Journal articles: 'Random walk numerical methods'

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Suciu, N., L. Schüler, S. Attinger, C. Vamoș, and P. Knabner. "Consistency issues in PDF methods." Analele Universitatii "Ovidius" Constanta - Seria Matematica 23, no. 3 (November 1, 2015): 187–208. http://dx.doi.org/10.1515/auom-2015-0055.

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Abstract Concentrations of chemical species transported in random environments need to be statistically characterized by probability density functions (PDF). Solutions to evolution equations for the one-point one-time PDF are usually based on systems of computational particles described by Itô equations. We establish consistency conditions relating the concentration statistics to that of the Itô process and the solution of its associated Fokker-Planck equation to that of the PDF equation. In this frame, we use a recently proposed numerical method which approximates PDFs by particle densities obtained with a global random walk (GRW) algorithm. The GRW-PDF approach is illustrated for a problem of contaminant transport in groundwater.

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HARA, TAKASHI, and GORDON SLADE. "THE LACE EXPANSION FOR SELF-AVOIDING WALK IN FIVE OR MORE DIMENSIONS." Reviews in Mathematical Physics 04, no. 02 (June 1992): 235–327. http://dx.doi.org/10.1142/s0129055x9200008x.

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This paper is a continuation of the companion paper [14], in which it was proved that the standard model of self-avoiding walk in five or more dimensions has the same critical behaviour as the simple random walk, assuming convergence of the lace expansion. In this paper we prove the convergence of the lace expansion, an upper and lower infrared bound, and a number of other estimates that were used in the companion paper. The proof requires a good upper bound on the critical point (or equivalently a lower bound on the connective constant). In an appendix, new upper bounds on the critical point in dimensions higher than two are obtained, using elementary methods which are independent of the lace expansion. The proof of convergence of the lace expansion is computer assisted. Numerical aspects of the proof, including methods for the numerical evaluation of simple random walk quantities such as the two-point function (or lattice Green function), are treated in an appendix.

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Nie, Da-Cheng, Zi-Ke Zhang, Qiang Dong, Chongjing Sun, and Yan Fu. "Information Filtering via Biased Random Walk on Coupled Social Network." Scientific World Journal 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/829137.

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The recommender systems have advanced a great deal in the past two decades. However, most researchers focus their attentions on mining the similarities among users or objects in recommender systems and overlook the social influence which plays an important role in users’ purchase process. In this paper, we design a biased random walk algorithm on coupled social networks which gives recommendation results based on both social interests and users’ preference. Numerical analyses on two real data sets,EpinionsandFriendfeed, demonstrate the improvement of recommendation performance by taking social interests into account, and experimental results show that our algorithm can alleviate the user cold-start problem more effectively compared with the mass diffusion and user-based collaborative filtering methods.

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Yang, Fan, Dongfang Liang, Xuefei Wu, and Yang Xiao. "On the application of the depth-averaged random walk method to solute transport simulations." Journal of Hydroinformatics 22, no. 1 (May 24, 2019): 33–45. http://dx.doi.org/10.2166/hydro.2019.015.

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Abstract Most numerical studies on solute mixing rely on mesh-based methods, and complicated schemes have been developed to enhance numerical stability and reduce artificial diffusion. This paper systematically studies the depth-averaged random walk scheme, which is a meshfree method with the merits of being highly robust and free of numerical diffusion. First, the model is used to solve instantaneous release problems in uniform flows. Extensive parametric studies are carried out to investigate the influences of the number of particles and the size of time steps. The predictions are shown to be independent of time steps but are sensitive to the particle numbers. Second, the model is applied to the solute transport problem along an estuary subject to extensive wetting and drying during tidal oscillations. Finally, the model is used to investigate the wind-induced chaotic mixing in a shallow basin. The effect of diffusion on the chaotic mixing is investigated. This study proposes a generic sampling method to interpret the output of the random walk method and highlights the importance of accurately taking diffusion into account in analysing the transport phenomena. The sampling technique also offers a guideline for estimating the total number of particles needed in the application.

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Nan, Tongchao, Jichun Wu, Kaixuan Li, and Jianguo Jiang. "Permeability Estimation Based on the Geometry of Pore Space via Random Walk on Grids." Geofluids 2019 (January 8, 2019): 1–10. http://dx.doi.org/10.1155/2019/9240203.

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In the literature, the mean penetration depth (MPD) calculated by “walk on spheres” or “walk on cubes” was used to quickly estimate the intrinsic permeability of digitized porous media. However, these two methods encounter difficulties such as irregular boundaries and the determination of arrivals at a boundary. In this study, an MPD method that is based on a more flexible “random walk on grid” (WOG) is explored. Moreover, the accurate MPDs for the pores of simple shapes are derived with Green’s functions to validate the WOG-based MPD. The results suggested that MPDs based on Green’s functions and WOG are consistent with each other; the factor C in the permeability expression is slightly dependent on roundness of the cross sections and is approximately 1.125 on average, according to analytical and numerical results. In a synthetic complex pore, the permeability estimated by WOG is comparable to, but greater than, the estimate based on the pore-scale dynamics simulation in COMSOL.

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Novak, Miroslav M. "Correlations in Computer Programs." Fractals 06, no. 02 (June 1998): 131–38. http://dx.doi.org/10.1142/s0218348x9800016x.

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Numerical and statistical methods are used to analyze and classify computer programs. Both computer source code and object files are examined. The results of the application of the Pearson and Spearman correlation methods to the source code are coupled with the random walk model applied to the binary code. One of the practical consequences of the analysis is the ability to quantify the degree of similarity between different computer programs and, hence, identify cases of plagiarism.

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ZHAO, XIAOJUN, JIE SUN, NA ZHANG, and PENGJIAN SHANG. "EXTREME EVENTS ANALYSIS OF NON-STATIONARY TIME SERIES BY USING HORIZONTAL VISIBILITY GRAPH." Fractals 28, no. 05 (August 2020): 2050089. http://dx.doi.org/10.1142/s0218348x20500899.

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In this paper, we analyze the extreme events of non-stationary time series in the framework of horizontal visibility graph (HVG). We give a new definition of extreme events, which incorporates the temporal structure of the series and the degree of the nodes in the HVG. An advantage of the new concept is that it does not require ad hoc treatment even when the non-stationarity arises in time series. We also use the information-theoretic methods to analyze the degree of nodes in the HVG. In the numerical analysis, we study the statistical characterizations of the extreme events of synthetic time series, including the random noises, periodic time series, random walk processes, and the long-range auto-correlated time series. Then, we study 9 time series in stock markets to identify the extreme events evolving in these non-stationary systems. Interestingly, we find that the daily closing price series perform rather close to the random walk processes, while the daily trading volume series behave quite similar to the random noises.

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Mainardi, Francesco. "On the Advent of Fractional Calculus in Econophysics via Continuous-Time Random Walk." Mathematics 8, no. 4 (April 21, 2020): 641. http://dx.doi.org/10.3390/math8040641.

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In this survey article, at first, the author describes how he was involved in the late 1990s on Econophysics, considered in those times an emerging science. Inside a group of colleagues the methods of the Fractional Calculus were developed to deal with the continuous-time random walks adopted to model the tick-by-tick dynamics of financial markets Then, the analytical results of this approach are presented pointing out the relevance of the Mittag-Leffler function. The consistence of the theoretical analysis is validated with fitting the survival probability for certain futures (BUND and BTP) traded in 1997 at LIFFE, London. Most of the theoretical and numerical results (including figures) reported in this paper were presented by the author at the first Nikkei symposium on Econophysics, held in Tokyo on November 2000 under the title “Empirical Science of Financial Fluctuations” on behalf of his colleagues and published by Springer. The author acknowledges Springer for the license permission of re-using this material.

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Burmeister, Louis C. "The Effect of Space-Dependent Thermal Conductivity on the Steady Central Temperature of a Cylinder." Journal of Heat Transfer 124, no. 1 (July 10, 2001): 195–97. http://dx.doi.org/10.1115/1.1418701.

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A transformation is presented that enables the center temperature of a cylinder to be expressed in terms of an integral of the peripheral temperature distribution for heat conduction with space-dependent thermal conductivity. Its predictions agree with exact answers and with numerical solutions obtained with finite difference methods for four test cases. The new result can be applied to a two-dimensional floating random-walk Monte Carlo procedure which previously was restricted to the case of constant thermal conductivity.

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Wang, Jingnan, and Ralf Korn. "Numerical Algorithms for Reflected Anticipated Backward Stochastic Differential Equations with Two Obstacles and Default Risk." Risks 8, no. 3 (July 1, 2020): 72. http://dx.doi.org/10.3390/risks8030072.

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We study numerical algorithms for reflected anticipated backward stochastic differential equations (RABSDEs) driven by a Brownian motion and a mutually independent martingale in a defaultable setting. The generator of a RABSDE includes the present and future values of the solution. We introduce two main algorithms, a discrete penalization scheme and a discrete reflected scheme basing on a random walk approximation of the Brownian motion as well as a discrete approximation of the default martingale, and we study these two methods in both the implicit and explicit versions respectively. We give the convergence results of the algorithms, provide a numerical example and an application in American game options in order to illustrate the performance of the algorithms.

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BESKOS, ALEXANDROS, GARETH ROBERTS, ANDREW STUART, and JOCHEN VOSS. "MCMC METHODS FOR DIFFUSION BRIDGES." Stochastics and Dynamics 08, no. 03 (September 2008): 319–50. http://dx.doi.org/10.1142/s0219493708002378.

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We present and study a Langevin MCMC approach for sampling nonlinear diffusion bridges. The method is based on recent theory concerning stochastic partial differential equations (SPDEs) reversible with respect to the target bridge, derived by applying the Langevin idea on the bridge pathspace. In the process, a Random-Walk Metropolis algorithm and an Independence Sampler are also obtained. The novel algorithmic idea of the paper is that proposed moves for the MCMC algorithm are determined by discretising the SPDEs in the time direction using an implicit scheme, parametrised by θ ∈ [0,1]. We show that the resulting infinite-dimensional MCMC sampler is well-defined only if θ = 1/2, when the MCMC proposals have the correct quadratic variation. Previous Langevin-based MCMC methods used explicit schemes, corresponding to θ = 0. The significance of the choice θ = 1/2 is inherited by the finite-dimensional approximation of the algorithm used in practice. We present numerical results illustrating the phenomenon and the theory that explains it. Diffusion bridges (with additive noise) are representative of the family of laws defined as a change of measure from Gaussian distributions on arbitrary separable Hilbert spaces; the analysis in this paper can be readily extended to target laws from this family and an example from signal processing illustrates this fact.

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Wang, M., ZB Sun, BC Zhang, ZX Pang, and DW Jiang. "A Dai–Yuan conjugate gradient algorithm of linear equation constrained optimization approach for optimal robust controller of bipedal robots." International Journal of Advanced Robotic Systems 17, no. 1 (January 1, 2020): 172988141989017. http://dx.doi.org/10.1177/1729881419890178.

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In this article, combined rapidly exponential control Lyapunov function with hybrid zero dynamics, a sufficiently descent projected Dai–Yuan approach is proposed, investigated, and analyzed for online solving optimal robust control problems with linear equation constraints of bipedal robots. Moreover, a new approach is developed for designing optimal robust controller. To demonstrate the effectiveness and feasibility of the proposed method, we will conduct numerical simulations on the model of three-link robot with nonlinear, impulsive, and under-actuated dynamics. Numerical results show that the bipedal robot can walk effectively and stability on the ground though the optimal robust controller when the parameters of the hybrid system model are disturbed three times. Furthermore, under the random noise condition, the bipedal robot can walk stably and effectively through online computing the nonlinear optimization problem for optimal robust controller. In addition, some classical control methods are compared with the developed approach in this article, numerical results are reported and analyzed to substantiate the feasibility and superiority of the proposed method for linear equation constrained optimization problem. Last, this article develops a systematic approach on exploiting optimal robust control technique to design hybrid system models for robustly and accurately via online solving linear equation constrained optimization problems.

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Jiang, Yan, Chi-Wang Shu, and Mengping Zhang. "High-order finite difference WENO schemes with positivity-preserving limiter for correlated random walk with density-dependent turning rates." Mathematical Models and Methods in Applied Sciences 25, no. 08 (April 28, 2015): 1553–88. http://dx.doi.org/10.1142/s0218202515500414.

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In this paper, we discuss high-order finite difference weighted essentially non-oscillatory schemes, coupled with total variation diminishing (TVD) Runge–Kutta (RK) temporal integration, for solving the semilinear hyperbolic system of a correlated random walk model describing movement of animals and cells in biology. Since the solutions to this system are non-negative, we discuss a positivity-preserving limiter without compromising accuracy. Analysis is performed to justify the maintenance of third-order spatial/temporal accuracy when the limiters are applied to a third-order finite difference scheme and third-order TVD-RK time discretization for solving this model. Numerical results are also provided to demonstrate these methods up to fifth-order accuracy.

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Zheng, Zhongtuan, Gaoxi Xiao, Guoqiang Wang, Guanglin Zhang, and Kaizhong Jiang. "Mean First Passage Time of Preferential Random Walks on Complex Networks with Applications." Mathematical Problems in Engineering 2017 (2017): 1–14. http://dx.doi.org/10.1155/2017/8217361.

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This paper investigates, both theoretically and numerically, preferential random walks (PRW) on weighted complex networks. By using two different analytical methods, two exact expressions are derived for the mean first passage time (MFPT) between two nodes. On one hand, the MFPT is got explicitly in terms of the eigenvalues and eigenvectors of a matrix associated with the transition matrix of PRW. On the other hand, the center-product-degree (CPD) is introduced as one measure of node strength and it plays a main role in determining the scaling of the MFPT for the PRW. Comparative studies are also performed on PRW and simple random walks (SRW). Numerical simulations of random walks on paradigmatic network models confirm analytical predictions and deepen discussions in different aspects. The work may provide a comprehensive approach for exploring random walks on complex networks, especially biased random walks, which may also help to better understand and tackle some practical problems such as search and routing on networks.

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Montanaro, Ashley. "Quantum speedup of Monte Carlo methods." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2181 (September 2015): 20150301. http://dx.doi.org/10.1098/rspa.2015.0301.

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Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently.

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Ma, Weiyuan, Changpin Li, and Jingwei Deng. "Synchronization in Tempered Fractional Complex Networks via Auxiliary System Approach." Complexity 2019 (November 25, 2019): 1–12. http://dx.doi.org/10.1155/2019/6071412.

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In the famous continuous time random walk (CTRW) model, because of the finite lifetime of biological particles, it is sometimes necessary to temper the power law measure such that the waiting time measure has a convergent first moment. The CTRW model with tempered waiting time measure is the so-called tempered fractional derivative. In this article, we introduce the tempered fractional derivative into complex networks to describe the finite life span or bounded physical space of nodes. Some properties of the tempered fractional derivative and tempered fractional systems are discussed. Generalized synchronization in two-layer tempered fractional complex networks via pinning control is addressed based on the auxiliary system approach. The results of the proposed theory are used to derive a sufficient condition for achieving generalized synchronization of tempered fractional networks. Numerical simulations are presented to illustrate the effectiveness of the methods.

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Barkovsky, Eugene Aleksandrovich, Anna Aleksandrovna Lazutina, and Andrew Vladimirovich Sokolov. "The Optimal Control of Two Work-Stealing Deques, Moving One After Another in a Shared Memory." Program Systems: Theory and Applications 10, no. 1 (2019): 19–32. http://dx.doi.org/10.25209/2079-3316-2019-10-1-19-32.

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In the parallel work-stealing load balancers, each core owns personal buffer of tasks called deque. One end of the deque is used by its owner to add and retrieve tasks, while the second end is used by other cores to steal tasks. In the paper two representation methods of deques are analyzed: partitioned serial cyclic representation of deques (one of the conventional techniques); and the new approach proposed by our team, without partition of shared memory in advance between deques moving one after another in a circle. Previously we analyzed these methods for representing FIFO queues in network applications, where the “One after another” way gave the best result for some values of the system parameters. Purpose of this research is to construct and analyze models of the process of work with two circular deques located in shared memory, where they movie one after another in a circle. The mathematical model is constructed in the form of a random walk by integer points in the pyramid. The simulation model is constructed using the Monte Carlo method. The used work-stealing strategy is stealing of one element. We propose the mathematical and simulation models of this process and carry out numerical experiments.

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Boluh, Kateryna, and Natalija Shchestyuk. "Simulating Stochastic Diffusion Processes and Processes with “Market” Time." Mohyla Mathematical Journal 3 (January 29, 2021): 25–30. http://dx.doi.org/10.18523/2617-70803202025-30.

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The paper focuses on modelling, simulation techniques and numerical methods concerned stochastic processes in subject such as financial mathematics and financial engineering. The main result of this work is simulation of a stochastic process with new market active time using Monte Carlo techniques.The processes with market time is a new vision of how stock price behavior can be modeled so that the nature of the process is more real. The iterative scheme for computer modelling of this process was proposed.It includes the modeling of diffusion processes with a given marginal inverse gamma distribution. Graphs of simulation of the Ornstein-Uhlenbeck random walk for different parameters, a simulation of the diffusion process with a gamma-inverse distribution and simulation of the process with market active time are presented.To simulate stochastic processes, an iterative scheme was used: xk+1 = xk + a(xk, tk) ∆t + b(xk, tk) √ (∆t) εk,, where εk each time a new generation with a normal random number distribution.Next, the tools of programming languages for generating random numbers (evenly distributed, normally distributed) are investigated. Simulation (simulation) of stochastic diffusion processes is carried out; calculation errors and acceleration of convergence are calculated, Euler and Milstein schemes. At the next stage, diffusion processes with a given distribution function, namely with an inverse gamma distribution, were modelled. The final stage was the modelling of stock prices with a new "market" time, the growth of which is a diffusion process with inverse gamma distribution. In the proposed iterative scheme of stock prices, we use the modelling of market time gains as diffusion processes with a given marginal gamma-inverse distribution.The errors of calculations are evaluated using the Milstein scheme. The programmed model can be used to predict future values of time series and for option pricing.

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Górska, Karolina, Zbigniew Muszyński, and Jarosław Rybak. "DISPLACEMENT MONITORING AND SENSITIVITY ANALYSIS IN THE OBSERVATIONAL METHOD." Studia Geotechnica et Mechanica 35, no. 3 (September 1, 2013): 25–43. http://dx.doi.org/10.2478/sgem-2013-0028.

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Abstract This work discusses the fundamentals of designing deep excavation support by means of observational method. The effective tools for optimum designing with the use of the observational method are both inclinometric and geodetic monitoring, which provide data for the systematically updated calibration of the numerical computational model. The analysis included methods for selecting data for the design (by choosing the basic random variables), as well as methods for an on-going verification of the results of numeric calculations (e.g., MES) by way of measuring the structure displacement using geodetic and inclinometric techniques. The presented example shows the sensitivity analysis of the calculation model for a cantilever wall in non-cohesive soil; that analysis makes it possible to select the data to be later subject to calibration. The paper presents the results of measurements of a sheet pile wall displacement, carried out by means of inclinometric method and, simultaneously, two geodetic methods, successively with the deepening of the excavation. This work includes also critical comments regarding the usefulness of the obtained data, as well as practical aspects of taking measurement in the conditions of on-going construction works.

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Xue, Pengfei, David Schwab, Xing Zhou, Chenfu Huang, Ryan Kibler, and Xinyu Ye. "A Hybrid Lagrangian–Eulerian Particle Model for Ecosystem Simulation." Journal of Marine Science and Engineering 6, no. 4 (September 26, 2018): 109. http://dx.doi.org/10.3390/jmse6040109.

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Current numerical methods for simulating biophysical processes in aquatic environments are typically constructed in a grid-based Eulerian framework or as an individual-based model in a particle-based Lagrangian framework. Often, the biogeochemical processes and physical (hydrodynamic) processes occur at different time and space scales, and changes in biological processes do not affect the hydrodynamic conditions. Therefore, it is possible to develop an alternative strategy to grid-based approaches for linking hydrodynamic and biogeochemical models that can significantly improve computational efficiency for this type of linked biophysical model. In this work, we utilize a new technique that links hydrodynamic effects and biological processes through a property-carrying particle model (PCPM) in a Lagrangian/Eulerian framework. The model is tested in idealized cases and its utility is demonstrated in a practical application to Sandusky Bay. Results show the integration of Lagrangian and Eulerian approaches allows for a natural coupling of mass transport (represented by particle movements and random walk) and biological processes in water columns which is described by a nutrient-phytoplankton-zooplankton-detritus (NPZD) biological model. This method is far more efficient than traditional tracer-based Eulerian biophysical models for 3-D simulation, particularly for a large domain and/or ensemble simulations.

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BAKE, S., D. G. W. MEYER, and U. RIST. "Turbulence mechanism in Klebanoff transition: a quantitative comparison of experiment and direct numerical simulation." Journal of Fluid Mechanics 459 (May 25, 2002): 217–43. http://dx.doi.org/10.1017/s0022112002007954.

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The mechanism of turbulence development in periodic Klebanoff transition in a boundary layer has been studied experimentally and in a direct numerical simulation (DNS) with controlled disturbance excitation. In order to compare the results quantitatively, the flow parameters were matched in both methods, thus providing complementary data with which the origin of turbulence in the transition process could be explained. Good agreement was found for the development of the amplitude and shape of typical disturbance structures, the Λ-vortices, including the development of ring-like vortices and spikes in the time traces. The origin and the spatial development of random velocity perturbations were measured in the experiment, and are shown together with the evolution of local high-shear layers. Since the DNS is capable of providing the complete velocity and vorticity fields, further conclusions are drawn based on the numerical data. The mechanisms involved in the flow randomization process are presented in detail. It is shown how the random perturbations which initially develop at the spike-positions in the outer part of the boundary layer influence the flow randomization process close to the wall. As an additional effect, the interaction of vortical structures and high-shear layers of different disturbance periods was found to be responsible for accelerating the transition to a fully developed turbulent flow. These interactions lead to a rapid intensification of a high-shear layer very close to the wall that quickly breaks down because of the modulation it experiences through interactions with vortex structures from the outer part of the boundary layer. The final breakdown process will be shown to be dominated by locally appearing vortical structures and shear layers.

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Wang, Gai-Ge, Amir Hossein Gandomi, Xin-She Yang, and Amir Hossein Alavi. "A novel improved accelerated particle swarm optimization algorithm for global numerical optimization." Engineering Computations 31, no. 7 (September 30, 2014): 1198–220. http://dx.doi.org/10.1108/ec-10-2012-0232.

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Purpose – Meta-heuristic algorithms are efficient in achieving the optimal solution for engineering problems. Hybridization of different algorithms may enhance the quality of the solutions and improve the efficiency of the algorithms. The purpose of this paper is to propose a novel, robust hybrid meta-heuristic optimization approach by adding differential evolution (DE) mutation operator to the accelerated particle swarm optimization (APSO) algorithm to solve numerical optimization problems. Design/methodology/approach – The improvement includes the addition of DE mutation operator to the APSO updating equations so as to speed up convergence. Findings – A new optimization method is proposed by introducing DE-type mutation into APSO, and the hybrid algorithm is called differential evolution accelerated particle swarm optimization (DPSO). The difference between DPSO and APSO is that the mutation operator is employed to fine-tune the newly generated solution for each particle, rather than random walks used in APSO. Originality/value – A novel hybrid method is proposed and used to optimize 51 functions. It is compared with other methods to show its effectiveness. The effect of the DPSO parameters on convergence and performance is also studied and analyzed by detailed parameter sensitivity studies.

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Fang, Ren, Qin Zhaohong, Zhang Zhong, Liu Zhenhao, Yuan Kai, and Wei Long. "Modeling and dynamic environment analysis technology for spacecraft." International Journal of Computational Materials Science and Engineering 07, no. 01n02 (June 2018): 1850007. http://dx.doi.org/10.1142/s2047684118500070.

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Spacecraft sustains complex and severe vibrations and acoustic environments during flight. Predicting the resulting structures, including numerical predictions of fluctuating pressure, updating models and random vibration and acoustic analysis, plays an important role during the design, manufacture and ground testing of spacecraft. In this paper, Monotony Integrative Large Eddy Simulation (MILES) is introduced to predict the fluctuating pressure of the fairing. The exact flow structures of the fairing wall surface under different Mach numbers are obtained, then a spacecraft model is constructed using the finite element method (FEM). According to the modal test data, the model is updated by the penalty method. On this basis, the random vibration and acoustic responses of the fairing and satellite are analyzed by different methods. The simulated results agree well with the experimental ones, which shows the validity of the modeling and dynamic environment analysis technology. This information can better support test planning, defining test conditions and designing optimal structures.

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Gao, Yu, and Zikai Wu. "Controlling the trapping efficiency in a family of scale-free tree networks." International Journal of Modern Physics B 32, no. 21 (August 6, 2018): 1850224. http://dx.doi.org/10.1142/s0217979218502247.

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Efficiently controlling the trapping process is very significant in the study of trapping problem in diverse dynamic processes. In this paper, we explore the trapping efficiency on a family of scale-free tree networks with a deep trap positioned at an initial node, which is controlled by three different strategies. In the first technique, the transition probability is modified by an edge weight parameter. In the second method, the transition probability is controlled by a delay parameter. In the third approach, we use the delay parameter and weight parameter simultaneously to control the trapping process. For all the three control methods, the analytical results of average trapping time (ATT) exactly agree with the numerical results. The result of the first control strategy shows that the average trapping time can scale sublinearly, linearly or superlinearly by modifying the weight parameter. The analytic expression of the ATT in the second method shows that the delay parameter can only modify the main coefficient of ATT, but cannot change the dominant behavior of trapping efficiency. The explicit expression of average trapping time when random walk on scale-free tree network is controlled by the third method shows that it is a fine control. We can get desired trapping efficiency by changing the weight parameter and the delay parameter simultaneously. This work provides a better understanding of controlling the trapping process in a family of scale-free tree networks.

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Sun, Chang Ning, Jing Cao, Hai Ming Liu, and Hui Min Zhao. "Reliability Analysis of Foundation Pit Based on Response Surface of Support Vector Machine." Advanced Materials Research 671-674 (March 2013): 240–44. http://dx.doi.org/10.4028/www.scientific.net/amr.671-674.240.

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Traditional analysis methods of reliability in the foundation pit engineering have larger error and larger amount of calculation. Therefore, the response surface method has attracted much attention because it can effectively use the finite element analysis method (FEAM) and reduce the number of the numerical simulation. This paper combines uniform design (UD) with support vector machine (SVM). On this base, a reliability analysis method of the foundation pit is put forward based on the response surface of support vector machine (RSSVM). The UD structures random samples and the FEAM is used to obtain corresponding response parameters including the lateral displacement of wall, settlement of ground, safety factor of overall stability and safety factor of against overturning. Then, SVM trains the above random samples and corresponding response parameters to get response surface (RS) respectively. The probability density distribution of each response parameter is obtained by combining the Monte Carlo method with RSSVM. The instance analysis shows that the method has high computing efficiency and less amount of calculation, and the result is reasonable. It provides an effective way for the reliability analysis of the foundation pit engineering.

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Toumelin, Emmanuel, Carlos Torres-Verdin, Boqin Sun, and Keh-Jim Dunn. "Limits of 2D NMR Interpretation Techniques to Quantify Pore Size, Wettability, and Fluid Type: A Numerical Sensitivity Study." SPE Journal 11, no. 03 (September 1, 2006): 354–63. http://dx.doi.org/10.2118/90539-pa.

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Summary Two-dimensional (2D) NMR techniques have been proposed as efficient methods to infer a variety of petrophysical parameters, including mixed fluid saturation, in-situ oil viscosity, wettability, and pore structure. However, no study has been presented to quantify the petrophysical limitations of such methods. We address this problem by introducing a pore-scale framework to accurately simulate suites of NMR measurements acquired in complex rock/fluid models. The general pore-scale framework considered in this paper is based on NMR random walks for multiphase fluid diffusion and relaxations, combined with Kovscek's pore-scale model for two-phase fluid saturation and wettability alteration. We use standard 2D NMR methods to interpret synthetic data sets for diverse petrophysical configurations, including two-phase saturations with different oil grades, mixed wettability, or carbonate pore heterogeneity. Results from our study indicate that for both water-wet and mixed-wet rocks, T2 (transverse relaxation)/D (diffusion) maps are reliable for fluid typing without the need for independently determined cutoffs. However, significant uncertainty exists in the estimation of fluid type, wettability, and pore structure with 2D NMR methods in cases of mixed-wettability states. Only light oil wettability can be reliably detected with 2D NMR interpretation methods. Diffusion coupling in carbonate rocks introduces additional problems that cannot be circumvented with current 2D NMR techniques. Introduction Wettability state and oil viscosity can play a significant role in the NMR response of saturated rocks. This property of NMR measurements has been discussed in recent papers (Freedman et al. 2003) for particular examples of rock systems. However, to date, no systematic study has been published of the reliability and accuracy of NMR methods to assess fluid viscosity and wettability, including cases of mixed wettability. This paper quantifies the sensitivity of 2D relaxation/diffusion NMR techniques to mixed wettability and fluid viscosity in generic rock models. Given that measurements are often made on rock samples with uncertain petrophysical properties and therefore uncertain corresponding measurement contributions, the work described in this paper is based on the numerical simulation of pore-scale systems. We introduce a general numerical model that simultaneously includes immiscible fluid viscosities, water or mixed wettability, variable fluid saturations and history, and disordered complexity of rock structure. Geometrical fluid distributions at the pore scale were considered a function of pore size, saturation history, and wettability following Kovscek et al.'s model of mixed-oil-wet rocks (1993). We simulated suites of NMR measurements with random walkers within these pore-scale geometries, and subsequently inverted into relaxation/diffusion NMR maps. The objective of this paper is to assess the accuracy of 2D NMR interpretation techniques to detect fluid and wettability types, and to quantify pore-size distributions. The first section of the paper summarizes the principles and limitations of current NMR petrophysical interpretation. We then summarize our pore-scale modeling procedure, its assumptions, and limitations. Subsequent sections analyze simulation results obtained for drainage and imbibition involving water-wettability and mixed-oil-wettability with partial saturations of water and different hydrocarbon types in a generic clay-free rock model. Next, we consider the case of coupled carbonate rocks with emphasis on the assessment of wettability and microporosity.

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Rottman, James W., John E. Simpson, and Peter K. Stansby. "The motion of a cylinder of fluid released from rest in a cross-flow." Journal of Fluid Mechanics 177 (April 1987): 307–37. http://dx.doi.org/10.1017/s0022112087000971.

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The two-dimensional motion of a cylinder of fluid released from rest into a flow that is uniform far upstream of the cylinder is studied. We consider cases where the cylinder is initially of circular cross-section and the fluid is either inviscid or viscous. For the inviscid fluid, we use analytical methods to determine the motion for small and large times after release and three numerical methods, the vortex-sheet method, the vortex-blob method and the vortex-in-cell method, to determine the intermediate-time motion. For the viscous-fluid problem we use the vortex-in-cell method with random walks to compute both the initial flow around the cylinder and the motion of the released fluid at a Reynolds number of 484. In the inviscid case, the released fluid deforms into a structure that resembles a vortex pair that propagates down stream at a speed less than the onset flow speed. In the viscous case, after a wake representative of a Kármán vortex street has developed, the released fluid usually deforms into an elongated horseshoe shape that travels downstream at a speed greater or less than the incident flow speed (depending on when in the vortex-shedding cycle the cylinder is released). The results of the numerical calculations are compared with some simple experiments in a water channel.

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Liu, Feng, Yuchao Yang, and Feng Xi. "Tensile Fracture Behavior of Corroded Pipelines: Part 2—Numerical Simulation Based on Monte Carlo Method." Advances in Materials Science and Engineering 2020 (April 4, 2020): 1–16. http://dx.doi.org/10.1155/2020/5708969.

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The experimental part in this companion paper revealed that the macroscopic mechanical performance of corroded pipes follows a decreasing trend with the increasing corrosion rate. Inspired by the surface topology by scanning electronic microscopy (SEM) and the scattered distribution of test data, a computational procedure based on the Monte Carlo simulation method was developed in this paper to understand the randomness of the crack propagation process and the performance degradation mechanism of the corroded pipelines. A total of 2700 random samples, which contain three corrosion rates of 15%, 45%, and 70% with each corrosion rate having three variances of 0.02 mm, 0.06 mm, and 0.10 mm, were generated and then were mapped to the shell section of the FE model. In the application of the material model considering the damage, a series of “numerical” tensile experiments were carried out. The simulation analysis indicated that the corrosion rate and the standard variance of the thickness collaboratively dominated the mechanical performance of the corroded specimen. Under the same standard deviation, the wall corresponding to the higher corrosion rate is more likely to cause stress concentration in the weak position, which makes the pipe more prone to fail. Furthermore, under the same corrosion rate, the increase of the standard deviation will aggravate the unevenness of the wall thickness distribution, and then the lower tensile load will cause damage at weak locations and lead to randomness of the crack propagation path, thereby reducing the pipe’s macroscopic strength and fracture strain. The analytical methods in this paper have the potential of being a useful tool for structural reliability assessments of aged pipelines and the full life cycle design of new pipeline networks.

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Corcioli, Alaís Camargo, Bruna Varanda Pessoa-Santos, Glaucia Nency Takara, Valéria Amorim Pires Di Lorenzo, and Mauricio Jamami. "Reported dyspnea and fatigue using different scales during the physical effort in COPD." Fisioterapia em Movimento 30, no. 2 (April 2017): 207–17. http://dx.doi.org/10.1590/1980-5918.030.002.ao01.

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Abstract Introduction: Therapy choice and its progression for patients with Chronic Obstructive Pulmonary Disease (COPD) should be based on their symptoms and clinical condition according to reports of dyspnea and fatigue. Therefore patient-reported scales have presented a key role during the communication with the patient. Objective: To verify if patients with COPD prefer the Modified Borg Scale (MBS), Visual Analogue Scale (VAS), Glasses Scale (GS), Faces Scale (FS) or Ratings of Perceived Exertion (RPE) during the six-minute walk test(6MWT), and to compare and correlate the scales with each other, with peripheral oxygen saturation (SpO2) and heart rate (HR). Methods: 28 patients with COPD (50% had mild to moderate COPD and 50% had severe to very severe) were evaluated by a respiratory and cognitive assessment. Additionally, they performed the 6MWT, in which the scales were applied simultaneously (random order) and patients reported their preference in the end of the test. Results: 57% of patients were illiterate or presented incomplete primary education and most of them (67%) chose the FS or GS. Significant positive correlations were observed between instruments for both dyspnea and fatigue in the end of the 6MWT, which the strongest was between MBS and FS (r = 0.95). Nevertheless, there was no correlation between the scales and SpO2 and HR. Conclusion: As the majority of patients preferred pictured to numerical scales we suggest their use as a resource for therapeutic evaluation; MBS might be replace by FS, even though they have different scores and not scaled proportionally. However, this change must be carefully considered because there is the risk of dubious interpretation.

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Budaev, B. V., and D. B. Bogy. "Random walk methods and wave diffraction." International Journal of Solids and Structures 39, no. 21-22 (October 2002): 5547–70. http://dx.doi.org/10.1016/s0020-7683(02)00364-5.

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Anta, Juan A. "Random walk numerical simulation for solar cell applications." Energy & Environmental Science 2, no. 4 (2009): 387. http://dx.doi.org/10.1039/b819979e.

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Qiu, Zirou, Ruslan Shaydulin, Xiaoyuan Liu, Yuri Alexeev, Christopher S. Henry, and Ilya Safro. "ELRUNA." ACM Journal of Experimental Algorithmics 26 (July 8, 2021): 1–32. http://dx.doi.org/10.1145/3450703.

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Networks model a variety of complex phenomena across different domains. In many applications, one of the most essential tasks is to align two or more networks to infer the similarities between cross-network vertices and to discover potential node-level correspondence. In this article, we propose ELRUNA ( el imination ru le-based n etwork a lignment), a novel network alignment algorithm that relies exclusively on the underlying graph structure. Under the guidance of the elimination rules that we defined, ELRUNA computes the similarity between a pair of cross-network vertices iteratively by accumulating the similarities between their selected neighbors. The resulting cross-network similarity matrix is then used to infer a permutation matrix that encodes the final alignment of cross-network vertices. In addition to the novel alignment algorithm, we improve the performance of local search , a commonly used postprocessing step for solving the network alignment problem, by introducing a novel selection method RAWSEM ( ra ndom- w alk-based se lection m ethod) based on the propagation of vertices’ mismatching across the networks. The key idea is to pass on the initial levels of mismatching of vertices throughout the entire network in a random-walk fashion. Through extensive numerical experiments on real networks, we demonstrate that ELRUNA significantly outperforms the state-of-the-art alignment methods in terms of alignment accuracy under lower or comparable running time. Moreover, ELRUNA is robust to network perturbations such that it can maintain a close-to-optimal objective value under a high level of noise added to the original networks. Finally, the proposed RAWSEM can further improve the alignment quality with a smaller number of iterations compared with the naive local search method. Reproducibility : The source code and data are available at https://tinyurl.com/uwn35an.

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Zhu, Pingping, Silvia Ferrari, Julian Morelli, Richard Linares, and Bryce Doerr. "Scalable Gas Sensing, Mapping, and Path Planning via Decentralized Hilbert Maps." Sensors 19, no. 7 (March 28, 2019): 1524. http://dx.doi.org/10.3390/s19071524.

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This paper develops a decentralized approach to gas distribution mapping (GDM) and information-driven path planning for large-scale distributed sensing systems. Gas mapping is performed using a probabilistic representation known as a Hilbert map, which formulates the mapping problem as a multi-class classification task and uses kernel logistic regression to train a discriminative classifier online. A novel Hilbert map information fusion method is presented for rapidly merging the information from individual robot maps using limited data communication. A communication strategy that implements data fusion among many robots is also presented for the decentralized computation of GDMs. New entropy-based information-driven path-planning methods are developed and compared to existing approaches, such as particle swarm optimization (PSO) and random walks (RW). Numerical experiments conducted in simulated indoor and outdoor environments show that the information-driven approaches proposed in this paper far outperform other approaches, and avoid mutual collisions in real time.

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Shao, Sihong, and Yunfeng Xiong. "Branching Random Walk Solutions to the Wigner Equation." SIAM Journal on Numerical Analysis 58, no. 5 (January 2020): 2589–608. http://dx.doi.org/10.1137/19m1272408.

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Zou, Gang, and Robert D. Skeel. "Robust Variance Reduction for Random Walk Methods." SIAM Journal on Scientific Computing 25, no. 6 (January 2004): 1964–81. http://dx.doi.org/10.1137/s1064827503424025.

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Goodman, Jonathan, and Neal Madras. "Random-walk interpretations of classical iteration methods." Linear Algebra and its Applications 216 (February 1995): 61–79. http://dx.doi.org/10.1016/0024-3795(93)00101-5.

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LI, KEQIN. "PERFORMANCE ANALYSIS AND EVALUATION OF RANDOM WALK ALGORITHMS ON WIRELESS NETWORKS." International Journal of Foundations of Computer Science 23, no. 04 (June 2012): 779–802. http://dx.doi.org/10.1142/s0129054112400369.

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We propose a model of dynamically evolving random networks and give an analytical result of the cover time of the simple random walk algorithm on a dynamic random symmetric planar point graph. Our dynamic network model considers random node distribution and random node mobility. We analyze the cover time of the parallel random walk algorithm on a complete network and show by numerical data that k parallel random walks reduce the cover time by almost a factor of k. We present simulation results for four random walk algorithms on random asymmetric planar point graphs. These algorithms include the simple random walk algorithm, the intelligent random walk algorithm, the parallel random walk algorithm, and the parallel intelligent random walk algorithm. Our random network model considers random node distribution and random battery transmission power. Performance measures include normalized cover time, probability distribution of the length of random walks, and load distribution.

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Castro, Isabel, and Carlos G. Pacheco. "Modeling and pricing with a random walk in random environment." International Journal of Financial Engineering 07, no. 04 (December 2020): 2050053. http://dx.doi.org/10.1142/s242478632050053x.

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We propose a parsimonious model for financial pricing that incorporates the existence of a random environment; such construction can be though as an extension of the Cox–Ross–Rubinstein (CRR) model. Our model is motivated from the Sinai random walk, but we mention the difficulty of applying such model if we try to use it with the CRR procedure. As it was done with Sinai’s walk, we provide a method to connect the most visited sites of the model with the minimum points of a function of the environment. We present some simulations and a numerical experiment to bring a new perspective.

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Klimenko, Lyudmila S., and Boris S. Maryshev. "Numerical simulation of microchannel blockage by the random walk method." Chemical Engineering Journal 381 (February 2020): 122644. http://dx.doi.org/10.1016/j.cej.2019.122644.

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Coulibaly, Ibrahim, and Christian Lécot. "Simulation of diffusion using quasi-random walk methods." Mathematics and Computers in Simulation 47, no. 2-5 (August 1998): 153–63. http://dx.doi.org/10.1016/s0378-4754(98)00100-1.

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Budaev, Bair, and David Bogy. "Application of random walk methods to wave propagation." Journal of the Acoustical Society of America 108, no. 5 (November 2000): 2593. http://dx.doi.org/10.1121/1.4743647.

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Budaev, B. V. "Application of Random Walk Methods to Wave Propagation." Quarterly Journal of Mechanics and Applied Mathematics 55, no. 2 (May 1, 2002): 209–26. http://dx.doi.org/10.1093/qjmam/55.2.209.

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Joshi, J. M. C. "Random walk over a hypersphere." International Journal of Mathematics and Mathematical Sciences 8, no. 4 (1985): 683–88. http://dx.doi.org/10.1155/s0161171285000758.

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In a recent paper the author had shown that a special case of S. M. Joshi transform (so named after the author's reverent father) of distributions(Sba f)(x)=〈f(y), lFl(a0;b0;ixy) lFl(a;b;−2ixy)〉is a characteristic function of a spherical distribution. Using the methods developed in that paper; the problem of distribution of the distanceCD, whereCandDare points niformly distributed in a hypersphere, has been discussed in the present paper. The form of characteristic function has also been obtained by the method of projected distribution. A generalization of Hammersley's result has also been developed. The main purpose of the paper is to show that although the use of characteristic functions, using the method of Bochner, is available in problems of random walk yet distributional S. M. Joshi transform can be used as a natural tool has been proved for the first time in the paper.

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El-Hadidy, Mohamed Abd Allah, and Hamdy M. Abou-Gabal. "Coordinated Search for a Random Walk Target Motion." Fluctuation and Noise Letters 17, no. 01 (January 23, 2018): 1850002. http://dx.doi.org/10.1142/s0219477518500025.

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This paper presents the cooperation between two searchers at the origin to find a Random Walk moving target on the real line. No information is not available about the target’s position all the time. Rather than finding the conditions that make the expected value of the first meeting time between one of the searchers and the target is finite, we show the existence of the optimal search strategy which minimizes this first meeting time. The effectiveness of this model is illustrated using a numerical example.

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Xiong, Hui, Liya Yao, Huachun Tan, and Wuhong Wang. "Pedestrian Walking Behavior Revealed through a Random Walk Model." Discrete Dynamics in Nature and Society 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/405907.

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This paper applies method of continuous-time random walks for pedestrian flow simulation. In the model, pedestrians can walk forward or backward and turn left or right if there is no block. Velocities of pedestrian flow moving forward or diffusing are dominated by coefficients. The waiting time preceding each jump is assumed to follow an exponential distribution. To solve the model, a second-order two-dimensional partial differential equation, a high-order compact scheme with the alternating direction implicit method, is employed. In the numerical experiments, the walking domain of the first one is two-dimensional with two entrances and one exit, and that of the second one is two-dimensional with one entrance and one exit. The flows in both scenarios are one way. Numerical results show that the model can be used for pedestrian flow simulation.

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Mandujano-Ramírez, Humberto J., José P. González-Vázquez, Gerko Oskam, Thomas Dittrich, Germa Garcia-Belmonte, Iván Mora-Seró, Juan Bisquert, and Juan A. Anta. "Charge separation at disordered semiconductor heterojunctions from random walk numerical simulations." Physical Chemistry Chemical Physics 16, no. 9 (2014): 4082. http://dx.doi.org/10.1039/c3cp54237h.

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Muñoz, Ana I., and J. Ignacio Tello. "Numerical resolution of a reinforced random walk model arising in haptotaxis." Applied Mathematics and Computation 256 (April 2015): 415–24. http://dx.doi.org/10.1016/j.amc.2015.01.043.

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Dimov, I., and O. Tonev. "Random walk on distant mesh points Monte Carlo methods." Journal of Statistical Physics 70, no. 5-6 (March 1993): 1333–42. http://dx.doi.org/10.1007/bf01049435.

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Ghoniem, Ahmed F., and Frederick S. Sherman. "Grid-free simulation of diffusion using random walk methods." Journal of Computational Physics 61, no. 1 (October 1985): 1–37. http://dx.doi.org/10.1016/0021-9991(85)90058-0.

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Neuts, Marcel F. "An interesting random walk on the non-negative integers." Journal of Applied Probability 31, no. 1 (March 1994): 48–58. http://dx.doi.org/10.2307/3215234.

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A particular random walk on the integers leads to a new, tractable Markov chain. Of the stationary probabilities, we discuss the existence, some analytic properties and a factorization which leads to an algorithmic procedure for their numerical computation. We also consider the positive recurrence of some variants which each call for different mathematical arguments. Analogous results are derived for a continuous version on the positive reals.

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Journal articles on the topic 'Random walk numerical methods'

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