 400 – 600K according to virial analysis. The combination of phase transition and gravity may be relevant for a wider range of astrophysical situations, such as proto-planetary disks.

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A. Fuglistaler and D. Pfenniger
Tue, 17 Mar 15
79/79

Comments: 24 pages, 44 figures. Submitted to A&A, recommended for publication

Temperature inversion in long-range interacting systems [CL]

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http://arxiv.org/abs/1502.04051


Temperature inversions occur in nature, e.g., in the solar corona and in interstellar molecular clouds: somewhat counterintuitively, denser parts of the system are colder than dilute ones. We propose a simple and appealing mechanism to spontaneously generate temperature inversions in systems with long-range interactions, by preparing them in inhomogeneous thermal equilibrium states and then applying an impulsive perturbation. In similar situations, short-range systems would typically relax to another thermal equilibrium, with uniform temperature profile. By contrast, in long-range systems, the interplay between wave-particle interaction and spatial inhomogeneity drives the system to nonequilibrium stationary states that generically exhibit temperature inversion. Our work underlines the crucial role the range of interparticle interaction plays in determining the nature of steady states attained when macroscopic systems are brought out of thermal equilibrium.

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T. Teles, S. Gupta and L. Casetti
Mon, 16 Feb 15
33/55

Comments: 5 pages, 5 figures, REVTeX 4-1

A Unifying Theory for Scaling Laws of Human Populations [CL]

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http://arxiv.org/abs/1501.00738


The spatial distribution of people exhibits clustering across a wide range of scales, from household (~$10^{-2}$ km) to continental (~$10^4$ km) scales. Empirical data indicates simple power-law scalings for the size distribution of cities (known as Zipf’s law), the geographic distribution of friends, and the population density fluctuations as a function of scale. We derive a simple statistical model that explains all of these scaling laws based on a single unifying principle involving the random spatial growth of clusters of people on all scales. The model makes important new predictions for the spread of diseases and other social phenomena.

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H. Lin and A. Loeb
Wed, 7 Jan 15
32/67

Comments: 13 pages, 2 figures, press embargo until published

The principle of stationary nonconservative action for classical mechanics and field theories [CL]

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http://arxiv.org/abs/1412.3082


We further develop a recently introduced variational principle of stationary action for problems in nonconservative classical mechanics and extend it to classical field theories. The variational calculus used is consistent with an initial value formulation of physical problems and allows for time-irreversible processes, such as dissipation, to be included at the level of the action. In this formalism, the equations of motion are generated by extremizing a nonconservative action $\mathcal{S}$, which is a functional of a doubled set of degrees of freedom. The corresponding nonconservative Lagrangian contains a potential $K$ which generates nonconservative forces and interactions. Such a nonconservative potential can arise in several ways, including from an open system interacting with inaccessible degrees of freedom or from integrating out or coarse-graining a subset of variables in closed systems. We generalize Noether’s theorem to show how Noether currents are modified and no longer conserved when $K$ is non-vanishing. Consequently, the nonconservative aspects of a physical system are derived solely from $K$. We show how to use the formalism with examples of nonconservative actions for discrete systems including forced damped harmonic oscillators, radiation reaction on an accelerated charge, and RLC circuits. We present examples for nonconservative classical field theories. Our approach naturally allows for irreversible thermodynamic processes to be included in an unconstrained variational principle. We present the nonconservative action for a Navier-Stokes fluid including the effects of viscous dissipation and heat diffusion, as well as an action that generates the Maxwell model for viscoelastic materials, which can be easily generalized to more realistic rheological models. We show that the nonconservative action can be derived as the classical limit of a more complete quantum theory.

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C. Galley, D. Tsang and L. Stein
Wed, 10 Dec 14
43/61

Comments: 42 pages, 4 figures, 1 table

Non-equilibrium statistical field theory for classical particles: Initially correlated grand canonical ensembles [CL]

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http://arxiv.org/abs/1412.2572


It was recently shown by Bartelmann et al. how correlated initial conditions can be introduced into the statistical field theory for classical particles pioneered by Das and Mazenko. In this paper we extend this development from the canonical to the grand canonical ensemble for a system satisfying statistical homogeneity and isotropy. We do this by translating the probability distribution for the initial phase space coordinates of the particles into an easy diagrammatic representation and then using a variant of the Mayer cluster expansion to sum over particle numbers. The grand canonical generating functional is then used in a structured approach to the derivation of the non-interacting cumulants of the two core collective fields, the density $\rho$ and the response field $B$. As a side-product we find several theorems pertaining to these cumulants which will be useful when investigating the interacting regime of the theory in future work.

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F. Fabis, D. Berg, E. Kozlikin, et. al.
Tue, 9 Dec 14
13/64

Comments: 16 pages, 15 figures

Cross-correlation Aided Transport in Stochastically Driven Accretion Flows [HEAP]

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http://arxiv.org/abs/1412.1752


Origin of linear instability resulting in rotating sheared accretion flows has remained a controversial subject for long. While some explanations of such non-normal transient growth of disturbances in the Rayleigh stable limit were available for magnetized accretion flows, similar instabilities in absence of magnetic perturbations remained unexplained. This dichotomy was resolved in two recent publications by Chattopadhyay, {\it et al} where it was shown that such instabilities, especially for non-magnetized accretion flows, were introduced through interaction of the inherent stochastic noise in the system (even a \enquote{cold} accretion flow at 3000K is too \enquote{hot} in the statistical parlance and is capable of inducing strong thermal modes) with the underlying Taylor-Couette flow profiles. Both studies, however, excluded the additional energy influx (or efflux) that could result from nonzero cross-correlation of a noise perturbing the velocity flow, say, with the noise that is driving the vorticity flow (or equivalently the magnetic field and magnetic vorticity flow dynamics). In this article we show that nonzero noise cross-correlations essentially renormalize the strength of temporal correlations. Apart from an overall boost in the energy rate (both for spatial and temporal correlations, and hence in the ensemble averaged energy spectra), this results in mutual competition in growth rates of affected variables often resulting in suppression of oscillating Alfven waves at small times while leading to faster saturations at relatively longer time scales. The effects are seen to be more pronounced with magnetic field fluxes where the noise cross-correlation magnifies the strength of the field concerned.

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S. Nath and A. Chattopadhyay
Fri, 5 Dec 14
32/56

Comments: 13 figures in main tex, 8 figures in online supplemental, accepted in Physical Review E

Non-equilibrium statistical field theory for classical particles: Basic kinetic theory [CL]

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http://arxiv.org/abs/1411.2809


Recently Mazenko and Das and Mazenko introduced a non-equilibrium field theoretical approach to describe the statistical properties of a classical particle ensemble starting from the microscopic equations of motion of each individual particle. We use this theory to investigate the transition from those microscopic degrees of freedom to the evolution equations of the macroscopic observables of the ensemble. For the free theory, we recover the continuity and Jeans equations of a collisionless gas. For a theory containing two-particle interactions in a canonical perturbation series, we find the macroscopic evolution equations to be described by the Born-Bogoliubov-Green-Kirkwood-Yvon hierarchy (BBGKY hierarchy) with a truncation criterion depending on the order in perturbation theory. This establishes a direct link between the classical and the field-theoretical approaches to kinetic theory that might serve as a starting point to investigate kinetic theory beyond the classical limits.

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C. Viermann, F. Fabis, E. Kozlikin, et. al.
Thu, 13 Nov 14
33/49

Comments: 10 pages, 0 figures

Non-equilibrium statistical field theory for classical particles: Initially correlated canonical ensembles [CL]

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http://arxiv.org/abs/1411.0806


Building upon the recent pioneering work by Mazenko and Das and Mazenko, we develop the generating functional for an initially correlated canonical ensemble of classical microscopic particles obeying Hamiltonian dynamics. Our primary target is cosmic structure formation, where initial Gaussian correlations in phase space are believed to be set by inflation. Despite this specific motivation, our results may be useful for wider classes of applications in different fields of physics where the non-equilibrium statistics of correlated classical particle ensembles is to be studied. We give an exact expression for the generating functional and work out two approximations with linear and quadratic initial momentum correlations in detail. Cumulants of the density or other collective fields can be immediately derived from our results once the initial correlations have been defined.

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M. Bartelmann, F. Fabis, D. Berg, et. al.
Wed, 5 Nov 14
42/61

Comments: 13 pages, no figures

Statistical mechanics of self-gravitating systems: mixing as a criterion for indistinguishability [GA]

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http://arxiv.org/abs/1410.7677


We propose an association between the phase-space mixing level of a self-gravitating system and the indistinguishability of its constituents (stars or dark matter particles). This represents a refinement in the study of systems exhibiting incomplete violent relaxation. Within a combinatorial analysis similar to that of Lynden-Bell, we make use of this association to obtain a distribution function that deviates from the Maxwell-Boltzmann distribution, increasing its slope for high energies. Considering the smallness of the occupation numbers for large distances from the center of the system, we apply a correction to Stirling’s approximation which increases the distribution slope also for low energies. The distribution function thus obtained presents some resemblance to the “S” shape of distributions associated with cuspy density profiles (as compared to the distribution function obtained from the Einasto profile), although it is not quite able to produce sharp cusps. We also argue how the association between mixing level and indistinguishability can provide a physical meaning to the assumption of particle-permutation symmetry in the N-particle distribution function, when it is used to derive the one-particle Vlasov equation, which raises doubts about the validity of this equation during violent relaxation.

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L. Silva, M. Lima, L. Sodre, et. al.
Wed, 29 Oct 14
74/81

Comments: Submitted to PRD; 12 pages, 6 figures

Modelling the influence of photospheric turbulence on solar flare statistics [SSA]

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http://arxiv.org/abs/1410.4542


Solar flares stem from the reconnection of twisted magnetic field lines in the solar photosphere. The energy and waiting time distributions of these events follow complex patterns that have been carefully considered in the past and that bear some resemblance with earthquakes and stockmarkets. Here we explore in detail the tangling motion of interacting flux tubes anchored in the plasma and the energy ejections resulting when they recombine. The mechanism for energy accumulation and release in the flow is reminiscent of self-organized criticality. From this model we suggest the origin for two important and widely studied properties of solar flare statistics, including the time-energy correlations. We first propose that the scale-free energy distribution of solar flares is largely due to the twist exerted by the vorticity of the turbulent photosphere. Second, the long-range temporal and time-energy correlations appear to arise from the tube-tube interactions. The agreement with satellite measurements is encouraging.

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M. Mendoza, A. Kaydul, L. Arcangelis, et. al.
Fri, 17 Oct 14
50/54

Comments: 24 pages, 8 figures

Rotation Curves and Nonextensive Statistics [GA]

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http://arxiv.org/abs/1409.6367


We investigate the influence of the nonextensive q-statistics and kinetic theory on galactic scales through the analysis of a devised sample of Spiral Rotation Curves. Largely supported by recent developments on the foundations of statistical mechanics and a plethora of astrophysical applications, the theory also provides an alternative interpretation to the empirical cored dark matter profiles observed in galaxies. We show that the observations could well be fitted with reasonable values for the mass model parameters, encouraging further investigation into q-statistcs on the distribution of dark matter from both observational and theoretical points of view.

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C. Martins, J. Lima and P. Chimenti
Wed, 24 Sep 14
61/62

Comments: 6 pages, 3 figures, 1 table

Hollow cores in Warm Dark Matter halos from the Vlasov-Poisson equation [CEA]

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http://arxiv.org/abs/1409.6244


We report the results of extended high–resolution numerical integrations of the Vlasov–Poisson equation for the collapse of spherically symmetric WDM halos. For thermal relics with mass $m=1\,$keV/$c^2$, we find collapsed halos with cores of size from $0.1$ to $0.6\,$kpc. The typical core is hollow, with the mass density decreasing towards the core center by almost three orders of magnitude from its maximum near the core radius $r_{\rm c}$. The core is in equilibrium with the diffused part of the halo but far from virialization. These properties are rooted in the conservation of the squared angular momentum and in the original excess, proper of WDM initial conditions, of kinetic energy in the core region. In a sample of more than one hundred simulated collapses, the values of $r_{\rm c}$ and of the core density $\rho_{\rm c}$ are in the range typical of dwarf spheroids, while the maximal circular velocities $V_{\rm max}$ are proper of small disk galaxies. The product $\mu_{\rm c}=\rho_{\rm c}r_{\rm c}$ takes values between $116\,M_\odot/$pc$^2$ and $283\,M_\odot/$pc$^2$, while the surface density $\mu_0$, as determined from a Burkert fit, is roughly three times larger. From these data and data obtained at smaller values of $m$, we extrapolate for one particular halo $\mu_{\rm c}=263(308)\,M_\odot/$pc$^2$ and $\mu_0=754(855)\,M_\odot/$pc$^2$ at $m=2(3.3)\,$keV/$c^2$, to be compared with the observed value $140^{+83}_{-52} M_\odot$/pc$^2$. In view of the many improvements and enhancements available, we conclude that WDM is a viable solution for explaining the presence and the size of cores in low mass galaxies.

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C. Destri
Tue, 23 Sep 14
54/60

Comments: N/A

Two physical explanations of the nonextensive parameter in a self-gravitating system [CL]

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http://arxiv.org/abs/1409.3384


We present two possible physical explanations of the nonextensive parameter in a self-gravitating system. One is related to the detailed balance in such system. With the detailed balance, the statistical balance of molecular energy is reached, under which the radiation energy “stored” in the molecules becomes important. Then the relation between the nonextensive parameter and the storage coefficient which measures the ability of molecules to store the radiation energy is constructed. The other explanation is from one dimensionless quantity called (logarithmic) temperature gradient defined in the stellar physics. In view of this, we find that in order to keep the nuclear reactions alive inside the Sun, the ratio of radiation pressure to the total pressure in the core must be more than 0.2833.

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Z. Yahui and D. Jiulin
Fri, 12 Sep 14
49/61

Comments: 10 pages, 2 figures

Nonequilibrium stationary states of 3D self-gravitating systems [CL]

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http://arxiv.org/abs/1409.2060


Three dimensional self-gravitating systems do not evolve to thermodynamic equilibrium, but become trapped in nonequilibrium quasistationary states. In this Letter we present a theory which allows us to a priori predict the particle distribution in a final quasistationary state to which a self-gravitating system will evolve from an initial condition which is isotropic in particle velocities and satisfies a virial constraint 2K=-U, where K is the total kinetic energy and U is the potential energy of the system.

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F. Benetti, A. Ribeiro-Teixeira, R. Pakter, et. al.
Tue, 9 Sep 14
14/83

Comments: N/A

Formation of Hydrocarbons from Hydrogenated Graphene in Circumstellar Clouds [CL]

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http://arxiv.org/abs/1408.4936


We describe a mechanism that explains the formation of hydrocarbons and hydrocarbyls from hydrogenated graphene/graphite; hard C-C bonds are weakened and broken by the synergistic effect of chemisorbed hydrogen and high temperature vibrations. Total energies, optimized structures, and transition states are obtained from Density Functional Theory simulations. These values have been used to determine the Boltzman probability for a thermal fluctuation to overcome the kinetic barriers, yielding the time scale for an event to occur. This mechanism can be used to rationalize the possible routes for the creation of small hydrocarbons and hydrocarbyls from etched graphene/graphite in stellar regions.

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J. Martinez, J. Martin-Gago, J. Cernicharo, et. al.
Fri, 22 Aug 14
31/49

Comments: 4.5 pages, 4 figures, 2 tables

Jeans instability and anti-screening in gravitational-antigravitational model of Universe [CL]

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http://arxiv.org/abs/1404.7122


The hypothesis of antigravitational interaction of elementary particles and antiparticles is considered on the basis of the simple two-component hydrodynamic model with gravitational repulsion and attraction. It is shown increasing of the Jeans instability rate, the presence of antiscreening and the dominative role of the gravitational repulsion as a possible mechanism for spatial separation of matter and antimatter in Universe, as well as the observable acceleration of the far galaxies. The sound wave is found for the two-component gravitational-antigravitational system, which starts for k = 0 in the case of annihilation neglecting. The suggested approach permits to reestablish the idea about baryon symmetry of Universe, causing its steady flatness of the large scale and accelerated Universe expansion.

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I. Gribov and S. Trigger
Wed, 30 Apr 14
31/68

Comments: 12 pages, 0 figures

Superposition Enhanced Nested Sampling [CL]

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http://arxiv.org/abs/1402.6306


The theoretical analysis of many problems in physics, astronomy and applied mathematics requires an efficient numerical exploration of multimodal parameter spaces that exhibit broken ergodicity. Monte Carlo methods are widely used to deal with these classes of problems, but such simulations suffer from a ubiquitous sampling problem: the probability of sampling a particular state is proportional to its entropic weight. Devising an algorithm capable of sampling efficiently the full phase space is a long-standing problem. Here we report a new hybrid method for the exploration of multimodal parameter spaces exhibiting broken ergodicity. Superposition enhanced nested sampling (SENS) combines the strengths of global optimization with the unbiased/athermal sampling of nested sampling, greatly enhancing its efficiency with no additional parameters. We report extensive tests of this new approach for atomic clusters that are known to have energy landscapes for which conventional sampling schemes suffer from broken ergodicity. We also introduce a novel parallelization algorithm for nested sampling.

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S. Martiniani, J. Stevenson, D. Wales, et. al.
Wed, 26 Feb 14
18/51

The statistical mechanics of self-gravitating Keplerian disks [GA]

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http://arxiv.org/abs/1401.5534


We describe the dynamics and thermodynamics of collisionless particle disks orbiting a massive central body, in the case where the disk mass is small compared to the central mass, the self-gravity of the disk dominates the non-Keplerian force, and the spread in semi-major axes is small. We show that with plausible approximations such disks have logarithmic two-body interactions and a compact phase space, and therefore exhibit thermodynamics that are simpler than most other gravitating systems, which require a confining box and artificial softening of the potential at small scales to be thermodynamically well-behaved. We solve for the microcanonical axisymmetric thermal equilibria and demonstrate the existence of a first-order phase transition to lopsided equilibria. We discuss the relation between thermal and dynamical instability in these systems and draw connections to astrophysical settings, as well as to the wider subject of the statistical mechanics of particles with logarithmic long-range interactions, such as point vortices in two-dimensional fluids.

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Thu, 23 Jan 14
7/70

Velocity filtration and temperature inversion in a system with long-range interactions [CL]

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http://arxiv.org/abs/1312.1614


Temperature inversion due to velocity filtration, a mechanism originally proposed to explain the heating of the solar corona, is demonstrated to occur also in a simple paradigmatic model with long-range interactions, the Hamiltonian mean-field model. Using molecular dynamics simulations, we show that when the system settles into an inhomogeneous quasi-stationary state in which the velocity distribution has suprathermal tails, the temperature and density profiles are anticorrelated: denser parts of the system are colder than dilute ones. We argue that this may be a generic property of long-range interacting systems.

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Fri, 6 Dec 13
46/55

Symmetry Breaking in d-Dimensional Self-gravitating Systems [CL]

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http://arxiv.org/abs/1311.4892


Systems with long-range interactions, such as self-gravitating clusters and magnetically confined plasmas, do not relax to the usual Boltzmann-Gibbs thermodynamic equilibrium, but become trapped in quasi-stationary states (QSS) the life time of which diverges with the number of particles. The QSS are characterized by the lack of ergodicity which can result in a symmetry broken QSS starting from a spherically symmetric particle distribution. We will present a theory which allows us to quantitatively predict the instability threshold for spontaneous symmetry breaking for a class of d-dimensional self-gravitating systems.

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Thu, 21 Nov 13
34/50

Universality in the dynamics of second-order phase transitions [CL]

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http://arxiv.org/abs/1311.1543


When traversing a symmetry breaking second order phase transition at a finite rate, topological defects form whose number dependence on the quench rate is given by simple power laws. We propose a general approach for the derivation of such scaling laws that is based on the analytical transformation of the associated equations of motion to a universal form rather than employing plausible physical arguments. We demonstrate the power of this approach by deriving the scaling of the number of topological defects in both homogenous and non-homogenous settings. The general nature and extensions of this approach is discussed.

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Fri, 8 Nov 13
9/58

Mathematical and Physical Ideas for Climate Science [CL]

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http://arxiv.org/abs/1311.1190


The climate is an excellent example of a forced, dissipative system dominated by nonlinear processes and featuring non-trivial dynamics of a vast range of spatial and temporal scales. The understanding of the climate’s structural and multiscale properties is crucial for the provision of a unifying picture of its dynamics an thd for the implementation of accurate and efficient numerical models. In this interdisciplinary review, we are guided by our interest in exploring the nexus between climate and concepts such as energy, entropy, symmetry, response, multiscale interactions, and its potential relevance in terms of numerical modeling. We describe the Nambu reformulation of fluid dynamics, and the possible potential of such theory for constructing numerical models of the geophysical fluids. We focus on the very promising results on the statistical mechanics of quasi-equilibrium geophysical flows, which are extremely useful in the direction of constructing a robust theory of geophysical macro turbulence. The second half of the review is dedicated to the non-equilibrium properties of the climate system. First, we describe some recent findings showing how to use basic concepts of macroscopic non-equilibrium thermodynamics for characterizing the energy and entropy budgets of the climate systems, with the ensuing protocols for intercomparing climate models and developing methods aimed at studying tipping points. These ideas can also create a link between climate science and the growing sector of astrophysics devoted to the investigation of exoplanetary atmospheres. We conclude by focusing on non-equilibrium statistical mechanics, which allows for framing in a unified way problems as different as climate response to forcings of general nature, the effect of altering the boundary conditions or the coupling between geophysical flows, and the derivation of parametrizations for numerical models.

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Wed, 6 Nov 13
29/56