Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

地磁对γγ方向角关联测量的影响

在γ-γ角关联实验中,发现能谱中全能峰的位置随探头方位角的改变而变化。本文通过不同的实验,验证了地磁对能谱测量的干扰以及对γ-γ方向角关联测量的影响。发现地磁对测量的影响主要来自光电倍增管,地磁方向与光电倍增管中电子飞行方向的夹角的改变,引起光电倍增管增益变化,最终给γ-γ方向角关联测量带来较大的影响。文中总结了如何减小地磁影响,改进γ-γ方向角关联实验测量的方法。     

Real-time assessment of carbon nanotube alignment in a polymer matrix under an applied electric field via polarized Raman spectroscopy

A technique has been developed utilizing polarized Raman spectroscopy to measure alignment of carbon nanotubes in situ in a polymer matrix under an applied electric field. Previous studies of alignment have been restricted to optically transparent solvents or polymerized specimens that prevent accurate analyses of alignment dynamics in polymers. The effects of electric field strength on the degree of alignment and the time to achieve an aligned state are discussed. The use of in situ, real-time polarized Raman spectroscopy provides a non-invasive technique for assessing carbon nanotube alignment, which can assist in determining processing conditions to improve the mechanical and electrical properties of aligned nanocomposites.     

Construction Theory of Function on Local Fields

We establish the construction theory of function based upon a local field K p as underlying space. By virture of the concept of pseudo-differential operator, we introduce "fractal calculus"(or, p-type calculus, or, Gibbs-Butzer calculus). Then, show the Jackson direct approximation theorems, Bermstein inverse approximation theorems and the equivalent approximation theorems for compact group D( Kp) and locally compact group K+p(= Kp), so that the foundation of construction theory of function on local fields is established. Moreover, the Jackson type, Bernstein type,and equivalent approximation theorems on the H ?lder-type space Cσ(Kp), σ 0, are proved; then the equivalent approximation theorem on Sobolev-type space Wrσ(Kp),σ≥ 0, 1 ≤ r +∞, is shown.     

超音速等离子体炬的磁流体动力学数值研究

针对设计的喉径2mm、工作电流为100A的拉瓦尔喷嘴,在二维轴对称模型的基础上,对超音速等离子体炬中的流动及其外部射流进行了数值模拟。通过在阳极喷嘴内部采用基于磁矢量势的磁流体动力学模型,避免了对磁感应强度的复杂积分计算,得到了喷嘴内部多场耦合的结果及外部射流的流动状态,分析了喷嘴内部电磁场对等离子体的加速作用及射流发展过程。结果显示,等离子体经历了亚音速→跨音速→超音速的发展过程,最终获得2.3 Ma的超音速射流。研究结果为超音速等离子体炬的工业应用提供了理论基础。     

MHD flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge

The steady flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge with magnetic field and radiation effects are studied. The governing equations of the hybrid nanofluid are converted to the similarity equations by techniques of the similarity transformation. The bvp4c function that is available in MATLAB software is utilized for solving the similarity equations numerically. The numerical results are obtained for selected different values of parameters. The results discover that two solutions exist, up to a certain value of the stretching/shrinking and suction strengths. The critical value in which the solution is in existence decreases as nanoparticle volume fractions for copper and wedge angle parameter increase. It is also found that the hybrid nanofluid enhances the heat transfer rate compared with the regular nanofluid. The reduction of the heat transfer rate is observed with the increase in radiation parameter. The temporal stability analysis is performed to analyze the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.     

Acoustoelastic effect simulation by time–space finite element formulation based on quadratic interpolation of the acceleration

Acoustoelastic effect describes the change of ultrasound velocity due to the initial stress. Its simulation involves a numerical analysis of nonlinear elastodynamics and requires high accuracy in the time domain. A time–space finite element formulation, derived from the quadratic interpolation of the acceleration within a time segment, is proposed for an accurate simulation of the acoustoelastic effect in the present study. Ten different integration schemes are generated based on this formulation and nine of them are found to be conditionally stable. Among the nine stable schemes, one is found to obtain a spectral radius of one when the normalized step ratio is less than 5.477, indicating no numerical dissipation or numerical divergence. Compared with integration schemes from previous studies, this integration scheme demonstrates better performance in calculation accuracy and energy conservation. A two-stage approach, namely the static stage and the dynamic stage, has been employed in the simulation of the acoustoelastic effect. The former stage is adopted to obtain the initial stress and the latter stage, where the proposed integration scheme is implemented, is adopted to simulate the ultrasound propagation in an initial stress state. The simulation results of the dynamic stage show that the ultrasound velocity increases in a compression stress state and decreases in a tension stress state for aluminum alloy, which is in good agreement with previous experimental studies. Together with the simulation result of the static stage, it is conjectured that the acoustoelastic effect results from the stress-dependent elastic modulus.     

HL-2M装置等离子体放电反馈控制系统

通过对HL-2M装置极向场线圈的参数和初始等离子放电控制需求的分析，基于实时采集系统和反射内存实时数据传输的先进控制集成技术，完成了整个HL-2M初始等离子体放电反馈控制系统的设计。新系统实现了稳定的1ms控制周期和实时数据传输，同时解决了实时控制周期和数据传输的延迟。实验结果表明新设计的等离子控制系统能满足初始等离子体极向场线圈电流控制的需求。     

Reentrant behavior of magnetic ordered phase in spin-crossover solids with quenched disordered ligand field

The Ising-like model of spin-crossover solid compounds with quenched random ligand field has been investigated by the mean-field (infinite-range) approximation. An exact solution for the problem is found within the replica formalism. The magnetic diagrams are obtained; the relations between the intermolecular coupling and the temperature as well as the reentrant phenomena of the magnetic ordered phase are discussed.