On wave action and phase in the non-canonical Hamiltonian formulation

The long time–evolution of disturbances to slowly–varying solutions of partial differential equations is subject to the adiabatic invariance of the wave action. Generally, this approximate conservation law is obtained under the assumption that the partial differential equations are derived from a variational principle or have a canonical Hamiltonian structure. Here, the wave action conservation is examined for equations that possess a non–canonical (Poisson) Hamiltonian structure. The linear evolution of disturbances in the form of slowly varying wavetrains is studied using a WKB expansion. The properties of the original Hamiltonian system strongly constrain the linear equations that are derived, and this is shown to lead to the adiabatic invariance of a wave action. The connection between this (approximate) invariance and the (exact) conservation laws of pseudo–energy and pseudomomentum that exist when the basic solution is exactly time and space independent is discussed. An evolution equation for the slowly varying phase of the wavetrain is also derived and related to Berry's phase.

Extending the use of canonical and microcanonical Monte Carlo algorithms to spin models

We describe the canonical and microcanonical Monte Carlo algorithms for different systems that can be described by spin models. Sites of the lattice, chosen at random, interchange their spin values, provided they are different. The canonical ensemble is generated by performing exchanges according to the Metropolis prescription whereas in the microcanonical ensemble, exchanges are performed as long as the total energy remains constant. A systematic finite size analysis of intensive quantities and a comparison with results obtained from distinct ensembles are performed and the quality of results reveal that the present approach may be an useful tool for the study of phase transitions, specially first-order transitions. (C) 2009 Elsevier B.V. All rights reserved.

Canonical quantum potential scattering theory

A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find nonlinear first-order differential equations for the low-energy scattering parameters such as scattering length and effective range. They significantly simplify typical calculations, as we illustrate for atom-atom and neutron-nucleus scattering systems. A generalization to charged particle scattering is also possible.

Classical strings in AdS(4) x CP(3) with three angular momenta

In this paper, rotating strings in three directions of AdS(4) x CP(3) geometry are studied; its divergent energy limit, and conserved charges are also determined. An interpretation of these configurations as either giant magnons or spiky strings is discussed.

Recognition by the Thyroid Hormone Receptor of Canonical DNA Response Elements

To shed more light on the molecular requirements for recognition of thyroid response elements (TRES) by thyroid receptors (TRs), we compared the specific aspects of DNA TRE recognition by different TR constructs. Using fluorescence anisotropy, we performed a detailed and hierarchical study of TR-TRE binding. This wits done by comparing the binding affinities of three different TR constructs for four different TRE DNA elements, including palindromic sequences and direct repeats (F2, PAL, DR-1, and DR-4) as well as their interactions with nonspecific DNA sequences. The effect of MgCl(2) on suppressing of nonselective DNA binding to TR was also investigated. Furthermore, we determined the dissociation constants of the hTR beta DBD (DNA binding domain) and hTR beta DBD-LBD (DNA binding and ligand binding domains) for specific TRES. We found that a minimum DNA recognition peptide derived from DBD (H1TR) is sufficient for recognition and interaction with TREs, whereas scrambled DNA sequences were unrecognized. Additionally, we determined that the TR DBD binds to F2, PAL, and DR-4 with high affinity and similar K(d) values. The TR DBD-LBD recognizes all the tested TRES but binds preferentially to F2, with even higher affinity. Finally, our results demonstrate the important role played by LBDs in modulating TR-DNA binding.

A canonical form for nonderogatory matrices under unitary similarity

A square matrix is nonderogatory if its Jordan blocks have distinct eigenvalues. We give canonical forms for (1) nonderogatory complex matrices up to unitary similarity, and (2) pairs of complex matrices up to similarity, in which one matrix has distinct eigenvalues. The types of these canonical forms are given by undirected and, respectively, directed graphs with no undirected cycles. (C) 2011 Elsevier Inc. All rights reserved.

Tridiagonal canonical matrices of bilinear or sesquilinear forms and of pairs of symmetric, skew-symmetric, or Hermitian forms

Tridiagonal canonical forms of square matrices under congruence or *congruence, pairs of symmetric or skew-symmetric matrices under congruence, and pairs of Hermitian matrices under *congruence are given over an algebraically closed field of characteristic different from 2. (C) 2008 Elsevier Inc. All rights reserved.

A simple demonstration of the existence of the jordan canonical form for any square matrix

All the demonstrations known to this author of the existence of the Jordan Canonical Form are somewhat complex - usually invoking the use of new spaces, and what not. These demonstrations are usually too difficult for an average Mathematics student to understand how he or she can obtain the Jordan Canonical Form for any square matrix. The method here proposed not only demonstrates the existence of such forms but, additionally, shows how to find them in a step by step manner. I do not claim that the following demonstration is in any way “elegant” (by the standards of elegance in fashion nowadays among mathematicians) but merely simple (undergraduate students taking a fist course in Matrix Algebra would understand how it works).

Attitude propagation using non-singular canonical variables

Three sets of non-singular canonical variables for the rotational motion are analyzed. These sets are useful when the angle between z-axis of a coordinate system fixed in artificial satellite ( here defined by the directions of principal moments of inertia of the satellite) and the rotational angular momentum vector is zero or when the angle between Z-inertial axis and rotational angular momentum vector is zero. The goal of this paper is to compare all these sets and to determine the benefits of their uses. With this objective, the dynamical equations of each set were derived, when mean hamiltonian associate with the gravity gradient torque is included. For the torque-free rotational motion, analytical solutions are computed for symmetrical satellite for each set of variables. When the gravity gradient torque is included, an analytical solution is shown for one of the sets and a numerical solution is obtained for one of the other sets. By this analysis we can conclude that: the dynamical equation for the first set is simple but it has neither clear geometrical nor physical meaning; the other sets have geometrical and physical meaning but their dynamical equations are more complex.

Study of Stability of Rotational Motion of Spacecraft with Canonical Variables

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Is the evolutionary history of the O-type P element in the saltans and willistoni groups of Drosophila similar to that of the canonical P element?

We studied the occurrence of O-type P elements in at least one species of each subgroup of the saltans group, in order to better understand the phylogenetic relationships among the elements within the saltans group and with those of species belonging to the willistoni group. We found that the O-type subfamily has a patchy distribution within the saltans group (it does not occur in D. neocordata and D. emarginata), low sequence divergence among species of the saltans group as well as in relation to species of the willistoni group, a lower rate of synonymous substitution for coding sequences compared to Adh, and phylogenetic incongruities. These findings suggest that the evolutionary history of the O-type subfamily within the saltans and willistoni groups follows the same model proposed for the canonical subfamily of P elements, i.e., events of horizontal transfer between species of the saltans and willistoni groups.

Absorption cross section of canonical acoustic holes

We compute numerically the absorption cross section of a canonical acoustic hole for sound waves with arbitrary frequencies. Our outputs are in full agreement with the expected low- and high-frequency limits.

Discrete and canonical quantum variables

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Measurement of the Polarization of W Bosons with Large Transverse Momenta in W plus jets Events at the LHC

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)