New theorems for bianisotropic media

The general volume equivalence theorem for bianisotropic scatterers is presented, where the equivalent electric and magnetic currents are determined by a pair of coupled vector integral equations. Moreover, using the general volume equivalence theorem and conventional image principle, image theory is developed for a bianisotropic body over an infinite perfect electric or magnetic conducting ground plane.     

A Hamilton-Jacobi formalism for thermodynamics

We show that classical thermodynamics has a formulation in terms of Hamilton-Jacobi theory, analogous to mechanics. Even though the thermodynamic variables come in conjugate pairs such as pressure/volume or temperature/entropy, the phase space is odd-dimensional. For a system with n thermodynamic degrees of freedom it is 2n+1-dimensional. The equations of state of a substance pick out an n-dimensional submanifold. A family of substances whose equations of state depend on n parameters define a hypersurface of co-dimension one. This can be described by the vanishing of a function which plays the role of a Hamiltonian. The ordinary differential equations (characteristic equations) defined by this function describe a dynamical system on the hypersurface. Its orbits can be used to reconstruct the equations of state. The ‘time’ variable associated to this dynamics is related to, but is not identical to, entropy. After developing this formalism on well-grounded systems such as the van der Waals gases and the Curie-Weiss magnets, we derive a Hamilton-Jacobi equation for black hole thermodynamics in General Relativity. The cosmological constant appears as a constant of integration in this picture.     

A Newman-Penrose formalism for gravitational instantons

A Euclidean version of the Newman-Penrose formalism is developed for the study of gravitational instantons. The formalism is explicitly based on theSU(2)×SU(2) spin structure of positive definite metrics. A Geroch-Held-Penrose formulation is also presented. The Euclidean analogues of several fundamental results in relativity are proved, including the Petrov classification and the Ehlers-Sachs, Goldberg-Sachs, and Mariot-Robinson theorems. In addition, the connection between Petrov type and the admissibility of complex structures is elucidated.     

A phase formalism for excitonic transitions

We develop a matrix formalism for the phase involved in quantum transitions experienced by excitons on the basis of the quantum mechanics of the hydrogen atom. Both photon emission and absorption within the context of the above transitions are modelled.     

A hamiltonian formalism for bosonic membranes

An action for bosonic membranes, which has no cosmological constant, is studied. The Hamiltonian formalism is developed, with a view to quantisation, using Dirac's method for constrained systems. The commutators of the independent canonical variables are evaluated in a co-ordinate gauge, at least to lowest order in ?.     

A Newman-Penrose-type formalism for space-times with torsion

The familiar Newman-Penrose formalism, in which the curvature of space-time is represented in terms of spin coefficients, is here extended to include the possibility of an asymmetric connection. It is hoped that this approach will be useful in dealing with certain problems in Einstein-Cartan theory, and also in other theories of gravitation that include torsion.     

A Lagrangean formalism for Hermitean matrix models

Eynard's formulation of Hermitean 1-matrix models in terms of intrinsic quantities of an associated hyperelliptic Riemann surface is rephrased as a Lagrangean field theory of a scalar particle propagating on the hyperelliptic surface with multiple self-interactions and particle–source interactions. Both types of interaction take place at the branch points of the hyperelliptic surface.     

A simple formalism for the BPS monopole

A simple formalism for the BPS monopole is obtained by generalizing the ADHM construction of multi-instantons to a Hilbert space. Both the potential itself and the Green's functions for different isospin can be obtained with very little effort from the instanton formulae.     

A consistent RPA formalism

This paper examines the quasi-boson and generator-coordinate derivations of the RPA and concludes that they make uncritical and inconsistent use of the assumption that ground state correlations be small. It is proposed that consistent derivations of the RPA to various orders can be carried out by explicit retention of a certain power of a parameter γ which is proportional to the norm of the ground state correlations. To illustrate such a method, it is proved that a consistent, non-trivial, linear RPA theory exists only if the residual potential is small enough for first order perturbation theory to be valid.     

A new nonlinear-wave-equation formalism for stimulated Brillioun scattering

A revised formalism of SBS is given based on a new optical nonlinear wave equation which explicitly accounts for the macroscopic spatial inhomogeneity resulting from the induced acoustic wave in the medium. The new equation applies to other scattering phenomena, and more generally to optical wave propagation and interaction in nanostructured media for which characteristic spatial scale lengths of material structures (existing or optically induced) are smaller than the optical wavelength.     

A space-time functional formalism for classical field equations

The equations derived by R.L. Levis and R.H. Kraichnan for a space-time functional for turbulence are further investigated in the general case of classical field equations. The compact form of the equations obtained allows for their different transformations and enables to discuss the effect of initial conditions on the final results.     

Three-dimensional step discontinuities in planar waveguides: Angular-spectrum representation of guided wavefields and generalized matrix-operator formalism

For obliquely incident guided modes the light propagation in slab waveguides with step discontinuities can be described by means of an angular-spectrum representation of the electromagnetic fields together with a generalized matrix-operator formalism. By means of a discretization of the radiation and evanescent modes, the computation of the reflection and transmission coefficients can be reduced to the numerical solution of algebraic equations. The TE-TM coupling, which takes place for oblique incidence, and the different evanescent field effects are discussed in detail.     

Spectral dyadic Green's function formulation for uniaxial bianisotropic superstrate-substrate structure

In this paper, spectral-domain dyadic Green's functions for the time harmonic electric current source embedded in a two-layer grounded uniaxial bianisotropic media are obtained using Fourier tranform. It is shown that in the uniaxial bianisotropic medium, total spectral electromagnetic field can also be separated into the superposition of transverse electric (TE) and transverse magnetic (TM) wave. Because of the generality of constitutive relations our results include the special cases of achiral, uniaxial, reciprocal and nonreciprocal biisotropic media.     

A global formalism for nonlinear waves in conservation laws

We introduce a unifying framework for treating all of the fundamental waves occurring in general systems ofn conservation laws. Fundamental waves are represented as pairs of states statisfying the Rankine-Hugoniot conditions; after trivial solutions have been eliminated by means of a blow-up procedure, these pairs form an (n+1)-dimensional manifold, the fundamental wave manifold. There is a distinguishedn-dimensional submanifold of containing a single one-dimensonal foliation that represents the rarefaction curves for all families. Similarly, there is a foliation of itself that represent shock curves. We identify othern-dimensional submanifolds of that are naturally interpreted as boundaries of regions of admissible shock waves. These submanifolds also have one-dimensional foliations, which represent curves of composite waves. This geometric framework promises to simplify greatly the study of the stability and bifurcation propertiesThis work was supported in part by: the NSF/CNP_q U.S.-Latin America Cooperative Science Program under Grant INT-8612605; the Institute for Mathematics and its Applications with funds provided by the National Science Foundation; the Air Force Office of Scientific Research under Grant AFOSR 90-0075; the National Science Foundation under Grant 8901884; the U.S. Department of Energy under Grant DE-FG02-90ER25084; the U.S. Army Research Office under Grant DAAL03-89-K-0017; the Financiadora de Estudos e Projetos; the Conselho Nacional de Desenvolvimento Científico e Tecnológica (CNP_q); the Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ); the Coordenação de Aperfeiçamento de Pessoal de Ensino Superior (CAPES); and the Sociedade Brasileira de Matemática (SBM)     

A remark on the Hamiltonian formalism for incompressible flows

We revisit the Hamiltonian formalism for incompressible flows as introduced by Oseledets. Our aim is to clarify some ambiguities in this formalism due to the nonintegrable singularity of the kernel which defines the Hamiltonian.