Ultrarelativistic generalized Lorentzians and the cosmic ray energy flux [HEAP]

We show that the rather tentative application of the ultrarelativistic generalized Lorentzian energy distribution to the spectrum of cosmic ray fluxes may provide evidence for either high TeV chemical potentials generated in the acceleration source region of the observed cosmic rays, or the presence of hypothetical particles of TeV rest mass. Such particles are not known in our accessible Universe at any accessible energies. If true they should have been produced in cosmic ray sources prior to acceleration. Conclusions of this kind depend on the validity of the generalized Lorentzian in application to cosmic rays, a hypothetical statistical mechanical equilibrium distribution occasionally encountered in observations.

R. Treumann and W. Baumjohann
Wed, 8 Mar 17
46/60

Comments: 5 pages, 1 figure, draft prepared for submission to a meeting on cosmic rays and power law tails

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

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.

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

Statistical mechanics of gravitating gas like galaxy [GA]

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.

A. Kashuba
Mon, 20 Feb 17
2/37

Kinetic theory of fermions in curved spacetime [CL]

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.

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

Isotropic-Nematic Phase Transitions in Gravitational Systems [GA]

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 $180^\circ$.

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

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

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.

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]

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.

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

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

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.

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]

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.

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

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

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.

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

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

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.

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

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

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

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

Comments: 4 pages, three figures, Revtex

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

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 $\gamma<\gamma_{c}\simeq 2.13$.

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

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

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.

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

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

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.

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]

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.

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

Theory of Thomson scattering in inhomogeneous media [CL]

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.

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]

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.

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]

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.

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]

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.

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

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

(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. 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] 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. 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] 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. 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] 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. 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] 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. 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] 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. 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] 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. 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] 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. D. Chiron and B. Marcos Tue, 5 Jan 16 35/104 Comments: 23 pages, 17 figures Black hole thermodynamics in finite time [CL] 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. 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] 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. 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] 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. 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] 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. 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] 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. 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] 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. 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] 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. 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] 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. 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] 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. H. Yu and J. Du Tue, 11 Aug 15 43/57 Comments: 8 pages, 39 references Crossing Statistics of Anisotropic Stochastic Surface [CL] 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. 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] 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. 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] 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. 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] 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. 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] 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. 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] 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. 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] 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. 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] 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. 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] 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. 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] 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. 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] 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. 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] 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. 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] 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.

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

Comments: 42 pages, 4 figures, 1 table