arXiv subjects
Publications and source records attributed to V. A. Malyshev.
We consider stochastic models of chemical reaction networks with time dependent input rates and several types of molecules. We prove that, in despite of strong time dependence of input rates, there is a kind of homeostasis phenomenon: far away from input nodes the mean numbers of molecules of each type become approximately constant (do not depend on time).
Mathematical problems with mean field and local type interaction related to stochastic chemical kinetics,are considered. Our main concern various definitions of reversibility, their corollaries (Boltzmann type equations, fluctuations, Onsager relations, etc.) and emergence of irreversibility.
For any system $\{i\}$ of particles with the trajectories $x_{i}(t)$ in $R^{d}$ on a finite time interval $[0,τ]$ we define the interaction graph $G$. Vertices of $G$ are the particles, there is an edge between two particles $i,j$ iff for some $t\in[0,τ]$ the distance between particles $i,j$ is not greater than some constant. We undertake a detailed study of this graph for infinite particle dynamics and prove exponential estimates for its finite connected components. This solves continuous percolation problem for a complicated geometrical objects - the tubes around particle trajectories.
In the first part of this paper we give a short review of the hierarchy of stochastic models, related to physical chemistry. In the basement of this hierarchy there are two models --- stochastic chemical kinetics and the Kac model for Boltzman equation. Classical chemical kinetics and chemical thermodynamics are obtained as some scaling limits in the models, introduced below. In the second part of this paper we specify some simple class of open chemical reaction systems, where one can still prove the existence of attracting fixed points. For example, Michaelis\tire Menten kinetics belongs to this class. At the end we present a simplest possible model of the biological network. It is a network of networks (of closed chemical reaction systems, called compartments), so that the only source of nonreversibility is the matter exchange (transport) with the environment and between the compartments. Keywords: chemical kinetics, chemical thermodynamics, Kac model, mathematical biology
We introduce an infinite particle system dynamics, which includes stochastic chemical kinetics models, the classical Kac model and free space movement. We study energy redistribution between two energy types (kinetic and chemical) in different time scales, similar to energy redistribution in the living cell. One example is considered in great detail, where the model provides main formulas of chemical thermodynamics.
We study Markov exclusion process for a particle system with a local interaction in the integer strip. This process models the exchange of velocities and particle-hole exchange of the liquid molecules. It is shown that the mean velocity profile corresponds to the behaviour which is characteristic for incompressible viscous liquid. We prove the existence of phase transition between laminar and turbulent profiles.
We consider a symmetric exclusion process on a discrete interval of $S$ points with various boundary conditions at the endpoints. We study the asymptotic decay of correlations as $S\to\infty$. The main result is asymptotic independence of a stationary distribution whem the points are far away from each other. We develop a new recurrent probabilistic approach which is an alternative to Derrida's algebraic technique.
A general class of Markov processes with a local interaction is introduced, which includes exclusion and Kawasaki processes as a very particular case. Bernoulli invariant measures are found for this class of processes.
We consider here probabilistic models of transportation flows. The main goal of this introduction is rather not to present various techniques for problem solving but to present some intuition to invent adequate and natural models having visual simplicity and simple (but rigorous) formulation, the main objects being cars not abstract flows. The papers consists of three parts. First part considers mainly linear flows on short time scale - dynamics of the flow due to changing driver behavior. Second part studies linear flow on longer time scales - individual car trajectory from entry to exit from the road. Part three considers collective car movement in complex transport networks.
We show that interference can be the principle of operation of an all-optical switch and other nanoscale plasmonic interference devices (PIDs). The optical response of two types of planar plasmonic waveguides is studied theoretically: bent chains and Y-shaped configurations of closely-spaced metallic nanospheres. We study symmetric Y-shape arrays as an example of an all-optical switch and demonstrate that effective phase- and amplitude-sensitive control of the output signal can be achieved due to interference effects.
Optical response of an artificial composite nano-dimer comprising a semiconductor quantum dot and a metal nanosphere is analyzed theoretically. We show that internal degrees of freedom of the system can manifest bistability and optical hysteresis as functions of the incident field intensity. We argue that these effects can be observed for the real world systems, such as a CdSe quantum dot and an Au nanoparticle hybrids. These properties can be revealed by measuring the optical hysteresis of the Rayleigh scattering. We show also that the total dipole moment of the system can be switched abruptly between its two stable states by small changes in the excitation intensity. The latter promises various applications in the field of all-optical processing at nanoscale, the most underlying of them being the volatile optical memory.
Optical response of artificial composite nanoscale molecules comprising a closely spaced noble metal nanoparticle and a semiconductor quantum dot have been studied theoretically. We consider a system composed of an Au particle and CdSe or CdSe/ZnSe quantum dot and predict optical bistability and hysteresis in its response, which suggests various applications, in particular, all-optical processing and optical memory.
The interaction of laser radiation with single J aggregates of cyanine dyes is theoretically analyzed and numerically simulated. The quantum mechanical calculations of the equilibrium geometry and the energies and intensities of the lowest singlet electronic transitions in pseudoisocyanine chloride and its linear (chain) oligomers are fulfilled. The data of these calculations can serve as parameters of the analyzed model of interaction of J aggregates with radiation in the oneparticle density matrix approximation. This model takes into account relaxation processes, the annihilation of excitations at neighboring molecules, and inho mogeneous broadening. Assuming that the inhomogeneous broadening is absent, calculations demonstrate the existence of spatial bistability, molecular switching waves, and dissipative solitons. The effect of the inhomogeneous broadening and the radiation intensity on the effective coherence length in linear (chain) J aggregates is analyzed
The local distribution of exciton levels in disordered cyanine-dye-based molecular nano-aggregates has been elucidated using fluorescence line narrowing spectroscopy. The observation of a Wigner-Dyson-type level spacing distribution provides direct evidence of the existence of level repulsion of strongly overlapping states in the molecular wires, which is important for the understanding of the level statistics, and therefore the `functional properties, of a large variety of nano-confined systems.
We predict the existence of exchange broadening of optical lineshapes in disordered molecular aggregates and a nonuniversal disorder scaling of the localization characteristics of the collective electronic excitations (excitons). These phenomena occur for heavy-tailed Lévy disorder distributions with divergent second moments - distributions that play a role in many branches of physics. Our results sharply contrast with aggregate models commonly analyzed, where the second moment is finite. They bear a relevance for other types of collective excitations as well.
We present a theoretical analysis of the environment effects on charge transport in double-stranded synthetic poly(G)-poly(C) DNA molecules attached to two ideal leads. Coupling of the DNA to the environment results in two effects: (i) localization of carrier functions due to the static disorder and (ii) phonon-induced scattering of the carrier between these localized states, resulting in hopping conductivity. A nonlinear Pauli master equation for populations of localized states is used to describe the hopping transport and calculate the electric current as a function of the applied bias. We demonstrate that, although the electronic gap in the density of states shrinks as the disorder increases, the voltage gap in the $I-V$ characteristics becomes wider. Simple physical explanation of this effect is provided.
We compare localization properties of one-dimensional Frenkel excitons with Gaussian and Lorentzian uncorrelated diagonal disorder. We focus on the states of the Lifshits tail, which dominate the optical response and low-temperature energy transport in molecular J-aggregates. The absence of exchange narrowing in chains with Lorentzian disorder is shown to manifest itself in the disorder scaling of the localization length distribution. Also, we show that the local exciton level structure of the Lifshits tail differs substantially for these two types of disorder: In addition to the singlets and doublets of localized states near the bare band edge, strongly resembling those found for Gaussian disorder, for Lorentzian disorder two other types of states are found in this energy region as well, namely multiplets of three or four states localized on the same chain segment and isolated states localized on short segments. Finally, below the Lifshits tail, Lorentzian disorder induces strongly localized exciton states, centered around low energy sites, with localization properties that strongly depend on energy. For Gaussian disorder with a magnitude that does not exceed the exciton bandwidth, the likelihood to find such very deep states is exponentially small.
We study the dynamics of an electron wave-packet in a two-dimensional square lattice with an aperiodic site potential in the presence of an external uniform electric field. The aperiodicity is described by $ε_{\bf m} = V\cos{(παm_x^{ν_x})}\cos{(παm_y^{ν_y})}$ at lattice sites $(m_x, m_y)$, with $πα$ being a rational number, and $ν_x$ and $ν_y$ tunable parameters, controlling the aperiodicity. Using an exact diagonalization procedure and a finite-size scaling analysis, we show that in the weakly aperiodic regime ($ν_x,ν_y < 1$), a phase of extended states emerges in the center of the band at zero field giving support to a macroscopic conductivity in the thermodynamic limit. Turning on the field gives rise to Bloch oscillations of the electron wave-packet. The spectral density of these oscillations may display a double peak structure signaling the spatial anisotropy of the potential landscape. The frequency of the oscillations can be understood using a semi-classical approach.