Application of small-angle X-ray scattering to the characterization and quantification of the drug transport nanosystem based on the soybean phosphatidylcholine.

Phospholipid transport nanosystem (PTNS) for drug delivery is based on soybean phosphatidylcholine. The morphology of PTNS is investigated by means of small-angle X-ray scattering. The obtained results allow one to answer the key question from the viewpoint of organization of drug incorporation whether the PTNS nanoparticles have a structure of micelles or vesicles. It is demonstrated that PTNS is a vesicular system with an average vesicle radius of 160 ± 2Å.

Time-periodic solitons in a damped-driven nonlinear Schrödinger equation.

Time-periodic solitons of the parametrically driven damped nonlinear Schrödinger equation are obtained as solutions of the boundary-value problem on a two-dimensional spatiotemporal domain. We follow the transformation of the periodic solitons as the strength of the driver is varied. The resulting bifurcation diagrams provide a natural explanation for the overall form and details of the attractor chart compiled previously via direct numerical simulations. In particular, the diagrams confirm the occurrence of the period-doubling transition to temporal chaos for small values of dissipation and the absence of such transitions for larger dampings. This difference in the soliton's response to the increasing driving strength can be traced to the difference in the radiation frequencies in the two cases. Finally, we relate the soliton's temporal chaos to the homoclinic bifurcation.

Soliton complexity in the damped-driven nonlinear Schrödinger equation: stationary to periodic to quasiperiodic complexes.

Stationary and oscillatory bound states, or complexes, of the damped-driven solitons are numerically path-followed in the parameter space. We compile a chart of the two-soliton attractors, complementing the one-soliton attractor chart.

Interactions of parametrically driven dark solitons. I. Néel-Néel and Bloch-Bloch interactions.

We study interactions between the dark solitons of the parametrically driven nonlinear Schrödinger equation, Eq. 1 . When the driving strength, h , is below sqrt[gamma(2)+1/9], two well-separated Néel walls may repel or attract. They repel if their initial separation 2z(0) is larger than the distance 2zu between the constituents in the unstable stationary complex of two walls. They attract and annihilate if 2z(0) is smaller than 2zu. Two Néel walls with h lying between sqrt[gamma(2)+1/9] and a threshold driving strength hsn attract for 2z(0)<2zu and evolve into a stable stationary bound state for 2z(0)>2zu. Finally, the Néel walls with h greater than hsn attract and annihilate-irrespective of their initial separation. Two Bloch walls of opposite chiralities attract, while Bloch walls of like chiralities repel-except near the critical driving strength, where the difference between the like-handed and oppositely handed walls becomes negligible. In this limit, similarly handed walls at large separations repel while those placed at shorter distances may start moving in the same direction or transmute into an oppositely handed pair and attract. The collision of two Bloch walls or two nondissipative Néel walls typically produces a quiescent or moving breather.

What can we learn about the lipid vesicle structure from the small-angle neutron scattering experiment?

Small-angle neutron scattering (SANS) on the unilamellar vesicle (ULV) populations (diameter 500 and 1,000 A) in D2O was used to characterize lipid vesicles from dimyristoylphosphatidylcholine (DMPC) at three phases: gel Lbeta', ripple Pbeta' and liquid Lalpha. Parameters of vesicle populations and internal structure of the DMPC bilayer were characterized on the basis of the separated form factor (SFF) model. Vesicle shape changes from nearly spherical in the Lalpha phase to elliptical in the Pbeta' and Lbeta' phases. This is true for vesicles prepared via extrusion through pores with the diameter 500 A. Parameters of the internal bilayer structure (thickness of the membrane and the hydrophobic core, hydration and the surface area of the lipid molecule) were determined on the basis of the hydrophobic-hydrophilic (HH) approximation of neutron scattering length density across the bilayer rhox and of the step function (SF) approximation of rhox. DMPC membrane thickness in the Lalpha phase (T = 30 degrees C) demonstrates a dependence on the membrane curvature for extruded vesicles. Prepared via extrusion through 500 A diameter pores, vesicle population in the Lalpha phase has the following characteristics: average value of minor semi-axis 266 +/- 2 A, ellipse eccentricity 1.11 +/- 0.02, polydispersity 26%, thickness of the membrane 48.9 +/- 0.2 A and of the hydrophobic core 19.9 +/- 0.4 A, surface area 60.7 +/- 0.5 A2 and number of water molecules 12.8 +/- 0.3 per DMPC molecule. Vesicles prepared via extrusion through pores with the diameter 1,000 A have polydispersity of 48% and membrane thickness of 45.5 +/- 0.6 A in the Lalpha phase. SF approximation was used to describe the DMPC membrane structure in Lbeta' (T = 10 degrees C) and Pbeta' (T = 20 degrees C) phases. Extruded DMPC vesicles in D2O have membrane thickness of 49.6 +/- 0.5 A in the Lbeta' phase and 48.3 +/- 0.6 A in the Pbeta' phase. The dependence of the DMPC membrane thickness on temperature was restored from the SANS experiment.

Parametrically driven dark solitons.

We show that unlike the bright solitons, the parametrically driven kinks are immune from instabilities for all dampings and forcing amplitudes; they can also form stable bound states. In the undamped case, the two types of stable kinks and their complexes can travel with nonzero velocities.

Two- and three-dimensional oscillons in nonlinear faraday resonance.

We study 2D and 3D localized oscillating patterns in a simple model system exhibiting nonlinear Faraday resonance. The corresponding amplitude equation is shown to have exact soliton solutions which are found to be always unstable in 3D. On the contrary, the 2D solitons are shown to be stable in a certain parameter range; hence the damping and parametric driving are capable of suppressing the nonlinear blowup and dispersive decay of solitons in two dimensions. The negative feedback loop occurs via the enslaving of the soliton's phase, coupled to the driver, to its amplitude and width.

Traveling solitons in the parametrically driven nonlinear Schrödinger equation.

We show that the (undamped) parametrically driven nonlinear Schrödinger equation has wide classes of traveling soliton solutions, some of which are stable. For small driving strengths stable nonpropagating and moving solitons co-exist while strongly forced solitons can only be stable when moving sufficiently fast.