Analyticity of the charge-monopole scattering amplitude

We study the analyticity in cosθ of the exact quantum-mechanical electric-charge-magnetic-monopole scattering amplitude by ascribing meaning to its formally divergent partial-wave expansion as the boundary value of an analytic function. This permits us to find an integral representation for the amplitude which displays its analytic structure. On the physical sheet we find only a branch-point singularity in the forward direction, while on each of the infinitely many unphysical sheets we find a logarithmic branch-point singularity in the backward direction as well as the same forward structure.

Completeness of the Coulomb wave functions in quantum mechanics

We give an explicit, direct, and fairly elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses only some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory; therefore it would form useful supplementary reading for a graduate course on quantum mechanics.

Squeezed states, metaplectic group, and operator möbius transformations

We present an analysis, based on the metaplectic group Mp(2), of the recently introduced single-mode inverse creation and annihilation operators and of the associated eigenstates of different two-photon annihilation operators. We motivate and obtain a quantum operator form of the classical Mobius or fractional linear transformation. The subtle relation to the two unitary irreducible representations of Mp(2) is brought out. For problems involving inverse operators the usefulness of the Bargmann analytic function representation of quantum mechanics is demonstrated. Squeezing, bunching, and photon-number distributions of the four families of states that arise in this context are studied both analytically and numerically

A Multicast Authentication Protocol (MAP) for Dynamic Multicast Groups in Wireless Networks

In this paper, we have proposed a centralized multicast authentication protocol (MAP) for dynamic multicast groups in wireless networks. In our protocol, a multicast group is defined only at the time of the multicasting. The authentication server (AS) in the network generates a session key and authenticates it to each of the members of a multicast group using the computationally inexpensive least common multiple (LCM) method. In addition, a pseudo random function (PRF) is used to bind the secret keys of the network members with their identities. By doing this, the AS is relieved from storing per member secrets in its memory, making the scheme completely storage scalable. The protocol minimizes the load on the network members by shifting the computational tasks towards the AS node as far as possible. The protocol possesses a membership revocation mechanism and is protected against replay attack and brute force attack. Analytical and simulation results confirm the effectiveness of the proposed protocol.

A Secure and Efficient Authentication Protocol (SEAP) for MANETs with Membership Revocation

In this paper, we propose a novel authentication protocol for MANETs requiring stronger security. The protocol works on a two-tier network architecture with client nodes and authentication server nodes, and supports dynamic membership. We use an external membership granting server (MGS) to provide stronger security with dynamic membership. However, the external MGS in our protocol is semi-online instead of being online, i.e., the MGS cannot initiate a connection with a network node but any network node can communicate with the MGS whenever required. To ensure efficiency, the protocol uses symmetric key cryptography to implement the authentication service. However, to achieve storage scalability, the protocol uses a pseudo random function (PRF) to bind the secret key of a client to its identity using the secret key of its server. In addition, the protocol possesses an efficient server revocation mechanism along with an efficient server re-assignment mechanism, which makes the protocol robust against server node compromise.

Optimal design of Functionally Graded Materials using a procedural model and Particle Swarm Optimization

A new method for the optimal design of Functionally Graded Materials (FGM) is proposed in this paper. Instead of using the widely used explicit functional models, a feature tree based procedural model is proposed to represent generic material heterogeneities. A procedural model of this sort allows more than one explicit function to be incorporated to describe versatile material gradations and the material composition at a given location is no longer computed by simple evaluation of an analytic function, but obtained by execution of customizable procedures. This enables generic and diverse types of material variations to be represented, and most importantly, by a reasonably small number of design variables. The descriptive flexibility in the material heterogeneity formulation as well as the low dimensionality of the design vectors help facilitate the optimal design of functionally graded materials. Using the nature-inspired Particle Swarm Optimization (PSO) method, functionally graded materials with generic distributions can be efficiently optimized. We demonstrate, for the first time, that a PSO based optimizer outperforms classical mathematical programming based methods, such as active set and trust region algorithms, in the optimal design of functionally graded materials. The underlying reason for this performance boost is also elucidated with the help of benchmarked examples. © 2011 Elsevier Ltd. All rights reserved.

Optical investigations of the effect of solvent and thermal annealing on the optoelectronic properties of Poly(3,4-ethylenedioxythiophene): poly(styrenesulfonate) films

Poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) is one of the most promising conducting polymers that can be used as transparent electrode or as buffer layer for organic electronic devices. However, when used as an electrode, its conductivity has to be optimized either by the addition of solvents or by post-deposition processing. In this work, we investigate the effect of the addition of the polar solvent dimethylsulfoxide (DMSO) to an aqueous PEDOT:PSS solution on its optical and electrical properties by the implementation of the Drude model for the analysis of the measured pseudo-dielectric function by Spectroscopic Ellipsometry from the near infrared to the visible-far ultraviolet spectral range. The results show that the addition of DMSO increases significantly the film conductivity, which reaches a maximum value at an optimum DMSO concentration as it has confirmed by experimentally measured conductivity values. The post-deposition thermal annealing has been found to have a smaller effect on the film conductivity. © 2013 Elsevier B.V.

基于GIS的区域土壤侵蚀模型设计

区域土壤侵蚀模型是国家和区域土壤侵蚀调查、水土保持宏观规划的支持工具。借鉴国外区域土壤侵蚀模型,以DEM栅格为空间单元,对区域土壤侵蚀的单元模型进行定量表达,包括降雨、植被截留、入渗,微地形填洼等,并利用GIS功能完成径流传递和汇集部分的计算,建立了区域土壤侵蚀模型。所建立模型在延河流域的试运算,结果接近现实,能反映土壤侵蚀时空分布趋势。模型的建立可为水土保持的宏观决策提供支持。

A four-phase confocal elliptical cylinder model for predicting the effective thermal conductivity of coated fibre composites

A four-phase confocal elliptical cylinder model is proposed from which a generalised self-consistent method is developed for predicting the thermal conductivity of coated fibre reinforced composites. The method can account for the influence of the fibre section shape ratio on conductivity, and the physical reasonableness of the model is demonstrated by using the fibre distribution function. An exact solution is obtained for thermal conductivity by applying conformal mapping and Laurent series expansion techniques of the analytic function. The solution to the three-phase confocal elliptical model, which simulates composites with idealised fibre-matrix interfaces, is arrived at as the degenerated case. A comparison with other available micromechanics methods, Hashin and Shtrikman's bounds and experimental data shows that the present method provides convergent and reasonable results for a full range of variations in fibre section shapes and for a complete spectrum of the fibre volume fraction. Numerical results show the dependence of the effective conductivities of composites on the aspect ratio of coated fibres and demonstrate that a coating is effective in enhancing the thermal transport property of a composite. The present solutions are helpful to analysis and design of composites.

人工源频率域大地电磁法正反演研究

The CSAMT method is playing an important role in the exploration of geothermal and the pre-exploration in tunnel construction project recently. In order to instruct the interpretation technique for the field data, the forward method from ID to 3D and inversion method in ID and 2D are developed in this paper for the artificial source magnetotelluric in frequency domain. In general, the artificial source data are inverted only after the near field is corrected on the basis of the assumption of half-homogeneous space; however, this method is not suitable for the complex structure because the assumption is not valid any more. Recently the new idea about inversion scheme without near field correction is published in order to avoid the near field correction error. We try to discuss different inversion scheme in ID and 2D using the data without near field correction.The numerical integration method is used to do the forward modeling in ID CSAMT method o The infinite line source is used in the 2D finite-element forward modeling, where the near-field effect is occurred as in the CSAMT method because of using artificial source. The pseudo-delta function is used to modeling the source distribution, which reduces the singularity when solving the finite-element equations. The effect on the exploration area is discussed when anomalous body exists under the source or between the source and exploration area; A series of digital test show the 2D finite element method are correct, the results of modeling has important significant for CSAMT data interpretation. For 3D finite-element forward modeling, the finite-element equation is derived by Galerkin method and the divergence condition is add forcedly to the forward equation, the forward modeling result of the half homogeneous space model is correct.The new inversion idea without near field correction is followed to develop new inversion methods in ID and 2D in the paper. All of the inversion schemes use the data without near field correction, which avoid introducing errors caused by near field correction. The modified grid parameter method and the layer-by-layer inversion method are joined in the ID inversion scheme. The RRI method with artificial source are developed and finite-element inversion method are used in 2D inversion scheme. The inversion results using digital data and the field data are accordant to the model and the known geology data separately, which means the inversion without near field correction is accessible. The feasibility to invert the data only in exploration area is discussed when the anomalous body exists between the source and the exploration area.

Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices

B.M. Brown, M. Marletta, S. Naboko, I. Wood: Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices, J. London Math. Soc., June 2008; 77: 700-718. The full text of this article will be made available in this repository in June 2009 Sponsorship: EPSRC,INTAS

A Hamiltonian approach to simulation of acoustic systems involving nonlinear interactions

Nonlinear interactions take place in most systems that arise in music acoustics, usually as a result of player-instrument coupling. Several time-stepping methods exist for the numerical simulation of such systems. These methods generally involve the discretization of the Newtonian description of the system. However, it is not always possible to prove the stability of the resulting algorithms, especially when dealing with systems where the underlying force is a non-analytic function of the phase space variables. On the other hand, if the discretization is carried out on the Hamiltonian description of the system, it is possible to prove the stability of the derived numerical schemes. This Hamiltonian approach is applied to a series of test models of single or multiple nonlinear collisions and the energetic properties of the derived schemes are discussed. After establishing that the schemes respect the principle of conservation of energy, a nonlinear single-reed model is formulated and coupled to a digital bore, in order to synthesize clarinet-like sounds.

Nonlinear hydrodynamic Langmuir waves in fully degenerate relativistic plasma

The combined effect of special relativity and electron degeneracy on Langmuir waves is analyzed by utilizing a rigorous fully relativistic hydrodynamic model. Assuming a traveling wave solution form, a set of conservation laws is identified, together with a pseudo-potential function depending on the relativistic parameter p<inf>F</inf>/(m c) (where p<inf>F</inf> is the Fermi momentum, m is the mass of the charge carriers and c the speed of light), as well as on the amplitude of the electrostatic energy perturbation.

Discrete commutative difference operator theory

The object of this thesis is to formulate a basic commutative difference operator theory for functions defined on a basic sequence, and a bibasic commutative difference operator theory for functions defined on a bibasic sequence of points, which can be applied to the solution of basic and bibasic difference equations. in this thesis a brief survey of the work done in this field in the classical case, as well as a review of the development of q~difference equations, q—analytic function theory, bibasic analytic function theory, bianalytic function theory, discrete pseudoanalytic function theory and finally a summary of results of this thesis

Studies in the geometry of the discrete plane

This thesis is an attempt to initiate the development of a discrete geometry of the discrete plane H = {(qmxo,qnyo); m,n e Z - the set of integers}, where q s (0,1) is fixed and (xO,yO) is a fixed point in the first quadrant of the complex plane, xo,y0 ¢ 0. The discrete plane was first considered by Harman in 1972, to evolve a discrete analytic function theory for geometric difference functions. We shall mention briefly, through various sections, the principle of discretization, an outline of discrete a alytic function theory, the concept of geometry of space and also summary of work done in this thesis