Fluctuations in mixtures of lamellar- and nonlamellar-forming lipids

We consider the role of nonlamellar-forming lipids in biological membranes by examining fluctuations, within the random phase approximation, of a model mixture of two lipids, one of which forms lamellar phases while the other forms inverted hexagonal phases. To determine the extent to which nonlamellar-forming lipids facilitiate the formation of nonlamellar structures in lipid mixtures, we examine the fluctuation modes and various correlation functions in the lamellar phase of the mixture. To highlight the role fluctuations can play, we focus on the lamellar phase near its limit of stability. Our results indicate that in the initial stages of the transition, undulations appear in the lamellae occupied by the tails, and that the nonlamellar-forming lipid dominates these undulations. The lamellae occupied by the head groups pinch off to make the tubes of the hexagonal phase. Examination of different correlations and susceptibilities makes quantitative the dominant role of the nonlamellar-forming lipids.Comment: 7 figures (better but larger in byte figures are available upon resuest), submitte

Some new applications for heat and fluid flows via fractional derivatives without singular kernel

This paper addresses the mathematical models for the heat-conduction equations and the Navier-Stokes equations via fractional derivatives without singular kernel.Comment: This is a preprint of a paper whose final and definite form will be published in Thermal Science. Paper Submitted 28/ Dec /2016; Revised 20/Jan/2016; Accepted for publication 21/Jan/201

Molecular theory of hydrophobic mismatch between lipids and peptides

Effects of the mismatch between the hydrophobic length, d, of transmembrane alpha helices of integral proteins and the hydrophobic thickness, D_h, of the membranes they span are studied theoretically utilizing a microscopic model of lipids. In particular, we examine the dependence of the period of a lamellar phase on the hydrophobic length and volume fraction of a rigid, integral, peptide. We find that the period decreases when a short peptide, such that d<D_h, is inserted. More surprising, we find that the period increases when a long peptide, such that d>D_h, is inserted. The effect is due to the replacement of extensible lipid tails by rigid peptide. As the peptide length is increased, the lamellar period continues to increase, but at a slower rate, and can eventually decrease. The amount of peptide which fails to incorporate and span the membrane increases with the magnitude of the hydrophobic mismatch |d-D_h|. We explicate these behaviors which are all in accord with experiment. Predictions are made for the dependence of the tilt of a single trans-membrane alpha helix on hydrophobic mismatch and helix density.Comment: 14 pages, 5 figure

A multigrid scheme for 3D Monge-Amp\`ere equations

The elliptic Monge-Amp\`ere equation is a fully nonlinear partial differential equation which has been the focus of increasing attention from the scientific computing community. Fast three dimensional solvers are needed, for example in medical image registration but are not yet available. We build fast solvers for smooth solutions in three dimensions using a nonlinear full-approximation storage multigrid method. Starting from a second-order accurate centered finite difference approximation, we present a nonlinear Gauss-Seidel iterative method which has a mechanism for selecting the convex solution of the equation. The iterative method is used as an effective smoother, combined with the full-approximation storage multigrid method. Numerical experiments are provided to validate the accuracy of the finite difference scheme and illustrate the computational efficiency of the proposed multigrid solver.Comment: 18 pages, 1 figure, 7 tables, 41 references. Accepted by International Journal of Computer Mathematics (published online: 21 Nov 2016

A new fractional derivative without singular kernel: Application to the modelling of the steady heat flow

In this article we propose a new fractional derivative without singular kernel. We consider the potential application for modeling the steady heat-conduction problem. The analytical solution of the fractional-order heat flow is also obtained by means of the Laplace transform.Comment: 1 figur

Distribution of lipids in non-lamellar phases of their mixtures

We consider a model of lipids in which a head group, characterized by its volume, is attached to two flexible tails of equal length. The phase diagram of the anhydrous lipid is obtained within self-consistent field theory, and displays, as a function of lipid architecture, a progression of phases: body-centered cubic, hexagonal, gyroid, and lamellar. We then examine mixtures of an inverted hexagonal forming lipid and a lamellar forming lipid. As the volume fractions of the two lipids vary, we find that inverted hexagonal, gyroid, or lamellar phases are formed. We demonstrate that the non-lamellar forming lipid is found preferentially at locations which are difficult for the lipid tails to reach. Variations in the volume fraction of each type of lipid tail are on the order of one to ten per cent within regions dominated by the tails. We also show that the variation in volume fraction is correlated qualitatively with the variation in mean curvature of the head-tail interface.Comment: 10 pages, 12 figures (better figures are available upon request), to appear in J. Chem. Phy

Constraining supersymmetry from the satellite experiments

In this paper we study the detectability of $\gamma$-rays from dark matter annihilation in the subhalos of the Milky Way by the satellite-based experiments, EGRET and GLAST. We work in the frame of supersymmetric extension of the standard model and assume the lightest neutralino being the dark matter particles. Based on the N-body simulation of the evolution of dark matter subhalos we first calculate the average intensity distribution of this new class of $\gamma$-ray sources by neutralino annihilation. It is possible to detect these $\gamma$-ray sources by EGRET and GLAST. Conversely, if these sources are not detected the nature of the dark matter particls will be constrained by these experiments, which, however, depending on the uncertainties of the subhalo profile.Comment: 19 pages, 5 gigures; references added, more discussions adde

Experimental high-intensity three-photon entangled source

We experimentally realize a high-intensity three-photon Greenberger-Horne-Zeilinger (GHZ) entanglement source directly following the proposal by Rarity and Tapster [J. G. Rarity and P. R. Tapster, Phys. Rev. A 59, R35 (1999)]. The threefold coincidence rate can be more than 200 Hz with a fidelity of 0.811, and the intensity can be further improved with moderate fidelity degradation. The GHZ entanglement is characterized by testing the Bell-Mermin inequality and using an entanglement witness operator. To optimize the polarization-entangled source, we theoretically analyze the relationship between the mean photon number of the single-photon source and the probability of parametric down-conversion.Comment: 4 pages, 4 figure

Bremsstrahlung Radiation as Coherent State in Thermal QED

Based on fully finite temperature field theory we investigate the radiation probability in the bremsstrahlung process in thermal QED. It turns out that the infrared divergences resulting from the emission and absorption of the real photons are canceled by the virtual photon exchange processes at finite temperature. The full quantum calculation results for soft photons radiation coincide completely with that obtained in the semi-classical approximation. In the framework of Thermofield Dynamics it is shown that the bremsstrahlung radiation in thermal QED is a coherent state, the quasiclassical behavior of the coherent state leads to above coincidence.Comment: 8 pages, 2 figure