Mirror Symmetry in Two Steps: A–I–B

We suggest an interpretation of mirror symmetry for toric varieties via an equivalence of two conformal field theories. The first theory is the twisted sigma model of a toric variety in the infinite volume limit (the A–model). The second theory is an intermediate model, which we call the I–model. The equivalence between the A–model and the I–model is achieved by realizing the former as a deformation of a linear sigma model with a complex torus as the target and then applying to it a version of the T–duality. On the other hand, the I–model is closely related to the twisted Landau-Ginzburg model (the B–model) that is mirror dual to the A–model. Thus, the mirror symmetry is realized in two steps, via the I–model. In particular, we obtain a natural interpretation of the superpotential of the Landau-Ginzburg model as the sum of terms corresponding to the components of a divisor in the toric variety. We also relate the cohomology of the supercharges of the I–model to the chiral de Rham complex and the quantum cohomology of the underlying toric variety.Partially supported by the DARPA grant HR0011-04-1-0031 and the NSF grant DMS-0303529.Partially supported by the Federal Program 40.052.1.1.1112, by the Grants INTAS 03-51-6346, NSh-1999/2003.2 and RFFI-04-01- 00637.     

Density functionals and model Hamiltonians: Pillars of many-particle physics

Density-functional theory (DFT) and model Hamiltonians are conceptually distinct approaches to the many-particle problem, which can be developed and applied independently. In practice, however, there are multiple connections between the two. This review focuses on these connections. After some background and introductory material on DFT and on model Hamiltonians, we describe four distinct, but complementary, connections between the two approaches: (i) the use of DFT as input for model Hamiltonians, in order to calculate model parameters such as the Hubbard U and the Heisenberg J. (ii) The use of model Hamiltonians as input for DFT, as in the LDA + U functional. (iii) The use of model Hamiltonians as theoretical laboratories to study aspects of DFT. (iv) The use of special formulations of DFT as computational tools for studying spatially inhomogeneous model Hamiltonians. We mostly focus on this fourth combination, model DFT, and illustrate it for the Hubbard model and the Heisenberg model. Other models that have been treated with DFT, such as the PPP model, the Gaudin–Yang δ$\delta$-gas model, the XXZ chain, variations of the Anderson and Kondo models and Hooke’s atom are also briefly considered. Representative applications of model DFT to electrons in crystal lattices, atoms in optical lattices, entanglement measures, dynamics and transport are described.     

Phase diagram of an Ising model with competitive interactions on a Husimi tree and its disordered counterpart

We consider an Ising competitive model defined over a triangular Husimi tree where loops, responsible for an explicit frustration, are even allowed. We first analyze the phase diagram of the model with fixed couplings in which a “gas of noninteracting dimers (or spin liquid) — ferro or antiferromagnetic ordered state” zero temperature transition is recognized in the frustrated regions. Then we introduce the disorder for studying the spin glass version of the model: the triangular ±J model. We find out that, for any finite value of the averaged couplings, the model exhibits always a finite temperature phase transition even in the frustrated regions, where the transition turns out to be a glassy transition. The analysis of the random model is done by applying a recently proposed method which allows us to derive the critical surface of a random model through a mapping with a corresponding nonrandom model.     

A φ4-TYPE BAG MODEL OF HADRONS——THE “RUBBER BAG” MODEL（Ⅰ）——THEORY

In this paper a new bag model of hadrons,the“Rubber Bag”model,is proposed.This model treats each hadron as a bag system in the centre-of-mass frame.The bag,with its outer radius R_e and inner radius（R_c-D）,is characterized by its“averagesurface tension”T and the quarks are confined in it“temporarily”.This model isa field theoretical model which can also be used for quantitative calculations.Thus,ithas the merits of the SLAC bag model as well as those of the MIT bag model.     

Noncritical holographic QCD in external electric field

We investigate behavior of a noncritical model in external electric field and explore its phase structure in the quenched approximation Nf?Nc. We compute the conductivity of QCD plasma in this model and compare it with the predictions of Sakai-Sugimoto model, D3-D7 system and lattice simulations. We find that, while the behavior of conductivity in noncritical model as a function of temperature and baryon density is similar to those of D3-D7 system, the phase diagram of noncritical model resembles the phase diagram of Sakai-Sugimoto model.     

Nonintersecting string model and graphical approach: Equivalence with a Potts model

Using a graphical method we establish the exact equivalence of the partition function of aq-state nonintersecting string (NIS) model on an arbitrary planar, even-valenced, lattice with that of a q²-state Potts model on a related lattice. The NIS model considered in this paper is one in which the vertex weights are expressible as sums of those of basic vertex types, and the resulting Potts model generally has multispin interactions. For the square and Kagomé lattices this leads to the equivalence of a staggered NIS model with Potts models with anisotropic pair interactions, indicating that these NIS models have a first-order transition forq > 2. For the triangular lattice the NIS model turns out to be the five-vertex model of Wu and Lin and it relates to a Potts model with two- and three-site interactions. The most general model we discuss is an oriented NIS model which contains the six-vertex model and the NIS models of Stroganov and Schultz as special cases.     

The predictive performance of a path-dependent exotic-option credit risk model in the emerging market

Most empirical research of the path-dependent, exotic-option credit risk model focuses on developed markets. Taking Taiwan as an example, this study investigates the bankruptcy prediction performance of the path-dependent, barrier option model in the emerging market. We adopt Duan’s (1994) [11], (2000) [12] transformed-data maximum likelihood estimation (MLE) method to directly estimate the unobserved model parameters, and compare the predictive ability of the barrier option model to the commonly adopted credit risk model, Merton’s model. Our empirical findings show that the barrier option model is more powerful than Merton’s model in predicting bankruptcy in the emerging market. Moreover, we find that the barrier option model predicts bankruptcy much better for highly-leveraged firms. Finally, our findings indicate that the prediction accuracy of the credit risk model can be improved by higher asset liquidity and greater financial transparency.     

The natural history of streptozotocin-stimulated non-alcoholic steatohepatitis mice followed by Gd-EOB-DTPA-enhanced MRI: Comparison with simple steatosis mice

PurposeTo clarify the development of HCC, temporal change of steatosis and Gd-EOB-DTPA enhancement of non-alcoholic steatohepatitis (NASH) model mice by magnetic resonance imaging (MRI).Materials and methodsAll animal experiments were approved by the institution's Animal Research Committee. MRI was performed on six NASH and six simple steatosis (SS) model mice every 2 weeks from the ages of 8 weeks to 16 weeks. The sequential changes in the number and size of the focal liver lesions detected on Gd-EOB-DTPA-enhanced MRI were evaluated. Additionally, the hepatic fat fraction (HFF), contrast-to-noise ratio (CNR) and relative enhancement (RE) were calculated at each time point. The temporal changes and correlations in these parameters were evaluated.ResultsAll alive NASH model mice demonstrated focal liver lesions from week 10, at the latest. Number of the lesions increased with time, and all the lesion enlarged with time. All the lesions larger than 1 mm were confirmed as hepatocellular carcinoma (HCC) pathologically. While the HFF remained constant in NASH model mice, HFF in SS model mice dramatically increased with time. CNR of the NASH model mice remained constant through the study period, while CNR in SS model mice decreased with time. Although no correlation was seen in NASH model mice, the HFF showed a negative correlation against CNR and RE in SS model mice.ConclusionDevelopment of HCC was observed using Gd-EOB-DTPA-enhanced MRI only in NASH model mice. Degree of steatosis and hepatic enhancement by Gd-EOB-DTPA was both constant in NASH model mice, while steatosis increased and hepatic enhancement decreased with time in SS model mice.     

Similarities between the lattice gas model and some other models of nuclear multifragmentation

We continue our development of the nuclear lattice gas model by exploring links and similarities with other theoretical approaches to nuclear multifragmentation: the percolation model and the statistical multifragmentation model. It is shown that there exists a limit where the lattice gas model reduces to the percolation model. The similarity between the lattice gas model and the statistical multifragmentation model is more indirect and we utilize the equations of state in the two models. By using the law of partial pressures we obtain P-ϱ diagrams for the statistical multifragmentation model and find that these are remarkably similar to those obtained in the lattice gas model via an exact evaluation of the nuclear partition function on the lattice. For completeness, we also compute the P-ϱ diagram for a system obeying pure classical molecular dynamics with a simple two-body force.     

A Timoshenko-beam-on-Pasternak-foundation analogy for cylindrical shells

A Timoshenko-beam-on-Pasternak-foundation model is developed for the analysis of thin elastic cylindrical shells. This model aims to bridge the gap between the Love-Kirchhoff theory and the approximate beam-on-elastic-foundation model of Vlasov (“long-wave” model), which accounts for only longitudinal stretching and circumferential bending. The new model improves on the assumptions of the “long-wave” model by accounting for the effects of two additional actions, namely, in-plane shearing and twist. The model is used to derive “explicit” design formulae for (1) the fundamental natural frequencies for vibration of a uniform cylindrical shell having six sets of end restraints, and (2) the circumferential modenumbers associated with the fundamental mode. A comprehensive comparative study of the predictions of both models against available results in the literature and results obtained by the finite-element method has shown that the proposed model significantly extends the limits of the validity of the “long-wave” model.     

A novel macroscopic traffic model based on generalized optimal velocity model

In this paper, we adopt the coarse graining method proposed by Lee H K et al. to develop a macroscopic model from the microscopic traffic model-GOVM. The proposed model inherits the parameter p which considers the influence of next-nearest car introduced in the GOVM model. The simulation results show that the new model is strictly consistent with the former microscopic model. Using this macroscopic model, we can avoid considering the details of each traffic on the road, and build more complex models such as road network model easily in the future.     

Rigidity of Interfaces in the Falicov–Kimball Model

We analyze the thermodynamic properties of interfaces in the three-dimensional Falicov–Kimball model, which can be viewed as a primitive quantum lattice model of crystalline matter. In the strong coupling limit, the ionic subsystem of this model is governed by the Hamiltonian of an effective classical spin model whose leading part is the Ising Hamiltonian. We prove that the 100 interface in this model, at half-filling, is rigid, as in the three-dimensional Ising model. However, despite the above similarities with the Ising model, the thermodynamic properties of its 111 interface are very different. We prove that even though this interface is expected to be unstable for the Ising model, it is stable for the Falicov–Kimball model at sufficiently low temperatures. This rigidity results from a phenomenon of ground-state selection and is a consequence of the Fermi statistics of the electrons in the model.     

A mixed-time-scale low-Reynolds-number one-equation turbulence model

In this paper, a new low-Reynolds-number (LRN) one-equation turbulence model for eddy viscosity is proposed. A mixed time scale, representing a combination of three time scales: two time scales made of strain-rate parameter S and vorticity parameter Ω and the turbulent time scale k/?, is introduced into this model. The proposed model is derived from an LRN k?? two-equation model where the mixed time scale has been proved to be very effective for predicting local flows over complex terrains. In the transport equation of the model, the mixed time scale is included in the production and the dissipation terms. The new model is evaluated in channel flows at various Reynolds numbers, boundary layer flows with or without pressure gradient and backward-facing step flows with different expansion ratios and Reynolds numbers. Then the grid convergence of the model is investigated. Finally, the model performance for different values of the weighting constant C_s in the mixed time scale is assessed. The results show that the proposed model reproduces the correct wall-limiting behaviour of turbulent quantities and performs well in the near-wall region of turbulent flows. The model could be expected to be adopted in hybrid Reynolds averaged Navier–Stokes/large eddy simulation methodology for complex wall-bounded flows at high Reynolds numbers.     

Thermodynamic modelling of miscibility in (InAs) x (GaAs)1−x solid solutions

Current methods used to model the solution thermodynamics of III–V compound semiconductors involve the use of the valence force field as the molecular model and the regular solution model (with the temperature independent interaction parameter and underlying assumption of random mixing) as the engineering model. In this study, excess free energy models (with three or less adjustable parameters) are investigated to predict the solid–solid miscibility of (InAs) _x (GaAs)_{1? x} . The models investigated include the Porter/one-constant Margules (OCM) model, the two-constant Margules (TCM) model and the non-random two liquid (NRTL) model. These models are fit to excess free energy values derived from free energy change of mixing (variation with composition) data available from molecular simulations at different temperatures. The parameters in all the models have been found to be temperature dependent. The coexistence compositions are best predicted by the NRTL model, indicating the need to consider non-random mixing effects present in these solid solutions. The TCM model predicts better equilibrium composition data as compared to the OCM model.     

An improved model for the acoustic radiation impedance of the mouth based on an equivalent electrical network

This paper proposes a model for acoustic radiation impedance of the mouth in the form of the equivalent electrical network. Five known models of radiation impedance are compared: radiation of a circular piston set in a spherical baffle: radiation of a circular piston set in an infinite baffle, the Flanagan model, the Wakita and Fant model, and the Stevens, Kasowski and Fant model. The proposed model most accurately approximates the radiation impedance of a circular piston set in a spherical baffle. Differences between the acoustic resistance and reactance calculated by the proposed model and the piston set in a spherical baffle of 9 cm radius are relatively small in the kr < 2 region. The deviations in calculated values of the acoustic resistance and the reactance are within ±0.023 × ρc/A_m and ±0.008 × ρc/A_m, respectively, where A_m denotes the area of the mouth aperture. The accuracy of the proposed model is demonstrated by vowel formant frequency calculations. Differences in formant frequencies calculated by applying the proposed model and the piston set in a spherical baffle model are less than 0.3%.     

The fundamental diagram of pedestrian model with slow reaction

The slow-to-start models are a classical cellular automata model in simulating vehicle traffic. However, to our knowledge, the slow-to-start effect has not been considered in modeling pedestrian dynamics. We verify the similar behavior between pedestrian and vehicle, and propose an new lattice gas (LG) model called the slow reaction (SR) model to describe the pedestrian’s delayed reaction in single-file movement. We simulate and reproduce Seyfried’s field experiments at the Research Centre Jülich, and use its empirical data to validate our SR model. We compare the SR model with the standard LG model. We tested different probabilities of slow reaction _ps$p_s$ in the SR model and found the simulation data of _ps=0.3$p_s=0.3$ fit the empirical data best. The RMS error of the mean velocity of the SR model is smaller than that of the standard LG model. In the range of _ps=0.1–0.3$p_s=0.1–0.3$, our fundamental diagram between velocity and density by simulation coincides with field experiments. The distribution of individual velocity in the fundamental diagram in the SR model agrees with the empirical data better than that of the standard LG model. In addition, we observe stop-and-go waves and phase separation in pedestrian flow by simulation. We reproduced the phenomena of uneven distribution of interspaces by the SR model while the standard LG model did not. The SR model can reproduce the evolution of spatio-temporal structures of pedestrian flow with higher fidelity to Seyfried’s experiments than the standard LG model.     

A full spectrum k-distribution based non-gray radiative property model for unburnt char

By using the concept of weighted sum of four gray particles and spectrum k-distribution (WSGP-SK), a non-gray radiative property model for unburnt char particles is developed. Based on the carbon burnout kinetic model for structure during oxidation, and the linear mixed approximation theory for complex index of refraction, spectral radiative properties of unburnt char particles are first calculated as function of the burnout ratio by Mie theory. Referring to the full spectrum k-distribution model, k-distribution is applied to reorder absorption and scattering efficiencies of particles. Then, weighting factors and efficiency factors of the non-gray radiative property model are directly obtained from Gaussian integral points of k-distribution. The model is validated against the benchmark solutions of line-by-line (LBL) model. Maximum relative errors of this model are 3% and 15% for radiative heat fluxes and source terms in non-isothermal inhomogeneous particulate media, respectively. The assumption of linearly varying radiative properties with burnout ratio (Lockwood et al. 1986) will result in a predicted deviation of 53% for radiative source terms. Results also show that this non-gray model is remarkably better than the Planck mean method. Moreover, a satisfactory comparison with LBL solutions is achieved in the gas and particle mixture by combining the non-gray WSGG-SK model (Guo et al. 2015). As a radiation sub-model, this non-gray radiative property model can significantly improve prediction accuracy of radiative heat transfer in oxy-fuel combustion.     

Surface anisotropy in nanomagnets: transverse or Néel?

Through the hysteresis loop and magnetization spatial distribution we study and compare two models for surface anisotropy in nanomagnets: a model with transverse anisotropy axes and Néel's model. While surface anisotropy in the transverse model induces several jumps in the hysteresis loop because of the cluster-wise switching of spins, in the Néel model the jumps correspond to successive coherent partial rotations of the whole bunch of spins. These calculations together with some hints from available experimental results, suggest that Néel's model for surface anisotropy is more appropriate.     

Defect chemistry and electrical properties of La1−xSrxCoO3−δ IV. Electrical properties

This paper considers electrical properties of La_1−xSr_xCoO_3−δ in terms of defect models, such as random defect model and the cluster model. It is shown that the experimental data of the electrical conductivity may be explained in terms of the random defect model rather than the cluster model.     

On the recombination mechanism of quarks into a baryon in proton fragmentation

The similarity and difference between our quark cascade model with recombination mechanism and Van Hove's quark fragmentation-recombination model are discussed. Van Hove's fragmentation-recombination model is extended to the model which describesx-dependence of the hadron spectra as well as the baryon multiplicities by using our diffusion equation. The recombination probability in Van Hove's model can be related with the recombination factor λ′ in our diffusion equation. Thex-dependence of the hadron spectra causes another restriction on the recombination probability in Van Hove's model. The inclusive spectra of mesons, proton andΔ ⁺⁺ in proton fragmentation and baryon multiplicities except∑ ^? multiplicity are explained by both our model with recombination mechanism and the model with recombination mechanism a la Van Hove. But the ration(∑ ^?)/n(∑ ^+;) may not be explained by naive quark-parton model with recombination mechanism without considering quark spin.