Rain, power laws, and advection

Localized rain events have been found to follow power-law size and duration distributions over several decades, suggesting parallels between precipitation and seismic activity [O. Peters et al., PRL 88, 018701 (2002)]. Similar power laws are generated by treating rain as a passive tracer undergoing advection in a velocity field generated by a two-dimensional system of point vortices.Comment: 7 pages, 4 figure

Sand stirred by chaotic advection

We study the spatial structure of a granular material, N particles subject to inelastic mutual collisions, when it is stirred by a bidimensional smooth chaotic flow. A simple dynamical model is introduced where four different time scales are explicitly considered: i) the Stokes time, accounting for the inertia of the particles, ii) the mean collision time among the grains, iii) the typical time scale of the flow, and iv) the inverse of the Lyapunov exponent of the chaotic flow, which gives a typical time for the separation of two initially close parcels of fluid. Depending on the relative values of these different times a complex scenario appears for the long-time steady spatial distribution of particles, where clusters of particles may or not appear.Comment: 4 pages, 3 figure

Vortex Images and q-Elementary Functions

In the present paper problem of vortex images in annular domain between two coaxial cylinders is solved by the q-elementary functions. We show that all images are determined completely as poles of the q-logarithmic function, where dimensionless parameter $q = r^2_2/r^2_1$ is given by square ratio of the cylinder radii. Resulting solution for the complex potential is represented in terms of the Jackson q-exponential function. By composing pairs of q-exponents to the first Jacobi theta function and conformal mapping to a rectangular domain we link our solution with result of Johnson and McDonald. We found that one vortex cannot remain at rest except at the geometric mean distance, but must orbit the cylinders with constant angular velocity related to q-harmonic series. Vortex images in two particular geometries in the $q \to \infty$ limit are studied.Comment: 17 page

Reversal of loss of bone mass in old mice treated with mefloquine

Aging is accompanied by imbalanced bone remodeling, elevated osteocyte apoptosis, and decreased bone mass and mechanical properties; and improved pharmacologic approaches to counteract bone deterioration with aging are needed. We examined herein the effect of mefloquine, a drug used to treat malaria and systemic lupus erythematosus and shown to ameliorate bone loss in glucocorticoid-treated patients, on bone mass and mechanical properties in young and old mice. Young 3.5-month-old and old 21-month-old female C57BL/6 mice received daily injections of 5 mg/kg/day mefloquine for 14 days. Aging resulted in the expected changes in bone volume and mechanical properties. In old mice mefloquine administration reversed the lower vertebral cancellous bone volume and bone formation; and had modest effects on cortical bone volume, thickness, and moment of inertia. Mefloquine administration did not change the levels of the circulating bone formation markers P1NP or alkaline phosphatase, whereas levels of the resorption marker CTX showed trends towards increase with mefloquine treatment. In addition, and as expected, aging bones exhibited an accumulation of active caspase3-expressing osteocytes and higher expression of apoptosis-related genes compared to young mice, which were not altered by mefloquine administration at either age. In young animals, mefloquine induced higher periosteal bone formation, but lower endocortical bone formation. Further, osteoclast numbers were higher on the endocortical bone surface and circulating CTX levels were increased, in mefloquine- compared to vehicle-treated young mice. Consistent with this, addition of mefloquine to bone marrow cells isolated from young mice led to increased osteoclastic gene expression and a tendency towards increased osteoclast numbers in vitro. Taken together our findings identify the age and bone-site specific skeletal effects of mefloquine. Further, our results highlight a beneficial effect of mefloquine administration on vertebral cancellous bone mass in old animals, raising the possibility of using this pharmacologic inhibitor to preserve skeletal health with aging

Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape

Lobe dynamics and escape from a potential well are general frameworks introduced to study phase space transport in chaotic dynamical systems. While the former approach studies how regions of phase space are transported by reducing the flow to a two-dimensional map, the latter approach studies the phase space structures that lead to critical events by crossing periodic orbit around saddles. Both of these frameworks require computation with curves represented by millions of points-computing intersection points between these curves and area bounded by the segments of these curves-for quantifying the transport and escape rate. We present a theory for computing these intersection points and the area bounded between the segments of these curves based on a classification of the intersection points using equivalence class. We also present an alternate theory for curves with nontransverse intersections and a method to increase the density of points on the curves for locating the intersection points accurately.The numerical implementation of the theory presented herein is available as an open source software called Lober. We used this package to demonstrate the application of the theory to lobe dynamics that arises in fluid mechanics, and rate of escape from a potential well that arises in ship dynamics.Comment: 33 pages, 17 figure

Smooth-filamental transition of active tracer fields stirred by chaotic advection

The spatial distribution of interacting chemical fields is investigated in the non-diffusive limit. The evolution of fluid parcels is described by independent dynamical systems driven by chaotic advection. The distribution can be filamental or smooth depending on the relative strength of the dispersion due to chaotic advection and the stability of the chemical dynamics. We give the condition for the smooth-filamental transition and relate the H\"older exponent of the filamental structure to the Lyapunov exponents. Theoretical findings are illustrated by numerical experiments.Comment: 4 pages, 3 figure

Jets, Stickiness and Anomalous Transport

Dynamical and statistical properties of the vortex and passive particle advection in chaotic flows generated by four and sixteen point vortices are investigated. General transport properties of these flows are found anomalous and exhibit a superdiffusive behavior with typical second moment exponent (\mu \sim 1.75). The origin of this anomaly is traced back to the presence of coherent structures within the flow, the vortex cores and the region far from where vortices are located. In the vicinity of these regions stickiness is observed and the motion of tracers is quasi-ballistic. The chaotic nature of the underlying flow dictates the choice for thorough analysis of transport properties. Passive tracer motion is analyzed by measuring the mutual relative evolution of two nearby tracers. Some tracers travel in each other vicinity for relatively large times. This is related to an hidden order for the tracers which we call jets. Jets are localized and found in sticky regions. Their structure is analyzed and found to be formed of a nested sets of jets within jets. The analysis of the jet trapping time statistics shows a quantitative agreement with the observed transport exponent.Comment: 17 pages, 17 figure

O(1/N_f) Corrections to the Thirring Model in 2<d<4

The Thirring model, that is, a relativistic field theory of fermions with a contact interaction between vector currents, is studied for dimensionalities 2<d<4 using the 1/N_f expansion, where N_f is the number of fermion species. The model is found to have no ultraviolet divergences at leading order provided a regularization respecting current conservation is used. Explicit O(1/N_f) corrections are computed, and the model shown to be renormalizable at this order in the massless limit; renormalizability appears to hold to all orders due to a special case of Weinberg's theorem. This implies there is a universal amplitude for four particle scattering in the asymptotic regime. Comparisons are made with both the Gross-Neveu model and QED.Comment: 22 pages in plain TeX, with 7 figs included using psfig.tex (Minor conceptual changes - algebra unaffected