Multiseries Lie groups and asymptotic modules for characterizing and solving integrable models

A multiseries integrable model (MSIM) is defined as a family of compatible flows on an infinite-dimensional Lie group of N-tuples of formal series around N given poles on the Riemann sphere. Broad classes of solutions to a MSIM are characterized through modules over rings of rational functions, called asymptotic modules. Possible ways for constructing asymptotic modules are Riemann-Hilbert and ∂̄ problems. When MSIM's are written in terms of the group coordinates, some of them can be contracted into standard integrable models involving a small number of scalar functions only. Simple contractible MSIM's corresponding to one pole, yield the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy. Two-pole contractible MSIM's are exhibited, which lead to a hierarchy of solvable systems of nonlinear differential equations consisting of (2 + 1) -dimensional evolution equations and of quite strong differential constraints. © 1989 American Institute of Physics.

Computations of the flow past a still sphere at moderate reynolds numbers using an immersed boundary method

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Spin 1 fields in Riemann-Cartan space-times via Duffin-Kemmer-Petiau theory

We consider massive spin 1 fields, in Riemann-Cartan space-times, described by Duffin-Kemmer-Petiau theory. We show that this approach induces a coupling between the spin 1 field and the space-time torsion which breaks the usual equivalence with the Proca theory, but that such equivalence is preserved in the context of the Teleparallel Equivalent of General Relativity.

Massless DKP fields in Riemann-Cartan spacetimes

We study massless Duffin-Kemmer-Petiau (DKP) fields in the context of Einstein-Cartan gravitation theory, interacting via minimal coupling procedure. In the case of an identically vanishing torsion (Riemannian spacetimes) we show that there exist local gauge symmetries which reproduce the usual gauge symmetries for the massless scalar and electromagnetic fields. on the other hand, similarly to what happens with the Maxwell theory, a nonvanishing torsion, in general, breaks the usual U(1) local gauge symmetry of the electromagnetic field or, from a different point of view, imposes conditions on the torsion.

Hopf solitons and area-preserving diffeomorphisms of the sphere

We consider a (3+1)-dimensional local field theory defined on the sphere S-2. The model possesses exact soliton solutions with nontrivial Hopf topological charges and an infinite number of local conserved currents. We show that the Poisson bracket algebra of the corresponding charges is isomorphic to that of the area-preserving diffeomorphisms of the sphere S-2. We also show that the conserved currents under consideration are the Noether currents associated to the invariance of the Lagrangian under that infinite group of diffeomorphisms. We indicate possible generalizations of the model.

General soliton matrices in the Riemann-Hilbert problem for integrable nonlinear equations

We derive the soliton matrices corresponding to an arbitrary number of higher-order normal zeros for the matrix Riemann-Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order solitons. Our soliton matrices explicitly give all higher-order multisoliton solutions to the nonlinear partial differential equations integrable through the matrix Riemann-Hilbert problem. We have applied these general results to the three-wave interaction system, and derived new classes of higher-order soliton and two-soliton solutions, in complement to those from our previous publication [Stud. Appl. Math. 110, 297 (2003)], where only the elementary higher-order zeros were considered. The higher-order solitons corresponding to nonelementary zeros generically describe the simultaneous breakup of a pumping wave (u(3)) into the other two components (u(1) and u(2)) and merger of u(1) and u(2) waves into the pumping u(3) wave. The two-soliton solutions corresponding to two simple zeros generically describe the breakup of the pumping u(3) wave into the u(1) and u(2) components, and the reverse process. In the nongeneric cases, these two-soliton solutions could describe the elastic interaction of the u(1) and u(2) waves, thus reproducing previous results obtained by Zakharov and Manakov [Zh. Eksp. Teor. Fiz. 69, 1654 (1975)] and Kaup [Stud. Appl. Math. 55, 9 (1976)]. (C) 2003 American Institute of Physics.

Reply to 'comment on 'Braneworld remarks in Riemann-Cartan manifolds''

In this brief reply, we elucidate some missing points in the comment (Khakshournia S 2009 Class. Quantum Grav. 26 178001) on our original paper (Hoff da Silva J M and da Rocha R 2009 Class. Quantum Grav. 26 055007), explicitly showing that the comment is unfounded in this context. We show that the term proposed equals zero, since the brane discontinuity is correctly defined in the torsion.

Braneworld remarks in Riemann-Cartan manifolds

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A RIEMANN INTEGRAL APPROACH TO FEYNMANS PATH-INTEGRAL

It is a well known result that the Feynman's path integral (FPI) approach to quantum mechanics is equivalent to Schrodinger's equation when we use as integration measure the Wiener-Lebesgue measure. This results in little practical applicability due to the great algebraic complexibity involved, and the fact is that almost all applications of (FPI) - ''practical calculations'' - are done using a Riemann measure. In this paper we present an expansion to all orders in time of FPI in a quest for a representation of the latter solely in terms of differentiable trajetories and Riemann measure. We show that this expansion agrees with a similar expansion obtained from Schrodinger's equation only up to first order in a Riemann integral context, although by chance both expansions referred to above agree for the free. particle and harmonic oscillator cases. Our results permit, from the mathematical point of view, to estimate the many errors done in ''practical'' calculations of the FPI appearing in the literature and, from the physical point of view, our results supports the stochastic approach to the problem.

Salt-induced sphere-to-disk transition of octadecyltrimethylammonium bromide micelles

We have used surface tension measurements, differential scanning calorimetry (DSC), dynamic light scattering (DLS), and cryo-transmission electron microscopy (cryo-TEM) to investigate the dynamic and structural behavior of octadecyltrimethylammonium bromide (C(18)TAB) micelles in water and NaBr solution. The surface tension data for fixed C(18)TAB concentrations of 25 mM and varied NaBr additions (0-50 mM) shows that the critical micelle concentration (cmc) increases after an initial decrease at 0.5 mM NaBr. This unusual effect has been explained using results from DSC and DLS. At low salt concentrations (below ca. 25 mM) the relaxation time distribution is bimodal with a dominant fast mode due to spherical micelles. Above ca. 35 mM NaBr disklike structures are favored and the relaxation time distribution is more closely unimodal. The postulated sphere-to-disk transition is supported by cryo-TEM micrographs. A pronounced increase in the micellar effective hydrodynamic radius (R-H) is observed as the NaBr concentration is increased above about 35 mM; below 35 mM the R-H of the spherical micelles changes Little with ionic strength.

Morphology and topography analysis of mesoporous titania templated by micrometric latex sphere arrays

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Sphere of influence and gravitational capture radius: a dynamical approach

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Composition of the first coordination sphere of Ni2+ in concentrated aqueous NiBr2 solutions by x-ray diffraction

Two concentrated solutions of NiBr2 have been examined by x-ray diffraction. The Fourier transformed scattering data indicate inner complex formation between Ni2 + and Br- ions. Average numbers of bonded bromide ions per nickel atom have been determined for each solution and the reliability of the complexation numbers as well as of the other structural parameters has been critically examined. © 1985 American Institute of Physics.

Bifundamental fuzzy 2-Sphere and fuzzy killing spinors

We review our construction of a bifundamental version of the fuzzy 2-sphere and its relation to fuzzy Killing spinors, first obtained in the context of the ABJM membrane model. This is shown to be completely equivalent to the usual (adjoint) fuzzy sphere. We discuss the mathematical details of the bifundamental fuzzy sphere and its field theory expansion in a model-independent way. We also examine how this new formulation affects the twisting of the fields, when comparing the field theory on the fuzzy sphere background with the compactification of the 'deconstructed' (higher dimensional) field theory.

Sedenions of Cayley-Dickson and the Cauchy-Riemann like relations

This work is an extension to sedenions of the Cauchy-Riemann relations, following a similar earlier construction made by one of the authors (M. Borges) to quaternions and octonions, see [1], [2], [3]. © 2011 Academic Publications.