An alternative approach to efficient simulation of micro/nanoscale phonon transport

Starting from the recently proposed energy-based deviational formulation for solving the Boltzmann equation [J.-P. Peraud and N. G. Hadjiconstantinou, Phys. Rev. B 84, 2011], which provides significant computational speedup compared to standard Monte Carlo methods for small deviations from equilibrium, we show that additional computational benefits are possible in the limit that the governing equation can be linearized. The proposed method exploits the observation that under linearized conditions (small temperature differences) the trajectories of individual deviational particles can be decoupled and thus simulated independently; this leads to a particularly simple and efficient algorithm for simulating steady and transient problems in arbitrary three-dimensional geometries, without introducing any additional approximation.Comment: 4 pages, 2 figure

Negative forms and path space forms

We present an account of negative differential forms within a natural algebraic framework of differential graded algebras, and explain their relationship with forms on path spaces.Comment: 12 pp.; the Introduction has been rewritten and mention of cohomology dropped in Proposition 3.2; material slightly reorganize

Loop Corrections in the Spectrum of 2D Hawking Radiation

We determine the one-loop and the two-loop back-reaction corrections in the spectrum of the Hawking radiation for the CGHS model of 2d dilaton gravity by evaluating the Bogoliubov coefficients for a massless scalar field propagating on the corresponding backgrounds. Since the back-reaction can induce a small shift in the position of the classical horizon, we find that a positive shift leads to a non-Planckian late-time spectrum, while a null or a negative shift leads to a Planckian late-time spectrum in the leading-order stationary-point approximation. In the one-loop case there are no corrections to the classical Hawking temperature, while in the two-loop case the temperature is three times greater than the classical value. We argue that these results are consistent with the behaviour of the Hawking flux obtained from the operator quantization only for the times which are not too late, in accordance with the limits of validity of the semiclassical approximation.Comment: 20 pages, latex, no figure

Low-power synthesis flow for regular processor design

Flow around an ICE2 high-speed train exiting a tunnel under the influence of a wind gust has been studied using numerical technique called detached eddy simulation. A wind gust boundary condition was derived to approximate previous experimental observations. The body of the train includes most important details including bogies, plugs, inter-car gaps and rotating wheels on the rail. The maximal yawing and rolling moments which possibly can cause a derailment or overturning were found to occur when approximately one third and one half of the train, respectively, has left the tunnel. These are explained by development of a strong vortex trailing along the upper leeward edge of the train. All aerodynamic forces and moments were monitored during the simulation and the underlying flow structures and mechanisms are explained

Future asymptotic expansions of Bianchi VIII vacuum metrics

Bianchi VIII vacuum solutions to Einstein's equations are causally geodesically complete to the future, given an appropriate time orientation, and the objective of this article is to analyze the asymptotic behaviour of solutions in this time direction. For the Bianchi class A spacetimes, there is a formulation of the field equations that was presented in an article by Wainwright and Hsu, and in a previous article we analyzed the asymptotic behaviour of solutions in these variables. One objective of this paper is to give an asymptotic expansion for the metric. Furthermore, we relate this expansion to the topology of the compactified spatial hypersurfaces of homogeneity. The compactified spatial hypersurfaces have the topology of Seifert fibred spaces and we prove that in the case of NUT Bianchi VIII spacetimes, the length of a circle fibre converges to a positive constant but that in the case of general Bianchi VIII solutions, the length tends to infinity at a rate we determine.Comment: 50 pages, no figures. Erronous definition of Seifert fibred spaces correcte

Schwinger Model Green functions with topological effects

The fermion propagator and the 4-fermion Green function in the massless QED2 are explicitly found with topological effects taken into account. The corrections due to instanton sectors k=+1,-1, contributing to the propagator, are shown to be just the homogenous terms admitted by the Dyson-Schwinger equation for S. In the case of the 4-fermion function also sectors k=+2,-2 are included into consideration. The quark condensates are then calculated and are shown to satisfy cluster property. The theta-dependence exhibited by the Green functions corresponds to and may be removed by performing certain chiral gauge transformation.Comment: 16 pages, in REVTE

The Quantum Mellin transform

We uncover a new type of unitary operation for quantum mechanics on the half-line which yields a transformation to ``Hyperbolic phase space''. We show that this new unitary change of basis from the position x on the half line to the Hyperbolic momentum $p_\eta$, transforms the wavefunction via a Mellin transform on to the critial line $s=1/2-ip_\eta$. We utilise this new transform to find quantum wavefunctions whose Hyperbolic momentum representation approximate a class of higher transcendental functions, and in particular, approximate the Riemann Zeta function. We finally give possible physical realisations to perform an indirect measurement of the Hyperbolic momentum of a quantum system on the half-line.Comment: 23 pages, 6 Figure

Perturbed Three Vortex Dynamics

It is well known that the dynamics of three point vortices moving in an ideal fluid in the plane can be expressed in Hamiltonian form, where the resulting equations of motion are completely integrable in the sense of Liouville and Arnold. The focus of this investigation is on the persistence of regular behavior (especially periodic motion) associated to completely integrable systems for certain (admissible) kinds of Hamiltonian perturbations of the three vortex system in a plane. After a brief survey of the dynamics of the integrable planar three vortex system, it is shown that the admissible class of perturbed systems is broad enough to include three vortices in a half-plane, three coaxial slender vortex rings in three-space, and `restricted' four vortex dynamics in a plane. Included are two basic categories of results for admissible perturbations: (i) general theorems for the persistence of invariant tori and periodic orbits using Kolmogorov-Arnold-Moser and Poincare-Birkhoff type arguments; and (ii) more specific and quantitative conclusions of a classical perturbation theory nature guaranteeing the existence of periodic orbits of the perturbed system close to cycles of the unperturbed system, which occur in abundance near centers. In addition, several numerical simulations are provided to illustrate the validity of the theorems as well as indicating their limitations as manifested by transitions to chaotic dynamics.Comment: 26 pages, 9 figures, submitted to the Journal of Mathematical Physic

Meson resonances, large N_c and chiral symmetry

We investigate the implications of large N_c and chiral symmetry for the mass spectra of meson resonances. Unlike for most other mesons, the mass matrix of the light scalars deviates strongly from its large-N_c limit. We discuss the possible assignments for the lightest scalar nonet that survives in the large-N_c limit.Comment: 14 page