Relaxation at late stages in an entropy barrier model for glassy systems

The ground state dynamics of an entropy barrier model proposed recently for describing relaxation of glassy systems is considered. At stages of evolution the dynamics can be described by a simple variant of the Ehrenfest urn model. Analytical expression for the relaxation times from an arbitrary state to the ground state is derived. Upper and lower bounds for the relaxation times as a function of system size are obtained.Comment: 9 pages no figures. to appear in J.Phys. A: Math. and 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

Lattice gas model in random medium and open boundaries: hydrodynamic and relaxation to the steady state

We consider a lattice gas interacting by the exclusion rule in the presence of a random field given by i.i.d. bounded random variables in a bounded domain in contact with particles reservoir at different densities. We show, in dimensions $d \ge 3$, that the rescaled empirical density field almost surely, with respect to the random field, converges to the unique weak solution of a non linear parabolic equation having the diffusion matrix determined by the statistical properties of the external random field and boundary conditions determined by the density of the reservoir. Further we show that the rescaled empirical density field, in the stationary regime, almost surely with respect to the random field, converges to the solution of the associated stationary transport equation

Probing Polarization and Dielectric Function of Molecules with Higher Order Harmonics in Scattering-near-field Scanning Optical Microscopy

The idealized system of an atomically flat metallic surface [highly oriented pyrolytic graphite (HOPG)] and an organic monolayer (porphyrin) was used to determine whether the dielectric function and associated properties of thin films can be accessed with scanning–near-field scanning optical microscopy (s-NSOM). Here, we demonstrate the use of harmonics up to fourth order and the polarization dependence of incident light to probe dielectric properties on idealized samples of monolayers of organic molecules on atomically smooth substrates. An analytical treatment of light/ sample interaction using the s-NSOM tip was developed in order to quantify the dielectric properties. The theoretical analysis and numerical modeling, as well as experimental data, demonstrate that higher order harmonic scattering can be used to extract the dielectric properties of materials with tens of nanometer spatial resolution. To date, the third harmonic provides the best lateral resolution(~50 nm) and dielectric constant contrast for a porphyrin film on HOPG

The Largest Cluster in Subcritical Percolation

The statistical behavior of the size (or mass) of the largest cluster in subcritical percolation on a finite lattice of size $N$ is investigated (below the upper critical dimension, presumably $d_c=6$). It is argued that as $N \to \infty$ the cumulative distribution function converges to the Fisher-Tippett (or Gumbel) distribution $e^{-e^{-z}}$ in a certain weak sense (when suitably normalized). The mean grows like $s_\xi^* \log N$, where $s_\xi^*(p)$ is a ``crossover size''. The standard deviation is bounded near $s_\xi^* \pi/\sqrt{6}$ with persistent fluctuations due to discreteness. These predictions are verified by Monte Carlo simulations on $d=2$ square lattices of up to 30 million sites, which also reveal finite-size scaling. The results are explained in terms of a flow in the space of probability distributions as $N \to \infty$. The subcritical segment of the physical manifold ($0 < p < p_c$) approaches a line of limit cycles where the flow is approximately described by a ``renormalization group'' from the classical theory of extreme order statistics.Comment: 16 pages, 5 figs, expanded version to appear in Phys Rev

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

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/

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

Nanoscale-confined Terahertz Polaritons in a van der Waals Crystal

Electromagnetic field confinement is crucial for nanophotonic technologies, since it allows for enhancing light-matter interactions, thus enabling light manipulation in deep sub-wavelength scales. In the terahertz (THz) spectral range, radiation confinement is conventionally achieved with specially designed metallic structures - such as antennas or nanoslits - with large footprints due to the rather long wavelengths of THz radiation. In this context, phonon polaritons - light coupled to lattice vibrations - in van der Waals (vdW) crystals have emerged as a promising solution for controlling light beyond the diffraction limit, as they feature extreme field confinements and low optical losses. However, experimental demonstration of nanoscale-confined phonon polaritons at THz frequencies has so far remained elusive. Here, we provide it by employing scattering-type scanning near-field optical microscopy (s-SNOM) combined with a free-electron laser (FEL) to reveal a range of low-loss polaritonic excitations at frequencies from 8 to 12 THz in the vdW semiconductor ${\alpha}-MoO_3$. We visualize THz polaritons with i) in-plane hyperbolic dispersion, ii) extreme nanoscale field confinement (below ${\lambda}_o/75$) and iii) long polariton lifetimes, with a lower limit of > 2 ps

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