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Related papers: Error Estimators for the Small-Biot Lumped Approxi…

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We consider a family of initial boundary value problems governed by a fractional diffusion equation with Caputo derivative in time, where the parameter is the Newton heat transfer coefficient linked to the Robin condition on the boundary.…

Analysis of PDEs · Mathematics 2021-05-06 Isolda Cardoso , Sabrina D. Roscani , Domingo A. Tarzia

We derive global estimates for the error in solutions of linear hyperbolic systems due to inaccurate boundary geometry. We show that the error is bounded by data and bounded in time when the solutions in the true and approximate domains are…

Numerical Analysis · Mathematics 2025-03-27 David A. Kopriva , Andrew R. Winters , Jan Nordström

We investigate the influence of the thermal properties of the boundaries in turbulent Rayleigh-B\'enard convection on analytical upper bounds on convective heat transport. We model imperfectly conducting bounding plates in two ways: using…

Fluid Dynamics · Physics 2010-08-17 Ralf W. Wittenberg

This work focuses on determining the coefficient of thermal diffusivity in a one-dimensional heat transfer process along a homogeneous and isotropic bar, embedded in a moving fluid with heat generation. A first type (Dirichlet) condition is…

Fluid Dynamics · Physics 2022-01-03 Guillermo Federico Umbricht , Diana Rubio

We consider the initial boundary value problem of non-homogeneous stochastic heat equation. The derivative of the solution with respect to time receives heavy random perturbation. The space boundary is Lipschitz and we impose non-zero…

Analysis of PDEs · Mathematics 2011-07-01 Tongkeun Chang , Kijung Lee , Minsuk Yang

We present a numerical analysis of a higher order unfitted space-time Finite Element method applied to a convection-diffusion model problem posed on a moving bulk domain. The method uses isoparametric space-time mappings for the geometry…

Numerical Analysis · Mathematics 2025-12-11 Fabian Heimann , Christoph Lehrenfeld , Janosch Preuß

We consider the space-time boundary element method (BEM) for the heat equation with prescribed initial and Dirichlet data. We propose a residual-type a posteriori error estimator that is a lower bound and, up to weighted $L_2$-norms of the…

Numerical Analysis · Mathematics 2022-01-11 Gregor Gantner , Raymond van Venetië

This paper deals with bounding the error on the estimation of quantities of interest obtained by finite element and domain decomposition methods. The proposed bounds are written in order to separate the two errors involved in the resolution…

Computational Physics · Physics 2015-02-11 Valentine Rey , Pierre Gosselet , Christian Rey

Thermal systems are an attractive setting for exploring the connections between the lumped-element approximations of elementary circuit theory and the partial-differential field equations of mathematical physics, a topic that has been…

Classical Physics · Physics 2018-10-22 Matthew Frick , Swapnil Gupta , John Bechhoefer

In this work we formulate an efficient method for the description of many-body localized systems in weak contact with thermal environments at temperature $T$. For this purpose we exploit the representation of the system in terms of…

Disordered Systems and Neural Networks · Physics 2019-07-08 Ling-Na Wu , Alexander Schnell , Giuseppe De Tomasi , Markus Heyl , André Eckardt

This paper studies a prototype of inverse initial boundary value problems whose governing equation is the heat equation in three dimensions. An unknown discontinuity embedded in a three-dimensional heat conductive body is considered. A {\it…

Analysis of PDEs · Mathematics 2015-12-03 Masaru Ikehata , Mishio Kawashita

We establish tight connections between entanglement entropy and the approximation error in Trotter-Suzuki product formulas for Hamiltonian simulation. Product formulas remain the workhorse of quantum simulation on near-term devices, yet…

Quantum Physics · Physics 2026-02-03 Prateek P. Kulkarni

One of the key objectives in investigating small stochastic systems is the development of micrometer-sized engines and the understanding of their thermodynamics. However, the primary mathematical tool used for this purpose, the overdamped…

Statistical Mechanics · Physics 2025-03-31 Shakul Awasthi , Hyunggyu Park , Jae Sung Lee

In this paper, we present first-order accurate numerical methods for solution of the heat equation with uncertain temperature-dependent thermal conductivity. Each algorithm yields a shared coefficient matrix for the ensemble set improving…

Numerical Analysis · Mathematics 2021-06-08 J. A. Fiordilino , M. Winger

The local heat transfer coefficient measurement with temperature oscillation induced by periodic thermal perturbation - usually via a Gaussian laser beam, was investigated for the impact of the spikiness (i.e., the standard deviation)…

Data Analysis, Statistics and Probability · Physics 2025-01-03 Zhongyuan Shi , Tao Dong , Zhaochu Yang

Disordered systems show deviations from the standard Debye theory of specific heat at low temperatures. These deviations are often attributed to two-level systems of uncertain origin. We find that a source of excess specific heat comes from…

Statistical Mechanics · Physics 2015-06-17 Ralph V. Chamberlin , Bryce F. Davis

We prove that the time required for sustained information scrambling in any Hamiltonian quantum system is universally at least logarithmic in the entanglement entropy of scrambled states. This addresses two foundational problems in…

Quantum Physics · Physics 2024-04-25 Amit Vikram , Laura Shou , Victor Galitski

Slender body theory facilitates computational simulations of thin fibers immersed in a viscous fluid by approximating each fiber using only the geometry of the fiber centerline curve and the line force density along it. However, it has been…

Analysis of PDEs · Mathematics 2019-02-01 Yoichiro Mori , Laurel Ohm , Daniel Spirn

Simulated tempering (ST) has attracted a great deal of attention in the last years, due to its capability to allow systems with complex dynamics to escape from regions separated by large entropic barriers. However its performance is…

Statistical Mechanics · Physics 2015-08-11 A. Valentim , Cláudio J. daSilva , Carlos E. Fiore

We show that a certain error estimate for a fully discrete finite element approximation of the solution of the heat equation which is defined in a two-dimensional Euclidean domain carries over to the case of a general linear parabolic…

Numerical Analysis · Mathematics 2016-04-22 Heiko Kröner