Two dimensional modulational instability in photorefractive media

We study theoretically and experimentally the modulational instability of broad optical beams in photorefractive nonlinear media. We demonstrate the impact of the anisotropy of the nonlinearity on the growth rate of periodic perturbations. Our findings are confirmed by experimental measurements in a strontium barium niobate photorefractive crystal.Comment: 8 figure

Surface-structure libraries: multifrequential oscillations in catalytic hydrogen oxidation on rhodium

Multifrequential oscillating spatiotemporal patterns in the catalytic hydrogen oxidation on rhodium have been observed in situ in the 10 -6 mbar pressure range using photoemission electron microscopy. The effect is manifested by periodic chemical waves, which travel over the polycrystalline Rh surface and change their oscillation frequency while crossing boundaries between different Rh(hkl) domains. Each crystallographically specific μm-sized Rh(hkl) domain exhibits an individual wave pattern and oscillation frequency, despite the global diffusional coupling of the surface reaction, altogether creating a structure library. This unique reaction behavior is attributed to the ability of stepped surfaces of high-Miller-index domains to facilitate the formation of subsurface oxygen, serving as a feedback mechanism of kinetic oscillations. Formation of a network of subsurface oxygen as a result of colliding reaction fronts was observed in situ. Microkinetic model analysis was used to rationalize the observed effects and to reveal the relation between the barriers for surface oxidation and oscillation frequency. Structural limits of the oscillations, the existence range of oscillations, as well as the effect of varying hydrogen pressure are demonstrated

RESEARCH OF LINEAR AND NONLINEAR PROCESSES AT FEMTOSECOND LASER RADIATION PROPAGATION IN THE MEDIUM SIMULATING THE HUMAN EYE VITREOUS

The paper deals with mathematical model of linear and nonlinear processes occurring at the propagation of femtosecond laser pulses in the vitreous of the human eye. Methods of computing modeling are applied for the nonlinear spectral equation solution describing the dynamics of a two-dimensional TE-polarized radiation in a homogeneous isotropic medium with cubic fast-response nonlinearity without the usage of slowly varying envelope approximation. Environments close to the optical media parameters of the eye were used for the simulation. The model of femtosecond radiation propagation takes into account the process dynamics for dispersion broadening of pulses in time and the occurence of the self-focusing near the retina when passing through the vitreous body of the eye. Dependence between the pulse duration on the retina has been revealed and the duration of the input pulse and the values of power density at which there is self-focusing have been found. It is shown that the main mechanism of radiation damage with the use of titanium-sapphire laser is photoionization. The results coincide with those obtained by the other scientists, and are usable for creation Russian laser safety standards for femtosecond laser systems

Strong Collapse Turbulence in Quintic Nonlinear Schr\"odinger Equation

We consider the quintic one dimensional nonlinear Schr\"odinger equation with forcing and both linear and nonlinear dissipation. Quintic nonlinearity results in multiple collapse events randomly distributed in space and time forming forced turbulence. Without dissipation each of these collapses produces finite time singularity but dissipative terms prevents actual formation of singularity. In statistical steady state of the developed turbulence the spatial correlation function has a universal form with the correlation length determined by the modulational instability scale. The amplitude fluctuations at that scale are nearly-Gaussian while the large amplitude tail of probability density function (PDF) is strongly non-Gaussian with power-like behavior. The small amplitude nearly-Gaussian fluctuations seed formation of large collapse events. The universal spatio-temporal form of these events together with the PDF for their maximum amplitudes define the power-like tail of PDF for large amplitude fluctuations, i.e., the intermittency of strong turbulence.Comment: 14 pages, 17 figure

Fourier transform and the Verlinde formula for the quantum double of a finite group

A Fourier transform S is defined for the quantum double D(G) of a finite group G. Acting on characters of D(G), S and the central ribbon element of D(G) generate a unitary matrix representation of the group SL(2,Z). The characters form a ring over the integers under both the algebra multiplication and its dual, with the latter encoding the fusion rules of D(G). The Fourier transform relates the two ring structures. We use this to give a particularly short proof of the Verlinde formula for the fusion coefficients.Comment: 15 pages, small errors corrected and references added, version to appear in Journal of Physics

Machine learning-based predictions of dietary restriction associations across ageing-related genes

BACKGROUND: Dietary restriction (DR) is the most studied pro-longevity intervention; however, a complete understanding of its underlying mechanisms remains elusive, and new research directions may emerge from the identification of novel DR-related genes and DR-related genetic features. RESULTS: This work used a Machine Learning (ML) approach to classify ageing-related genes as DR-related or NotDR-related using 9 different types of predictive features: PathDIP pathways, two types of features based on KEGG pathways, two types of Protein–Protein Interactions (PPI) features, Gene Ontology (GO) terms, Genotype Tissue Expression (GTEx) expression features, GeneFriends co-expression features and protein sequence descriptors. Our findings suggested that features biased towards curated knowledge (i.e. GO terms and biological pathways), had the greatest predictive power, while unbiased features (mainly gene expression and co-expression data) have the least predictive power. Moreover, a combination of all the feature types diminished the predictive power compared to predictions based on curated knowledge. Feature importance analysis on the two most predictive classifiers mostly corroborated existing knowledge and supported recent findings linking DR to the Nuclear Factor Erythroid 2-Related Factor 2 (NRF2) signalling pathway and G protein-coupled receptors (GPCR). We then used the two strongest combinations of feature type and ML algorithm to predict DR-relatedness among ageing-related genes currently lacking DR-related annotations in the data, resulting in a set of promising candidate DR-related genes (GOT2, GOT1, TSC1, CTH, GCLM, IRS2 and SESN2) whose predicted DR-relatedness remain to be validated in future wet-lab experiments. CONCLUSIONS: This work demonstrated the strong potential of ML-based techniques to identify DR-associated features as our findings are consistent with literature and recent discoveries. Although the inference of new DR-related mechanistic findings based solely on GO terms and biological pathways was limited due to their knowledge-driven nature, the predictive power of these two features types remained useful as it allowed inferring new promising candidate DR-related genes. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12859-021-04523-8