Efficient simulations of Hartree-Fock equations by an accelerated gradient descent method.

We develop convergence acceleration procedures that enable a gradient descent-type iteration method to efficiently simulate Hartree-Fock equations for many particles interacting both with each other and with an external potential. Our development focuses on three aspects: (i) optimization of a parameter in the preconditioning operator; (ii) adoption of a technique that eliminates the slowest-decaying mode to the case of many equations (describing many particles); and (iii) a novel extension of the above technique that allows one to eliminate multiple modes simultaneously. We illustrate performance of the numerical method for the two-dimensional model of the first layer of helium atoms above a graphene sheet.

Toward determining amyloid fibril structures using experimental constraints from Raman spectroscopy.

We present structural models for three different amyloid fibril polymorphs prepared from amylin20-29 (sequence SNNFGAILSS) and amyloid-β25-35 (Aβ25-35) (sequence GSNKGAIIGLM) peptides. These models are based on the amide C=O bond and Ramachandran ψ-dihedral angle data from Raman spectroscopy, which were used as structural constraints to guide molecular dynamics (MD) simulations. The resulting structural models indicate that the basic structural motif of amylin20-29 and Aβ25-35 fibrils is extended β-strands.

Spinodal de-wetting of light liquids on graphene.

We demonstrate theoretically the possibility of spinodal de-wetting in heterostructures made of light-atom liquids (hydrogen, helium, and nitrogen) deposited on suspended graphene. Extending our theory of film growth on two-dimensional (2D) materials to include analysis of surface instabilities via the hydrodynamic Cahn-Hilliard-type equation, we characterize in detail the spatial and temporal scales of the resulting spinodal de-wetting patterns. Both linear stability analysis and direct numerical simulations of the surface hydrodynamics show micron-sized (generally material dependent) patterns of 'dry' regions.

All-optical regenerator of multi-channel signals.

One of the main reasons why nonlinear-optical signal processing (regeneration, logic, etc.) has not yet become a practical alternative to electronic processing is that the all-optical elements with nonlinear input-output relationship have remained inherently single-channel devices (just like their electronic counterparts) and, hence, cannot fully utilise the parallel processing potential of optical fibres and amplifiers. The nonlinear input-output transfer function requires strong optical nonlinearity, e.

NALM-based, phase-preserving 2R regenerator of high-duty-cycle pulses.

We explore the potential of the nonlinear amplifying loop mirror (NALM)-based phase-preserving 2R (reamplification and reshaping) regenerator for simultaneous regeneration of multiple wavelength-division-multiplexed (WDM) channels. While not considering nonlinear multi-channel propagation, we address two issues of the phase-preserving NALM that appear to us as the major obstacles in adopting it for realistic WDM applications: a high operating power and a detrimental effect of non-small (33% - 50%) pulse duty cycles. After thorough optimization, we find a new operating regime of this regenerator with the non-small duty-cycle capability and approximately an order of magnitude reduction of the required operating power.

A comparative study of noisy signal evolution in 2R all-optical regenerators with normal and anomalous average dispersions using an accelerated Multicanonical Monte Carlo method.

In [Opt. Express 15, 10061 (2007)] we proposed a new regime of multichannel all-optical regeneration that required anomalous average dispersion. This regime is superior to the previously studied normal-dispersion regime when signal distortions are deterministic in their temporal shape.

Influence of the Raman effect on dispersion-managed solitons and their interchannel collisions.

We calculate the self-frequency shift experienced by a soliton in a dispersion-managed fiber that is due to the Raman effect, as well as the energy and frequency shifts that result from a collision of such solitons with different wavelengths. We find that dispersion management suppresses both types of frequency shift but does not significantly affect the energy shift that is accumulated over a large propagation distance. The latter shift may represent a potential problem for wavelength-division-multiplexed systems with several gigabits per second in a single channel.

Enhanced robustness of dispersion-managed solitons with respect to polarization mode dispersion.

Polarization mode dispersion causes solitons to emit background radiation, which degrades transmission quality. It is shown theoretically and confirmed by numerical simulations that dispersion-managed solitons can trap part of that radiation into localized eigenmodes, thus yielding improvement in transmission quality compared with that of conventional solitons.

Effects of precompensation and postcompensation on timing jitter in dispersion-managed systems.

We present an analytic theory of timing jitter in dispersion-managed light-wave systems that is based on the moment method and the assumption of a chirped Gaussian pulse. We apply the theory to a soliton system and show that 50% postcompensation of the accumulated dispersion can reduce the jitter by a factor of 2. We also apply the theory to a low-power light-wave system employing the return-to-zero format and find that timing jitter can be minimized along the fiber link for an optimal choice of precompensation and postcompensation.

Efficient modeling of phase jitter in dispersion-managed soliton systems.

The variational method is used to derive correlation equations that model phase jitter in dispersion-managed soliton systems. The predictions of these correlation equations are consistent with numerical solutions of the nonlinear Schrödinger equation on which they are based.

A new robust regime for a dispersion-managed multichannel 2R regenerator.

We study the performance of a multichannel version [M. Vasilyev and T.I.

All-optical multichannel 2R regeneration in a fiber-based device.

We propose the design of an all-optical 2R regenerator capable of handling multiple wavelength-division-multiplexed channels simultaneously. It extends the known concept of off-center filtering of self-phase-modulation-broadened signal spectra. The novel feature of the proposed device is a dispersion map that strongly suppresses interchannel impairments.

Probability-density function for energy perturbations of isolated optical pulses.

The mathematical methods required to model simple stochastic processes are reviewed briefly. These methods are used to determine the probability-density function (PDF) for noise-induced energy perturbations of isolated (solitary) optical pulses in fiber communication systems. The analytical formula is consistent with the numerical solution of the energymoment equation.

Persistent oscillations of scalar and vector dispersion-managed solitons.

We show that both orthogonal and parallel internal modes exist on the background of a dispersion-managed (DM) soliton in randomly birefringent fibers. The orthogonal modes exist for arbitrarily small values of the dispersion map strength, while the parallel modes exist only when the map strength exceeds a certain threshold value. We demonstrate that initial perturbations of a DM soliton's profile that consist of one or more internal modes, exhibit nearly stable oscillations over very long propagation distances, before decaying into radiation.