Related papers: Nevanlinna-type theory based on heat diffusion
In this paper we obtain a Nevanlinna-type formula for the matrix Hamburger moment problem in a general case. We only assume that the problem is solvable and has more that one solution. We express the matrix coefficients of the corresponding…
We develop a theory of holomorphic differentials on a certain class of non-compact Riemann surfaces obtained by opening infinitely many nodes.
Basic examples show that coincidence theory is intimately related to central subjects of differential topology and homotopy theory such as Kervaire invariants and divisibility properties of Whitehead products and of Hopf invariants. We…
The nonisothermal single-component theory of droplet nucleation (Alekseechkin, 2014) is extended to binary case; the droplet volume V, composition x, and temperature T are the variables of the theory. An approach based on macroscopic…
The classical Stefan problem, concerning mere heat-transfer during solid-liquid phase transition, is here enhanced towards mechanical effects. The Eulerian description at large displacements is used with convective and Zaremba-Jaumann…
The topological band theory predicts that bulk materials with nontrivial topological phases support topological edge states. This phenomenon is universal for various wave systems and has been widely observed for electromagnetic and acoustic…
In this paper, we prove the diffusion phenomenon for the linear wave equation with space-dependent damping. We prove that the asymptotic profile of the solution is given by a solution of the corresponding heat equation in the $L^2$-sense.
It has recently been shown theoretically that the time-dependent heat conduction equation is form-invariant under curvilinear coordinate transformations. Thus, in analogy to transformation optics, fictitious transformed space can be mapped…
We proved a matrix Li-Yau-Hamilton type gradient estimates for the positive solutin of the heat equation on complete Kaehler manifolds with nonnegative bisectional curvature. As a consequence we obtain a comparison theorem for the distance…
We study heat transfer from a heated nanoparticle into surrounding fluid, using molecular dynamics simulations. We show that the fluid next to the nanoparticle can be heated well above its boiling point without a phase change. Under…
We obtain results on approximation of holomorphic maps by algebraic maps, jet transversality theorems for holomorphic and algebraic maps, and the homotopy principle for holomorphic submersions of Stein manifolds to certain algebraic…
Let $L_t:=\Delta_t+Z_t$ for a $C^{1,1}$-vector field $Z$ on a differential manifold $M$ with boundary $\partial M$, where $\Delta_t$ is the Laplacian induced by a time dependent metric $g_t$ differentiable in $t\in [0,T_c)$. We first…
We calculate the thermal diffusivity $D = \kappa/c_{\rho}$ and butterfly velocity $v_B$ in holographic models that flow to AdS$_2 \times R^{d}$ fixed points in the infra-red. We show that both these quantities are governed by the same…
We derive necessary conditions for a complex projective structure on a complex surface to arise via the Levi-Civita connection of a (pseudo-)K\"ahler metric. Furthermore we show that the (pseudo-)K\"ahler metrics defined on some domain in…
A diffusion process associated with the real sub-Laplacian $\Delta_b$, the real part of the complex Kohn-Spencer laplacian $\square_b$, on a strictly pseudoconvex CR manifold is constructed via the Eells-Elworthy-Malliavin method by taking…
The stability of a thermocapillary flow in an extended cylindrical geometry is analyzed. This flow occurs in a thin liquid layer with a disk shape when a radial temperature gradient is applied along the horizontal free surface. Besides the…
Here, we outline a theory of radiative heat transfer based on an equivalent electrical network representation for the hot material slabs in an arbitrary multilayered environment with arbitrary distribution of temperatures and…
It is known that the holographic thermal propagator in 4 spacetime dimensions can be related to the Nekrasov-Shatashvili limit of the $\Omega$-deformed ${\cal N}=2$ supersymmetric $SU(2)$ Yang-Mills theory with $N_f=4$ hypermultiplets.…
In this work we define a deformation theory for the Coupled K\"ahler-Yang-Mills equations in arXiv:1102.0991, generalizing work of Sz\'ekelyhidi on constant scalar curvature K\"ahler metrics. We use the theory to find new solutions of the…
In this paper thermal conductivity and thermal diffusivity of a two layer system is examined from the theoretical point of view. We use the one dimensional heat diffusion equation with the appropriate solution in each layer and boundary…