Abstract:
Intrabeam scattering is the major mechanism resulting in a growth of beam emittances and fast luminosity degradation in the Tevatron. As a result in the case of optimal collider operation only about 40% of antiprotons are used to the store end and the rest are discarded. Beam cooling is the only effective remedy to increase the particle burn rate and, consequently, the luminosity. Unfortunately neither electron nor stochastic cooling can be effective at the Tevatron energy and bunch density. Thus the optical stochastic cooling (OSC) is the only promising technology capable to cool the Tevatron beam. Possible ways of such cooling implementation in the Tevatron and advances in the OSC cooling theory are discussed in this paper. The technique looks promising and potentially can double the average Tevatron luminosity without increasing its peak value and the antiproton production.

Abstract:
We examine high-order dynamical correlations of defects (vortices, disclinations etc) in thin films starting from the Langevin equation for the defect motion. We demonstrate that dynamical correlation functions $F_{2n}$ of vorticity and disclinicity behave as $F_{2n}\sim y^2/r^{4n}$ where $r$ is the characteristic scale and $y$ is the fugacity. As a consequence, below the Berezinskii-Kosterlitz-Thouless transition temperature $F_{2n}$ are characterized by anomalous scaling exponents. The behavior strongly differs from the normal law $F_{2n}\sim F_2^n$ occurring for simultaneous correlation functions, the non-simultaneous correlation functions appear to be much larger. The phenomenon resembles intermittency in turbulence.

Abstract:
We investigate statistical properties of the passive scalar near boundaries (walls) in random (turbulent) flows assuming weakness of its diffusion. Then at advanced stages of the passive scalar mixing its unmixed residue is concentrated in a narrow diffusive layer near the wall and its transport to bulk goes through the peripheral region (laminar sublayer). We conducted Lagrangian numerical simulations of the process for different space dimensions $d$ and revealed structures responsible for the transport that are passive scalar tongues pulled from the diffusive boundary layer to bulk. We investigated statistical properties of the passive scalar and of the passive scalar integrated along the wall. Moments of both objects demonstrate scaling behavior outside the diffusive boundary layer. We propose an analytical scheme for explanation scaling of the passive scalar, the obtained exponents agree reasonably with numerics in 3d.

Abstract:
We investigate turbulence in dilute polymer solutions when polymers are strongly stretched by the flow. We establish power-law spectrum of velocity, which is not associated with a flux of a conserved quantity, in two cases. The first case is the elastic waves range of high Reynolds number turbulence of polymer solutions above the coil-stretch transition. The second case is the elastic turbulence, where chaotic flow is excited due to elastic instabilities at small Reynolds numbers.

Abstract:
Theory of fast binary chemical reaction, ${\cal A}+{\cal B}\to{\cal C}$, in a statistically stationary chaotic flow at large Schmidt number ${Sc}$ and large Damk\"ohler number ${Da}$ is developed. For stoichiometric condition we identify subsequent stages of the chemical reaction. The first stage corresponds to the exponential decay, $\propto\exp(-\lambda t)$ (where $\lambda$ is the Lyapunov exponent of the flow), of the chemicals in the bulk part of the flow. The second and the third stages are related to the chemicals remaining in the boundary region. During the second stage the amounts of ${\cal A}$ and ${\cal B}$ decay $\propto 1/\sqrt{t}$, whereas the decay law during the third stage is exponential, $\propto\exp(-\gamma t)$, where $\gamma\sim\lambda/\sqrt{Sc}$.

Abstract:
We investigate experimentally a two-dimensional rocking ratchet for cold atoms, realized by using a driven three-beam dissipative optical lattice. AC forces are applied in perpendicular directions by phase-modulating two of the lattice beams. As predicted by the general theory [S. Denisov et al., Phys. Rev. Lett. 100, 224102 (2008)], we observe a rectification phenomenon unique to high-dimensional rocking ratchets, as determined by two single-harmonic drivings applied in orthogonal directions. Also, by applying two bi-harmonic forces in perpendicular directions, we demonstrate the possibility of generating a current in an arbitrary direction within the optical lattice plane.

Abstract:
We demonstrate that at long times the rate of passive scalar decay in a turbulent, or simply chaotic, flow is dominated by regions (in real space or in inverse space) 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 (particularly in the viscous range, where the velocity is smooth). 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.

Abstract:
We consider high-order correlation functions of the passive scalar in the Kraichnan model. Using the instanton formalism we find the scaling exponents $\zeta_n$ of the structure functions $S_n$ for $n\gg1$ under the additional condition $d\zeta_2\gg1$ (where $d$ is the dimensionality of space). At $nn_c$ they are $n$-independent: $\zeta_n=\zeta_2 n_c/4$. We also estimate $n$-dependent factors in $S_n$, particularly their behavior at $n$ close to $n_c$.

Abstract:
A new type of an optical interferometer is discussed the phase difference between the interfering beams in which is substantially wavelength dependent. It is shown that the function measured with this device is an integral transform of the field correlation function. Possible applications for data encoding and spectral linewidth measurements are considered.