Related papers: Solving partial differential equations on near-ter…
This paper is devoted to the numerical approximation of a nonlinear temperature balance equation, which describes the heat evolution of a magnetically confined plasma in the edge region of a tokamak. The nonlinearity implies some numerical…
Thermodynamic computing has emerged as a promising paradigm for accelerating computation by harnessing the thermalization properties of physical systems. This work introduces a novel approach to solving quadratic programming problems using…
We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…
We study a model that intermediates among the wave, heat, and transport equations. The approach considers the propagation of initial disturbances in a one-dimensional medium that can vibrate. The medium is nonlinear in such a form that…
For quantum many-body systems in one dimension, computational complexity theory reveals that the evaluation of ground-state energy remains elusive on quantum computers, contrasting the existence of a classical algorithm for temperatures…
Nonperturbative Flow Equations within an effective constituent quark model for two quark flavors with Heat-Kernel methods are studied.
In this work, we propose an efficient and robust multigrid method for solving the time-fractional heat equation. Due to the nonlocal property of fractional differential operators, numerical methods usually generate systems of equations for…
We present three different neural network algorithms to calculate thermodynamic properties as well as dynamic correlation functions at finite temperatures for quantum lattice models. The first method is based on purification, which allows…
We propose a general framework to compare the values of a physical quantity pertaining to two - or more - physical setups, in the finite-precision scenario. Such a situation requires us to compare between two "patches" on the real line…
Quantum computing is gaining increased attention as a potential way to speed up simulations of physical systems, and it is also of interest to apply it to simulations of classical plasmas. However, quantum information science is…
In order to improve the presently used ad hoc flux limiter treatment of parallel heat flux transport in edge plasma fluid codes we consider here a generalized version of the Fourier law implementing a non-local kernel for the heat flux…
We develop an arithmetic analogue of linear partial differential equations in two independent ``space-time'' variables. The spatial derivative is a Fermat quotient operator, while the time derivative is the usual derivation. This allows us…
We formulate theoretical modeling approaches and develop practical computational simulation methods for investigating the non-equilibrium statistical mechanics of fluid interfaces with passive and active immersed particles. Our approaches…
In this paper, we study the flux identification problem for a nonlinear time-fractional viscoelastic equation with a general source function based on the boundary measurements. We prove that the direct problem is well-posed, i.e., the…
We present a simplified model of data flow on processors in a high performance computing framework involving computations necessitating inter-processor communications. From this ordinary differential model, we take its asymptotic limit,…
Thermodynamic and flash equilibrium calculations are the cornerstones of simulation process calculations. The iterative approach, a widely used nonlinear problem-solving technique, relies on derivative calculations throughout the procedure…
The transport of conserved quantities like spin and charge is fundamental to characterizing the behavior of quantum many-body systems. Numerically simulating such dynamics is generically challenging, which motivates the consideration of…
Solving finite-temperature properties of quantum many-body systems is generally challenging to classical computers due to their high computational complexities. In this article, we present experiments to demonstrate a hybrid…
This thesis is devoted to the theoretical study of slow thermodynamic processes in non-equilibrium stochastic systems. Its main result is a physically and mathematically consistent construction of relevant thermodynamic quantities in the…
Differential geometry offers a powerful framework for optimising and characterising finite-time thermodynamic processes, both classical and quantum. Here, we start by a pedagogical introduction to the notion of thermodynamic length. We…