Biomedical subjects

R F Rodríguez

Publications and source records attributed to R F Rodríguez.

5 recordsLinked to original sources

PubMed2006

Moving embedded lattice solitons.

It was recently proved that solitons embedded in the spectrum of linear waves may exist in discrete systems, and explicit solutions for isolated unstable embedded lattice solitons (ELS) of a differential-difference version of a higher-order nonlinear Schrodinger equation were found [Gonzalez-Perez-Sandi, Fujioka, and Malomed, Physica D 197, 86 (2004)]. The discovery of these ELS gives rise to relevant questions such as the following: (1) Are there continuous families of ELS? (2) Can ELS be stable? (3) Is it possible for ELS to move along the lattice? (4) How do ELS interact? The present work addresses these questions by showing that a novel equation (a discrete version of a complex modified Korteweg-de Vries equation that includes next-nearest-neighbor couplings) has a two-parameter continuous family of exact ELS. These solitons can move with arbitrary velocities across the lattice, and the numerical simulations demonstrate that these ELS are completely stable. Moreover, the numerical tests show that these ELS are robust enough to withstand collisions, and the result of a collision is only a shift in the positions of the solitons. The model may apply to the description of a Bose-Einstein condensate with dipole-dipole interactions between the atoms, trapped in a deep optical-lattice potential.

Journal Article↗

PubMed2004

Anisotropy and nonequilibrium effects on the light scattered from suspension in a nematic solvent.

We investigate the effects produced on the light scattering spectrum by the anisotropic diffusion of impurities in an incompressible nematic solvent. The spectrum is calculated by using a fluctuating hydrodynamic description when the system is both in a fully thermodynamic equilibrium state and in a nonequilibrium steady state induced by a dye-concentration gradient. In the former state, the isotropic pretransitional phase as well as the nematic phase of the solvent are considered. This spectrum is symmetric (Lorentzian) with respect to the frequency shifts, but anisotropic through its explicit dependence on the ratio of the diffusion coefficients of the dye parallel and normal to the mean molecular axis of the nematic. The values of these coefficients were taken from experimental measurements of diffusion of methylred and nitrosodimethylaniline in a N -( p -methoxybenzylidene)- p -butylaniline (MBBA) solvent. This anisotropy changes the height and the width at mid height with respect to the isotropic case in amounts which for MBBA vary up to 36% and 26%. We also calculate the spectrum in the presence of a concentration gradient of the dye and find that its presence gives rise to an asymmetry of the spectrum in its dependence on the frequency shift; its maximum increases and is displaced with respect to its equilibrium position. The size and direction of this shift are proportional to the magnitude of the dye-concentration gradient and depend on its relative orientation with respect to the scattering vector. For small dimensionless concentration gradients ( approximately 10(-2) ), this effect is maximum when these vectors are parallel and the scattering angle is low ( approximately 1 degrees ). The maximum degree of departure from equilibrium is significant and turns out to be approximately 55%. In view of the significant changes in the spectrum, our theoretical analysis suggests that these effects might be observable.

Journal Article↗

PubMed2003

Absorption effects in liquid crystal waveguides.

An analytical and numerical study of the propagation of optical fields through a nematic hybrid slab is developed. We take into account explicitly the absorption of radiation by the liquid crystal by introducing a complex dielectric tensor. For a low intensity beam we first derive the eikonal equation and from it we calculate the ray trajectories in the optical limit. We show that in the presence of absorption, there are no caustics within the slab. Then we consider the WKB limit and calculate the field transverse magnetic modes, their number and their cutoff frequencies. We show that for both limits the agreement between our analytical and numerical results for the propagation constants is excellent, while there are larger differences in the analytically and numerically calculated field amplitudes. These differences show that absorption effects are important for this quantity and have their origin in the fact that the chosen parameter values in our exact numerical calculations, strictly speaking, do not lie within the limits of validity of the WKB approximation. Although a more precise comparison between these approaches requires the use of different sets of values of the relevant parameters, our analysis shows the effects and complications arising from the inclusion of absorption. Finally, we discuss the scope and limitations of our approach.

Journal Article↗

PubMed2003

Standard and embedded solitons in nematic optical fibers.

A model for a non-Kerr cylindrical nematic fiber is presented. We use the multiple scales method to show the possibility of constructing different kinds of wave packets of transverse magnetic modes propagating through the fiber. This procedure allows us to generate different hierarchies of nonlinear partial differential equations which describe the propagation of optical pulses along the fiber. We go beyond the usual weakly nonlinear limit of a Kerr medium and derive a complex modified Korteweg-de Vries equation (CM KdV) which governs the dynamics for the amplitude of the wave packet. In this derivation the dispersion, self-focussing, and diffraction in the nematic fiber are taken into account. It is shown that this CM KdV equation has two-parameter families of bright and dark complex solitons. We show analytically that under certain conditions, the bright solitons are actually double-embedded solitons. We explain why these solitons do not radiate at all, even though their wave numbers are contained in the linear spectrum of the system. We study (numerically and analytically) the stability of these solitons. Our results show that these embedded solitons are stable solutions, which is an interesting property since in most systems the embedded solitons are weakly unstable solutions. Finally, we close the paper by making comments on the advantages as well as the limitations of our approach, and on further generalizations of the model and method presented.

Journal Article↗

PubMed2002

Flow dissipation effects in a nonlinear nematic fiber.

Dissipative effects due to the presence of hydrodynamic flow in a cylindrical fiber whose cladding is an initially quiescent incompressible nematic liquid crystal are analyzed. An analytic and iterative solution of the nematodynamic equations coupled to the Maxwell's equations describing the propagation of a narrow wave packet of transverse magnetic modes is provided. We derive a generalized nonlinear Schröedinger equation for the amplitude of this propagating wave packet that takes into account the dissipation in the nematic's reorientation and the hydrodynamical effects. For the solitonlike solution of this equation we find that the penetration length and the real part of the nonlinear refraction index increase by a factor of 1.75, with respect to those values obtained in the absence of hydrodynamical flow. The imaginary part remains unaltered.

Journal Article↗