Steering and switching of soliton-like beams via interaction in a nanocolloid with positive polarizability.

We unveil different regimes for the interaction between two orthogonally polarized soliton-like beams in a colloidal suspension of nanoparticles with positive polarizability. The interaction is always attractive. However, it noticeably changes as a function of the angle and the power distribution between the input beams. For small angles, both interacting solitons fuse into a single entity, whose propagation direction can be continuously steered. As the interaction angle increases, the resulting self-collimated beam can be practically switched between two positions when the power imbalance between the beams is changed. For interaction angles larger than ∼10°, the result is no longer a single emerging soliton when the input power is balanced between the two beams.

Vortex confinement and bending with nonlocal solitons.

We investigate the routing of vortex beams in nonlocal media by means of coaxial, co-propagating spatial optical solitons. By introducing a refractive index perturbation in the form of a localized defect or a dielectric interface, the soliton waveguide can be curved and, therefore, can deviate the collinear vortex, effectively routing it, while preventing its destabilization and breakup.

Reorientational versus Kerr dark and gray solitary waves using modulation theory.

We develop a modulation theory model based on a Lagrangian formulation to investigate the evolution of dark and gray optical spatial solitary waves for both the defocusing nonlinear Schrödinger (NLS) equation and the nematicon equations describing nonlinear beams, nematicons, in self-defocusing nematic liquid crystals. Since it has an exact soliton solution, the defocusing NLS equation is used as a test bed for the modulation theory applied to the nematicon equations, which have no exact solitary wave solution. We find that the evolution of dark and gray NLS solitons, as well as nematicons, is entirely driven by the emission of diffractive radiation, in contrast to the evolution of bright NLS solitons and bright nematicons. Moreover, the steady nematicon profile is nonmonotonic due to the long-range nonlocality associated with the perturbation of the optic axis. Excellent agreement is obtained with numerical solutions of both the defocusing NLS and nematicon equations. The comparisons for the nematicon solutions raise a number of subtle issues relating to the definition and measurement of the width of a dark or gray nematicon.

Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays.

We show how discrete solitary waves in one and two-dimensional waveguide arrays can be steered across the lattice via the introduction of a longitudinal periodic modulation of the nonlinear response. Through parametric energy transfer from the modulation to the solitary wave, the latter can increase its width and overcome the Peierls-Nabarro potential to propagate freely.

Vector vortex solitons in nematic liquid crystals.

We analyze the existence and stability of two-component vector solitons in nematic liquid crystals for which one of the components carries angular momentum and describes a vortex beam. We demonstrate that the nonlocal, nonlinear response can dramatically enhance the field coupling leading to the stabilization of the vortex beam when the amplitude of the second beam exceeds some threshold value. We develop a variational approach to describe this effect analytically.

Modulation analysis of large-scale discrete vortices.

The behavior of large-scale vortices governed by the discrete nonlinear Schrödinger equation is studied. Using a discrete version of modulation theory, it is shown how vortices are trapped and stabilized by the self-consistent Peierls-Nabarro potential that they generate in the lattice. Large-scale circular and polygonal vortices are studied away from the anticontinuum limit, which is the limit considered in previous studies. In addition numerical studies are performed on large-scale, straight structures, and it is found that they are stabilized by a nonconstant mean level produced by standing waves generated at the ends of the structure. Finally, numerical evidence is produced for long-lived, localized, quasiperiodic structures.

A mathematical analysis for the cardiovascular control adaptations in chronic renal failure.

A model of baroreflex control of blood pressure (BP) is proposed in terms of a delay differential equation and this is used to predict the adaptation of short-term cardiovascular control in chronic renal failure (CRF) patients. Cardiac pump dynamics are explored by means of plots of blood flow vs. mean BP. The parameters of the model were determined from available data and from a sensitivity analysis. The model predicts stable and unstable equilibria close to the steady BP. It is shown that the unstable equilibrium point generates a quasiperiodic solution with two main harmonics for healthy subjects. We also show that the parameters for CRF patients predict solutions whose spectra exhibit a small high frequency component. This is due to the coalescence of the equilibrium points. The heart rate variability (HRV) time series and power spectra from healthy volunteers and CRF patients were compared with the model predictions. As an adequate measure of the sympathovagal balance we use the LF/HF index obtained from the power spectrum. The model allows the interpretation of the variability of the LF/HF index in terms of a specific set of cardiovascular parameters which are known to change from healthy to CRF patients. Comparisons of the changes in the LF/HF index predicted by the model are in agreement with actual observations for both the healthy and the CRF patients. These results show that the cardiac pump has a more restricted response in CRF patients. The model quantifies the cardiovascular adaptations to the CRF condition in terms of increased peripheral resistance and baroreflex delay and decreased arterial compliance, cardiac period, and stroke volume.

Synaptic integration in electrically coupled neurons.

Interactions among chemical and electrical synapses regulate the patterns of electrical activity of vertebrate and invertebrate neurons. In this investigation we studied how electrical coupling influences the integration of excitatory postsynaptic potentials (EPSPs). Pairs of Retzius neurons of the leech are coupled by a nonrectifying electrical synapse by which chemically induced synaptic currents flow from one neuron to the other. Results from electrophysiology and modeling suggest that chemical synaptic inputs are located on the coupled neurites, at 7.5 microm from the electrical synapses. We also showed that the space constant of the coupled neurites was 100 microm, approximately twice their length, allowing the efficient spread of synaptic currents all along both coupled neurites. Based on this cytoarchitecture, our main finding was that the degree of electrical coupling modulates the amplitude of EPSPs in the driving neurite by regulating the leak of synaptic current to the coupled neurite, so that the amplitude of EPSPs in the driving neurite was proportional to the value of the coupling resistance. In contrast, synaptic currents arriving at the coupled neurite through the electrical synapse produced EPSPs of constant amplitude. This was because the coupling resistance value had inverse effects on the amount of current arriving and on the impedance of the neurite. We propose that by modulating the amplitude of EPSPs, electrical synapses could regulate the firing frequency of neurons.