相关论文: Cloaking via mapping for the heat equation
We introduce "stochastic cloaking," where a region of space is concealed from an ensemble of diffusing particles whose individual trajectories are governed by a stochastic (Langevin) equation. Our simulations reveal how different…
Recent research has uncovered a remarkable ability to manipulate and control electromagnetic fields to produce effects such as perfect imaging and spatial cloaking. To achieve spatial cloaking, the index of refraction is manipulated to flow…
The invariance under co-ordinate transformations of a set of partial differential equations can lead to the possibility of invisibility cloaking, whereby an anomaly in the interior of a body is shielded from an external observer. The form…
This paper concerns the analysis of a passive, broadband approximate cloaking scheme for the Helmholtz equation in ${\mathbb R}^d$ for $d=2$ or $d=3$. Using ideas from transformation optics, we construct an approximate cloak by ``blowing…
We present a new stochastic analysis for steady and transient one-dimensional heat conduction problem based on the homogenization approach. Thermal conductivity is assumed to be a random field K consisting of random variables of a total…
Invisible cloak has long captivated the popular conjecture and attracted intensive research in various communities of wave dynamics, e.g., optics, electromagnetics, acoustics, etc. However, their inhomogeneous and extreme parameters imposed…
Transformation optics originating from the invariance of Maxwell's equations under the coordinate mapping has enabled the design and demonstration of many fascinating electromagnetic devices that were unconceivable or deemed impossible…
The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…
Inverse problems of recovering heat transfer coefficient from integral measurements are considered. The heat transfer coefficient occurs in the transmission conditions of imperfect contact type or the Robin type boundary conditions. It is…
We design a device that generates fields canceling out a known probing field inside a region to be cloaked while generating very small fields far away from the device. The fields we consider satisfy the Laplace equation, but the approach…
We characterise the trace spaces arising from intersections of weighted, vector-valued Sobolev spaces, where the weights are powers of the distance to the boundary. These weighted function spaces are particularly suitable for treating…
Coordinate-transformation approaches to invisibility cloaking rely on the design of an anisotropic, spatially inhomogeneous "transformation medium" capable of suitably re-routing the energy flux around the region to conceal without causing…
We design sources for the two-dimensional Helmholtz equation that can cloak an object by cancelling out the incident field in a region, without the sources completely surrounding the object to hide. As in previous work for real positive…
The macroscopic control of ubiquitous heat flow remains poorly explored due to the lack of a fundamental theoretical method. Here, by establishing temperature-dependent transformation thermotics for treating materials whose conductivity…
This paper analyzes a transient thermo-electromagnetic problem arising in the modeling of induction heating processes. Unlike previous studies that focused on steady-state scenarios, we consider a time-dependent thermal problem coupled with…
We study the homogenization of a steady diffusion equation in a highly heterogeneous medium made of two subregions separated by a periodic barrier through which the flow is proportional to the jump of the temperature by a layer conductance…
The heat equation is considered in the complex medium consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies an impedance boundary condition is imposed. An equation for the limiting…
We study the diffusive limit approximation for a nonlinear radiative heat transfer system that arises in the modeling of glass cooling, greenhouse effects and in astrophysics. The model is considered with the reflective radiative boundary…
This work deals with the problem of determining a non-homogeneous heat conductivity profile in a steady-state heat conduction boundary-value problem with mixed Dirichlet-Neumann boundary conditions over a bounded domain in $\mathbb{R}^n$,…
The heat equation is considered in the complex system consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies a Newton-type boundary condition is imposed. An equation for the limiting…