Analytic solution of Guyer-Krumhansl equation for laser flash experiments

The existence of non-Fourier heat conduction is known for a long time in small and low temperature systems. The deviation from Fourier's law has been found at room temperature in heterogeneous materials like rocks and metal foams \cite{Botetal16, Vanetal17}. These experiments emphasized that the so-called Guyer-Krumhansl equation is adequate for modeling complex materials. In this paper an analytic solution of Guyer-Krumhansl equation is presented considering boundary conditions from laser flash experiment. The solutions are validated with the help of a numerical code \cite{KovVan15} developed for generalized heat equations

On the rarefied gas experiments

There are limits of validity of classical constitutive laws such as Fourier and Navier-Stokes equations, phenomena beyond those limits have been experimentally found many decades ago. However, it is still not clear what theory would be appropriate to model different non-classical phenomena under different conditions considering either the low-temperature or composite material structure. In this paper, a modeling problem of rarefied gases is addressed. It covers the mass density dependence of material parameters, the scaling properties of different theories and aspects of how to model an experiment. In the following, two frameworks and their properties are discussed. One of them is the kinetic theory based Rational Extended Thermodynamics; the other one is the non-equilibrium thermodynamics with internal variables and current multipliers. In order to compare these theories, an experiment performed by Rhodes is analyzed in detail. It is shown that the density dependence of material parameters has a severe impact on modeling capabilities and can lead to very different results

Heat equations beyond Fourier: from heat waves to thermal metamaterials

In the past decades, numerous heat conduction models beyond Fourier have been developed to account for the large gradients, fast phenomena, wave propagation, or heterogeneous material structure, such as being typical for biological systems, superlattices, or thermal metamaterials. It became a challenge to orient among the models, mainly due to their various thermodynamic backgrounds and possible compatibility issues. Additionally, in light of the recent findings on the field of non-Fourier heat conduction, it is not even straightforward how to interpret and utilize a non-Fourier heat equation, primarily when one aims to thermally design the material structure to construct the new generation of thermal metamaterials. Adding that numerous modeling strategies can be found in the literature accompanying different interpretations even for the same heat equation makes it even more difficult to orient ourselves and find a comprehensive picture of this field of research. Therefore, this review aims to ease the orientation among advanced heat equations beyond Fourier by discussing properties concerning their possible practical applications in light of experiments. We start from the simplest model with basic principles and notions, then proceed toward the more complex models related to coupled phenomena such as ballistic heat conduction. We do not enter the often complicated technical details of each thermodynamic framework but do not aim to compare each approach. However, we still briefly present their background to highlight their origin and the limitations acting on the models. Additionally, the field of non-Fourier heat conduction has become quite segmented, and that paper also aims to provide a common ground, a comprehensive mutual understanding of the basics of each model, together with what phenomenon they can be applied to

Random transverse-field Ising chain with long-range interactions

We study the low-energy properties of the long-range random transverse-field Ising chain with ferromagnetic interactions decaying as a power alpha of the distance. Using variants of the strong-disorder renormalization group method, the critical behavior is found to be controlled by a strong-disorder fixed point with a finite dynamical exponent z_c=alpha. Approaching the critical point, the correlation length diverges exponentially. In the critical point, the magnetization shows an alpha-independent logarithmic finite-size scaling and the entanglement entropy satisfies the area law. These observations are argued to hold for other systems with long-range interactions, even in higher dimensions.Comment: 6 pages, 4 figure

Non-equilibrium theories of rarefied gases: internal variables and extended thermodynamics

Limits of classical constitutive laws such as Fourier and Navier-Stokes equations are discovered since decades. However, the proper extensions -- generalizations of these are not unique. They differ in the underlying physical principles and in modeling capabilities. In this paper, two different theories are discussed and compared to each other, namely the kinetic theory-based Rational Extended Thermodynamics (RET) and non-equilibrium thermodynamics with internal variables (NET-IV). First, the paper starts with the case of rigid heat conductors summarizing the result achieved so far. Then a typical example of compressible bodies is shown by presenting the first generalization for rarefied gases, called Meixner's theory. It is further extended using generalized entropy current in the framework of NET-IV. It is shown how its structure is related to RET and how the compatibility between them can be acquired