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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 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.
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.
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.
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.
Ambipolar drift in turbulent fluids are considered. Using mean-field electrodynamics, a two-scale theory originally used to study hydromagnetic dynamos, it is shown that magnetic fields can be advected by small-scale magnetosonic (compressional) turbulence or generated by Alfvenic (helical) turbulence. A simple dynamo theory is made and is compared with standard theories in which dissipation is caused by turbulent diffusion. The redistribution of magnetic flux in interstellar clouds is also discussed.
We study a model for two competing species that explicitly accounts for effects due to discreteness, stochasticity and spatial extension of populations. The two species are equally preferred by the environment and do better when surrounded by others of the same species. We observe that the final outcome depends on the initial densities (uniformly distributed in space) of the two species. The observed phase transition is a continuous one and key macroscopic quantities like the correlation length of clusters and the time-to-extinction diverge at a critical point. Away from the critical point, the dynamics can be described by a mean-field approximation. Close to the critical point, however, there is a crossover to power-law behavior because of the gross mismatch between the largest and smallest scales in the system. We have developed a theory based on surface effects, which is in good agreement with the observed behavior. The course-grained reaction-diffusion system obtained from the mean-field dynamics agrees well with the particle system.
Colloidal suspensions have proven to be excellent model systems for the study of condensed matter and its phase behavior. Many of the properties of colloidal suspensions can be investigated with a systematic variation of the characteristics of the systems and, in addition, the energy, length and time scales associated with them allow for experimental probing of otherwise inaccessible regimes. The latter property also makes colloidal systems vulnerable to external influences such as gravity. Experiments performed in micro-ravity by Chaikin and Russell have been invaluable in extracting the true behavior of the systems without an external field. Weitz and Pusey intend to use mixtures of colloidal particles with additives such as polymers to induce aggregation and form weak, tenuous, highly disordered fractal structures that would be stable in the absence of gravitational forces. When dispersed in a polarizable medium, colloidal particles can ionize, emitting counterions into the solution. The standard interaction potential in these charged colloidal suspensions was first obtained by Derjaguin, Landau, Verwey and Overbeek. The DLVO potential is obtained in the mean-field linearized Poisson-Boltzmann approximation and thus has limited applicability. For more precise calculations, we have used ab initio density functional theory. In our model, colloidal particles are charged hard spheres, the counterions are described by a continuum density field and the solvent is treated as a homogeneous medium with a specified dielectric constant. We calculate the effective forces between charged colloidal particles by integrating over the solvent and counterion degrees of freedom, taking into account the direct interactions between the particles as well as particle-counterion, counterion-counterion Coulomb, counterion entropic and correlation contributions. We obtain the effective interaction potential between charged colloidal particles in different configurations. We evaluate two- and three-body forces in the bulk as well as study the influence of soft walls. We qualitatively explain the effects of the walls on the forces and demonstrate that many-body effects are negligible in our system. With adjustments in the parameters, the DLVO pair-potential can describe the results quantitatively. Besides electrostatic interactions, entropic depletion effects that arise from (hard-core) exclusion play an important role in determining the behavior of multi-component colloidal suspensions. A standard theory for depletion forces is due to Asakura and Oosawa and is based on the ideal gas approximation. To go beyond this approximation, we have studied entropic forces in molecular dynamics simulations of systems of hard spheres (the effects of the solvent have been ignored). The effective depletion forces for these systems can be found either from equilibrium distribution functions or from direct momentum transfer calculations. Our results obtained by either method show qualitative differences from the Asakura-Oosawa forces, indicating a longer range, higher value at contact and most importantly a more complicated structure, comprising of several maxima and minima. Our calculations include the determination of effective forces between two spheres, a hard sphere and a wall, and the behavior of a hard sphere near a step-edge and a corner. We also demonstrate that such entropic forces do not necessarily satisfy pairwise additivity.
The kinetic pathways resulting from the formation of coherent gamma'-precipitates from the gamma-matrix are studied for two Ni-Al-Cr alloys with similar gamma'-precipitate volume fractions at 873 K. The details of the phase decompositions of Ni-7.5Al-8.5Cr at.% and Ni-5.2Al-14.2Cr at.% for aging times from 1/6 to 1024 h are investigated by atom-probe tomography, and are found to differ significantly from a mean-field description of coarsening. The morphologies of the gamma'-precipitates of the alloys are similar, though the degrees of gamma'-precipitate coagulation and coalescence differ. Quantification within the framework of classical nucleation theory reveals that differences in the chemical driving forces for phase decomposition result in differences in the nucleation behavior of the two alloys. The temporal evolution of the gamma'-precipitate average radii and the gamma-matrix supersaturations follow the predictions of classical coarsening models. The compositional trajectories of the gamma-matrix phases of the alloys are found to follow approximately the equilibrium tie-lines, while the trajectories of the gamma'-precipitates do not, resulting in significant differences in the partitioning ratios of the solute elements.
Using first-order smoothing theory, Fourier analysis and perturbation methods, the evolution equation of the wave spectrum as well as the nonlinear forces generated by random Alfven waves in a finite-beta plasma with phenomenological Landau-damping effects are obtained. The effect of microscale random Alfven waves on the propagation of large-scale hydromagnetic waves is also investigated by solving the mean-field equations. It is shown that parallel-propagating random Alfven waves are modulationally stable and that obliquely propagating random Alfven waves can be modulationally unstable when the energy of random waves is converted to slow magnetoacoustic waves that can be Landau-damped, providing a dissipation mechanism for the Alfven waves.
We expand the fluctuating flow variables of Boussinesq convection in the planform functions of linear theory. Our proposal is to consider a drastic truncation of this expansion as a possible useful approximation scheme for studying cellular convection. With just one term included, we obtain a fairly simple set of equations which reproduces some of the qualitative properties of cellular convection and whose steady-state form has already been derived by Roberts (1966). This set of 'modal equations' is analyzed at slightly supercritical and at very high Rayleigh numbers. In the latter regime the Nusselt number varies with Rayleigh number just as in the mean-field approximation with one horizontal scale when the boundaries are rigid. However, the Nusselt number now depends also on the Prandtl number in a way that seems compatible with experiment. The chief difficulty with the approach is the absence of a deductive scheme for deciding which planforms should be retained in the truncated expansion.