Related papers: Heat bullets
This paper investigates the theoretical implications of applying Darcy's law to premixed flames, a topic of growing interest in research on flame propagation in porous media and confined geometries. A multiple-scale analysis is carried out…
Transport phenomena plays an important role in science and technology. In the wide variety of applications both advection and diffusion may appear. Regarding diffusion, for long times, different type of decay rates are possible for…
We obtain uniform in time bounds for the solutions to a class of thermo-diffusive systems with classical and fractional diffusions. In the classical diffusion case, the nonlinearities are assumed to be at most exponentially growing, while…
The probability distribution for vacuum fluctuations of the energy flux in two dimensions will be constructed, along with the joint distribution of energy flux and energy density. Our approach will be based on previous work on probability…
We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis in the right-hand side. The input of hysteresis is given by a vector-valued function of space and time. Such systems describe hysteretic…
The three--dimensional incompressible viscous Boussinesq equations, under the assumption of hydrostatic balance, govern the large scale dynamics of atmospheric and oceanic motion, and are commonly called the primitive equations. To overcome…
We have constructed new formulae for generation of solutions for the nonlinear heat equation and for the Burgers equation that are based on linearizing nonlocal transformations and on nonlocal symmetries of linear equations. Found nonlocal…
The critical dimension necessary for a flame to propagate in suspensions of fuel particles in oxidizer is studied analytically and numerically. Two types of models are considered: First, a continuum model, wherein the individual particulate…
We study a second-order parabolic equation with divergence form elliptic operator, having piecewise constant diffusion coefficients with two points of discontinuity. Such partial differential equations appear in the modelization of…
Thermal waves are caused by pure diffusion: their amplitude is decreased by more than a factor of 500 within a propagation distance of one wavelength. The diffusion equation, which describes the temperature as a function of space and time,…
We discuss a class of diffusion-type partial differential equations on a bounded interval and discuss the possibility of replacing the boundary conditions by certain linear conditions on the moments of order 0 (the total mass) and of…
We advance an exact, explicit form for the solutions to the fractional diffusion-advection equation. Numerical analysis of this equation shows that its solutions resemble power-laws.
Convection-diffusion problems arise in the modelling of many physical processes. Their typical solutions exhibit boundary and/or interior layers. Despite the linear nature of the differential operator, these problems pose still-unanswered…
The dynamics of the movement of gas is discussed for two-chambered polarized He-3 target cells of the sort that have been used successfully for many electron scattering experiments. A detailed analysis is presented showing that diffusion is…
We propose a one-dimensional (1D) diffusion equation (heat equation) for systems in which the diffusion constant (thermal diffusivity) varies alternately with a spatial period $a$. We solve the time evolution of the field (temperature)…
The Cauchy problem for the linearization of a system of equations arising in the kinetic theory of a condensed gas of bosons near the critical temperature around one of its equilibria is solved for radially symmetric initial data. It is…
We study spatio-temporal bursting in a three-scale reaction diffusion equation organized by the winged cusp singularity. For large time-scale separation the model exhibits traveling bursts, whereas for large space-scale separation the model…
The one-dimensional problem of the nonlinear heat equation is considered. We assume that the heat flow in the origin of coordinates is the power function of time and the initial temperature is zero. Approximate solutions of the problem are…
In this tutorial, we aim to directly recreate some of our "aha" moments when exploring the impact of heat diffusion on the spatial resolution limit of photothermal imaging. Our objective is also to communicate how this physical limit can…
We consider the Cauchy problem for the heat diffusion equation in the whole space consisting of three layers with different constant conductivities, where initially the upper and middle layers have temperature 0 and the lower layer has…