Renormalization Group Flow of the Two-Dimensional O(N) Spin Model

We develop a new block spin transformation and apply it to the 2D O(N) spin model. The transformation does not yield complicated non-local terms and then the transformation recursion formula seems to be controllable for any initial inverse temperature > 0. The main part of the block spin transformation of the model with large N converges to a massive state, no matter how low the initial temperature 1/ is, and is close to the flow of the hierarchical model advocated by Dyson and Wilson several decades ago.     

A Re-Examination of the Arguments for Baryon Parity Doublets

The arguments for baryon parity doubling are re-examined by use of a spin formalism developed by the author together with B. E. LAURENT . It is shown that the transformation between good parity amplitudes and helicity flip and non-flip amplitudes in πN scattering is ambiguous. It is further shown that the unitary condition for boson-fermion scattering gives no information of the parity of intermediate states contributing to a good parity amplitude. These ambiguities follow from the fact that for boson-fermion scattering the CPT transformation of an amplitude does not commute with the projection on a definite parity. It is finally shown how a Regge pole model with linear trajectories without parity doubling can be constructed without any specific dynamical assumptions or artifices. The constraints on the residues needed in this case do not violate any general principles.     

Asymptotic dynamics of the dual billiard transformation

Given a strictly convex plane curve, the dual billiard transformation is the transformation of its exterior defined as follows: given a pointx outside the curve, draw a support line to it from the point and reflectx at the support point. We show that the dual billiard transformation far from the curve is well approximated by the time 1 transformation of a Hamiltonian flow associated with the curve.     

Flow equations and the strong-coupling expansion for the Hubbard model

Applying the method of continuous unitary transformations to a class of Hubbard models, we reexamine the derivation of thet/U expansion for the strong-coupling case. The flow equations for the coupling parameters of the higher order effective interactions can be solved exactly, resulting in a systematic expansion of the Hamiltonian in powers oft/U, valid for any lattice in arbitrary dimension and for general band filling. The expansion ensures a correct treatment of the operator products generated by the transformation, and only involves the explicit recursive calculation of numerical coefficients. This scheme provides a unifying framework to study the strong-coupling expansion for the Hubbard model, which clarifies and circumvents several difficulties inherent to earlier approaches. Our results are compared with those of other methods, and it is shown that the freedom in the choice of the unitary transformation that eliminates interactions between different Hubbard bands can affect the effective Hamiltonian only at ordert ³/U² or higher.     

Letter: Parametrization of the Kerr-NUT Solution

The dragging of the Kerr-NUT solution does not tend to zero at infinity. To modify this solution in order to produce a good asymptotic behaviour we transform it by introducing two further parameters with the aid of a SU(1,1) transformation followed by a unitary transformation. By imposing a certain relation between these parameters we obtain a new solution with a good asymptotic behaviour for any value of l, the NUT parameter. The new solution corresponds to a parametrized Kerr solution and we show that l is linked to the form of its ergosphere.     

A class of nonmixing dynamical systems with monotonic semigroup property

In order to illustrate the class of conservative dynamical systems for which a Boltzmann entropy can be obtained under finite coarse-graining [2], we consider dynamical systems defined by the shift transformation on K , where K is any finite set of integers. We give a class of non-Markovian invariant measures that verify the Chapman-Kolmogorov equation (equivalent to a Boltzmann entropy) for any positive stochastic matrix and that are ergodic but not weakly mixing.     

Selective appearance of ϵ-martensitic transformation and dynamic strain aging in Fe–Mn–C austenitic steels

The influence of stress-induced ε-martensitic transformation on the serrated flow behavior associated with dynamic strain aging was investigated. The ε-martensitic transformation was controlled by changing the deformation temperature and adding Si to Fe–17Mn–xSi–0.3?C alloys. The addition of Si promoted the ε-martensitic transformation, and suppressed the slip deformation due to solution hardening. The initiation of serrations around room temperature was delayed by the promotion of ε-martensitic transformation which initiated plastic deformation. The critical stress for the occurrence of serrations and the critical stress for the occurrence of slip deformation were found to have a linear relationship.     

Renormalization group approach to spin glass systems

A renormalization group transformation suitable for spin glass models and, more generally, for disordered models, is presented. The procedure is non-standard in both the nature of the additional interactions and the coarse graining transformation, that is performed on the overlap probability measure. Universality classes are thus naturally defined on a large set of models, going from and Gaussian spin glasses to Ising and fully frustrated models, and others. The proposed analysis is tested numerically on the Edwards-Anderson model in d = 4. Good estimates of the critical index ν and of T _c are obtained, and an RG flow diagram is sketched for the first time. Received 17 November 2000     

On Ulam-von Neumann transformations

We define and study Ulam-von Neumann transformations which are certain interval mappings and conjugate toq(x)=1–2x ² on [–1,1]. We use a singular metric on [–1,1] to study a Ulam-von Neumann transformation. This singular metric is universal in the sense that it does not depend on any particular mapping but only on the exponent of this mapping at its unique critical point. We give the smooth classification of Ulam-von Neumann transformations by their eigenvalues at periodic points and exponents and asymmetries.The author is partially supported by a PSC-CUNY grant and a NSF grant.     

Flow equations and extended Bogoliubov transformation for the Heisenberg antiferromagnet near the classical limit

The Heisenberg spin-S quantum antiferromagnet is studied near the large-spin limit, applying a new continuous unitary transformation which extends the usual Bogoliubov transformation to higher order in the 1/S-expansion of the Hamiltonian. This allows to diagonalize the bosonic Hamiltonian resulting from the Holstein-Primakoff representation beyond the conventional spin-wave approximation. The zero-temperature flow equations derived from the extension of the Bogoliubov transformation to order for the ground-state energy, the spin-wave velocity, and the staggered magnetization are solved exactly and yield results which are in agreement with those obtained by a perturbative treatment of the magnon interactions. Received: 19 March 1998 / Revised: 2 June 1998 / Accepted: 8 June 1998     

Rotating frames in special relativity analyzed in light of a recent article by M. Strauss

The argument of Einstein for non-Euclidity on a rotating disk is analyzed and found valid. The kinematic reason for the non-Euclidean geometry is stated explicitly and provides a kinematic resolution of Ehrenfest's paradox. The transformation from an inertial frameK to a rotating frame, the axis of which is at rest inK, is discussed. It is concluded in favor of the Galilean-like transformation employed by Møller. The method used by Møller in obtaining the intrinsic spatial geometry in any frame is examined. It is found to be adequate, provided that only coordinates with a proper metrical significance are used. In this connection the distinction between global and local geometry is found to be essential.     

Dynamics of density waves in a two dimensional funnel on an inclined plane

We report here experiments on two-dimensional funnel flow of diameter glass beads on an inclined plane. We have investigated the properties of the flow according to the outlet size D of the funnel and the gravity. We have identified three different regimes. For small funnel outlet sizes, there is no significant change in flow density: the flow is rather steady and homogeneous. For intermediate outlet sizes (), the flow is intermittent, consisting of spatially ordered density waves propagating upwards. At bigger outlet sizes, density waves do not exhibit any ordering and the flow dynamics becomes chaotic. In addition, we find that the flow dynamics is independent of the funnel opening angle except close to the channel flow configuration. Finally, it is stressed that the interactions between the beads and the inclined plane play a crucial role in the mechanism of formation of density waves. Received: 9 July 1998 / Received in final form and Accepted: 18 September 1998     

Two remarks on the computer study of differentiable dynamical systems

In the first part of this note we find conditions under which the frequency spectrum of a transformation exhibits delta functions. In the second part we show that if an ergodic flow on anm-dimensional manifold hasm–1 strictly negative characteristic exponents, then the measure is concentrated either on a fixed point or on a closed attracting orbit.     

On the universality of geometrical and transport exponents of rigidity percolation

We develop a three-parameter position-space renormalization group method and investigate the universality of geometrical and transport exponents of rigidity (vector) percolation in two dimensions. To do this, we study site-bond percolation in which sites and bonds are randomly and independently occupied with probabilitiess andb, respectively. The global flow diagram of the renormalization transformation is obtained which shows that thegeometrical exponents of the rigid clusters in both site and bond percolation belong to the same universality class, and possibly that of random (scalar) percolation. However, if we use the same renormalization transformation to calculate the critical exponents of the elastic moduli of the system in bond and site percolation, we find them to be very different (although the corresponding values of the correlation length exponent are the same). This indicates that the critical exponent of the elastic moduli of rigidity percolation may not be universal, which is consistent with some of the recent numerical simulations.     

基于水平集方法二维模型的软性磨粒两相流流场特性分析方法

两相流场特性分析是软性磨粒流精密加工方法的技术关键. 针对此问题, 利用水平集方法(LSM)结构拓扑变换原理, 建立了描述磨粒流在另一流体中运动变化的二维模型. 该模型中, 用LSM捕捉两相流之间的界面, 从而对两相流的运动情况和相关参数进行模拟仿真, 深入讨论了磨粒流加工机理. 研究表明: 以LSM原理建立的二维模型, 成功地仿真模拟了两相流相变过程; 利用k-ε湍流模型与Preston方程相结合的数值分析方法, 对流道内各区域的速度等流场特性进行讨论, 为软性磨粒流加工提供了前期基础性研究. 关键词： 水平集方法 结构化表面 软性磨粒流 k-ε湍流模型')" href="#">k-ε湍流模型     

Geometrical effects on shallow donor impurities in quantum wires

We have studied theoretically the impurity binding energy for wires of different shapes (V-shaped quantum wire (V-QWR) and rectangular wire) with a variational procedure without using any coordinate transformation. The effective potential for V-QWR used in this work consists of a square well potential in the z-direction and full graded well potential in the x-direction. Our results are in good agreement with previous theoretical results, found by the coordinate transformation method. Furthermore, it is shown that the impurity binding energy in quantum wires is sensitive to the geometrical effects.     

Some linear Bäcklund transformations

Dirac's equation is a first-order auto-Bäcklund transformation for the Klein-Gordon equation in 4 variables, this equation being second-order in each of the 4 variables. Here first-order auto-Bäcklund transformations are given for any linear equation of arbitrary (possibly different) order in each of n variables (n arbitrary). This class of equations includes, for example, any of the linearised versions of the KdV hierarchy or equations, and the n-dimensional diffusion equation.     

Decay of Correlations and Invariance Principles for Dispersing Billiards with Cusps, and Related Planar Billiard Flows

Following recent work of Chernov, Markarian, and Zhang, it is known that the billiard map for dispersing billiards with zero angle cusps has slow decay of correlations with rate 1/n. Since the collisions inside a cusp occur in quick succession, it is reasonable to expect a much faster decay rate in continuous time. In this paper we prove that the flow is rapid mixing: correlations decay faster than any polynomial rate. A consequence is that the flow admits strong statistical properties such as the almost sure invariance principle, even though the billiard map does not. The techniques in this paper yield new results for other standard examples in planar billiards, including Bunimovich flowers and stadia.     

Absence of dynamical crossover in the vortex creep near by the second peak effect in superconducting Hg-1201 single crystals

DC magnetic relaxation measurements in HgBa₂CuO₄ single crystals are analyzed nearby the fishtail line. It is found that in this case, it is not necessary to introduce any crossover from plastic creep to elastic creep models at the fishtail line. This type of fishtail effect comes only from a competition between a critical current at low temperature which increases versus field and the activation energy, which decreases versus field. According to the doping level of the compound, the fishtail effect can be observed or not, without any correlation with a vortex phase transition. Moreover, in this type of fishtail effect, there is no history effects as recently observed in YBaCu₂O₃ by the partial magnetization loop technique, suggesting that the transition from plastic to elastic flow is here hidden by the disorder of these materials. Received 11 January 2000