Extreme-value statistics of work done in stretching a polymer in a gradient flow.

We analyze the statistics of work generated by a gradient flow to stretch a nonlinear polymer. We obtain the large deviation function (LDF) of the work in the full range of appropriate parameters by combining analytical and numerical tools. The LDF shows two distinct asymptotes: "near tails" are linear in work and dominated by coiled polymer configurations, while "far tails" are quadratic in work and correspond to preferentially fully stretched polymers. We find the extreme value statistics of work for several singular elastic potentials, as well as the mean and the dispersion of work near the coil-stretch transition. The dispersion shows a maximum at the transition.

Wrinkling of vesicles during transient dynamics in elongational flow.

Recent experiments by Kantsler et al. [Phys. Rev. Lett. 99, 178102 (2007)10.1103/PhysRevLett.99.178102] have shown that the relaxational dynamics of a vesicle in external elongation flow is accompanied by the formation of wrinkles on a membrane. Motivated by these experiments we present a theory describing the dynamics of a wrinkled membrane. The formation of wrinkles is related to the dynamical instability induced by negative surface tension of the membrane. For quasispherical vesicles we perform analytical study of the wrinkle structure dynamics. We derive the expression for the instability threshold and identify three stages of the dynamics. The scaling laws for the temporal evolution of wrinkling wavelength and surface tension are established, confirmed numerically, and compared to experimental results.

Statistics of entropy production in linearized stochastic systems.

We consider a wide class of linear stochastic problems driven off the equilibrium by a multiplicative asymmetric force. The force breaks detailed balance, maintained otherwise, thus producing entropy. The large deviation function of the entropy production in the system is calculated explicitly. The general result is illustrated using an example of a polymer immersed in a gradient flow and subject to thermal fluctuations.

Dynamics of nearly spherical vesicles in an external flow.

Tank-treading, tumbling, and trembling are different types of the vesicle behavior in an external flow. We derive a dynamical equation enabling us to establish a state of nearly spherical vesicles. For a 2D external flow, the character of the vesicle dynamics is determined by two dimensionless parameters, depending on the vesicle excess area, fluid viscosities, membrane viscosity and bending modulus, strength of the flow, and ratio of the elongational and rotational components of the flow. The tank-treading to tumbling transition occurs via a saddle-node bifurcation, whereas the tank-treading to trembling transition occurs via a Hopf bifurcation. A slowdown of vesicle dynamics should be observed in a vicinity of a point separating the transition lines. We show that the slowdown can be described by a power law with two different critical exponents 1/4 and 1/2 corresponding to the slowdown of tumbling and trembling cycles.

Passive scalar evolution in peripheral regions.

We consider the evolution of a passive scalar (concentration of pollutants or temperature) in a chaotic (turbulent) flow. A universal asymptotic behavior of the passive scalar decay (homogenization) related to peripheral regions (near walls) is established. The passive scalar moments and their pair correlation function in the peripheral region are analyzed. A special case investigated in our paper is the passive scalar decay along a pipe.

Information capacity of optical fiber channels with zero average dispersion.

We study the statistics of optical data transmission in a noisy nonlinear fiber channel with a weak dispersion management and zero average dispersion. Applying analytical expressions for the output probability density functions both for a nonlinear channel and for a linear channel with additive and multiplicative noise we calculate in a closed form a lower bound estimate on the Shannon capacity for an arbitrary signal-to-noise ratio.

Air parcel random walk and droplet spectra broadening in clouds.

We study the effect of turbulent flow on the droplet growth in a cloud during the condensation phase. Using the air parcel model, we describe analytically how the size distribution of droplets evolves at the different stages of parcel movement. We show that turbulent random walk superimposed on an accelerated ascent of the parcel makes the relative width of droplet distribution to grow initially as t(1/2) and then decay as t(-3/2).