Exciton Dynamics in a Helical Molecular Aggregate

The formation of excitons in a helical molecular nanochain is considered. The model equations are derived with allowance for a spatial dispersion of the polarization of optical transitions treated in the approximation of nearest-neighbor interaction and constant dipole moment of molecules. Models of the medium are formulated, which determine the formation of polarization domains. Some examples are considered, which show that a helical medium admits the formation of stable localized structures (solitons) due to the curvature of the molecular chain. These features of the nanosystem can produce a critical influence on the luminescent properties of the chiral medium.     

Соllective Fluorescence of Composite Nanoparticles

Fluorescence of a suspension of spherical nanoparticles consisting of a gold core surrounded by silicon dioxide doped with fluorescein molecules is experimentally studied. The model of a composite nanoparticle is investigated theoretically and experimentally, taking into account polarization fluctuations. It is shown that a local nonlinear feedback in the system leads to characteristic temperature dependences of the fluorescence linewidth and intensity. As the medium was cooled from room temperature to liquid nitrogen temperature, the fluorescence spectrum narrowed and its intensity strongly increased. A comparison of experimental data with numerical calculations showed that the changes observed in experiments are not explained by the temperature dependence of the parameters of elements of a nanoparticle. The analysis of the dynamics of polarization phases of dye molecules showed that the synergetic effect should be taken into account, which forms the basis of plasmon–polariton superradiance.     

On the slow growth of the main characteristics of entire functions

We obtain a necessary and sufficient condition for the slow growth at infinity in terms of the coefficients in the series expansion of an entire function. Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 206–214, February, 1999.     

Amplification of extremely short pulses in optical media

The dynamics of pulses with durations comparable to the inverse transition frequency that propagate in an optical medium is studied in terms of two integrable systems of Maxwell-Bloch equations. The first model describes the field interaction with a nondegenerate medium with a permanent dipole moment and permanent external pumping. A general formula is derived for the N-soliton solution. Particular solutions are used as examples to investigate the effect of permanent dipole moment and pumping on the soliton dynamics. The second model describes the interaction between two-component electric-field pulses and a two-level degenerate medium with permanent upper-level pumping. For different initial magnetic-sublevel populations, soliton solutions are used as examples to show that pumping causes a change in polarization dynamics. A two-soliton solution is used to analyze the interaction of solitons in a two-level medium with external pumping.     

Ion and water transport during lithium chloride concentration from aqueous organic solutions by electrodialysis

The concentration of lithium chloride from aqueous organic solutions with different volume concentrations of N,N-dimethylacetamide (DMAA) was studied experimentally. An extended model of the limiting electrodialysis concentration of electrolytes from mixed media was developed. The model takes into account the osmotic and electroosmotic mechanisms of the transfer of water and organic solvent, as well as the electromigration and diffusion mechanisms of the salt transfer. Using the experimental data and the extended model, we evaluated the transport parameters of the MK-40/MA-40 membrane pair in aprotic solutions of variable compositions and studied how they changed with an increase in the volume fraction of DMAA in a mixed solution. The contribution of each of these mechanisms of ion and water transport to the electrodialysis concentration of electrolyte from aqueous and organic aqueous solutions was determined. Electroosmotic transfer was found to be the main mechanism of the solvent transfer that limits the stage of the electrodialysis concentration of the electrolyte from aqueous and organic aqueous solutions.     

Ion Transport in a Three-Layered Ion-Exchange Membrane: A Mathematical Model

An ion transport model is considered. The model is based on the Nernst–Planck equations, the elements of nonequilibrium thermodynamics, the principle of local equilibrium, and the concept of a virtual solution. The model is applied to an ion-exchange membrane with two diffusion layers for the cases of electrotransport of two and three types of ions. To determine transfer coefficients L ^* _j in the Nernst–Planck equations, two approaches are used. In the phenomenological approach, L ^* _j are found from experimental data on the electroconductivity and transport numbers. In the modeling approach, values of L ^* _j are sought for from a model of a microheterogeneous membrane. The obtained boundary-value problem is solved using a numerical method of parallel shooting developed earlier, which perfectly fits specific features of the problem formulation (utilizing the Nernst–Planck equations in all the three layers and the concept of a virtual solution).     

Control of excitons in a bent bunch of molecular aggregates by dipole–dipole interaction with quantum dots

The nonlocal dipole–dipole interaction is studied between excitations in chromophores forming a bunch or a tube of J-aggregates and closely spaced quantum dots (QDs). Equations describing the evolution of exciton pulses in a quasi-one-dimensional medium are derived taking into account the interaction with the transition resonant to nanoparticles. It is shown that the efficient controllable resonance energy transfer can occur in the system between QDs and an exciton pulse. The efficiency of this process significantly increases if the bunch of aggregates is deformed to bend nanoparticles round. It is shown that the interaction of permanent dipole moments of QDs and chromophores leads to the formation of a potential barrier or a well. It is found that the combined influence of these factors can be used to efficiently control the dynamics of pulses in aggregates.     

Dynamics of solitons in periodic systems with different nonlinear media

To analyze pulse dynamics in an optical system consisting of a periodic sequence of nonlinear media, a composite model is used. It includes a model of the resonance interaction of an ultrashort light pulse with the energy transition of the medium with allowance made for an upper level pump and an almost integrable model that describes the propagation of the light field in the other medium with a cubic nonlinearity and dispersion. Additional allowance is made for losses and other kinds of interaction by introducing perturbation terms. On the bases of the inverse scattering transform and perturbation theory, a simple method for analyzing specific features of soliton evolution in periodic systems of this kind is developed. It is used to describe various modes of soliton evolution in such a system, including chaotic dynamics.