Dyadic Equation Research Articles

Simulation of absorption spectra of molecular aggregates: A hierarchy of stochastic pure state approach.

Simulation of spectroscopic observables for molecular aggregates with strong and structured coupling of electronic excitation to vibrational degrees of freedom is an important but challenging task. The Hierarchy of Pure States (HOPS) provides a formally exact solution based on local, stochastic trajectories. Exploiting the localization of HOPS for the simulation of absorption spectra in large aggregates requires a formulation in terms of normalized trajectories. Here, we provide a normalized dyadic equation where the ket- and bra-states are propagated in different electronic Hilbert spaces. This work opens the door to applying adaptive HOPS methods for the simulation of absorption spectra.

IJARCCE - Computer and Communication Engineering

2 Abstract: The Problem of illegal manipulation and distribution of digital video is becoming a big issue. To solve this problem, a new technology has been proposed. Basically, it is a process of embedding copy right information into bit streams of any video. In this particular scheme, the randomly segmentation and reconstruction of embedded secrete data is done without knowing the original host video. During the embedding process, secret data is embedded in individual video frames using the DWT's frequency domains. In this proposed work, a DWT video watermark technique has been introduced for securing data. We proposed a Haar wavelet based digital watermark technique to secure data. In Haar wavelet, Dyadic equation is used to embed the copy right information in video bit streams.

Global regularity for a logarithmically supercritical hyperdissipative dyadic equation

We prove global existence of smooth solutions for a slightly supercritical dyadic model. We consider a generalized version of the dyadic model introduced by Katz-Pavlovic [2005] and add a viscosity term with critical exponent and a supercritical correction. This model catches for the dyadic a conjecture that for Navier-Stokes equations was formulated by Tao [2009].

Decomposable Medium Conditions in Four-Dimensional Representation

The well-known TE/TM decomposition of time-harmonic electromagnetic fields in uniaxial anisotropic media is generalized in terms of four-dimensional differential-form formalism by requiring that the field two-form satisfies an orthogonality condition with respect to two given bivectors. Conditions for the electromagnetic medium in which such a decomposition is possible are derived and found to define three subclasses of media. It is shown that the previously known classes of generalized Q-media and generalized P-media are particular cases of the proposed decomposable media (DCM) associated to a quadratic equation for the medium dyadic. As a novel solution, another class of special decomposable media (SDCM) is defined by a linear dyadic equation. The paper further discusses the properties of medium dyadics and plane-wave propagation in all the identified cases of DCM and SDCM.

Cylindrical Vector Wave Function Representations of the Dyadic Green's Functions for Cylindrical Multilayered Gyrotropic Bianisotropic Media - Abstract

This paper presents a rigorous and concise formulation of the complete eigenfunction expansions of the dyadic Green's functions for cylindrical multilayered gyrotropic bianisotropic media. The media may consist of any number of layers bounded by optional impedance/ admittance walls. Both electric and magnetic dyadic Green's functions for arbitrary field and source locations are derived simultaneously making use of the principle of scattering superposition. Based on the theory of distributions, the singularities and discontinuities associated with unbounded dyadic Green's functions are deduced directly from Maxwell dyadic equations. Using the discontinuity relations obtained, the eigenfunction expansions outside the source point are constructed in terms of an expedient set of cylindrical vector functions. For the scattered dyadic Green's functions, their scattering coefficient matrices are determined without cumbersome operations while providing good physical insights into the scattering mechanism. These coefficients are expressed in compact and convenient forms involving global reflection and transmission matrices. Corresponding to the impedance/admittance boundary walls, the global reflection matrices are related directly to the wall impedance/admittance dyadics. For illustration, the general expressions of dyadic Green's functions are applied to the configuration of a perfect conducting cylinder coated with gyrotropic bianisotropic medium.

Dyadic Green's functions for circular waveguides filled with biisotropic media

This paper presents an alternative approach to the method of G/sub m/ for constructing the complete eigenfunction expansions of the dyadic Green's functions for circular waveguides with perfectly conducting walls and filled with homogeneous biisotropic media. The eigenfunction expansions are constructed using the discontinuity relations obtained from Maxwell's dyadic equations treated in the distribution sense. The orthogonality relations for waveguide modes are derived based on the modified reciprocity theorem involving a complementary medium. To illustrate the distinctions between different sets of biisotropic constitutive relations, the dyadic Green's functions are determined for Post-Jaggard and Drude-Born-Federov relations.

Polarization and space-frequency coherence in radiometric emission

New results are derived for the relationship between polarization and coherence in radiometric fields. We consider the vector theory of coherence for thermal radiation emission from a planar, opaque, specular surface held at fixed, uniform temperature, in the asymptotic limit in which a radiometric description of the field is applicable. Three dyadic equations are derived here, which relate the three cross-spectral tensors to the components of the Stokes vector characterizing the polarization state of the field in transport theory. The second-order coherence properties of the radiometric field are determined once the Stokes vector has been specified.

On the Eigenfunction Expansions of the Dyadic Green's Functions for Bianisotropic Media

This paper presents a novel approach for constructing the complete eigenfunction expansions of electric and magnetic dyadic Green's functions for general linear bianisotropic media. The eigenfunctions are expressed in terms of linear combinations of commonly employed solenoidal and irrotational vector wave functions. Based on the theory of distributions, the source point singularities required for complete expansions of the dyadic Green's functions are derived directly from Maxwell dyadic equations without any integration. Apart from the singularities, the discontinuities associated with the eigenfunction expansions across the source point are also obtained as by-products. These discontinuity relations constitute the fundamental equations from which the eigenfunction expansions outside the source point can be constructed. This approach is parallel to the utilization of Lorentz reciprocity theorem for relating eigenwaves with sources and it is applicable directly to both nonreciprocal as well as reciprocal media. Furthermore, the discontinuity relations also yield directly the jump conditions for electric and magnetic fields across a current sheet.

Singularities and Discontinuities in the Eigenfunction Expansions of the Dyadic Green's Functions for Biisotropic Media

Based on the theory of distributions, this paper presents a simple derivation of the singularities and discontinuities associated with the eigenfunction expansions of the dyadic Green's functions for biisotropic media. The approach deals directly with Maxwell equations cast into dyadic forms prior to explicit determination of the dyadic Green's function formula. For both electric and magnetic dyadic Green's functions, the source point singularities are obtained without any integration and the discontinuities in their tangential and normal components across the source point are determined in compact forms directly from Maxwell dyadic equations. From the discontinuity relations, boundary conditions involving the tangential and normal components of electric and magnetic fields are derived. Due to the availability of different sets of constitutive relations characterizing a biisotropic medium, the singularities and discontinuities are discussed based on the commonly used Post-Jaggard and Drude-Born-Federov relations.

A three--dimensional dyadic Walburn-Schneck constitutive equation for blood.

A three-dimension dyadic form of the Walburn-Schneck constitutive equation for blood is presented. The dyadic equation is demonstrated to have the symmetries of material frame indifference and flow reversal and to be consistent with the scalar equation in Couette flow. The problem of flow in a tube or circular cross section is solved as an example.

A critical study of DGF at the source region in circular waveguides (I)

This is the second part of our work on the dyadic Green’s functions (DGF) at the source region in circular waveguides. With the application of the main results of the first part, a systematic investigation on the general properties of DGF at the source region is given. The dyadic version of the boundary conditions for Maxwell’s equations is derived and the completeness of the expansion of the transverse current source in circular waveguides in terms of the vector eigenfunctionsM andN is proved. It is shown that the electric and the magnetic DGF satisfy the basic dyadic equations.

Symbolic Vector and Dyadic Analysis

A computer program is described which performs symbolic algebra and calculus with vectors and dyadics. Implemented on the MACSYMA algebraic manipulation system, it is intended to be a reasonably complete analysis system for applications such as plasma physics and fluid dynamics. It includes manipulations of dot and cross products; gradient, divergence, curl and Laplacian operators; directional derivatives and outer products. Vector and dyadic equations can be automatically expanded into components for arbitrary orthogonal coordinate systems. Designed primarily for 2-dimensional and 3-dimensional use, the program also has some capability for higher dimensions. The internal structure of the code is discussed with regard to efficiency considerations. Example calculations and execution times are presented.