Reducibility of Quantum Representations of Mapping Class Groups

In this paper we provide a general condition for the reducibility of the Reshetikhin–Turaev quantum representations of the mapping class groups. Namely, for any modular tensor category with a special symmetric Frobenius algebra with a non-trivial genus one partition function, we prove that the quantum representations of all the mapping class groups built from the modular tensor category are reducible. In particular, for SU(N) we get reducibility for certain levels and ranks. For the quantum SU(2) Reshetikhin–Turaev theory we construct a decomposition for all even levels. We conjecture this decomposition is a complete decomposition into irreducible representations for high enough levels.     

Near-equilibrium measurements of nonequilibrium free energy

A central endeavor of thermodynamics is the measurement of free energy changes. Regrettably, although we can measure the free energy of a system in thermodynamic equilibrium, typically all we can say about the free energy of a nonequilibrium ensemble is that it is larger than that of the same system at equilibrium. Herein, we derive a formally exact expression for the probability distribution of a driven system, which involves path ensemble averages of the work over trajectories of the time-reversed system. From this we find a simple near-equilibrium approximation for the free energy in terms of an excess mean time-reversed work, which can be experimentally measured on real systems. With analysis and computer simulation, we demonstrate the accuracy of our approximations for several simple models.     

Design and development of a new architecture of sliceable bandwidth variable transponder

In this paper we propose a new sliceable bandwidth variable transponder (SBVT) architecture with the separate analysis on the transmitter and receiver section. In transmission section we propose a distance module (DM) which is a programmable module. It divides a data stream/main stream (which employs a super-channel) into sub-stream and assigned modulation technique to each sub-stream based on their light path distance detailing the concept of sub-channel. In this paper, we have also proposed an algorithm for the distance module. Next we propose a modulation and transmission module (M&TM), where, planar light wave circuit (PLC) is used for enabling three modulation techniques (PM-16QAM, PM-QPSK and PM-BPSK). Finally, we propose the receiving section, which is designed to support three modulation techniques. It consists of two demodulator circuits, one for PM-16QAM/PM-QPSK and the other for PM-BPSK. In this proposed work, we focus on the multi-mode interference (MMI) devices (MMI coupler and MMI splitter) because of their photonic integration technology which is necessary for the implementation of SBVT. Lastly, we propose an elastic optical node architecture which removes the limitations of previously discussed node architecture for long distance communication.     

Dynamics of texture for spinor condensates

We study a dynamics of texture for a two-component spinor bose condensate. This is carried out by adopting a time dependent Landau-Ginzburg Lagrangian for a spinor order parameter. By using a polar form of the spinor order parameter, we obtain a field equation for the texture. In particular we consider a one dimensional model in which we can obtain analytic forms for the textures in terms of elliptic functions of several kinds. We find that these solutions are characterized by a modulus parameter, and changes in this parameter cause structural changes of texture.     

On the design of broadband quasioptical systems for submillimeter-wave radio-astronomy receivers

In this paper, we summarize the issues that should be considered when designing broadband quasioptical systems for submillimetre-wave radioastronomy receivers. We cover topics such as bandwidth, cross-talk, truncation, and aberrations, and we argue that it should be possible to manufacture high-efficiency systems that have several octaves of bandwidth. A key feature of the paper is that we use the language of multimode Gaussian optics throughout, and in this way, we emphasize that a receiver is a diffraction-limited imaging system rather than just a collection of components for guiding Gaussian beams. The whole discussion is conducted in terms of a particular system we are constructing for the James Clerk Maxwell Telescope in Hawaii.     

Occurrence, Repetition and Matching of Patterns in the Low-temperature Ising Model

We continue our study of the exponential law for occurrences and returns of patterns in the context of Gibbsian random fields. For the low-temperature plus-phase of the Ising model, we prove exponential laws with error bounds for occurrence, return, waiting and matching times. Moreover we obtain a Poisson law for the number of occurrences of large cylindrical events and a Gumbel law for the maximal overlap between two independent copies. As a by-product, we derive precise fluctuation results for the logarithm of waiting and return times. The main technical tool we use, in order to control mixing, is disagreement percolation     

Observation of nanometer-scale optical property discrimination by use of a near-field scanning apertureless microscope

We examine fundamental issues related to discriminating structural and optical features in near-field scanning apertureless microscopy. We report a series of controlled experiments with nanosphere-sized standard spheres in which we observed significant differences in resolution and structure between an atomic-force microscope image and a simultaneously acquired near-field optical (NFO) image. Further, in experiments that employed a mix of dyed and undyed nanospheres we found that we can observe differences in the same NFO image for adjacent nanospheres. Therefore we conclude that near-field scanning apertureless microscopy not only meets the criteria for a NFO image but also is capable of measuring optical properties below the diffraction limit. The two-point resolution was at least 200 nm when we were detecting optical phase and 50 nm when we were detecting optical intensity. The edge response was typically 15 nm, and the minimum observable features were of the order of 3 nm.     

TDGL方程的微扰理论

在一阶近似下,获得了微扰对TDGL(TimeDependentGinzburgLandau)方程的静态孤子解的影响,即求得了孤子参数随时间慢变量的变化情况和一阶修正的一般表达式,以及一个特例的具体表式 关键词： 静态孤子 孤子微扰论     

Analysis of domain-solutions in reaction-diffusion systems

We investigate a standard model for bistable reaction-diffusion-systems, which shares characteristic properties with the van-der-Pol oscillator for distributed generators and the FitzHugh-Nagumo system. In this system we study the effect of a long ranging inhibitor. As a main result we show the existence of two inhomogeneous stationary solutions—the smaller one is always a saddle which corresponds to a critical nucleus, while the larger one arises as astable solution. In carrying out the linear stability analysis for these solutions, we have to treat the Schrödinger-equation for a double-well potential. This is done approximately by a supersymmetric approach which yields the eigenvalues and eigenfunctions of the Schrödinger-equation. Furthermore we compare our analytical findings with numerical results-especially the occurrence of oscillating solutions is shown.     

Asymptotic behavior of the Rayleigh-Taylor instability

We investigate long time numerical simulations of the inviscid Rayleigh-Taylor instability at Atwood number one using a boundary integral method. We are able to attain the asymptotic behavior for the spikes predicted by Clavin and Williams for which we give a simplified demonstration. In particular, we observe that the spike's curvature evolves as t(3), while the overshoot in acceleration shows good agreement with the suggested 1/t(5) law. Moreover, we obtain consistent results for the prefactor coefficients of the asymptotic laws. Eventually we exhibit the self-similar behavior of the interface profile near the spike.     

一类延迟混沌系统沿主轴方向上Lyapunov指数的计算方法

提出了一种计算延迟混沌系统沿主轴方向上Lyapunov指数的方法：矩阵迭代法.给出了其计算方法的原理及推导过程;同时推导了一类泰勒展开法,介绍了已有的Wolf替代法计算延迟混沌系统的Lyapunov指数.分析了三种不同计算方法的优缺点,最后进行了数值模拟,验证方法的有效性. 关键词： Lyapunov指数 延迟混沌系统 矩阵迭代法 泰勒展开法     

A model for the packing of irregularly shaped grains

In this paper we will attempt to address the problem of the packing properties of granular materials composed of irregularly shaped grains (using configurational statistical mechanics). In particular, we will develop a model for a system of irregular grains based upon perturbing a packing of mono- or poly-disperse spheres. In the mono-disperse case we will show that the system packs less densely than a packing of perfect spheres, except when local correlations between configurations of grains are taken into account. The opposite is found to be true for a perturbation expansion based upon poly-disperse spheres. Finally we will show that for a bi-disperse packing of spheres phase segregation occurs for any size ratio and discuss whether this is to be expected.     

Assessment of different fixation protocols on the presence of membrane-bound vesicles in Caco-2 cells: A multidimensional view by means of correlative light and 3-D transmission electron microscopy

Herein, we present a comparative analysis of a variety of chemical and physical fixation protocols for the specific visualisation of the membrane-bound vesicles (MBVs) in the Caco-2 colorectal cancer (CRC) cell line. In so doing, we validated the applicability of specific specimen preparation protocols for the preservation and contrasting of membrane-associated vesicles. Next, by employing the best respective chemical (GOT) and physical (SHPF) fixation methods for the application of transmission electron tomography and modelling we were able to characterise MBVs in three-dimensions and at the nanometer scale. In the second part of this study, we employ a correlative light and electron microscopy (CLEM) approach in order to determine which vesicular compartments are implicated in the uptake of FITC-BSA as a model protein drug. In so doing, we provide a solid foundation for future studies investigating chemotherapeutic drug uptake, transport and fate in cancer cell lines.     

Construction of a unitary analytic scattering amplitude (I). Scalar particles

By imposing cos θ analyticity, we extend earlier investigations into the problem of constructing a unitary scattering amplitude from experimental measurements. The new approach is superior to earlier work, inasmuch as (a) the partial waves fall off exponentially, (b) we can handle cross sections with zeros, (c) we have a convergent Newton-Kantorovich interaction even when the fixed-point theorems do not apply, (d) we can study bifurcation points, (e) in the inelastic region, we find that analyticity does not remove the continuum ambiguity, (f) for quasi-elastic reactions (e.g. photoproduction) we resolve the Watson ambiguity for the phase shifts. We work at fixed energy, and throughout this first paper we neglect spin and isospin.     

Compression of digital holograms via adaptive-sparse representation

Efficient storage and transmission of digital holograms (DHs) requires the development of appropriate compression techniques for such a special class of images. In this Letter, we investigate a method to compress DHs using a sparse matrix representation. Using digital holography to numerically manage complex wave fields, we are able to apply an adaptive mask, based on a threshold filter, to the object wave field. From there, we store the result of this filtering by sparse representation. In this Letter, we demonstrate that using sparse representation allows for a high compression factor with minimal loss in the quality of the reconstructed image. This technique is efficient for storage and transmission of DHs.     

Integrating factors and conservation theorems for Hamilton‘s canonical equations of motion of variable mass nonholonmic nonconservative dynamical systems

We present a general approach to the construction of conservation laws for variable mass noholonmic nonconservative systems.First,we give the definition of integrating factors,and we study in detail the necessary conditions for the existence of the conserved quantities,Then,we establish the conservatioin theorem and its inverse theorem for Hamilton‘s canonical equations of motion of variable mass nonholonomic nonocnservative dynamical systems.Finally,we give an example to illustrate the application of the results.     

Linear stability of the spatially homogeneous equilibria of the Vlasov-Poisson system with collisions

In this work we study the stability of the spatially homogeneous solutions of the Vlasov-Poisson system (Vlasov equilibria) when a collision term, in the form of a BGK operator with velocity-dependent collision frequency, is added to the Vlasov equation. Generalizing earlier results, obtained for the same collision model with a constant collision frequency, we find the spectrum and the eigenfunctions of the linear transport operator and derive a new linear dispersion relation for the linearized kinetic equations. Finally, we present some numerical results.     

Investigation of Heisenberg algebra for a modified anti-de Sitter and modified antiSnyder models

In this paper,we consider a possible modification of the de Sitter and anti-de Sitter space for the extended uncertainty principle.For the modified anti-de Sitter model we discuss the representation and wave functions of the momentum operator for a one-dimensional box problem.Also,we consider modified Snyder and anti-Snyder models for the generalized uncertainty principle.Then,we assume the Hamiltonian with different potential and solve the Heisenberg algebra for the modified(anti)-de Sitter and(anti)-Snyder models in both position and in the momentum space.     

Generalization of Drinfeld Quantum Affine Algebras

Drinfeld gave a current realization of the quantum affine algebras as a Hopf algebra with a simple comultiplication for the quantum current operators. In this Letter, we will present a generalization of such a realization of quantum Hopf algebras. As a special case, we will choose the structure functions for this algebra to be elliptic functions to derive certain elliptic quantum groups as a Hopf algebra, which degenerates into quantum affine algebras if we take certain degeneration of the structure functions.     

Cluster synchronization in networks of distinct groups of maps

In this paper, we study cluster synchronization in general bi-directed networks of nonidentical clusters, where all nodes in the same cluster share an identical map. Based on the transverse stability analysis, we present sufficient conditions for local cluster synchronization of networks. The conditions are composed of two factors: the common inter-cluster coupling, which ensures the existence of an invariant cluster synchronization manifold, and communication between each pair of nodes in the same cluster, which is necessary for chaos synchronization. Consequently, we propose a quantity to measure the cluster synchronizability for a network with respect to the given clusters via a function of the eigenvalues of the Laplacian corresponding to the generalized eigenspace transverse to the cluster synchronization manifold. Then, we discuss the clustering synchronous dynamics and cluster synchronizability for four artificial network models: (i) p-nearest-neighborhood graph; (ii) random clustering graph; (iii) bipartite random graph; (iv) degree-preferred growing clustering network. From these network models, we are to reveal how the intra-cluster and inter-cluster links affect the cluster synchronizability. By numerical examples, we find that for the first model, the cluster synchronizability regularly enhances with the increase of p, yet for the other three models, when the ratio of intra-cluster links and the inter-cluster links reaches certain quantity, the clustering synchronizability reaches maximal.