A stochastic approximation scheme and convergence theorem for particle interactions with perfectly reflecting boundary conditions

2006 ◽  
Vol 12 (3) ◽  
Author(s):  
C. G. Wells
Keyword(s):  
Boundary Conditions ◽  
Stochastic Approximation ◽  
Convergence Theorem ◽  
Approximation Scheme ◽  
Particle Interactions

A two Timescale Stochastic Approximation Scheme for Simulation-Based Parametric Optimization

1998 ◽  
Vol 12 (4) ◽  
pp. 519-531 ◽  
Author(s):  
Shalabh Bhatnagar ◽  
Vivek S. Borkar
Keyword(s):  
Stochastic Approximation ◽  
Perturbation Analysis ◽  
Parametric Optimization ◽  
Approximation Scheme ◽  
Infinitesimal Perturbation Analysis ◽  
Simulation Based ◽  
Infinitesimal Perturbation ◽  
Two Timescale Stochastic Approximation

A two timescale stochastic approximation scheme which uses coupled iterations is used for simulation-based parametric optimization as an alternative to traditional “infinitesimal perturbation analysis” schemes. It avoids the aggregation of data present in many other schemes. Its convergence is analyzed, and a queueing example is presented.

scholarly journals On fixed gain recursive estimators with discontinuity in the parameters

2019 ◽  
Vol 23 ◽  
pp. 217-244
Author(s):  
Huy N. Chau ◽  
Chaman Kumar ◽  
Miklós Rásonyi ◽  
Sotirios Sabanis
Keyword(s):  
Stochastic Approximation ◽  
Approximation Scheme ◽  
Tracking Error ◽  
Mixing Condition ◽  
Underlying Process ◽  
Recursive Estimators

In this paper, we estimate the expected tracking error of a fixed gain stochastic approximation scheme. The underlying process is not assumed Markovian, a mixing condition is required instead. Furthermore, the updating function may be discontinuous in the parameter.

Molecular Dynamics Computations of Flow in Constricted and Wavy Nano Channels

2009 ◽  
Author(s):  
D. D. Marsh ◽  
S. P. Vanka ◽  
I. M. Jasiuk ◽  
M. L. Knothe Tate
Keyword(s):  
Molecular Dynamics ◽  
Boundary Conditions ◽  
Particle Interactions ◽  
Pressure Drops ◽  
Lennard Jones ◽  
Depth Direction ◽  
Depth Dimension ◽  
Non Equilibrium Molecular Dynamics ◽  
Dynamics Simulations ◽  
Stochastic Boundary

This paper explores flow in complex nano-sized channels by use of molecular dynamics. Due to the small nature of these channels and to better capture wall effects, non-equilibrium molecular dynamics simulations were performed. Straight, constricted and sawtooth channels were studied. The function used for modeling the particle interactions is the Lennard-Jones 6–12 potential. Stochastic boundary conditions are used in conjunction with periodic boundary conditions in a 3D domain. Computational enhancements including cell subdivision and neighbor listing provide increased efficiency. The channels were homogeneous in the depth dimension and the results were averaged in the depth direction in order to improve averages. Velocity profiles at several locations were computed and are presented in the paper. The eventual goal of this research is to study the effects of time-dependent inflow and pressure drops so as to understand the flow in nano channels in the human bone.

Distributed Parameter Identification Using the Method of Characteristics

1971 ◽  
Vol 93 (2) ◽  
pp. 73-78 ◽  
Author(s):  
William T. Carpenter ◽  
Michael J. Wozny ◽  
Raymond E. Goodson
Keyword(s):  
Distributed Systems ◽  
Parameter Identification ◽  
Stochastic Approximation ◽  
Method Of Characteristics ◽  
Approximation Scheme ◽  
Multidimensional Systems ◽  
Distributed Parameter ◽  
The Method Of Characteristics ◽  
Noisy Measurements ◽  
And Diffusion

A method is presented for estimating parameters in distributed systems which can be analyzed by the method of characteristics. Both the very real problems of noisy measurements and limited available measurement transducers are discussed in some depth. Convergent algorithms are developed using a Robbins-Munro stochastic approximation scheme. The extension of these methods to the identification of function multidimensional systems, and diffusion terms is considered.

scholarly journals Stochastic Recursive Inclusions in Two Timescales with Nonadditive Iterate-Dependent Markov Noise

2020 ◽  
Vol 45 (4) ◽  
pp. 1405-1444
Author(s):  
Vinayaka G. Yaji ◽  
Shalabh Bhatnagar
Keyword(s):  
Asymptotic Behavior ◽  
Markov Chain ◽  
Convex Optimization ◽  
Objective Function ◽  
Recent Work ◽  
Differential Inclusion ◽  
Stochastic Approximation ◽  
Optimization Problem ◽  
Approximation Scheme ◽  
Convex Optimization Problem

In this paper, we study the asymptotic behavior of a stochastic approximation scheme on two timescales with set-valued drift functions and in the presence of nonadditive iterate-dependent Markov noise. We show that the recursion on each timescale tracks the flow of a differential inclusion obtained by averaging the set-valued drift function in the recursion with respect to a set of measures accounting for both averaging with respect to the stationary distributions of the Markov noise terms and the interdependence between the two recursions on different timescales. The framework studied in this paper builds on a recent work by Ramaswamy and Bhatnagar, by allowing for the presence of nonadditive iterate-dependent Markov noise. As an application, we consider the problem of computing the optimum in a constrained convex optimization problem, where the objective function and the constraints are averaged with respect to the stationary distribution of an underlying Markov chain. Further, the proposed scheme neither requires the differentiability of the objective function nor the knowledge of the averaging measure.

Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

1970 ◽  
Vol 28 ◽  
pp. 360-361
Author(s):  
John W. Coleman
Keyword(s):  
Boundary Conditions ◽  
High Performance ◽  
Force Fields ◽  
Optical Design ◽  
Direct Conversion ◽  
Design Engineering ◽  
Design Data ◽  
Scalar Potentials ◽  
Geometric Elements ◽  
At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

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