A stochastic-Lagrangian particle system for the Navier-Stokes equations

This paper is based on a formulation of the Navier-Stokes equations developed by P. Constantin and the first author (\texttt{arxiv:math.PR/0511067}, to appear), where the velocity field of a viscous incompressible fluid is written as the expected value of a stochastic process. In this paper, we take $N$ copies of the above process (each based on independent Wiener processes), and replace the expected value with $\frac{1}{N}$ times the sum over these $N$ copies. (We remark that our formulation requires one to keep track of $N$ stochastic flows of diffeomorphisms, and not just the motion of $N$ particles.) We prove that in two dimensions, this system of interacting diffeomorphisms has (time) global solutions with initial data in the space \holderspace{1}{\alpha} which consists of differentiable functions whose first derivative is $\alpha$ H\"older continuous (see Section \ref{sGexist} for the precise definition). Further, we show that as $N \to \infty$ the system converges to the solution of Navier-Stokes equations on any finite interval $[0,T]$. However for fixed $N$, we prove that this system retains roughly $O(\frac{1}{N})$ times its original energy as $t \to \infty$. Hence the limit $N \to \infty$ and $T\to \infty$ do not commute. For general flows, we only provide a lower bound to this effect. In the special case of shear flows, we compute the behaviour as $t \to \infty$ explicitly.Comment: v3: Typo fixes, and a few stylistic changes. 17 pages, 2 figure

Tibial tuberosity fracture in adult as an unusual pattern of injury

Tibial tuberosity avulsion is an uncommon fracture in adults, such lesions typically seen in adolescent male with well-developed quadriceps, ligaments when they are stronger than growth plate. We described a case of 51-year-old gentlemen had direct trauma to left knee, no risk factors were identified, not able to walk, difficulty in straight leg raise test, radiograph of left knee showed tibial tuberosity avulsion fracture. The fracture was treated with open reduction and internal fixation, f/u with successful rehabilitation which results in good range of motion and excellent function at knee joint. The aim of study is present unusual and rare case of tibial tuberosity Avulsion fracture in adult, early diagnosis, surgical mode of treatment, post-surgery rehabilitation and possible complications

Covariant Calculation of General Relativistic Effects in an Orbiting Gyroscope Experiment

We carry out a covariant calculation of the measurable relativistic effects in an orbiting gyroscope experiment. The experiment, currently known as Gravity Probe B, compares the spin directions of an array of spinning gyroscopes with the optical axis of a telescope, all housed in a spacecraft that rolls about the optical axis. The spacecraft is steered so that the telescope always points toward a known guide star. We calculate the variation in the spin directions relative to readout loops rigidly fixed in the spacecraft, and express the variations in terms of quantities that can be measured, to sufficient accuracy, using an Earth-centered coordinate system. The measurable effects include the aberration of starlight, the geodetic precession caused by space curvature, the frame-dragging effect caused by the rotation of the Earth and the deflection of light by the Sun.Comment: 7 pages, 1 figure, to be submitted to Phys. Rev.

Quantum Entanglement and Teleportation in Higher Dimensional Black Hole Spacetimes

We study the properties of quantum entanglement and teleportation in the background of stationary and rotating curved space-times with extra dimensions. We show that a maximally entangled Bell state in an inertial frame becomes less entangled in curved space due to the well-known Hawking-Unruh effect. The degree of entanglement is found to be degraded with increasing the extra dimensions. For a finite black hole surface gravity, the observer may choose higher frequency mode to keep high level entanglement. The fidelity of quantum teleporation is also reduced because of the Hawking-Unruh effect. We discuss the fidelity as a function of extra dimensions, mode frequency, black hole mass and black hole angular momentum parameter for both bosonic and fermionic resources.Comment: 15 pages, 10 figures,contents expande

MAR-Mediated Dystrophin Expression in Mesoangioblasts for Duchenne Muscular Dystrophy Cell Therapy

A cornerstone of autologous cell therapy for Duchenne muscular dystrophy is the engineering of suitable cells to express dystrophin in a stable fashion upon differentiation to muscle fibers. Most viral transduction methods are typically restricted to the expression of truncated recombinant dystrophin derivatives and by the risk of insertional mutagenesis, while non-viral vectors often suffer from inefficient transfer, expression and/or silencing

Laser isotope separation of <SUP>13</SUP>C: a comparative study

IR laser chemistry of (CF3Br/Cl2) mixture and neat CF2HCl are examined in the context of 13C enrichment. Decomposition extent, enrichment factor and energy absorbed are measured for both systems at their respective optimum conditions. A direct comparison is obtained by keeping extraneous factors such as laser, its pulse duration, cell, irradiation geometry etc. the same. The halogen scavenged CF3Br MPD requires lower fluence compared to neat CF2HCl irradiation. Overall throughput for a product with 60-65% 13C content in a single stage is the same for both systems requiring a similar amount of energy. However, at lower enrichment levels, CF2HCl MPD is better than (CF3Br/Cl2) photolysis in terms of both product yield and energy absorption

Progress in development of tapes and magnets made from Bi-2223 superconductors

Long lengths of (Bi,Pb)2Sr2Ca2Cu3O(x) tapes made by powder-in-tube processing have been wound into coils. Performance of the coils has been measured at temperatures of 4.2 to 77 K, and microstructures have been examined by x-ray diffraction and electron microscopy and then related to superconducting properties. A summary of recent results and an overview of future goals are presented

Perturbative stability of the QCD analysis of DIS data

We perform pQCD analysis of the existing DIS data for charged leptons with account of corrections up to the NNLO. The parton distributions, value of strong coupling constant, and high-twist terms are extracted and their stability with respect to account of the NNLO corrections is analyzed. All the quantities are generally stable within their experimental errors. Obtained value of the strong coupling constant is $\alpha_s^{\rm NNLO}(M_{\rm Z})=0.1143\pm 0.0014 ({\rm exp})$ with a guess $\alpha_s^{\rm NNNLO}(M_{\rm Z})\sim 0.113$.Comment: 4 pages, LATEX, 3 figures (EPS). Talk presented at the 37th Rencontres de Moriond, QCD and Hadronic Interactions, Les Arcs 1800 (France), March 16-23 200