A three-loop check of the 'a - maximization' in SQCD with adjoint(s)

The 'a - maximization' was introduced by K. Inrtiligator and B. Wecht for finding anomalous dimensions of chiral superfields at the IR fixed points of the RG flow. Using known explicit calculations of anomalous dimensions in the perturbation theory of SQCD (with one or two additional adjoint fields), it is checked here at the three-loop level.Comment: 5 pages; the title changed, the text improved and expande

Statistics of anomalously localized states at the center of band E=0 in the one-dimensional Anderson localization model

We consider the distribution function $P(|\psi|^{2})$ of the eigenfunction amplitude at the center-of-band (E=0) anomaly in the one-dimensional tight-binding chain with weak uncorrelated on-site disorder (the one-dimensional Anderson model). The special emphasis is on the probability of the anomalously localized states (ALS) with $|\psi|^{2}$ much larger than the inverse typical localization length $\ell_{0}$. Using the solution to the generating function $\Phi_{an}(u,\phi)$ found recently in our works we find the ALS probability distribution $P(|\psi|^{2})$ at $|\psi|^{2}\ell_{0} >> 1$. As an auxiliary preliminary step we found the asymptotic form of the generating function $\Phi_{an}(u,\phi)$ at $u >> 1$ which can be used to compute other statistical properties at the center-of-band anomaly. We show that at moderately large values of $|\psi|^{2}\ell_{0}$, the probability of ALS at E=0 is smaller than at energies away from the anomaly. However, at very large values of $|\psi|^{2}\ell_{0}$, the tendency is inverted: it is exponentially easier to create a very strongly localized state at E=0 than at energies away from the anomaly. We also found the leading term in the behavior of $P(|\psi|^{2})$ at small $|\psi|^{2}<< \ell_{0}^{-1}$ and show that it is consistent with the exponential localization corresponding to the Lyapunov exponent found earlier by Kappus and Wegner and Derrida and Gardner.Comment: 25 pages, 9 figure

Semi-analytical dark matter halos and the Jeans equation

Although N-body studies of dark matter halos show that the density profiles, rho(r), are not simple power-laws, the quantity rho/sigma^3, where sigma(r) is the velocity dispersion, is in fact a featureless power-law over ~3 decades in radius. In the first part of the paper we demonstrate, using the semi-analytic Extended Secondary Infall Model (ESIM), that the nearly scale-free nature of rho/sigma^3 is a robust feature of virialized halos in equilibrium. By examining the processes in common between numerical N-body and semi-analytic approaches, we argue that the scale-free nature of rho/sigma^3 cannot be the result of hierarchical merging, rather it must be an outcome of violent relaxation. The empirical results of the first part of the paper motivate the analytical work of the second part of the paper, where we use rho/sigma^3 proportional to r^{-alpha} as an additional constraint in the isotropic Jeans equation of hydrostatic equilibrium. Our analysis shows that the constrained Jeans equation has different types of solutions, and in particular, it admits a unique ``periodic'' solution with alpha=1.9444. We derive the analytic expression for this density profile, which asymptotes to inner and outer profiles of rho ~ r^{-0.78}, and rho ~ r^{-3.44}, respectively.Comment: 37 pg, 14 fig. Accepted to ApJ: added two figures and extended discussion. Note that an earlier related paper (conference proceedings) astro-ph/0412442 has a mistake in eq.(2.2); the correct version is eq.(5) of the present submissio

The Radial Orbit Instability in Collisionless N-Body Simulations

Using a suite of self-gravitating, collisionless N-body models, we systematically explore a parameter space relevant to the onset and behavior of the radial orbit instability (ROI), whose strength is measured by the systemic axis ratios of the models. We show that a combination of two initial conditions, namely the velocity anisotropy and the virial ratio, determines whether a system will undergo ROI and exactly how triaxial the system will become. A third initial condition, the radial shape of the density profile, plays a smaller, but noticeable role. Regarding the dynamical development of the ROI, the instability a) begins after systems collapse to their most compact configuration and b) evolves fastest when a majority of the particles have radially anisotropic orbits while there is a lack of centrally-concentrated isotropic orbits. We argue that this is further evidence that self-reinforcing torques are the key to the onset of the ROI. Our findings support the idea that a separate orbit instability plays a role in halting the ROI.Comment: accepted for publication in ApJ. 9 figures in emulateapj styl

Disrupting the wall accumulation of human sperm cells by artificial corrugation

Many self-propelled microorganisms are attracted to surfaces. This makes their dynamics in restricted geometries very different from that observed in the bulk. Swimming along walls is beneficial for directing and sorting cells, but may be detrimental if homogeneous populations are desired, such as in counting microchambers. In this work, we characterize the motion of human sperm cells $60 \mu m$ long, strongly confined to $25 \mu m$ shallow chambers. We investigate the nature of the cell trajectories between the confining surfaces and their accumulation near the borders. Observed cell trajectories are composed of a succession of quasi-circular and quasi-linear segments. This suggests that the cells follow a path of intermittent trappings near the top and bottom surfaces separated by stretches of quasi-free motion in between the two surfaces, as confirmed by depth resolved confocal microscopy studies. We show that the introduction of artificial petal-shaped corrugation in the lateral boundaries removes the tendency of cells to accumulate near the borders, an effect which we hypothesize may be valuable for microfluidic applications in biomedicine.Comment: 9 pages, latex. In accepted version on April 14, v2: abstract modified, information added to Sec. II.A and experiments added to Sec. III.A and Fig.3. Sec. III.C was deleted. Requested references adde

Variation of the hopping exponent in disordered silicon MOSFETs

We observe a complex change in the hopping exponent value from 1/2 to 1/3 as a function of disorder strength and electron density in a sodium-doped silicon MOSFET. The disorder was varied by applying a gate voltage and thermally drifting the ions to different positions in the oxide. The same gate was then used at low temperature to modify the carrier concentration. Magnetoconductivity measurements are compatible with a change in transport mechanisms when either the disorder or the electron density is modified suggesting a possible transition from a Mott insulator to an Anderson insulator in these systems.Comment: 6 pages, 5 figure

Case management of malaria: Treatment and chemoprophylaxis

Malaria case management is a vital component of programmatic strategies for malaria control and elimination. Malaria case management encompasses prompt and effective treatment to minimise morbidity and mortality, reduce transmission and prevent the emergence and spread of antimalarial drug resistance. Malaria is an acute illness that may progress rapidly to severe disease and death, especially in non-immune populations, if not diagnosed early and promptly treated with effective drugs. In this article, the focus is on malaria case management, addressing treatment, monitoring for parasite drug resistance, and the impact of drug resistance on treatment policies; it concludes with chemoprophylaxis and treatment strategies for malaria elimination in South Africa

Maximally inhomogeneous G\"{o}del-Farnsworth-Kerr generalizations

It is pointed out that physically meaningful aligned Petrov type D perfect fluid space-times with constant zero-order Riemann invariants are either the homogeneous solutions found by G\"{o}del (isotropic case) and Farnsworth and Kerr (anisotropic case), or new inhomogeneous generalizations of these with non-constant rotation. The construction of the line element and the local geometric properties for the latter are presented.Comment: 4 pages, conference proceeding of Spanish Relativity Meeting (ERE 2009, Bilbao