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1
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.
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Tkachenko, V., A. Tsipotan, A. Aleksandrovsky, and V. Slabko. "Three-dimensional model of quantum dots' self-assembly under the action of laser radiation." Computer Optics 41, no. 4 (2017): 577–80. http://dx.doi.org/10.18287/2412-6179-2017-41-577-580.
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This study considered a process of quantum dots' self-assembly into nanostructure arrays with predefined geometry, which proceeds in the external resonant laser field. We considered the simplest case of assembling a stable structure of two particles. The problem was solved numerically using a three-dimensional model of Brownian dynamics. The idea of the method is that the attraction of the dots occurs due to the interaction of resonantly induced dipole moments, with the dots being then captured by the Van der Waals force. Finally, a three-dimensional model was considered; the average nanoparticle aggregation time as a function of the laser radiation wavelength was calculated; the probability of such structures' being formed was estimated for the calculated average aggregation time and for the laser pulse duration used in the experiment. The wavelength of the maximum probability was found to be shifted from the single particle resonance wavelength of 525 nm to the red area of 535 nm, which is in qualitative agreement with the redshift of the resonance wavelength of interacting particles.
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Koken, Mete, Ismail Aydin, and Akis Sahin. "Application of computational fluid dynamics to predict hydrodynamic downpull on high head gates." Engineering Computations 34, no. 4 (June 12, 2017): 1191–203. http://dx.doi.org/10.1108/ec-04-2016-0137.
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Purpose High head gates are commonly used in hydropower plants for flow regulation and emergence closure. Hydrodynamic downpull can be a critical parameter in design of the lifting mechanism. The purpose of this paper is to show that a simplified two-dimensional (2D) computational fluid dynamics solution can be used in the prediction of the downpull force on the gate lip by comparison of computed results to experimentally measured data. Design/methodology/approach In this study, ANSYS FLUENT CFD software was used to obtain 2D numerical solution for the flow field around a generic gate model located in a power intake structure which was previously used in an experimental study. Description of the flow domain, computational grid resolution, requirements on setting appropriate boundary conditions and methodology in describing downpull coefficient are discussed. Total number of 245 simulations for variable gate lip geometry and gate openings were run. The downpull coefficient evaluated from the computed pressure field as function of gate opening and lip angle are compared with the experimental results. Findings The computed downpull coefficient agrees well with the previous experimental results, except one gate with small lip angle where a separation bubble forms along the lip, which is responsible from this deviation. It is observed that three-dimensional (3D) effects are confined to the large gate openings where downpull is minimum or even reversed. Research limitations/implications In large gate openings, three dimensionality of the flow around gate slots plays an important role and departure from 2D solutions become more pronounced. In that case, one might need to perform a 3D solution instead. Practical implications This paper presents a very fast and accurate way to predict downpull force on high head gates in the absence of experimental data. Originality/value An extensive amount of simulations are run within the scope of this study. It is shown that knowing its limitations, 2D numerical models can be used to calculate downpull for a wide range of gate openings without the need of expensive experimental models.
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Song, Hao, Eric Brown, Russell Hawkins, and Penger Tong. "Dynamics of large-scale circulation of turbulent thermal convection in a horizontal cylinder." Journal of Fluid Mechanics 740 (February 6, 2014): 136–67. http://dx.doi.org/10.1017/jfm.2013.655.
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AbstractA systematic study of the effects of cell geometry on the dynamics of large-scale flows in turbulent thermal convection is carried out in horizontal cylindrical cells of different lengths filled with water. Four different flow modes are identified with increasing aspect ratio $\Gamma $. For small aspect ratios ($\Gamma \leq 0.16$), the flow is highly confined in a thin disc-like cell with a quasi-two-dimensional (quasi-2D) large-scale circulation (LSC) in the circular plane of the cell. For larger aspect ratios ($\Gamma >0.16$), we observe periodic switching of the angular orientation $\theta $ of the rotation plane of LSC between the two longest diagonals of the cell. The sides of the container along which the LSC oscillates changes at a critical aspect ratio $\Gamma _{c}\simeq 0.82$. The measured switching period is equal to the LSC turnover time for $\Gamma \leq \Gamma _c$, shows a sharp increase at $\Gamma _{c}$ and decays exponentially to the LSC turnover time with increasing $\Gamma $. For $\Gamma \geq 1.3$, a periodic rocking of LSC along the long axis of the cylinder is also observed. The measured probability density function $P(\theta )$ of the LSC orientation $\theta $ peaks at the two diagonal positions, and its shape is described by a phenomenological model proposed by Brown & Ahlers (Phys. Fluids, vol. 20, 2008b, 075101; J. Fluid Mech., vol. 638, 2009, pp. 383–400). Using this model, we describe the dynamics of the LSC orientation $\theta $ by stochastic motion in a double-well potential. The potential is predicted from a model in which the sidewall shape produces an orientation-dependent pressure on the LSC. This model also captures key features of the four flow modes. The experiment reveals an interesting array of rich dynamics of LSC in the horizontal cylinders, which are very different from those observed in the upright cylindrical convection cells. The success of the model for both upright and horizontal cylinders suggests that it can be applied to different geometries.
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Short, Mark, and James J. Quirk. "The effect of compaction of a porous material confiner on detonation propagation." Journal of Fluid Mechanics 834 (November 17, 2017): 434–63. http://dx.doi.org/10.1017/jfm.2017.736.
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The fluid mechanics of the interaction between a porous material confiner and a steady propagating high explosive (HE) detonation in a two-dimensional slab geometry is investigated through analytical oblique wave polar analysis and multi-material numerical simulation. Two HE models are considered, broadly representing the properties of either a high- or low-detonation-speed HE, which permits studies of detonation propagating at speeds faster or slower than the confiner sound speed. The HE detonation is responsible for driving the compaction front in the confiner, while, in turn, the high material density generated in the confiner as a result of the compaction process can provide a strong confinement effect on the HE detonation structure. Polar solutions that describe the local flow interaction of the oblique HE detonation shock and equilibrium state behind an oblique compaction wave with rapid compaction relaxation rates are studied for varying initial solid volume fractions of the porous confiner. Multi-material numerical simulations are conducted to study the effect of detonation wave driven compaction in the porous confiner on both the detonation propagation speed and detonation driving zone structure. We perform a parametric study to establish how detonation confinement is influenced both by the initial solid volume fraction of the porous confiner and by the time scale of the dynamic compaction relaxation process relative to the detonation reaction time scale, for both the high- and low-detonation-speed HE models. The compaction relaxation time scale is found to have a significant influence on the confinement dynamics, with slower compaction relaxation time scales resulting in more strongly confined detonations and increased detonation speeds. The dynamics of detonation confinement by porous materials when the detonation is propagating either faster or slower than the confiner sound speed is found to be significantly different from that with solid material confiners.
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Singh, Sundeep, and Roderick Melnik. "Coupled Multiphysics Modelling of Sensors for Chemical, Biomedical, and Environmental Applications with Focus on Smart Materials and Low-Dimensional Nanostructures." Chemosensors 10, no. 5 (April 25, 2022): 157. http://dx.doi.org/10.3390/chemosensors10050157.
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Low-dimensional nanostructures have many advantages when used in sensors compared to the traditional bulk materials, in particular in their sensitivity and specificity. In such nanostructures, the motion of carriers can be confined from one, two, or all three spatial dimensions, leading to their unique properties. New advancements in nanosensors, based on low-dimensional nanostructures, permit their functioning at scales comparable with biological processes and natural systems, allowing their efficient functionalization with chemical and biological molecules. In this article, we provide details of such sensors, focusing on their several important classes, as well as the issues of their designs based on mathematical and computational models covering a range of scales. Such multiscale models require state-of-the-art techniques for their solutions, and we provide an overview of the associated numerical methodologies and approaches in this context. We emphasize the importance of accounting for coupling between different physical fields such as thermal, electromechanical, and magnetic, as well as of additional nonlinear and nonlocal effects which can be salient features of new applications and sensor designs. Our special attention is given to nanowires and nanotubes which are well suited for nanosensor designs and applications, being able to carry a double functionality, as transducers and the media to transmit the signal. One of the key properties of these nanostructures is an enhancement in sensitivity resulting from their high surface-to-volume ratio, which leads to their geometry-dependant properties. This dependency requires careful consideration at the modelling stage, and we provide further details on this issue. Another important class of sensors analyzed here is pertinent to sensor and actuator technologies based on smart materials. The modelling of such materials in their dynamics-enabled applications represents a significant challenge as we have to deal with strongly nonlinear coupled problems, accounting for dynamic interactions between different physical fields and microstructure evolution. Among other classes, important in novel sensor applications, we have given our special attention to heterostructures and nucleic acid based nanostructures. In terms of the application areas, we have focused on chemical and biomedical fields, as well as on green energy and environmentally-friendly technologies where the efficient designs and opportune deployments of sensors are both urgent and compelling.
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Singh, Sundeep, and Roderick Melnik. "Coupled Multiphysics Modelling of Sensors for Chemical, Biomedical, and Environmental Applications with Focus on Smart Materials and Low-Dimensional Nanostructures." Chemosensors 10, no. 5 (April 25, 2022): 157. http://dx.doi.org/10.3390/chemosensors10050157.
Full textAbstract:
Low-dimensional nanostructures have many advantages when used in sensors compared to the traditional bulk materials, in particular in their sensitivity and specificity. In such nanostructures, the motion of carriers can be confined from one, two, or all three spatial dimensions, leading to their unique properties. New advancements in nanosensors, based on low-dimensional nanostructures, permit their functioning at scales comparable with biological processes and natural systems, allowing their efficient functionalization with chemical and biological molecules. In this article, we provide details of such sensors, focusing on their several important classes, as well as the issues of their designs based on mathematical and computational models covering a range of scales. Such multiscale models require state-of-the-art techniques for their solutions, and we provide an overview of the associated numerical methodologies and approaches in this context. We emphasize the importance of accounting for coupling between different physical fields such as thermal, electromechanical, and magnetic, as well as of additional nonlinear and nonlocal effects which can be salient features of new applications and sensor designs. Our special attention is given to nanowires and nanotubes which are well suited for nanosensor designs and applications, being able to carry a double functionality, as transducers and the media to transmit the signal. One of the key properties of these nanostructures is an enhancement in sensitivity resulting from their high surface-to-volume ratio, which leads to their geometry-dependant properties. This dependency requires careful consideration at the modelling stage, and we provide further details on this issue. Another important class of sensors analyzed here is pertinent to sensor and actuator technologies based on smart materials. The modelling of such materials in their dynamics-enabled applications represents a significant challenge as we have to deal with strongly nonlinear coupled problems, accounting for dynamic interactions between different physical fields and microstructure evolution. Among other classes, important in novel sensor applications, we have given our special attention to heterostructures and nucleic acid based nanostructures. In terms of the application areas, we have focused on chemical and biomedical fields, as well as on green energy and environmentally-friendly technologies where the efficient designs and opportune deployments of sensors are both urgent and compelling.
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GUENDELMAN, EDUARDO, ALEXANDER KAGANOVICH, EMIL NISSIMOV, and SVETLANA PACHEVA. "HIDING AND CONFINING CHARGES VIA "TUBE-LIKE" WORMHOLES." International Journal of Modern Physics A 26, no. 30n31 (December 20, 2011): 5211–39. http://dx.doi.org/10.1142/s0217751x11054851.
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We describe two interesting effects in wormhole physics. First, we find that a genuinely charged matter source of gravity and electromagnetism may appear electrically neutral to an external observer — a phenomenon opposite to the famous Misner–Wheeler "charge without charge" effect. We show that this phenomenon takes place when coupling a bulk gravity/nonlinear-gauge-field system self-consistently to a codimension-one charged lightlike brane as a matter source. The "charge-hiding" effect occurs in a self-consistent wormhole solution of the above coupled gravity/nonlinear-gauge-field/lightlike-brane system which connects a noncompact "universe," comprising the exterior region of Schwarzschild–(anti-)de Sitter (or purely Schwarzschild) black hole beyond the internal (Schwarzschild) horizon, to a Levi-Civita–Bertotti–Robinson-type ("tube-like") "universe" with two compactified dimensions via a wormhole "throat" occupied by the charged lightlike brane. In this solution the whole electric flux produced by the charged lightlike brane is expelled into the compactified Levi-Civita–Bertotti–Robinson-type "universe" and, consequently, the brane is detected as neutral by an observer in the Schwarzschild–(anti-)de Sitter "universe." Next, the above "charge-hiding" solution can be further generalized to a truly charge-confining wormhole solution when we couple the bulk gravity/nonlinear-gauge-field system self-consistently to two separate codimension-one charged lightlike branes with equal in magnitude but opposite charges. The latter system possesses a "two-throat" wormhole solution, where the "left-most" and the "right-most" "universes" are two identical copies of the exterior region of the neutral Schwarzschild–de Sitter black hole beyond the Schwarzschild horizon, whereas the "middle" "universe" is of generalized Levi-Civita–Bertotti–Robinson "tube-like" form with geometry dS2 ×S2 (dS2 being the two-dimensional de Sitter space). It comprises the finite-extent intermediate region of dS2 between its two horizons. Both "throats" are occupied by the two oppositely charged lightlike branes and the whole electric flux produced by the latter is confined entirely within the middle finite-extent "tube-like" "universe." A crucial ingredient is the special form of the nonlinear gauge field action, which contains both the standard Maxwell term as well as a square root of the latter. This theory was previously shown to produce a QCD-like confining dynamics in flat space–time.
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Mirzaeian, N., and K. Alba. "Monodisperse particle-laden exchange flows in a vertical duct." Journal of Fluid Mechanics 847 (May 21, 2018): 134–60. http://dx.doi.org/10.1017/jfm.2018.325.
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We study buoyancy-driven exchange flow of two mixtures in a vertical narrow duct (two-dimensional channel as well as pipe) theoretically. While the light mixture is assumed always to be a pure fluid, the heavy mixture can be selected as either a pure or a particle-laden fluid. A small width-to-length ratio considered for the duct ($\unicode[STIX]{x1D6FF}\ll 1$) has been used as the perturbation parameter in developing a lubrication model (negligible inertia). In particular, we have adopted the methodology of Zhou et al. (Phys. Rev. Lett., vol. 94, 2005, 117803) for free-surface particle-laden film flows and extended it to a lock exchange system in confined geometry under the Boussinesq approximation. The resulting model is in the form of the classical Riemann problem and has been solved numerically using a robust total variation diminishing finite difference scheme. Both pure and particle-laden cases are investigated in detail. It is observed that the interface between the two fluids takes a self-similar shape at long times. In the case that both heavy and light fluids are pure, the dynamics of the flow is governed by two dimensionless quantities, namely the Reynolds number, $Re$, and the viscosity ratio, $\unicode[STIX]{x1D705}$, of the light and heavy fluids. The interpenetration of the heavy and light layers increases with $Re$ but decreases with $\unicode[STIX]{x1D705}$. Also, the heights of the heavy and light fronts change with $\unicode[STIX]{x1D705}$ but remain unchanged with $Re$. In the case of the particle-laden flow, however, four additional dimensionless parameters emerge, namely the initial volume fraction of particles, $\unicode[STIX]{x1D719}_{0}$, the ratio of particle diameter to duct width, $r_{p}$, and the density ratios of particles to carrying fluid, $\unicode[STIX]{x1D709}$, and of light fluid to carrying fluid, $\unicode[STIX]{x1D702}$. The effect of these parameters on the dynamics of the flow has been quantified through a systematic approach. In the presence of solid particles, the interface between the heavy and light layers becomes more curved compared to the case of pure fluids. This modification occurs due to the change of heavy mixture viscosity alongside the duct. Novel particle-rich zones are further discovered in the vicinity of the advancing heavy and light fronts. These zones are associated with different transport rates of the fluid and solid particles. The degree of particle enrichment remains the same with $Re$, is enhanced by $\unicode[STIX]{x1D705}$, $r_{p}$ and $\unicode[STIX]{x1D702}$, and is slightly diminished with $\unicode[STIX]{x1D719}_{0}$ and $\unicode[STIX]{x1D709}$. On the other hand, the stretched exchange zone between the heavy and light fronts grows with $r_{p}$, $\unicode[STIX]{x1D702}$ and $Re$, but decays with $\unicode[STIX]{x1D719}_{0}$, $\unicode[STIX]{x1D705}$ and $\unicode[STIX]{x1D709}$.
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Chen, Jiang-Xing, Renbo Yuan, Rufei Cui, and Liyan Qiao. "The dynamics and self-assembly of chemically self-propelled sphere dimers." Nanoscale, 2021. http://dx.doi.org/10.1039/d0nr06368a.
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Abbasi, Mehdi, Alexander Farutin, Abdessamad Nait-Ouhra, Hamid Ez-Zahraouy, Abdelilah Benyoussef, and Chaouqi Misbah. "Dynamics and rheology of a single two-dimensional multilobe vesicle in a confined geometry." Physical Review Fluids 7, no. 9 (September 13, 2022). http://dx.doi.org/10.1103/physrevfluids.7.093603.
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Kavokine, Nikita, Paul Robin, and Lydéric Bocquet. "Interaction confinement and electronic screening in two-dimensional nanofluidic channels." Journal of Chemical Physics, August 29, 2022. http://dx.doi.org/10.1063/5.0102002.
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The transport of fluids at the nanoscale is fundamental to manifold biological and industrial processes, ranging from neurotransmission to ultrafiltration. Yet, it is only recently that well-controlled channels with cross- sections as small as a few molecular diameters became an experimental reality. When aqueous electrolytes are confined within such channels, the Coulomb interactions between the dissolved ions are reinforced due to dielectric contrast at the channel walls: we dub this effect 'interaction confinement'. Yet, no systematic way of computing these confined interactions has been proposed beyond the limiting cases of perfectly metallic or perfectly insulating channel walls. Here, we introduce a new formalism, based on the so-called surface response functions, that expresses the effective Coulomb interactions within a two-dimensional channel in terms of the wall's electronic structure, described to any desired level of precision. We use it to demonstrate that in few-nanometer-wide channels, the ionic interactions can be tuned by the wall material's screening length. We illustrate this approach by implementing these interactions in brownian dynamics simulations of a strongly confined electrolyte, and show that the resulting ionic conduction can be adjusted between Ohm's law and a Wien effect behavior. Our results provide a quantitative approach to tuning nanoscale ion transport through the electronic properties of the channel wall material.
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Federico, Salvatore, Giorgio Ferrari, and Patrick Schuhmann. "Singular Control of the Drift of a Brownian System." Applied Mathematics & Optimization, April 29, 2021. http://dx.doi.org/10.1007/s00245-021-09779-3.
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AbstractWe consider a standard Brownian motion whose drift can be increased or decreased in a possibly singular manner. The objective is to minimize an expected functional involving the time-integral of a running cost and the proportional costs of adjusting the drift. The resulting two-dimensional degenerate singular stochastic control problem has interconnected dynamics and it is solved by combining techniques of viscosity theory and free boundary problems. We provide a detailed description of the problem’s value function and of the geometry of the state space, which is split into three regions by two monotone curves. Our main result shows that those curves are continuously differentiable with locally Lipschitz derivative and solve a system of nonlinear ordinary differential equations.
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Murray, Cherry A., Wolfgang Sprenger, Raj Seshadri, and Jane E. Cerise. "Dynamical Buckling Transitions of a Confined Colloidal Monolayer." MRS Proceedings 366 (1994). http://dx.doi.org/10.1557/proc-366-163.
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ABSTRACTWhen a rigid two-dimensional triangular crystalline layer of colloidal spheres confined between two smooth repulsive walls is gradually given freedom to move out of plane, it buckles dynamically undergoing several Peierls transitions involving different soft phonon modes before forming a two layer crystal with square in-plane symmetry. We have mapped out the complex phase diagram of the buckling transitions as a function of sphere density and wall separation. Digital imaging is used to study the instantaneous particle positions and trajectories of the uniform, highly charged 0.3 μm diameter polystyrene spheres that comprise the crystalline layer in water suspension. Brownian motion of the spheres creates a true thermodynamic system with a real temperature, which is studied using video microscopy. We follow the collective dynamics of the system as well as individual particle motions and the motions and rearrangements of topological defects and domains. At sufficiently low sphere densities the system melts into a fluid. As the wall separation increases to the point of two layer formation we observe square symmetry in the fluid correlation volumes.
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Hutchinson, A. J., R. J. Gusinow, and M. Grae Worster. "The evolution of a viscous gravity current in a confined geometry." Journal of Fluid Mechanics 959 (March 15, 2023). http://dx.doi.org/10.1017/jfm.2023.81.
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We describe a theoretical and experimental study of an axisymmetric viscous gravity current with a constant flux, confined to the space between two horizontal parallel plates. The effect of confinement results in two regions of flow: an inner region where the fluid is in contact with both plates and an outer annular region where the fluid forms a gravity current along the lower plate. We present a simple theoretical model that describes the flow dynamics by a single dimensionless parameter $J$ , which is the ratio of the characteristic height of an unconfined gravity current to the height of the confined space. Theoretical height profiles display the same characteristics as unconfined gravity currents until $J \approx 0.48$ , where a rapid change in behaviour occurs as confinement comes into effect. For larger values of $J$ , the confined viscous gravity current gradually tends to Hele-Shaw flow, with the transition essentially complete by $J \approx 2$ . We compare the findings from our theoretical model with the results of a series of experiments using golden syrup with various fluxes and gap spacings. Although the data aligns with the major aspects of the model, it is clear that other physics is at play and a single non-dimensional parameter is not sufficient to capture the flow behaviour fully. We speculate on the factors absent in our model that may be responsible for this mismatch.
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Bressloff, Paul C. "Trapping of an active Brownian particle at a partially absorbing wall." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 479, no. 2273 (May 2023). http://dx.doi.org/10.1098/rspa.2023.0086.
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Active matter concerns the self-organization of energy consuming elements such as motile bacteria or self-propelled colloids. A canonical example is an active Brownian particle (ABP) that moves at a constant speed while its direction of motion undergoes rotational diffusion. When ABPs are confined within a channel, they tend to accumulate at the channel walls, even when inter-particle interactions are ignored. Each particle pushes on the boundary until a tumble event reverses its direction. The wall thus acts as a sticky boundary. In this article, we consider a natural extension of sticky boundaries that allow for a particle to be permanently absorbed (killed) whilst attached to a wall. In particular, we investigate the first passage time (FPT) problem for an ABP in a two-dimensional channel where one of the walls is partially permeable. Calculating the exact FPT statistics requires solving a non-trivial two-way diffusion boundary value problem. We follow a different approach by separating out the dynamics away from the absorbing wall from the dynamics of absorption and escape whilst attached to the wall. By using probabilistic methods, we derive an explicit expression for the mean first passage time of absorption, assuming that the arrival statistics of particles at the wall are known. Our method also allows us to incorporate a more general encounter-based model of absorption.
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Khatri, Narender, and Raymond Kapral. "Inertial effects on rectification and diffusion of active Brownian particles in an asymmetric channel." Journal of Chemical Physics, March 7, 2023. http://dx.doi.org/10.1063/5.0141696.
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Micro- and nano-swimmers moving in a fluid solvent confined by structures that produce entropic barriers are often described by overdamped active Brownian particle dynamics, where viscous effects are large and inertia plays no role. However, inertial effects should be considered for confined swimmers moving in media where viscous effects are no longer dominant. Here, we study how inertia affects the rectification and diffusion of self-propelled particles in a two-dimensional asymmetric channel. We show that most of the particles accumulate at the channel walls as the masses of the particles increase. Furthermore, the average particle velocity has a maximum as a function of the mass, indicating that particles with an optimal mass $M^{*}_{\rm op}$ can be sorted from a mixture with particles of other masses. In particular, we find that the effective diffusion coefficient exhibits an enhanced diffusion peak as a function of the mass, which is a signature of the accumulation of most of the particles at the channel walls. The dependence of $M^{*}_{\rm op}$ on the rotational diffusion rate, self-propulsion force, aspect ratio of the channel, and active torque is also determined. The results of this study could stimulate the development of strategies for controlling the diffusion of self-propelled particles in entropic ratchet systems.
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Guan, Liyang, Li Tian, Meiying Hou, and Yilong Han. "Dynamics of a vibration-driven single disk." Scientific Reports 11, no. 1 (August 16, 2021). http://dx.doi.org/10.1038/s41598-021-95672-6.
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AbstractGranular particles exhibit rich collective behaviors on vibration beds, but the motion of an isolated particle is not well understood even for uniform particles with a simple shape such as disks or spheres. Here we measured the motion of a single disk confined to a quasi-two-dimensional horizontal box on a vertically vibrating stage. The translational displacements obey compressed exponential distributions whose exponent $$\beta$$ β increases with the frequency, while the rotational displacements exhibit unimodal distributions at low frequencies and bimodal distributions at high frequencies. During short time intervals, the translational displacements are subdiffusive and negatively correlated, while the rotational displacements are superdiffusive and positively correlated. After prolonged periods, the rotational displacements become diffusive and their correlations decay to zero. Both the rotational and the translational displacements exhibit white noise at low frequencies, and blue noise for translational motions and Brownian noise for rotational motions at high frequencies. The translational kinetic energy obeys Boltzmann distribution while the rotational kinetic energy deviates from it. Most energy is distributed in translational motions at low frequencies and in rotational motions at high frequencies, which violates the equipartition theorem. Translational and rotational motions are not correlated. These experimental results show that the random diffusion of such driven particles is distinct from thermal motion in both the translational and rotational degrees of freedom, which poses new challenges to theory. The results cast new light on the motion of individual particles and the collective motion of driven granular particles.
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Hoang, D. A., L. M. Portela, C. R. Kleijn, M. T. Kreutzer, and V. van Steijn. "Dynamics of droplet breakup in a T-junction." Journal of Fluid Mechanics 717 (February 7, 2013). http://dx.doi.org/10.1017/jfm.2013.18.
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AbstractThe breakup of droplets due to creeping motion in a confined microchannel geometry is studied using three-dimensional numerical simulations. Analogously to unconfined droplets, there exist two distinct breakup phases: (i) a quasi-steady droplet deformation driven by the externally applied flow; and (ii) a surface-tension-driven three-dimensional rapid pinching that is independent of the externally applied flow. In the first phase, the droplet relaxes back to its original shape if the externally applied flow stops; if the second phase is reached, the droplet will always break. Also analogously to unconfined droplets, there exist two distinct critical conditions: (i) one that determines whether the droplet reaches the second phase and breaks, or it reaches a steady shape and does not break; and (ii) one that determines when the rapid autonomous pinching starts. We analyse the second phase using stop–flow simulations, which reveal that the mechanism responsible for the autonomous breakup is similar to the end-pinching mechanism for unconfined droplets reported in the literature: the rapid pinching starts when, in the channel mid-plane, the curvature at the neck becomes larger than the curvature everywhere else. The same critical condition is observed in simulations in which we do not stop the flow: the breakup dynamics and the neck thickness corresponding to the crossover of curvatures are similar in both cases. This critical neck thickness depends strongly on the aspect ratio, and, unlike unconfined flows, depends only weakly on the capillary number and the viscosity contrast between the fluids inside and outside the droplet.
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Zhang, Lizhong, Omer Blaes, and Yan-Fei Jiang. "Radiative relativistic magnetohydrodynamic simulations of neutron star column accretion in Cartesian geometry." Monthly Notices of the Royal Astronomical Society, July 9, 2022. http://dx.doi.org/10.1093/mnras/stac1815.
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Abstract High luminosity accretion on to a strongly magnetized neutron star results in a radiation pressure dominated, magnetically confined accretion column. We investigate the dynamics of these columns using two-dimensional radiative relativistic magnetohydrodynamic simulations, restricting consideration to modest accretion rates where the height of the column is low enough that Cartesian geometry can be employed. The column structure is dynamically maintained through high-frequency oscillations of the accretion shock at ≃ 10–25 kHz. These oscillations arise because it is necessary to redistribute the power released at the accretion shock through bulk vertical motions, both to balance the cooling and to provide vertical pressure support against gravity. Sideways cooling always dominates the loss of internal energy. In addition to the vertical oscillations, photon bubbles form in our simulations and add additional spatial complexity to the column structure. They are not themselves responsible for the oscillations, and they do not appear to affect the oscillation period. However, they enhance the vertical transport of radiation and increase the oscillation amplitude in luminosity. The time-averaged column structure in our simulations resembles the trends in standard 1D stationary models, the main difference being that the time-averaged height of the shock front is lower because of the higher cooling efficiency of the 2D column shape.
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Hong, Daniel C., Su Yue, and Douglas A. Kurtze. "Dynamics of Granular Materials: Flows, Relaxation and Convection." MRS Proceedings 367 (1994). http://dx.doi.org/10.1557/proc-367-483.
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AbstractUsing the diffusing void model of granular flows, we study the dynamic response of granular materials, in particular, the relaxation of granular pile, pipe flow of granular materials, and the convection of granular media in a two dimensional box subjected to vibrations. We first study the relaxation of a one dimensional granular pile of height L in a confined geometry under repeated tapping within the context of the diffusing void model. The reduction of height as a function of the number of taps is proportional to the accumulated void density at the top layer. The relaxation process is characterized by the two dynamic exponents z and z' which describe the time dependence of the height reduction, Δh(t) ≈ tz and the total relaxation time, T(L) ≈ Lz'. While the governing equation is nonlinear, we find numerically that z=z'=l, which is robust against perturbations and independent of the initial void distributions. We then show that the existence of a steady state traveling wave solution is responsible for such a linear behavior. Next, we examine the case where each void is able to maintain its overall topology as a round object that can subject itself to compression. In this regime, the governing equations for voids reduce to traffic equations and numerical solutions reveal that a cluster of voids arrives at the top periodically, which is manifested by the appearance of periodic solutions in the density at the top. In this case, the relaxation proceeds via a stick-slip process and the reduction of the height is sudden and discontinuous. We then carry out the long wave analysis to demonstrate the existence of the KdV solitons in the traffic equations. Finally, we show our preliminary studies on granular convection in a box. We observe the appearance of two rolls when the control parameter exceeds the critical value, which then undergoes bifurcations to four rolls.
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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." Journal of Engineering for Gas Turbines and Power 132, no. 2 (November 2, 2009). http://dx.doi.org/10.1115/1.3078784.
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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 similar to a General Atomics gas-turbine-modular helium reactor 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 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 resolutions compared with similar facilities at smaller scales. A three-dimensional particle image velocimetry system was used to collect the data. Inlet-jet Reynolds numbers (based on the jet diameter and the time-mean bulk velocity) are approximately 4300 and 12,400. Uncertainty analyses and a discussion of the standard problem are included. The measurements reveal developing, nonuniform, 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.