Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy
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Kostyantyn Kechedzhi↗
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Random-anisotropy Blume-Emery-Griffiths model
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.
Maritan, Amos↗
Building Reliable Forecasts of Solar Activity
Solar ionizing radiation critically depends on the level of the Sun’s magnetic activity. For robust physics-based forecasts, we employ the procedure of data assimilation, which combines theoretical modeling and observational data such that uncertainties in both the model and the observations are taken into account. Currently we are working in two major directions: 1) development of a new long-term forecast procedure on time-scales of the 11-year solar cycle, using a 2-dimensional mean-field dynamo model and synoptic magnetograms; 2) development of 3-dimensional radiative MHD (Magnetohydrodynamic) simulations to investigate the origin and precursors of local manifestations of magnetic activity, such as the formation of magnetic structures and eruptive dynamics.
Kitiashvili, Irina↗
Structure of a fluid interface near the critical point
The structure of the liquid-liquid interface of three very different mixtures (carbon disulfide + methanol, methanol + cyclohexane + deuterated cyclohexane, and nitrobenzene + n-decane) has been studied using ellipsometry in the reduced temperature range between 0.0009 and 0.042. Although the elliptical thickness varies by an order of magnitude between these mixtures, the data from all three mixtures can be scaled to the same universal constant by a combined mean-field plus capillary-wave model of the interface. The universal constant determined experimentally is significantly less than the theoretical value.
Schmidt, James W.↗
Specific heats and thermodynamic critical fields in Zn-doped YBa2Cu3O(7-x) according to an induced-pairing model
Electronic specific heats and thermodynamic critical fields are calculated in a mean-field version of an induced-pairing model for superconductivity, and compared with results of Loram et al. (1990) on YBa2(Cu(1-y)Zn(y))3O(7-x). This model involves induction of pairing of holes in a wideband by strongly bound electronlike pairs. It is assumed that the planar hole concentration for no Zn addition is close to, but slightly higher than, that for the maximum Tc, and that it increases by 0.015 per planar Cu ion for each increase of y by 0.01. Parameters of the model are taken to be the same as in a previous publication in which energy gaps were discussed, except that an effective hybridization parameter is adjusted for each Zn concentration to give agreement with the observed Tc. Results are presented for y = 0.0, 0.01, and 0.03. The agreement with experiment is good for thermodynamic critical fields, and is fair for specific heats. For specimens with larger y, with relatively low T(c)s, it is argued that the model should be supplemented to include effects of a BCS-type interaction amongst the wideband carriers.
Eagles, D. M.↗
Incoherent vs. coherent behavior in the normal state of copper oxide superconductors
The self-consistent quantum fluctuations around the mean-field Hartree-Fock state of the Hubbard model provide a very good description of the ground state and low temperature properties of a 2-D itinerant antiferromagnet. Very good agreement with numerical calculations and experimental data is obtained by including the one- and two-loop spin wave corrections to various physical quantities. In particular, the destruction of the long-range order above the Neel temperature can be understood as a spontaneous generation of a length-scale epsilon(T), which should be identified as the spin correlation length. For finite doping, the question of the Hartree-Fock starting point becomes a more complex one since an extra hole tends to self-trap in antiferromagnetic background. Such quantum defects in an underlying antiferromagnetic state can be spin-bags or vortex-like structures and tend to suppress the long-range order. If motion of the holes occurs on a time-scale shorter than the one associated with the motion of these quantum defects of a spin background, one obtains several important empirical features of the normal state of CuO superconductors like linear T-dependence of resistivity, the cusp in the tunneling density of states, etc. As opposed to a familiar Fermi-liquid behavior, the phenomenology of the above system is dominated by a large incoherent piece of a single hole propagator, resulting in many unusual normal state properties.
Tesanovic, Zlatko↗
Effective Forces Between Colloidal Particles
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.
Tehver, Riina↗
Three-Dimensional Magnetohydrodynamic Modeling of the Solar Wind Including Pickup Protons and Turbulence Transport
To study the effects of interstellar pickup protons and turbulence on the structure and dynamics of the solar wind, we have developed a fully three-dimensional magnetohydrodynamic solar wind model that treats interstellar pickup protons as a separate fluid and incorporates the transport of turbulence and turbulent heating. The governing system of equations combines the mean-field equations for the solar wind plasma, magnetic field, and pickup protons and the turbulence transport equations for the turbulent energy, normalized cross-helicity, and correlation length. The model equations account for photoionization of interstellar hydrogen atoms and their charge exchange with solar wind protons, energy transfer from pickup protons to solar wind protons, and plasma heating by turbulent dissipation. Separate mass and energy equations are used for the solar wind and pickup protons, though a single momentum equation is employed under the assumption that the pickup protons are comoving with the solar wind protons.We compute the global structure of the solar wind plasma, magnetic field, and turbulence in the region from 0.3 to 100 AU for a source magnetic dipole on the Sun tilted by 0 deg - .90 deg and compare our results with Voyager 2 observations. The results computed with and without pickup protons are superposed to evaluate quantitatively the deceleration and heating effects of pickup protons, the overall compression of the magnetic field in the outer heliosphere caused by deceleration, and the weakening of corotating interaction regions by the thermal pressure of pickup protons.
Usmanov, Arcadi V.↗
Dynamical effects on the core-mantle boundary from depth-dependent thermodynamical properties of the lower mantle
A common assumption in modeling dynamical processes in the lower mantle is that both the thermal expansivity and thermal conductivity are reasonably constant. Recent work from seismic equation of state leads to substantially higher values for the thermal conductivity and much lower thermal expansivity values in the deep mantle. The dynamical consequences of incorporating depth-dependent thermodynamic properties on the thermal-mechanical state of the lower mantle are examined with the spherical-shell mean-field equations. It is found that the thermal structure of the seismically resolved anomalous zone at the base of the mantle is strongly influenced by these variable properties and, in particular, that the convective distortion of the core-mantle boundary (CMB) is reduced with the decreasing thermal expansivity. Such a reduction of the dynamically induced topography from pure thermal convection would suggest that some other dynamical mechanism must be operating at the CMB.
Zhang, Shuxia↗
Effects of Solute Concentrations on Kinetic Pathways in Ni-Al-Cr Alloys
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.
Booth-Morrison, Christopher↗
Three-Fluid Magnetohydrodynamic Modeling of the Solar Wind in the Outer Heliosphere
We have developed a three-fluid, fully three-dimensional magnetohydrodynamic model of the solar wind plasma in the outer heliosphere as a co-moving system of solar wind protons, electrons, and interstellar pickup protons, with separate energy equations for each species. Our approach takes into account the effects of electron heat conduction and dissipation of Alfvenic turbulence on the spatial evolution of the solar wind plasma and interplanetary magnetic fields. The turbulence transport model is based on the Reynolds decomposition of physical variables into mean and fluctuating components and uses the turbulent phenomenologies that describe the conversion of fluctuation energy into heat due to a turbulent cascade. We solve the coupled set of the three-fluid equations for the mean-field solar wind and the turbulence equations for the turbulence energy, cross helicity, and correlation length. The equations are written in the rotating frame of reference and include heating by turbulent dissipation, energy transfer from interstellar pickup protons to solar wind protons, and solar wind deceleration due to the interaction with the interstellar hydrogen. The numerical solution is constructed by the time relaxation method in the region from 0.3 to 100 AU. Initial results from the novel model are presented.
Usmanov, Arcadi V.↗
Critical Slowing Down in Time-to-Extinction: An Example of Critical Phenomena in Ecology
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.
Gandhi, Amar↗
The mean magnetic field of the sun - Observations at Stanford
A solar telescope has been built to study the organization and evolution of large-scale solar magnetic fields and velocities. The observations are made using a Babcock-type magnetograph connected to a 22.9-m vertical Littrow spectrograph. Sun-as-a-star integrated-light measurements of the mean solar magnetic field have been made daily since May 1975. The typical mean-field magnitude has been about 0.15 G, with a typical measurement error of less than 0.05 G. The mean-field polarity pattern is essentially identical to the interplanetary-magnetic-field sector structure (seen near earth with a four-day lag). The differences in the observed structures can be understood in terms of a 'warped current sheet' model.
Scherrer, P. H.↗
Stellar fibril magnetic systems. II - Two-dimensional magnetohydrodynamic equations. III - Convective counterflow
The dynamics of magnetic fibrils in the convective zone of a star is investigated analytically, deriving mean-field equations for the two-dimensional transverse motion of an incompressible fluid containing numerous small widely spaced circular cylinders. The equations of Parker (1982) are extended to account for the inertial effects of local flow around the cylinders. The linear field equation for the stream function at the onset of convection is then rewritten, neglecting large-scale heat transport, and used to construct a model of convective counterflow. The Kelvin impulse and fluid momentum, convective motion initiated by a horizontal impulse, and the effects of a viscous boundary layer are considered in appendices.
Parker, E. N.↗
Ordering and phase transitions in random-field Ising systems
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).
Maritan, Amos↗
Advances and Challenges in Observations and Modeling of the Global-Sun Dynamics and Dynamo
Computational heliophysics has shed light on the fundamental physical processes inside the Sun, such as the differential rotation, meridional circulation, and dynamo-generation of magnetic fields. However, despite the substantial advances, the current results of 3D MHD simulations are still far from reproducing helioseismic inferences and surface observations. The reason is the multi-scale nature of the solar dynamics, covering a vast range of scales, which can-not be solved with the current computational resources. In such a situation, significant progress has been achieved by the mean-field approach, based on the separation of small-scale turbulence and large-scale dynamics. The mean-field simulations can reproduce solar observations, qualitatively and quantitatively, and uncover new phenomena. However, they do not reveal the complex physics of large-scale convection, solar magnetic cycles, and the magnetic self-organization that causes sunspots and solar eruptions. Thus, developing a synergy of these approaches seems to be a necessary but very challenging task.
SMD↗