Drinfeld twists of the open XXZ chain with non-diagonal boundary terms

The Drinfeld twists or factorizing F-matrices for the open XXZ spin chain with non-diagonal boundary terms are constructed. It is shown that in the F-basis the two sets of pseudo-particle creation operators simultaneously take completely symmetric and polarization free form. The explicit and completely symmetric expressions of the two sets of Bethe states of the model are obtained.     

An F-Twisted XYZ Model

We construct a factorizing twist for a face type model equivalent to the XYZ model. Completely symmetric expressions for the operators of the monodromy matrix are obtained.     

Scalar products of the open XYZ chain with non-diagonal boundary terms

With the help of the F-basis provided by the Drinfeld twist or factorizing F-matrix of the eight-vertex solid-on-solid (SOS) model, we obtain the determinant representations of the scalar products of Bethe states for the open XYZ chain with non-diagonal boundary terms. By taking the on shell limit, we obtain the determinant representations (or Gaudin formula) of the norms of the Bethe states.     

Loop effects in the Ising spin glass on the Bethe-like lattices

Equations for the spin glass order in the Ising spin glass model on the Bethe-like lattices with and without small loops are studied. For each lattice, equations are obtained by using and not using the replica method. Within the replica symmetric approximation, equations obtained by the two ways are shown to be identical. To see the effects of the small loops and the replica symmetry breaking, a spin glass order parameter is investigated as a function of the connectivity of the lattices close to the transition temperature. Replica symmetry breaking is enhanced by the existence of small loops.     

Bethe lattice spin glass: The effects of a ferromagnetic bias and external fields. II. Magnetized spin-glass phase and the de Almeida-Thouless line

In this and the companion paper, we analyze the ±J Ising spin-glass model on the Bethe lattice with fixed uncorrelated boundary conditions. Phase diagrams are derived as a function of temperature vs. concentration of ferromagnetic bonds and, for a symmetric distribution of bonds, external field vs. temperature. In this part we characterize magnetized spin-glass (MSG) phases by divergence of an appropriate susceptibility: at zero field this signals the existence of an intermediate MSG phase; at nonzero field, this is used to identify the de Almeida-Thouless line.     

Radiometry and Radiation Efficiency of Twisted Gaussian Schell-Model Sources

Wavefields endowed with the coherence-induced property of optical twist have recently attracted a good deal of theoretical and experimental attention. We present the generalized radiometric theory of fields generated by twisted Gaussian Schell-model sources. The effects introduced by the novel, rotationally symmetric, twist phenomenon in the radiant intensity, generalized radiance, radiant emittance (irradiance), and the radiation efficiency are assessed. The radiance becomes directionally skewed as a result of the twist, whereas the radiant intensity remains axially symmetric. The twist reduces the radiation efficiency and broadens the radiation distribution, in agreement with the notion that the twist decreases the effective coherence. Several special cases, such as quasihomogeneous sources, are analyzed in detail. The radiometric results, which are physically consistent with the superposition models of twisted sources, are demonstrated by illustrative examples.     

Bethe lattice spin glass: The effects of a ferromagnetic bias and external fields. I. Bifurcation analysis

We present a rigorous analysis of the ±J Ising spin-glass model on the Bethe lattice with fixed uncorrelated boundary conditions. Phase diagrams are derived as a function of temperature vs. concentration of ferromagnetic bonds and, for a symmetric distribution of bonds, external field vs. temperature. In this part we characterize the bulk ordered phases using bifurcation theory: we prove the existence of a distribution of single-site magnetizations far inside the lattice which is stable with respect to changes in the boundary conditions.     

Wavelength Shift of Cladding Mode Resonances in a Mechanically Induced LPFG by Twisting the Fiber

The long-period fiber grating is mechanically induced over a twisted fiber and its characteristics are investigated. The amplitude as well as the wavelength shift of the resonance is studied in response to the applied twist and pressures. These resonances decrease in amplitude and shift to shorter wavelength side as the applied twist increases. The spectral responses of a grating assembly formed by two grating sections in series, one section with a twisted fiber and other with an untwisted fiber, are also investigated. Shearing stress and photo-elasticity causes the fiber to be circularly birefringent and the mechanically induced grating formed over the twisted fiber region causes the appearance of two resonances shifted away from the resonances of the untwisted grating section. At higher twist rates, resonant wavelength shift becomes insensitive to applied pressures, showing a reduction in the induced linear birefringence. The wavelength shift is almost symmetric with respect to the applied twist rate in clockwise and counterclockwise directions.     

Wavelength Shift of Cladding Mode Resonances in a Mechanically Induced LPFG by Twisting the Fiber

Abstract

The long-period fiber grating is mechanically induced over a twisted fiber and its characteristics are investigated. The amplitude as well as the wavelength shift of the resonance is studied in response to the applied twist and pressures. These resonances decrease in amplitude and shift to shorter wavelength side as the applied twist increases. The spectral responses of a grating assembly formed by two grating sections in series, one section with a twisted fiber and other with an untwisted fiber, are also investigated. Shearing stress and photo-elasticity causes the fiber to be circularly birefringent and the mechanically induced grating formed over the twisted fiber region causes the appearance of two resonances shifted away from the resonances of the untwisted grating section. At higher twist rates, resonant wavelength shift becomes insensitive to applied pressures, showing a reduction in the induced linear birefringence. The wavelength shift is almost symmetric with respect to the applied twist rate in clockwise and counterclockwise directions.     

Pion mean free path in nuclear matter

The mean free paths for true absorption and inelastic scattering-as well as true absorption alone-of pions in symmetric nuclear matter are deduced from two sets of optical model parameters.     

A Note on the Bethe Ansatz Solution of the Supersymmetric t-J Model

The three different sets of Bethe ansatz equations describing the Bethe ansatz solution of the supersymmetric t-J model are known to be equivalent. Here we give a new, simplified proof of this fact which relies on the properties of certain polynomials. We also show that the corresponding transfer matrix eigenvalues agree.     

界面旋转角对双晶镁力学性质影响的分子动力学模拟

采用分子动力学模拟方法,研究了在拉伸载荷下晶界对双晶镁变形机制的影响,对不同旋转角度的模型以及对称与非对称结构的模型进行了研究.模拟结果表明:应变加载方向与晶向所成角度对双晶镁塑形变形阶段的流动应力能够产生明显的影响;对称结构的双晶镁模型的塑性性质明显优于非对称结构模型.研究结果还发现,由于晶界区域不同的位错成核及发射等运动,大角度双晶模型的塑性响应明显优于对应小角度模型的塑性响应.     

Nonmonotonic Behavior in Hard-Core and Widom–Rowlinson Models

We give two examples of nonmonotonic behavior in symmetric systems exhibiting more than one critical point at which spontanoous symmetry breaking appears or disappears. The two systems are the hard-core model and the Widom–Rowlinson model, and both examples take place on a variation of the Cayley tree (Bethe lattice) devised by Schonmann and Tanaka. We obtain similar, though less constructive, examples of nonmonotonicity via certain local modifications of any graph, e.g., the square lattice, which is known to have a critical point for either model. En route we discuss the critical behavior of the Widom–Rowlinson model on the ordinary Cayley tree. Some results about monotonicity of the phase transition phenomenon relative to graph structure are also given.     

Crystals and quasicrystals: A continuum model

We construct the first model of particles in the plane with completely symmetric, short range, two body interactions which has quasiperiodic, but no periodic, ground states.Supported in part by NSF Grant No. DMS-8501911     

The complete set of twists for the twisted Eguchi-Kawai model

We solve the twist problem of the Eguchi-Kawai model completely and present a large class of new twists. Some of these new twists are useful for economic Monte-Carlo simulations of theSU(N) model for largeN.     

Strengthening effects of various grain boundaries with nano-spacing as barriers of dislocation motion from molecular dynamics simulations

Strengthening in metals is traditionally achieved through the controlled creation of various grain boundaries (GBs), such as low-angle GBs, high-angle GBs, and twin boundaries (TBs). In the present study, a series of large-scale molecular dynamics simulations with spherical nanoindentation and carefully designed model were conducted to investigate and compare the strengthening effects of various GBs with nano-spacing as barriers of dislocation motion. Simulation results showed that high-angle twist GBs and TBs are similar barriers and low-angle twist GBs are less effective in obstructing dislocation motion. Corresponding atomistic mechanisms were also given. At a certain indentation depth, dislocation transmission and dislocation nucleation from the other side of boundaries were observed for low-angle twist GBs, whereas dislocations were completely blocked by high-angle twist GBs and TBs at the same indentation depth. The current findings should provide insights for comprehensive understanding of the strengthening effects of various GBs at nanoscale.     

装配同轴度的局部成像检测算法研究

在局部成像检测过程中,由于复杂零件外形轮廓或放置状态的不同,使得零件与成像面坐标轴之间产生了一定的夹角,造成获取的对称点集中存在非对称点集或对称点不存在的问题,若采用传统Hough变换、拟合法检测装配同轴度存在较大误差。针对上述问题,提出了装配同轴度的局部成像检测算法,提取图像的上下边缘点集,结合Hough线性变换,统计两点集对投影到霍夫空间的参数空间点,并搜索其累积数量的最大值点,该点对应的对称轴即为最优对称轴。仿真结果表明,该方法可以高精度地提取最优对称轴,同轴度误差仅为0.002 7。因此,采用装配同轴度的局部成像检测方法是有效可行的。     

The falling cat as a port-controlled Hamiltonian system

In this article, the falling cat is modeled as two jointed axial symmetric cylinders with arbitrary twist under the constraint of the vanishing total angular momentum. As a control system with the constraint taken into account, this model is formulated as a port-controlled Hamiltonian system defined on the cotangent bundle of the shape space for the jointed cylinders. A control is then designed as a function on the cotangent bundle, according to a standard procedure. Thus, the equations of motion are determined on the cotangent bundle together with the control. The whole motion as a vibrational motion of the falling cat is obtained after integrating the constraint equation of the vanishing total angular momentum. An example of the falling cat is given in which the model turns a somersault to approach a target state in equilibrium with an expected rotation after finishing a vibrational motion.     

Dynamical ordering of symmetric non-Birkhoff periodic points in reversible monotone twist mappings

We study the coexistence of symmetric non-Birkhoff periodic orbits of C(1) reversible monotone twist mappings on the cylinder. We prove the equivalence of the existence of non-Birkhoff periodic orbits and that of transverse homoclinic intersections of stable and unstable manifolds of the fixed point. We derive the positional relation of symmetric Birkhoff and non-Birkhoff periodic orbits and obtain the dynamical ordering of symmetric non-Birkhoff periodic orbits. An extension of the Sharkovskii ordering to two-dimensional mappings has been carried out. In the proof of various properties of the mappings, reversibility plays an essential role. (c) 2002 American Institute of Physics.     

Exact solution of the Gaudin model with Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions

We study the exact solution of the Gaudin model with Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions. The energy and Bethe ansatz equations of the Gaudin model can be obtained via the off-diagonal Bethe ansatz method. Based on the off-diagonal Bethe ansatz solutions, we construct the Bethe states of the inhomogeneous X X X Heisenberg spin chain with the generic open boundaries. By taking a quasi-classical limit, we give explicit closed-form expression of the Bethe states of the Gaudin model. From the numerical simulations for the small-size system, it is shown that some Bethe roots go to infinity when the Gaudin model recovers the U(1) symmetry. Furthermore,it is found that the contribution of those Bethe roots to the Bethe states is a nonzero constant. This fact enables us to recover the Bethe states of the Gaudin model with the U(1) symmetry. These results provide a basis for the further study of the thermodynamic limit, correlation functions, and quantum dynamics of the Gaudin model.