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Tamás Fülöp

Publications and source records attributed to Tamás Fülöp.

At least 19 recordsLinked to original sources
arXiv2026

Exact analytical solution for the non-selfadjoint problem of Maxwell--Cattaneo--Vernotte heat conduction with heat-transfer boundary condition

The most well-known beyond-Fourier heat conduction model, the Maxwell--Cattaneo--Vernotte equation is solved analytically in the presence of heat transfer boundary condition. In contrast to the corresponding Fourier problem, this boundary condition renders the underlying differential operator non-selfadjoint. With a suitable scalar product, the adjoint eigenvalue problem is established. The resulting left and right eigenfunctions constitute a biorthogonal system, allowing the expansion coefficients to be determined from arbitrary square-integrable initial conditions. This enables a convenient infinite-sum analytical solution, which is presented and thoroughly investigated for various values of the model parameters (including near-Fourier and highly hyperbolic regimes) and for two practically important initial conditions (equilibrium and flash pulse initiated). The spectral structure is analyzed in detail, including the occurrence of real, imaginary, and complex-conjugate eigenvalue roots, their asymptotic distribution, and their dependence on the dimensionless relaxation time and Biot number. We find good agreement with corresponding finite-difference numerical solutions. The comparison also illustrates the effects of spectral truncation (i.e., the Gibbs phenomenon) and numerical dissipation near propagating thermal-wave fronts. Completeness of the eigenfunction set is numerically demonstrated. The initial condition induced by the flash pulse is derived analytically. The results provide an analytical benchmark for non-selfadjoint hyperbolic heat conduction, unveil how boundary heat transfer and relaxation time influence the transition between Fourier-like diffusion and thermal-wave propagation, and open the possibility to find and investigate beyond-Fourier heat conduction via heat transfer in experiments and practical applications.

math-ph↗
arXiv2025

The piston effect in supercritical fluids investigated via a reversible-irreversible vector field splitting-based explicit time integration scheme

In the vicinity of the liquid--vapor critical point, supercritical fluids behave strongly compressibly and, in parallel, thermophysical properties have strong state dependence. These lead to various peculiar phenomena, one of which being the piston effect where a sudden heating induces a mechanical pulse. The coupling between thermal and mechanical processes, in the linear approximation, yields a non-trivially rich thermoacoustics. The numerous applications of supercritical fluids raise the need for reliable yet fast and efficient numerical solution for thermoacoustic time and space dependence in this sensitive domain. Here, we present a second-order accurate, fully explicit staggered space-time grid finite difference method for such coupled linear thermoacoustic problems. Time integration is based on the splitting of the state space vector field representing the interactions that affect the dynamics into reversible and irreversible parts, which splitting procedure leads to decoupled wave and heat equations. The former is a hyperbolic partial differential equation, while the latter is a parabolic one, therefore, different time integration algorithms must be amalgamated to obtain a reliable, dispersion error-free, and dissipation error-free numerical solution. Finally, the thermoacoustic approximation of the supercritical piston effect is investigated via the developed method.

math.NA↗
arXiv2025

On the coordinate system-dependence of the accuracy of symplectic numerical methods

Symplectic numerical methods have become a widely-used choice for the accurate simulation of Hamiltonian systems in various fields, including celestial mechanics, molecular dynamics and robotics. Even though their characteristics are well-understood mathematically, relatively little attention has been paid in general to the practical aspect of how the choice of coordinates affects the accuracy of the numerical results, even though the consequences can be computationally significant. The present article aims to fill this gap by giving a systematic overview of how coordinate transformations can influence the results of simulations performed using symplectic methods. We give a derivation for the non-invariance of the modified Hamiltonian of symplectic methods under coordinate transformations, as well as a sufficient condition for the non-preservation of a first integral corresponding to a cyclic coordinate for the symplectic Euler method. We also consider the possibility of finding order-compensating coordinate transformations that improve the order of accuracy of a numerical method. Various numerical examples are presented throughout.

math.NA↗
arXiv2024

Improving the accuracy of the Newmark method through backward error analysis

We use backward error analysis for differential equations to obtain modified or distorted equations describing the behaviour of the Newmark scheme applied to the transient structural dynamics equation. Based on the newly derived distorted equations, we give expressions for the numerically or algorithmically distorted stiffness and damping matrices of a system simulated using the Newmark scheme. Using these results, we show how to construct compensation terms from the original parameters of the system, which improve the performance of Newmark simulations. The required compensation terms turn out to be slight modifications to the original system parameters (e.g. the damping or stiffness matrices), and can be applied without changing the time step or modifying the scheme itself. Two such compensations are given: one eliminates numerical damping, while the other achieves fourth-order accurate calculations using the traditionally second-order Newmark method. The performance of both compensation methods is evaluated numerically to demonstrate their validity, and they are compared to the uncompensated Newmark method, the generalized-$α$ method and the 4th-order Runge--Kutta scheme.

math.NA↗
arXiv2024

Four spacetime dimensional simulation of rheological waves in solids and the merits of thermodynamics

The recent results attained from a thermodynamically conceived numerical scheme applied on wave propagation in viscoelastic/rheological solids are generalized here, both in the sense that the scheme is extended to four spacetime dimensions and in the aspect of the virtues of a thermodynamical approach. Regarding the scheme, the arrangement of which quantity is represented where in discretized spacetime, including the question of appropriately realizing the boundary conditions, is nontrivial. In parallel, placing the problem in the thermodynamical framework proves to be beneficial in regards to monitoring and controlling numerical artefacts - instability, dissipation error, and dispersion error. This, in addition to the observed preciseness, speed, and resource-friendliness, makes the thermodynamically extended symplectic approach that is presented here advantageous above commercial finite element software solutions.

physics.class-ph↗
arXiv2023

Thermodynamically extended symplectic numerical simulation of viscoelastic, thermal expansion and heat conduction phenomena in solids

Symplectic numerical schemes for reversible dynamical systems predict the solution reliably over large times as well, and are a good starting point for extension to schemes for simulating irreversible situations like viscoelastic wave propagation and heat conduction coupled via thermal expansion occuring in rocks, plastics, biological samples etc. Dissipation error (artificial nonpreservation of energies and amplitudes) of the numerical solution should be as small as possible since it should not be confused with the real dissipation occuring in the irreversible system. In addition, the other well-known numerical artefact, dispersion error (artificial oscillations emerging at sharp changes), should also be minimal to avoid confusion with the true wavy behaviour. The continuum thermodynamical aspects (respect for balances with fluxes, systematic constitutive relationships between intensive quantities and fluxes, the second law of thermodynamics with positive definite entropy production, and the spacetime-based kinematic viewpoint) prove valuable for obtaining such extended schemes and for monitoring the solutions. Generalizing earlier works in this direction, here, we establish and investigate such a numerical scheme for one-dimensional viscoelastic wave propagation in the presence of heat conduction coupled via thermal expansion, demonstrating long-term reliability and the applicability of thermodynamics-based quantities in supervising the quality of the solution.

physics.class-ph↗
arXiv2021

Analytical solution method for rheological problems of solids

In classical continuum theory, Volterra's principle [1, 2] is a long-known method to solve linear rheological (viscoelastic) problems derived from the corresponding elastic ones. Here, we introduce and present another approach that is simpler to apply (no operator inverse is required to compute but only linear ordinary differential equations to solve). Our method starts with the known elastic solution, replaces the elasticity coefficients with time dependent functions, derives differential equations on them, and determines the solution corresponding to the initial conditions. We present several examples solved via this new method, like tunnels and spherical hollows opened in various initial stress states, and pressurizing of thick-walled tubes and spherical tanks. These examples are useful for applications and, in parallel, are suitable for testing and validating numerical methods of various kinds.

physics.class-ph↗
arXiv2021

A case study of non-Fourier heat conduction using Internal Variables and GENERIC

Applying simultaneously the methodology of Non-Equilibrium Thermodynamics with Internal Variables (NET-IV) and the framework of General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC), we demonstrate that, in heat conduction theories, entropy current multipliers can be interpreted as relaxed state variables. Fourier's law and its various extensions -- the Maxwell-Cattaneo-Vernotte, Guyer-Krumhansl, Jeffreys type, Ginzburg-Landau (Allen-Cahn) type and ballistic-diffusive -- heat conduction equations are derived in both formulations. Along these lines, a comparison of NET-IV and GENERIC is also performed. Our results may pave the way for microscopic/multiscale understanding of beyond-Fourier heat conduction, and open new ways for numerical simulations of heat-conduction problems.

physics.class-ph↗
arXiv2021

Size effects and beyond-Fourier heat conduction in room-temperature experiments

It is a long-lasting task to understand heat conduction phenomena beyond Fourier. Besides the low-temperature experiments on extremely pure crystals, it has turned out recently that heterogeneous materials with macro-scale size can also show thermal effects that cannot be modelled by the Fourier equation. This is called over-diffusive propagation, different from low-temperature observations, and is found in numerous samples made from metal foam, rocks, and composites. The measured temperature history is indeed similar to what Fourier's law predicts but the usual evaluation cannot provide reliable thermal parameters. This paper is a report on our experiments on several rock types, each type having multiple samples with different thicknesses. We show that size-dependent thermal behaviour can occur for both Fourier and non-Fourier situations. Moreover, based on the present experimental data, we find an empirical relation between the Fourier and non-Fourier parameters, which may be helpful in later experiments to develop a more robust and reliable evaluation procedure.

physics.class-ph↗
arXiv2020

Thermodynamical extension of a symplectic numerical scheme with half space and time shift demonstrated on rheological waves in solids

On the example of the Poynting-Thomson-Zener rheological model for solids, which exhibits both dissipation and wave propagation - with nonlinear dispersion relation -, we introduce and investigate a finite difference numerical scheme. Our goal is to demonstrate its properties and to ease the computations in later applications for continuum thermodynamical problems. The key element is the positioning of the discretized quantities with shifts by half space and time steps with respect to each other. The arrangement is chosen according to the spacetime properties of the quantities and of the equations governing them. Numerical stability, dissipative error and dispersive error are analysed in detail. With the best settings found, the scheme is capable of making precise and fast predictions. Finally, the proposed scheme is compared to a commercial finite element software, COMSOL, which demonstrates essential differences even on the simplest - elastic - level of modelling.

physics.class-ph↗
arXiv2019

Kluitenberg-Verhás rheology of solids in the GENERIC framework

The internal variable methodology of nonequilibrium thermodynamics, with a symmetric tensorial internal variable, provides an important rheological model family for solids, the so-called Kluitenberg-Verhás model family [1]. This model family is distinguished not only from theoretical aspects but also on experimental grounds (see [2] for plastics and [3, 4, 5] for rocks). In this article, we present and discuss how the internal variable formulation of the Kluitenberg-Verhás model family can be presented in the nonequilibrium thermodynamical framework GENERIC (General Equation for the Non-Equilibrium Reversible-Irreversible Coupling) [6, 7, 8, 9], for the benefit of both thermodynamical methodologies as well as for promising practical applications.

cond-mat.stat-mech↗
arXiv2018

Emergence of non-Fourier hierarchies

The non-Fourier heat conduction phenomenon on room temperature is analyzed from various aspects. The first one shows its experimental side, in what form it occurs and how we treated it. It is demonstrated that the Guyer-Krumhansl equation can be the next appropriate extension of Fourier's law for room temperature phenomena in modeling of heterogeneous materials. The second approach provides an interpretation of generalized heat conduction equations using a simple thermomechanical background. Here, Fourier heat conduction is coupled to elasticity via thermal expansion, resulting in a particular generalized heat equation for the temperature field. Both of the aforementioned approaches show the size dependency of non-Fourier heat conduction. Finally, a third approach is presented, called pseudo-temperature modeling. It is shown that non-Fourier temperature history can be produced by mixing different solutions of Fourier's law. That kind of explanation indicates the interpretation of underlying heat conduction mechanics behind non-Fourier phenomena.

cond-mat.stat-mech↗
arXiv2017

Probability current in zero-spin relativistic quantum mechanics

We show that the antisymmetric spinor tensor representation of spin-0 relativistic quantum mechanics provides a conserved current with positive definite timelike component, interpretable as probability density. The construction runs in complete analogy to the spin-1/2 case, and provides an analogously natural one-particle Hilbert space description for spin 0. Except for the free particle, the obtained formulation proves to be inequivalent to the one based on the Klein--Gordon equation. The second quantized version may lead to new field theoretical interaction terms for zero-spin particles.

quant-ph↗
arXiv2017

A Thermoelastoplastic Material Model for Finite-Strain Cyclic Plasticity of Metals

In this paper we present a thermodynamically consistent material model which is capable of modelling ductile-to brittle failure mode transition in ductile material undergoing deformations at high strain rates, and demonstrate the performance of the model in a numerical study using a fully coupled thermal-structural finite element analysis of a notched aluminium alloy specimen loaded in cyclic tension. The model is based on an objective representation of the deformation and stress measures and on a rate type constitutive equations. It does not only complies with the principles of material modelling, but it also uses constitutive equations, evolution equations and even "normality rules" during return mapping which can be expressed in terms of power conjugate stress and strain measures, or their objective rates.

cond-mat.mtrl-sci↗
arXiv2017

Second order equation of motion for electromagnetic radiation back-reaction

We take the viewpoint that the physically acceptable solutions of the Lorentz--Dirac equation for radiation back-reaction are actually determined by a second order equation of motion, the self-force being given as a function of spacetime location and velocity. We propose three different methods to obtain this self-force function. For two example systems, we determine the second order equation of motion exactly in the nonrelativistic regime via each of these three methods, the three methods leading to the same result. We reveal that, for both systems considered, back-reaction induces a damping proportional to velocity and, in addition, it decreases the effect of the external force.

math-ph↗
arXiv2015

Objective thermomechanics

An irreversible thermodynamical theory of solids is presented where the kinematic quantities are defined in an automatically objective way. Namely, auxiliary elements like reference frame, reference time and reference configuration are avoided by formulating the motion of the continuum on spacetime directly. Solids are distinguished from fluids by possessing not only an instantaneous metric tensor but also a relaxed metric. The elastic state variable is defined through comparing these two metrics. Thermal expansion is conceived as temperature dependence of the relaxed metric and plasticity, an irreversible change in the relaxed metric, is described via a plastic change rate tensor. Thermomechanics is built around these -- finite deformation -- kinematic quantities by starting from mechanics and adding thermodynamical requirements gradually. The obtained theory is not restricted to isotropic media.

physics.class-ph↗
arXiv2015

Elastic, thermal expansion, plastic and rheological processes - theory and experiment

Rocks are important examples for solid materials where, in various engineering situations, elastic, thermal expansion, rheological/viscoelastic and plastic phenomena each may play a remarkable role. Nonequilibrium continuum thermodynamics provides a consistent way to describe all these aspects in a unified framework. This we present here in a formulation where the kinematic quantities allow arbitrary nonzero initial (e.g., in situ) stresses and such initial configurations which - as a consequence of thermal or remanent stresses - do not satisfy the kinematic compatibility condition. The various characteristic effects accounted by the obtained theory are illustrated via experimental results where loaded solid samples undergo elastic, thermal expansion and plastic deformation and exhibit rheological behaviour. From the experimental data, the rheological coefficients are determined, and the measured temperature changes are also explained by the theory.

cond-mat.soft↗