Related papers: The Heaviside equation for laser heating of the fu…
Constitutive equations are proposed for the relaxation of a glassy material in contact with a thermal reservoir. The dynamics of a single state variable, identified as an effective temperature accounts for the emergence of glassy behavior…
The investigation of thermal convection of a fluid with the dependence of thermal diffusivity on temperature in a vertical Hele Shaw cell heated from below has been fulfilled theoretically.The expression for equilibrium temperature…
In this paper we consider the heat equation with a strongly singular potential and show that it has a very weak solution. Our analysis is devoted to general hypoelliptic operators and is developed in the setting of graded Lie groups. The…
In this paper we explore the weak solutions of the Cauchy problem and an inverse source problem for the heat equation in the quantum calculus, formulated in abstract Hilbert spaces. For this we use the Fourier series expansions. Moreover,…
The correct accounting for thermal effects is always a challenge when one needs to make quantitative predictions for any laser applications. In such complicated devices as quantum cascade lasers temperature strongly affects the operational…
Various sharp pointwise estimates for the gradient of solutions to the heat equation are obtained. The Dirichlet and Neumann conditions are prescribed on the boundary of a half-space. All data belong to the Lebesgue space $L^p$. Derivation…
In this paper we study Cauchy problem for thermoelastic plate equations with friction or structural damping in $\mathbb{R}^n$, $n\geq1$, where the heat conduction is modeled by Fourier's law. We explain some qualitative properties of…
We reanalyse the work of Cleuren et al., Phys. Rev. Lett. 109, 248902 (2012), in the light of Jiang et al. Phys. Rev. B 85, 075412 (2012). The condition for cooling enforces its rate to be exponentially small at low temperatures. Thus, the…
The study of blow-up solution of time-fractional heat equations is of significant and wide-ranging interest for its multitude of applications. These types of equations are used to model several real problems in science and engineering. This…
Based on the phenomenological theory of heat diffusion, we show that the generated peak temperature $T_{\text{max}}$ after absorption of a laser pulse strongly depends on the pulse duration. We identify three different heat conduction…
In this paper we consider the overdetermined Cauchy problem for the heat equation. We prove that if the problem has a nontrivial nonnegative solution with a certain sequence of similar level sets, then the solution must be radially…
We follow the time evolution of nonabelian gauge bosons from far-from-equilibrium initial conditions to thermal equilibrium by numerically solving an effective kinetic equation that becomes accurate in the weak coupling limit. We consider…
This paper is concerned with the hypercoercivity property of solutions to the Cauchy problem on the linear Boltzmann equation with a confining potential force. We obtain the exponential time rate of solutions converging to the steady state…
The solution to the initial and Dirichlet boundary value problem for a semilinear, one dimensional heat equation is approximated by a numerical method that combines the Besse relaxation scheme in time (C. R. Acad. Sci. Paris S{\'e}r. I,…
Upon rapid quenching of temperature of a glass forming liquid, the system falls out of equilibrium due its finite relaxation time. Additionally, the relaxation becomes progressively slower with time. The created nonequilibrium state of the…
The laser flash method for measuring thermal diffusivity of solids involves subjecting the front face of a small sample to a heat pulse of radiant energy and recording the resulting temperature rise on the opposite (rear) surface. For the…
An expression for the two-particle relaxation time of collective excitations on a distorted Fermi surface in the diffusion approach to kinetic theory is obtained. The general case of momentum-dependent diffusion and drift coefficients is…
The creation of well-thermalized, hot and dense plasmas is attractive for warm dense matter studies. We investigate collisionally induced energy absorption of an ultraintense and ultrashort laser pulse in a solid copper target using…
We study the existence of solutions for Darcy's problem coupled with the heat equation under singular forcing; the right-hand side of the heat equation corresponds to a Dirac measure. The studied model allows thermal diffusion and viscosity…
In this paper the Weyl equation for temperature field induced by laser beam interaction with matter is proposed and solved. Depending on the scattering mechanism the temperature field oscillate or is damped. Key words: Thermal processes,…