Biomedical subjects

M Chertkov

Publications and source records attributed to M Chertkov.

17 recordsLinked to original sources

PubMed2005

Diagnosis of weaknesses in modern error correction codes: a physics approach.

One of the main obstacles to the wider use of the modern error-correction codes is that, due to the complex behavior of their decoding algorithms, no systematic method which would allow characterization of the bit-error-rate (BER) is known. This is especially true at the weak noise where many systems operate and where coding performance is difficult to estimate because of the diminishingly small number of errors. We show how the instanton method of physics allows one to solve the problem of BER analysis in the weak noise range by recasting it as a computationally tractable minimization problem.

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PubMed2005

Effects of surface tension on immiscible Rayleigh-Taylor turbulence.

We present phenomenology describing the internal structure of a turbulent zone, produced as the result of the push of a heavy fluid into a light one, for the case of immiscible fluids. One finds that the Kolmogorov cascade is realized within a range that grows with time, viz., scales between the mixing zone width, L proportional variant t(2), and the viscous scale, eta proportional variant t(-1/4). Surface-tension effects lead to formation of an emulsionlike state. Density fluctuations on scales larger than the typical drop size, l, are governed by the Obukhov-Corrsin cascade. If l >> eta, a wave energy cascade, related to capillary waves propagating along the surfaces of drops, is formed at scales below l, l proportional variant t(-2/5).

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PubMed2005

Dynamical generalization of nonequilibrium work relation.

The evolution of systems in contact with thermal, chaotic, or turbulent surroundings-often modeled with stochastic equations of motion-can be particularly complex when these equations of motion are nonautonomous, that is, when external parameters of the surroundings are varied with time. In this paper we establish a rigorous equality relating the nonautonomous behavior of such a system, to solutions of the corresponding autonomous equations of motion, for arbitrary initial conditions. If the system is initially in thermal equilibrium, we recover previously known results relating nonequilibrium work values to equilibrium probability distributions. We discuss specific examples of our result, and suggest an experimental setting in which it might be verified.

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PubMed2004

Error correction on a tree: an instanton approach.

We introduce a method that allows analytical or semianalytical estimating of the post-error correction bit error rate (BER) when a forward-error correction is utilized for transmitting information through a noisy channel. The generic method that applies to a variety of error-correction schemes in the regimes where the BER is low is illustrated using the example of a finite-size code approximated by a treelike structure. Exploring the statistical physics formulation of the problem we find that the BER decreases with the signal-to-noise ratio nonuniformly, i.e., crossing over through a sequence of phases. The higher the signal-to-noise ratio the lower the symmetry of the phase dominating BER.

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PubMed2003

Probability of anomalously large bit-error rate in long haul optical transmission.

We consider a linear model of optical transmission through a fiber with birefringent disorder in the presence of amplifier noise. Both disorder and noise are assumed to be weak, i.e., the average bit-error rate (BER) is small. The probability distribution function (PDF) of rare violent events leading to the values of BER much larger than its typical value is estimated. We show that the PDF has a long algebraic-like tail.

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PubMed2003

Boundary effects on chaotic advection-diffusion chemical reactions.

A theory of a fast binary chemical reaction, A+B-->C, in a statistically stationary bounded chaotic flow at large Peclet number Pe and large Damköhler number Da is described. The first stage correspondent to formation of the developed lamellar structure in the bulk part of the flow is terminated by an exponential decay, proportional, variant exp((-lambdat) (where lambda is the Lyapunov exponent of the flow), of the chemicals in the bulk. The second and the third stages are due to the chemicals remaining in the boundary region. During the second stage, the amounts of A and B decay proportional, variant 1/sqrt[t], whereas the decay law during the third stage is exponential, proportional, variant exp((-gammat), where gamma approximately lambda/sqrt[Pe].

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PubMed2003

Shedding and interaction of solitons in weakly disordered optical fibers.

The propagation of the soliton pattern through optical fiber with weakly disordered dispersion coefficient is considered. Solitons perturbed by this disorder radiate and, as a consequence, decay. The average radiation profile is found. Emergence of a long-range intrachannel interaction between the solitons (mediated by this radiation) is reported. We show that soliton in a multisoliton pattern experiences a random jitter: intersoliton separation is zero mean Gaussian random field. Fluctuations of this separation are estimated by deltay approximately Dz(2)square root mu, where D measures the disorder strength, z is the propagation distance, and mu stands for the transmission rate (number of solitons per unit length of the fiber). Direct numerical simulations are used to validate theoretical predictions for single soliton decay and two-soliton interaction. Relevance of these results to fiber optics communication technology is discussed.

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PubMed2003

Decay of scalar turbulence revisited.

We demonstrate that at long times the rate of passive scalar decay in a turbulent, or simply chaotic, flow is dominated by regions where mixing is less efficient. We examine two situations. The first is of a spatially homogeneous stationary turbulent flow with both viscous and inertial scales present. It is shown that at large times scalar fluctuations decay algebraically in time at all spatial scales. The second example explains chaotic stationary flow in a disk/pipe. The boundary region of the flow controls the long-time decay, which is algebraic at some transient times, but becomes exponential, with the decay rate dependent on the scalar diffusion coefficient, at longer times.

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PubMed2001

Pulse confinement in optical fibers with random dispersion.

Short-range correlated uniform noise in the dispersion coefficient, inherent in many types of optical fibers, broadens and eventually destroys all initially ultra-short pulses. However, under the constraint that the integral of the random component of the dispersion coefficient is set to zero (pinned), periodically or quasi-periodically along the fiber, the dynamics of the pulse propagation changes dramatically. For the case that randomness is present in addition to constant positive dispersion, the pinning restriction significantly reduces average pulse broadening. If the randomness is present in addition to piece-wise constant periodic dispersion with positive residual value, the pinning may even provide probability distributions of pulse parameters that are numerically indistinguishable from the statistically steady case. The pinning method can be used to both manufacture better fibers and upgrade existing fiber links.

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PubMed2000

Geometry of Lagrangian dispersion in turbulence.

Turbulent flows disperse Lagrangian particles resulting in the growth of pairwise separations and, for sets of three or more particles, in a nontrivial dynamics of their configuration. The shape of such clusters is controlled by the competition between coherent straining of the cluster and the independent random motion of the particles due to small scale velocity fluctuations. We introduce a statistical description of the geometry of the Lagrangian clusters and predict a self-similar distribution of shapes, which should be observable in the inertial range of scales in high Reynolds numbers flows.

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PubMed2000

Polymer stretching by turbulence

The stretching of a polymer chain by a large-scale chaotic flow is considered. The steady state which emerges as a balance of the turbulent stretching and anharmonic resistance of the chain is quantitatively described, i.e., the dependency on the flow parameters (Lyapunov exponent statistics) and the chain characteristics (the number of beads and the interbead elastic potential) is made explicit.

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PubMed1996