Stochastic Dynamics Simulations Research Articles

Stochastic Dynamic Simulation Model Applied to Public Lawyers Using Petri Nets

The aim of this article is to present a method of assignment of defence lawyers to causes, using tools Petri nets, decision trees and Monte Carlo method. It presents a simulation model of assignment applied to law activities, specifically to defender lawyers contracted by tender, using Petri Nets, Montecarlo and decision trees. The main difficulty of this assignment task is how to distribute equally the workload along the year between two kinds of lawyers: defender lawyers’ staff and external (tendered) defender lawyer. The system utilized for analyzing task assignment is stochastic, parallel, concurrent and dynamic.

You can run, you can hide: The epidemiology and statistical mechanics of zombies.

We use a popular fictional disease, zombies, in order to introduce techniques used in modern epidemiology modeling, and ideas and techniques used in the numerical study of critical phenomena. We consider variants of zombie models, from fully connected continuous time dynamics to a full scale exact stochastic dynamic simulation of a zombie outbreak on the continental United States. Along the way, we offer a closed form analytical expression for the fully connected differential equation, and demonstrate that the single person per site two dimensional square lattice version of zombies lies in the percolation universality class. We end with a quantitative study of the full scale US outbreak, including the average susceptibility of different geographical regions.

Intrinsic fault tolerance of multilevel Monte Carlo methods

Monte Carlo (MC) and multilevel Monte Carlo (MLMC) methods applied to solvers for Partial Differential Equations with random input data are proved to exhibit intrinsic failure resilience. Sufficient conditions are provided for non-recoverable loss of a random fraction of MC samples not to fatally damage the asymptotic accuracy versus work of a MC simulation. Specifically, the convergence behavior of MLMC methods on massively parallel hardware with runtime faults is analyzed mathematically and investigated computationally. Our mathematical model assumes node failures which occur uncorrelated of MC sampling and with general sample failure statistics on the different levels and which also assume absence of checkpointing, i.e., we assume irrecoverable sample failures with complete loss of data. Modifications of the MLMC with enhanced resilience are proposed. The theoretical results are obtained under general statistical models of CPU failure at runtime. Particular attention is paid to node failures with so-called Weibull failure models on massively parallel stochastic finite volume computational fluid dynamics simulations are discussed. We discuss the resilience of massively parallel stochastic Finite Volume computational fluid dynamics simulations.

Stochastic 3D modeling of Ostwald ripening at ultra-high volume fractions of the coarsening phase

We present a (dynamic) stochastic simulation model for 3D grain morphologies undergoing a grain coarsening phenomenon known as Ostwald ripening. For low volume fractions of the coarsening phase, the classical LSW theory predicts a power-law evolution of the mean particle size and convergence toward self-similarity of the particle size distribution; experiments suggest that this behavior holds also for high volume fractions. In the present work, we have analyzed 3D images that were recorded in situ over time in semisolid Al–Cu alloys manifesting ultra-high volume fractions of the coarsening (solid) phase. Using this information we developed a stochastic simulation model for the 3D morphology of the coarsening grains at arbitrary time steps. Our stochastic model is based on random Laguerre tessellations and is by definition self-similar—i.e. it depends only on the mean particle diameter, which in turn can be estimated at each point in time. For a given mean diameter, the stochastic model requires only three additional scalar parameters, which influence the distribution of particle sizes and their shapes. An evaluation shows that even with this minimal information the stochastic model yields an excellent representation of the statistical properties of the experimental data.

Influence of Binder Property and Interaction on Electrode Microstructure Formation in Energy Storage

Energy storage, such as lithium-ion batteries (LIBs), is key enabler for grid energy storage and vehicle electrification. The electrode microstructure, which is affected by processing scheme, plays an important role in determining the electrode property and performance.1-5In the multiphase electrode slurry, physicochemical interactions affect the assembly of active material and conductive additive particles. Additionally, the pattern of nanoparticle assembly is also affected by the solvent evaporation rate. Polymer-mediated nanoparticle assembly can be a promising method to control a composite microstructure.6 However, there are only a few studies focusing on the effect of binder interaction (such as binder molecular weight) on the electrode microstructure formation and the relative performance.7, 8 In the present study, we developed a mesoscale model accompanied by stochastic dynamics simulation to illustrate the influence of binder interaction and evaporation on microstructures during the electrode processing. Present simulations demonstrate that the lower drying temperature can produce electrode films with micropores as shown in Figs. 1 (a) ~ (c). The depth of micropores tends to increase as binder length (L) increases. Drying temperature affects binder distribution along thickness direction as shown in Fig. 1 (d). The lower drying temperature reduces the fraction of on-surface binder. Additionally, binder length also affects the binder distribution. It can be seen in Fig. 1 (d), that an increase of binder length is beneficial for keep high volume fraction of binder in the film which has implication in better mechanical stability of the electrode film. Refernces 1. J. Li, B. L. Armstrong, J. Kiggans, C. Daniel, and D. L. Wood III, Langmuir, 28 (8), 3783-3790 (2012). 2. H. Zheng, R. Yang, G. Liu, X. Song, and V. S. Battaglia, The Journal of Physical Chemistry C, 116 (7), 4875-4882 (2012). 3. G. Liu, H. Zheng, S. Kim, Y. Deng, A. Minor, X. Song, and V. Battaglia, J Electrochem Soc, 155 (12), A887-A892 (2008). 4. Z. Liu and P. P. Mukherjee, J Electrochem Soc, 161 (8), E3248-E3258 (2014). 5. Z. Liu, V. Battaglia, and P. P. Mukherjee, Langmuir, 30 (50), 15102-15113 (2014). 6. P. Akcora, H. Liu, S. K. Kumar, J. Moll, Y. Li, B. C. Benicewicz, L. S. Schadler, D. Acehan, A. Z. Panagiotopoulos, V. Pryamitsyn, V. Ganesan, J. Ilavsky, P. Thiyagarajan, R. H. Colby, and J. F. Douglas, Nat Mater, 8 (4), 354-359 (2009). 7. B.-R. Lee and E.-S. Oh, The Journal of Physical Chemistry C, 117 (9), 4404-4409 (2013). 8. N. Tasić, Z. Branković, Z. Marinković-Stanojević, and G. Branković, Science of Sintering, 44 (3), 365-372 (2012). Figure 1

A novel multi-agent decentralized win or learn fast policy hill-climbing with eligibility trace algorithm for smart generation control of interconnected complex power grids

This paper proposes a multi-agent smart generation control scheme for the automatic generation control coordination in interconnected complex power systems. A novel multi-agent decentralized win or learn fast policy hill-climbing with eligibility trace algorithm is developed, which can effectively identify the optimal average policies via a variable learning rate under various operation conditions. Based on control performance standards, the proposed approach is implemented in a flexible multi-agent stochastic dynamic game-based smart generation control simulation platform. Based on the mixed strategy and average policy, it is highly adaptive in stochastic non-Markov environments and large time-delay systems, which can fulfill automatic generation control coordination in interconnected complex power systems in the presence of increasing penetration of decentralized renewable energy. Two case studies on both a two-area load–frequency control power system and the China Southern Power Grid model have been done. Simulation results verify that multi-agent smart generation control scheme based on the proposed approach can obtain optimal average policies thus improve the closed-loop system performances, and can achieve a fast convergence rate with significant robustness compared with other methods.

Kalman Filter or VAR Models to Predict Unemployment Rate in Romania?

Abstract This paper brings to light an economic problem that frequently appears in practice: For the same variable, more alternative forecasts are proposed, yet the decision-making process requires the use of a single prediction. Therefore, a forecast assessment is necessary to select the best prediction. The aim of this research is to propose some strategies for improving the unemployment rate forecast in Romania by conducting a comparative accuracy analysis of unemployment rate forecasts based on two quantitative methods: Kalman filter and vector-auto-regressive (VAR) models. The first method considers the evolution of unemployment components, while the VAR model takes into account the interdependencies between the unemployment rate and the inflation rate. According to the Granger causality test, the inflation rate in the first difference is a cause of the unemployment rate in the first difference, these data sets being stationary. For the unemployment rate forecasts for 2010-2012 in Romania, the VAR models (in all variants of VAR simulations) determined more accurate predictions than Kalman filter based on two state space models for all accuracy measures. According to mean absolute scaled error, the dynamic-stochastic simulations used in predicting unemployment based on the VAR model are the most accurate. Another strategy for improving the initial forecasts based on the Kalman filter used the adjusted unemployment data transformed by the application of the Hodrick-Prescott filter. However, the use of VAR models rather than different variants of the Kalman filter methods remains the best strategy in improving the quality of the unemployment rate forecast in Romania. The explanation of these results is related to the fact that the interaction of unemployment with inflation provides useful information for predictions of the evolution of unemployment related to its components (i.e., natural unemployment and cyclical component).

English

This paper applies dynamic stochastic simulation methods to assess sustainable public debt management policies in Zimbabwe. The methodology applied involves estimating a fiscal reaction function and using it to simulate public debt path using a stochastic approach and historical information on drivers of public debt accumulation and their volatility. The results from the baseline scenario show that Zimbabwe’s public debt would not deviate much from the desired regional indicative target in the SADC region of 60 percent in the medium to long-term. The policy implication is the need for policy makers to proactively respond to the changing macroeconomic environment and to implement countercyclical fiscal policies to limit the probability of debt from exploding.   Key words: Public debt dynamics, debt sustainability, stochastic simulation, fiscal reaction function.

A comparative study on the effect of hydrodynamic interactions in the non-sequential deposition of concentrated colloidal dispersions: stochastic rotation dynamics and Brownian dynamics simulations

Irreversible adsorption of particles onto a flat surface as a consequence of sedimentation colloidal suspension has been studied by two simulation techniques: Brownian dynamics (BD) and stochastic rotation dynamics (SRD). The purpose of using both methods is to investigate the effect of hydrodynamic interactions on adsorption kinetics and structure of the first monolayer of sediment obtained from the sedimentation of a concentrated and monodisperse colloidal suspension. Three systems were studied, characterised by the Péclet numbers: 0.1, 1.0 and 10. To physically understand the kinetic behaviour, simulation results were analysed using a kinetic model based on chemical reactions. High values of jamming limit (θ∞ > 0.61) were obtained for both simulation techniques, with the SRD showing the highest figures (0.631) due to the hydrodynamics effect that takes into account the fluid backflow produced on particle sedimentation. A two-step adsorption mechanism was proposed based on the observed kinetic behaviour.

Multiagent Stochastic Dynamic Game for Smart Generation Control

AbstractThis paper proposes a multiagent (MA) smart generation control (SGC) scheme for the coordination of automatic generation control (AGC) in power grids with system uncertainties. Under the control performance standards, SGC will undergo a non-Markov random process, of which the optimal solution can be resolved online by the reinforcement learning. Therefore, an MA decentralized correlated equilibrium Q(λ)-learning algorithm, and an MA stochastic dynamic game-based SGC simulation platform (SGC-SP) have been proposed for its implementation, which can achieve AGC coordination in a highly uncertain environment resulting from the increasing penetration of renewable energy. Single-agent Q-learning, Q(λ)-learning, R(λ)-learning, and proportional integral control are implemented and embedded in SGC-SP for the control performance analysis. Two case studies on both a two-area power system and the China Southern Power Grid model have been done, which verify its effectiveness and scalability.

Efficient Calculation of Low Energy Configurations of Nanoparticle Ensembles for Magnetoresistive Sensor Devices by Means of Stochastic Spin Dynamicsand Monte Carlo Methods

We present results of Monte Carlo and stochastic spin dynamics simulations of a magnetic nanoparticle model system based on experimentally produced samples. Thermodynamic investigations as well as spin dynamics studies show characteristic features, both resembling magnetic dipole glass behaviour. While spin dynamics studies at T = 0 yield a multitude of low energy configurations, thermodynamic simulations show a clear transition between a paramagnetic and a frozen magnetic state. Moreover, we demonstrate the application of experimentally inspired demagnetization protocols to compute low energy configurations of the systems under consideration efficiently.

Direct prediction of residual dipolar couplings of small molecules in a stretched gel by stochastic molecular dynamics simulations.

Residual dipolar couplings are highly useful NMR parameters for calculating and refining molecular structures, dynamics, and interactions. For some applications, however, it is inevitable that the preferred orientation of a molecule in an alignment medium is calculated a priori. Several methods have been developed to predict molecular orientations and residual dipolar couplings. Being beneficial for macromolecules and selected small-molecule applications, such approaches lack sufficient accuracy for a large number of organic compounds for which the fine structure and eventually the flexibility of all involved molecules have to be considered or are limited to specific, well-studied liquid crystals. We introduce a simplified model for detailed all-atom molecular dynamics calculations with a polymer strand lined up along the principal axis as a new approach to simulate the preferred orientation of small to medium-sized solutes in polymer-based, gel-type alignment media. As is shown by a first example of strychnine in a polystyrene/CDCl3 gel, the simulations potentially enable the accurate prediction of residual dipolar couplings taking into account structural details and dynamic averaging effects of both the polymer and the solute.

Stochastic dynamic simulation of the 100-kyr cycles in climate system

Based upon the stochastic resonance theory, the formation mechanism of 100-kyr cycles in climate system is numerically studied in the perspective of stochastic dynamics. In this study, firstly we combine the idealized albedo model with the geological evidence and observation in climate system to construct a new albedo model. Secondly, a bistable nonlinear system is constructed by introducing the albedo model into zero-dimensional energy balance model. Finally, based on this new system, with the solar radiation cycles and stochastic perturbation simultaneously taken into account, the variation of 100-kyr cycles is analyzed by numerical simulations. The results show that, when the noise intensity reaches a certain value, the stochastic resonance can be triggered. However, the noise intensity in this level does not exist in the actual climate system. In order to explain the formation mechanism of 100-kyr glacial-interglacial cycles forced by the weak solar radiation cycles, besides the solar radiation stochastic perturbation, the stochastic dynamic effects of the other “non-solar” radiation stochastic perturbation in the climate change processes should also be considered. The stochastic dynamic simulations taking the two types of stochastic perturbation into consideration show that, when the two types of appropriately observable stochastic perturbation are introduced, the stochastic resonance also can be generated. In this situation, the contribution rate of solar radiation stochastic perturbation is about 38%, which proves the importance of solar radiation stochastic perturbation in the formation of 100-kyr climate cycles. solar radiation, climate change, stochastic dynamics, stochastic resonance, energy balance model

Structure-affinity properties of a high-affinity ligand of FKBP12 studied by molecular simulations of a binding intermediate.

With a view to explaining the structure-affinity properties of the ligands of the protein FKBP12, we characterized a binding intermediate state between this protein and a high-affinity ligand. Indeed, the nature and extent of the intermolecular contacts developed in such a species may play a role on its stability and, hence, on the overall association rate. To find the binding intermediate, a molecular simulation protocol was used to unbind the ligand by gradually decreasing the biasing forces introduced. The intermediate was subsequently refined with 17 independent stochastic boundary molecular dynamics simulations that provide a consistent picture of the intermediate state. In this state, the core region of the ligand remains stable, notably because of the two anchoring oxygen atoms that correspond to recurrent motifs found in all FKBP12 ligand core structures. Besides, the non-core regions participate in numerous transient intermolecular and intramolecular contacts. The dynamic aspect of most of the contacts seems important both for the ligand to retain at least a part of its configurational entropy and for avoiding a trapped state along the binding pathway. Since the transient and anchoring contacts contribute to increasing the stability of the intermediate, as a corollary, the dissociation rate constant of this intermediate should be decreased, resulting in an increase of the affinity constant . The present results support our previous conclusions and provide a coherent rationale for explaining the prevalence in high-affinity ligands of (i) the two oxygen atoms found in carbonyl or sulfonyl groups of dissimilar core structures and of (ii) symmetric or pseudo-symmetric mobile groups of atoms found as non-core moieties. Another interesting aspect of the intermediate is the distortion of the flexible 80 s loop of the protein, mainly in its tip region, that promotes the accessibility to the bound state.

Hydrogen storage in heat welded random CNT network structures

The objective of this study is to investigate hydrogen storage capability of heat welded random carbon nanotube (CNT) network structures. To achieve this objective, different three-dimensional random CNT network structures are generated by using a stochastic algorithm and molecular dynamic simulations. The interaction of CNT networks with hydrogen molecules is then examined via grand canonical Monte Carlo calculations. Hydrogen adsorption capacity of CNT networks having an arbitrarily natured morphology, adjustable porous structure and large surface ratio is investigated. The results show that if cross link density of random CNT networks decreases, hydrogen storage capability of CNT networks increases in terms of the gravimetric capacity. It is observed that random CNT networks could uptake 8.85 wt.% hydrogen at 77 K and this result is very comparable with the results reported in literature where generally ideal ordered nanostructures having no topological irregularities are considered.

Optimal Integrated Strategies to Control an Invasive Weed

Although there have been numerous studies on the economics of weed control in agriculture, relatively few studies have focused on weeds in natural ecosystems. A stochastic dynamic simulation model and a stochastic dynamic programming model are developed to: (A) identify the combination of control options that is optimal for blackberry (Rubus anglocandicans) in Australian natural ecosystems, (B) assess whether an integrated control strategy is superior to chemical‐only strategies, (C) evaluate the net benefits of biological control (a rust and grazing by goats), and (D) determine how changes in model parameters affect the optimal control strategy. The results indicate that, while an integrated strategy combining chemical and nonchemical control methods may be optimal in certain circumstances, it is not necessarily superior to a chemical‐dominant strategy in all cases. The results show that grazing goats for control of blackberry can be optimal despite uncertainty about its effectiveness. Policy makers need to be aware of the trade‐offs between choosing more effective control options that may impose environmental and health risks versus less effective control strategies that are safer to the environment and human health.

Solvation free energies in [bmim]-based ionic liquids: Anion effect toward solvation of amino acid side chain analogues

Stochastic molecular dynamics simulations were performed to investigate the solvation free energy of 15 neutral amino acid side chain analogues in aqueous and five, 1-butyl-3-methylimidazolium ([BMIM])-based ionic liquids. The results in aqueous were found highly correlated with previous experimental and simulation data. Meanwhile, [BMIM]-based RTILs showed better solvation thermodynamics than water to an extent that they were capable of solvating molecules immiscible in water. Non-polar analogues showed stronger solvation in hydrophobic RTIL anions such as [PF6]− and [Tf2N]− while polar analogues showed stronger solvation in the more hydrophilic RTIL anions such as [Cl]−, [TfO]− and [BF4]−.

An ex ante analysis on the use of activity meters for automated estrus detection: To invest or not to invest?

The technical performance of activity meters for automated detection of estrus in dairy farming has been studied, and such meters are already used in practice. However, information on the economic consequences of using activity meters is lacking. The current study analyzes the economic benefits of a sensor system for detection of estrus and appraises the feasibility of an investment in such a system. A stochastic dynamic simulation model was used to simulate reproductive performance of a dairy herd. The number of cow places in this herd was fixed at 130. The model started with 130 randomly drawn cows (in a Monte Carlo process) and simulated calvings and replacement of these cows in subsequent years. Default herd characteristics were a conception rate of 50%, an 8-wk dry-off period, and an average milk production level of 8,310kg per cow per 305 d. Model inputs were derived from real farm data and expertise. For the analysis, visual detection by the farmer (“without” situation) was compared with automated detection with activity meters (“with” situation). For visual estrus detection, an estrus detection rate of 50% and a specificity of 100% were assumed. For automated estrus detection, an estrus detection rate of 80% and a specificity of 95% were assumed. The results of the cow simulation model were used to estimate the difference between the annual net cash flows in the “with” and “without” situations (marginal financial effect) and the internal rate of return (IRR) as profitability indicators. The use of activity meters led to improved estrus detection and, therefore, to a decrease in the average calving interval and subsequent increase in annual milk production. For visual estrus detection, the average calving interval was 419 d and average annual milk production was 1,032,278kg. For activity meters, the average calving interval was 403 d and the average annual milk production was 1,043,398kg. It was estimated that the initial investment in activity meters would cost €17,728 for a herd of 130 cows, with an additional cost of €90 per year for the replacement of malfunctioning activity meters. Changes in annual net cash flows arising from using an activity meter included extra revenues from increased milk production and number of calves sold, increased costs from more inseminations, calvings, and feed consumption, and reduced costs from fewer culled cows and less labor for estrus detection. These changes in cash flows were caused mainly by changes in the technical results of the simulated dairy herds, which arose from differences in the estrus detection rate and specificity between the “with” and “without” situations. The average marginal financial effect in the “with” and “without” situations was €2,827 for the baseline scenario, with an average IRR of 11%. The IRR is a measure of the return on invested capital. Investment in activity meters was generally profitable. The most influential assumptions on the profitability of this investment were the assumed culling rules and the increase in sensitivity of estrus detection between the “without” and the “with” situation.

Structure, entanglements and dynamics of polymer nanocomposites containing spherical nanoparticles

We investigate the effect of nanoparticles on polymer structure, nanoparticle dynamics and topological constraints (entanglements) in polymer melts for nanoparticle loading above percolation threshold as high as 40.9% using stochastic molecular dynamics (MD) simulations. An increase in the number of entanglements (decrease of Ne with 40.9% volume fraction of nanoparticles dispersed in the polymer matrix) in the nanocomposites is observed as evidenced by larger contour lengths of the primitive paths. Attraction between polymers and nanoparticles affects the entanglements in the nanocomposites and alters the primitive path. The diffusivity of small sized nanoparticles deviates significantly from the Stokes- Einstein relation.

Dissipative particle dynamics simulation of dilute polymer solutions—Inertial effects and hydrodynamic interactions

We examine the accuracy of dissipative particle dynamics (DPD) simulations of polymers in dilute solutions with hydrodynamic interaction (HI), at the theta point, modeled by setting the DPD conservative interaction between beads to zero. We compare the first normal-mode relaxation time extracted from the DPD simulations with theoretical predictions from a normal-mode analysis for theta chains. We characterize the influence of bead inertia within the coil by a ratio Lm/Rg, where Lm is the ballistic distance over which bead inertia is lost, and Rg is the radius of gyration of the polymer coil, while the HI strength per bead h* is determined by the ratio of bead hydrodynamic radius (rH) to the equilibrium spring length. We show how to adjust h* through the spring length and monomer mass, and how to optimize the accuracy of DPD for fixed h* by increasing the friction coefficient (γ ≥ 9) and by incorporating a nonlinear distance dependence into the frictional interaction. Even with this optimization, DPD simulations exhibit deviations of over 20% from the theoretical normal-mode predictions for high HI strength with h* ≥ 0.20, for chains with as many as 100 beads, which is a larger deviation than is found for Stochastic rotation dynamics simulations for similar chains lengths and values of h*.