Brownian Motion and Partial Differential Equations

1998 ◽  
pp. 239-280 ◽  
Author(s):  
Ioannis Karatzas ◽  
Steven E. Shreve
Keyword(s):  
Brownian Motion ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential

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.

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.

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