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Mean Field Theory (mean + field_theory)
Selected AbstractsComparisons and connections between mean field dynamo theory and accretion disc theoryASTRONOMISCHE NACHRICHTEN, Issue 1 2010E.G. Blackman Abstract The origin of large scale magnetic fields in astrophysical rotators, and the conversion of gravitational energy into radiation near stars and compact objects via accretion have been subjects of active research for a half century. Magnetohydrodynamic turbulence makes both problems highly nonlinear, so both subjects have benefitted from numerical simulations.However, understanding the key principles and practical modeling of observations warrants testable semi-analytic mean field theories that distill the essential physics. Mean field dynamo (MFD) theory and alpha-viscosity accretion disc theory exemplify this pursuit. That the latter is a mean field theory is not always made explicit but the combination of turbulence and global symmetry imply such. The more commonly explicit presentation of assumptions in 20th century textbook MFDT has exposed it to arguably more widespread criticism than incurred by 20th century alpha-accretion theory despite complementary weaknesses. In the 21st century however, MFDT has experienced a breakthrough with a dynamical saturation theory that consistently agrees with simulations. Such has not yet occurred in accretion disc theory, though progress is emerging. Ironically however, for accretion engines, MFDT and accretion theory are presently two artificially uncoupled pieces of what should be a single coupled theory. Large scale fields and accretion flows are dynamically intertwined because large scale fields likely play a key role in angular momentum transport. I discuss and synthesize aspects of recent progress in MFDT and accretion disc theory to suggest why the two likely conspire in a unified theory (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Kinetics of the volume phase transition in poly(n -isopropylacrylamide) gels prepared under high pressureJOURNAL OF POLYMER SCIENCE (IN TWO SECTIONS), Issue 13 2001Tadayosi Kitada Abstract New poly(N -isopropylacrylamide) gels were prepared under high pressure (ca. 200 MPa) during gelation. The preparation-pressure dependence of the deswelling speed of the gels was measured with a conventional T-jump method. The deswelling time of a gel rod 2.2 mm in diameter prepared at 193 MPa was about 200 s, 1000 times faster than that of a homogeneous poly(N -isopropylacrylamide) gel. Moreover, the collective diffusion coefficient, the thermal fluctuation, and the ensemble-average intensity of the swollen gel networks were obtained with dynamic light scattering measurements. Both the enthalpy and entropy of the gels were estimated from equilibrium swelling curves with the Flory,Huggins interaction parameter evaluated with mean field theory based on the Flory-type of the Gibbs free-energy formula. It was found that the networks of the gels had an inhomogeneous structure newly introduced by the preparation pressure. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2315,2325, 2001 [source] Block Copolymers Under Shear FlowMACROMOLECULAR THEORY AND SIMULATIONS, Issue 4 2005Igor Rychkov Abstract Summary: Microphase separation transition in block copolymer melts and solutions in equilibrium and under shear flow is reviewed. The non-equilibrium molecular dynamics (NEMD) computer simulation methodology is presented in detail including the derivation of the SLLOD equations of motion, Gaussian thermostat, and operator-splitting symplectic integrators. Results of our recent NEMD computer simulation studies of diblock copolymers in a selective solvent under shear flow are presented. Shear-dependent structural, rheological, and microscopical properties are described. New phase transitions are discovered. The parallel-perpendicular orientational transition in a weak-strong flow is revealed. Theoretical approaches are reviewed including the Edwards Hamiltonian, Landau-Ginzburg model, self-consistent mean field theory, field-theoretic simulation, as well as the time-dependent Landau-Ginzburg framework and its application to the studies of complex fluids. [source] Quantum phase transition between antiferromagnetic and charge order in the Hubbard,Holstein modelPHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 3 2010Johannes Bauer Abstract We explore the quantum phase transitions between two ordered states in the infinite dimensional Hubbard,Holstein model at half filling. Our study is based on the dynamical mean field theory (DMFT) combined with the numerical renormalization group (NRG), which allows us to handle both strong electron,electron and strong electron,phonon interactions. The transition line is characterized by an effective electron,electron interaction. Depending on this effective interaction and the phonon frequency ,0 one finds either a continuous transition or discontinuous transition. Here, the analysis focuses on the behavior of the system when the electron,electron repulsion U and the phonon-mediated attraction , are equal. We first discuss the adiabatic and antiadiabatic limiting cases. For finite ,0 we study the differences between the antiferromagnetic (AFM) and charge order, and find that when present the AFM state has a lower energy on the line. [source] Optical properties of correlated materials , Or why intelligent windows may look dirty,PHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 9 2009Jan M. Tomczak Abstract Materials with strong electronic Coulomb correlations play an increasing role in modern materials applications. "Thermochromic" systems, which exhibit thermally induced changes in their optical response, provide a particularly interesting case. The optical switching associated with the metal,insulator transition of vanadium dioxide (VO2), for example, has been proposed for use in numerous applications, ranging from anti-laser shields to "intelligent" windows, which selectively filter radiative heat in hot weather conditions. Are present-day electronic structure techniques able to describe, or , eventually even predict , such a kind of behavior? How far are we from materials design using correlated oxides? These are the central questions we try to address in this article. We review recent attempts of calculating optical properties of correlated materials within dynamical mean field theory, and summarize results for VO2 obtained within a novel scheme aiming at particularly simple and efficient calculations of optical transition matrix elements within localized basis sets. Finally, by optimizing the geometry of "intelligent windows," we argue that this kind of technique can, in principle, be used to provide guidance for experiments, thus giving a rather optimistic answer to the above questions. [source] On the CTMA for the infinite U Anderson impurity modelPHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 7 2007Hellmut Keiter Abstract If one wants to deal with strongly correlated electron lattice systems within dynamical mean field theory, one needs an impurity solver, i.e. a solution for the dynamics of the Anderson magnetic impurity problem. The most ambitious approach to that problem has been the consistent t-matrix approximation (CTMA). The basic integral equations could be solved with a slow variable approximation, which compared well with a direct numerical solution. Fermi-liquid behavior was not obtained, presumably the normalscattering potential was treated approximately only. We show, how the normal scattering potential can be included exactly. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A micromechanical model for the elastic properties of semicrystalline thermoplastic polymersPOLYMER ENGINEERING & SCIENCE, Issue 3 2004X. Guan This paper presents a micromechanical analysis of the elastic properties of semicrystalline thermoplastic materials. A lamellar stack aggregate model reported in the literature is used to derive tighter bounds and a self-consistent scheme for the elastic modulus, and it is shown that the existing geometric models of the microstructures are not effective in predicting experimentally measured modulus of semicrystalline materials. Toward addressing this limitation, a model based on Mori-Tanaka's mean field theory is developed by treating the semicrystalline materials as short-fiber reinforced composites, in which the lamella crystalline phase is modeled as randomly embedded anisotropic ellipsoidal inclusions, and the amorphous phase as an isotropic matrix. The lamellae are characterized by two independent aspect ratios from three distinct geometric axes in general. Existing morphological studies on polyethylene (PE) and a syndiotactic polystyrene (sPS) are used to deduce the corresponding lamella aspect ratios, based on which the theoretical model is applied to predict the elastic modulus of the two material systems. The model predictions are shown to compare well with the reported measurements on the elastic moduli of PE and sPS. Polym. Eng. Sci. 44:433,451, 2004. © 2004 Society of Plastics Engineers. [source] Making the transition temperature of cuprate superconductors higher by using the field-effect-transistor geometryANNALEN DER PHYSIK, Issue 1-2 2004M. Hayashi Abstract We present a possibility to raise the transition temperature of cuprate superconductors by using the field-effect-transistor type devices. The basic mechanism is based on the proximity effect of the two off-diagonal-long-range-orders in the superconducting phase of the cuprates, namely, the singlet resonating-valence-bond order and the bose condensation. Our model is based on the mean field theory of the t - J model. [source] Comparisons and connections between mean field dynamo theory and accretion disc theoryASTRONOMISCHE NACHRICHTEN, Issue 1 2010E.G. Blackman Abstract The origin of large scale magnetic fields in astrophysical rotators, and the conversion of gravitational energy into radiation near stars and compact objects via accretion have been subjects of active research for a half century. Magnetohydrodynamic turbulence makes both problems highly nonlinear, so both subjects have benefitted from numerical simulations.However, understanding the key principles and practical modeling of observations warrants testable semi-analytic mean field theories that distill the essential physics. Mean field dynamo (MFD) theory and alpha-viscosity accretion disc theory exemplify this pursuit. That the latter is a mean field theory is not always made explicit but the combination of turbulence and global symmetry imply such. The more commonly explicit presentation of assumptions in 20th century textbook MFDT has exposed it to arguably more widespread criticism than incurred by 20th century alpha-accretion theory despite complementary weaknesses. In the 21st century however, MFDT has experienced a breakthrough with a dynamical saturation theory that consistently agrees with simulations. Such has not yet occurred in accretion disc theory, though progress is emerging. Ironically however, for accretion engines, MFDT and accretion theory are presently two artificially uncoupled pieces of what should be a single coupled theory. Large scale fields and accretion flows are dynamically intertwined because large scale fields likely play a key role in angular momentum transport. I discuss and synthesize aspects of recent progress in MFDT and accretion disc theory to suggest why the two likely conspire in a unified theory (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | |||||||||||||