Reactive Turbulent Flow in Low-Dimensional, Disordered Media

We analyze the reactions $A+A \to \emptyset$ and $A + B \to \emptyset$ occurring in a model of turbulent flow in two dimensions. We find the reactant concentrations at long times, using a field-theoretic renormalization group analysis. We find a variety of interesting behavior, including, in the presence of potential disorder, decay rates faster than that for well-mixed reactions.Comment: 6 pages, 4 figures. To appear in Phys. Rev.

Optimal client recommendation for market makers in illiquid financial products

The process of liquidity provision in financial markets can result in prolonged exposure to illiquid instruments for market makers. In this case, where a proprietary position is not desired, pro-actively targeting the right client who is likely to be interested can be an effective means to offset this position, rather than relying on commensurate interest arising through natural demand. In this paper, we consider the inference of a client profile for the purpose of corporate bond recommendation, based on typical recorded information available to the market maker. Given a historical record of corporate bond transactions and bond meta-data, we use a topic-modelling analogy to develop a probabilistic technique for compiling a curated list of client recommendations for a particular bond that needs to be traded, ranked by probability of interest. We show that a model based on Latent Dirichlet Allocation offers promising performance to deliver relevant recommendations for sales traders.Comment: 12 pages, 3 figures, 1 tabl

Spectrum of the Fokker-Planck operator representing diffusion in a random velocity field

We study spectral properties of the Fokker-Planck operator that represents particles moving via a combination of diffusion and advection in a time-independent random velocity field, presenting in detail work outlined elsewhere [J. T. Chalker and Z. J. Wang, Phys. Rev. Lett. {\bf 79}, 1797 (1997)]. We calculate analytically the ensemble-averaged one-particle Green function and the eigenvalue density for this Fokker-Planck operator, using a diagrammatic expansion developed for resolvents of non-Hermitian random operators, together with a mean-field approximation (the self-consistent Born approximation) which is well-controlled in the weak-disorder regime for dimension d>2. The eigenvalue density in the complex plane is non-zero within a wedge that encloses the negative real axis. Particle motion is diffusive at long times, but for short times we find a novel time-dependence of the mean-square displacement, $\sim t^{2/d}$ in dimension d>2, associated with the imaginary parts of eigenvalues.Comment: 8 pages, submitted to Phys Rev

Resonant enhanced diffusion in time dependent flow

Explicit examples of scalar enhanced diffusion due to resonances between different transport mechanisms are presented. Their signature is provided by the sharp and narrow peaks observed in the effective diffusivity coefficients and, in the absence of molecular diffusion, by anomalous transport. For the time-dependent flow considered here, resonances arise between their oscillations in time and either molecular diffusion or a mean flow. The effective diffusivities are calculated using multiscale techniques.Comment: 18 latex pages, 11 figure

Malvinas-slope water intrusions on the northern Patagonia continental shelf

The Patagonia continental shelf located off southeastern South America is bounded offshore by the Malvinas Current, which extends northward from northern Drake Passage (~55° S) to nearly 38° S. The transition between relatively warm-fresh shelf waters and Subantarctic Waters from the western boundary current is characterized by a thermohaline front extending nearly 2500 km. We use satellite derived sea surface temperature, and chlorophyll-<I>a</I> data combined with hydrographic and surface drifter data to document the intrusions of slope waters onto the continental shelf near 41° S. These intrusions create vertically coherent localized negative temperature and positive salinity anomalies extending onshore about 150 km from the shelf break. The region is associated with a center of action of the first mode of non-seasonal sea surface temperature variability and also relatively high chlorophyll-<I>a</I> variability, suggesting that the intrusions are important in promoting the local development of phytoplankton. The generation of slope water penetrations at this location may be triggered by the inshore excursion of the 100 m isobath, which appears to steer the Malvinas Current waters over the outer shelf

Enhacement in the dymanic response of a viscoelastic fluid flowing through a longitudinally vibrating tube

We analyzed effects of elasticity on the dynamics of fluids in porous media by studying a flow of a Maxwell fluid in a tube, which oscillates longitudinally and is subject to oscillatory pressure gradient. The present study investigates novelties brought about into the classic Biot's theory of propagation of elastic waves in a fluid-saturated porous solid by inclusion of non-Newtonian effects that are important, for example, for hydrocarbons. Using the time Fourier transform and transforming the problem into the frequency domain, we calculated: (A) the dynamic permeability and (B) the function $F(\kappa)$ that measures the deviation from Poiseuille flow friction as a function of frequency parameter $\kappa$. This provides a more complete theory of flow of Maxwell fluid through the longitudinally oscillating cylindrical tube with the oscillating pressure gradient, which has important practical applications. This study has clearly shown transition from dissipative to elastic regime in which sharp enhancements (resonances) of the flow are found

Viscous Instanton for Burgers' Turbulence

We consider the tails of probability density functions (PDF) for different characteristics of velocity that satisfies Burgers equation driven by a large-scale force. The saddle-point approximation is employed in the path integral so that the calculation of the PDF tails boils down to finding the special field-force configuration (instanton) that realizes the extremum of probability. We calculate high moments of the velocity gradient $\partial_xu$ and find out that they correspond to the PDF with $\ln[{\cal P}(\partial_xu)]\propto-(-\partial_xu/{\rm Re})^{3/2}$ where ${\rm Re}$ is the Reynolds number. That stretched exponential form is valid for negative $\partial_xu$ with the modulus much larger than its root-mean-square (rms) value. The respective tail of PDF for negative velocity differences $w$ is steeper than Gaussian, $\ln{\cal P}(w)\sim-(w/u_{\rm rms})^3$, as well as single-point velocity PDF $\ln{\cal P}(u)\sim-(|u|/u_{\rm rms})^3$. For high velocity derivatives $u^{(k)}=\partial_x^ku$, the general formula is found: $\ln{\cal P}(|u^{(k)}|)\propto -(|u^{(k)}|/{\rm Re}^k)^{3/(k+1)}$.Comment: 15 pages, RevTeX 3.

Dispersion Coefficients by a Field-Theoretic Renormalization of Fluid Mechanics

We consider subtle correlations in the scattering of fluid by randomly placed obstacles, which have been suggested to lead to a diverging dispersion coefficient at long times for high Peclet numbers, in contrast to finite mean-field predictions. We develop a new master equation description of the fluid mechanics that incorporates the physically relevant fluctuations, and we treat those fluctuations by a renormalization group procedure. We find a finite dispersion coefficient at low volume fraction of disorder and high Peclet numbers.Comment: 4 pages, 1 figure; to appear in Phys. Rev. Let