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61.
Heat Kernel Asymptotics of Zaremba Boundary Value Problem 总被引:1,自引:0,他引:1
The Zaremba boundary-value problem is a boundary value problem for Laplace-type second-order partial differential operators
acting on smooth sections of a vector bundle over a smooth compact Riemannian manifold with smooth boundary but with discontinuous
boundary conditions, which include Dirichlet boundary conditions on one part of the boundary and Neumann boundary conditions
on another part of the boundary. We study the heat kernel asymptotics of Zaremba boundary value problem. The construction
of the asymptotic solution of the heat equation is described in detail and the heat kernel is computed explicitly in the leading
approximation. Some of the first nontrivial coefficients of the heat kernel asymptotic expansion are computed explicitly.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
62.
Finite chains of a two-state random Potts spin model with periodic boundary conditions are studied within Glauber dynamics. The spin exchange is assumed random with frustration between ferro and antiferromagnetic values (±J). Time-dependent fluctuations are induced by periodic temperature oscillations. Master type differential equations for spin correlation functions are solved within linear response theory. The spectrum of relaxation times are calculated at different temperatures. The ±J Potts glass chains undergo a zero temperature phase transition. The barriers against inversion of the spin chain take only two values; 0 and 2|J|. The temperature behaviour of specific heat is characterized by rounded peaks. The frequency dependence displays two plateaus for the real part of specific heat and two corresponding peaks for the imaginary part. The dynamic specific heat is not affected by the longest relaxing mode like susceptibility. The time separation of the modes is demonstrated by the Cole-Cole plots. 相似文献
63.
潜热型热功能流体强化换热分析 总被引:4,自引:0,他引:4
本文建立了分析带有相变微胶囊的潜热型热功能流体的流动和换热过程数理模型,应用有限差分法和移动热源法进行联合求解。计算结果表明,相变微胶囊的加入:较好地提高了流体的换热性能。获得了相变颗粒大小和体积分数对强化换热影响等结果。计算结果对该类流体的设计和应用提供了理论依据。 相似文献
64.
Taking both the heterogeneous catalytic processes, including the surface formation of particles with excited internal degrees of freedom, and the processes of multicomponent diffusion and heat transfer in the MESOX apparatus fully into account makes it possible to obtain a recombination coefficient and an accommodation coefficient of the oxygen-atoms-on-quartz recombination energy which are in good agreement with the experimental data. The heterogeneous catalysis model constructed can be used effectively for predicting the heat fluxes to the surface of reentry vehicles on their entry into the Earth’s atmosphere. 相似文献
65.
66.
67.
J.-L. Garden 《Thermochimica Acta》2007,452(2):85-105
What is really measured in dynamic calorimetric experiments is still an open question. This paper is devoted to this question, which can be usefully envisaged by means of macroscopic non-equilibrium thermodynamics. From the pioneer work of De Donder on chemical reactions and with other authors along the 20th century, the question is tackled under an historical point of view. A special attention is paid about the notions of frequency dependent complex heat capacity and entropy production due to irreversible processes occurring during an experiment. This phenomenological approach based on thermodynamics, not widely spread in the literature of calorimetry, could open significant perspectives on the study of macro-systems undergoing physico-chemical transformations probed by dynamic calorimetry. 相似文献
68.
林支桂 《数学物理学报(B辑英文版)》1998,(3)
1IntroductionInthispaper,weconsidertheinitial-boundaryvalueproblem,where"o(x)isnon-negativesmoothfunctionsatisfying"o.(0)=0,"o.(1)=1'Whenconsideringtheblow-upofsolution,thefollowingproblemarisenaturally:Doesblow-upoccur?Howdoesthesolutionapproachtheblow-uptime'!Andwilersisthehotspotlocated(blow-upset)?WelookattheheatequationwithanonlillearboundaryconditiollHerefiisaboundeddomaininR",p>1isarealnumber.IthasbeenknownforalongtimethattheDroblelil(1.1).(1.2)withAL(~,0)--'no(x)doesnothaveaglobals… 相似文献
69.
本文将布拉格方程推广应用到高聚物的结构研究中,得到了经不同剂量辐照的聚乙烯单晶的长周期,并辅以示差扫描量热法研究了γ-射线辐照对聚乙烯单晶结构的影响. 相似文献
70.
Unconventional antiferromagnetic correlations of the doped Haldane gapsystem Y 2 BaNi 1 - x Zn x O 5
V. Villar R. Mélin C. Paulsen J. Souletie E. Janod C. Payen 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,25(1):39-51
We make a new proposal to describe the very low temperature susceptibility of the doped Haldane gap compound Y2BaNi1-xZnxO5. We propose a new mean field model relevant for this compound. The ground state of this mean field model is unconventional
because antiferromagnetism coexists with random dimers. We present new susceptibility experiments at very low temperature.
We obtain a Curie-Weiss susceptibility χ(
T
) ∼
C
/(Θ +
T
) as expected for antiferromagnetic correlations but we do not obtain a direct signature of antiferromagnetic long range order.
We explain how to obtain the “impurity” susceptibility
(
T
) by subtracting the Haldane gap contribution to the total susceptibility. In the temperature range [1 K, 300 K] the experimental
data are well fitted by T
(
T
) =
C
imp
1 +
T
imp
/
T
. In the temperature range [100 mK, 1 K] the experimental data are well fitted by T
(
T
) =
A
ln(
T
/
T
c
), where T
c
increases with x. This fit suggests the existence of a finite Néel temperature which is however too small to be probed directly in our experiments.
We also obtain a maximum in the temperature dependence of the ac-susceptibility
(
T
) which suggests the existence of antiferromagnetic correlations at very low temperature.
Received 17 July 2001 相似文献