The Bloch Approximation in Periodically Perforated Media

We consider a periodically heterogeneous and perforated medium filling an open domain Ω of ℝ^N. Assuming that the size of the periodicity of the structure and of the holes is O(ε), we study the asymptotic behavior, as ε → 0, of the solution of an elliptic boundary value problem with strongly oscillating coefficients posed in Ω^ε (Ω^ε being Ω minus the holes) with a Neumann condition on the boundary of the holes. We use Bloch wave decomposition to introduce an approximation of the solution in the energy norm which can be computed from the homogenized solution and the first Bloch eigenfunction. We first consider the case where Ωis ℝ^N and then localize the problem for a bounded domain Ω, considering a homogeneous Dirichlet condition on the boundary of Ω.     

三维拟线性热弹性力学方程区域内部解的奇性传播规律

本文利用频率分析对角化的方法,研究了三维拟线性热弹性力学方程区域内部解的奇性传播规律. 首先从微局部观点出发,利用仿微分算子和拟微分算子将方程仿线性化和对角化.然后,利用穿梭法和经典的双曲方程和抛物方程理论,证明了区域内部解的奇性传播也是沿耦合方程组的双曲算子的零次特征带传播,并且当初值的奇性沿方程组的双曲算子的前向光锥传播时,时间t也具有很好的正则性.     

Sharp Estimates in Bergman and Besov Spaces on Bounded Symmetric Domains

Sharp estimates of the point-evaluation functional in weighted Bergman spaces L ^p _a (Ω, dν _α) and for the point-evaluation derivalive functional in Besov spaces B ^p (Ω) are obtained for bounded symmetric domains Ω in ℂ ⁿ . Received October 25, 1999, Accepted December 6, 2000     

An <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>-Theory of SPDEs on Lipschitz Domains

Stochastic partial differential equations are considered on Lipschitz domains. Existence and uniqueness results are given in weighted Sobolev spaces, and Hölder estimates of the solutions are also obtained. The number of derivatives of the solutions can be any real number, in particular, it can be negative and fractional. It is allowed that the coefficients of the equations blow up near the boundary.     

Membrane lipid domains and dynamics as detected by Laurdan fluorescence

2-Dimethylamino-6-lauroylnaphthalene (Laurdan) is a membrane probe of recent characterization, which shows high sensitivity to the polarity of its environment. Steady-state Laurdan excitation and emission spectra have different maxima and shape in the two phospholipid phases, due to differences in the polarity and in the amount of dipolar relaxation. In bilayers composed of a mixture of gel and liquid-crystalline phases, the properties of Laurdan excitation and emission spectra are intermediate between those obtained in the pure phases. These spectral properties are analyzed using the generalized polarization (GP). TheGP value can be used for the quantitation of each phase. The wavelength dependence of theGP value is used to ascertain the coexistence of different phase domains in the bilayer. Moreover, by following the evolution of Laurdan emission vs. time after excitation, the kinetics of phase fluctuation in phospholipid vesicles composed of coexisting gel and liquid-crystalline phases was determined.GP measurements performed in several cell lines did not give indications of coexistence of phase domains in their membranes. In natural membranes, Laurdan parameters indicate a homogeneously fluid environment, with restricted molecular motion in comparison with the phospholipid liquid-crystalline phase. The influence of cholesterol on the phase properties of the two phospholipid phases is proposed to be the cause of the phase behavior observed in natural membranes. In bilayers composed of different phospholipids and various cholesterol concentrations, Laurdan response is very similar to that arising from cell membranes. In the absence of cholesterol, from the steady-state and time-resolved measurements of Laurdan in phospholipid vesicles, the condition for the occurrence of separate coexisting domains in the bilayer has been determined: the molecular ratio between the two phases must be in the range between 30% and 70%. Below and above this range, a single homogeneous phase is observed, with the properties of the more concentrated phase, slightly modified by the presence of the other. Moreover, in this concentration range, the calculated dimension of the domains is very small, between 20 and 50 Å.     

A renormalization group explanation of numerical observations of analyticity domains

A recent paper considers the dependence of the size of analyticity domains of some functions appearing in KAM theory as a function of the distance to breakdown. They tentatively conclude that the relation is linear. In this note we argue that McKay's renormalization group picture predicts a power-law dependence with an exponent close to 1 but not equal to 1.     

Magnetic Anisotropy and the Appearance of Stripe Magnetic Domains in Co/Fe Multilayers

Thin Co/Fe multilayers were e-beam evaporated in ultra-high vacuum, keeping constant the Co layer thickness and varying that of Fe in the 0.5÷15 nm range. By increasing the Fe layer thickness, a component of magnetization perpendicular to the film plane rises up, and long and parallel magnetic domains (stripe domains) appear. The phenomenon is explained on the basis of the competition between the magnetoelastic anisotropy induced by stresses at the interfaces, and the shape anisotropy constraining the magnetization in the film plane. This revised version was published online in August 2006 with corrections to the Cover Date.     

A numerical model for the flooding and drying of irregular domains

A numerical technique for the modelling of shallow water flow in one and two dimensions is presented in this work along with the results obtained in different applications involving unsteady flows in complex geometries. A cell‐centred finite volume method based on Roe's approximate Riemann solver across the edges of both structured and unstructured cells is presented. The discretization of the bed slope source terms is done following an upwind approach. In some applications a problem arises when the flow propagates over adverse dry bed slopes, so a special procedure has been introduced to model the advancing front. It is shown that this modification reproduces exactly steady state of still water in configurations with strong variations in bed slope and contour. The applications presented are mainly related with unsteady flow problems. The scheme is capable of handling complex flow domains as will be shown in the simulations corresponding to the test cases that are going to be presented. Comparisons of experimental and numerical results are shown for some of the tests. Copyright © 2002 John Wiley & Sons, Ltd.     

Pole-type singularities and the numerical conformal mapping of doubly-connected domains

Let f be the function which maps conformally a given doubly-connected domain Ω onto a circular annulus, and let $\text{H(z)=}\text{f′(z)}\text{f(z)}\text{?}\text{1}\text{z}$. In this paper we consider the problem of determining the main singularities of the function H in compl($\text{Ω∪?Ω}$). Our purpose is to provide information regarding the location and nature of such singularities, and to explain how this information can be used to improve the efficiency of certain expansion methods for numerical conformal mapping.