Justification for the use of Markovian Langevin statistics in the modelling of activated surface diffusion.

Low temperature surface diffusion is driven by the thermally activated hopping of adatoms between adsorption sites. Helium spin-echo techniques, capable of measuring the sub-picosecond motion of individual adatoms, have enabled the bench-marking of many important adsorbate-substrate properties. The well-known Markovian Langevin equation has emerged as the standard tool for the interpretation of such experimental data, replacing adatom-substrate interactions with stochastic white noise and linear friction. However, the consequences of ignoring the colored noise spectrum and non-linearities inherent to surface systems are not known. Through the computational study of three alternative models of adatom motion, we show that the hopping rate and jump distributions of an adatom are fixed to within a few percent by the potential energy surface and a new generalized energy exchange rate parameter alone, independent of the model used. This result justifies the use of the Markovian Langevin equation, regardless of the true statistical nature of adatom forces, provided results are quoted in terms of the new energy exchange rate parameter. Moreover, numerous mechanisms for the effect of noise correlations and non-linear friction on the energy exchange rate are proposed which likely contribute to activated surface diffusion and activated processes more generally.

Spectral computation of reactive bi-directional hydromagnetic non-Newtonian convection flow from a stretching upper parabolic surface in non-Darcyporous medium

This paper presents a mathematical model for bi-directional convection magnetohydrodynamic (MHD) tangent hyperbolic nanofluid flow from the upper horizontal subsurface of a stretching parabolic surface to a non-Darcian porous medium, as a simulation of nanocoating. Chemical reaction, activation energy and thermo solutal buoyancy effects are included. The Darcy–Brinkman–Forchheimer model is deployed which permits the analysis of inertial (second order) porous drag effects. The Buongiorno nanoscale model is deployed which includes Brownian motion and thermophoresis effects. The dimensionless, transformed, nonlinear, coupled ordinary differential equations are solved by implementing the spectral relaxation method (SRM). Validation with previous studies is included. The numerical influence of key parameters on transport characteristics is evaluated and visualized graphically. Velocity is elevated (and momentum boundary layer thickness is reduced) with increasing wall thickness parameter, permeability parameter, Forchheimer parameter, Weissenberg (rheological) parameter and modified Hartmann (magnetic body force) number. Velocity enhancement is also computed with increment in stretching rate parameter, rheological power-law index, thermal Grashof number, and species (solutal) Grashof number, and momentum boundary layer thickness diminishes. Temperature is suppressed with increasing stretching rate index and Prandtl number whereas it is substantially elevated with increasing Brownian motion and thermophoresis parameters. Velocity and temperature profiles are reduced adjacent to the parabolic surface with larger wall thickness parameter for stretching rate index [Formula: see text]1, whereas the reverse behavior is observed for stretching rate index [Formula: see text]1. Nanoparticle concentration magnitude is depleted with larger numeric of Lewis number and the Brownian motion parameter, whereas it is enhanced with greater values of the stretching index and thermophoresis parameter. The nanoparticle concentration magnitude is reduced with an increase in chemical reaction rate parameter whereas it is boosted with activation energy parameter. Skin friction, Nusselt number and Sherwood number are also computed. The study is relevant to electromagnetic nanomaterials coating processes with complex chemical reactions.

E-Bayesian Estimation of Reliability Characteristics of a Weibull Distribution with Applications

Given a progressively type-II censored sample, the E-Bayesian estimates, which are the expected Bayesian estimates over the joint prior distributions of the hyper-parameters in the gamma prior distribution of the unknown Weibull rate parameter, are developed for any given function of unknown rate parameter under the square error loss function. In order to study the impact from the selection of hyper-parameters for the prior, three different joint priors of the hyper-parameters are utilized to establish the theoretical properties of the E-Bayesian estimators for four functions of the rate parameter, which include an identity function (that is, a rate parameter) as well as survival, hazard rate and quantile functions. A simulation study is also conducted to compare the three E-Bayesian and a Bayesian estimate as well as the maximum likelihood estimate for each of the four functions considered. Moreover, two real data sets from a medical study and industry life test, respectively, are used for illustration. Finally, concluding remarks are addressed.

APPLICATION OF STOCHASTIC MODEL FOR LENGTHY EPIDEMIC FORECASTING

In this paper we consider a stochastic discrete-time epidemic model, with the infectivity depending on the age of infection and existing formula for the maximum likelihood estimation of the parameter responsible for the rate of the infection spread. In order to utilize the real number of infection cases statistics, a detection rate parameter is introduced. A program for automatic parameter estimation using past data with future epidemic simulation is developed. We present the comparison between the simulation of COVID-19 cases in Kyiv and real data using manual and automatic parameter estimation. We consider the possibility of the epidemic partition into several intervals with different parameters in order to simulate lengthy epidemics with significant changes in dynamics. We present the comparison between different numbers of partitions for long-term COVID-19 simulation in Kyiv (Ukraine) and Czech Republic, which have different dynamics of the epidemic development.

Implementasi Recurrent Neural Network dalam Memprediksi Kepadatan Restoran Berbasis LSTM

In this modern era, restaurants are becoming very popular, especially in big cities. However, this can lead to density or queues of visitors at a restaurant, which should be avoided during the current Covid-19 pandemic. So that accurate information that can predict the density of restaurant will be very useful. In predicting the density of restaurants, data processing on the number of visitors obtained from one of the restaurants is carried out using artificial intelligence in the form of LSTM (Long Short Term Memory) RNN (Recurrent Neural Network). The results of the research on Recurrent Neural Network based on LSTM (Long Short Term Memory) at the best learning rate parameter of 0.001 and a maximum epoch of 2000 resulted in an MSE value of 0.00000278 on the training data and 0.0069 on the test data

A Logistic Approach for Kinetics of Isothermal Pyrolysis of Cellulose

A kinetic model is proposed to fit isothermal thermogravimetric data obtained from cellulose in an inert atmosphere at different temperatures. The method used here to evaluate the model involves two steps: (1) fitting of single time-derivative thermogravimetric curves (DTG) obtained at different temperatures versus time, and (2) fitting of the rate parameter values obtained at different temperatures versus temperature. The first step makes use of derivative of logistic functions. For the second step, the dependence of the rate factor on temperature is evaluated. That separation of the curve fitting from the analysis of the rate factor resulted to be very flexible since it proved to work for previous crystallization studies and now for thermal degradation of cellulose.