Second-Order Fluid Flow Models: Reflected Brownian Motion in a Random Environment

1995 ◽  
Vol 43 (1) ◽  
pp. 77-88 ◽  
Author(s):  
Rajeeva L. Karandikar ◽  
Vidyadhar G. Kulkarni
Keyword(s):  
Brownian Motion ◽  
Fluid Flow ◽  
Random Environment ◽  
Second Order ◽  
Reflected Brownian Motion ◽  
Flow Models

scholarly journals Jackson network in a random environment: strong approximation

2020 ◽  
pp. 144-149
Author(s):  
Elena Bashtova ◽  
◽  
Elena Lenena ◽  
Keyword(s):  
Brownian Motion ◽  
Random Environment ◽  
Strong Approximation ◽  
Random Variables ◽  
Reflected Brownian Motion ◽  
Jackson Network ◽  
Positive Orthant ◽  
Queue Lengths ◽  
Regenerative Input ◽  
Environment Influence

We consider a Jackson network with regenerative input flows in which every server is subject to a random environment influence generating breakdowns and repairs. They occur in accordance with two independent sequences of i.i.d. random variables. We establish a theorem on the strong approximation of the vector of queue lengths by a reflected Brownian motion in positive orthant.

The Fluctuating Lattice Boltzmann

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Brownian Motion ◽  
Fluid Flow ◽  
Lattice Boltzmann ◽  
Thermal Fluctuations ◽  
Directed Motion ◽  
Statistical Fluctuations ◽  
Lattice Boltzmann Models ◽  
Motion Versus ◽  
The Way

Fluid flow at nanoscopic scales is characterized by the dominance of thermal fluctuations (Brownian motion) versus directed motion. Thus, at variance with Lattice Boltzmann models for macroscopic flows, where statistical fluctuations had to be eliminated as a major cause of inefficiency, at the nanoscale they have to be summoned back. This Chapter illustrates the “nemesis of the fluctuations” and describe the way they have been inserted back within the LB formalism. The result is one of the most active sectors of current Lattice Boltzmann research.

Moderate deviation principle for multivalued stochastic differential equations

2019 ◽  
Vol 20 (03) ◽  
pp. 2050015 ◽  
Author(s):  
Hua Zhang
Keyword(s):  
Brownian Motion ◽  
Weak Convergence ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Moderate Deviation ◽  
Reflected Brownian Motion ◽  
Moderate Deviation Principle ◽  
Deviation Principle ◽  
Weak Convergence Approach

In this paper, we prove a moderate deviation principle for the multivalued stochastic differential equations whose proof are based on recently well-developed weak convergence approach. As an application, we obtain the moderate deviation principle for reflected Brownian motion.

Flow Features Analysis of Throttle Notches of Proportional Direct Valve

2011 ◽  
Vol 189-193 ◽  
pp. 2285-2288
Author(s):  
Wen Hua Jia ◽  
Chen Bo Yin ◽  
Guo Jin Jiang
Keyword(s):  
Fluid Flow ◽  
Dynamic Behavior ◽  
Flow Rate ◽  
Discharge Coefficient ◽  
3D Models ◽  
Operating Conditions ◽  
Flow Models ◽  
Flow Features ◽  
Rate Discharge ◽  
Spool Valve

Flow features, specially, flow rate, discharge coefficient and efflux angle under different operating conditions are numerically simulated, and the effects of shapes and the number of notches on them are analyzed. To simulate flow features, 3D models are developed as commercially available fluid flow models. Most construction machineries in different conditions require different actions. Thus, in order to be capable of different actions and exhibit good dynamic behavior, flow features should be achieved in designing an optimized proportional directional spool valve.

scholarly journals Second-order limit laws for occupation times of fractional Brownian motion

2017 ◽  
Vol 54 (2) ◽  
pp. 444-461 ◽  
Author(s):  
Fangjun Xu
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Method Of Moments ◽  
Second Order ◽  
Hurst Index ◽  
Occupation Times ◽  
Limit Laws ◽  
Additive Functionals ◽  
Finite Dimensional ◽  
Functional Version

Abstract We prove a second-order limit law for additive functionals of a d-dimensional fractional Brownian motion with Hurst index H = 1 / d, using the method of moments and extending the Kallianpur–Robbins law, and then give a functional version of this result. That is, we generalize it to the convergence of the finite-dimensional distributions for corresponding stochastic processes.

Study of the Response of PW Traffic Flow Model to a Bottleneck on a Circular Road and its Suitability for Heterogeneous Traffic Conditions

2021 ◽  
Vol 9 (4) ◽  
pp. 460-463
Keyword(s):  
Fluid Flow ◽  
Traffic Flow ◽  
Flow Model ◽  
Equation Model ◽  
Heterogeneous Traffic ◽  
Flow Conditions ◽  
Flow Models ◽  
Traffic Conditions ◽  
Model Response ◽  
Traffic Flow Models

The traffic flow conditions in developing countries are predominantly heterogeneous. The early developed traffic flow models have been derived from fluid flow to capture the behavior of the traffic. The very first two-equation model derived from fluid flow is known as the Payne-Whitham or PW Model. Along with the traffic flow, this model also captures the traffic acceleration. However, the PW model adopts a constant driver behavior which cannot be ignored, especially in the situation of heterogeneous traffic.This research focuses on testing the PW model and its suitability for heterogeneous traffic conditions by observing the model response to a bottleneck on a circular road. The PW model is mathematically approximated using the Roe Decomposition and then the performance of the model is observed using simulations.

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