Modulational instability in nonlocal Kerr-type media with random parameters

Modulational instability of continuous waves in nonlocal focusing and defocusing Kerr media with stochastically varying diffraction (dispersion) and nonlinearity coefficients is studied both analytically and numerically. It is shown that nonlocality with the sign-definite Fourier images of the medium response functions suppresses considerably the growth rate peak and bandwidth of instability caused by stochasticity. Contrary, nonlocality can enhance modulational instability growth for a response function with negative-sign bands.Comment: 6 pages, 12 figures, revTeX, to appear in Phys. Rev.

Modulational instability and nonlocality management in coupled NLS system

The modulational instability of two interacting waves in a nonlocal Kerr-type medium is considered analytically and numerically. For a generic choice of wave amplitudes, we give a complete description of stable/unstable regimes for zero group-velocity mismatch. It is shown that nonlocality suppresses considerably the growth rate and bandwidth of instability. For nonzero group-velocity mismatch we perform a geometrical analysis of a nonlocality management which can provide stability of waves otherwise unstable in a local medium.Comment: 15 pages, 12 figures, to be published in Physica Script

Formation of an integrated system for monitoring the food security of the region

The agro-industrial complex at the current stage of operation requires a comprehensive analysis of the main directions of agricultural development and its development prospects, assessment of indicators determining the level of accessibility of food products - according to the global food security index, which allowed us to identify the main problems in ensuring the availability of food products. The subject of the study is the formation of an integrated system for monitoring food security in the agro-industrial complex of the region. The paper presents a comparative description of the methodological approaches to assessing the food security of the region. Indicators of the Russian Federation that are not fully synchronized with the main indicators of FAO food security have been identified. The aim and objective of the study is the introduction of progressive methodological approaches to assessing the physical accessibility of food products, which involves assessing the level of development of the distribution infrastructure taking into account the FAO system of food safety indicators, which allows an objective assessment of the volume of domestic production, determine the country's comparative advantages in the production of basic food products, and also evaluate the effectiveness of this production. The identified systemic threats to the food security of the region make it possible to justify the reserves for improving the functioning of the regional agri-food market. The necessity of applying a systematic approach to assessing the level of regional food security, which consists in consolidating the organizational, managerial, financial, economic and regulatory mechanisms for regulating the food security of the region, is substantiated. This will provide an information basis for determining development priorities and guidelines, identifying problems and threats in the food sector, taking into account regional characteristics, increasing the efficiency of forms and methods of food flow movement based on the use of effective management methods, the capabilities of modern information technologies and logistic ties

Aperiodicity in one-way Markov cycles and repeat times of large earthquakes in faults

A common use of Markov Chains is the simulation of the seismic cycle in a fault, i.e. as a renewal model for the repetition of its characteristic earthquakes. This representation is consistent with Reid's elastic rebound theory. Here it is proved that in {\it any} one-way Markov cycle, the aperiodicity of the corresponding distribution of cycle lengths is always lower than one. This fact concurs with observations of large earthquakes in faults all over the world

Optical and structural properties of sol-gel derived materials embedded in porous anodic alumina

Structure composing a xerogel, doped with lanthanide ions (erbium, terbium and europium), embedded in porous anodic alumina (PAA) have been fabricated and their optical and electrical characterisitics have been studied. Erbium photoluminescence at 1.53 µm from titania xerogel/PAA was found to increase with the number of xerogel layers and erbium concnetration for the excitation wavelength 532 nm, matching the area of transparency of both titania xerogel and PAA. Visible green and red electroluminescence was observed for terbium- and europium-doped IN2O3 and SnO2 xerogels embedded in porous anodic alumina. The improvement of the electrical properties of the xerogel/PAA cell is discussed, taking into account the observed ability of conducting In2O3:Sn (ITO) nanoparticles to penetrate into the anodic alumina pores

Scale free networks of earthquakes and aftershocks

We propose a new metric to quantify the correlation between any two earthquakes. The metric consists of a product involving the time interval and spatial distance between two events, as well as the magnitude of the first one. According to this metric, events typically are strongly correlated to only one or a few preceding ones. Thus a classification of events as foreshocks, main shocks or aftershocks emerges automatically without imposing predefined space-time windows. To construct a network, each earthquake receives an incoming link from its most correlated predecessor. The number of aftershocks for any event, identified by its outgoing links, is found to be scale free with exponent $\gamma = 2.0(1)$. The original Omori law with $p=1$ emerges as a robust feature of seismicity, holding up to years even for aftershock sequences initiated by intermediate magnitude events. The measured fat-tailed distribution of distances between earthquakes and their aftershocks suggests that aftershock collection with fixed space windows is not appropriate.Comment: 7 pages and 7 figures. Submitte

Mean first-passage times of non-Markovian random walkers in confinement

The first-passage time (FPT), defined as the time a random walker takes to reach a target point in a confining domain, is a key quantity in the theory of stochastic processes. Its importance comes from its crucial role to quantify the efficiency of processes as varied as diffusion-limited reactions, target search processes or spreading of diseases. Most methods to determine the FPT properties in confined domains have been limited to Markovian (memoryless) processes. However, as soon as the random walker interacts with its environment, memory effects can not be neglected. Examples of non Markovian dynamics include single-file diffusion in narrow channels or the motion of a tracer particle either attached to a polymeric chain or diffusing in simple or complex fluids such as nematics \cite{turiv2013effect}, dense soft colloids or viscoelastic solution. Here, we introduce an analytical approach to calculate, in the limit of a large confining volume, the mean FPT of a Gaussian non-Markovian random walker to a target point. The non-Markovian features of the dynamics are encompassed by determining the statistical properties of the trajectory of the random walker in the future of the first-passage event, which are shown to govern the FPT kinetics.This analysis is applicable to a broad range of stochastic processes, possibly correlated at long-times. Our theoretical predictions are confirmed by numerical simulations for several examples of non-Markovian processes including the emblematic case of the Fractional Brownian Motion in one or higher dimensions. These results show, on the basis of Gaussian processes, the importance of memory effects in first-passage statistics of non-Markovian random walkers in confinement.Comment: Submitted version. Supplementary Information can be found on the Nature website : http://www.nature.com/nature/journal/v534/n7607/full/nature18272.htm