Related papers: A note on an invariant for one-dimensional heat co…
Thermal transistor is an efficient heat control device which can act as a heat switch as well as a heat modulator. In this paper, we study systematically one-dimensional and two-dimensional thermal transistors. In particular, we show how to…
Understanding heat transport in one-dimensional systems remains a major challenge in theoretical physics, both from the quantum as well as from the classical point of view. In fact, steady states of one-dimensional systems are commonly…
We study vibrational energy transport in a quasi 1-D harmonic chain with both longitudinal and transverse vibrations. We demonstrate via both numerical simulation and theoretic analysis that for 1-D atomic chain connected by 3D harmonic…
We present a Fourier finite element modeling of light emission of dipolar emitters coupled to infinitely long waveguides. Due to the translational symmetry, the three-dimensional (3D) coupled waveguide-emitter system can be decomposed into…
The paper suggests a resolution for recent controversy over convergence of heat conductivity in one-dimensional chains with asymmetric nearest-neighbor potential. We conjecture that the convergence is promoted not by the mere asymmetry of…
In this note, we study the arithmetic nature of values of modular functions, meromorphic modular forms and meromorphic quasi-modular forms with respect to arbitrary congruence subgroups, that have algebraic Fourier coefficients. This…
This review summarizes recent studies of thermal transport in nanoscaled semiconductors. Different from bulk materials, new physics and novel thermal properties arise in low dimensional nanostructures, such as the abnormal heat conduction,…
This paper presents a web application for visualizing the tonality of a piece of music -- the organization of its chords and scales -- at a high level of abstraction and with coordinated playback. The application applies the discrete…
In this paper we show an alternative way of defining Fourier Series and Transform by using the concept of convolution with exponential signals. This approach has the advantage of simplifying proofs of transforms properties and, in our view,…
This paper is devoted to the study of the one dimensional non homogeneous heat equation coupled to Dirichlet Boundary Conditions. We obtain the explicit expression of the solution of the linear equation by means of a direct integral in an…
The goal of this paper is to reconstruct spatially distributed dielectric constants from complex-valued scattered wave field by solving a 3D coefficient inverse problem for the Helmholtz equation at multi-frequencies. The data are generated…
This paper studies a prototype of inverse initial boundary value problems whose governing equation is the heat equation in three dimensions. An unknown discontinuity embedded in a three-dimensional heat conductive body is considered. A {\it…
We develop a Born-Oppenheimer type formalism for the description of quantum thermal transport along hybrid nanoscale objects. Our formalism is suitable for treating heat transfer in the off-resonant regime, where e.g., the relevant…
This paper is devoted to the study of the flatness property of linear time-invariant fractional systems. In the framework of polynomial matrices of the fractional derivative operator, we give a characterization of fractionally flat outputs…
We link the problem of estimating the lower Hausdorff dimension of PDE or Fourier constrained measures with Harnack's inequalities for the heat equation. Our approach provides new estimates in the case of Fourier constraints.
We consider a semi-infinite one-dimensional phase-change material with two unknown constant thermal coefficients among the latent heat per unit mass, the specific heat, the mass density and the thermal conductivity. Aiming at the…
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…
We consider a model of heat conduction networks consisting of oscillators in contact with heat baths at different temperatures. Our aim is to generalize the results concerning the existence and uniqueness of the stationnary state already…
Let $L = -1/4 (\sum_{j=1}^n(X_j^2+Y_j^2)+i\gamma T)$ where $\gamma$ is a complex number, $X_j$, $Y_j$, and $T$ are the left invariant vector fields of the Heisenberg group structure for $R^n \times R^n \times R$. We explicitly compute the…
We consider a one-dimensional one-phase inverse Stefan problem for the heat equation. It consists in recovering a boundary influx condition from the knowledge of the position of the moving front, and the initial state. We derived a…