Renormalization connection between the eight-vertex model and the gaussian model

A generalized version of the Villain model is defined which contains the eight-vertex model as a special case. A renormalization pattern is formulated in terms of this Villain model by which critical line(s) in the eight-vertex model are connected with the Gaussian fixed line. Gaussian equivalents are found for various operators along the Baxter line. The relation between the present results and those recently obtained by Kadanoff and Brown is discussed.     

最优速度模型与元胞自动机模型的比较研究

用解析分析与数值仿真的手段研究了一种典型的车辆跟驰模型(OV模型)与元胞自动机模型(NS模型)之间的区别与联系.首先通过对模型规则的分析,证明了确定NS模型是OV模型的一种离散形式.随后针对两模型更复杂的具体形式,通过数值仿真的手段进行了模型的密度-流量关系与模型在开放边界下的动态特性的研究.实验结果表明,从现象来看,OV模型与NS模型具有非常近似的性质,但两种模型的机制不相同,并且各自具有不能相互替代的优势.为交通流模型的使用和改进提供了参考.     

Equivalence between the Mueller Regge model and the multiperipheral model

It is proven that a large class of pionization Mueller Regge models are equivalent to the multiperipheral model. An orthogonal similarity transformation is found which allows one to transform in either direction between equivalent multiperipheral and Mueller models. Models with charge are discussed and the problem of constructing charge conserving Mueller models is solved.     

On the equivalence between sine-Gordon model and Thirring model in the chirally broken phase of the Thirring model

We investigate the equivalence between Thirring model and sine-Gordon model in the chirally broken phase of the Thirring model. This is unlike all other available approaches where the fermion fields of the Thirring model were quantized in the chiral symmetric phase. In the path integral approach we show that the bosonized version of the massless Thirring model is described by a quantum field theory of a massless scalar field and exactly solvable, and the massive Thirring model bosonizes to the sine-Gordon model with a new relation between the coupling constants. We show that the non-perturbative vacuum of the chirally broken phase in the massless Thirring model can be described in complete analogy with the BCS ground state of superconductivity. The Mermin–Wagner theorem and Coleman's statement concerning the absence of Goldstone bosons in the 1+1-dimensional quantum field theories are discussed. We investigate the current algebra in the massless Thirring model and give a new value of the Schwinger term. We show that the topological current in the sine-Gordon model coincides with the Noether current responsible for the conservation of the fermion number in the Thirring model. This allows one to identify the topological charge in the sine-Gordon model with the fermion number. Received: 16 December 2000 / Revised version: 23 April 2001 / Published online: 13 June 2001     

The parameter conversion from the Kedem-Katchalsky model into the two-parameter model

Cryopreservation is an important process for preserving cells and tissues. The process itself can, however, cause damage to cells and tissues. During addition and removal of a cryoprotective agent (CPA), cells are subjected to imbalanced osmotic pressures between the intracellular and extracellular solutions. Cells can be injured if these shrinkage and swelling events are beyond their tolerable limits. The characteristics of the cell volume changes during these processes depend on the types of CPA, the methods of adding and removing of the CPA and the permeability of cells to CPA and water. The typical models of this transportation are the two-parameter (2-p) model and the Kedem-Katchalsky (K-K) model. The K-K model is more general than the 2-p model. However, there is evidence that in many cases water and CPAs do not permeate through common pathways, hence the use of the reflection coefficient in the K-K model may be unnecessary and in some cases it may create conceptual errors. Therefore, the 2-p model is more suitable for use as a transport model than the K-K model. The aim of this study is to use the values of the K-K model parameters from data in the literature to calculate the corresponding parameters for the 2-p model. The results from these simulations demonstrate that the cell volume changes during CPA addition and removal from the K-K model can be closely estimated by the 2-p model.     

On the chiral hubbard model and the chiral Kondo lattice model

The integrability of the one-dimensional chiral Hubbard model is discussed in the limit of strong interaction,U=. The system is shown to be integrable in the sense of the existence of an infinite number of constants of motion. The system is related to a chiral Kondo lattice model at strong interactionJ=+.     

Two-site model and its relation to the polaron-crystal model

A symmetric two-site, one-electron model is treated within perturbation theory in electron wavefunction overlap from different sites. The significant role of the double degeneracy of levels in the unperturbed Hamiltonian is pointed out. It is shown that as a result of this the terms of the perturbative expansion for the correction to the energy of an unperturbed level produce different results depending on the parity of the order. Namely, even terms give rise to a level shift (an analog of the polaron shift in the polaron-crystal model), while odd terms result in splitting (an analog of the polaron band width). Also, the shift of the levels decreases with increasing vibronic coupling constant by a power law, and their splitting, exponentially. This is in full accord with the well-known results of small-radius polaron theory. Fiz. Tverd. Tela (St. Petersburg) 39, 2159–2167 (December 1997)     

Using the camera pin-hole model restrictions to calibrate the lens distortion model

Camera calibration required the computation of camera pin-hole and lens distortion models. The lens distortion is estimated alone or together with the pin-hole model, by using some existing lens distortion non-metric or self-calibration methods. If both models are computed together, then the models are adjusted to training data, but not to real camera. This is because both pin-hole and lens distortion models are coupled. If they are computed separately, difficulties arise since calibration of lens distortion alone is an unstable process. To improve existing camera calibration methods, this paper proposes a metric calibration method to compute lens distortion separately from the pin-hole model. This method is solved under stable conditions, independently of the computed lens distortion model, since pin-hole and distortion models are computed separately. Images of a planar template are used. First, using distorted control points extracted from images, a set of undistorted points which fits in the pin-hole model are computed. Second, with distorted and undistorted control points, lens distortion is calibrated by using a metric calibration process.     

Diagonalization of the elliptic Ruijsenaars model. Correspondence with the Belavin model

Studied is the elliptic Ruijsenaars model, which is a difference analogue of the Calogero-Sutherland-Moser model. Using a novel relationship between the elliptic Ruijsenaars operator and the transfer matrix of the Belavin model, we diagonalize the Ruijsenaars operator by the algebraic Bethe ansatz method. Received: 29 January 1998 / Accepted: 17 April 1998     

Correlations in the XY model and screw dislocations in the solid-on-solid model

An exact relation is proven between the two-point correlation function of the classical XY model and the free energy of a step associated with two screw dislocations on a crystal surface described by a solid-on-solid model. This result suggests a way to obtain the XY critical exponent η_c from Monte Carlo studies of the solid-on-solid model.     

On the connection between the principal chiral model and the multiflavour chiral Gross-Neveu model

The infinite flavour limit of the multiflavour chiral Gross-Neveu (MCGN) partition function is shown to be equal to the principal chiral σ-model (PCM) partition function where in addition one integrates over twisted boundary conditions. This last interpretation restricts the space of states to the left (or right) singlet sector. In the course of this derivation, a rigorous paramagnetic inequality for the Dirac determinant is proved. The critical (conformal invariant) points of the MCGN are investigated in connection with critical WZW σ-models.     

Metastability in the Hamiltonian mean field model and Kuramoto model

We briefly discuss the state of the art on the anomalous dynamics of the Hamiltonian mean field (HMF) model. We stress the important role of the initial conditions for understanding the microscopic nature of the intriguing metastable quasi-stationary states (QSS) observed in the model and the connections to Tsallis statistics and glassy dynamics. We also present new results on the existence of metastable states in the Kuramoto model and discuss the similarities with those found in the HMF model. The existence of metastability seems to be quite a common phenomenon in fully coupled systems, whose origin could be also interpreted as a dynamical mechanism preventing or hindering synchronization.     

Chiral Potts model as a descendant of the six-vertex model

We observe that theN-state integrable chiral Potts model can be considered as a part of some new algebraic structure related to the six-vertex model. As a result, we obtain a functional equation which is supposed to determine all the eigenvalues of the chiral Potts model transfer matrix.     

The NCSTAR model as an alternative to the GWR model

This paper compares the GWR model, usually used to integrate and examine the spatial heterogeneity of a relationship, and the NCSTAR model. The former will give a vector of local parameter estimates for each observation of the data set, according to its nearest neighbors in space. However, it supposes that all variables enter linearly the model. To correct this failure, a NCSTAR model is proposed. It can be seen as a linear model which coefficients are given by the outputs of an ANN model. These outputs can be related not only to geographical variables but also to social, financial or economic variables (according the nature of the relationship under study) via a nonlinear function which functional form has not to be specified. Moreover, the confidence intervals for the NCSTAR estimates can be computed.