Any-order propagation of the nonlinear Schroedinger equation

We derive an exact propagation scheme for nonlinear Schroedinger equations. This scheme is entirely analogous to the propagation of linear Schroedinger equations. We accomplish this by defining a special operator whose algebraic properties ensure the correct propagation. As applications, we provide a simple proof of a recent conjecture regarding higher-order integrators for the Gross-Pitaevskii equation, extend it to multi-component equations, and to a new class of integrators.Comment: 10 pages, no figures, submitted to Phys. Rev.

Visualizing the logistic map with a microcontroller

The logistic map is one of the simplest nonlinear dynamical systems that clearly exhibit the route to chaos. In this paper, we explored the evolution of the logistic map using an open-source microcontroller connected to an array of light emitting diodes (LEDs). We divided the one-dimensional interval $[0,1]$ into ten equal parts, and associated and LED to each segment. Every time an iteration took place a corresponding LED turned on indicating the value returned by the logistic map. By changing some initial conditions of the system, we observed the transition from order to chaos exhibited by the map.Comment: LaTeX, 6 pages, 3 figures, 1 listin

Scalar-Tensor Cosmological Models

We analyze the qualitative behaviors of scalar-tensor cosmologies with an arbitrary monotonic $\omega(\Phi)$ function. In particular, we are interested on scalar-tensor theories distinguishable at early epochs from General Relativity (GR) but leading to predictions compatible with solar-system experiments. After extending the method developed by Lorentz-Petzold and Barrow, we establish the conditions required for convergence towards GR at $t\rightarrow\infty$. Then, we obtain all the asymptotic analytical solutions at early times which are possible in the framework of these theories. The subsequent qualitative evolution, from these asymptotic solutions until their later convergence towards GR, has been then analyzed by means of numerical computations. From this analysis, we have been able to establish a classification of the different qualitative behaviors of scalar-tensor cosmological models with an arbitrary monotonic $\omega(\Phi)$ function.Comment: uuencoded compressed postscript file containing 41 pages, with 9 figures, accepted for publication in Physical Review

Hyperextended Scalar-Tensor Gravity

We study a general Scalar-Tensor Theory with an arbitrary coupling funtion $\omega (\phi )$ but also an arbitrary dependence of the ``gravitational constant'' $G(\phi )$ in the cases in which either one of them, or both, do not admit an analytical inverse, as in the hyperextended inflationary scenario. We present the full set of field equations and study their cosmological behavior. We show that different scalar-tensor theories can be grouped in classes with the same solution for the scalar field.Comment: latex file, To appear in Physical Review

A note on the integrable discretization of the nonlinear Schr\"odinger equation

We revisit integrable discretizations for the nonlinear Schr\"odinger equation due to Ablowitz and Ladik. We demonstrate how their main drawback, the non-locality, can be overcome. Namely, we factorize the non-local difference scheme into the product of local ones. This must improve the performance of the scheme in the numerical computations dramatically. Using the equivalence of the Ablowitz--Ladik and the relativistic Toda hierarchies, we find the interpolating Hamiltonians for the local schemes and show how to solve them in terms of matrix factorizations.Comment: 24 pages, LaTeX, revised and extended versio

Conservation laws of semidiscrete canonical Hamiltonian equations

There are many evolution partial differential equations which can be cast into Hamiltonian form. Conservation laws of these equations are related to one-parameter Hamiltonian symmetries admitted by the PDEs. The same result holds for semidiscrete Hamiltonian equations. In this paper we consider semidiscrete canonical Hamiltonian equations. Using symmetries, we find conservation laws for the semidiscretized nonlinear wave equation and Schrodinger equation.Comment: 19 pages, 2 table

Micromagnetic simulations of interacting dipoles on a fcc lattice: Application to nanoparticle assemblies

Micromagnetic simulations are used to examine the effects of cubic and axial anisotropy, magnetostatic interactions and temperature on M-H loops for a collection of magnetic dipoles on fcc and sc lattices. We employ a simple model of interacting dipoles that represent single-domain particles in an attempt to explain recent experimental data on ordered arrays of magnetoferritin nanoparticles that demonstrate the crucial role of interactions between particles in a fcc lattice. Significant agreement between the simulation and experimental results is achieved, and the impact of intra-particle degrees of freedom and surface effects on thermal fluctuations are investigated.Comment: 10 pages, 9 figure

Nucleosynthesis Constraints on Scalar-Tensor Theories of Gravity

We study the cosmological evolution of massless single-field scalar-tensor theories of gravitation from the time before the onset of $e^+e^-$ annihilation and nucleosynthesis up to the present. The cosmological evolution together with the observational bounds on the abundances of the lightest elements (those mostly produced in the early universe) place constraints on the coefficients of the Taylor series expansion of $a(\phi)$, which specifies the coupling of the scalar field to matter and is the only free function in the theory. In the case when $a(\phi)$ has a minimum (i.e., when the theory evolves towards general relativity) these constraints translate into a stronger limit on the Post-Newtonian parameters $\gamma$ and $\beta$ than any other observational test. Moreover, our bounds imply that, even at the epoch of annihilation and nucleosynthesis, the evolution of the universe must be very close to that predicted by general relativity if we do not want to over- or underproduce $^{4}$He. Thus the amount of scalar field contribution to gravity is very small even at such an early epoch.Comment: 15 pages, 2 figures, ReVTeX 3.1, submitted to Phys. Rev. D1

On integrability of Hirota-Kimura type discretizations

We give an overview of the integrability of the Hirota-Kimura discretization method applied to algebraically completely integrable (a.c.i.) systems with quadratic vector fields. Along with the description of the basic mechanism of integrability (Hirota-Kimura bases), we provide the reader with a fairly complete list of the currently available results for concrete a.c.i. systems.Comment: 47 pages, some minor change

Boson Stars in General Scalar-Tensor Gravitation: Equilibrium Configurations

We study equilibrium configurations of boson stars in the framework of general scalar-tensor theories of gravitation. We analyse several possible couplings, with acceptable weak field limit and, when known, nucleosynthesis bounds, in order to work in the cosmologically more realistic cases of this kind of theories. We found that for general scalar-tensor gravitation, the range of masses boson stars might have is comparable with the general relativistic case. We also analyse the possible formation of boson stars along different eras of cosmic evolution, allowing for the effective gravitational constant far out form the star to deviate from its current value. In these cases, we found that the boson stars masses are sensitive to this kind of variations, within a typical few percent. We also study cases in which the coupling is implicitly defined, through the dependence on the radial coordinate, allowing it to have significant variations in the radius of the structure.Comment: 19 pages in latex, 3 figures -postscript- may be sent via e-mail upon reques