Stochastic homogenization of nonlinear evolution equations with space-time nonlocality

In this paper we consider the homogenization problem of nonlinear evolution equations with space-time non-locality, the problems are given by Beltritti and Rossi [JMAA, 2017, 455: 1470-1504]. When the integral kernel $J(x,t;y,s)$ is re-scaled in a suitable way and the oscillation coefficient $\nu(x,t;y,s)$ possesses periodic and stationary structure, we show that the solutions $u^{\varepsilon}(x,t)$ to the perturbed equations converge to $u_{0}(x,t)$, the solution of corresponding local nonlinear parabolic equation as scale parameter $\varepsilon\rightarrow 0^{+}$. Then for the nonlocal linear index $p=2$ we give the convergence rate such that $||u^\varepsilon -u_{0}||_{_{L^{2}(\mathbb{R}^{d}\times(0,T))}}\leq C\varepsilon$. Furthermore, we obtain that the normalized difference $\frac{1}{\varepsilon}[u^{\varepsilon}(x,t)-u_{0}(x,t)]-\chi(\frac{x}{\varepsilon}, \frac{t}{\varepsilon^{2}}) \nabla_{x}u_{0}(x,t)$ converges to a solution of an SPDE with additive noise and constant coefficients. Finally, we give some numerical formats for solving non-local space-time homogenization.Comment: 24 pages, 1 figur

Analysis of a chemostat model for bacteria and virulent bacteriophage

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Homogenization of the distribution-dependent stochastic abstract fluid models

In this paper, we study the homogenization of the distribution-dependent stochastic abstract fluid models by combining the $two\!-\!scale$ convergence and martingale representative approach. A general framework of the homogenization research is established for stochastic abstract fluid models, which is the type of genuine-nonlinear partial differential equations including the (distribution-dependent) stochastic Navier-Stokes equations, stochastic magneto-hydrodynamic equations, stochastic Boussinesq equations, stochastic micropolar equations, stochastic Allen-Cahn equations.Comment: no comment

Prediction of Water Consumption in Hospitals Based on a Modified Grey GM (0, 1∣sin) Model of Oscillation Sequence: The Example of Wuhan City

Water shortage is one of the main factors limiting urban construction and development. Scientific forecasting of water consumption is an important approach for the rational allocation of water resources. Taking the hospitals in Wuhan City as an example and basing the analysis on the characteristics of actual water consumption, we proposed a modified grey GM (0, 1∣sin) model of oscillation sequence. Using the grey theory, the variable weight-strengthening buffer operator (VWSBO) was introduced into this model to weaken the interference of the disturbance term on the data sequence. The actual quarterly total water consumption data for hospitals in Wuhan City during the period from 2010 to 2012 were used to verify the effectiveness and practicality of this modified grey GM (0, 1∣sin) model in predicting water consumption. In terms of the model’s fitting performance, the mean absolute percentage error (MAPE) of the modified model was 3.77%, indicating a higher prediction accuracy than the traditional grey GM (0, 1∣sin) model of oscillation sequences. Therefore, the modified grey GM (0, 1∣sin) model we established in this study can provide a scientific reference for administrative departments to forecast water consumption

Categorization of Orthologous Gene Clusters in 92 Ascomycota Genomes Reveals Functions Important for Phytopathogenicity

Phytopathogenic Ascomycota are responsible for substantial economic losses each year, destroying valuable crops. The present study aims to provide new insights into phytopathogenicity in Ascomycota from a comparative genomic perspective. This has been achieved by categorizing orthologous gene groups (orthogroups) from 68 phytopathogenic and 24 non-phytopathogenic Ascomycota genomes into three classes: Core, (pathogen or non-pathogen) group-specific, and genome-specific accessory orthogroups. We found that (i) ~20% orthogroups are group-specific and accessory in the 92 Ascomycota genomes, (ii) phytopathogenicity is not phylogenetically determined, (iii) group-specific orthogroups have more enriched functional terms than accessory orthogroups and this trend is particularly evident in phytopathogenic fungi, (iv) secreted proteins with signal peptides and horizontal gene transfers (HGTs) are the two functional terms that show the highest occurrence and significance in group-specific orthogroups, (v) a number of other functional terms are also identified to have higher significance and occurrence in group-specific orthogroups. Overall, our comparative genomics analysis determined positive enrichment existing between orthogroup classes and revealed a prediction of what genomic characteristics make an Ascomycete phytopathogenic. We conclude that genes shared by multiple phytopathogenic genomes are more important for phytopathogenicity than those that are unique in each genome

Stochastic Nonlinear Thermoelastic System Coupled Sine-Gordon Equation Driven by Jump Noise

This paper considers a stochastic nonlinear thermoelastic system coupled sine-Gordon equation driven by jump noise. We first prove the existence and uniqueness of strong probabilistic solution of an initial-boundary value problem with homogeneous Dirichlet boundary conditions. Then we give an asymptotic behavior of the solution