Calabi-Yau 4-folds and toric fibrations

We present a general scheme for identifying fibrations in the framework of toric geometry and provide a large list of weights for Calabi-Yau 4-folds. We find 914 164 weights with degree d ≤ 150 whose maximal Newton polyhedra are reflexive and 525 572 weights with degree d ≤ 4000 that give rise to weighted projective spaces such that the polynomial defining a hypersurface of trivial canonical class is transversal. We compute all Hodge numbers, using Batyrev's formulas (derived by toric methods) for the first and Vafa's formulas (obtained by counting of Ramond ground states in N = 2 LG models) for the latter class, checking their consistency for the 109 308 weights in the overlap. Fibrations of k-folds, including the elliptic case, manifest themselves in the N lattice in the following simple way: The polyhedron corresponding to the fiber is a subpolyhedron of that corresponding to the k-fold, whereas the fan determining the base is a linear projection of the fan corresponding to the k-fold.     

Quantum superreplication of states and gates

Although the no-cloning theorem forbids perfect replication of quantum information, it is sometimes possible to produce large numbers of replicas with vanishingly small error. This phenomenon, known as quantum superreplication, can occur for both quantum states and quantum gates. The aim of this paper is to review the central features of quantum superreplication and provide a unified view of existing results. The paper also includes new results. In particular, we show that when quantum superreplication can be achieved, it can be achieved through estimation up to an error of size O(M/N²), where N and M are the number of input and output copies, respectively. Quantum strategies still offer an advantage for superreplication in that they allow for exponentially faster reduction of the error. Using the relation with estimation, we provide i) an alternative proof of the optimality of Heisenberg scaling in quantum metrology, ii) a strategy for estimating arbitrary unitary gates with a mean square error scaling as log N/N², and iii) a protocol that generates O(N²) nearly perfect copies of a generic pure state U|0>while using the corresponding gate U only N times. Finally, we point out that superreplication can be achieved using interactions among k systems, provided that k is large compared to M²/N².     

电压控制不连续导电模式DC-DC变换器的熵特性研究

结合DC-DC变换器非线性特性随反馈增益k变化的关系,以及熵能够反映序列总体统计特征的特点,提出一种基于熵估计DC-DC变换器非线性行为的新方法. 以一阶电压反馈不连续导电模式 DCM Buck和Boost变换器为例,详细分析了不同反馈增益k和初值x₀形成的数值序列及熵的分布情况. 研究结果表明：DC-DC变换器的熵由反馈增益k决定,与初值x₀无关,最终小于理论极大值log₂N （N为统计区间个数）;熵能够准确区分DC-DC变换器的倍周期分岔和混沌行为,从而得到一种新的可量化的DC-DC变换器非线性动力学行为指标;完善了该类变换器非线性动力学分析的理论和方法. 关键词： DC-DC变换器 熵 混沌 k')" href="#">反馈增益k     

Branes, geometry and N = 1 duality with product gauge groups of SO and Sp

We study N = 1 dualities in four-dimensional supersymmetric gauge theories as the world volume theory of D4 branes with one compact direction in type IIA string theory. We generalize the previous work for SO(N_c1) × Sp(N_c2) with the superpotential W = TrX⁴ to the case of W = TrX^4(k+1) in terms of brane configuration. We conjecture that the new dualities for the product gauge groups of SO(N_c1) × Sp(N_c2) × SO(N_c3), SO(N_c1) × Sp(N_c2) × SO(N_c3) × Sp(N_c4) and higher multiple product gauge groups can be obtained by reversing the ordering of NS5 branes and D6 branes while preserving the linking numbers. We also describe the above dualities in terms of wrapping D6 branes around 3-cycles of Calabi-Yau threefolds in type IIA string theory. The theory with adjoint matter can be regarded as taking multiple copies of NS5 brane in the configuration of brane or geometric approaches.     

三种湍流模式数值模拟直角弯管内三维分离流动的比较

采用有限体积法数值离散雷诺时均Navier Stokes方程,模拟了方形截面90°大曲率弯曲管道内的三维湍流流动.用3种湍流模式(标准k-ε湍流模式、RNG k-ε湍流模式、Realizable k-ε湍流模式)求解该问题.给出了数学模型和计算结果,并与实验数据进行了比较.结果表明,采用RNG k-ε湍流模式并结合两层壁面模型的处理,能有效准确地求解强曲率影响的管道内及近壁区湍流的流动.     

Solvent fluctuations and viscosity-dependent rates of solution reactions in a regime indescribable by the transition state theory

An organic molecule isomerizes in viscous solvents when appropriate cavities are formed around it in the course of slow diffusive thermal fluctuations of solvent molecules. The isomerization occurs when fast twisting (vibrational) fluctuations around a bond get to have large amplitudes in such cavities. This situation can be described by the two-reaction-coordinate model of Sumi and Marcus originally proposed for electron transfer reactions. In fact, the rate constant derived from this model fits nicely to that observed for thermal Z→E isomerization of substituted azobenzenes and N-benzylideneanilines. The rate constant is influenced by slow speeds of diffusive motions of solvent molecules, whose relaxation time τ is usually proportional to the solvent viscosity η. It has a form of k = 1/(k_TST⁻¹+k_f⁻¹), where k_TST, independent of τ, represents the rate constant expected from the transition state theory (TST), while k_f ∝ τ⁻ with 0 < ≤ 1 represents the part controlled by solvent fluctuations. An analytic expression of for the isomerization reactions is given in terms of physical parameters underlying the reaction mechanism with cavity formation.

This rate-constant formula is a general one applicable widely also to other solution reactions, covering from the TST-validated regime for a small τ to the TST-invalidated one for a large τ. In the former, k approaches k_TST since k_f k_TST, while in the latter, k approaches k_f since k_f k_TST, becoming decreasing with a decrease in the typical speed (∝ τ⁻¹) of solvent fluctuations. The dependence of k ≈ k_f ∝ η⁻ in the non-TST regime has often been observed also in biological reactions such as enzymatic ones. In this case, it is not appropriate to say that reactions are controlled by slow speeds of solvent fluctuations, but we should rather say that enzymes utilize this situation, which has been called conformational gating, in the course of solvent-fluctuation-driven conformational fluctuations of proteins. It has important meanings in protein functions.     

Supersymmetry in boundary integrable models

Quantum integrable models that possess N = 2 supersymmetry are investigated on the half-space. Conformal perturbation theory is used to identify some N = 2 supersymmetric boundary integrable models, and the effective boundary Landau-Ginzburg formulations are constructed. It is found that N = 2 supersymmetry largely determines the boundary action in terms of the bulk, and in particular, the boundary bosonic potential is |W|², where W is the bulk superpotential. Supersymmetry is also investigated using the affine quantum group symmetry of exact scattering matrices, and the affine quantum group symmetry of boundary reflection matrices is analyzed both for supersymmetric and more general models. Some N = 2 supersymmetry preserving boundary reflection matrices are given, and their connection with the boundary Landau-Ginzburg actions is discussed.     

Vicious random walkers and a discretization of Gaussian random matrix ensembles

The vicious random walker problem on a one-dimensional lattice is considered. Many walkers take simultaneous steps on the lattice and the configurations in which two of them arrive at the same site are prohibited. It is known that the probability distribution of N walkers after M steps can be written in a determinant form. Using an integration technique borrowed from the theory of random matrices, we show that arbitrary kth order correlation functions of the walkers can be expressed as quaternion determinants whose elements are compactly expressed in terms of symmetric Hahn polynomials.     

Possible candidates for finite supersymmetric grand unified theories

A realistic finite grand unified model has to accomodate at least three generations of ordinary fermions. When this criterion is imposed, we found that only a few models of the SU(N), SO(2N), SO(2N+1) and exceptional groups can survive as candidates for possible realistic finite supersymmetric grand unified models. All possible solutions are obtained, but the SU(5) model is excluded.     

Quenched master field equations for unitary matrix models

We derive the quenched master field equations for constrained systems such as the O(N) non-linear sigma model, U(N)×U(N) chiral models, and U(N) lattice gauge theory. The master equations are algebraic, and involve quenching in both the space and “fifth” (Langevin) time directions. The quenched master field for the O(N) nonlinear sigma model is found exactly. The 0-dimensional unitary matrix model is solved perturbatively, and we recover the Gross-Witten result. The master equation for the U(N)×U(N) chiral model is set up for non-perturbative approximation methods, and some qualitative results are obtained.     

Poisson-Lie T-duality and complex geometry in N = 2 superconformal WZNW models

Poisson-Lie T-duality in N = 2 superconformal WZNW models on the real Lie groups is considered. It is shown that Poisson-Lie T-duality is governed by the complexifications of the corresponding real groups endowed with Semenov-Tian-Shansky symplectic forms, i.e. Heisenberg doubles. Complex Heisenberg doubles are used to define on the group manifolds of the N = 2 superconformal WZNW models the natural actions of the isotropic complex subgroups forming the doubles. It is proved that with respect to these actions N = 2 superconformal WZNW models admit Poisson-Lie symmetries. The Poisson-Lie T-duality transformation maps each model onto itself but acts non-trivially on the space of classical solutions.     

Chiral symmetry for positive and negative parity nucleons

We investigate the role of chiral symmetry in the properties of positive and negative parity nucleons (N and N^*). When we consider two kinds of nucleons, two distinctive types of chiral assignment for N^* can be introduced. There are interesting differences between the two assignments in the properties of nucleons, which are studied using linear sigma models based on the two assignments. Behavior of N and N^* in the nuclear medium is also investigated using these linear models.     

湍流模型在复杂流场数值模拟中的应用

采用4种湍流模型:代数Baldwin Lomax(B-L)模型、半方程Johnson King(J-K)模型的两个版本(J-K90A和J K92)以及两方程k-g模型,分别数值模拟了导弹超音速流动、NASATND-712标模和民机翼身组合体(两区C-O网格)跨音速流动.采用中心有限体积和多步Runge-Kutta方法数值积分三维可压缩雷诺平均Navier-Stokes(N-S)方程组.k-g湍流模型方程的求解采用类似于N-S方程组的方法进行.所有湍流模型均能很好地模拟附体及小分离流动;对于大攻角、分离剧烈的导弹流动,k-g和J-K92模型与实验吻合更好;B-L模型在模拟民机跨音速流动时,它所捕捉的激波位置较其余3种模型靠后.利用多块网格模拟民机翼身组合体流场时,k-g模型的模拟能力强于其余3种模型.     

The self-dual Chern-Simons CP(N) models

We study the Chern-Simons CP(N) models with a global U(1) symmetry and found the self-dual models among them. The Bogomolnyi-type bound in these self-dual models is a nontrivial generalization of that in the pure CP(N) models. Our models have quite a rich vacuum and soliton structure and approach the many known gauged self-dual models in an appropriate limit.     

一端附壁高分子链的Monte Carlo研究

采用简立方格点上的Monte Carlo模拟,研究一端被无限大不可穿透平面壁吸附的高分子链的均方末端距<R²>,以及高分子链的质量中心到平面吸附壁的平均距离<Z>,与链长N、参数u(u=e^-ε/kT,ε是链骨架原子间的相互作用能量,k是玻耳兹曼常数,T是热力学温度)的关系。结果表明:<R²>和<Z>都服从标度律,<R²>=αN^γ,<Z>=βN^η,其中,γ、η、α、β都是u的函数;u从1减小到0.5,则γ从1.01增大到1.19,η从0.51增大到0.60.     

Solitary waves in a class of sine-Gordon-type equations

A new class of sine-Gordon-type Lagrangians is studied for solitary-wave solutions. The potential is a series with N terms, N varying from 1 to ∞, and N=1 corresponding to the usual sine-Gordon form. The large- and small-x limits of the solutions are obtained analytically for arbitrary N. The large-x behaviour is shown to be distinct for N even or odd. Also, the solutions for arbitrarily large but finite N are found to differ exponentially from the N=∞ solution, for asymptotically large x.     

The angular intensity correlation functions C(1) and C(10) for the scattering of light from randomly rough dielectric and metal surfaces

We study the statistical properties of the scattering matrix S(q|k) for the problem of the scattering of light of frequency ω from a randomly rough one-dimensional surface, defined by the equation x₃=ζ(x₁), where the surface profile function ζ(x₁) constitutes a zero-mean, stationary, Gaussian random process. This is done by studying the effects of S(q|k) on the angular intensity correlation function C(q,k|q',k')=〈I(q|k)I(q'|k')〉-〈I(q|k)〉〈I(q'|k')〉, where the intensity I(q|k) is defined in terms of S(q|k) by I(q|k)=L^-1₁(ω/c)|S(q|k)|², with L₁ the length of the x₁ axis covered by the random surface. We focus our attention on the C⁽¹⁾ and C⁽¹⁰⁾ correlation functions, which are the contributions to C(q,k|q',k') proportional to δ(q-k-q'+k') and δ(q-k+q'-k'), respectively. The existence of both of these correlation functions is consistent with the amplitude of the scattered field obeying complex Gaussian statistics in the limit of a long surface and in the presence of weak surface roughness. We show that the deviation of the statistics of the scattering matrix from complex circular Gaussian statistics and the C⁽¹⁰⁾ correlation function are determined by exactly the same statistical moment of S(q|k). As the random surface becomes rougher, the amplitude of the scattered field no longer obeys complex Gaussian statistics but obeys complex circular Gaussian statistics instead. In this case the C⁽¹⁰⁾ correlation function should therefore vanish. This result is confirmed by numerical simulation calculations.     

Effective action for D-branes on SU(2)/U(1) gauged WZW model

Dynamics of D-branes on SU(2)/U(1) gauged WZW model are investigated. We find the effective action for infinite k, where k is the level of WZW model. We also consider finite k correction to the effective action which is compatible with Fedosov's deformation quantization of the background.     

The O(N) vector model in the large-N limit revisited: multicritical points and double scaling limit

The multicritical points of the O(N)-invariant N vector model in the large-N limit are re-examined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit N → ∞ while the coupling g → g_c in a correlated manner (the double scaling limit) a massless bound state O(N) singlet is formed and powers of 1/N are compensated by IR singularities. The persistence of the N → ∞ results beyond the leading order is then studied with particular interest in the possible existence of a phase with propagating small mass vector fields and a massless singlet bound state. We point out that under certain conditions the double scaled theory of the singlet field is non-interacting in critical dimensions.