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981.
This paper is concerned with the large time behavior of solutions to two types of nonlinear diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball. We are interested in the critical global exponent q0 and the critical Fujita exponent qc for the problems considered, and show that q0=qc for the multi-dimensional porous medium equation and non-Newtonian filtration equation with nonlinear boundary sources. This is quite different from the known results that q0<qc for the one-dimensional case. 相似文献
982.
Dennis Kretschmann Dirk Schlingemann Reinhard F. Werner 《Journal of Functional Analysis》2008,255(8):1889-1904
We show a continuity theorem for Stinespring's dilation: two completely positive maps between arbitrary C∗-algebras are close in cb-norm if and only if we can find corresponding dilations that are close in operator norm. The proof establishes the equivalence of the cb-norm distance and the Bures distance for completely positive maps. We briefly discuss applications to quantum information theory. 相似文献
983.
Meng Yuan Wenlong Xu Ying Yang Suying Li Haiyan Yang Jun Gao Heqing Jiang Menglong Yang 《Chemphyschem》2023,24(24):e202300587
Studying the characteristics and molecular mechanisms of liquid self-diffusion coefficient and viscosity changes is of great significance for, e. g., chemical and petroleum processing. As examples of highly complex liquid,an asphaltene-free high-acid and high-viscosity crude oil and its extracted fractions were studied by comparing their 1H DOSY diffusion maps. The crude oil exhibited a polydisperse diffusion distribution, including multiple diffusion portions with diffusion coefficients much smaller than that of any single fraction in independent diffusion. The main mechanism that leads to the decreases in the diffusion coefficients of crude oil is attributed to diffusion resistance enhanced by Dynamical Molecular-Interaction Networks (DMINs), rather than by enlargement of the diffusion species caused by molecular aggregation. Constructed through the synergistic interactions of various polar molecules in crude oil, DMINs dynamically bind polar molecules, trap polarizable molecules, and spatially hinder the free motion of non-polar molecules. Overall, this reduces the mobility of all molecular species, as illustrated by the decreased diffusion coefficients. This study demonstrates that DOSY is a powerful NMR method to investigate molecular motion abilities also in complex mixtures. In addition, the insights in the influence of the interaction matrix on the molecular mobility also help to understand the contribution of “structural viscosity” to the viscosity of heavy oil. 相似文献
984.
985.
MCGUINNESS M. J.; PLEASE C. P.; FOWKES N.; MCGOWAN P.; RYDER L.; FORTE D. 《IMA Journal of Management Mathematics》2000,11(1):49-70
Three models are presented for the wetting of whole grains ofcereal. Two are for temperatures below gelatinization temperatures,one of which incorporates the effects of swelling of the grain.A third model is presented for wetting of a grain at temperaturesabove gelatinization, and hence cooking the grain. The modelsare developed as partial differential equations, and solvedin a variety of ways. A model that ignores swelling at temperaturesbelow gelatinization is solved for wetting times by using theconcept of mean action time, which reduces the problem to anexactly solvable linear Poisson equation. The other two models,which include swelling and cooking respectively, are solvedapproximately, taking advantage of the steep nonlinear diffusionfronts that develop. The aim of the modelling is to improveunderstanding of the cooking of whole-grain cereals prior toprocessing into breakfast cereals. Moisture penetration curvesare obtained and compared. Regions where the penetration rateis approximately linear are noted, suggesting that nonlineardiffusion equations are a promising way to model grain wettingand cooking. 相似文献
986.
肖筱南 《厦门大学学报(自然科学版)》2007,46(2):161-163
在完备概率空间(Ω,F,P)中,讨论了一类带非超前泛函的条件Gauss随机扩散过程方程组解的连续惟一性及其具有连续惟一强解的条件,并在方程组存在相应连续惟一强解的情况下,讨论了σ-代数Ftξ和Ftξ0,-W的相合性,得到了关于更新过程-W=(-Wt),t≥0包含有与可观测过程ξ相同“信息”的结果Ftξ=Ft0ξ,-W,0≤t≤T,该结论对于进一步研究此类过程的某些最优控制问题具有重要意义. 相似文献
987.
以酸性红12作为多苯环长链发色有机物的代表,通过对有效扩散系数的测定,确定其在介孔材料颗粒体上的吸附等温式和平衡接近率随时间变化的关系.利用非稳态扩散传质与非稳态热传导过程类比速率方程相似的特点,应用Peterson的热传导近似公式,用计算机求解超越方程,得到了酸性红12在介孔复合材料颗粒内的有效扩散系数并进行了拟合验证,得出该传质过程的主要作用力类型. 相似文献
988.
M. Rezulski 《Optics & Laser Technology》1986,18(2)
Vignetting in the optical system of an electro-optical distance meter is described, and the impact of the measuring conditions is dealt with. The method of analysis, involving numerical calculations, is given and the results for three typical cases are shown. 相似文献
989.
M. M. Lafisheva M. Kh. Shkhanukov-Lafishev 《Computational Mathematics and Mathematical Physics》2008,48(10):1875-1884
Locally-one-dimensional difference schemes for the fractional diffusion equation in multidimensional domains are considered. Stability and convergence of locally one-dimensional schemes for this equation are proved. 相似文献
990.
CHEN Lihua 《武汉大学学报:自然科学英文版》2008,13(1):9-13
The singularly perturbed initial boundary value problems for the reaction diffusion system are raised. Firstly, under suitable conditions, using a iteration technique, the differential inequalities theorem is constructed and introducing two auxiliary functions the existence and uniqueness theorem of solution for the basic reaction diffusion system is proved. Using the singularly perturbed method the formal asymptotic expressions of the solution are constructed with power series theory. By using the comparison theorem the existence and its asymptotic behavior of solution for the original problem are studied. Finally, using method of estimate inequalities, the structure of solutions for the problem is discussed thoroughly in three cases and asymptotic solution of the original problem is given. The asymptotic behavior of solution in the three cases is proved. 相似文献