Relevant bibliographies by topics / Random flow field

Academic literature on the topic 'Random flow field'

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Published: 4 June 2021
Last updated: 19 February 2022

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Journal articles on the topic "Random flow field"

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Breyer, L. A., and G. O. Roberts. "A New Method for Coupling Random Fields." LMS Journal of Computation and Mathematics 5 (2002): 77–94. http://dx.doi.org/10.1112/s146115700000070x.

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AbstractGiven a Markov chain, a stochastic flow that simultaneously constructs sample paths started at each possible initial value can be constructed as a composition of random fields. Here, a method is described for coupling flows by modifying an arbitrary field (consistent with the Markov chain of interest) by an independence Metropolis-Hastings iteration. The resulting stochastic flow is shown to have many desirable coalescence properties, regardless of the form of the original flow.
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IJZERMANS, RUTGER H. A., ELENA MENEGUZ, and MICHAEL W. REEKS. "Segregation of particles in incompressible random flows: singularities, intermittency and random uncorrelated motion." Journal of Fluid Mechanics 653 (April 13, 2010): 99–136. http://dx.doi.org/10.1017/s0022112010000170.

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The results presented here are part of a long-term study in which we analyse the segregation of inertial particles in turbulent flows using the so called full Lagrangian method (FLM) to evaluate the ‘compressibility’ of the particle phase along a particle trajectory. In the present work, particles are advected by Stokes drag in a random flow field consisting of counter-rotating vortices and in a flow field composed of 200 random Fourier modes. Both flows are incompressible and, like turbulence, have structure and a distribution of scales with finite lifetime. The compressibility is obtained by first calculating the deformation tensor Jij associated with an infinitesimally small volume of particles following the trajectory of an individual particle. The fraction of the initial volume occupied by the particles centred around a position x at time t is denoted by |J|, where J ≡ det(Jij) and Jij ≡ ∂xi(x0, t)/∂x0,j, x0 denoting the initial position of the particle. The quantity d〈ln|J|〉/dt is shown to be equal to the particle averaged compressibility of the particle velocity field 〈∇ · v〉, which gives a measure of the rate-of-change of the total volume occupied by the particle phase as a continuum. In both flow fields the compressibility of the particle velocity field is shown to decrease continuously if the Stokes number St (the dimensionless particle relaxation time) is below a threshold value Stcr, indicating that the segregation of particles continues indefinitely. We show analytically and numerically that the long-time limit of 〈∇ · v〉 for sufficiently small values of St is proportional to St2 in the flow field composed of random Fourier modes, and to St in the flow field consisting of counter-rotating vortices. If St > Stcr, however, the particles are ‘mixed’. The level of mixing can be quantified by the degree of random uncorrelated motion (RUM) of particles which is a measure of the decorrelation of the velocities of two nearby particles. RUM is zero for fluid particles and increases rapidly with the Stokes number if St > Stcr, approaching unity for St ≫ 1. The spatial averages of the higher-order moments of the particle number density are shown to diverge with time indicating that the spatial distribution of particles may be very intermittent, being associated with non-zero values of RUM and the occurrence of singularities in the particle velocity field. Our results are consistent with previous observations of the radial distribution function in Chun et al. (J. Fluid Mech., vol. 536, 2005, p. 219).
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S&z.xl;luż;alec, Andrzej. "Temperature field in random conditions." International Journal of Heat and Mass Transfer 34, no. 1 (January 1991): 55–58. http://dx.doi.org/10.1016/0017-9310(91)90172-b.

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Kawaguchi, Takaaki. "Plastic flow in a driven random-field XY model." Physics Letters A 251, no. 1 (January 1999): 73–78. http://dx.doi.org/10.1016/s0375-9601(98)00851-2.

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Smirnov, A., S. Shi, and I. Celik. "Random Flow Generation Technique for Large Eddy Simulations and Particle-Dynamics Modeling." Journal of Fluids Engineering 123, no. 2 (February 16, 2001): 359–71. http://dx.doi.org/10.1115/1.1369598.

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A random flow generation (RFG) technique is presented, which can be used for initial/inlet boundary generation in LES (Large-Eddy-Simulations) or particle tracking in LES/RANS (Reynolds-Averaged Navier-Stokes) computations of turbulent flows. The technique is based on previous methods of synthesizing divergence-free vector fields from a sample of Fourier harmonics and allows to generate non-homogeneous anisotropic flow field representing turbulent velocity fluctuations. It was validated on the cases of boundary layer and flat plate flows. Applications of the technique to LES and particle tracking are considered.
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Kolokolov, I. V., V. V. Lebedev, and G. A. Sizov. "Magnetic field correlations in random flow with strong steady shear." Journal of Experimental and Theoretical Physics 113, no. 2 (August 2011): 339–51. http://dx.doi.org/10.1134/s1063776111060033.

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SIGURGEIRSSON, H., and A. M. STUART. "INERTIAL PARTICLES IN A RANDOM FIELD." Stochastics and Dynamics 02, no. 02 (June 2002): 295–310. http://dx.doi.org/10.1142/s021949370200042x.

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The motion of an inertial particle in a Gaussian random field is studied. This is a model for the phenomenon of preferential concentration, whereby inertial particles in a turbulent flow can correlate significantly. Mathematically the motion is described by Newton's second law for a particle on a 2-D torus, with force proportional to the difference between a background fluid velocity and the particle velocity itself. The fluid velocity is defined through a linear stochastic PDE of Ornstein–Uhlenbeck type. The properties of the model are studied in terms of the covariance of the noise which drives the stochastic PDE. Sufficient conditions are found for almost sure existence and uniqueness of particle paths, and for a random dynamical system with a global random attractor. The random attractor is illustrated by means of a numerical experiment, and the relevance of the random attractor for the understanding of particle distributions is highlighted.
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ZIRBEL, CRAIG L., and WOJBOR A. WOYCZYŃSKI. "ROTATION OF PARTICLES IN POLARIZED BROWNIAN FLOWS." Stochastics and Dynamics 02, no. 01 (March 2002): 109–29. http://dx.doi.org/10.1142/s0219493702000339.

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We consider the rotation of tangent vectors and the mutual rotation of two particles undergoing motion in a random two-dimensional velocity field. We look at random fields whose laws are invariant under translations and rotations, but not reflections. These polarized fields are intermediate between homogeneous and isotropic fields, and may possess a preferred sense of rotation. The covariance of such a field must have a certain form which we describe. In a Brownian flow based on a polarized random field, we show that tangent vectors can rotate at a constant asymptotic rate, and that under certain conditions, two particles will rotate about each other at the same asymptotic rate. For illustration we present simulations of a polarized Gaussian field and of particles moving in a polarized Brownian flow.
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van Gogh, M. A., T. Bauer, L. De Angelis, and L. Kuipers. "Poynting singularities in the transverse flow-field of random vector waves." Optics Letters 45, no. 9 (April 28, 2020): 2600. http://dx.doi.org/10.1364/ol.389301.

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Adhikari, Sondipon, Akshat Rastogi, and Bishakh Bhattacharya. "Piezoelectric vortex induced vibration energy harvesting in a random flow field." Smart Materials and Structures 29, no. 3 (February 19, 2020): 035034. http://dx.doi.org/10.1088/1361-665x/ab519f.

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Dissertations / Theses on the topic "Random flow field"

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Piao, Dongzhen. "Speeding Up Gibbs Sampling in Probabilistic Optical Flow." Research Showcase @ CMU, 2014. http://repository.cmu.edu/dissertations/481.

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In today’s machine learning research, probabilistic graphical models are used extensively to model complicated systems with uncertainty, to help understanding of the problems, and to help inference and predict unknown events. For inference tasks, exact inference methods such as junction tree algorithms exist, but they suffer from exponential growth of cluster size and thus is not able to handle large and highly connected graphs. Approximate inference methods do not try to find exact probabilities, but rather give results that improve as algorithm runs. Gibbs sampling, as one of the approximate inference methods, has gained lots of traction and is used extensively in inference tasks, due to its ease of understanding and implementation. However, as problem size grows, even the faster algorithm needs a speed boost to meet application requirement. The number of variables in an application graphical model can range from tens of thousands to billions, depending on problem domain. The original sequential Gibbs sampling may not return satisfactory result in limited time. Thus, in this thesis, we investigate in ways to speed up Gibbs sampling. We will study ways to do better initialization, blocking variables to be sampled together, as well as using simulated annealing. These are the methods that modifies the algorithm itself. We will also investigate in ways to parallelize the algorithm. An algorithm is parallelizable if some steps do not depend on other steps, and we will find out such dependency in Gibbs sampling. We will discuss how the choice of different hardware and software architecture will affect the parallelization result. We will use optical flow problem as an example to demonstrate the various speed up methods we investigated. An optical flow method tries to find out the movements of small image patches between two images in a temporal sequence. We demonstrate how we can model it using probabilistic graphical model, and solve it using Gibbs sampling. The result of using sequential Gibbs sampling is demonstrated, with comparisons from using various speed up methods and other optical flow methods.
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Connell, R. J. "Unstable equilibrium : modelling waves and turbulence in water flow." Diss., Lincoln University, 2008. http://hdl.handle.net/10182/592.

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This thesis develops a one-dimensional version of a new data driven model of turbulence that uses the KL expansion to provide a spectral solution of the turbulent flow field based on analysis of Particle Image Velocimetry (PIV) turbulent data. The analysis derives a 2nd order random field over the whole flow domain that gives better turbulence properties in areas of non-uniform flow and where flow separates than the present models that are based on the Navier-Stokes Equations. These latter models need assumptions to decrease the number of calculations to enable them to run on present day computers or super-computers. These assumptions reduce the accuracy of these models. The improved flow field is gained at the expense of the model not being generic. Therefore the new data driven model can only be used for the flow situation of the data as the analysis shows that the kernel of the turbulent flow field of undular hydraulic jump could not be related to the surface waves, a key feature of the jump. The kernel developed has two parts, called the outer and inner parts. A comparison shows that the ratio of outer kernel to inner kernel primarily reflects the ratio of turbulent production to turbulent dissipation. The outer part, with a larger correlation length, reflects the larger structures of the flow that contain most of the turbulent energy production. The inner part reflects the smaller structures that contain most turbulent energy dissipation. The new data driven model can use a kernel with changing variance and/or regression coefficient over the domain, necessitating the use of both numerical and analytical methods. The model allows the use of a two-part regression coefficient kernel, the solution being the addition of the result from each part of the kernel. This research highlighted the need to assess the size of the structures calculated by the models based on the Navier-Stokes equations to validate these models. At present most studies use mean velocities and the turbulent fluctuations to validate a models performance. As the new data driven model gives better turbulence properties, it could be used in complicated flow situations, such as a rock groyne to give better assessment of the forces and pressures in the water flow resulting from turbulence fluctuations for the design of such structures. Further development to make the model usable includes; solving the numerical problem associated with the double kernel, reducing the number of modes required, obtaining a solution for the kernel of two-dimensional and three-dimensional flows, including the change in correlation length with time as presently the model gives instant realisations of the flow field and finally including third and fourth order statistics to improve the data driven model velocity field from having Gaussian distribution properties. As the third and fourth order statistics are Reynolds Number dependent this will enable the model to be applied to PIV data from physical scale models. In summary, this new data driven model is complementary to models based on the Navier-Stokes equations by providing better results in complicated design situations. Further research to develop the new model is viewed as an important step forward in the analysis of river control structures such as rock groynes that are prevalent on New Zealand Rivers protecting large cities.
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Federico, Vittorio Di, and Shlomo P. Neuman. "Effect Of Filtering On Autocorrelation, Flow, And Transport In Random Fractal Fields." Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1995. http://hdl.handle.net/10150/614142.

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" Fractal" concepts have become the focus of much interest in the earth sciences during the last fifteen years. The term "fractal" is especially appealing from a semantic point of view in that Mandelbrot [ 1983] derived it from the Latin "fractus ", describing the appearance of a broken stone. In this report, we focus on issues of flow and contaminant transport in porous media. Here, fractal concepts have been widely associated with attempts to explain scale- effects such as the apparent growth of effective longitudinal dispersion with the scale of observation. However, a much broader range of topics has been explored in the literature on fractals, which can be roughly divided into two broad categories. The first category concerns a fractal description of medium geometry, over a given range of scales [Adler, 1992]. Within this category, the fractal geometry is considered to be either deterministic (self -similar) or random (statistically self -similar, or self -affine) [Voss 1985]. The second category views medium physical properties (porosity, log- conductivity) as random fields, most commonly with statistical self -similarity of second -order moments such as structure function ( variogram) or autocovariance. In this report, we focus on random fractal fields. We start with an introduction in Chapter 1 of isotropic random fractal fields and the scaling properties of corresponding power -law variogram and spectral densities in one, two, and three dimensions. We then derive new expressions for autocovariance functions corresponding to truncated power -law spectral densities; demonstrate that the power -law variogram and associated power spectra can be constructed as weighted integrals of exponential autocovariance functions and their spectra, representing an infinite hierarchy of unconelated homogeneous isotropic fields (modes); and analyze the effect of filtering out (truncating) high and low frequency modes from this hierarchy in the realand spectral domains. In Chapter 2, we derive first -order results relative to early preasymptotic, and late time asymptotic, transport in media characterized by a truncated log -conductivity power -law spectral density. In Chapter 3, we return to the multiscale log- conductivity fields constructed in Chapter 1; present some general results for early preasymptotic and late time asymptotic transport; and obtain complete first -order results for flow and transport, at preasymptotic and asymptotic stages, in two dimensions. In Chapter 4, we explore the multiscale behavior of conductivity from an aquifer in Mobile, Alabama, using different methods of data reduction. In Chapter 5, we summarize our main conclusions.
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Okhulkova, Tatiana. "Integration of uncertainty and definition of critical thresholds for CO2 storage risk assessment." Thesis, Université Paris-Saclay (ComUE), 2015. http://www.theses.fr/2015SACLC021/document.

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L'objectif principal de la thèse est de définir comment l'incertitude peut être prise en compte dans leprocessus d'évaluation des risques pour le stockage de CO2 et de quantifier, à l'aide de modèles numériques,les scénarios de fuite par migration latérale et à travers la couverture. Les scénarios choisis sont quantifiéspar l'approche de modélisation de système pour laquelle des modèles numériques prédictifs ad-hoc sontdéveloppés. Une étude probabiliste de propagation d'incertitude paramétrique par un méta-modèle depolynômes de chaos est réalisée. La problématique de la prise en compte de la variabilité spatiale comme unesource d'incertitude est éclairée et une étude comparative entre représentations homogène et hétérogène de laperméabilité est fournie
The main goal of the thesis is to define how the uncertainty can be accounted for in the process of riskassessment for CO2 storage and to quantify by means of numerical models the scenarii of leakage by lateralmigration and through the caprock. The chosen scenarii are quantified using the system modeling approachfor which ad-hoc predictive numerical models are developed. A probabilistic parametric uncertaintypropagation study using polynomial chaos expansion is performed. Matters of spatial variability are alsodiscussed and a comparison between homogeneous and heterogeneous representations of permeability isprovided
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Karci, Mehmet Haydar. "Higher Order Levelable Mrf Energy Minimization Via Graph Cuts." Phd thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/12609408/index.pdf.

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A feature of minimizing images of a class of binary Markov random field energies is introduced and proved. Using this, the collection of minimizing images of levels of higher order, levelable MRF energies is shown to be a monotone collection. This implies that these images can be combined to give minimizing images of the MRF energy itself. Due to the recent developments, second and third order binary MRF energies of the mentioned class are known to be exactly minimized by maximum flow/minimum cut computations on appropriately constructed graphs. With the aid of these developments an exact and efficient algorithm to minimize levelable second and third order MRF energies, which is composed of a series of maximum flow/minimum cut computations, is proposed and applications of the proposed algorithm to image restoration are given.
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Kwatra, Vivek. "Example-based Rendering of Textural Phenomena." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/7214.

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This thesis explores synthesis by example as a paradigm for rendering real-world phenomena. In particular, phenomena that can be visually described as texture are considered. We exploit, for synthesis, the self-repeating nature of the visual elements constituting these texture exemplars. Techniques for unconstrained as well as constrained/controllable synthesis of both image and video textures are presented. For unconstrained synthesis, we present two robust techniques that can perform spatio-temporal extension, editing, and merging of image as well as video textures. In one of these techniques, large patches of input texture are automatically aligned and seamless stitched with each other to generate realistic looking images and videos. The second technique is based on iterative optimization of a global energy function that measures the quality of the synthesized texture with respect to the given input exemplar. We also present a technique for controllable texture synthesis. In particular, it allows for generation of motion-controlled texture animations that follow a specified flow field. Animations synthesized in this fashion maintain the structural properties like local shape, size, and orientation of the input texture even as they move according to the specified flow. We cast this problem into an optimization framework that tries to simultaneously satisfy the two (potentially competing) objectives of similarity to the input texture and consistency with the flow field. This optimization is a simple extension of the approach used for unconstrained texture synthesis. A general framework for example-based synthesis and rendering is also presented. This framework provides a design space for constructing example-based rendering algorithms. The goal of such algorithms would be to use texture exemplars to render animations for which certain behavioral characteristics need to be controlled. Our motion-controlled texture synthesis technique is an instantiation of this framework where the characteristic being controlled is motion represented as a flow field.
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WU, CHIA-YING, and 吳佳嬴. "Experimental Study on the Random Wave Dissipation by Stepped Submerged Embankment with Interaction of Flow Field." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/g9757k.

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碩士
東南科技大學
營建與空間設計系營建科技與防災碩士班
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This thesis is about by using the glass cross-section tank we did a series of study and experiment about submerged breakwater. According to different conditions such as different heights of submerged breakwater, different amplitude and period of the wave, and in the forward or reverse flow field, we found out the reflectivity, penetration rate, the loss rate, and the mechanism of the model. Taiwan is an island country with vast coastal and extensive offshore waters. Because of the extreme climate worldwide, the rising sea level, the Typhoons during summer and fall, and the huge waves, those problems brought to the crisis of the coastline retrogression. The numerous man-made facilities at the coast reduced the amount of sands from the upstream, and led to the erosion of the coastline as well. As a result, the waves became random and irregular due to the changes of the flow field. In order to find out the mechanism of the waves in reality and to protect the marine, we used the irregular waves to do the experiments. We focused on the effect of waves and flow field on the reflectivity, penetration rate, and the loss rate of the step-type submerged breakwater.
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Metzger, Jakob Johannes. "Branched Flow and Caustics in Two-Dimensional Random Potentials and Magnetic Fields." Doctoral thesis, 2010. http://hdl.handle.net/11858/00-1735-0000-0006-B4D6-8.

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Metzger, Jakob Johannes [Verfasser]. "Branched flow and caustics in two-dimensional random potentials and magnetic fields / vorgelegt von Jakob Johannes Metzger." 2010. http://d-nb.info/1007346671/34.

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Vasylkivska, Veronika S. "Stochastic analysis of flow and transport in porous media." Thesis, 2012. http://hdl.handle.net/1957/33728.

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Random fields are frequently used in computational simulations of real-life processes. In particular, in this work they are used in modeling of flow and transport in porous media. Porous media as they arise in geological formations are intrinsically deterministic but there is significant uncertainty involved in determination of their properties such as permeability, porosity and diffusivity. In many situations description of properties of the porous media is aided by a limited number of observations at fixed points. These observations constrain the randomness of the field and lead to conditional simulations. In this work we propose a method of simulating the random fields which respect the observed data. An advantage of our method is that in the case that additional data becomes available it can be easily incorporated into subsequent representations. The proposed method is based on infinite series representations of random fields. We provide truncation error estimates which bound the discrepancy between the truncated series and the random field. We additionally provide the expansions for some processes that have not yet appeared in the literature. There are several approaches to efficient numerical computations for partial differential equations with random parameters. In this work we compare the solutions of flow and transport equations obtained by conditional simulations with Monte Carlo (MC) and stochastic collocation (SC) methods. Due to its simplicity MC method is one of the most popular methods used for the solution of stochastic equations. However, it is computationally expensive. The SC method is functionally similar to the MC method but it provides the faster convergence of the statistical moments of the solutions through the use of the carefully chosen collocation points at which the flow and transport equations are solved. We show that for both methods the conditioning on measurements helps to reduce the uncertainty of the solutions of the flow and transport equations. This especially holds in the neighborhood of the conditioning points. Conditioning reduces the variances of solutions helping to quantify the uncertainty in the output of the flow and transport equations.
Graduation date: 2013
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Book chapters on the topic "Random flow field"

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Chappet de Vangel, Benoît, and Bernard Girau. "Randomly Spiking Dynamic Neural Fields Driven by a Shared Random Flow." In Artificial Neural Networks and Machine Learning – ICANN 2016, 357–64. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-44778-0_42.

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Piao, Dongzhen, Prahlad G. Menon, and Ole J. Mengshoel. "Computing Probabilistic Optical Flow Using Markov Random Fields." In Computational Modeling of Objects Presented in Images. Fundamentals, Methods, and Applications, 241–47. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09994-1_22.

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Ciprut, Philippe, Max-Olivier Hongler, and Yves Salama. "Random Production Flows. An Exactly Solvable Fluid Model." In Seminar on Stochastic Analysis, Random Fields and Applications, 125–35. Basel: Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8681-9_9.

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Dyskin, A. V. "Crack Development in Spatially Random Stress Fields Generated by Point Defects. Fracture in Compression." In IUTAM Symposium on Non–Linear Singularities in Deformation and Flow, 63–74. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4736-1_7.

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O’Donoughue, Patrick, Olivier Robin, and Alain Berry. "Inference of Random Excitations from Contactless Vibration Measurements on a Panel or Membrane Using the Virtual Fields Method." In Flinovia—Flow Induced Noise and Vibration Issues and Aspects-II, 357–72. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-76780-2_22.

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Herzog, Sebastian, and Claus Wagner. "Development of Artificial Neural Networks with Integrated Conditional Random Fields Capable of Predicting Non-linear Dynamics of the Flow Around Cylinders." In Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 71–79. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-25253-3_7.

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Zinn-Justin, Jean. "Stability of renormalization group fixed points and decay of correlations." In From Random Walks to Random Matrices, 101–10. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198787754.003.0007.

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Chapter 7 is devoted to a discussion of the renormalization group (RG) flow when the effective field theory that describes universal properties of critical phenomena depends on several coupling constants. The universal properties of a large class of macroscopic phase transitions with short range interactions can be described by statistical field theories involving scalar fields with quartic interactions. The simplest critical systems have an O(N) orthogonal symmetry and, therefore, the corresponding field theory has only one quartic interaction. However, in more general physical systems, the flow of quartic interactions is more complicated. This chapter examines these systems from the RG viewpoint. RG beta functions are shown to generate a gradient flow. Some examples illustrate the notion of emergent symmetry. The local stability of fixed points is related to the value of the scaling field dimension.
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Weitbrecht, Volker, Wim Uijttewaal, and Gerhard Jirka. "A random walk approach for investigating near- and far-field transport phenomena in rivers with groin fields." In River Flow 2004, 1157–66. CRC Press, 2004. http://dx.doi.org/10.1201/b16998-151.

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Cardaliaguet, Pierre, François Delarue, Jean-Michel Lasry, and Pierre-Louis Lions. "Mean Field Game System with a Common Noise." In The Master Equation and the Convergence Problem in Mean Field Games, 85–127. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691190716.003.0004.

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This chapter talks about the unique solvability of the mean field games (MFGs) system with common noise. In terms of a game with a finite number of players, the common noise describes some noise that affects all the players in the same way, so that the dynamics of one given particle reads a certain master equation. It explains the use of the standard convention from the theory of stochastic processes that consists in indicating the time parameter as an index in random functions. Using a continuation like argument instead of the classical strategy based on the Schauder fixed-point theorem, this chapter investigates the existence and uniqueness of a solution. It discusses the effect of the common noise in randomizing the MFG equilibria so that it becomes a random flow of measures.
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Jerison, David, Lionel Levine, and Scott Sheffield. "Internal DLA for Cylinders." In Advances in Analysis, edited by Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, and Stephen Wainger. Princeton University Press, 2014. http://dx.doi.org/10.23943/princeton/9780691159416.003.0008.

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This chapter discusses the continuum limit of internal Diffusion-Limited Aggregation (DLA), a random lattice growth model governed by a deterministic fluid flow equation known as Hele-Shaw flow. The internal DLA model was introduced in 1986 by Meakin and Deutch to describe chemical processes such as electropolishing, etching, and corrosion. The chapter focuses primarily on fluctuations, and seeks to prove the analogous results for the lattice cylinder. In the case of the cylinder, the fluctuations are described in terms of the Gaussian Free Field exactly. The main tools used in the proofs are martingales. As the chapter shows, the martingale property in this context is the counterpart in probability theory of well-known conservation laws for Hele-Shaw flow.
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Conference papers on the topic "Random flow field"

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Giasemidis, Georgios, John F. Wheater, and Stefan Zohren. "Spectral dimension flow on continuum random multigraph." In THE SIXTH INTERNATIONAL SCHOOL ON FIELD THEORY AND GRAVITATION-2012. AIP, 2012. http://dx.doi.org/10.1063/1.4758993.

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Nagawkar, Jethro R., Marc W. Brittain, and Leifur T. Leifsson. "Multifidelity Aerodynamic Flow Field Prediction Using Random Forests." In AIAA AVIATION 2021 FORUM. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2021. http://dx.doi.org/10.2514/6.2021-3089.

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Thomson, J., and Jorge Vinals. "Cavity flow induced by an effective random gravitational field." In 32nd Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1994. http://dx.doi.org/10.2514/6.1994-438.

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4

Reeks, Michael W., Luca Fabbro, and Alfredo Soldati. "In Search of Random Uncorrelated Particle Motion (RUM) in a Simple Random Flow Field." In ASME 2006 2nd Joint U.S.-European Fluids Engineering Summer Meeting Collocated With the 14th International Conference on Nuclear Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/fedsm2006-98383.

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DNS studies of dispersed particle motion in isotropic homogeneous turbulence [1] have revealed the existence of a component of random uncorrelated motion (RUM) dependent on the particle inertia τp (normalised particle response time or Stoke number). This paper reports the presence of RUM in a simple linear random smoothly varying flow field of counter rotating vortices where the two-particle velocity correlation was measured as a function of spatial separation. Values of the correlation less than one for zero separation indicated the presence of RUM. In terms of Stokes number, the motion of the particles in one direction corresponds to either a heavily damped (τp < 0.25) or lightly damped (τp > 0.25) harmonic oscillator. In the lightly damped case the particles overshoot the stagnation lines of the flow and are projected from one vortex to another (the so-called sling-shot effect). It is shown that RUM occurs only when τp > 0.25, increasing monotonically with increasing Stokes number. Calculations of the particle pair separation distribution function show that equilibrium of the particle concentration field is never reached, the concentration at zero separation increasing monotonically with time. This is consistent with the calculated negative values of the average Liapounov exponent (finite compressibility) of the particle velocity field.
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5

Vargo, Erik, and Christine P. Taylor. "Similarity Scoring with Random Field Models for Traffic Flow Management Applications." In 2018 Aviation Technology, Integration, and Operations Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2018. http://dx.doi.org/10.2514/6.2018-3671.

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Vargo, Erik, and Christine P. Taylor. "Correction: Similarity Scoring with Random Field Models for Traffic Flow Management Applications." In 2018 Aviation Technology, Integration, and Operations Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2018. http://dx.doi.org/10.2514/6.2018-3671.c1.

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Ahn, Jinyoung, Eunjeong Ko, and Eun Yi Kim. "Real-time highway traffic flow estimation based on 3D Markov Random Field." In 2014 IEEE 17th International Conference on Intelligent Transportation Systems (ITSC). IEEE, 2014. http://dx.doi.org/10.1109/itsc.2014.6957709.

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Kawaguchi, Takaaki. "Scaling behavior of plastic flow in the driven random-field XY model." In Third tohwa university international conference on statistical physics. AIP, 2000. http://dx.doi.org/10.1063/1.1291664.

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Cheng, Way Lee, and Reza Sadr. "A Numerical Approach in Predicting Flow Field Induced by Randomly Moving Nano Particles." In ASME 2013 4th International Conference on Micro/Nanoscale Heat and Mass Transfer. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/mnhmt2013-22113.

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There have been several reports that suspending nano-particles in a fluid, or nanofluids, can enhance heat transfer properties such as conductivity. However, the extend of the reported enhancement is inconsistent in the literature and the exact mechanisms that govern these observations (or phenomena) are not fully understood. Although the interaction between the fluid and suspended particles is suspected to be the main contributor to this phenomenon, literature shows contradicting conclusions in the underlying mechanism responsible for these effects. This highlights the need for development of computational tools in this area. In this study, a computational approach is developed for simulating the induced flow field by randomly moving particles suspended in a quiescent fluid. Brownian displacement is used to describe the random walk of the particles in the fluid. The steady state movement is described with simplified Navier-Stokes equation to solve for the induced fluid flow around the moving particles with constant velocity at small time steps. The unsteady behavior of the induced flow field is approximated using the velocity profiles obtained from FLUENT. Initial results show that random movements of Brownian particles suspended in the fluid induce a random flow disturbance in the flow field. It is observed that the flow statistics converge asymptotically as time-step reduces. Moreover, inclusion of the transitional movement of the particles significantly affects the results.
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Samy, Roger A., and Daniel Duclos. "Pyramidal Markov random field (MRF) models for optical flow estimation applied to target detection." In SPIE's International Symposium on Optical Engineering and Photonics in Aerospace Sensing, edited by Nagaraj Nandhakumar. SPIE, 1994. http://dx.doi.org/10.1117/12.179033.

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