Related papers: Gelfand type problem for two phase porous media
We discuss two problems which are particularly challenging for approximations in time-dependent density functional theory (TDDFT) to capture: momentum-distributions in ionization processes, and memory-dependence in real-time dynamics. We…
A generalised form of time-translation-invariance permits to re-derive the known generic phenomenology of ageing, which arises in classical many-body systems after a quench from an initially disordered system to a temperature $T\leq T_c$,…
In this paper we study a model of randomly colliding particles interacting with a thermal bath. Collisions between particles are modeled via the Kac master equation while the thermostat is seen as an infinite gas at thermal equilibrium at…
Analytical relations for the glass transition temperature, $T_g$, and the crystal melting temperature, $T_m$, are developed on the basis of nonaffine lattice dynamics. The proposed relations explain: (i) the seemingly universal factor of…
The propagation of unstable interfaces is at the origin of remarkable patterns that are observed in various areas of science as chemical reactions, phase transitions, growth of bacterial colonies. Since a scalar equation generates usually…
The central problem in the physics of immiscible two-phase flow in porous media is to find a proper description of the flow at scales large enough so that the medium may be regarded as a continuum: the scale-up problem. So far, the only…
We consider \begin{align*} \label{HS} \left\{ \begin{array}{l} u_{tt} = (\gamma(\Theta) u_{xt})_x + a (\gamma(\Theta) u_x)_x +(f(\Theta))_x, \\[1mm] \Theta_t = D\Theta_{xx} + \Gamma(\Theta) u_{xt}^2 + F(\Theta) u_{xt}, \end{array}\right.…
We consider a new Stefan-type problem for the classical heat equation with a latent heat and phase-change temperature depending of the variable time. We prove the equivalence of this Stefan problem with a class of boundary value problems…
Melt supercooling leads to glass formation. Liquid-to-liquid phase transitions are observed depending on thermal paths. Viscosity, density and surface tension thermal dependences measured at heating and subsequent cooling show hysteresis…
We study two two-level atomic quantum systems (qubits) placed close to a body held at a temperature different from that of the surrounding walls. While at thermal equilibrium the two-qubit dynamics is characterized by not entangled steady…
The kernel of the evolution equation is used to build a mathematical theory of thermal phenomena of gaseous and condensed matter. The group velocity of sound and the molar density are proposed to be its two thermal variables that replace…
A novel regularized fracture model for crack propagation in porous media is proposed. Our model is obtained through homogenization theory and formal asymptotic expansions. We start with a regularized quasi-static fracture model posed in a…
We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in…
In this paper we prove a local-in-time existence theorem for an initial-boundary value problem related to a model of temperature-dependent phase segregation that generalizes the standard Allen-Cahn's model. The problem is ruled by a system…
The off-equilibrium probability distribution of the heat exchanged by a ferromagnet in a time interval after a quench below the critical point is calculated analytically in the large-N limit. The distribution is characterized by a singular…
The paper analyzes the phenomenon of turbulent thermal diffusion in the Earth atmosphere, its relation to the turbulent diffusion and its potential impact on aerosol distribution. This phenomenon was predicted theoretically more than 10…
A cool phase of the interstellar medium has been observed in many giant elliptical galaxies, but its origin remains unclear. We propose that uneven heating from Type Ia supernovae (SNe Ia), together with radiative cooling, can lead to the…
We study a nonlocal version of the two-phase Stefan problem, which models a phase transition problem between two distinct phases evolving to distinct heat equations. Mathematically speaking, this consists in deriving a theory for…
The present article is dedicated to the forward and backward solution of a transient one-phase Stefan problem. In the forward problem, we compute the evolution of the initial domain for a Stefan problem where the melting temperature varies…
In this paper we consider spherically symmetric general fluids with heat flux, motivated by causal thermodynamics, and give the appropriate set of conditions that define separating shells defining the divide between expansion and collapse.…