Ice Gouge Depth Determination Via an Efficient Stochastic Dynamics Technique

A simplified model of the motion of a grounding iceberg for determining the gouge depth into the seabed is proposed. Specifically, taking into account uncertainties relating to the soil strength, a nonlinear stochastic differential equation governing the evolution of the gouge length/depth in time is derived. Further, a recently developed Wiener path integral (WPI) based approach for solving approximately the nonlinear stochastic differential equation is employed; thus, circumventing computationally demanding Monte Carlo based simulations and rendering the approach potentially useful for preliminary design applications. The accuracy/reliability of the approach is demonstrated via comparisons with pertinent Monte Carlo simulation (MCS) data.

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Monte-Carlo simulation of a stochastic differential equation

Plasma Science and Technology ◽

10.1088/2058-6272/aa8f3f ◽

2017 ◽

Vol 19 (12) ◽

pp. 125001 ◽

Cited By ~ 1

Author(s):

Arif ULLAH ◽

Majid KHAN ◽

M KAMRAN ◽

R KHAN ◽

Zhengmao SHENG

Keyword(s):

Differential Equation ◽

Monte Carlo Simulation ◽

Monte Carlo ◽

Stochastic Differential Equation

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Generalized mathematical model of cancer heterogeneity

10.1101/2020.05.25.115725 ◽

2020 ◽

Author(s):

Motohiko Naito

Keyword(s):

Mathematical Modeling ◽

Differential Equation ◽

Mathematical Model ◽

Stochastic Process ◽

Monte Carlo Simulation ◽

Monte Carlo ◽

Stochastic Differential Equation ◽

Cancer Growth ◽

Cancer Heterogeneity ◽

Growth Properties

AbstractThe number of reports on mathematical modeling related to oncology is increasing with advances in oncology. Even though the field of oncology has developed significantly over the years, oncology-related experiments remain limited in their ability to examine cancer. To overcome this limitation, in this study, a stochastic process was incorporated into conventional cancer growth properties to obtain a generalized mathematical model of cancer growth. Further, an expression for the violation of symmetry by cancer clones that leads to cancer heterogeneity was derived by solving a stochastic differential equation. Monte Carlo simulations of the solution to the derived equation validate the theories formulated in this study. These findings are expected to provide a deeper understanding of the mechanisms of cancer growth, with Monte Carlo simulation having the potential of being a useful tool for oncologists.

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Density-based Monte Carlo filter and its applications in nonlinear stochastic differential equation models

Computers in Biology and Medicine ◽

10.1016/j.compbiomed.2012.11.003 ◽

2013 ◽

Vol 43 (2) ◽

pp. 135-143

Author(s):

Guanghui Huang ◽

Jianping Wan ◽

Hui Chen

Keyword(s):

Differential Equation ◽

Monte Carlo ◽

Stochastic Differential Equation ◽

Differential Equation Models ◽

Nonlinear Stochastic Differential Equation

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An approximation result and Monte Carlo simulation of the adapted solution of the one-dimensional backward stochastic differential equation

Random Operators and Stochastic Equations ◽

10.1515/rose-2018-0011 ◽

2018 ◽

Vol 26 (3) ◽

pp. 131-142

Author(s):

A. Sghir ◽

D. Seghir ◽

S. Hadiri

Keyword(s):

Differential Equation ◽

Monte Carlo Simulation ◽

Monte Carlo ◽

Stochastic Differential Equation ◽

Backward Stochastic Differential Equation ◽

Multidimensional Case ◽

Reference Trajectory ◽

Approximation Result ◽

One Dimensional ◽

The One

Abstract In this paper, we give an approximation result for the adapted solution of the one-dimensional backward stochastic differential equation driven by a one-dimensional Brownian motion (BSDE for short). To prove our main result, we linearize the generator of the BSDE around a deterministic nominal reference trajectory by using a Taylor series expansion. We then find an approximate linear model of the BSDE. A test of our method is given with a numerical scheme driven by the Monte Carlo simulation. We believe that our result is new and valid for the multidimensional case.

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Multicriteria Optimization for System Configuration Using Monte Carlo Simulation and RAM Analysis

Volume 3: Structures, Safety and Reliability ◽

10.1115/omae2016-54274 ◽

2016 ◽

Author(s):

Adriana Miralles Schleder ◽

Paula Cyrineu Araujo ◽

Marcelo Ramos Martins

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Performance Indicators ◽

Time Interval ◽

Preliminary Design ◽

System Configuration ◽

Conflicting Objectives ◽

Ram Analysis ◽

Complex System Design ◽

Rational Process

Currently, engineers should to deal with conflicting objectives, especially concerning safety and economics constraints. It is necessary to take into account performance indicators like reliability and availability coupled with economic criteria such as the costs of acquisition, maintenance and plant downtime. This paper aims at bringing up a rational process of selecting the optimal configuration of the system in the preliminary design phase considering these conflicting indicators. Here, it is proposed a coupled approach using Monte Carlo Simulation and Genetic Algorithms to define the system configuration and the time interval between preventive maintenances in order to maximize the availability and the expected profit with the system operation considering possible constraints about the number of maintenance teams. The approach proposed in this paper has shown to be promising for solving complex system design related to realistic scenarios in which conflicting performance and economic objectives must be taken into account.

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