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A. V. Paraskevov

Publications and source records attributed to A. V. Paraskevov.

10 recordsLinked to original sources
arXiv2021

Damped oscillations of the probability of random events followed by absolute refractory period: exact analytical results

There are numerous examples of natural and artificial processes that represent stochastic sequences of events followed by an absolute refractory period during which the occurrence of a subsequent event is impossible. In the simplest case of a generalized Bernoulli scheme for uniform random events followed by the absolute refractory period, the event probability as a function of time can exhibit damped transient oscillations. Using stochastically-spiking point neuron as a model example, we present an exact and compact analytical description for the oscillations without invoking the standard renewal theory. The resulting formulas stand out for their relative simplicity, allowing one to analytically obtain the amplitude damping of the 2nd and 3rd peaks of the event probability.

q-bio.NC↗
arXiv2021

Analytical solution of linearized equations of the Morris-Lecar neuron model at large constant stimulation

The classical biophysical Morris-Lecar model of neuronal excitability predicts that upon stimulation of the neuron with a sufficiently large constant depolarizing current there exists a finite interval of the current values where periodic spike generation occurs. Above the upper boundary of this interval, there is four-stage damping of the spike amplitude: 1) minor primary damping, which reflects a typical transient to stationary dynamic state, 2) plateau of nearly undamped periodic oscillations, 3) strong damping, and 4) reaching a constant asymptotic value of the neuron potential. We have shown that in the vicinity of the asymptote the Morris-Lecar equations can be reduced to the standard equation for exponentially damped harmonic oscillations. Importantly, all coefficients of this equation can be explicitly expressed through parameters of the original Morris-Lecar model, enabling direct comparison of the numerical and analytical solutions for the neuron potential dynamics at later stages of the spike amplitude damping.

q-bio.NC↗
arXiv2018

A spatially resolved network spike in model neuronal cultures reveals nucleation centers, circular traveling waves and drifting spiral waves

We show that in model neuronal cultures, where the probability of interneuronal connection formation decreases exponentially with increasing distance between the neurons, there exists a small number of spatial nucleation centers of a network spike, from where the synchronous spiking activity starts propagating in the network typically in the form of circular traveling waves. The number of nucleation centers and their spatial locations are unique and unchanged for a given realization of neuronal network but are different for different networks. In contrast, if the probability of interneuronal connection formation is independent of the distance between neurons, then the nucleation centers do not arise and the synchronization of spiking activity during a network spike occurs spatially uniform throughout the network. Therefore one can conclude that spatial proximity of connections between neurons is important for the formation of nucleation centers. It is also shown that fluctuations of the spatial density of neurons at their random homogeneous distribution typical for the experiments $\textit{in vitro}$ do not determine the locations of the nucleation centers. The simulation results are qualitatively consistent with the experimental observations.

q-bio.NC↗
arXiv2012

Ring-shaped spatial pattern of exciton luminescence formed due to the hot carrier transport in a locally photoexcited electron-hole bilayer

A consistent explanation of the formation of a ring-shaped pattern of exciton luminescence in GaAs/AlGaAs double quantum wells is suggested. The pattern consists of two concentric rings around the laser excitation spot. It is shown that the luminescence rings appear due to the in-layer transport of hot charge carriers at high photoexcitation intensity. Interestingly, one of two causes of this transport might involve self-organized criticality (SOC) that would be the first case of the SOC observation in semiconductor physics. We test this cause in a many-body numerical model by performing extensive molecular dynamics simulations. The results show good agreement with experiments. Moreover, the simulations have enabled us to identify the particular kinetic processes underlying the formation of each of these two luminescence rings.

cond-mat.mes-hall↗
arXiv2012

On the radiative lifetime of free-moving two-dimensional excitons

A simple microscopic mechanism explaining the linear dependence of the radiative lifetime of free-moving two-dimensional excitons on their effective temperature is suggested. It is shown that there exists a characteristic effective temperature (of about few Kelvin) defined by the exciton-acoustic phonon interaction at which the radiative lifetime is minimal. Below this temperature the lifetime starts to increase with decreasing temperature. The correspondence with previous theoretical and experimental results is discussed.

cond-mat.mes-hall↗
arXiv2010

Ring-shaped luminescence patterns in a locally photoexcited electron-hole bilayer

We report the results of molecular dynamics simulation of a spatiotemporal evolution of the locally photoexcited electrons and holes localized in two separate layers. It is shown that the ring-shaped spatial pattern of luminescence forms due to the strong in-layer Coulomb interaction at high photoexcitation power. In addition, the results predict (i) stationary spatial oscillations of the electron density in quasi one-dimensional case and (ii) dynamical phase transition in the expansion of two-dimensional electron cloud when threshold electron concentration is reached. A possible reason of the oscillations and a theoretical interpretation of the transition are suggested.

cond-mat.mes-hall↗
arXiv2009

Comment on "Formation Mechanism and Low-Temperature Instability of Exciton Rings"

This is an extended version of the Comment that contains the criticism against an applicability of the diffusive transport model for the explanation of the ring-shaped spatial pattern formation in the exciton photoluminescence for the GaAs/AlGaAs double quantum wells [Phys. Rev. Lett. 92, 117404 (2004)]. The model has been used in other similar papers published in the PRL and the PRB afterwards.

cond-mat.mes-hall↗
arXiv2007

On the microscopic theory of the exciton ring fragmentation

The description is presented for the dependence of the indirect exciton condensate density at the ring as a function of the polar angle at zero temperature with the involvement of the processes of formation and recombination of the excitons. In particular, starting from the quasi one-dimensional Gross-Pitaevskii equation with a spatially uniform generating term, we derive an exact analytical solution yielding the fragmentation of an exciton ring which is probably observed in the experiments.

cond-mat.mes-hall↗
arXiv2005

On the stability of the coherent state of a two-level atom Bose gas in the resonant laser field at zero temperature

It is shown that a Bose gas of two-level atoms in the intense resonant laser field at zero temperature is a mixture of two condensates with a definite ratio of the densities. The criteria of stability are found for the stationary states of such system against the increment of the amplitudes of quasi Bogoliubov elementary excitations. Besides the usual acoustic mode the gap mode is shown to exist and the magnitude of the gap is proportional to the laser field amplitude. The involvement of the gas nonideality under definite conditions results in an instability and decay of the condensates.

cond-mat.other↗