Energy cascade in internal wave attractors

One of the pivotal questions in the dynamics of the oceans is related to the cascade of mechanical energy in the abyss and its contribution to mixing. Here, we propose internal wave attractors in the large amplitude regime as a unique self-consistent experimental and numerical setup that models a cascade of triadic interactions transferring energy from large-scale monochro-matic input to multi-scale internal wave motion. We also provide signatures of a discrete wave turbulence framework for internal waves. Finally, we show how beyond this regime, we have a clear transition to a regime of small-scale high-vorticity events which induce mixing. Introduction

Shape dependent finite-size effect of critical two-dimensional Ising model on a triangular lattice

Using the bond-propagation algorithm, we study the finite-size behavior of the critical two-dimensional Ising model on a finite triangular lattice with free boundaries in five shapes: triangle, rhombus, trapezoid, hexagon and rectangle. The critical free energy, internal energy and specific heat are calculated. The accuracy of the free energy reaches $10^{-26}$. Based on accurate data on several finite systems with linear size up to N=2000, we extract the bulk, surface and corner parts of the free energy, internal energy and specific heat accurately. We confirm the conformal field theory prediction of the corner free energy to be universal and find logarithmic corrections in higher order terms in the critical free energy for the rhombus, trapezoid, and hexagon shaped systems, which are absent for the triangle and rectangle shaped systems. The logarithmic edge corrections due to edges parallel or perpendicular to the bond directions in the internal energy are found to be identical, while the logarithmic edge corrections due to corresponding edges in the free energy and the specific heat are different. The corner internal energy and corner specific heat for angles $\pi/3$, $\pi/2$ and $2\pi/3$ are obtained, as well as higher order corrections. Comparing with the corner internal energy and corner specific heat previously found on a rectangle of the square lattice (Phys. Rev. E. 86 041149 (2012)), we conclude that the corner internal energy and corner specific heat for the rectangle shape are not universal.Comment: arXiv admin note: text overlap with arXiv:1207.454

Thermal Casimir effect for neutrino and electromagnetic fields in closed Friedmann cosmological model

We calculate the total internal energy, total energy density and pressure, and the free energy for the neutrino and electromagnetic fields in Einstein and closed Friedmann cosmological models. The Casimir contributions to all these quantities are separated. The asymptotic expressions for both the total internal energy and free energy, and for the Casimir contributions to them are found in the limiting cases of low and high temperatures. It is shown that the neutrino field does not possess a classical limit at high temperature. As for the electromagnetic field, we demonstrate that the total internal energy has the classical contribution and the Casimir internal energy goes to the classical limit at high temperature. The respective Casimir free energy contains both linear and logarithmic terms with respect to the temperature. The total and Casimir entropies for the neutrino and electromagnetic fields at low temperature are also calculated and shown to be in agreement with the Nernst heat theorem.Comment: 23 pages, to appear in Phys. Rev.

Heavy quark thermodynamics in full QCD

We analyze the large-distance behaviour of static quark-anti-quark pair correlations in QCD. The singlet free energy is calculated and the entropy contribution to it is identified allowing us to calculate the excess internal energy. The free energy has a sharp drop in the critical region, leading to sharp peaks in both excess entropy and internal energy.Comment: talk given at Quark Matter 200

Energy Flow Puzzle of Soliton Ratchets

We study the mechanism of directed energy transport for soliton ratchets. The energy flow appears due to the progressive motion of a soliton (kink) which is an energy carrier. However, the energy current formed by internal system deformations (the total field momentum) is zero. We solve the underlying puzzle by showing that the energy flow is realized via an {\it inhomogeneous} energy exchange between the system and the external ac driving. Internal kink modes are unambiguously shown to be crucial for that transport process to take place. We also discuss effects of spatial discretization and combination of ac and dc external drivings.Comment: 4 pages, 3 figures, submitted to PR

A variational principle for two-fluid models

A variational principle for two-fluid mixtures is proposed. The Lagrangian is constructed as the difference between the kinetic energy of the mixture and a thermodynamic potential conjugated to the internal energy with respect to the relative velocity of phases. The equations of motion and a set of Rankine-Hugoniot conditions are obtained. It is proved also that the convexity of the internal energy guarantees the hyperbolicity of the one-dimensional equations of motion linearized at rest.Comment: 7 page

Swarms with canonical active Brownian motion

We present a swarm model of Brownian particles with harmonic interactions, where the individuals undergo canonical active Brownian motion, i.e. each Brownian particle can convert internal energy to mechanical energy of motion. We assume the existence of a single global internal energy of the system. Numerical simulations show amorphous swarming behavior as well as static configurations. Analytic understanding of the system is provided by studying stability properties of equilibria.Comment: 5 pages, 3 figure