The converse problem for the multipotentialisation of evolution equations and systems

We propose a method to identify and classify evolution equations and systems that can be multipotentialised in given target equations or target systems. We refer to this as the {\it converse problem}. Although we mainly study a method for $(1+1)$-dimensional equations/system, we do also propose an extension of the methodology to higher-dimensional evolution equations. An important point is that the proposed converse method allows one to identify certain types of auto-B\"acklund transformations for the equations/systems. In this respect we define the {\it triangular-auto-B\"acklund transformation} and derive its connections to the converse problem. Several explicit examples are given. In particular we investigate a class of linearisable third-order evolution equations, a fifth-order symmetry-integrable evolution equation as well as linearisable systems.Comment: 31 Pages, 7 diagrams, submitted for consideratio

A proof of Jarzynski's non-equilibrium work theorem for dynamical systems that conserve the canonical distribution

We present a derivation of the Jarzynski identity and the Crooks fluctuation theorem for systems governed by deterministic dynamics that conserves the canonical distribution such as Hamiltonian dynamics, Nose-Hoover dynamics, Nose-Hoover chains and Gaussian isokinetic dynamics. The proof is based on a relation between the heat absorbed by the system during the non-equilibrium process and the Jacobian of the phase flow generated by the dynamics.Comment: 12 page

Photon-Photon Interaction in a Photon Gas

Using the effective Lagrangian for the low energy photon-photon interaction the lowest order photon self energy at finite temperature and in non-equilibrium is calculated within the real time formalism. The Debye mass, the dispersion relation, the dielectric tensor, and the velocity of light following from the photon self energy are discussed. As an application we consider the interaction of photons with the cosmic microwave background radiation.Comment: REVTEX, 7 pages, 1 PostSrcipt figur

A nonlocal connection between certain linear and nonlinear ordinary differential equations/oscillators

We explore a nonlocal connection between certain linear and nonlinear ordinary differential equations (ODEs), representing physically important oscillator systems, and identify a class of integrable nonlinear ODEs of any order. We also devise a method to derive explicit general solutions of the nonlinear ODEs. Interestingly, many well known integrable models can be accommodated into our scheme and our procedure thereby provides further understanding of these models.Comment: 12 pages. J. Phys. A: Math. Gen. 39 (2006) in pres

The use of high-resolution terrain data in gravity field prediction

Different types of gravity prediction methods for local and regional gravity evaluation are developed, tested, and compared. Four different test areas were particularly selected in view of different prediction requirements. Also different parts of the spectrum of the gravity field were considered

Florística e fitossociologia em áreas de manejo de açaizais no estuário amazônico.

Este estudo teve como objetivo analisar a composição florística e a fitossociologia em três regiões do estuário amazônico em que é praticado o manejo de açaizais nativos. Nas regiões foram instaladas 30 parcelas de 0,5 ha e amostradas todas as espécies arbóreas e palmeiras com DAP ? 5 cm, mediu-se também a circunferência a altura do peito (CAP) com fita métrica de precisão de 1mm. Foram inventariados 10821 indivíduos, representados por 114 espécies, 96 gêneros e 33 famílias. As famílias mais representativas foram Arecaceae (9 espécies e 8007 indivíduos), seguida por Rubiaceae (2 espécies e 522 indivíduos),Myristicaceae (1 espécie e 268 indivíduos), Malvaceae (10 espécies e 264 indivíduos) e Euphorbiaceae (4 espécies e 247 indivíduos). Constatou-se que a riqueza nas áreas de manejo inventariadas permaneceu alta apesar da pressão antrópica que essas áreas sofrem

Polarizations and differential calculus in affine spaces

Within the framework of mappings between affine spaces, the notion of $n$-th polarization of a function will lead to an intrinsic characterization of polynomial functions. We prove that the characteristic features of derivations, such as linearity, iterability, Leibniz and chain rules, are shared -- at the finite level -- by the polarization operators. We give these results by means of explicit general formulae, which are valid at any order $n$, and are based on combinatorial identities. The infinitesimal limits of the $n$-th polarizations of a function will yield its $n$-th derivatives (without resorting to the usual recursive definition), and the above mentioned properties will be recovered directly in the limit. Polynomial functions will allow us to produce a coordinate free version of Taylor's formula

Piezoelectric-based apparatus for strain tuning

We report the design and construction of piezoelectric-based apparatus for applying continuously tuneable compressive and tensile strains to test samples. It can be used across a wide temperature range, including cryogenic temperatures. The achievable strain is large, so far up to 0.23% at cryogenic temperatures. The apparatus is compact and compatible with a wide variety of experimental probes. In addition, we present a method for mounting high-aspect-ratio samples in order to achieve high strain homogeneity.Comment: 8 pages, 8 figure

Euler configurations and quasi-polynomial systems

In the Newtonian 3-body problem, for any choice of the three masses, there are exactly three Euler configurations (also known as the three Euler points). In Helmholtz' problem of 3 point vortices in the plane, there are at most three collinear relative equilibria. The "at most three" part is common to both statements, but the respective arguments for it are usually so different that one could think of a casual coincidence. By proving a statement on a quasi-polynomial system, we show that the "at most three" holds in a general context which includes both cases. We indicate some hard conjectures about the configurations of relative equilibrium and suggest they could be attacked within the quasi-polynomial framework.Comment: 21 pages, 6 figure