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High Intensity Focused Ultrasound (HIFU) is a promising therapy for thermal ablation and hyperthermia, characterised by it noninvasiveness, high penetration depth. Effective HIFU thermo-therapy requires the ability to accurately predict…

Medical Physics · Physics 2020-07-14 Gajendra Singh , Anup Paul , Himanshu Shekhar , Abhijit Paul

We analyse the linear kinetic transport equation with a BGK relaxation operator. We study the large scale hyperbolic limit $(t,x)\to (t/\eps,x/\eps)$. We derive a new type of limiting Hamilton-Jacobi equation, which is analogous to the…

Analysis of PDEs · Mathematics 2012-02-13 Emeric Bouin , Vincent Calvez

Situations where a spontaneous process of energy or matter transfer is enhanced by an external device are widespread in nature (human sweating system, enzyme catalysis, facilitated diffusion across bio-membranes, industrial heat…

Statistical Mechanics · Physics 2010-07-21 Karen Hovhannisyan , Armen E. Allahverdyan

Solutions to hyperbolic conservation laws can be approximated in many different ways: by vanishing viscosity, relaxations, discrete or semi-discrete numerical schemes, approximation with a nonlocal flux, etc$\ldots$ For some of these…

Analysis of PDEs · Mathematics 2026-05-04 Alberto Bressan , Laura Caravenna , Wen Shen

We propose a numerical approach for solving conjugate heat transfer problems using the finite volume method. This approach combines a semi-implicit scheme for fluid flow, governed by the incompressible Navier-Stokes equations, with an…

Numerical Analysis · Mathematics 2025-03-18 Liang Fang , Xiandong Liu , Lei Zhang

Differentially rotating, "advection-dominated" accretion flows are considered in which the heat generated by viscous dissipation is retained in the fluid. The equations of time-dependent quasi-spherical accretion are solved in a simplified…

Astrophysics · Physics 2009-10-31 G. I. Ogilvie

This paper is concerned with the asymptotic stability of the solution to an initial-boundary value problem on the half line for a hyperbolic-elliptic coupled system of the radiating gas, where the data on the boundary and at the far field…

Analysis of PDEs · Mathematics 2021-07-12 Shanming Ji , Minyi Zhang , Changjiang Zhu

The aim of this paper is to study the metastable properties of the solutions to a hyperbolic relaxation of the classic Cahn-Hilliard equation in one space dimension, subject to either Neumann or Dirichlet boundary conditions. To perform…

Analysis of PDEs · Mathematics 2021-03-22 Raffaele Folino , Corrado Lattanzio , Corrado Mascia

In this paper we prove that if $u$ is a solution to second order hyperbolic equation $\partial^2_tu+a(x)\partial_tu-(div_x\left(A(x)\nabla_x u\right)+b(x)\cdot\nabla_x u+c(x)u)=0$ and $u$ is flat on a segment $\{x_0\}\times (-T,T)$ then $u$…

Analysis of PDEs · Mathematics 2020-10-13 Sergio Vessella

We demonstrate a novel approach to thermometry at the nanoscale exploiting a superconducting weak link. Such a weak link probed with nanosecond current pulses serves as a temperature sensing element and, due to the fast inherent dynamics,…

Superconductivity · Physics 2018-11-07 M. Zgirski , M. Foltyn , A. Savin , M. Meschke , J. Pekola

The task of finding optimal protocols that minimize the energetic cost of thermodynamic processes of long yet finite duration $\tau$ is a pressing one. We approach this problem here in a rigorous and systematic fashion by means of the…

Statistical Mechanics · Physics 2022-11-28 Artur Soriani , Eduardo Miranda , Marcus V. S. Bonança

We present an effective thermal open boundary condition for convective heat transfer problems on domains involving outflow/open boundaries. This boundary condition is energy-stable, and it ensures that the contribution of the open boundary…

Fluid Dynamics · Physics 2019-10-23 X. Liu , Z. Xie , S. Dong

The objective of this work is to show that adiabatic processes can be very similar to isothermal ones. First, we show that the criteria for the compatibility of linear-response theory with the Second Law of Thermodynamics for thermally…

Statistical Mechanics · Physics 2023-06-19 Pierre Nazé

We study relaxational behavior from a highly excited state for a composite system in partial contact with a heat bath, motivated by an experimental report of long-term energy storage in protein molecules. The system consists of two coupled…

Statistical Mechanics · Physics 2009-10-31 Naoko Nakagawa , Kunihiko Kaneko , Teruhisa S. Komatsu

In this paper we study the interaction problem between a nonlinear thermoelastic plate and a compressible viscous fluid with the adiabatic constant $\gamma>12/7$. The existence of a weak solution for this problem is obtained by constructing…

Analysis of PDEs · Mathematics 2020-10-06 Srđan Trifunović , Ya-Guang Wang

We consider in this contribution a simplified idealized one-dimensional model in a nuclear core reactor coupling the diffusion equation on the neutron flux withthe enthalpy equation for the water which collects the heat produced by this…

Numerical Analysis · Mathematics 2025-03-11 Olivier Lafitte , François Dubois

Heat flux exchanged between two hot bodies at subwavelength separation distances can exceed the limit predicted by the blackbody theory. However this super-Planckian transfer is restricted to these separation distances. Here we demonstrate…

Mesoscale and Nanoscale Physics · Physics 2016-09-05 Riccardo Messina , Philippe Ben-Abdallah , Brahim Guizal , Mauro Antezza , Svend-Age Biehs

In this paper we investigate the asymptotic behavior and decay of the solution of the discrete in time $N$-dimensional heat equation. We give a convergence rate with which the solution tends to the discrete fundamental solution, and the…

Analysis of PDEs · Mathematics 2021-02-23 Edgardo Alvarez , Luciano Abadias

Using the recently derived Dissipation Theorem and a corollary of the Transient Fluctuation Theorem (TFT), namely the Second Law Inequality, we derive the unique time independent, equilibrium phase space distribution function for an ergodic…

Statistical Mechanics · Physics 2015-05-13 Denis J. Evans , Debra J. Searles , Stephen R. Williams

This paper is concerned with the stability of steady solutions to initial-boundary-value problems of reaction-hyperbolic systems for axonal transport. Under proper structural assumptions, we clarify the relaxation structure of the…

Analysis of PDEs · Mathematics 2011-09-19 Hao Yan , Wen-An Yong