Density functional theory of a Gay—Berne film between aligning walls

It is shown that the simple Onsager second-virial approximation of density functional theory can successfully describe the orientational structure of a Gay-Berne film confined between aligning plates. The theory takes as input the density profile as determined by computer simulation and semi-quantitatively reproduces the variation in the nematic order parameter throughout the film, at different temperatures and for different surface potential strengths, without any adjustable parameters. In this context the validity of an earlier analytical approach is discussed where the density, order parameter and tilt angle profiles were assumed to be step functions.     

REITERATED HOMOGENIZATION OF NONLINEAR MONOTONE OPERATORS

61. IntroductionLet us consider the clajss of partial differential equations of the form--div(a.(x, Du.)) ~ f on fi, us E Wt,p(fl), (1.1)where a6 is increasingly oscillating as E -- 0, fi is an open bounded subset of R", 1 < p < cot1/p 1/q = 1 and f E W--"q(fl). The homogenization problem for (l.1) consists of the studyof the asymptotic behavior of solutions net as e - 0. In many important cases nE convergesweakly in WI'p(n) to the solution no of the homogenized problem--div(b(Duo)) = f …     

Uniqueness Theorems for the Inverse Problem of Elastodynamic Boundary Scattering

A uniqueness theorem is established for the elastodynamic problemof direct scattering of harmonic small-amplitude waves by anobstacle embedded in an isotropic medium with spatially varyingparameters. Uniqueness theorems are then developed for the inverseproblem of boundary determination of the obstacle associatedwith this direct scattering problem. In particular, it is shownfor nondegenerate elastodynamic problems that knowledge of boththe lamellar and the solenoidal far-field patterns is necessaryto reconstruct the obstacle's boundary.     

Homogenization of a Class of Nonlinear Variational Inequalities with Applications in Fluid Film Flow

The authors consider the homogenization of a class of nonlinear variational inequalities, which include rapid oscillations with respect to a parameter. The homogenization of the corresponding class of differential equations is also studied. The results are applied to some models for the pressure in a thin fluid film fluid between two surfaces which are in relative motion. This is an important problem in the lubrication theory. In particular, the analysis includes the effects of surface roughness on both faces and the phenomenon of cavitation. Moreover, the fluid can be modeled as Newtonian or non-Newtonian by using a Rabinowitsch fluid model.     

Homogenization of Reynolds Equation by Two-Scale Convergence

To increase the hydrodynamic performance in different machine elements, as e.g. journal bearings and thrust bearings, during lubrication it is important to understand the influence of surface roughness. In this connection one encounters homogenization of the incompressible Reynolds equation, where the roughness of the lubricated surface is assumed to be periodic. This problem has recently been studied in more engineering-oriented papers by using the formal method of multiple scale expansion. In this paper, we rigorously prove both homogenization and corrector results by using two-scale convergence, which may be regarded as a justification of the formal multiple scale expansion method described above. Moreover, some numerical illustrations and results are presented.     

REITERATED HOMOGENIZATION OF DEGENERATE NONLINEAR ELLIPTIC EQUATIONS

The authors study homogenization of some nonlinear partial differential equations of theform-div(a(hx,h~2x,Du_h))=f,where a is periodic in the first two arguments and monotonein the third.In particular the case where a satisfies degenerated structure conditions is studied.It is proved that u_h converges weakly in W_0~(1,1)(Ω)to the unique solution of a limit problem ash→∞.Moreover,explicit expressions for the limit problem are obtained.     

LUX C, D AND E GENES OF THE Vibrio fischeri LUMINESCENCE OPERON CODE FOR THE REDUCTASE, TRANSFERASE, AND SYNTHETASE ENZYMES INVOLVED IN ALDEHYDE BIOSYNTHESIS

Abstract
The lux C, D, and E genes of the Vibrio fischeri luminescence operon code for three polypeptides of 54, 33, and 42 kDa, respectively, which are required for synthesis of the aldehyde substrate for the luminescent reaction. These polypeptides have been identified in V. fischeri and V. harveyi as well as in recombinant E. colt harboring the cloned genes by specific acylation with [³H]fatty acid, showing that they are components of a fatty acid reductase system with reductase, synthetase and transferase activities. By using glycerol in the assay and/or extraction buffer and decreasing the reducing agent, the levels of the acylation of the 54 and 42 kDa polypeptides have been greatly increased. As a consequence, it was possible to demonstrate that the 54 kDa polypeptide coded by the lux C gene has reductase activity. In a subclone missing the lux E gene, the 42 kDa polypeptide was missing and the 54 kDa polypeptide could not be acylated in vitro with tetradecanoic acid (+ATP) and only to a low level in vivo indicating that the synthetase enzyme, responsible for fatty acid activation, is coded by the lux E gene. In vitro acylation with tetradecanoyl CoA of the 33 kDa polypeptide coupled with the specific cleavage of acyl-ACP only in E. coli extracts transformed with DNA containing the lux D gene, demonstrated that the lux D gene coded for the transferase enzyme.     

Computer simulations of adsorbed liquid crystal films

The structures adopted by adsorbed thin films of Gay-Beme particles in the presence of a coexisting vapour phase are investigated by molecular dynamics simulation. The films are adsorbed at a flat substrate which favours planar anchoring, whereas the nematic-vapour interface favours normal alignment. On cooling, a system with a high molecule-substrate interaction strength exhibits substrate-induced planar orientational ordering and considerable stratification is observed in the density profiles. In contrast, a system with weak molecule-substrate coupling adopts a director orientation orthogonal to the substrate plane, owing to the increased influence of the nematic-vapour interface. There are significant differences between the structures adopted at the two interfaces, in contrast with the predictions of density functional treatments of such systems.