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

Revisit of cosmic age problem

We investigate the cosmic age problem associated with 9 extremely old globular clusters in M31 galaxy and 1 very old high-$z$ quasar APM 08279 + 5255 at $z=3.91$. These 9 globular clusters have not been used to study the cosmic age problem in the previous literature. By evaluating the age of the universe in the $\Lambda$CDM model with the observational constraints from the SNIa, the BAO, the CMB, and the independent $H_0$ measurements, we find that the existence of 5 globular clusters and 1 high-$z$ quasar are in tension (over 2$\sigma$ confidence level) with the current cosmological observations. So if the age estimates of these objects are correct, the cosmic age puzzle still remains in the standard cosmology. Moreover, we extend our investigations to the cases of the interacting dark energy models. It is found that although the introduction of the interaction between dark sectors can give a larger cosmic age, the interacting dark energy models still have difficulty to pass the cosmic age test.Comment: 11 pages, 5 figures, 1 table, accepted for publication in PR

Bicycle-Sharing System Analysis and Trip Prediction

Bicycle-sharing systems, which can provide shared bike usage services for the public, have been launched in many big cities. In bicycle-sharing systems, people can borrow and return bikes at any stations in the service region very conveniently. Therefore, bicycle-sharing systems are normally used as a short-distance trip supplement for private vehicles as well as regular public transportation. Meanwhile, for stations located at different places in the service region, the bike usages can be quite skewed and imbalanced. Some stations have too many incoming bikes and get jammed without enough docks for upcoming bikes, while some other stations get empty quickly and lack enough bikes for people to check out. Therefore, inferring the potential destinations and arriving time of each individual trip beforehand can effectively help the service providers schedule manual bike re-dispatch in advance. In this paper, we will study the individual trip prediction problem for bicycle-sharing systems. To address the problem, we study a real-world bicycle-sharing system and analyze individuals' bike usage behaviors first. Based on the analysis results, a new trip destination prediction and trip duration inference model will be introduced. Experiments conducted on a real-world bicycle-sharing system demonstrate the effectiveness of the proposed model.Comment: 11 pages, 11 figures, accepted by 2016 IEEE MDM Conferenc

How AD Can Help Solve Differential-Algebraic Equations

A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of so called index reduction or regularisation, to prepare them for numerical solution. This is often done with the help of a computer algebra system. We show in two significant cases that it can be done efficiently by pure algorithmic differentiation. The first is the Dummy Derivatives method, here we give a mainly theoretical description, with tutorial examples. The second is the solution of a mechanical system directly from its Lagrangian formulation. Here we outline the theory and show several non-trivial examples of using the "Lagrangian facility" of the Nedialkov-Pryce initial-value solver DAETS, namely: a spring-mass-multipendulum system, a prescribed-trajectory control problem, and long-time integration of a model of the outer planets of the solar system, taken from the DETEST testing package for ODE solvers

Relative entropy of entanglement of a kind of two qubit entangled states

We in this paper strictly prove that some block diagonalizable two qubit entangled state with six none zero elements reaches its quantum relative entropy entanglement by the a separable state having the same matrix structure. The entangled state comprises local filtering result state as a special case.Comment: 5 page

Spontaneous symmetry breaking and quantum Hall valley ordering on the surface of topological hexaborides

A number of strongly correlated heavy fermion compounds, such as samarium (Sm), ytterbium (Yb), plutonium (Pu) hexaboride, are predicted to become topological insulators at low temperatures. These systems support massless Dirac fermions near certain (three) points of the surface Brillouin zone, hereafter referred to as the valleys. In strong perpendicular magnetic fields, the conical Dirac dispersions of these surface states quench onto three sets of Landau levels and we predict various possible hierarchies of incompressible quantum Hall states on the surface of hexaborides. In addition, we address the effects of strong electron-electron interaction within the surface zeroth Landau levels. Specifically, we show that depending on the relative strength of the long-range (Coulomb-type) and the finite-range (Hubbard-type) interactions the ground state can display either a valley-polarized or a valley-coherent distribution of electronic density. We also show that the transition between two valley-polarized states is always discontinuous, while that between a valley-polarized and a valley-coherent phase is continuous. The Zeeman splitting and/or an applied uniaxial strain on the surface can drive the system through various quantum phase transitions and place it in different broken-symmetry phases. Application of uniaxial strain is also shown to considerably modify the precise sequence of quantum Hall states. We also highlight the role of topology in determining the broken symmetry phases, disorder on the surface of topological hexaborides in strong magnetic fields.Comment: 14 pages, 7 figure

Magneto-optical properties of Co/ZnO multilayer films

Multilayer films of ZnO with Co were deposited on glass substrates then annealed in a vacuum. The magnetisation of the films increased with annealing but not the magnitude of the magneto-optical signals. The dielectric functions for the films were calculated using the MCD spectra. A Maxwell Garnett theory of a metallic Co/ZnO mixture is presented. The extent to which this explains the MCD spectra taken on the films is discussed.Comment: This paper was presented at ICM (2009) and is accepted in this form for the proceeding