General technique of calculating drift velocity and diffusion coefficient in arbitrary periodic systems

We develop a practical method of computing the stationary drift velocity V and the diffusion coefficient D of a particle (or a few particles) in a periodic system with arbitrary transition rates. We solve this problem both in a physically relevant continuous-time approach as well as for models with discrete-time kinetics, which are often used in computer simulations. We show that both approaches yield the same value of the drift, but the difference between the diffusion coefficients obtained in each of them equals V*V/2. Generalization to spaces of arbitrary dimension and several applications of the method are also presented.Comment: 12 pages + 2 figures, RevTeX. Submitted to J. Phys. A: Math. Ge

Characteristics of ferroelectric-ferroelastic domains in N{\'e}el-type skyrmion host GaV4_4S8_8

GaV$_4$S$_8$ is a multiferroic semiconductor hosting N{\'e}el-type magnetic skyrmions dressed with electric polarization. At T$_s$ = 42K, the compound undergoes a structural phase transition of weakly first-order, from a non-centrosymmetric cubic phase at high temperatures to a polar rhombohedral structure at low temperatures. Below T$_s$, ferroelectric domains are formed with the electric polarization pointing along any of the four $\left< 111 \right>$ axes. Although in this material the size and the shape of the ferroelectric-ferroelastic domains may act as important limiting factors in the formation of the N{\'e}el-type skyrmion lattice emerging below T$_C$=13\:K, the characteristics of polar domains in GaV$_4$S$_8$ have not been studied yet. Here, we report on the inspection of the local-scale ferroelectric domain distribution in rhombohedral GaV$_4$S$_8$ using low-temperature piezoresponse force microscopy. We observed mechanically and electrically compatible lamellar domain patterns, where the lamellae are aligned parallel to the (100)-type planes with a typical spacing between 100 nm-1.2 $\mu$m. We expect that the control of ferroelectric domain size in polar skyrmion hosts can be exploited for the spatial confinement and manupulation of N{\'e}el-type skyrmions

Generalized model for dynamic percolation

We study the dynamics of a carrier, which performs a biased motion under the influence of an external field E, in an environment which is modeled by dynamic percolation and created by hard-core particles. The particles move randomly on a simple cubic lattice, constrained by hard-core exclusion, and they spontaneously annihilate and re-appear at some prescribed rates. Using decoupling of the third-order correlation functions into the product of the pairwise carrier-particle correlations we determine the density profiles of the "environment" particles, as seen from the stationary moving carrier, and calculate its terminal velocity, V_c, as the function of the applied field and other system parameters. We find that for sufficiently small driving forces the force exerted on the carrier by the "environment" particles shows a viscous-like behavior. An analog Stokes formula for such dynamic percolative environments and the corresponding friction coefficient are derived. We show that the density profile of the environment particles is strongly inhomogeneous: In front of the stationary moving carrier the density is higher than the average density, $\rho_s$, and approaches the average value as an exponential function of the distance from the carrier. Past the carrier the local density is lower than $\rho_s$ and the relaxation towards $\rho_s$ may proceed differently depending on whether the particles number is or is not explicitly conserved.Comment: Latex, 32 pages, 4 ps-figures, submitted to PR

Hopping Transport in the Presence of Site Energy Disorder: Temperature and Concentration Scaling of Conductivity Spectra

Recent measurements on ion conducting glasses have revealed that conductivity spectra for various temperatures and ionic concentrations can be superimposed onto a common master curve by an appropriate rescaling of the conductivity and frequency. In order to understand the origin of the observed scaling behavior, we investigate by Monte Carlo simulations the diffusion of particles in a lattice with site energy disorder for a wide range of both temperatures and concentrations. While the model can account for the changes in ionic activation energies upon changing the concentration, it in general yields conductivity spectra that exhibit no scaling behavior. However, for typical concentrations and sufficiently low temperatures, a fairly good data collapse is obtained analogous to that found in experiment.Comment: 6 pages, 4 figure

Near-field examination of perovskite-based superlenses and superlens-enhanced probe-object coupling

A planar slab of negative index material works as a superlens with sub-diffraction-limited imaging resolution, since propagating waves are focused and, moreover, evanescent waves are reconstructed in the image plane. Here, we demonstrate a superlens for electric evanescent fields with low losses using perovskites in the mid-infrared regime. The combination of near-field microscopy with a tunable free-electron laser allows us to address precisely the polariton modes, which are critical for super-resolution imaging. We spectrally study the lateral and vertical distributions of evanescent waves around the image plane of such a lens, and achieve imaging resolution of wavelength/14 at the superlensing wavelength. Interestingly, at certain distances between the probe and sample surface, we observe a maximum of these evanescent fields. Comparisons with numerical simulations indicate that this maximum originates from an enhanced coupling between probe and object, which might be applicable for multifunctional circuits, infrared spectroscopy, and thermal sensors.Comment: 20 pages, 6 figures, published as open access article in Nature Communications (see http://www.nature.com/ncomms/

Motion of a driven tracer particle in a one-dimensional symmetric lattice gas

We study the dynamics of a tracer particle subject to a constant driving force $E$ in a one-dimensional lattice gas of hard-core particles whose transition rates are symmetric. We show that the mean displacement of the driven tracer grows in time, $t$, as $\sqrt{\alpha t}$, rather than the linear time dependence found for driven diffusion in the bath of non-interacting (ghost) particles. The prefactor $\alpha$ is determined implicitly, as the solution of a transcendental equation, for an arbitrary magnitude of the driving force and an arbitrary concentration of the lattice gas particles. In limiting cases the prefactor is obtained explicitly. Analytical predictions are seen to be in a good agreement with the results of numerical simulations.Comment: 21 pages, LaTeX, 4 Postscript fugures, to be published in Phys. Rev. E, (01Sep, 1996

Profiling allele-specific gene expression in brains from individuals with autism spectrum disorder reveals preferential minor allele usage.

One fundamental but understudied mechanism of gene regulation in disease is allele-specific expression (ASE), the preferential expression of one allele. We leveraged RNA-sequencing data from human brain to assess ASE in autism spectrum disorder (ASD). When ASE is observed in ASD, the allele with lower population frequency (minor allele) is preferentially more highly expressed than the major allele, opposite to the canonical pattern. Importantly, genes showing ASE in ASD are enriched in those downregulated in ASD postmortem brains and in genes harboring de novo mutations in ASD. Two regions, 14q32 and 15q11, containing all known orphan C/D box small nucleolar RNAs (snoRNAs), are particularly enriched in shifts to higher minor allele expression. We demonstrate that this allele shifting enhances snoRNA-targeted splicing changes in ASD-related target genes in idiopathic ASD and 15q11-q13 duplication syndrome. Together, these results implicate allelic imbalance and dysregulation of orphan C/D box snoRNAs in ASD pathogenesis

Survival and residence times in disordered chains with bias

We present a unified framework for first-passage time and residence time of random walks in finite one-dimensional disordered biased systems. The derivation is based on exact expansion of the backward master equation in cumulants. The dependence on initial condition, system size, and bias strength is explicitly studied for models with weak and strong disorder. Application to thermally activated processes is also developed.Comment: 13 pages with 2 figures, RevTeX4; v2:minor grammatical changes, typos correcte

A COL7A1 Mutation Causes Dystrophic Epidermolysis Bullosa in Rotes Höhenvieh Cattle

We identified a congenital mechanobullous skin disorder in six calves on a single farm of an endangered German cattle breed in 2010. The condition presented as a large loss of skin distal to the fetlocks and at the mucosa of the muzzle. All affected calves were euthanized on humane grounds due to the severity, extent and progression of the skin and oral lesions. Examination of skin samples under light microscopy revealed detachment of the epidermis from the dermis at the level of the dermo epidermal junction, leading to the diagnosis of a subepidermal bullous dermatosis such as epidermolysis bullosa. The pedigree was consistent with monogenic autosomal recessive inheritance. We localized the causative mutation to an 18 Mb interval on chromosome 22 by homozygosity mapping. The COL7A1 gene encoding collagen type VII alpha 1 is located within this interval and COL7A1 mutations have been shown to cause inherited dystrophic epidermolysis bullosa (DEB) in humans. A SNP in the bovine COL7A1 exon 49 (c.4756C>T) was perfectly associated with the observed disease. The homozygous mutant T/T genotype was exclusively present in affected calves and their parents were heterozygous C/T confirming the assumed recessive mode of inheritance. All known cases and genotyped carriers were related to a single cow, which is supposed to be the founder animal. The mutant T allele was absent in 63 animals from 24 cattle breeds. The identified mutation causes a premature stop codon which leads to a truncated protein representing a complete loss of COL7A1 function (p.R1586*). We thus have identified a candidate causative mutation for this genetic disease using only three cases to unravel its molecular basis. Selection against this mutation can now be used to eliminate the mutant allele from the Rotes Höhenvieh breed