Particle trajectories in linearized irrotational shallow water flows

We investigate the particle trajectories in an irrotational shallow water flow over a flat bed as periodic waves propagate on the water's free surface. Within the linear water wave theory, we show that there are no closed orbits for the water particles beneath the irrotational shallow water waves. Depending on the strength of underlying uniform current, we obtain that some particle trajectories are undulating path to the right or to the left, some are looping curves with a drift to the right and others are parabolic curves or curves which have only one loop

Leukocyte chemotaxis: from lysosomes to motility

Chemoattractants direct the extravasation of leukocytes to the site of immune response. New data highlight the role of synaptotagmins and Rab proteins in leukocyte chemotaxis

A comprehensive insight in the MOCVD of aluminum through interaction between reactive transport modeling and targeted growth experiments

Growth experiments and reactive transport modeling were combined to formulate a comprehensive predictive model for aluminum growth from dimethylethylamine alane. The growth-rate profile was experimentally investigated as a function of substrate temperature. The reactive transport model, built under the computational fluid dynamics software PHOENICS, was used to reproduce the experimental measurements and to contribute to the understanding of the aluminum growth process, under sub-atmospheric pressure conditions. The growth mechanism of aluminum films was based on well established in literature reaction order and activation energy of homogeneous and heterogeneous chemical reactions. The reactive transport model was used further to investigate the effect of some key operating parameters on the process output. Simulation results are suggestive of modifications in the operating parameters that could enhance the growth rate and the spatial uniformity of the film thickness

Coercivity and stability results for an extended Navier-Stokes system

In this article we study a system of equations that is known to {\em extend} Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergence-free. Our aim is to contribute to an understanding of the role of divergence and pressure in developing energy estimates capable of controlling the nonlinear terms. We address questions of global existence and stability in bounded domains with no-slip boundary conditions. Even in two space dimensions, global existence is open in general, and remains so, primarily due to the lack of a self-contained $L^2$ energy estimate. However, through use of new $H^1$ coercivity estimates for the linear equations, we establish a number of global existence and stability results, including results for small divergence and a time-discrete scheme. We also prove global existence in 2D for any initial data, provided sufficient divergence damping is included.Comment: 29 pages, no figure

Shape optimization of a showerhead system for the control of growth uniformity in a MOCVD reactor using CFD-based evolutionary algorithms

A steady state, laminar flow coupled with heat transfer, gas-phase and surface chemistry, is numerically solved for the optimal design of a showerhead gas delivery system in an axis-symmetrical MOCVD reactor. The design method involves an evolutionary algorithm based on CFD simulations. A finite-volume CFD code for aluminum growth provides the numerical predictions of the growth rate and its spatial variation over the substrate. A multilevel evolutionary algorithm is used to continuously adjust the shape of the shower plate so as to minimize the spatial variation of the growth rate. A 5-variable parameterization of the shower plate is investigated and a near-optimal solution is proposed and compared to the original configuration of the shower plate

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

Aproksimacija drugog reda za srednji pomak čestice uronjene u toplinsku kupku uz prisustvo vanjske sile

The interaction of a quantum particle with a heat bath of quantum oscillators under the influence of an external force has been studied and the mean displacement of this particle has been computed up to second order approximation in the propagator. The heat bath has been considered as Brownian and the characteristic frequencies are close to the characteristic frequency of the particle. The mean displacement of the particle has been found to oscillate with time. The temperature dependence of the mean displacement follows an exponential function of e-1/T.Razmatrano je međudjelovanje kvantne čestice s toplinskom kupkom kvantnih oscilatora uz prisustvo vanjske sile. Određen je srednji pomak čestice do približenja drugog reda za propagator. Toplinska kupka Brownovskog je tipa s karakterističnim frekvencijama bliskim karakterističnoj frekvenciji čestice. Nađeno je da srednji pomak čestice oscilira u vremenu

Ionization potentials in the limit of large atomic number

By extrapolating the energies of non-relativistic atoms and their ions with up to 3000 electrons within Kohn-Sham density functional theory, we find that the ionization potential remains finite and increases across a row, even as $Z\rightarrow\infty$. The local density approximation becomes chemically accurate (and possibly exact) in some cases. Extended Thomas-Fermi theory matches the shell-average of both the ionization potential and density change. Exact results are given in the limit of weak electron-electron repulsion.Comment: 4 pages, 5 figure

Excessive weight gain after remission of depression in a schizophrenic patient treated with risperidone: case report

BACKGROUND: The use of atypical antipsychotics in schizophrenic patients has been associated with a risk of weight gain. Similarly, recovery from depression is often followed by improved appetite, greater food intake and potential increase in weight. CASE PRESENTATION: A Caucasian 33-year-old schizophrenic female patient was being treated with 6 mg/day of risperidone and 15 mg/day of clorazepate. She developed depressive symptomatology and 40 mg/day of fluoxetine was gradually added to her treatment regimen for about 9 months. After the remission of depression, and the discontinuation of fluoxetine, she experienced an increase in appetite and subsequently excessive weight gain of 52 kg. Re-administration of fluoxetine did not reverse the situation. The patient developed diabetes mellitus, which was successfully controlled with metformin 1700 mg/day. The addition at first of orlistat 360 mg/day and later of topiramate 200 mg/day has helped her to lose a significant part of the weight gained (30 kg). CONCLUSION: The case suggests a probable association between the remission of depressive symptomatology and weight gain in a schizophrenic patient