On the number of points in a lattice polytope

In this article we will show that for every natural $d$ and $n>1$ there exists a natural number $t$ such that for every $d$-dimensional simplicial complex $\mathcal{T}$ with vertices in $\mathbb{Z}^d$, the number of lattice points in the $t^{\mathrm{th}}$ dilate of $\mathcal{T}$ is exactly $\chi(\mathcal{T})$ modulo $n$, where $\chi(\mathcal{T})$ is the Euler characteristic of $\mathcal{T}$.Comment: 3 page

Mathematical modeling of a thermovoltaic cell

A new type of battery named 'Vaporvolt' cell is in the early stage of its development. A mathematical model of a CuO/Cu 'Vaporvolt' cell is presented that can be used to predict the potential and the transport behavior of the cell during discharge. A sensitivity analysis of the various transport and electrokinetic parameters indicates which parameters have the most influence on the predicted energy and power density of the 'Vaporvolt' cell. This information can be used to decide which parameters should be optimized or determined more accurately through further modeling or experimental studies. The optimal thicknesses of electrodes and separator, the concentration of the electrolyte, and the current density are determined by maximizing the power density. These parameter sensitivities and optimal design parameter values will help in the development of a better CuO/Cu 'Vaporvolt' cell

Quadrupole-scissors modes and nonlinear mode coupling in trapped two-component Bose-Einstein condensates

We theoretically investigate quadrupolar collective excitations in two-component Bose-Einstein condensates and their nonlinear dynamics associated with harmonic generation and mode coupling. Under the Thomas-Fermi approximation and the quadratic polynomial ansatz for density fluctuations, the linear analysis of the superfluid hydrodynamic equations predicts excitation frequencies of three normal modes constituted from monopole and quadrupole oscillations, and those of three scissors modes. We obtain analytically the resonance conditions for the second harmonic generation in terms of the trap aspect ratio and the strength of intercomponent interaction. The numerical simulation of the coupled Gross-Pitaevskii equations vindicates the validity of the analytical results and reveals the dynamics of the second harmonic generation and nonlinear mode coupling that lead to nonlinear oscillations of the condensate with damping and recurrence reminiscent of the Fermi-Pasta-Ulam problem.Comment: 10 pages, 5 figures, revtex

Viscosity of gauge theory plasma with a chemical potential from AdS/CFT correspondence

We compute the strong coupling limit of the shear viscosity for the N=4 super-Yang-Mill theory with a chemical potential. We use the five-dimensional Reissner-Nordstrom-anti-deSitter black hole, so the chemical potential is the one for the R-charges U(1)_R^3. We compute the quasinormal frequencies of the gravitational and electromagnetic vector perturbations in the background numerically. This enables one to explicitly locate the diffusion pole for the shear viscosity. The ratio of the shear viscosity eta to the entropy density s is eta/s=1/(4pi) within numerical errors, which is the same result as the one without chemical potential.Comment: 11 pages, 5 figures, ReVTeX4; v2: minor improvements; v3: explanations added and improved; v4: version to appear in PR

Spin textures in rotating two-component Bose-Einstein condensates

We investigate two kinds of coreless vortices with axisymmetric and nonaxisymmetric configurations in rotating two-component Bose-Einstein condensates. Starting from the Gross-Pitaevskii energy functional in a rotating frame, we derive a nonlinear sigma model generalized to the two-component condensates. In terms of a pseudospin representation, an axisymmetric vortex and a nonaxisymmetric one correspond to spin textures referred to as a "skyrmion" and a "meron-pair", respectively. A variational method is used to investigate the dependence of the sizes of the stable spin textures on system parameters, and the optimized variational function is found to reproduce well the numerical solution. In the SU(2) symmetric case, the optimal skyrmion and meron-pair are degenerate and transform to each other by a rotation of the pseudospin. An external rf-field that couples coherently the hyperfine states of two components breaks the degeneracy in favor of the meron-pair texture due to an effective transverse pseudomagnetic field. The difference between the intracomponent and intercomponent interactions yields a longitudinal pseudomagnetic field and a ferromagnetic or an antiferromagnetic pseudospin interaction, leading to a meron-pair texture with an anisotropic distribution of vorticity.Comment: 14 pages, 15 figure

Atypical protein kinase C (PKCzeta/lambda) is a convergent downstream target of the insulin-stimulated phosphatidylinositol 3-kinase and TC10 signaling pathways.

Insulin stimulation of adipocytes resulted in the recruitment of atypical PKC (PKCzeta/lambda) to plasma membrane lipid raft microdomains. This redistribution of PKCzeta/lambda was prevented by Clostridium difficile toxin B and by cholesterol depletion, but was unaffected by inhibition of phosphatidylinositol (PI) 3-kinase activity. Expression of the constitutively active GTP-bound form of TC10 (TC10Q/75L), but not the inactive GDP-bound mutant (TC10/T31N), targeted PKCzeta/lambda to the plasma membrane through an indirect association with the Par6-Par3 protein complex. In parallel, insulin stimulation as well as TC10/Q75L resulted in the activation loop phosphorylation of PKCzeta. Although PI 3-kinase activation also resulted in PKCzeta/lambda phosphorylation, it was not recruited to the plasma membrane. Furthermore, insulin-induced GSK-3beta phosphorylation was mediated by both PI 3-kinase-PKB and the TC10-Par6-atypical PKC signaling pathways. Together, these data demonstrate that PKCzeta/lambda can serve as a convergent downstream target for both the PI 3-kinase and TC10 signaling pathways, but only the TC10 pathway induces a spatially restricted targeting to the plasma membrane

On two pieces of folklore in the AdS/CFT duality

In the AdS/CFT duality, it is often said that a local symmetry in a bulk theory corresponds to a global symmetry in the corresponding boundary theory, but the global symmetry can become local when one couples with an external source. As a result, the GKP-Witten relation gives a response function instead of a Green function. We explore this point in details using the example of holographic superconductors. We point out that these points play a crucial role to interpret the holographic London equation properly.Comment: 11 pages, ReVTeX4.1; v2: added discussio

On-demand single-photon state generation via nonlinear absorption

We propose a method for producing on-demand single-photon states based on collision-induced exchanges of photons and unbalanced linear absorption between two single-mode light fields. These two effects result in an effective nonlinear absorption of photons in one of the modes, which can lead to single photon states. A quantum nonlinear attenuator based on such a mechanism can absorb photons in a normal input light pulse and terminate the absorption at a single-photon state. Because the output light pulses containing single photons preserve the properties of the input pulses, we expect this method to be a means for building a highly controllable single photon source.Comment: 5 pages, 2 figures, to appear in PRA. To be published in PR

All-electrical detection of the relative strength of Rashba and Dresselhaus spin-orbit interaction in quantum wires

We propose a method to determine the relative strength of Rashba and Dresselhaus spin-orbit interaction from transport measurements without the need of fitting parameters. To this end, we make use of the conductance anisotropy in narrow quantum wires with respect to the directions of an in-plane magnetic field, the quantum wire and the crystal orientation. We support our proposal by numerical calculations of the conductance of quantum wires based on the Landauer formalism which show the applicability of the method to a wide range of parameters.Comment: 4 pages, 4 figure

Vortex molecules in coherently coupled two-component Bose-Einstein condensates

A vortex molecule is predicted in rotating two-component Bose-Einstein condensates whose internal hyperfine states are coupled coherently by an external field. A vortex in one component and that in the other are connected by a domain wall of the relative phase, constituting a "vortex molecule", which features a nonaxisymmetric (pseudo)spin texture with a pair of merons. The binding mechanism of the vortex molecule is discussed based on a generalized nonlinear sigma model and a variational ansatz. The anisotropy of vortex molecules is caused by the difference in the scattering lengths, yielding a distorted vortex-molecule lattice in fast rotating condensates.Comment: 4 pages, 4 figures, greatly revised versio