scholarly journals MOVIMENTO BROWNIANO: APLICAÇÃO EM ESTRATÉGIAS DE BUSCA

2019 ◽  
Vol 5 (4) ◽  
pp. 0392-0402
Author(s):  
Matheus Dias Carvalho ◽  
Ricardo de Carvalho Falcão ◽  
Antonio Marcos de Oliveira Siqueira
Keyword(s):  
Distribution Function ◽  
Brownian Motion ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Metabolic Rate ◽  
Stationary State ◽  
Analytical Solutions ◽  
Random Processes ◽  
Graphical Form ◽  
Partial Differential

This article has elucidated information about Brownian Motion in the ring, something that is still little explored in the literature. In addition, the ideas of feed, metabolic rate and stochastic restart to the walker were added, features that have been gaining ground recently in the study of random processes. This paper structured partial differential equations governing this process for the immortal case of walker, and later found analytical solutions to these expressions. The representation of stationary state was also performed in graphical form, thus obtaining the distribution function of probability required. In order to briefly approach the walker in a deadly process, a graph was produced that presents the function between the number of steps taken by a walker before his death and his metabolic capacity.Este artigo elucidou informações a respeito do movimento browniano no anel, algo ainda pouco explorado na literatura. Além disso, foram adicionadas as ideias de alimentação, taxa metabólica e reinício estocástico ao caminhante, características que vem ganhando espaço recentemente no estudo de processos aleatórios. Esse artigo realizou a estruturação das equações diferenciais parciais que regem tal processo para o caso de um caminhante imortal, além de posteriormente encontrar soluções analíticas para estas expressões. A representação do estado estacionário do caminhante também foi realizada na forma gráfica, obtendo assim as funções distribuição de probabilidade requeridas. Com o intuito de abordar brevemente o caminhante em um processo mortal, foi produzido um gráfico que apresenta a função entre o número de passos dados por um caminhante antes de sua morte e sua capacidade metabólica.

scholarly journals A Table Lookup Method for Exact Analytical Solutions of Nonlinear Fractional Partial Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Ji Juan-Juan ◽  
Guo Ye-Cai ◽  
Zhang Lan-Fang ◽  
Zhang Chao-Long
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Space Time ◽  
Hyperbolic Function ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Table Lookup ◽  
Exact Analytical Solutions ◽  
Function Solution

A table lookup method for solving nonlinear fractional partial differential equations (fPDEs) is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1)-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.

scholarly journals Mathematical analysis of non-Newtonian nanofluid transport phenomena past a truncated cone with Newtonian heating

2018 ◽  
Vol 15 (1) ◽  
pp. 17-35 ◽  
Author(s):  
Nagendra Nallagundla ◽  
C. H. Amanulla ◽  
M. Suryanarayana Reddy
Keyword(s):  
Brownian Motion ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Biot Number ◽  
Lewis Number ◽  
Casson Fluid ◽  
External Boundary ◽  
Partial Differential ◽  
Truncated Cone ◽  
Highly Nonlinear

In the present study, we analyze the heat, momentum and mass (species) transfer in external boundary layer flow of Casson nanofluid past a truncated cone surface with Biot Number effect is studied theoretically. The effects of Brownian motion and thermophoresis are incorporated in the model in the presence of both heat and nanoparticle mass transfer Biot Number effect. The governing partial differential equations (PDEs) are transformed into highly nonlinear, coupled, multi-degree non-similar partial differential equations consisting of the momentum, energy and concentration equations via. Appropriate non-similarity transformations. These transformed conservation equations are solved subject to appropriate boundary conditions with a second order accurate finite difference method of the implicit type. The influences of the emerging parameters i.e. Casson fluid parameter (?), Brownian motion parameter (Nb) and thermophoresis parameter (Nt), Lewis number (Le), Buoyancy ratio parameter (N ), Prandtl number (Pr) and Biot number (Bi) on velocity, temperature and nano-particle concentration distributions is illustrated graphically and interpreted at length.  Validation of solutions with a Nakamura tri-diagonal method has been included. The study is relevant to enrobing processes for electric-conductive nano-materials of potential use in aerospace and other industries.

SEMI-ANALYTICAL SOLUTIONS FOR THE BRUSSELATOR REACTION–DIFFUSION MODEL

2017 ◽  
Vol 59 (2) ◽  
pp. 167-182 ◽  
Author(s):  
H. Y. ALFIFI
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Partial Differential ◽  
Analytical Results ◽  
Transient Solutions ◽  
The Impact

Semi-analytical solutions are derived for the Brusselator system in one- and two-dimensional domains. The Galerkin method is processed to approximate the governing partial differential equations via a system of ordinary differential equations. Both steady-state concentrations and transient solutions are obtained. Semi-analytical results for the stability of the model are presented for the identified critical parameter value at which a Hopf bifurcation occurs. The impact of the diffusion coefficients on the system is also considered. The results show that diffusion acts to stabilize the systems better than the equivalent nondiffusive systems with the increasing critical value of the Hopf bifurcation. Comparison between the semi-analytical and numerical solutions shows an excellent agreement with the steady-state transient solutions and the parameter values at which the Hopf bifurcations occur. Examples of stable and unstable limit cycles are given, and Hopf bifurcation points are shown to confirm the results previously calculated in the Hopf bifurcation map. The usefulness and accuracy of the semi-analytical results are confirmed by comparison with the numerical solutions of partial differential equations.

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