Development of variable‐magnification X‐ray Bragg optics

A novel X‐ray Bragg optics is proposed for variable‐magnification of an X‐ray beam. This X‐ray Bragg optics is composed of two magnifiers in a crossed arrangement, and the magnification factor, M, is controlled through the azimuth angle of each magnifier. The basic properties of the X‐ray optics such as the magnification factor, image transformation matrix and intrinsic acceptance angle are described based on the dynamical theory of X‐ray diffraction. The feasibility of the variable‐magnification X‐ray Bragg optics was verified at the vertical‐wiggler beamline BL‐14B of the Photon Factory. For X‐ray Bragg magnifiers, Si(220) crystals with an asymmetric angle of 14° were used. The magnification factor was calculated to be tunable between 0.1 and 10.0 at a wavelength of 0.112 nm. At various magnification factors (M≥ 1.0), X‐ray images of a nylon mesh were observed with an air‐cooled X‐ray CCD camera. Image deformation caused by the optics could be corrected by using a 2 × 2 transformation matrix and bilinear interpolation method. Not only absorption‐contrast but also edge‐contrast due to Fresnel diffraction was observed in the magnified images.     

基于波变量补偿的阻抗匹配时延双边遥操作

通信时延是遥操作系统中固有的问题,它会严重影响遥操作的性能,降低系统的稳定性和跟踪性。基于无源理论的波变量法可以保证遥操作系统在任意时延下稳定,是解决时延问题的一个重要方法。然而,波变量法带来的波反射会阻扰有用信号的传输,降低了主从端信号的跟踪性,严重时甚至会导致整个系统振荡。针对这一问题,提出了一种基于波变量补偿的阻抗匹配双边遥操作系统结构,旨在减少波反射,提高操作者的临场感和系统的跟踪性。通过仿真实验,结果表明所提方法能够保证固定时延条件下遥操作系统的稳定性,并具有较好的跟踪性。     

Magnetic properties of the low dimensional spin system (VO)PO:ESR and susceptibility

Experimental results on magnetic resonance (ESR) and magnetic susceptibility are given for single crystalline (VO)₂P₂O₇. The crystal growth procedure is briefly discussed. The susceptibility is interpreted numerically using a model with alternating spin chains. We determine J =51 K and . Furthermore we find a spin gap of meV from our ESR measurements. Using elastic constants no indication of a phase transition forcing the dimerization is seen below 300 K. Received: 22 December 1997 / Accepted: 17 March 1998     

Monte-Carlo study of correlations in quantum spin chains at non-zero temperature

Antiferromagnetic Heisenberg spin chains with various spin values (S=1/2,1,3/2,2,5/2) are studied numerically with the quantum Monte-Carlo method. Effective spin S chains are realized by ferromagnetically coupling n=2S antiferromagnetic spin chains with S=1/2. The temperature dependence of the uniform susceptibility, the staggered susceptibility, and the static structure factor peak intensity are computed down to very low temperatures, . The correlation length at each temperature is deduced from numerical measurements of the instantaneous spin-spin correlation function. At high temperatures, very good agreement with exact results for the classical spin chain is obtained independent of the value of S. For the S=2 chain which has a gap , the correlation length and the uniform susceptibility in the temperature range are well predicted by the semi-classical theory of Damle and Sachdev. Received: 23 December 1997 / Revised and Accepted: 11 March 1998     

High-temperature series analysis of the p-state Potts glass model on d-dimensional hypercubic lattices

We analyze recently extended high-temperature series expansions for the “Edwards-Anderson” spin-glass susceptibility of the p-state Potts glass model on d-dimensional hypercubic lattices for the case of a symmetric bimodal distribution of ferro- and antiferromagnetic nearest-neighbor couplings . In these star-graph expansions up to order 22 in the inverse temperature , the number of Potts states p and the dimension d are kept as free parameters which can take any value. By applying several series analysis techniques to the new series expansions, this enabled us to determine the critical coupling K_c and the critical exponent of the spin-glass susceptibility in a large region of the two-dimensional (p,d)-parameter space. We discuss the thus obtained information with emphasis on the lower and upper critical dimensions of the model and present a careful comparison with previous estimates for special values of p and d. Received: 25 May 1998 / Revised and Accepted: 11 August 1998     

Solution of Time-Dependent Diffusion Equations with Variable Coefficients Using Multiwavelets

A new numerical algorithm is developed for the solution of time-dependent differential equations of diffusion type. It allows for an accurate and efficient treatment of multidimensional problems with variable coefficients, nonlinearities, and general boundary conditions. For space discretization we use the multiwavelet bases introduced by Alpert (1993,SIAM J. Math. Anal.24, 246–262), and then applied to the representation of differential operators and functions of operators presented by Alpert, Beylkin, and Vozovoi (Representation of operators in the multiwavelet basis, in preparation). An important advantage of multiwavelet basis functions is the fact that they are supported only on non-overlapping subdomains. Thus multiwavelet bases are attractive for solving problems in finite (non periodic) domains. Boundary conditions are imposed with a penalty technique of Hesthaven and Gottlieb (1996,SIAM J. Sci. Comput., 579–612) which can be used to impose rather general boundary conditions. The penalty approach was extended to a procedure for ensuring the continuity of the solution and its first derivative across interior boundaries between neighboring subdomains while time stepping the solution of a time dependent problem. This penalty procedure on the interfaces allows for a simplification and sparsification of the representation of differential operators by discarding the elements responsible for interactions between neighboring subdomains. Consequently the matrices representing the differential operators (on the finest scale) have block-diagonal structure. For a fixed order of multiwavelets (i.e., a fixed number of vanishing moments) the computational complexity of the present algorithm is proportional to the number of subdomains. The time discretization method of Beylkin, Keiser, and Vozovoi (1998, PAM Report 347) is used in view of its favorable stability properties. Numerical results are presented for evolution equations with variable coefficients in one and two dimensions.     

Random magnetic interactions and spin glass order competing with superconductivity: Interference of the quantum Parisi phase

We analyse the competition between spin glass (SG) order and local pairing superconductivity (SC) in the fermionic Ising spin glass with frustrated fermionic spin interaction and nonrandom attractive interaction. The phase diagram is presented for all temperatures T and chemical potentials μ. SC-SG transitions are derived for the relevant ratios between attractive and frustrated-magnetic interaction. Characteristic features of pairbreaking caused by random magnetic interaction and/or by spin glass proximity are found. The existence of low-energy excitations, arising from replica permutation symmetry breaking (RPSB) in the Quantum Parisi Phase, is shown to be relevant for the SC-SG phase boundary. Complete 1-step RPSB-calculations for the SG-phase are presented together with a few results for -step breaking. Suppression of reentrant SG-SC-SG transitions due to RPSB is found and discussed in context of ferromagnet-SG boundaries. The relative positioning of the SC and SG phases presents a theoretical landmark for comparison with experiments in heavy fermion systems and high superconductors. We find a crossover line traversing the SG-phase with as its quantum critical (end)point in complete RPSB, and scaling is proposed for its vicinity. We argue that this line indicates a random field instability and suggest Dotsenko-Mézard vector replica symmetry breaking to occur at low temperatures beyond. Received 26 November 1998 and Received in final form 25 January 1999     

Parkinsonian oscillations and their suppression by closed-loop deep brain stimulation based on fuzzy concept

This paper provides an adaptive closed-loop strategy for suppressing the pathological oscillations of the basal ganglia based on a variable universe fuzzy algorithm. The pathological basal ganglia oscillations in the theta (4-9 Hz) and beta (12-35 Hz) frequency bands have been demonstrated to be associated with the tremor and rigidity/bradykinesia symptoms in Parkinson's disease (PD). Although the clinical application of open-loop deep brain stimulation (DBS) is effective, the stimulation waveform with the fixed parameters cannot be self-adjusted as the disease progresses, and thus the stimulation effects go poor. To deal with this difficult problem, a variable universe fuzzy closed-loop strategy is proposed to modulate different PD states. We establish a cortico-basal ganglia-thalamocortical network model to simulate pathological oscillations and test the control effect. The results suggest that the proposed closed-loop control strategy can accommodate the variation of brain states and symptoms, which may become an alternative method to administrate the symptoms in PD.     

Branched polymers in a wedge geometry in three dimensions

We investigate the statistical and dimensional properties of uniform star polymers attached by the branching vertex of degreef in a wedge geometry in three dimensions and described by the wedge angles and. We show that the growth constant is equal to ^f , where is the self-avoiding walk limit. Thef and (, ) dependences of the corresponding critical exponent _f (, ) are studied using Monte Carlo techniques. In the casef=1, our results are compared with existing predictions obtained from series expansion and renormalization group methods. We have also estimated the amplitudes for the mean square radius of gyration and the mean square end-to-end branch length. Our results for the ratio of the mean square radius of gyration of anf-star to that of a linear polymer of the same degree of polymerization attached in a similar wedge, and the analogous ratio for the mean square end-to-end branch length, are consistent with these ratios being lattice-independent quantities.     

A numerical method to compute exactly the partition function with application toZ(n) theories in two dimensions

I present a new method to exactly compute the partition function of a class of discrete models in arbitrary dimensions. The time for the computation for ann-state model on anL ^d lattice scales like . I show examples of the use of this method by computing the partition function of the 2D Ising and 3-state Potts models for maximum lattice sizes 10×10 and 8×8, respectively. The critical exponentsv and and the critical temperature one obtains from these are very near the exactly known values. The distribution of zeros of the partition function of the Potts model leads to the conjecture that the ratio of the amplitudes of the specific heat below and above the critical temperature is unity.