Related papers: Convection Effects and Optimal Insulation: Modelli…
We consider a Brownian particle with diffusion coefficient $D$ in a $d$-dimensional ball of radius $R$ with reflecting boundaries. We study the maximum $M_x(t)$ of the trajectory of the particle along the $x$-direction at time $t$. In the…
We develop two methods to calculate the momentum distribution of the insulating (Mott and charge-density-wave) phases of the extended Bose-Hubbard model with on-site and nearest-neighbor boson-boson repulsions on $d$-dimensional hypercubic…
In this article, we study the unique determination of convection term and the time-dependent density coefficient appearing in a convection-diffusion equation from partial Dirichlet to Neumann map measured on boundary.
We study lower and upper bounds for the density of a diffusion process in ${\mathbb{R}}^n$ in a small (but not asymptotic) time, say $\delta$. We assume that the diffusion coefficients $\sigma_1,\ldots,\sigma_d$ may degenerate at the…
We consider Rayleigh-B\'enard convection in a layer of fluid between rough no-slip boundaries where the top and bottom boundary heights are functions of the horizontal coordinates with square-integrable gradients. We use the background…
Systems under external confinement and constraints often show interesting properties. In this thesis, we study some systems under external confinement. We begin by finding out the probability distribution of end-to-end separation of a Worm…
We consider the two-dimensional problem of recovering globally in time the heat distribution on the surface of a layer inside of a heat conducting body from two interior temperature measurements. The problem is ill-posed. The approximation…
Here we summarize the results from our direct numerical simulations (DNS) and experimental measurements on rotating Rayleigh-B\'enard (RB) convection. Our experiments and simulations are performed in cylindrical samples with an aspect ratio…
Probing the ideal limit of interfacial thermal conductance (ITC) in two-dimensional (2D) heterointerfaces is of paramount importance for assessing heat dissipation in 2D-based nanoelectronics. Using graphene/hexagonal boron nitride…
The thermal response function given to a unit-step dissipation accurately characterizes the thermal system. Instead of the thermal response function the so-called structure function describing three-dimensional as the equivalent model of…
A series of numerical simulations of Rayleigh-B{\'e}nard convection in a cubic cavity are conducted in order to examine the structure of the thermal boundary layer in case of mixed boundary conditions. The main goal of the study is the…
We study the influence of thermal boundary conditions on large aspect ratio Rayleigh-B\'enard convection by a joint analysis of experimental and numerical data sets for a Prandl number $\mathrm{Pr = 7}$ and Rayleigh numbers $\mathrm{Ra =…
Due to their low density and large specific surface area, metal foams are increasingly used as cellular materials that combine excellent structural and thermal properties. Their cellular structure makes them particularly suitable for use in…
Heat transport in turbulent thermal convection increases with the thermal forcing, but in almost all studies the rate of this increase is slower than it would be if transport became independent of the molecular diffusivities -- the heat…
Convection in the metallic cores of terrestrial planets is likely to be subjected to lateral variations in heat flux through the outer boundary imposed by creeping flow in the overlying silicate mantles. Boundary anomalies can significantly…
In this paper, the insulated conductivity model with two touching or close-to-touching inclusions is considered in $\mathbb{R}^{d}$ with $d\geq3$. We establish the pointwise upper bounds on the gradient of the solution for the generalized…
The excess adsorption $\Gamma $ in two-dimensional Ising strips $(\infty \times L)$ subject to identical boundary fields, at both one-dimensional surfaces decaying in the orthogonal direction $j$ as $-h_1j^{-p}$, is studied for various…
Previous numerical studies have shown that the "ultimate regime of thermal convection" can be attained in a Rayleigh-Benard cell when the kinetic and thermal boundary layers are eliminated by replacing the walls with periodic boundary…
Direct numerical simulations are carried out to investigate the effect of the wall temperature on the behavior of oblique shock-wave/turbulent boundary layer interactions at freestream Mach number $2.28$ and shock angle of the wedge…
Thermal rectification can occur when heat is transferred asymmetrically. We consider in this work, the case of a composite wall with one conductive and radiative layer. Both Rosseland and surface radiation approximations are used for taking…