Adjustment of vorticity fields with specified values of Casimir invariants as initial condition for simulated annealing of an incompressible, ideal neutral fluid and its MHD in two dimensions

2015 ◽  
Vol 774 ◽  
pp. 443-459 ◽  
Author(s):  
Y. Chikasue ◽  
M. Furukawa
Keyword(s):  
Simulated Annealing ◽  
Finite Number ◽  
Stationary State ◽  
Two Dimensions ◽  
Annealing Process ◽  
Initial Condition ◽  
Vorticity Field ◽  
Casimir Invariants

A method is developed to adjust a vorticity field to satisfy specified values for a finite number of Casimir invariants. The developed method is tested numerically for a neutral fluid in two dimensions. The adjusted vorticity field is adopted as an initial condition for simulated annealing (SA) of an incompressible, ideal neutral fluid and its magnetohydrodynamics (MHD), where SA enables us to obtain a stationary state of the fluid. Since the Casimir invariants are kept unchanged during the annealing process, the obtained stationary state has the required values of the Casimir invariants specified by our method.

Simulated annealing process in general state space

1991 ◽  
Vol 23 (04) ◽  
pp. 866-893 ◽  
Author(s):  
Heikki Haario ◽  
Eero Saksman
Keyword(s):  
Stochastic Process ◽  
Simulated Annealing ◽  
State Space ◽  
Annealing Process ◽  
General State ◽  
Arbitrary State ◽  
Strong And Weak Convergence ◽  
General State Space ◽  
Rate Of Cooling ◽  
Space Conditions

The stochastic process corresponding to the simulated annealing optimization algorithm is generalized to the case of an arbitrary state space. Conditions for the strong and weak convergence of the process are established. In addition the relation between the size of the generating distributions and the possible rate of cooling is studied.

Instability of pressure-driven gas–liquid two-layer channel flows in two and three dimensions

2018 ◽  
Vol 849 ◽  
pp. 1-34 ◽  
Author(s):  
Lennon Ó Náraigh ◽  
Peter D. M. Spelt
Keyword(s):  
Flow Pattern ◽  
Linear Theory ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Channel Flows ◽  
Three Dimensions ◽  
Nonlinear Behaviour ◽  
Two Dimensional ◽  
Vorticity Field ◽  
Flow Pattern Map

We study unstable waves in gas–liquid two-layer channel flows driven by a pressure gradient, under stable stratification, not assumed to be set in motion impulsively. The basis of the study is direct numerical simulation (DNS) of the two-phase Navier–Stokes equations in two and three dimensions for moderately large Reynolds numbers, accompanied by a theoretical description of the dynamics in the linear regime (Orr–Sommerfeld–Squire equations). The results are compared and contrasted across a range of density ratios $r=\unicode[STIX]{x1D70C}_{liquid}/\unicode[STIX]{x1D70C}_{gas}$. Linear theory indicates that the growth rate of small-amplitude interfacial disturbances generally decreases with increasing $r$; at the same time, the cutoff wavenumbers in both streamwise and spanwise directions increase, leading to an ever-increasing range of unstable wavenumbers, albeit with diminished growth rates. The analysis also demonstrates that the most dangerous mode is two-dimensional in all cases considered. The results of a comparison between the DNS and linear theory demonstrate a consistency between the two approaches: as such, the route to a three-dimensional flow pattern is direct in these cases, i.e. through the strong influence of the linear instability. We also characterize the nonlinear behaviour of the system, and we establish that the disturbance vorticity field in two-dimensional systems is consistent with a mechanism proposed previously by Hinch (J. Fluid Mech., vol. 144, 1984, p. 463) for weakly inertial flows. A flow-pattern map constructed from two-dimensional numerical simulations is used to describe the various flow regimes observed as a function of density ratio, Reynolds number and Weber number. Corresponding simulations in three dimensions confirm that the flow-pattern map can be used to infer the fate of the interface there also, and show strong three-dimensionality in cases that exhibit violent behaviour in two dimensions, or otherwise the development of behaviour that is nearly two-dimensional behaviour possibly with the formation of a capillary ridge. The three-dimensional vorticity field is also analysed, thereby demonstrating how streamwise vorticity arises from the growth of otherwise two-dimensional modes.

Application of very fast simulated annealing and differential evolution in the search for FO-CRS wavefield attributes

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. O81-O92
Author(s):  
German Garabito ◽  
João Carlos R. Cruz
Keyword(s):  
Global Optimization ◽  
Simulated Annealing ◽  
Differential Evolution ◽  
Seismic Data ◽  
Optimization Algorithms ◽  
Two Dimensions ◽  
Seismic Section ◽  
Data Set ◽  
Computational Costs ◽  
Very Fast Simulated Annealing

The finite-offset common-reflection-surface (FO-CRS) stack method can be used to simulate any common-offset (CO) seismic section by stacking prestack seismic data along the surfaces defined by the paraxial hyperbolic traveltime approximation. In two dimensions, the FO-CRS stacking operator depends on five kinematic wavefield attributes for every time sample of the target CO section. The main problem with this method is identifying a computationally efficient data-driven search strategy for accurately determining the best set of FO-CRS attributes that produce the optimal coherence measure of the seismic signal in the prestack data. Identifying a global optimization algorithm with the best performance is a challenge when solving this optimization problem. This is because the objective function is multimodal and involves a large volume of data, which leads to high computational costs. We introduced a comparative and competitive study through the application of two global optimization algorithms that simultaneously search the FO-CRS attributes from the prestack seismic data, very fast simulated annealing (VFSA) and the differential evolution (DE). By applying this FO-CRS stack to the Marmousi synthetic seismic data set, we have compared the performances of the two optimization algorithms with regard to their efficiency and effectiveness in estimating the five FO-CRS attributes. To analyze the robustness of the two algorithms, we apply them to real land seismic data and show their ability to find the near-optimal attributes and to improve reflection events in noisy data with a very low fold. We reveal that VFSA is efficient in reaching the optimal coherence value with the lowest computational costs, and that DE is effective and reliable in reaching the optimal coherence for determining the best five searched-for attributes. Regardless of the differences, the FO-CRS stack produces enhanced and regularized high-quality CO sections using both global optimization methods.

Research on Image Technology with Application of K-Means Based on Genetic Simulated Annealing Algorithm in CT Image Segmentation

2014 ◽  
Vol 1022 ◽  
pp. 269-272
Author(s):  
Ling Li Zhu ◽  
Lan Wang
Keyword(s):  
Genetic Algorithm ◽  
Image Segmentation ◽  
Simulated Annealing ◽  
Clustering Analysis ◽  
Simulated Annealing Algorithm ◽  
Local Optimum ◽  
Initial Condition ◽  
Ct Image ◽  
Genetic Simulated Annealing Algorithm ◽  
Annealing Algorithm

Aiming at the characteristic of medical images, this paper presents the improved genetic simulated annealing algorithm with K-means clustering analysis and applies in medical CT image segmentation. This improved genetic simulated annealing algorithm can be used to globally optimize k-means image segmentation functions to solve the locality and the sensitiveness of the initial condition. It can automatically adjust the parameters of genetic algorithm according to the fitness values of individuals and the decentralizing degree of individuals of the population and keep the variety of population for rapidly converging, and it can effectively avoid appearing precocity and plunging into local optimum. The example shows that the method is feasible, and better segmentation results have got to satisfy the request for 3D reconstruction, compared with k-means image segmentation and genetic algorithm based image segmentation.

Polynomial-Rate Convergence to the Stationary State for the Continuum-Time Limit of the Minority Game

2008 ◽  
Vol 45 (02) ◽  
pp. 376-387
Author(s):  
Matteo Ortisi
Keyword(s):  
Asymptotic Behavior ◽  
Invariant Measure ◽  
Stationary State ◽  
Waiting Time ◽  
Upper Bound ◽  
Time Limit ◽  
Initial Condition ◽  
Minority Game ◽  
Special Case ◽  
The Continuum

In this paper we show that the continuum-time version of the minority game satisfies the criteria for the application of a theorem on the existence of an invariant measure. We consider the special case of a game with a ‘sufficiently’ asymmetric initial condition, where the number of possible choices for each individual is S = 2 and Γ < +∞. An upper bound for the asymptotic behavior, as the number of agents grows to infinity, of the waiting time for reaching the stationary state is then obtained.

scholarly journals COMBINING SPECTRAL SEQUENCING AND PARALLEL SIMULATED ANNEALING FOR THE MINLA PROBLEM

2003 ◽  
Vol 13 (01) ◽  
pp. 77-91 ◽  
Author(s):  
JORDI PETIT
Keyword(s):  
Simulated Annealing ◽  
High Probability ◽  
Annealing Process ◽  
Input Graph ◽  
Linear Arrangement ◽  
Solution Quality ◽  
Large Graphs ◽  
Distributed Memory Machines ◽  
Arrangement Problem ◽  
Linear Arrangement Problem

In this paper we present and analyze new sequential and parallel heuristics to approximate the Minimum Linear Arrangement problem (MinLA). The heuristics consist in obtaining a first global solution using Spectral Sequencing and improving it locally through Simulated Annealing. In order to accelerate the annealing process, we present a special neighborhood distribution that tends to favor moves with high probability to be accepted. We show how to make use of this neighborhood to parallelize the Metropolis stage on distributed memory machines by mapping partitions of the input graph to processors and performing moves concurrently. The paper reports the results obtained with this new heuristic when applied to a set of large graphs, including graphs arising from finite elements methods and graphs arising from VLSI applications. Compared to other heuristics, the measurements obtained show that the new heuristic improves the solution quality, decreases the running time and offers an excellent speedup when ran on a commodity network made of nine personal computers.

General solution of a Boltzmann equation, and the formation of Maxwellian tails

1981 ◽  
Vol 374 (1758) ◽  
pp. 371-400 ◽  
Keyword(s):  
Boltzmann Equation ◽  
General Solution ◽  
Cross Section ◽  
Relative Velocity ◽  
Collision Cross Section ◽  
Two Dimensions ◽  
Time Interval ◽  
Initial Condition ◽  
Finite Time Interval ◽  
Classical Boltzmann Equation

A classical Boltzmann equation is studied. The equation describes the evolution towards the Maxwellian equilibrium state of a homogeneous, isotropic gas where the collision cross section is inversely proportional to the relative velocity of the colliding particles. After Tjon & Wu (1979), the problem is transformed into a mathematically equivalent one, itself a model Boltzmann equation in two dimensions. Working in the context of the latter equation, a formal derivation of the general solution is presented. First a countable ensemble of particular solutions, called pure solutions , is constructed. From these, via a non-linear combination mechanism, the general solution is obtained in a form appropriate for direct numerical computation. The validity of the solution depends upon its containment in a well defined Hilbert space H~ Given that the initial condition lies within H~ it is proved that at least for a small finite time interval it remains in H~.

Simulated annealing process in general state space

1991 ◽  
Vol 23 (4) ◽  
pp. 866-893 ◽  
Author(s):  
Heikki Haario ◽  
Eero Saksman
Keyword(s):  
Stochastic Process ◽  
Simulated Annealing ◽  
State Space ◽  
Annealing Process ◽  
General State ◽  
Arbitrary State ◽  
Strong And Weak Convergence ◽  
General State Space ◽  
Rate Of Cooling ◽  
Space Conditions

The stochastic process corresponding to the simulated annealing optimization algorithm is generalized to the case of an arbitrary state space. Conditions for the strong and weak convergence of the process are established. In addition the relation between the size of the generating distributions and the possible rate of cooling is studied.

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