Coherent potential approximation for a disordered diatomic linear chain having diagonal and off-diagonal randomness

A coherent potential approximation (cpa) for a mixed diatomic linear chain including both mass and force constant changes has been developed. In this case an impurity atom substituted at a particular site in one of the sublattices couples with two nearest neighbour atoms in the other sublattices. The diatomic linear chain is therefore considered as a tetratomic linear chain, the size of the unit cell being twice the original. Thecpa density of states and the dielectric susceptibility have been calculated. The numerical values of the later have been calculated in theata (averaget-matrix approximation) limit. Comparison of these results with the experimental and other computer calculations show a qualitative agreement.     

On the number of invariant measures for higher-dimensional chaotic transformations

LetS be a bounded region inR ^N and letP={S _l } _i=1 ^m be a partition ofS into a finite number of closed subsets having piecewiseC ² boundaries of finite (N–1)-dimensional measure. Let :SS be piecewiseC ² onP and expanding in the sense that there exists 0<<1 such that for anyi=1,2,...,m, DT _i ^–1<, whereDT _i ^–1 is the derivative matrix ofT _i ^–1 and · is the Euclidean matrix norm. We prove that for some classes of such mappings, for example, Jabtonski transformations or convexity-preserving transformations, the number of crossing points constitutes a bound for the number of ergodic absolutely continuous -invariant measures. We give examples showing that in general the simple bound of one-dimensional dynamics cannot be generalized to higher dimensions. In fact, we show that it is possible to construct piecewise expandingC ² transformations on a fixed partition with a finite number of elements but which have an arbitrarily large number of ergodic, absolutely continuous invariant measures.     

Novel oxidatively removable protecting groups and linkers for solid-phase synthesis of oligosaccharides

Summary Several new para-substituted benzyl- or phenyl-type protecting groups and their application to linkers for solid-phase synthesis are described.p-Acylaminobenzyl groups have higher acid stability than thep-methoxybenzyl (MPM) group, but are readily cleaved with 2,3-dichloro-5,6-dicyanobenzoquinone (DDQ). Thep-azidobenzyl (Azb) group also has higher acid stability than the MPM group and can be removed much faster than the MPM group by DDQ oxidation after conversion of the azide group into the corresponding iminophosphorane. The acid stability of thep-azido-m-chlorobenzyl group (Cl-Azb) is higher than that of the Azb group. The former can be readily removed by DDQ oxidation after conversion of the azide group into the iminophosphorane. Thep-acylaminophenyl glycoside linker can be readily obtained fromp-nitrophenyl glycoside and can be readily cleaved by ammonium cerium(IV) nitrate (CAN) oxidation. This type of linker should be useful not only for the solid-phase synthesis of oligosaccharides but also for general solid-phase synthesis.     

A posteriori error estimation and basis adaptivity for reduced-basis approximation of nonaffine-parametrized linear elliptic partial differential equations

In this paper, we extend the earlier work [M. Barrault, Y. Maday, N. C. Nguyen, A.T. Patera, An “empirical interpolation” method: application to efficient reduced-basis discretization of partial differential equations, C.R. Acad. Sci. Paris, Série I 339 (2004) 667–672; M.A. Grepl, Y. Maday, N.C. Nguyen, A.T. Patera, Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations, M2AN Math. Model. Numer. Anal. 41 (3) (2007) 575–605.] to provide a posteriori error estimation and basis adaptivity for reduced-basis approximation of linear elliptic partial differential equations with nonaffine parameter dependence. The essential components are (i) rapidly convergent reduced-basis approximations – (Galerkin) projection onto a space spanned by N global hierarchical basis functions which are constructed from solutions of the governing partial differential equation at judiciously selected points in parameter space; (ii) stable and inexpensive interpolation procedures – methods which allow us to replace nonaffine parameter functions with a coefficient-function expansion as a sum of M products of parameter-dependent coefficients and parameter-independent functions; (iii) a posteriori error estimation – relaxations of the error-residual equation that provide inexpensive yet sharp error bounds for the error in the outputs of interest; (iv) optimal basis construction – processes which make use of the error bounds as an inexpensive surrogate for the expensive true error to explore the parameter space in the quest for an optimal sampling set; and (v) offline/online computational procedures – methods which decouple the generation and projection stages of the approximation process. The operation count for the online stage – in which, given a new parameter value, we calculate the output of interest and associated error bounds – depends only on N, M, and the affine parametric complexity of the problem; the method is thus ideally suited for repeated and reliable evaluation of input–output relationships in the many-query or real-time contexts.     

Neutrino masses and mixing in supersymmetric theories

It has been known for sometime that supersymmetric theories with R-parity violation provide a natural framework where small neutrino masses can be generated. We discuss neutrino masses and mixing in these theories in the presence of trilinear lepton number violating couplings. It will be shown that simultaneous solutions to solar and atmospheric neutrino problems can be realized in these models.     

Quantized Berry phase in twisted Bloch momentum space as a topological order parameter for spin chains

We show that a quantized Berry phase in Bloch momentum space can serve as a topological order parameter to the quantum phases of a gapped spin chain system with time-reversal invariance. Specifically, we study this approach analytically in a class of XY spin-1/2 chain with multiple sites interactions in a transverse field. In order to derive a proper definition of the Berry curvature in a two-dimensional parameter space, we performed a local gauge transformation to the spin chain system by a twist operator, which endows the Hamiltonian of the system with the topology of a torus T²$T^2$ without changing its energy spectrum. We show that a topological _Z2$Z_2$ order parameter can be obtained as a quantized Berry phase by a loop integral of the Berry gauge potential along quarter of the Brillouin zone, which determines the zero-temperature phase diagram of the system.     

Homotopy of the classical configuration space for the two-magnon sector of a magnetic Heisenberg ring

A finite Heisenberg magnetic ring with an arbitrary single-node spin and two spin deviations from the ferromagnetic saturation is considered as the system of two Bethe pseudoparticles. The set of all relevant magnetic configurations spans a surface which can be recognised as a Mőbius strip. The dynamics of the system imposes the double twist of all regular orbits of the translation symmetry group.     

Slope parameter and scaling of differential cross-section of Λ-p scattering

The claim of Mohapatra and Maharana thattb(s) is a better scaling variable thant(lns)² is put to test in the case of Λ-p scattering, after parametrizingb(s) asC ₁ +C ₂(lns)α. It was observed that in this case the data also prefer anα value which is close to those obtained by Mohapatra and Maharana for other scattering processes.     

1/L Expansions for a Class of PT-symmetric Potentials

The 1/L perturbative series for a special class of PT-symmetric potentials with centrifugal repulsive core are computed. Reality of obtained spectra is shown.     

Effective-field theory of spin glasses and the coherent-anomaly method. II. Double-Cluster approximation

An improved version of a cluster-effective-field theory for spin glasses, namely the double-cluster approximation, is formulated. The present version is based not on theself-consistency condition, but on thedouble-cluster-consistency condition. The advantages of the approximation combined with the coherentanomaly method are discussed. The critical data of the spin-glass susceptibility are estimated for the two-, three-, and four-dimensional ±J models.     

Quenched Large Deviation Principle for the Overlap of a p-Spins System

In this note, we prove a quenched large deviation result for the overlap of a p-spins interaction system at high temperature. The rate function of the large deviation principle is proved to be deterministic, and some of its basic properties are studied. Our result is based on a pure state result for a multidimensional p-spins system combined with a careful application of the Gärtner–Ellis Theorem     

Spectrofluorimetric method for the simultaneous determination of zinc and cadmium

The simultaneous determination of zinc and cadmium using derivative synchronous and multiwavelength synchronous spectrofluorimetry is described. Effects of experimental variables on the fluorescence intensities and on the spectral resolution of the fluorescent chelates of these metals with 8-(p-toluenesulfonamido)-quinoline (TSQ) in a sodium lauryl sulfate micellar medium have been studied. Mixtures containing 10–200 g L^–1 Zn and 15–250 g L^–1 Cd have been analyzed with good results. The proposed method has been applied to a biological sample.     

The effect of magnetic fields and boundary conditions on the Couette flow of nematics

The paper discusses the theory of Couette flow of a nematic liquid crystal. The apparent viscosity, orientation and velocity profiles are computed forp-azoxyanisole as functions of shear rate and magnetic field for symmetric and asymmetric molecular alignments at the boundaries and for different relative radii of the cylinders. For symmetric homeotropic boundary condition an azimuthal field exhibits a threshold analogous to a Freedericksz transition. An expression is also derived for the Freedericksz threshold in the hydrostatic case.     

The quadrupole plus pairing interaction model in large configuration space for W,Os and Pt nuclei

The equilibrium deformations of tungsten, osmium and platinum nuclei are studied with the self-consistent quadrupole plus pairing interaction model by considering all the nucleons in nucleus explicitly. It is shown that similar results can be obtained by performing calculations with or without the assumption of an inert core. The only difference is in the strength of the quadrupole and pairing interactions to be employed in the respective calculations. The experimental static quadrupole moments and theB (E2) values are correctly reproduced by performing calculations with bare nucleon charge for all the nucleons.     

The effect of magnetic fields and boundary conditions on the shear flow of nematics

The flow of a nematic liquid crystal between plane parallel plates, with one plate moving with uniform velocity relative to the other, is discussed. The apparent viscosity, orientation and velocity profiles are computed forp-azoxyanisole as functions of shear rate and magnetic field for symmetric and asymmetric molecular alignment at the plates. For symmetric homeotropic boundary condition, a magnetic field applied along the flow direction exhibits a threshold reminiscent of a Freedericksz transition in the hydrostatic case. In general the apparent viscosity for the asymmetric boundary condition is less than that for the symmetric case.     

Application of fast Pade approximation in simulating photonic crystal nanocavities by FDTD technology

The exact calculation of mode quality factor Q is a key problem in the design of high-Q photonic crystal nanocavity. On the basis of further investigation on conventional Pade approximation, FDM and DFT, Pade approximation with Baker’s algorithm is enhanced through introducing multiple frequency search and parabola interpolation. Though Pade approximation is a nonlinear signal processing method and only short time sequence is needed, we find the different length of sequence requirements for 2D and 3D FDTD, which is very important to obtain convergent and accurate results. By using the modified Pade approximation method and 3D FDTD, the 2D slab photonic crystal nanocavity is analyzed and high-Q multimode can be solved quickly instead of large range high-resolution scanning. Monitor position has also been investigated. These results are very helpful to the design of photonic crystal nanocavity devices.