Kink-excitation of N-system under spatio-temporal noise

Random walk of the nonlinear localized excitations in a dissipative N-system, i.e., the influence of the irregular perturbations on the kink-shaped excitations in a system characterized by nonlinearities of "N-type", is analyzed. The “evolution” of the randomly walking excitation is described by the onedimensional PDE (partial differential equation) of the parabolic type. The analysis of the considered excitations is performed for the case of the disturbing torque which is randomly distributed in space and time, and makes up the white Gaussian noise. An iterative scheme of perturbation technique is presented to derive the randomly perturbed solutions of the considered evolution equation in a general case of N-system. The average characteristics of the “steady state” of the randomly walking kink-excitations are examined in detail. The explicit expressions that describe the considered random walk are presented for the particular case of the kink-shaped excitations of the free electron gas in semiconductors

Front Dynamics with Delays in a Spatially Extended Bistable System: Computer Simulation

Front dynamics with delays in a spatially extended bistable system of the reaction-diffusion type is studied by the use of nonlinear partial differential equation (PDE) of the parabolic type. The response of the self-ordered front, joining two steady states of the different stability in the system, to the multi-harmonic (step-like) force is examined. The relaxation rate of the system, that characterizes the delayed response of the front to the alternating current (ac) drive, is found to be sensitive to the peculiarities (shape) of the rate function (nonlinearity) of the governing PDE. By using computer simulations of the drift motion of the ac driven bistable front (BF) we are able to show that the characteristic relaxation time of the system decreases with the increasing outer slope parameters of the rate function and is not sensitive to the inner one

Triukšmo itaka netiesiniams elektroniniams kietojo kūno dariniams

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Fronts in a continuous bistable system under periodically oscillating forcing

The propagation of a stable front in a dissipative bistable system that is influenced by the periodically oscillating forcing is examined. The evolution of the front is described by the nonlinear PDE (partial differential equation) of the parabolic type with the considered rate function of N-type. The one-dimensional front propagation is examined within the adiabatic approximation, i.e., the oscillations of the disturbing forcing are assumed to be slow enough. The pulling effect of the fronts is found, i.e., it is shown that the mean velocity of the perturbed front is increased as compared to that of the unperturbed front. The explicit expressions which describe the characteristic parameters of the perturbed front are presented for the particular case of the cubic polynomial rate function

Self-Ordered Front under Temporally Irregular Forcing: Ratchet-Like Transport of the Quasi-Periodically Forced Front

Ratchet-like transport of the quasi-periodically forced "bistable" front joining two states of the different stability in the reaction-diffusion system is considered by use of the piecewise linear rate (reaction) function of the reaction kinetics. We approximate the oscillatory force acting on the front in the system by the bi-harmonic forcing functions being a superposition of the single-harmonic components (the Fourier modes) of the different frequencies, either commensurate or incommensurable ones. By considering the response of the self-ordered front to the oscillatory forces used we analyze the effect of the temporally irregular oscillations of the ac forcing on the ratchet-like shuttling of the ac driven front. By comparing the average characteristics of the spurious drift derivable in both cases of the periodically and quasi-periodically forced fronts we show that the temporally irregular fluctuations of the oscillatory force shrink the spurious drift of the front. More specifically, we find the performance of the ratchet-like shuttling of the self-ordered fronts is much lesser pronounced with the quasi-periodic, temporally irregular ac forcing if compared to that derivable by the rigorously periodic forcing, in both cases of the symmetrical and asymmetrical rate functions satisfying the different symmetry. The average characteristics of the spurious drift, that describe the dependence of the mean drift velocity of the ac driven front versus both the amplitude (strength) and the frequency of the oscillatory forces used are presented

Front Dynamics with Time Delays in a Bistable System of the Reaction-Diffusion Type: Role of the Symmetry of the Rate Function

The retardation effects in dynamics of the ac driven "bistable" fronts joining two states of the different stability in a bistable system of the reaction-diffusion type are investigated by use of the macroscopic kinetic equation of the reaction kinetics. We approximate the rate (reaction) function in the governing equation of "bistable" fronts by the piecewise linear dependence of the flexible symmetry, encompassing both cases of the symmetrical and asymmetrical rate functions. By numerically simulating the drift motion of the ac driven front being subjected to the time-dependent step-like (rectangular) forcing we investigate the lag time between the ac force and the instantaneous velocity of the ac driven front. We find that the time lags derivable by the symmetrical and asymmetrical rate functions notably differ, namely, we show that (a) the lag time is a function of the outer slope coefficients of the rate function and is not sensitive to the inner, (b) it has only weak dependence on the strength of the applied forcing, (c) the retardation effects (time lags) in the front dynamics are describable adequately enough by use of the perturbation theory. Another aspect of the front dynamics discussed in this report is the influence of the retardation effects on the ratchet-like transport of the ac driven fronts being described by the asymmetrical rate functions of the "low" symmetry. By considering the response of "bistable" front to the single-harmonic ac force we find that the occurrence of the time lags in the oscillatory motion of the ac driven front shrink the spurious drift of the front; the spurious drift practically disappears if the frequency of the oscillatory force significantly exceeds the characteristic relaxation rate of the system. Furthermore, the occurrence of the time lags in the front dynamics leads to the vanishing of the reversals in the directed net motion of the ac driven fronts, being always inherent in the case of the slow (quasi-stationary) ac drive, i.e., the possibilities of controlling the directed net motion of the self-ordered fronts by the low- and high-frequency zero-mean ac forces radically differ

Total Syntheses of Xiamycins A, C, F, H and Oridamycin A and Preliminary Evaluation of their Anti‐Fungal Properties

Divergent and enantiospecific total syntheses of the indolosesquiterpenoids xiamycins A, C, F, H and oridamycin A have been accomplished. The syntheses, which commence from (R)-carvone, employ a key photoinduced benzannulation sequence to forge the carbazole moiety characteristic of these natural products. Late-stage diversification from a common intermediate enabled the first syntheses of xiamycins C and F, and an unexpected one-pot oxidative decarboxylation, which may prove general, led to xiamycin H. All synthetic intermediates and the natural products were tested for anti-fungal activity. Xiamycin H emerged as an inhibitor of three agriculturally relevant fungal pathogens

Novel biodegradable protonic ionic liquid for the Fischer indole synthesis reaction

Novel eco-friendly tetramethylguanidinium propanesulfonic acid trifluoromethylacetate ([TMGHPS][TFA]) ionic liquid was developed as catalyst and medium for the Fischer indole synthesis of a wide variety of hydrazines and ketones. The indole products were isolated in high yields and with minimal amounts of organic solvent. This reaction showed that [TMGHPS][TFA] can be regenerated and reused with reproducible yields without eroding the integrity of the ionic liquid