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Academic literature on the topic 'Brownian Dynamics - Two Dimensional Confined Geometry'
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Journal articles on the topic "Brownian Dynamics - Two Dimensional Confined Geometry"
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Osada, Hirofumi. "Stochastic geometry and dynamics of infinitely many particle systems—random matrices and interacting Brownian motions in infinite dimensions." Sugaku Expositions 34, no. 2 (October 12, 2021): 141–73. http://dx.doi.org/10.1090/suga/461.
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We explain the general theories involved in solving an infinite-dimensional stochastic differential equation (ISDE) for interacting Brownian motions in infinite dimensions related to random matrices. Typical examples are the stochastic dynamics of infinite particle systems with logarithmic interaction potentials such as the sine, Airy, Bessel, and also for the Ginibre interacting Brownian motions. The first three are infinite-dimensional stochastic dynamics in one-dimensional space related to random matrices called Gaussian ensembles. They are the stationary distributions of interacting Brownian motions and given by the limit point processes of the distributions of eigenvalues of these random matrices. The sine, Airy, and Bessel point processes and interacting Brownian motions are thought to be geometrically and dynamically universal as the limits of bulk, soft edge, and hard edge scaling. The Ginibre point process is a rotation- and translation-invariant point process on R 2 \mathbb {R}^2 , and an equilibrium state of the Ginibre interacting Brownian motions. It is the bulk limit of the distributions of eigenvalues of non-Hermitian Gaussian random matrices. When the interacting Brownian motions constitute a one-dimensional system interacting with each other through the logarithmic potential with inverse temperature β = 2 \beta = 2 , an algebraic construction is known in which the stochastic dynamics are defined by the space-time correlation function. The approach based on the stochastic analysis (called the analytic approach) can be applied to an extremely wide class. If we apply the analytic approach to this system, we see that these two constructions give the same stochastic dynamics. From the algebraic construction, despite being an infinite interacting particle system, it is possible to represent and calculate various quantities such as moments by the correlation functions. We can thus obtain quantitative information. From the analytic construction, it is possible to represent the dynamics as a solution of an ISDE. We can obtain qualitative information such as semi-martingale properties, continuity, and non-collision properties of each particle, and the strong Markov property of the infinite particle system as a whole. Ginibre interacting Brownian motions constitute a two-dimensional infinite particle system related to non-Hermitian Gaussian random matrices. It has a logarithmic interaction potential with β = 2 \beta = 2 , but no algebraic configurations are known.The present result is the only construction.
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Tian, Jiting, Walter Kob, and Jean-Louis Barrat. "Are strongly confined colloids good models for two dimensional liquids?" Journal of Chemical Physics 156, no. 16 (April 28, 2022): 164903. http://dx.doi.org/10.1063/5.0086749.
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Quasi-two-dimensional (quasi-2D) colloidal hard-sphere suspensions confined in a slit geometry are widely used as two-dimensional (2D) model systems in experiments that probe the glassy relaxation dynamics of 2D systems. However, the question to what extent these quasi-2D systems indeed represent 2D systems is rarely brought up. Here, we use computer simulations that take into account hydrodynamic interactions to show that dense quasi-2D colloidal bi-disperse hard-sphere suspensions exhibit much more rapid diffusion and relaxation than their 2D counterparts at the same area fraction. This difference is induced by the additional vertical space in the quasi-2D samples in which the small colloids can move out of the 2D plane, therefore allowing overlap between particles in the projected trajectories. Surprisingly, this difference in the dynamics can be accounted for if, instead of using the surface density, one characterizes the systems by means of a suitable structural quantity related to the radial distribution function. This implies that in the two geometries, the relevant physics for glass formation is essentially identical. Our results provide not only practical implications on 2D colloidal experiments but also interesting insights into the 3D-to-2D crossover in glass-forming systems.
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Urbani, Raphael, Fabian Westermeier, Benjamin Banusch, Michael Sprung, and Thomas Pfohl. "Brownian and advective dynamics in microflow studied by coherent X-ray scattering experiments." Journal of Synchrotron Radiation 23, no. 6 (October 6, 2016): 1401–8. http://dx.doi.org/10.1107/s1600577516012613.
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Combining microfluidics with coherent X-ray illumination offers the possibility to not only measure the structure but also the dynamics of flowing samples in a single-scattering experiment. Here, the power of this combination is demonstrated by studying the advective and Brownian dynamics of colloidal suspensions in microflow of different geometries. Using an experimental setup with a fast two-dimensional detector and performing X-ray correlation spectroscopy by calculating two-dimensional maps of the intensity auto-correlation functions, it was possible to evaluate the sample structure and furthermore to characterize the detailed flow behavior, including flow geometry, main flow directions, advective flow velocities and diffusive dynamics. By scanning a microfocused X-ray beam over a microfluidic device, the anisotropic auto-correlation functions of driven colloidal suspensions in straight, curved and constricted microchannels were mapped with the spatial resolution of the X-ray beam. This method has not only a huge potential for studying flow patterns in complex fluids but also to generally characterize anisotropic dynamics in materials.
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Gauthier, Guillaume, Matthew T. Reeves, Xiaoquan Yu, Ashton S. Bradley, Mark A. Baker, Thomas A. Bell, Halina Rubinsztein-Dunlop, Matthew J. Davis, and Tyler W. Neely. "Giant vortex clusters in a two-dimensional quantum fluid." Science 364, no. 6447 (June 27, 2019): 1264–67. http://dx.doi.org/10.1126/science.aat5718.
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Adding energy to a system through transient stirring usually leads to more disorder. In contrast, point-like vortices in a bounded two-dimensional fluid are predicted to reorder above a certain energy, forming persistent vortex clusters. In this study, we experimentally realize these vortex clusters in a planar superfluid: a 87Rb Bose-Einstein condensate confined to an elliptical geometry. We demonstrate that the clusters persist for long time periods, maintaining the superfluid system in a high-energy state far from global equilibrium. Our experiments explore a regime of vortex matter at negative absolute temperatures and have relevance for the dynamics of topological defects, two-dimensional turbulence, and systems such as helium films, nonlinear optical materials, fermion superfluids, and quark-gluon plasmas.
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Swan, James W., and John F. Brady. "The hydrodynamics of confined dispersions." Journal of Fluid Mechanics 687 (October 17, 2011): 254–99. http://dx.doi.org/10.1017/jfm.2011.351.
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AbstractA method is proposed for computing the low-Reynolds-number hydrodynamic forces on particles comprising a suspension confined by two parallel, no-slip walls. This is constructed via the two-dimensional analogue of Hasimoto’s solution (J. Fluid Mech., vol. 5, 1959, pp. 317–328) for a periodic array of point forces in a viscous, incompressible fluid, and, like Hasimoto, the summation of interactions is accelerated by substitution and superposition of ‘Ewald-like’ forcing. This method is akin to the accelerated Stokesian dynamics technique (J. Fluid Mech., vol. 448, 2001, pp. 115–146) and models the suspension dynamics with log–linear computational scaling. The effectiveness of this approach is demonstrated with a calculation of the high-frequency dynamic viscosity of a colloidal dispersion as function of volume fraction and channel width. Similarly, the short-time self-diffusivity for and the sedimentation rate of spherical particles in a confined suspension are determined. The results demonstrate the influence of confining geometry on the transport of small particles, which is becoming increasingly important for micro- and biofluidics.
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Lamura, Antonio. "Numerical Study of a Confined Vesicle in Shear Flow at Finite Temperature." Mathematics 10, no. 19 (September 30, 2022): 3570. http://dx.doi.org/10.3390/math10193570.
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The dynamics and rheology of a vesicle confined in a channel under shear flow are studied at finite temperature. The effect of finite temperature on vesicle motion and system viscosity is investigated. A two-dimensional numerical model, which includes thermal fluctuations and is based on a combination of molecular dynamics and mesoscopic hydrodynamics, is used to perform a detailed analysis in a wide range of the Peclet numbers (the ratio of the shear rate to the rotational diffusion coefficient). The suspension viscosity is found to be a monotonous increasing function of the viscosity contrast (the ratio of the viscosity of the encapsulated fluid to that of the surrounding fluid) both in the tank-treading and the tumbling regime due to the interplay of different temperature-depending mechanisms. Thermal effects induce shape and inclination fluctuations of the vesicle which also experiences Brownian diffusion across the channel increasing the viscosity. These effects reduce when increasing the Peclet number.
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Lefauve, Adrien, J. L. Partridge, Qi Zhou, S. B. Dalziel, C. P. Caulfield, and P. F. Linden. "The structure and origin of confined Holmboe waves." Journal of Fluid Mechanics 848 (June 5, 2018): 508–44. http://dx.doi.org/10.1017/jfm.2018.324.
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Finite-amplitude manifestations of stratified shear flow instabilities and their spatio-temporal coherent structures are believed to play an important role in turbulent geophysical flows. Such shear flows commonly have layers separated by sharp density interfaces, and are therefore susceptible to the so-called Holmboe instability, and its finite-amplitude manifestation, the Holmboe wave. In this paper, we describe and elucidate the origin of an apparently previously unreported long-lived coherent structure in a sustained stratified shear flow generated in the laboratory by exchange flow through an inclined square duct connecting two reservoirs filled with fluids of different densities. Using a novel measurement technique allowing for time-resolved, near-instantaneous measurements of the three-component velocity and density fields simultaneously over a three-dimensional volume, we describe the three-dimensional geometry and spatio-temporal dynamics of this structure. We identify it as a finite-amplitude, nonlinear, asymmetric confined Holmboe wave (CHW), and highlight the importance of its spanwise (lateral) confinement by the duct boundaries. We pay particular attention to the spanwise vorticity, which exhibits a travelling, near-periodic structure of sheared, distorted, prolate spheroids with a wide ‘body’ and a narrower ‘head’. Using temporal linear stability analysis on the two-dimensional streamwise-averaged experimental flow, we solve for three-dimensional perturbations having two-dimensional, cross-sectionally confined eigenfunctions and a streamwise normal mode. We show that the dispersion relation and the three-dimensional spatial structure of the fastest-growing confined Holmboe instability are in good agreement with those of the observed confined Holmboe wave. We also compare those results with a classical linear analysis of two-dimensional perturbations (i.e. with no spanwise dependence) on a one-dimensional base flow. We conclude that the lateral confinement is an important ingredient of the confined Holmboe instability, which gives rise to the CHW, with implications for many inherently confined geophysical flows such as in valleys, estuaries, straits or deep ocean trenches. Our results suggest that the CHW is an example of an experimentally observed, inherently nonlinear, robust, long-lived coherent structure which has developed from a linear instability. We conjecture that the CHW is a promising candidate for a class of exact coherent states underpinning the dynamics of more disordered, yet continually forced stratified shear flows.
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Ooshida, Takeshi, Susumu Goto, and Michio Otsuki. "Collective Motion of Repulsive Brownian Particles in Single-File Diffusion with and without Overtaking." Entropy 20, no. 8 (August 2, 2018): 565. http://dx.doi.org/10.3390/e20080565.
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Subdiffusion is commonly observed in liquids with high density or in restricted geometries, as the particles are constantly pushed back by their neighbors. Since this “cage effect” emerges from many-body dynamics involving spatiotemporally correlated motions, the slow diffusion should be understood not simply as a one-body problem but as a part of collective dynamics, described in terms of space–time correlations. Such collective dynamics are illustrated here by calculations of the two-particle displacement correlation in a system of repulsive Brownian particles confined in a (quasi-)one-dimensional channel, whose subdiffusive behavior is known as the single-file diffusion (SFD). The analytical calculation is formulated in terms of the Lagrangian correlation of density fluctuations. In addition, numerical solutions to the Langevin equation with large but finite interaction potential are studied to clarify the effect of overtaking. In the limiting case of the ideal SFD without overtaking, correlated motion with a diffusively growing length scale is observed. By allowing the particles to overtake each other, the short-range correlation is destroyed, but the long-range weak correlation remains almost intact. These results describe nested space–time structure of cages, whereby smaller cages are enclosed in larger cages with longer lifetimes.
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Kummali, Mohammed Musthafa, David Cole, and Siddharth Gautam. "Effect of Pore Connectivity on the Behavior of Fluids Confined in Sub-Nanometer Pores: Ethane and CO2 Confined in ZSM-22." Membranes 11, no. 2 (February 5, 2021): 113. http://dx.doi.org/10.3390/membranes11020113.
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The behavior of fluids under nano-confinement varies from that in bulk due to an interplay of several factors including pore connectivity. In this work, we use molecular dynamics simulations to study the behavior of two fluids—ethane and CO2 confined in ZSM-22, a zeolite with channel-like pores of diameter 0.55 nm isolated from each other. By comparing the behavior of the two fluids in ZSM-22 with that reported earlier in ZSM-5, a zeolite with pores of similar shape and size connected to each other via sinusoidal pores running perpendicular to them, we reveal the important role of pore connectivity. Further, by artificially imposing pore connectivity in ZSM-22 via inserting a 2-dimensional slab-like inter-crystalline space of thickness 0.5 nm, we also studied the effect of the dimensionality and geometry of pore connectivity. While the translational motion of both ethane and CO2 in ZSM-22 is suppressed as a result of connecting the pores by perpendicular quasi-one-dimensional pores of similar dimensions, the effect of connecting the pores by inserting the inter-crystalline space is different on the translational motion of the two fluids. For ethane, pores connected via inter-crystalline space facilitate translational motion but suppress rotational motion, whereas in the case of CO2, both types of motion are suppressed by pore connection due to the strong interaction of CO2 with the surface of the substrate.
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Sullivan, P. A., P. A. Charest, and T. Ma. "Heave Stiffness of an Air Cushion Vehicle Bag-and-Finger Skirt." Journal of Ship Research 38, no. 04 (December 1, 1994): 302–7. http://dx.doi.org/10.5957/jsr.1994.38.4.302.
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The heave stiffness of a bag-and-finger flexible skirt air cushion is investigated analytically and experimentally. The investigations use a two-dimensional section of the skirt confined between end-plates and moving in heave. This simplified geometry facilitates analysis involving a minimum of empiricism. Experiments show that the airflows, including leaks between fingers and at the end-plates, can be modeled as orifice-like. The analysis assumes that the fingers can be modeled as rigid massless bodies. Three models of the bag, based on combinations of massless inelastic membranes and rigid links, are investigated. The predictions and experiments are in good agreement and show that modest geometry changes can have large effects on heave stiffness. It is suggested that these simple skirt models can provide useful insights into the dynamics.
Conference papers on the topic "Brownian Dynamics - Two Dimensional Confined Geometry"
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McIlroy, Hugh M., Donald M. McEligot, and Robert J. Pink. "Measurement of Flow Phenomena in a Lower Plenum Model of a Prismatic Gas-Cooled Reactor." In 16th International Conference on Nuclear Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/icone16-48734.
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Mean-velocity-field and turbulence data are presented that measure turbulent flow phenomena in an approximately 1:7 scale model of a region of the lower plenum of a typical prismatic gas-cooled reactor (GCR) similar to a General Atomics Gas-Turbine-Modular Helium Reactor (GTMHR) design. The data were obtained in the Matched-Index-of-Refraction (MIR) facility at Idaho National Laboratory (INL) and are offered for assessing computational fluid dynamics (CFD) software. This experiment has been selected as the first Standard Problem endorsed by the Generation IV International Forum. Results concentrate on the region of the lower plenum near its far reflector wall (away from the outlet duct). The flow in the lower plenum consists of multiple jets injected into a confined cross flow — with obstructions. The model consists of a row of full circular posts along its centerline with half-posts on the two parallel walls to approximate geometry scaled to that expected from the staggered parallel rows of posts in the reactor design. The model is fabricated from clear, fused quartz to match the refractive-index of the working fluid so that optical techniques may be employed for the measurements. The benefit of the MIR technique is that it permits optical measurements to determine flow characteristics in complex passages in and around objects to be obtained without locating intrusive transducers that will disturb the flow field and without distortion of the optical paths. An advantage of the INL system is its large size, leading to improved spatial and temporal resolution compared to similar facilities at smaller scales. A three-dimensional (3-D) Particle Image Velocimetry (PIV) system was used to collect the data. Inlet jet Reynolds numbers (based on the jet diameter and the time-mean bulk velocity) are approximately 4,300 and 12,400. Uncertainty analyses and a discussion of the standard problem are included. The measurements reveal developing, non-uniform, turbulent flow in the inlet jets and complicated flow patterns in the model lower plenum. Data include three-dimensional vector plots, data displays along the coordinate planes (slices) and presentations that describe the component flows at specific regions in the model. Information on inlet conditions is also presented.
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Darbandi, Masoud, Ehsan Asgari, Morteza Hajikaram, and Gerry E. Schneider. "CFD-Aided Simulation of Frost Growth Inside a Narrow Duct With Uniform Wall Temperature Variation." In ASME 2014 12th International Conference on Nanochannels, Microchannels, and Minichannels collocated with the ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/icnmm2014-22193.
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In this paper, we study the frost formation and growth at the walls of a duct with uniform wall temperature variation. The simulation is performed for laminar flow regime considering suitable semi-empirical models incorporated with computational fluid dynamics (CFD) method. The frost growth is considered to be normal to the duct surface. Since the duct aspect ratio is high, we perform our simulations in two-dimensional zones. To simulate the frost layer properly, we solve both the energy and mass balance equations implementing some semi-empirical correlations on the frost side. At this stage, we suitably predict the required heat flux value at the solid boundary and the heat transfer coefficient, which are required to be used in the CFD calculations in the next stage. So, next is to use the CFD tool to calculate the required heat transfer parameters at the air side. Since the frost growth is performed locally along the wall, the achieved frost growth rate can be applied at any specific location independently. We also investigate the effects of various environmental parameters on the frost growth rate. The current achieved results are verified by comparing them with previous available experimental data. After verification the numerical algorithm, we investigate the frost growth in a duct with uniform wall temperature variation. We assume that the variation of temperature would be gradually and uniform with time. We eventually present the effects of different parameters affecting the frost growth along the duct surface. One significant contribution of this work is to address the effects of inlet boundary location on the frost growth. In this regard, the inlet boundary is placed initially at real entrance and then at a location far upstream of the real entrance. We evaluate the effect of this boundary location on frost thickness. The use of CFD is unavoidable in this study because we need its capability to compute the required wall heat flux condition, which is an input to our semi-empirical analysis in this problem with an unsteady thermal boundary condition situation, in which the wall temperature continuously varies with time. It should be noted that, our chosen empirical method estimate the wall heat flux based on the Nusselt number value. Therefore, CFD largely helps to correct the actual heat flux at the airside. Another contribution of this work is to study frost formation in confined flow cases, in which the flow is developing both hydrodynamically and thermally. Evidently this is in contrast to the frost growth over a simple flat plate like geometry.