Latest achievements in generalized Lorenz‐Mie theories: A commented reference database

Generalized Lorenz‐Mie theories form a set of analytical approaches dealing with the interaction between electromagnetic arbitrary shaped beams and a class of particles possessing enough symmetries to allow one to use the method of separation of variables. This paper provides a commented reference database concerning generalized Lorenz‐Mie theories for the period 2009‐2013.     

Generalized Lorenz‐Mie Theory for a Sphere with an Eccentrically Located Inclusion,and Optical Chaos

This paper deals with the case when a homogeneous spherical particle (called the inclusion) is embedded at an arbitrary location inside a sphere (called the main or host sphere). Similarly as for previous Generalized Lorenz‐Mie Theories, many applications are expected from this theory, in particular in the field of optical particle characterization. Another interesting prospect concerns the behavior of morphology‐dependent resonances (MDRs). From an electromagnetic point of view, these MDRs correspond to solutions of characteristic equations associated with boundary conditions and lead to internal fields which are concentrated near the rim of the scatterer. It is also shown that this geometrical optics approximation (expressed in terms of rays) is equivalent to a mechanical problem (expressed in terms of trajectories). This mechanical problem leads to chaotic behavior corresponding to optical chaos phenomena in the optical language. We therefore exhibit a class of particles (i) for which the electromagnetic problem is exactly solvable in the framework of a GLMT and (ii) which exhibits chaotic signatures. It is expected that these chaotic signatures would be revealed in salient features of the scattering diagrams, opening the way to refined optical particle characterization in the presence of inhomogeneities.     

Interferometric Sizing of Single‐Axis Birefringent Glass Fibers

This paper deals with the on‐line sizing of small diameter glass fibers (i.e. d<30 μm) produced for textiles and reinforcement applications. Two models based on the Lorenz‐Mie Theory are introduced to predict the basic light scattering properties and the response of a phase Doppler interferometer (PDI) to the sizing of infinite glass fibers. Among other parameters, these models take into account particular effects such as the fiber's single‐axis birefringence and the fiber's refractive index dependence on its cooling rate (i.e. diameter). Both effects have a weak influence on the mean response of the PDI but a strong influence on the resonance structures of its phase‐diameter relationship. Two optical set‐ups were selected from a numerical optimization procedure and tested experimentally. Experimental results are presented demonstrating the validity of the models and the ability of the developed PDI set‐ups to study some features of the fiber drawing‐process: fluctuations of the fiber diameter when the nozzle is submitted to a convective perturbation and, when the fiber take‐up velocity is modulated, the detection of hollow fibers.     

Improving the accuracy of laser particle sizer with Mie scattering theory

Using the classical Mie scattering theory and Fraunhofer diffraction theory,adetailed analysis of the differences of the light energy distribution falling on the multi-elementconcentric photo-detector of a diffraction based laser particle sizer is given.Numerical calcula-tions and computer simulation are carried out. Experimental studies are also made with latexspheres as Standard Reference Material.Our research shows that when the classical Mie scat-tering theory is used,the accuracy of the particle sizer can be essentially improved not only inthe small size range,but also for large paticles.At the same time the time needed for data re-duction in both cases is almost the same.     

The Lorenz Number and the Lorenz Gauge—Known Concepts,Unknown Physicist

Ludvig Lorenz was Denmark's first theoretical physicist of international recognition. Despite his important contributions to a broad range of experimental and theoretical physics, he generally appears as a somewhat peripheral figure in histories of late‐nineteenth‐century physics and is completely overshadowed by his near‐namesake H. A. Lorentz. Herein, a selected number of Lorenz's works is introduced with an eye on those which are still of relevance to modern physics and today eponymously associated with his name. These contributions are known as the Lorenz number, the Lorenz gauge, the Lorenz–Lorentz law or formula, and the Lorenz–Mie scattering theory.     

New Method for Finding a Series of Exact Solutions to Generalized Breaking Soliton Equation

In this paper, a new generalized extended tanh-function method is presented for constructing soliton-like,period-form solutions of nonlinear evolution equations (NEEs). This method is more powerful than the extended tanhfunction method [Phys. Lett. A 277 (2000) 212] and the modified extended tanh-function method [Phys. Lett. A 285 (2001) 355]. Abundant new families of the exact solutions of Bogoyavlenskii‘s generalized breaking soliton equation are obtained by using this method and symbolic computation system Maple.     

New Method for Finding a Series of Exact Solutions to Generalized Breaking Soliton Equation

In this paper, a new generalized extended tanh-function method is presented for constructing soliton-like,period-form solutions of nonlinear evolution equations (NEEs). This method is more powerful than the extended tanhfunction method [Phys. Left. A 277 (2000) 212] and the modified extended tanh-function method [Phys. Left. A 285 (2001) 355]. Abundant new families of the exact solutions of Bogoyavlenskii‘s generalized breaking soliton equation are obtained by using this method and symbolic computation system Maple.     

Generalized Value Distribution for Herglotz Functions and Spectral Theory

We generalize the theory of value distribution for a class of functions defined as boundary values of Herglotz functions, by considering other measures than Lebesgue measure. The link with compositions of Herglotz functions is presented, and precise relations for the associated measures are obtained. We also consider uniformly convergent sequences of Herglotz functions on compact subsets of the upper half-plane, and prove that the corresponding sequence of Herglotz measures and the generalized value distribution of these functions also converge.     

A New Generalized Riccati Equation Rational Expansion Method to Generalized Burgers-Fisher Equation with Nonlinear Terms of Any Order

In this paper, based on a new more general ansitz, a new algebraic method, named generalized Riccati equation rational expansion method, is devised for constructing travelling wave solutions for nonlinear evolution equations with nonlinear terms of any order. Compared with most existing tanh methods for finding travelling wave solutions, the proposed method not only recovers the results by most known algebraic methods, but also provides new and more general solutions. We choose the generalized Burgers-Fisher equation with nonlinear terms of any order to illustrate our method. As a result, we obtain several new kinds of exact solutions for the equation. This approach can also be applied to other nonlinear evolution equations with nonlinear terms of any order.     

A New Generalized Riccati Equation Rational Expansion Method to Generalized Burgers-Fisher Equation with Nonlinear Terms of Any Order

In this paper, based on a new more general ansatz, a new algebraic method, named generalized Riccati equation rational expansion method, is devised for constructing travelling wave solutions for nonlinear evolution equations with nonlinear terms of any order. Compared with most existing tanh methods for finding travelling wave solutions, the proposed method not only recovers the results by most known algebraic methods, but also provides new and more general solutions. We choose the generalized Burgers-Fisher equation with nonlinear terms of any order to illustrate our method. As a result, we obtain several new kinds of exact solutions for the equation. This approach can also be applied to other nonlinear evolution equations with nonlinear terms of any order.     

Estimating the bound for the generalized Lorenz system

A chaotic system is bounded, and its trajectory is confined to a certain region which is called the chaotic attractor. No matter how unstable the interior of the system is, the trajectory never exceeds the chaotic attractor. In the present paper, the sphere bound of the generalized Lorenz system is given, based on the Lyapunov function and the Lagrange multiplier method. Furthermore, we show the actual parameters and perform numerical simulations.     

Application of the Generalized Differential Quadrature Method in Solving Burgers'Equations

The aim of this paper is to obtain numerical solutions of the one-dimensional, two-dimensional and coupled Burgers' equations through the generalized differential quadrature method (GDQM). The polynomial-based differential quadrature (PDQ) method is employed and the obtained system of ordinary differential equations is solved via the total variation diminishing Runge-Kutta (TVD-RK) method. The numerical solutions are satisfactorily coincident with
the exact solutions. The method can compete against the methods applied in the literature.     

A Generalized Algebraic Method for Constructing a Series of Explicit Exact Solutions of a (1+1)-Dimensional Dispersive Long Wave Equation

Making use of a new and more general ansatz, we present the generalized algebraic method to uniformlyconstruct a series of new and general travelling wave solution for nonlinear partial differential equations. As an applicationof the method, we choose a (1 1)-dimensional dispersive long wave equation to illustrate the method. As a result, wecan successfully obtain the solutions found by the method proposed by Fan [E. Fan, Comput. Phys. Commun. 153 (2003)17] and find other new and more general solutions at the same time, which include polynomial solutions, exponentialsolutions, rational solutions, triangular periodic wave solutions, hyperbolic and soliton solutions, Jacobi and Weierstrassdoubly periodic wave solutions.     

Theory of invariants‐based formulation of Hamiltonians with application to strained zinc‐blende crystals

Group theoretical methods and theory are combined to determine spin‐dependent contributions to the effective conduction band Hamiltonian. To obtain the constants in the effective Hamiltonian, in general all invariants of the Hamiltonian have to be determined. Hence, we present a systematic approach to keep track of all possible invariants and apply it to the Hamiltonian of crystals with zinc‐blende symmetry, in order to find all possible contributions to effective quantities such as effective mass, g‐factor and Dresselhaus constant. Additional spin‐dependent contributions to the effective Hamiltonian arise in the presence of strain. In particular, with regard to the constants C₃ and D which describe spin‐splitting linear in the components of k and ε , considering all possible terms allowed by symmetry is crucial.     

Pseudospin symmetry of the Dirac equation for a MSbius square plus Mie type potential with a Coulomb-like tensor interaction via SUSYQM

We investigate the approximate solution of the Dirac equation for a combination of Mobius square and Mie type potentials under the pseudospin symmetry limit by using supersymmetry quantum mechanics. We obtain the bound-state energy equation and the corresponding spinor wave functions in an approximate analytical manner. We comment on the system via various useful figures and tables.     

Dynamic Collision Frequency in Kelbg‐Pseudopotential‐Modelled Plasmas and the Method of Moments with Local Constraints

The dense plasma dynamic collision frequency is modeled by the first two terms of its asymptotic expansion at high frequencies and its values at a few interpolation points on the real axis. This makes the dynamic collision frequency a non‐rational function whose extension onto the upper half‐plane of the complex frequency is holomorphic with a non‐negative imaginary part and with a continuous extension to the real axis. The validity of the suggested analytic form of the latter is tested against the simulation data, where the Kelbg effective potential was used. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

使用广义粗网有限差分方法加速中子输运特征线方法

提出广义粗网有限差分方法(GCMFD),可以使用三维任意几何形状的粗网格来加速中子输运特征线方法(MOC),同时给出确定广义粗网有限差分方法中宽度因子的方法.将广义粗网有限差分方法应用到三维特征线方法程序TCM中,若干基准题的验证表明,广义粗网有限差分方法可以使用任意形状粗网格来加速特征线方法,使用自动调整宽度因子的方法后,广义粗网格有限差分方法可以得到较好的加速效果.     

Light Scattering by Cylindrical Fibers with High Aspect Ratio Using the Null‐Field Method with Discrete Sources

The problem of computing light scattering by cylindrical fibers with high aspect ratio in the framework of the Null‐Field method with discrete sources is treated. Numerical experiments for investigating the scattering properties of two fiber geometries are performed using distributed spherical vector wave functions as discrete sources.