Interactions between Membrane Inclusions on Fluctuating Membranes

We model membrane proteins as anisotropic objects characterized by symmetric-traceless tensors and determine the coupling between these order-parameters and membrane curvature. We consider the interactions between transmembrane proteins that respect up-down (reflection) symmetry of bilayer membranes and that have circular or non-circular cross-sectional areas in the tangent-plane of membranes. Using a field theoretic approach, we find non-entropic $1/R^{4}$ interactions between reflection-symmetry-breaking transmembrane proteins with circular cross-sectional area and entropic $1/R^{4}$ interactions between transmembrane proteins with circular cross-section that do not break up-down symmetry in agreement with previous calculations. We also find anisotropic $1/R^{4}$ interactions between reflection-symmetry-conserving transmembrane proteins with non-circular cross-section, anisotropic $1/R^{2}$ interactions between reflection-symmetry-breaking transmembrane proteins with non-circular cross-section, and non-entropic $1/R^{4}$ many-particle interactions among non-transmembrane proteins. For large $R$, these interactions might provide the dominant force inducing aggregation of the membrane proteins.Comment: REVTEX, 29 pages with 4 postscript figures compressed using uufiles. Introduction and Discussion sections revised. To appear in J. Phys. France I (September

Casimir torque

We develop a formalism for the calculation of the flow of angular momentum carried by the fluctuating electromagnetic field within a cavity bounded by two flat anisotropic materials. By generalizing a procedure employed recently for the calculation of the Casimir force between arbitrary materials, we obtain an expression for the torque between anisotropic plates in terms of their reflection amplitude matrices. We evaluate the torque in 1D for ideal and realistic model materials.Comment: 8 pages, 4 figs, Submitted to Proc. of QFEXT'05, to appear in J. Phys.

Effect of linear polarisability and local fields on surface SHG

A discrete dipole model has been developed to describe Surface Second Harmonic Generation by centrosymmetric semiconductors. The double cell method, which enables the linear reflection problem to be solved numerically for semi-infinite systems, has been extended for the nonlinear case. It is shown that a single layer of nonlinear electric dipoles at the surface and nonlocal effects allows to describe the angle of incidence dependent anisotropic SHG obtained from oxidised Si(001) wafers. The influence of the linear response, turns out to be essential to understand the anisotropic SHG-process

A Phase-Field Model of Spiral Dendritic Growth

Domains of condensed-phase monolayers of chiral molecules exhibit a variety of interesting nonequilibrium structures when formed via pressurization. To model these domain patterns, we add a complex field describing the tilt degree of freedom to an (anisotropic) complex-phase-field solidification model. The resulting formalism allows for the inclusion of (in general, non-reflection symmetric) interactions between the tilt, the solid-liquid interface, and the bond orientation. Simulations demonstrate the ability of the model to exhibit spiral dendritic growth.Comment: text plus Four postscript figure file

N=2 boundary supersymmetry in integrable models and perturbed boundary conformal field theory

Boundary integrable models with N=2 supersymmetry are considered. For the simplest boundary N=2 superconformal minimal model with a Chebyshev bulk perturbation we show explicitly how fermionic boundary degrees of freedom arise naturally in the boundary perturbation in order to maintain integrability and N=2 supersymmetry. A new boundary reflection matrix is obtained for this model and N=2 boundary superalgebra is studied. A factorized scattering theory is proposed for a N=2 supersymmetric extension of the boundary sine-Gordon model with either (i) fermionic or (ii) bosonic and fermionic boundary degrees of freedom. Exact results are obtained for some quantum impurity problems: the boundary scaling Lee-Yang model, a massive deformation of the anisotropic Kondo model at the filling values g=2/(2n+3) and the boundary Ashkin-Teller model.Comment: 14 pages, LaTeX file with amssymb; v2: typos corrected, references added, to appear in Nucl. Phys.

Determination of crystal orientation fabric from seismic wideangle data

It is known from ice core analyses that the crystal orientation fabric (COF) of ice sheets is anisotropic and changes over depth. A better understanding of these anisotropies as well as their remote detection is important to optimize flow models for ice. Here we show how seismic wideangle measurements can be used to determine the COF remotely. We demonstrate the principle formalism how observed seismic traveltimes can be related to COF properties by a forward model and then apply the formalism to field data. The eigenvalues that describe the ice fabric of the ice core EDML (Dronning Maud Land, Antarctca) are set into a relationship with the elasticity tensor. From the elasticity tensor the expected seismic velocities and reflection coefficients are calculated. Additionally we calculate the value eta from the Thomsen-parameters epsilon and delta. The value eta gives a measure of the anisotropy of vertical transverse isotropic (VTI)-media and is an important tool for the NMO-correction of anisotropic data. The approximation of reflection horizons as hyperbolas is not valid anymore in anisotropic media. The calculation of the moveout is therefore performed by a 4th order NMO-correction with the rms-velocity and the effective eta value as variables. This approach is applied to data from a wideangle survey shot at Halvfarryggen, Dronning Maud Land, Antarctica. From this data we derived rms-velocities and effective eta values. These values were than recalculated to interval velocities and interval eta values to give a hint on the measure of anisotropy of the different layers. The results give first insight into the anisotropies at Halvfarryggen

Light scattering from an isotropic layer between uniaxial crystals

We develop a model for the reflection and transmission of plane waves by an isotropic layer sandwiched between two uniaxial crystals of arbitrary orientation. In the laboratory frame, reflection and transmission coefficients corresponding to the principal polarization directions in each crystal are given explicitly in terms of the c-axis and propagation directions. The solution is found by first deriving explicit expressions for reflection and transmission amplitude coefficients for waves propagating from an arbitrarily oriented uniaxial anisotropic material into an isotropic material. By combining these results with Lekner's (1991) earlier treatment of waves propagating from isotropic media to anisotropic media and employing a matrix method we determine a solution to the general form of the multiple reflection case. The example system of a wetted interface between two ice crystals is used to contextualize the results.Comment: 18 pages, 9 figures,updated with changes made to published versio

Analysis of fluid substitution in a porous and fractured medium

To improve quantitative interpretation of seismic data, we analyze the effect of fluid substitution in a porous and fractured medium on elastic properties and reflection coefficients. This analysis uses closed-form expressions suitable for fluid substitution in transversely isotropic media with a horizontal symmetry axis (HTI). For the HTI medium, the effect of changing porosity and water saturation on (1) P-wave moduli, (2) horizontal and vertical velocities, (3) anisotropic parameters, and (4) reflection coefficients are examined. The effects of fracture density on these four parameters are also studied. For the model used in this study, a 35% increase in porosity lowers the value of P-wave moduli by maximum of 45%. Consistent with the reduction in P-wave moduli, P-wave velocities also decrease by maximum of 17% with a similar increment in porosity. The reduction is always larger for the horizontal P-wave modulus than for the vertical one and is nearly independent of fracture density. The magnitude of the anisotropic parameters of the fractured medium also changes with increased porosity depending on the changes in the value of P-wave moduli. The reflection coefficients at an interface of the fractured medium with an isotropic medium change in accordance with the above observations and lead to an increase in anisotropic amplitude variation with offset (AVO) gradient with porosity.Additionally, we observe a maximum increase in P-wave modulus and velocity by 30% and 8%, respectively, with a 100% increase in water saturation. Water saturation also changes the anisotropic parameters and reflection coefficients. Increase in water saturation considerably increases the magnitude of the anisotropic AVO gradient irrespective of fracture density. From this study, we conclude that porosity and water saturation have a significant impact on the four studied parameters and the impacts are seismically detectable