Learning to Design Synergetic Computers with an Extended Symmetric Diffusion Network

1999 ◽  
Vol 11 (6) ◽  
pp. 1475-1491
Author(s):  
Koji Okuhara ◽  
Shunji Osaki ◽  
Masaaki Kijima
Keyword(s):  
Image Processing ◽  
Planck Equation ◽  
Boltzmann Distribution ◽  
Order Parameters ◽  
Discrete State ◽  
Drift Term ◽  
Nonlinear Potential ◽  
Associative Function ◽  
Special Case ◽  
Symmetric Diffusion

This article proposes an extended symmetric diffusion network that is applied to the design of synergetic computers. The state of a synergetic computer is translated to that of order parameters whose dynamics is described by a stochastic differential equation. The order parameter converges to the Boltzmann distribution, under some condition on the drift term, derived by the Fokker-Planck equation. The network can learn the dynamics of the order parameters from a nonlinear potential. This property is necessary to design the coefficient values of the synergetic computer. We propose a searching function for the image processing executed by the synergetic computer. It is shown that the image processing with the searching function is superior to the usual image-associative function of synergetic computation. The proposed network can be related, as a special case, to the discrete-state Boltzmann machine by some transformation. Finally, the extended symmetric diffusion network is applied to the estimation problem of an entire density function, as well as the proposed searching function for the image processing.

On the Edge Singularity of an Actuator Disk with Large Constant Normal Load

1977 ◽  
Vol 21 (02) ◽  
pp. 125-131
Author(s):  
G. H. Schmidt ◽  
J. A. Sparenberg
Keyword(s):  
Potential Theory ◽  
Normal Load ◽  
Curved Surface ◽  
Singular Behavior ◽  
Nonlinear Potential Theory ◽  
Edge Singularity ◽  
Actuator Disk ◽  
Nonlinear Potential ◽  
Constant Normal Load ◽  
Special Case

In this paper some aspects of the nonlinear potential theory of actuator disks are considered. A rather general formulation of the problem for a prescribed load on a curved surface is given. For the special case of constant normal load and no incoming velocity the singular behavior of the flow at the edge of the disk is discussed.

Radio Aids to Navigation

1948 ◽  
Vol 1 (01) ◽  
pp. 15-21
Author(s):  
Robert Watson-Watt
Keyword(s):  
Dual Problem ◽  
Weather Forecasting ◽  
Dead Reckoning ◽  
Random Variable ◽  
Time Schedule ◽  
Freedom Of Choice ◽  
Drift Term ◽  
Science And Art ◽  
Special Case

The objectives of navigation have, in the special case of air services, been summed up, in an ‘R.S.V.P.’ formula, as Regularity, Safety, Versatility and Punctuality. The formula holds for all navigation, since the object of every operator and every master is to carry his passenger or freight in safety on a preconceived time schedule, with virtually complete freedom of choice, by owner or master, of type of craft, of time of departure and of route. The enemies of this freedom of choice and of the preconceived schedule are almost wholly meteorological or astronomical; the only serious enemies are meteorological. The continuing concern of the ‘navigator’ proper is to avoid, detect and rectify departures from the preselected route and schedule. The whole task of ‘navigation’ is unfulfilled without an infallible look-out for dangerous obstacles, which may be at fixed and known absolute positions, or at random, variable and unknown positions relative to the craft. Good ‘eyes’ naturally or artificially aided and a good clock would be the only indispensable tools of whole navigation, were it not for those imperfections of the science and art of weather forecasting which leave the drift term in dead reckoning such a deplorably variable and unmanageable element in the dual problem of the navigator. That dual problem is ‘Where am I now?’ and ‘Where shall I be inxminutes from now?’ The unpredictability of the drift term and the imperfections of the navigator and his instruments prevent the answer to the second question emerging mechanically from the answers to the two much simpler and essentially similar questions: ‘Where am I now?’ and ‘Where was Iyminutes ago?’

scholarly journals Scaling collapse and structure functions: identifying self-affinity in finite length time series

2005 ◽  
Vol 12 (6) ◽  
pp. 767-774 ◽  
Author(s):  
S. C. Chapman ◽  
B. Hnat ◽  
G. Rowlands ◽  
N. W. Watkins
Keyword(s):  
Time Series ◽  
Finite Length ◽  
Planck Equation ◽  
Structure Functions ◽  
Affine Scaling ◽  
Theoretical Understanding ◽  
Scaling Properties ◽  
Formidable Challenge ◽  
Special Case

Abstract. Empirical determination of the scaling properties and exponents of time series presents a formidable challenge in testing, and developing, a theoretical understanding of turbulence and other out-of-equilibrium phenomena. We discuss the special case of self affine time series in the context of a stochastic process. We highlight two complementary approaches to the differenced variable of the data: i) attempting a scaling collapse of the Probability Density Functions which should then be well described by the solution of the corresponding Fokker-Planck equation and ii) using structure functions to determine the scaling properties of the higher order moments. We consider a method of conditioning that recovers the underlying self affine scaling in a finite length time series, and illustrate it using a Lévy flight.

On the interpretation of vibrational relaxation times

1983 ◽  
Vol 61 (6) ◽  
pp. 1253-1266 ◽  
Author(s):  
Heshel Teitelbaum
Keyword(s):  
Shock Tube ◽  
Thermal Effects ◽  
Vibrational Energy ◽  
Chemical Activation ◽  
Relaxation Times ◽  
Boltzmann Distribution ◽  
Vibrational Energy Level ◽  
Rate Laws ◽  
Transfer Processes ◽  
Special Case

Rate laws for the evolution of vibrational energy level populations are derived when the Bethe–Teller law is obeyed. It is assumed that a Boltzmann distribution is maintained via rapid V–V processes. A variety of different rate laws result depending on the size and direction of the perturbation, the extent from equilibrium, and how classical the oscillator is at the initial and final conditions. An earlier analysis by Breshears is shown to be a special case. A prescription is given for procedures to compare relaxation times obtained from shock tube experiments and from laser-induced fluorescence experiments, when T–V energy transfer processes are rate-determining. Corrections for thermal effects are included. Shock tube, fluorescence, and chemical activation experiments are proposed which provide meaningful conditions for testing the Bethe–Teller law and for testing the existence of a Boltzmann distribution.

Combined Effect of Surface Roughness and Heterogeneity of Wall Potential on Electroosmosis in Microfluidic/Nanofuidic Channels

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
S. Bhattacharyya ◽  
A. K. Nayak
Keyword(s):  
Channel Wall ◽  
Stokes Equations ◽  
Axial Flow ◽  
Planck Equation ◽  
Boltzmann Distribution ◽  
Vortical Flow ◽  
Mixing Efficiency ◽  
Wall Roughness ◽  
Electrokinetic Flow ◽  
Ζ Potential

The motivation of the present study is to generate vortical flow by introducing channel wall roughness in the form of a wall mounted block that has a step-jump in ζ-potential on the upper face. The characteristics for the electrokinetic flow are obtained by numerically solving the Poisson equation, the Nernst–Planck equation, and the Navier–Stokes equations, simultaneously. A numerical method based on the pressure correction iterative algorithm (SIMPLE) is adopted to compute the flow field and mole fraction of the ions. The potential patch induces a strong recirculation vortex, which in turn generates a strong pressure gradient. The strength of the vortex, which appears adjacent to the potential patch, increases almost linearly with the increase in ζ-potential. The streamlines follow a tortuous path near the wall roughness. The average axial flow rate over the block is enhanced significantly. We found that the ionic distribution follow the equilibrium Boltzmann distribution away from the wall roughness. The solutions based on the Poisson–Boltzmann distribution and the Nernst–Planck model are different when the inertial effect is significant. The combined effects due to geometrical modulation of the channel wall and heterogeneity in ζ-potential is found to produce a stronger vortex, and hence a stronger mixing, compared with either of these. Increase in ζ-potential increases both the transport rate and mixing efficiency. A novelty of the present configuration is that the vortex forms above the obstacle even when the patch potential is negative.

Recent Developments in Material Microstructure: a Theory of Coarsening

2015 ◽  
Vol 1753 ◽  
Author(s):  
K. Barmak ◽  
E. Eggeling ◽  
M. Emelianenko ◽  
Y. Epshteyn ◽  
D. Kinderlehrer ◽  
...  
Keyword(s):  
Steady State ◽  
Energy Density ◽  
Grain Boundary ◽  
Cellular Networks ◽  
Empirical Distribution ◽  
Relative Length ◽  
Planck Equation ◽  
Boltzmann Distribution ◽  
Grain Boundary Character Distribution ◽  
Lattice Misorientation

ABSTRACTCellular networks are ubiquitous in nature. Most engineered materials are polycrystalline microstructures composed of a myriad of small grains separated by grain boundaries, thus comprising cellular networks. The recently discovered grain boundary character distribution (GBCD) is an empirical distribution of the relative length (in 2D) or area (in 3D) of interface with a given lattice misorientation and normal. During the coarsening, or growth, process, an initially random grain boundary arrangement reaches a steady state that is strongly correlated to the interfacial energy density. In simulation, if the given energy density depends only on lattice misorientation, then the steady state GBCD and the energy are related by a Boltzmann distribution. This is among the simplest non-random distributions, corresponding to independent trials with respect to the energy. Why does such simplicity emerge from such complexity? Here we describe an entropy based theory which suggests that the evolution of the GBCD satisfies a Fokker-Planck Equation, an equation whose stationary state is a Boltzmann distribution.

scholarly journals Non-equilibrium properties of an active nanoparticle in a harmonic potential

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Falko Schmidt ◽  
Hana Šípová-Jungová ◽  
Mikael Käll ◽  
Alois Würger ◽  
Giovanni Volpe
Keyword(s):  
Effective Temperature ◽  
Rotational Diffusion ◽  
Planck Equation ◽  
Experimental System ◽  
Boltzmann Distribution ◽  
Harmonic Potential ◽  
Directed Motion ◽  
Active Particles ◽  
Active Nanoparticles ◽  
Non Equilibrium

AbstractActive particles break out of thermodynamic equilibrium thanks to their directed motion, which leads to complex and interesting behaviors in the presence of confining potentials. When dealing with active nanoparticles, however, the overwhelming presence of rotational diffusion hinders directed motion, leading to an increase of their effective temperature, but otherwise masking the effects of self-propulsion. Here, we demonstrate an experimental system where an active nanoparticle immersed in a critical solution and held in an optical harmonic potential features far-from-equilibrium behavior beyond an increase of its effective temperature. When increasing the laser power, we observe a cross-over from a Boltzmann distribution to a non-equilibrium state, where the particle performs fast orbital rotations about the beam axis. These findings are rationalized by solving the Fokker-Planck equation for the particle’s position and orientation in terms of a moment expansion. The proposed self-propulsion mechanism results from the particle’s non-sphericity and the lower critical point of the solution.

A QUASI-LINEAR STOCHASTIC FOKKER–PLANCK EQUATION IN σ-FINITE MEASURES

2008 ◽  
Vol 08 (03) ◽  
pp. 475-504
Author(s):  
PETER M. KOTELENEZ
Keyword(s):  
Planck Equation ◽  
Transport Equations ◽  
Number Density ◽  
First Order ◽  
Borel Measures ◽  
Stochastic Transport ◽  
Fokker Planck Equations ◽  
Finite Measures ◽  
Special Case ◽  
Fokker Planck

Solutions of quasi-linear stochastic Fokker–Planck equations for the number density of a system of solute particles in suspension are derived. The initial values and the solutions take values in a class of σ-finite Borel measures over Rd where d ≥ 1. The stochastic driving noise is defined by Itô differentials. For the special case of semi-linear stochastic Fokker–Planck equations, the solutions can be represented as solutions of first-order stochastic transport equations driven by Stratonovich differentials.

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