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The mean-field theory of dilute spin-glasses is studied in the limit where the average coordination number is finite. The zero-temperature phase diagram is calculated and the relationship between the spin-glass phase and the percolation transition is discussed. The present formalism is applicable also to graph optimization problems.
The fluctuation spectrum that must arise in a mean field dynamo generation of galactic fields if the initial field is weak is considered. A kinetic equation for its evolution is derived and solved. The spectrum evolves by transfer of energy from one magnetic mode to another by interaction with turbulent velocity modes. This kinetic equation is valid in the limit that the rate of evolution of the magnetic modes is slower than the reciprocal decorrelation time of the turbulent modes. This turns out to be the case by a factor greater than 3. Most of the fluctuation energy concentrates on small scales, shorter than the hydrodynamic turbulent scales. The fluctuation energy builds up to equipartition with the turbulent energy in times that are short compared to the e-folding time of the mean field. The turbulence becomes strongly modified before the dynamo amplification starts. Thus, the kinematic assumption of the mean dynamo theory is invalid. Thus, the galactic field must have a primordial origin, although it may subsequently be modified by dynamo action.
The excess conductivity behavior of highly oriented YBa2Cu3O(7-x) thin films prepared by both coevaporation and laser ablation was studied in detail in the reduced-temperature range 9 x 10(exp -4) is less than t is less than 1. The excess conductivity in all the films studied was found to diverge sharply near T(sub c), in agreement with the conventional mean-field theory. However, the detailed temperature dependence could not be fitted to either the power-law or the logarithmic functional forms as predicted by the theory. The excess conductivity of all the films was found to be exponentially dependent on the temperature over nearly three decades for 9 x 10(exp -4) is less than t is less than 10(exp -1), in contradiction to the mean-field theory.
A new method, based on Effective mean Field Theory, is proposed for the evaluation of the optical/dielectric properties of inhomogeneous materials, in which the real and imaginary parts of the dielectric function are determined by solving a simultaneous non-linear equation.
A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all red-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. This paper shows that the same information theoretic mathematical structure, known as Product Distribution (PD) theory, addresses both issues. In this, PD theory not only provides a principle formulation of bounded rationality and a set of new types of mean field theory in statistical physics; it also shows that those topics are fundamentally one and the same.
The partial structure factors of classical simple liquid mixtures near phase separation are dicussed. The theory is developed for particles interacting through pair potentials, and is thus appropriate both to insulating fluids, and also to metallic systems if these may be described by an effective ion-ion pair interaction. The motivation arose from consideration of metallic liquid mixtures, in which resistive anomalies have been observed near phase separation. A mean field theory correction appropriate to 3 pair potential for the effects of correlated motions in the reference fluid is studied. The work is cast in terms of functions which are closely related to the direct correlation functions of Ornstein and Zernike. The results are qualitatively in accord with physical expectations. Quantitative agreement with experiment seems to turn on the selection of the hard core reference potential in terms of the metallic effective pair potential. It is suggested that the present effective pair potentials are perhaps not properly used to calculate the metallic structure factors at long wavelength.
The previously developed Ginzburg-Landau theory for calculating the crystal-melt interfacial tension of bcc elements to treat the classical one-component plasma (OCP), the charged fermion system, and the Bose crystal. For the OCP, a direct application of the theory of Shih et al. (1987) yields for the surface tension 0.0012(Z-squared e-squared/a-cubed), where Ze is the ionic charge and a is the radius of the ionic sphere. Bose crystal-melt interface is treated by a quantum extension of the classical density-functional theory, using the Feynman formalism to estimate the relevant correlation functions. The theory is applied to the metastable He-4 solid-superfluid interface at T = 0, with a resulting surface tension of 0.085 erg/sq cm, in reasonable agreement with the value extrapolated from the measured surface tension of the bcc solid in the range 1.46-1.76 K. These results suggest that the density-functional approach is a satisfactory mean-field theory for estimating the equilibrium properties of liquid-solid interfaces, given knowledge of the uniform phases.
The elements of the cycle are summarized. The basic advantages include high entropy density in the magnetic material, completely reversible processes, convenient control of the entropy by the applied field, the feature that heat transfer is possible during all processes, and the ability of the ideal cycle to attain Carnot efficiency. The mean field theory is used to predict the entropy of a ferromagnet in an applied field and also the isothermal entropy change and isentropic temperature change caused by applying a field. The results for isentropic temperature change are compared with experimental data on Gd. Coarse mixtures of ferromagnetic materials with different Curie points are proposed to modify the path of the cycle in the T-S diagram in order to improve the efficiency or to increase the specific power.
There is the prospect of a fundamental new application for magnetic materials as the working substance in thermodynamic cycles. Recuperative cycles which use a rare-earth ferromagnetic material near its Curie point in the field of a superconducting magnet appear feasible for applications from below 20 K to above room temperature. The elements of the cycle, advanced in an earlier paper, are summarized. The basic advantages include high entropy density in the magnetic material, completely reversible processes, convenient control of the entropy by the applied field, the feature that heat transfer is possible during all processes, and the ability of the ideal cycle to attain Carnot efficiency. The mean field theory is used to predict the entropy of a ferromagnet in an applied field and also the isothermal entropy change and isentropic temperature change caused by applying a field. Results are presented for J = 7/2 and g = 2. The results for isentropic temperature change are compared with experimental data on Gd. Coarse mixtures of ferromagnetic materials with different Curie points are proposed to modify the path of the cycle in the T-S diagram in order to improve the efficiency or to increase the specific power.
The magnetic field patterns in the region beneath the solar photosphere is determined. An approximate method for downward extrapolation of line of sight magnetic field measurements taken at the solar photosphere was developed. It utilizes the mean field theory of electromagnetism in a form thought to be appropriate for the solar convection zone. A way to test that theory is proposed. The straightforward application of the lowest order theory with the complete model fit to these data does not indicate the existence of any reasonable depth at which flux conservation is achieved.
A study has been conducted of steady convection with adiabatic and viscous heating for variable viscosity in the Boussinesq limit using the mean-field theory. A strong nonlinear coupling is found between the thermodynamic constants governing adiabatic heating and the rheological parameters. The range of rheological values for which adiabaticity would occur throughout the mantle has been established. Too large an activation volume, greater than 6 cu cm/mol for the cases examined, would produce unreasonably high temperature at the bottom of the mantle (greater than 6000 K) and superadiabatic gradients, especially in the lower mantle. Radiogenic heating plays a profound role in controlling dynamically mantle temperatures. Present values for the averaged mantle heat production would yield objectionably high temperatures in the lower mantle.
An exact analysis of the Ising model with infinite-range interactions in a random field and a local mean-field theory in three dimensions is carried out leading to a phase diagram with several coexistence surfaces and lines of critical points. The results show that the phase diagram depends crucially on whether the distribution of random fields is symmetric or not. Thus, Ising-like phase transitions in a porous medium (the asymmetric case) are in a different universality class from the conventional random-field model (symmetric case).
The results are described of studies of a random-anisotropy Blume-Emery-Griffiths spin-1 Ising model using mean-field theory, transfer-matrix calculations, and position-space renormalization-group calculations. The interplay between the quenched randomness of the anisotropy and the annealed disorder introduced by the spin-1 model leads to a rich phase diagram with a variety of phase transitions and reentrant behavior. The results may be relevant to the study of the phase separation of He-3 - He-4 mixtures in porous media in the vicinity of the superfluid transition.
Recognition of partially occluded objects has been an important issue to airport security because occlusion causes significant problems in identifying and locating objects during baggage inspection. The neural network approach is suitable for the problems in the sense that the inherent parallelism of neural networks pursues many hypotheses in parallel resulting in high computation rates. Moreover, they provide a greater degree of robustness or fault tolerance than conventional computers. The annealed Hopfield network which is derived from the mean field annealing (MFA) has been developed to find global solutions of a nonlinear system. In the study, it has been proven that the system temperature of MFA is equivalent to the gain of the sigmoid function of a Hopfield network. In our early work, we developed the hybrid Hopfield network (HHN) for fast and reliable matching. However, HHN doesn't guarantee global solutions and yields false matching under heavily occluded conditions because HHN is dependent on initial states by its nature. In this paper, we present the annealed Hopfield network (AHN) for occluded object matching problems. In AHN, the mean field theory is applied to the hybird Hopfield network in order to improve computational complexity of the annealed Hopfield network and provide reliable matching under heavily occluded conditions. AHN is slower than HHN. However, AHN provides near global solutions without initial restrictions and provides less false matching than HHN. In conclusion, a new algorithm based upon a neural network approach was developed to demonstrate the feasibility of the automated inspection of threat objects from x-ray images. The robustness of the algorithm is proved by identifying occluded target objects with large tolerance of their features.
This paper addresses the development of a nonlinear optimal control methodology for magnetostrictive actuators. At moderate to high drive levels, the output from these actuators is highly nonlinear and contains significant magnetic and magnetomechanical hysteresis. These dynamics must be accommodated by models and control laws to utilize the full capabilities of the actuators. A characterization based upon ferromagnetic mean field theory provides a model which accurately quantifies both transient and steady state actuator dynamics under a variety of operating conditions. The control method consists of a linear perturbation feedback law used in combination with an optimal open loop nonlinear control. The nonlinear control incorporates the hysteresis and nonlinearities inherent to the transducer and can be computed offline. The feedback control is constructed through linearization of the perturbed system about the optimal system and is efficient for online implementation. As demonstrated through numerical examples, the combined hybrid control is robust and can be readily implemented in linear PDE-based structural models.
We have used the z-scan technique at a wavelength (532 nm) near the transmission window of bulk gold to measure the nonlinear absorption coefficient of continuous approximately 50-Angstrom-thick gold films, deposited onto surface-modified quartz substrates. For highly absorbing media such as metals, we demonstrate that determination of either the real or imaginary part of the third-order susceptibility requires a measurement of both nonlinear absorption and nonlinear refraction, i.e. both open- and closed-aperture z-scans must be performed. Closed-aperture z-scans did not yield a sufficient signal for the determination of the nonlinear refraction. However, open-aperture z-scans yielded values ranging from Beta = 1.9 x 10(exp -3) to 5.3 x 10(exp -3) cm/W in good agreement with predictions which ascribe the nonlinear response to a Fermi smearing mechanism. We note that the sign of the nonlinearity is reversed from that of gold nanoparticle composites, in accordance with the predictions of mean field theories.
Raman spectra & photoluminescence studies in PbTiO3, have been carried out, as a function of particle size, temperature, pressure and dopants. There appears respectively a distinct temperature-induced soft mode phase transition in each sample whose Curie temperature can be determined from the mean-field theory. The detailed Curie temperature shift in the modified PbTiO3 ceramics by Ba, Sr, La and Zr, has been investigated as a function of particle size. Pressure-induced phase transitions display an obvious diffuse behavior. Room temperature photoluminescence for nanocrystalline Ba(1-x)Pb(x)TiO3 have been observed. These studies favor preparations of high efficiency PbTiO3 sensors.
High temperature Raman spectra of nanocrystalline Pb(0.8)Ba(0.2)TiO3, Pb(0.8)Sr(0.2) TiO3, Pb(0.8)La(0.2)TiO3 and Pb(0.8)Ba(0.2)TiO3, have been measured, as a function of particle size. There appears respectively a distinct temperature-induced soft mode phase transition in every sample whose Curie temperature can be determined from the mean-field theory. The detailed Curie temperature shift in modified PbTi03 ceramics by Ba, Sr, La, and Zr, has also been investigated as a function of particle size. This study will favor preparations of high efficiency PbTi03 sensors with an adjustable Curie temperature.