Remark about Heat Diffusion on Periodic Spaces
نویسنده
چکیده
Let M be a complete Riemannian manifold with a free cocompact Z-action. Let k(t, m1, m2) be the heat kernel on M . We compute the asymptotics of k(t, m1, m2) in the limit in which t → ∞ and d(m1, m2) ∼ √ t. We show that in this limit, the heat diffusion is governed by an effective Euclidean metric on R coming from the Hodge inner product on H(M/Z;R).
منابع مشابه
A remark on boundedness of composition operators between weighted spaces of holomorphic functions on the upper half-plane
In this paper, we obtain a sucient condition for boundedness of composition operators betweenweighted spaces of holomorphic functions on the upper half-plane whenever our weights are standardanalytic weights, but they don't necessarily satisfy any growth condition.
متن کاملAnalytical Analysis of The Dual-phase-lag Heat Transfer Equation in a Finite Slab with Periodic Surface Heat Flux (RESEARCH NOTE)
This work uses the dual-phase-lag (DPL) model of heat conduction to demonstrate the effect of temperature gradient relaxation time on the result of non-Fourier hyperbolic conduction in a finite slab subjected to a periodic thermal disturbance. DPL model combines the wave features of hyperbolic conduction with a diffusion-like feature of the evidence not captured by the hyperbolic case. For the ...
متن کاملA remark on Remainders of homogeneous spaces in some compactifications
We prove that a remainder $Y$ of a non-locally compact rectifiable space $X$ is locally a $p$-space if and only if either $X$ is a Lindel"{o}f $p$-space or $X$ is $sigma$-compact, which improves two results by Arhangel'skii. We also show that if a non-locally compact rectifiable space $X$ that is locally paracompact has a remainder $Y$ which has locally a $G_{delta}$-diagonal, then...
متن کاملNew fixed and periodic point results on cone metric spaces
In this paper, several fixed point theorems for T-contraction of two maps on cone metric spaces under normality condition are proved. Obtained results extend and generalize well-known comparable results in the literature.
متن کامل. cl as s - ph ] 1 S ep 2 00 8 Dumbbell diffusion in a spatially periodic potential
We present a numerical investigation of the Brownian motion and diffusion of a dumbbell in a two-dimensional periodic potential. Its dynamics is described by a Langevin model including the hydrodynamic interaction. With increasing values of the amplitude of the potential we find along the modulated spatial directions a reduction of the diffusion constant and of the impact of the hydrodynamic in...
متن کامل