ON THE GROSS–PITAEVSKII EQUATION WITH STRONGLY ANISOTROPIC CONFINEMENT: FORMAL ASYMPTOTICS AND NUMERICAL EXPERIMENTS

2005 ◽  
Vol 15 (05) ◽  
pp. 767-782 ◽  
Author(s):  
WEIZHU BAO ◽  
PETER A. MARKOWICH ◽  
CHRISTIAN SCHMEISER ◽  
RADA M. WEISHÄUPL
Keyword(s):  
Asymptotic Approximation ◽  
Numerical Experiments ◽  
Three Dimensional ◽  
Approximation Error ◽  
Fixed Number ◽  
Pitaevskii Equation ◽  
Strongly Coupled ◽  
Confining Potential ◽  
Formal Asymptotics ◽  
Formal Limit

The three-dimensional (3D) Gross–Pitaevskii equation with strongly anisotropic confining potential is analyzed. The formal limit as the ratio of the frequencies ε tends to zero provides a denumerable system of two-dimensional Gross–Pitaevskii equations, strongly coupled through the cubic nonlinearities. To numerically solve the asymptotic approximation only a finite number of limiting equations is considered. Finally, the approximation error for a fixed number of equations is compared for different ε tending to zero. On the other hand, the approximation error for an increasing number of terms in the approximation is observed.

On Pattern Selection in Three-Dimensional Bénard-Marangoni Flows

2012 ◽  
Vol 11 (3) ◽  
pp. 893-924 ◽  
Author(s):  
Arne Morten Kvarving ◽  
Tormod Bjøntegaard ◽  
Einar M. Rønquist
Keyword(s):  
Numerical Experiments ◽  
Initial Conditions ◽  
Computational Study ◽  
Fluid Layer ◽  
Three Dimensional ◽  
Fixed Number ◽  
Random Initial Condition ◽  
Initial Condition ◽  
Convection Pattern ◽  
Number Of Cells

AbstractIn this paper we study Bénard-Marangoni convection in confined containers where a thin fluid layer is heated from below. We consider containers with circular, square and hexagonal cross-sections. For Marangoni numbers close to the critical Marangoni number, the flow patterns are dominated by the appearance of the well-known hexagonal convection cells. The main purpose of this computational study is to explore the possible patterns the system may end up in for a given set of parameters. In a series of numerical experiments, the coupled fluid-thermal system is started with a zero initial condition for the velocity and a random initial condition for the temperature. For a given set of parameters we demonstrate that the system can end up in more than one state. For example, the final state of the system may be dominated by a steady convection pattern with a fixed number of cells, however, the same system may occasionally end up in a steady pattern involving a slightly different number of cells, or it may end up in a state where most of the cells are stationary, while one or more cells end up in an oscillatory state. For larger aspect ratio containers, we are also able to reproduce dislocations in the convection pattern, which have also been observed experimentally. It has been conjectured that such imperfections (e.g., a localized star-like pattern) are due to small irregularities in the experimental setup (e.g., the geometry of the container). However, we show, through controlled numerical experiments, that such phenomena may appear under otherwise ideal conditions. By repeating the numerical experiments for the same non-dimensional numbers, using a different random initial condition for the temperature in each case, we are able to get an indication of how rare such events are. Next, we study the effect of symmetrizing the initial conditions. Finally, we study the effect of selected geometry deformations on the resulting convection patterns.

scholarly journals Investigation of Improved Cooperative Coevolution for Large-Scale Global Optimization Problems

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 146
Author(s):  
Aleksei Vakhnin ◽  
Evgenii Sopov
Keyword(s):  
Global Optimization ◽  
Evolutionary Algorithms ◽  
Numerical Experiments ◽  
Large Scale ◽  
Optimization Problems ◽  
State Of The Art ◽  
Fixed Number ◽  
High Dimensional ◽  
Cooperative Coevolution ◽  
Large Scale Problems

Modern real-valued optimization problems are complex and high-dimensional, and they are known as “large-scale global optimization (LSGO)” problems. Classic evolutionary algorithms (EAs) perform poorly on this class of problems because of the curse of dimensionality. Cooperative Coevolution (CC) is a high-performed framework for performing the decomposition of large-scale problems into smaller and easier subproblems by grouping objective variables. The efficiency of CC strongly depends on the size of groups and the grouping approach. In this study, an improved CC (iCC) approach for solving LSGO problems has been proposed and investigated. iCC changes the number of variables in subcomponents dynamically during the optimization process. The SHADE algorithm is used as a subcomponent optimizer. We have investigated the performance of iCC-SHADE and CC-SHADE on fifteen problems from the LSGO CEC’13 benchmark set provided by the IEEE Congress of Evolutionary Computation. The results of numerical experiments have shown that iCC-SHADE outperforms, on average, CC-SHADE with a fixed number of subcomponents. Also, we have compared iCC-SHADE with some state-of-the-art LSGO metaheuristics. The experimental results have shown that the proposed algorithm is competitive with other efficient metaheuristics.

scholarly journals Prandtl Number in Classical Hard-Sphere and One-Component Plasma Fluids

Molecules ◽  
2021 ◽  
Vol 26 (4) ◽  
pp. 821
Author(s):  
Sergey Khrapak ◽  
Alexey Khrapak
Keyword(s):  
Prandtl Number ◽  
Hard Sphere ◽  
Solid Phase ◽  
Freezing Point ◽  
Three Dimensional ◽  
Order Unity ◽  
Strongly Coupled ◽  
Dielectric Fluids ◽  
Weakly Coupled ◽  
Component Plasma

The Prandtl number is evaluated for the three-dimensional hard-sphere and one-component plasma fluids, from the dilute weakly coupled regime up to a dense strongly coupled regime near the fluid-solid phase transition. In both cases, numerical values of order unity are obtained. The Prandtl number increases on approaching the freezing point, where it reaches a quasi-universal value for simple dielectric fluids of about ≃1.7. Relations to two-dimensional fluids are briefly discussed.

scholarly journals Three-dimensional 𝒩 = 2 supersymmetric gauge theories and partition functions on Seifert manifolds: A review

2019 ◽  
Vol 34 (23) ◽  
pp. 1930011 ◽  
Author(s):  
Cyril Closset ◽  
Heeyeon Kim
Keyword(s):  
Correlation Functions ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Partition Functions ◽  
Exact Results ◽  
Strongly Coupled ◽  
Seifert Manifolds ◽  
Recent Developments ◽  
Supersymmetric Gauge ◽  
Chern Simons

We give a pedagogical introduction to the study of supersymmetric partition functions of 3D [Formula: see text] supersymmetric Chern–Simons-matter theories (with an [Formula: see text]-symmetry) on half-BPS closed three-manifolds — including [Formula: see text], [Formula: see text], and any Seifert three-manifold. Three-dimensional gauge theories can flow to nontrivial fixed points in the infrared. In the presence of 3D [Formula: see text] supersymmetry, many exact results are known about the strongly-coupled infrared, due in good part to powerful localization techniques. We review some of these techniques and emphasize some more recent developments, which provide a simple and comprehensive formalism for the exact computation of half-BPS observables on closed three-manifolds (partition functions and correlation functions of line operators). Along the way, we also review simple examples of 3D infrared dualities. The computation of supersymmetric partition functions provides exceedingly precise tests of these dualities.

Acceleration of the EM-like reconstruction method for diffuse optical tomography with ordered-subsets method

2014 ◽  
Vol 22 (3) ◽  
Author(s):  
Caifang Wang
Keyword(s):  
Numerical Experiments ◽  
Imaging Modality ◽  
Random Medium ◽  
Optical Tomography ◽  
Back Propagation ◽  
Three Dimensional ◽  
Diffuse Optical Tomography ◽  
Optical Parameters ◽  
Reconstruction Method ◽  
Boundary Measurements

Abstract.Diffuse optical tomography (DOT) is an optical imaging modality, which provides the spatial distribution of the optical parameters inside a random medium. A propagation back-propagation method named EM-like reconstruction method for stationary DOT problem has been proposed yet. This method is really time consuming. Hence the ordered-subsets (OS) technique for this reconstruction method is studied in this paper. The boundary measurements of DOT are grouped into nonoverlapping and overlapping ordered sequence of subsets with random partition, sequential partition and periodic partition, respectively. The performance of OS methods is compared with the standard EM-like reconstruction method with two-dimensional and three-dimensional numerical experiments. The numerical experiments indicate that reconstruction of nonoverlapping subsets with periodic partition, overlapping subsets with periodic partition and standard EM-like method provide very similar acceptable reconstruction results. However, reconstruction of nonoverlapping subsets with periodic partition spends a minimum of time to get proper results.

Effects of Wheel-Shaft-Fluid Coupling and Local Wheel Deformations on the Global Behavior of Shaft Lines

2002 ◽  
Vol 124 (4) ◽  
pp. 953-957 ◽  
Author(s):  
D. Lornage ◽  
E. Chatelet ◽  
G. Jacquet-Richardet
Keyword(s):  
Three Dimensional ◽  
Fluid Film ◽  
Global Behavior ◽  
Three Dimensional Model ◽  
Fluid Films ◽  
Strongly Coupled ◽  
Proposed Model ◽  
Structural Deformations ◽  
Time Marching ◽  
Fluid Coupling

Rotating parts of turbomachines are generally studied using different uncoupled approaches. For example, the dynamic behavior of shafts and wheels are considered independently and the influence of the surrounding fluid is often taken into account in an approximate way. These approaches, while often sufficiently accurate, are questionable when wheel-shaft coupling is observed or when fluid elements are strongly coupled with local structural deformations (leakage flow between wheel and casing, fluid bearings mounted on a thin-walled shaft, etc.). The approach proposed is a step toward a global model of shaft lines. The whole flexible wheel-shaft assembly and the influence of specific fluid film elements are considered in a fully three-dimensional model. In this paper, the proposed model is first presented and then applied to a simple disk-shaft assembly coupled with a fluid film clustered between the disk and a rigid casing. The finite element method is used together with a modal reduction for the structural analysis. As thin fluid films are considered, the Reynolds equation is solved using finite differences in order to obtain the pressure field. Data are transferred between structural and fluid meshes using a general method based on an interfacing grid concept. The equations governing the whole system are solved within a time-marching procedure. The results obtained show significant influence of specific three-dimensional features such as disk-shaft coupling and local disk deformations on global behavior.

Reconstruction of the Reservoir Fine Structure by Using Scattering Attributes

2021 ◽  
Author(s):  
Vladimir Cheverda ◽  
Vadim Lisitsa ◽  
Maksim Protasov ◽  
Galina Reshetova ◽  
Andrey Ledyaev ◽  
...  
Keyword(s):  
Seismic Data ◽  
Numerical Experiments ◽  
Seismic Waves ◽  
Fractured Reservoirs ◽  
Three Dimensional ◽  
Geological Structure ◽  
Discrete Elements ◽  
Digital Twin ◽  
The North ◽  
Slip Surfaces

Abstract To develop the optimal strategy for developing a hydrocarbon field, one should know in fine detail its geological structure. More and more attention has been paid to cavernous-fractured reservoirs within the carbonate environment in the last decades. This article presents a technology for three-dimensional computing images of such reservoirs using scattered seismic waves. To verify it, we built a particular synthetic model, a digital twin of one of the licensed objects in the north of Eastern Siberia. One distinctive feature of this digital twin is the representation of faults not as some ideal slip surfaces but as three-dimensional geological bodies filled with tectonic breccias. To simulate such breccias and the geometry of these bodies, we performed a series of numerical experiments based on the discrete elements technique. The purpose of these experiments is the simulation of the geomechanical processes of fault formation. For the digital twin constructed, we performed full-scale 3D seismic modeling, which made it possible to conduct fully controlled numerical experiments on the construction of wave images and, on this basis, to propose an optimal seismic data processing graph.

scholarly journals A Triggering Mechanism for Rapid Intensification of Tropical Cyclones

2015 ◽  
Vol 72 (7) ◽  
pp. 2666-2681 ◽  
Author(s):  
Yoshiaki Miyamoto ◽  
Tetsuya Takemi
Keyword(s):  
Boundary Layer ◽  
Numerical Experiments ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Tangential Velocity ◽  
Convective Cell ◽  
Rapid Intensification ◽  
Rotating Fluid ◽  
Coriolis Parameter ◽  
Maximum Tangential Velocity

Triggering processes for the rapidly intensifying phase of a tropical cyclone (TC) were investigated on the basis of numerical experiments using a three-dimensional nonhydrostatic model. The results revealed that the rapid intensification of the simulated TC commenced following the formation of a circular cloud, which occurred about 12 h after the TC became essentially axisymmetric. The circular cloud (eyewall) evolved from a cloudy convective cell that was originally generated near the radius of maximum wind speed (RMW). The development of the convective cell in the eyewall was closely related to the radial location of the strong boundary layer convergence of axisymmetric flow. The radius of maximum convergence (RMC) was small relative to the RMW when the TC vortex was weak, which is consistent with the boundary layer theory for a rotating fluid system on a frictional surface. As the TC intensified, the RMC approached the RMW. An eyewall was very likely to form in the simulated TC when the RMC approached the RMW. Because the RMC is theoretically determined by a Rossby number defined by the maximum tangential velocity, RMW, and Coriolis parameter, a series of numerical experiments was conducted by changing the three parameters. The results were consistent with the hypothesis that intensification occurs earlier for larger Rossby numbers. This finding indicates that initial TC vortices with larger Rossby numbers are more likely to experience rapid intensification and, hence, to evolve into strong hurricanes.

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