Crystalline structure in the confined-deconfined mixed phase: Neutron stars

We review the differences in first order phase transition of single and multi-component systems, and then discuss the crystalline structure expected to exist in the mixed confined-deconfined phase of hadronic matter. The particular context of neutron stars is chosen for illustration. The qualitative results are general and apply for example to the vapor-liquid transition in subsaturated asymmetric nuclear matter.     

Three-dimensional boundary conditions for numerical simulations of reactive compressible flows with complex thermochemistry

The Navier–Stokes characteristic boundary conditions (NSCBC) is a very efficient numerical strategy to treat boundary conditions in fully compressible solvers. The present work is an extension of the 3D-NSCBC method proposed by Yoo et al. and Lodato et al. in order to account for multi-component reactive flows with detailed chemistry and complex transport. A new approach is proposed for the outflow boundary conditions which enables clean exit of non-normal flows, and the specific treatment of all kinds of edges and corners is carefully addressed. The proposed methodology is successfully validated on various challenging multi-component reactive flow configurations.     

Soret effect in solid—II

Atomistic features of the Soret effect in multi-component systems, especially those in binary systems, are treated by the path probability method of irreversible statistical mechanics based on a rigid lattice model as an extension of our earlier treatment of the effect in one-component systems. While in one-component systems, particles tend to accumulate toward the low temperature side in the present model, in two-component systems, the constituent components can accumulate on opposite sides as long as the vacancy concentration is low. Explanations of the features in the multi-component Soret effect which do not appear in one-component systems are specifically given. The difference between the Soret effect and the demixing effect under a temperature gradient is also discussed.     

Nonabelian KP hierarchy with Moyal algebraic coefficients

A higher dimensional analogue of the KP hierarchy is presented. Fundamental constituents of the theory are pseudo-differential operators with Moyal algebraic coefficients. The new hierarchy can be interpreted as large-N limit of multi-component (gl (N) symmetric) KP hierarchies. Actually, two different hierarchies are constructed. The first hierarchy consists of commuting flows and may be thought of as a straightforward extension of the ordinary and multi-component KP hierarchies. The second one is a hierarchy of noncommuting flows, and related to Moyal algebraic deformations of selfdual gravity. Both hierarchies turn out to possess quasi-classical limit, replacing Moyal algebraic structures by Poisson algebraic structures. The language of W-infinity algebras provides a unified point of view to these results.     

A construction of Multidimensional Dubrovin-Novikov Brackets

A method for the construction of classes of examples of multi-dimensional, multi-component Dubrovin-Novikov brackets of hydrodynamic type is given. This is based on an extension of the original construction of Gelfand and Dorfman which gave examples of Novikov algebras in terms of structures defined from com- mutative, associative algebras. Given such an algebra, the construction involves only linear algebra.     

Optical parametric oscillator based difference frequency laser source for photoacoustic trace gas spectroscopy in the 3 μm mid-IR range

We report on the extension of the emission wavelength range of a nanosecond pulsed commercial optical parametric oscillator (OPO) towards the infrared. By difference frequency mixing the idler of the OPO with the fundamental of its Nd:YAG pump laser the wavelength range from 2.5–4.5 μm is covered at considerable pulse energies. This laser source is then applied for the first time to photoacoustic trace gas spectroscopy in the fundamental C---H stretch band located around 3.3 μm. Spectra of single- and multi-component gas mixtures of volatile organic compounds are recorded and analyzed with respect to composition and concentration. The detection limits for the individual substances within the gas mixtures are found in the lower parts per million (ppm) range.     

New Matrix Lie Algebra, a Powerful Tool for Constructing Multi-component C-KdV Equation Hierarchy

A set of new multi-component matrix Lie algebra is constructed, which is devoted to obtaining a new loop algebra A-2M. It follows that an isospectral problem is established. By making use of Tu scheme, a Liouville integrable multi-component hierarchy of soliton equations is generated, which possesses the multi-component Hamiltonian structures. As its reduction cases, the multi-component C-KdV hierarchy is given. Finally, the multi-component integrable coupling system of C-KdV hierarchy is presented through enlarging matrix spectral problem.     

The quadratic-form identity for constructing Hamiltonian structures of the Guo hierarchy

The trace identity is extended to the quadratic-form identity. The Hamiltonian structures of the multi-component Guo hierarchy, integrable coupling of Guo hierarchy and (2+1)-dimensional Guo hierarchy are obtained by the quadratic-form identity. The method can be used to produce the Hamiltonian structures of the other integrable couplings or multi-component hierarchies.     

Dual Hierarchies of a Multi-Component Camassa——Holm System

In this paper, we derive the bi-Hamiltonian structure of a multi-component Camassa-Holm system, which associates with the multi-component AKNS hierarchy and multi-component KN hierarchy via the tri-Hamiltonian duality method. Furthermore, the spectral problems of the dual hierarchies may be obtained.     

The extended trace identity and its application

The trace identity is extended to the general loop algebra. The Hamiltonian structures of the integrable systems concerning vector spectral problems and the multi-component integrable hierarchy can be worked out by using the extended trace identity. As its application, we have obtained the Hamiltonian structures of the Yang hierarchy, the Korteweg-de--Vries (KdV) hierarchy, the multi-component Ablowitz--Kaup--Newell--Segur (M-AKNS) hierarchy, the multi-component Ablowitz--Kaup--Newell--Segur Kaup--Newell (M-AKNS--KN) hierarchy and a new multi-component integrable hierarchy separately.     

Theory of nuclear magnetic spin-rotational relaxation for asymmetric molecules

A stochastic differential equation study of nuclear magnetic relaxation by spin-rotational interactions was successfully completed for spherical, symmetric rotator and linear molecules. This theory has now been extended to asymmetric rotator molecules by first establishing the conditions under which such an extension is mathematically feasible and then investigating the consequences of accepting these conditions.     

New Matrix Lie Algebra and Its Application

A set of new matrix Lie algebra and its corresponding loop algebra are constructed. By making use of Tu scheme, a Liouville integrable multi-component hierarchy of soliton equation is generated. As its reduction cases, the multi-component Tu hierarchy is given. Finally, the multi-component integrable coupling system of Tu hierarchy is presented through enlarging matrix spectral problem.     

Multi-component Levi Hierarchy and Its Multi-component Integrable Coupling System

A simple 3M-dimensional loop algebra X is produced, whose commutation operation defined by us is A1 as simple and straightforward as that in the loop algebra A1. It follows that a general scheme for generating multi-component integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then by making use of the Tu scheme the well-known multi-component Levi hierarchy is obtained. Finally, an expanding loop algebra FM of the loop algebra .X is presented, based on the FM, the multi-component integrable coupling system of the multi-component Levi hierarchy is worked out. The method in this paper can be applied to other nonlinear evolution equation hierarchies.     

Multi-component C-KdV Hierarchy of Soliton Equations and Its Multi-component Integrable Coupling System

A new simple loop algebra G M is constructed, which is devoted to establishing an isospectral problem. By making use of Tu scheme, the multi-component C-KdV hierarchy is obtained. Further, an expanding loop algebra FM of the loop algebra G M is presented. Based on FM , the multi-component integrable coupling system of the multi-component C-KdV hierarchy is worked out. The method can be used to other nonlinear evolution equations hierarchy.     

Similarity Reductions of (2+1)-Dimensional Multi-component Broer-Kaup System

Painlevé property of the (2+1)-dimensional multi-component Broer-Kaup (BK) system is considered by using the standard Weiss-Kruskal approaches. Applying the Clarkson and Kruskal (CK) direct method to the (2+1)-dimensional multi-component BK system, some types of similarity reductions are obtained. By solving the reductions, one can get the solutions of the (2+1)-dimensional multi-component BK system.     

Multi-component Dirac equation hierarchy and its multi-component integrable couplings system

A general scheme for generating a multi-component integrable equation hierarchy is proposed. A simple 3M-dimensional loop algebra \tilde{X} is produced. By taking advantage of \tilde{X}, a new isospectral problem is established and then by making use of the Tu scheme the multi-component Dirac equation hierarchy is obtained. Finally, an expanding loop algebra \tilde{F}_M of the loop algebra \tilde{X} is presented. Based on the \tilde{F}_M, the multi-component integrable coupling system of the multi-component Dirac equation hierarchy is investigated. The method in this paper can be applied to other nonlinear evolution equation hierarchies.     

Total Fluorescence Fingerprinting of Pesticides: A Reliable Approach for Continuous Monitoring of Soils and Waters

The present work relates to the creation/extension of a database of Total Excitation-Emission and Total Synchronous Fluorescence Matrices (TEEMs and TSFMs) along with optimal Synchronous Fluorescence Spectra (SFS) to fingerprint pesticides widely used in Morocco. This spectrometric multi-component fingerprinting may permit the direct detection of pesticides persisting in soil or water. The objective of the current investigation is to detect four pesticide remains in agricultural soils by applying the spectrometric fingerprinting results. They are the commercial: i) insecticide Axlera 5G (carbamate), ii) fungicide Orsalis 5% SC (triazole), iii) insecticide Force 0,5 G (pyrethrinoid) and iv) insecticide Proclaim 05 SG (non-assigned). The agricultural plantations monitored are located in the great agricultural Doukkala region at the western Atlantic side of Morocco, where these chemicals are in large sale and use.     

Chaogates: morphing logic gates that exploit dynamical patterns

Chaotic systems can yield a wide variety of patterns. Here we use this feature to generate all possible fundamental logic gate functions. This forms the basis of the design of a dynamical computing device, a chaogate, that can be rapidly morphed to become any desired logic gate. Here we review the basic concepts underlying this and present an extension of the formalism to include asymmetric logic functions.     

Properties of supersymmetric integrable systems of KP type

The recently proposed supersymmetric extensions of reduced Kadomtsev-Petviashvili (KP) integrable hierarchies in N = 1, 2 superspace are shown to contain in the purely bosonic limit new types of ordinary non-supersymmetric integrable systems. The latter are coupled systems of several multi-component non-linear Schr?dinger-like hierarchies whose basic nonlinear evolution equations contain additional quintic and higher-derivative nonlinear terms. Also, we obtain the N = 2 supersymmetric extension of Toda chain model as Darboux-B?cklund orbit of the simplest reduced N = 2 super-KP hierarchy and find its explicit solution. Received 13 September 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: nissimov@inrne.bas.bg RID="b" ID="b"e-mail: svetlana@inrne.bas.bg