Covariant hysteretic constitutive theory for Maxwell’s equations: application to axially rotating media

This paper explores a class of non-linear constitutive relations for materials with memory in the framework of covariant macroscopic Maxwell theory. Based on earlier models for the response of hysteretic ferromagnetic materials to prescribed slowly varying magnetic background fields, generalized models are explored that are applicable to accelerating hysteretic magneto-electric substances coupled self-consistently to Maxwell fields. Using a parameterized model consistent with experimental data for a particular material that exhibits purely ferroelectric hysteresis when at rest in a slowly varying electric field, a constitutive model is constructed that permits a numerical analysis of its response to a driven harmonic electromagnetic field in a rectangular cavity. This response is then contrasted with its predicted response when set in uniform rotary motion in the cavity.     

A periodic FMM for Maxwell’s equations in 3D and its applications to problems related to photonic crystals

This paper presents an FMM (Fast Multipole Method) for periodic boundary value problems for Maxwell’s equations in 3D. The effect of periodicity is taken into account with the help of the periodised moment to local expansion (M2L) transformation formula, which includes lattice sums. We verify the proposed method by comparing the obtained numerical results with analytic solutions for models of the multi-layered dielectric slab. We then apply the proposed method to scattering problems for periodic two-dimensional arrays of dielectric spheres and compare the obtained energy transmittances with those from the previous studies. We also consider scattering problems for woodpile crystals, where we find a passband related to a localised mode. Through these numerical tests we conclude that the proposed method is efficient and accurate.     

Point classification of second order ODEs and its application to Painlevé equations

The first part of this work is a review of the point classification of second order ODEs done by Ruslan Sharipov. His works were published in 1997-1998 in the Electronic Archive at LANL. The second part is an application of this classification to Painlevé equations. In particular, it allows us to solve the equivalence problem for Painlevé equations in an algorithmic form.     

Analogue of the Cole-Hopf transform for the incompressible Navier–Stokes equations and its application

We consider the Navier–Stokes equations written in the stream function in two dimensions and vector potentials in three dimensions, which are critical dependent variables. On this basis, we introduce an analogue of the Cole-Hopf transform, which exactly reduces the Navier–Stokes equations to the heat equations with a potential term (i.e. the nonlinear Schrödinger equation at imaginary times). The following results are obtained. (i) A regularity criterion immediately obtains as the boundedness of condition for the potential term when the equations are recast in a path-integral form by the Feynman-Kac formula. (ii) This in turn gives an additional characterisation of possible singularities for the Navier–Stokes equations. (iii) Some numerical results for the two-dimensional Navier–Stokes equations are presented to demonstrate how the potential term captures near-singular structures. Finally, we extend this formulation to higher dimensions, where the regularity issues are markedly open.     

Lie algebraic approach to τ-functions and its equations

A general construction of equations satisfied by the components of -functions is given by considering the tensor products of modules. As an example, the homogeneous basic realization of is given, leading to NLS equations.     

An extended functional transformation method and its application in some evolution equations

In this paper, an extended functional transformation is given to solve some nonlinear evolution equations. This function, in fact,is a solution of the famous KdV equation, so this transformation gives a transformation between KdV equation and other soliton equations. Then many new exact solutions can be given by virtue of the solutions of KdV equation.     

Robinson–Trautman solutions to Einstein’s equations

Solutions to Einstein’s equations in the form of a Robinson–Trautman metric are presented. In particular, we derive a pure radiation solution which is non-stationary and involves a mass m, The resulting spacetime is of Petrov Type II A special selection of parametric values throws up the feature of the particle ‘rocket’, a Type D metric. A suitable transformation of the complex coordinates allows the metrics to be expressed in real form. A modification, by setting m to zero, of the Type II metric thereby converting it to Type III, is then shown to admit a null Einstein–Maxwell electromagnetic field.     

Maslov’s canonical operator for degenerate hyperbolic equations

We present a version of Maslov’s canonical operator to be used when constructing asymptotic solutions of hyperbolic equations degenerating in a special way on the boundary of the spatial domain.     

Sonocatalytic–Fenton reaction for enhanced OH radical generation and its application to lignin degradation

The present study demonstrated that the combined use of the sonocatalytic reaction (using ultrasound and titanium dioxide) and the Fenton reaction exhibited synergistically enhanced hydroxyl (OH) radical generation. Dihydroxybenzoic acid (DHBA) concentration as index of OH radical generation was 13 and 115 μM at 10 min in the sonocatalytic reaction and Fenton reaction, respectively. On the other hand, the DHBA concentration was 378 μM at 10 min in the sonocatalytic–Fenton reaction. The sonocatalytic–Fenton reaction was used for degradation of lignin. The lignin degradation ratio was 1.8%, 49.9%, and 60.0% at 180 min in the sonocatalytic reaction, Fenton reaction, and sonocatalytic–Fenton reaction, respectively. Moreover, the sonocatalytic–Fenton reaction was applied to pretreatment of lignocellulosic biomass to enhance subsequent enzymatic saccharification. The cellulose saccharification ratio was 11%, 14%, 16% and 25% at 360 min of pretreatment by control reaction, the sonocatalytic reaction, Fenton reaction, and sonocatalytic–Fenton reaction, respectively.     

A combination of Yang’s equations forSU(2) gauge fields and Charap’s equations for pion dynamics with exact solutions

Two sets of nonlinear partial differential equations originating from two different physical situations have been combined and a new set of nonlinear partial differential equations has been formed wherefrom the previous two sets can be obtained as particular cases. One of the two sets of equations was obtained by Yang [1] while discussing the condition of self-duality ofSU(2) gauge fields on Euclidean four-dimensional space. The second one was reported by Charap [2] for the chiral invariant model of pion dynamics under tangential parametrization. Using the same type of ansatz in each case De and Ray [16] and Ray [7] obtained physical solutions of the two sets of equations. Here exact solutions of the combined set of equations with particular values of the coupling constants have been obtained for a similar ansatz. These solutions too are physical in nature.     

On the application of wavelet transform to the solution of integral equations for acoustic radiation and scattering

1 IlltroductionIt is well Anown that Boundary Element Method (BEM), based on boundary integralequation, leads the reduction of the dimensionallty of the problem by one because the prob1emis formulated in terms of the flelds on botmdary ouly BEM, hOWver, generates algebraicequations with full matrices, whose solutions are moe eapensive than that of the bandedmatrices of FEM[1'2]. On the other hand, in boundary integral forInulations, an integral operatorhas the global behavior, that can b…     

Auditory model inversion and its application

Auditory model has been applied to several aspects of speech signal processing field, and appears to be effective in performance. This paper presents the inverse transform of each stage of one widely used auditory model. First of all it is necessary to invert correlogram and reconstruct phase information by repetitious iterations in order to get auditory-nerve firing rate. The next step is to obtain the negative parts of the signal via the reverse process of the HWR (Half Wave Rectification). Finally the functions of inner hair cell/synapse model and Gammatone filters have to be inverted. Thus the whole auditory model inversion has been achieved. An application of noisy speech enhancement based on auditory model inversion algorithm is proposed. Many experiments show that this method is effective in reducing noise. Especially when SNR of noisy speech is low it is more effective than other methods. Thus this auditory model inversion method given in this paper is applicable to speech enhancement field.     

Characterization of electro-acoustics impedance and its application to active noise control

Characteristics of radiation impedance and its inducing variation of electrical impedance for a controllable source have been investigated. An impedance-based error criterion has been proposed and its application to Active Noise Control is demonstrated through a coil driven loudspeaker. A general formula of radiation impedance is derived for two control strategies, according to the criterion of total acoustic power output. The radiation impedances of some commonly used sound sources are calculated. We discuss in detail the relation between variation of the input electrical impedance and radiation impedance for the two control strategies. The measured data of the input electrical impedance from a loudspeaker agree fairly well with theoretical analysis. An AC- bridge circuit is designed in order to measure the weak variation of electrical impedance resulted from radiation impedance. The bridge relative output is unique for a certain control strategy, from which an impedance-based error criterion is then proposed and the implementation of its application to an active control system is analyzed. Numerical results of such criterion are presented. An analogue control system is set up and experiments are carried out in a semi-anechoic chamber to verify the new control approach.     

Scanning Hartmann test method and its application to lens aberration measurement

A scanning Hartmann test method is proposed and its measurement principle is described. The scanning Hartmann test setup is formed by modifying the Hartmann screen of the conventional Hartmann test setup. With the rotation of the scanning Hartmann screen and the improved hole arrangement, the whole information of the lens to be tested in the full aperture can be obtained. The measurement accuracy of the aberration is improved and the local error of the lens can be got. In the method, no change of the Hartmann screen is needed for measuring the lenses of different aperture sizes. Experimental results of aberration measurements of two lenses are given to verify the usefulness of the setup.     

Analytic MRCI gradient for excited states: formalism and application to the n-π∗ valence- and n-(3s,3p) Rydberg states of formaldehyde

The previously developed formalism for the calculation of the analytic multireference (MR) CI energy gradient with respect to nuclear coordinates based on a single-state MCSCF calculation was extended to the case of state-averaged MCSCF. This extension is of particular importance for calculations of electronically excited states and enables automatic high-level geometry optimizations and saddle point searches on excited-state energy surfaces. Beyond MR-CI, the present analytic gradient method is also available for the MR-ACPF/AQCC methods including size-extensivity corrections for the multireference case. Full geometry optimizations for six electronic states of formaldehyde (valence and Rydberg states) are reported.     

Edge enhancement by using two-wave mixing and its application to pattern recognition

Coupling theory is employed to analyze coupling gain and a new optical system is proposed for image edge enhancement, in which the ordinarily discarded background light is recycled as a pump source to amplify the signal light. We demonstrate the principle of optical correlation and compare the discrimination capability of two kinds of correlators by computer simulation. The results show that edge enhancement preprocessing can improve discrimination capability effectively.     

Numerical approach for the evolution of spin-boson systems and its application to the Buck–Sukumar model

We study the evolution properties of spin-boson systems by a systematic numerical iteration approach, which performs well in the whole coupling regime. This approach evaluates a set of coefficients in the formal expression of the time-dependent Schr?dinger equation by expanding the initial state in Fock space. This set of coefficients is unique for the spin-boson Hamiltonian studied, allowing one to calculate the time evolution from different initial states. To complement our numerical calculations, we apply the method to the Buck–Sukumar model. We find that when the ground-state energy of the model is unbounded and no ground state exists in a certain parameter space, the time evolution of the physical quantities is naturally unstable.     

Hochschild cohomology of the Weyl algebra and Vasiliev’s equations

We propose a simple injective resolution for the Hochschild complex of the Weyl algebra. By making use of this resolution, we derive explicit expressions for nontrivial cocycles of the Weyl algebra with coefficients in twisted bimodules as well as for the smash products of the Weyl algebra and a finite group of linear symplectic transformations. A relationship with the higher-spin field theory is briefly discussed.