Stochastic Model Simulation Using Kronecker Product Analysis and Zassenhaus Formula Approximation

2013 ◽  
Vol 10 (5) ◽  
pp. 1125-1136 ◽  
Author(s):  
Mehmet Umut Caglar ◽  
Ranadip Pal
Keyword(s):  
Stochastic Model ◽  
Kronecker Product ◽  
Model Simulation ◽  
Product Analysis ◽  
Zassenhaus Formula

A stochastic model, simulation, and application to aggregation of cadmium sulfide nanocrystals upon evaporation of the Langmuir–Blodgett matrix

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Kirill Svit ◽  
Konstantin Zhuravlev ◽  
Sergey Kireev ◽  
Karl K. Sabelfeld
Keyword(s):  
Stochastic Model ◽  
Cadmium Sulfide ◽  
Model Simulation ◽  
Surrounding Medium ◽  
Real Life ◽  
Langmuir Blodgett ◽  
Cluster Aggregation ◽  
Aggregation Processes ◽  
The Matrix ◽  
Sulfide Nanocrystals

Abstract A stochastic model of nanocrystals clusters formation is developed and applied to simulate an aggregation of cadmium sulfide nanocrystals upon evaporation of the Langmuir–Blodgett matrix. Simulations are compared with our experimental results. The stochastic model suggested governs mobilities both of individual nanocrystals and its clusters (arrays). We give a comprehensive analysis of the patterns simulated by the model, and study an influence of the surrounding medium (solvent) on the aggregation processes. In our model, monomers have a finite probability of separation from the cluster which depends on the temperature and binding energy between nanocrystals, and can also be redistributed in the composition of the cluster, leading to its compaction. The simulation results obtained in this work are compared with the experimental data on the aggregation of CdS nanocrystals upon evaporation of the Langmuir–Blodgett matrix. This system is a typical example from real life and is noteworthy in that the morphology of nanocrystals after evaporation of the matrix cannot be described exactly by a model based only on the motion of individual nanocrystals or by a cluster-cluster aggregation model.

Simulation of High-Resolution Precipitable Water Data by a Stochastic Model with a Random Trigger

2016 ◽  
Vol 08 (02) ◽  
pp. 1650006 ◽  
Author(s):  
Kimberly Leung ◽  
Max Velado ◽  
Aneesh Subramanian ◽  
Guang J. Zhang ◽  
Richard C. J. Somerville ◽  
...  
Keyword(s):  
Stochastic Model ◽  
Climate Models ◽  
Time Window ◽  
Model Simulation ◽  
Precipitable Water ◽  
Cumulative Distribution ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Ice Period

We use a stochastic differential equation (SDE) model with a random precipitation trigger for mass balance to simulate the 20 s temporal resolution column precipitable water vapor (PWV) data during the tropical warm pool international cloud experiment (TWP-ICE) period of January 20 to February 15, 2006 at Darwin, Australia. The trigger is determined by an exponential cumulative distribution function, the time step size in the SDE simulation, and a random precipitation indicator uniformly distributed over [0, 1]. Compared with the observed data, the simulations have similar means, extremes, skewness, kurtosis, and overall shapes of probability distribution, and are temporally well synchronized for increasing and decreasing, but have about 20% lower standard deviation. Based on a 1000-day run, the correlations between the model data and the observations in TWP-ICE period were computed in a moving time window of 25 days and show quasi-periodic variations between (−0.675, 0.697). This shows that the results are robust for the stochastic model simulation of the observed PWV data, whose fractal dimension is 1.9, while the dimension of the simulated data is also about 1.9. This agreement and numerous sensitivity experiments form a test on the feasibility of using an SDE model to simulate precipitation processes in more complex climate models.

scholarly journals T-Growth Stochastic Model: Simulation and Inference via Metaheuristic Algorithms

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 959
Author(s):  
Antonio Barrera ◽  
Patricia Román-Román ◽  
Francisco Torres-Ruiz
Keyword(s):  
Stochastic Model ◽  
Diffusion Process ◽  
Model Simulation ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Procedure ◽  
Metaheuristic Algorithms ◽  
Mathematical Treatment ◽  
Linear Differential ◽  
Lognormal Diffusion Process

The main objective of this work is to introduce a stochastic model associated with the one described by the T-growth curve, which is in turn a modification of the logistic curve. By conveniently reformulating the T curve, it may be obtained as a solution to a linear differential equation. This greatly simplifies the mathematical treatment of the model and allows a diffusion process to be defined, which is derived from the non-homogeneous lognormal diffusion process, whose mean function is a T curve. This allows the phenomenon under study to be viewed in a dynamic way. In these pages, the distribution of the process is obtained, as are its main characteristics. The maximum likelihood estimation procedure is carried out by optimization via metaheuristic algorithms. Thanks to an exhaustive study of the curve, a strategy is obtained to bound the parametric space, which is a requirement for the application of various swarm-based metaheuristic algorithms. A simulation study is presented to show the validity of the bounding procedure and an example based on real data is provided.

scholarly journals A Stochastic Model for Kala-azar Transmission Dynamics in Libo Kemkem, Ethiopia

2022 ◽  
Author(s):  
Sewmehon Shimekaw Alemu
Keyword(s):  
Stochastic Model ◽  
Health Informatics ◽  
Model Simulation ◽  
Transmission Rate ◽  
Sir Model ◽  
Infected Group ◽  
Closed Population ◽  
Kala Azar ◽  
Stochastic Sir Model ◽  
Over Time

Abstract The objective of this paper is to analyse and demonstrate the dynamics of Kala-azar infected group using stochastic model, particularly using simple SIR model with python script over time. The model is used under a closed population with N = 100, transmission rate coefficient β = 0.09, recovery rate γ = 0.03 and initial condition I(0) = 1. In the paper it is discussed how the Kala-azar infected group behaves through simple SIR model. The paper is completed with stochastic SIR model simulation result and shows stochasticity of the dynamics of Kala-azar infected population over time. Fig. 2 below depicts continuous fluctuations which tells us the disease evolves with stochastic nature and shows random process.Subject: Infectious Disease, Global Health, Health Informatics and Statistical and Computational Physics

A Fruitful Stochastic Model

1964 ◽  
Vol 9 (7) ◽  
pp. 273-276
Author(s):  
ANATOL RAPOPORT
Keyword(s):  
Stochastic Model

Model, simulation and experiments for a Buoyancy Organic Rankine Cycle

2020 ◽  
Vol 92 (1) ◽  
pp. 10906
Author(s):  
Jeroen Schoenmaker ◽  
Pâmella Gonçalves Martins ◽  
Guilherme Corsi Miranda da Silva ◽  
Julio Carlos Teixeira
Keyword(s):  
Model Simulation ◽  
Organic Rankine Cycle ◽  
Thermodynamic Cycle ◽  
Rankine Cycle ◽  
Test Body ◽  
Working Fluid ◽  
Proof Of Concept ◽  
Energy Scenario ◽  
New Type ◽  
Fluid Reservoir

Organic Rankine Cycle (ORC) systems are increasingly gaining relevance in the renewable and sustainable energy scenario. Recently our research group published a manuscript identifying a new type of thermodynamic cycle entitled Buoyancy Organic Rankine Cycle (BORC) [J. Schoenmaker, J.F.Q. Rey, K.R. Pirota, Renew. Energy 36, 999 (2011)]. In this work we present two main contributions. First, we propose a refined thermodynamic model for BORC systems accounting for the specific heat of the working fluid. Considering the refined model, the efficiencies for Pentane and Dichloromethane at temperatures up to 100 °C were estimated to be 17.2%. Second, we show a proof of concept BORC system using a 3 m tall, 0.062 m diameter polycarbonate tube as a column-fluid reservoir. We used water as a column fluid. The thermal stability and uniformity throughout the tube has been carefully simulated and verified experimentally. After the thermal parameters of the water column have been fully characterized, we developed a test body to allow an adequate assessment of the BORC-system's efficiency. We obtained 0.84% efficiency for 43.8 °C working temperature. This corresponds to 35% of the Carnot efficiency calculated for the same temperature difference. Limitations of the model and the apparatus are put into perspective, pointing directions for further developments of BORC systems.

A Stochastic Model for Evolution of Altruistic Genes

1996 ◽  
Vol 6 (4) ◽  
pp. 445-453 ◽  
Author(s):  
Roberta Donato
Keyword(s):  
Stochastic Model

A Stochastic Model for the Inheritance of the Cancer Proneness Phenotype

1987 ◽  
Vol 26 (03) ◽  
pp. 117-123
Author(s):  
P. Tautu ◽  
G. Wagner
Keyword(s):  
Stochastic Model ◽  
Gaussian Process ◽  
Covariance Function ◽  
Neoplastic Disease ◽  
Disease Phenotype ◽  
Probabilistic Representation ◽  
Temporal Behaviour ◽  
Continuous Trait ◽  
Continuous Parameter ◽  
Level Zero

SummaryA continuous parameter, stationary Gaussian process is introduced as a first approach to the probabilistic representation of the phenotype inheritance process. With some specific assumptions about the components of the covariance function, it may describe the temporal behaviour of the “cancer-proneness phenotype” (CPF) as a quantitative continuous trait. Upcrossing a fixed level (“threshold”) u and reaching level zero are the extremes of the Gaussian process considered; it is assumed that they might be interpreted as the transformation of CPF into a “neoplastic disease phenotype” or as the non-proneness to cancer, respectively.

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