Versal deformations of a Dirac type differential operator

If we are given a smooth differential operator in the variable $x\in {\mathbb R}/2\pi {\mathbb Z},$ its normal form, as is well known, is the simplest form obtainable by means of the \mbox{Diff}(S^1)-group action on the space of all such operators. A versal deformation of this operator is a normal form for some parametric infinitesimal family including the operator. Our study is devoted to analysis of versal deformations of a Dirac type differential operator using the theory of induced \mbox{Diff}(S^1)-actions endowed with centrally extended Lie-Poisson brackets. After constructing a general expression for tranversal deformations of a Dirac type differential operator, we interpret it via the Lie-algebraic theory of induced \mbox{Diff}(S^1)-actions on a special Poisson manifold and determine its generic moment mapping. Using a Marsden-Weinstein reduction with respect to certain Casimir generated distributions, we describe a wide class of versally deformed Dirac type differential operators depending on complex parameters

Lattice Boltzmann method simulations of Stokes number effects on particle trajectories in a wall-bounded flow

Experimental studies of particle-laden flows in a pipe show that the spatial distribution of the particles across the radius of the pipe is dependent on the Stokes number [Timothy C. W. Lau & Graham J. Nathan, J. Fluid Mech. 2014]. It has been suggested that the Saffman lift effect [Saffman, 1965] makes a significant contribution to this spatial distribution. The Saffman lift effect has been studied in prior works by several authors and the relative contribution of the lift force has been studied within the context of various forces acting on particles in a flow. The lift force depends on the particle size and the velocity of the particle relative to the gas phase. In this study, the lattice Boltzmann method is employed to study the mechanism of particle migration of an isolated particle moving in a wall-bounded flow. The boundary condition proposed by Bouzidi et al. [2001][23], which involves the bounce-back scheme modified to account for fractional link distances between the wall and the fluid node, is used for the particles. The force acting on the particle is found by adding the momentum lost by all the fluid molecules as they bounce back from the particle surface along the link joining the particle and the fluid boundary nodes. This force is used to update the position of the particle after every streaming step. The torque acting on the particle is determined similarly and is used to update the angular velocity of the particle. It is found that at low Stokes number the particle behaves like a neutrally buoyant particle and exhibits the Segré-Silberberg effect. With increasing Stokes number, the particle exhibits an oscillatory behavior about its mean position. For large Stokes number, the particle oscillations are significant. If the ratio of channel height to particle diameter is increased, the particle moves closer to the wall and the oscillatory behavior is evident at lower Stokes number.Anand Samuel Jebakumar, Kannan N.Premnath, John Abraha

Vasodilator response to galvanic current stimulation of the skin accurately detects acetylsalicylic acid intake: A study in 400 vascular patients

Background and aims The first cause of low-dose acetylsalicylic-acid (ASA) inefficacy is poor adherence to treatment. No non-invasive technique is available to assess ASA intake. Current-induced vasodilation (CIV) was found abolished in healthy volunteers after low-dose ASA intake. We tested clinical characteristics, treatments, and comorbid conditions influencing CIV amplitude in vascular patients. Methods CIV was tested in 400 patients (277 males and 123 females, aged 65.4 ± 13.4 years). We focused on clinical characteristics, treatments, and comorbid conditions as covariates of CIV amplitude. We studied the CIV amplitude to covariate relationships with multivariate linear regression and receiver operating characteristics (ROC). Results The multivariate linear model determined that ASA intake within the last 48 h and the interaction between ASA intake and body mass index (BMI) were the sole covariates associated with CIV amplitude. For the whole population, the area under the ROC curve (AUC) for CIV to predict ASA intake was 0.853 [95% confidence interval (CI): 0.814–0.892]. Considering separately the areas observed for non-obese (BMI ≤30, n = 303) and obese (BMI>30, n = 93) patients, the AUC [95% CI] was 0.873 [0.832–0.915] and 0.776 [0.675–0.878], respectively (p = 0.083). Conclusions ASA is the only drug that affects the amplitude of CIV response observed after galvanic current application to the skin of vascular patients. CIV depends on BMI but not age or gender. As such, CIV appears to be a potential objective marker of ASA intake and could facilitate future non-invasive assessments of adherence to ASA treatment

Mass loss by a scalar charge in an expanding universe

We study the phenomenon of mass loss by a scalar charge -- a point particle that acts a source for a noninteracting scalar field -- in an expanding universe. The charge is placed on comoving world lines of two cosmological spacetimes: a de Sitter universe, and a spatially-flat, matter-dominated universe. In both cases, we find that the particle's rest mass is not a constant, but that it changes in response to the emission of monopole scalar radiation by the particle. In de Sitter spacetime, the particle radiates all of its mass within a finite proper time. In the matter-dominated cosmology, this happens only if the charge of the particle is sufficiently large; for smaller charges the particle first loses some of its mass, but then regains it all eventually.Comment: 11 pages, RevTeX4, Accepted for Phys. Rev.

A spatially-VSL gravity model with 1-PN limit of GRT

A scalar gravity model is developed according the 'geometric conventionalist' approach introduced by Poincare (Einstein 1921, Poincare 1905, Reichenbach 1957, Gruenbaum1973). In principle this approach allows an alternative interpretation and formulation of General Relativity Theory (GRT), with distinct i) physical congruence standard, and ii) gravitation dynamics according Hamilton-Lagrange mechanics, while iii) retaining empirical indistinguishability with GRT. In this scalar model the congruence standards have been expressed as gravitationally modified Lorentz Transformations (Broekaert 2002). The first type of these transformations relate quantities observed by gravitationally 'affected' (natural geometry) and 'unaffected' (coordinate geometry) observers and explicitly reveal a spatially variable speed of light (VSL). The second type shunts the unaffected perspective and relates affected observers, recovering i) the invariance of the locally observed velocity of light, and ii) the local Minkowski metric (Broekaert 2003). In the case of a static gravitation field the model retrieves the phenomenology implied by the Schwarzschild metric. The case with proper source kinematics is now described by introduction of a 'sweep velocity' field w: The model then provides a hamiltonian description for particles and photons in full accordance with the first Post-Newtonian approximation of GRT (Weinberg 1972, Will 1993).Comment: v1: 11 pages, GR17 conf. paper, Dublin 2004, v2: WEP issue solved, section on acceleration transformation added, text improved, more references, same results, v3: typos removed, footnotes, added and references updated, v4: appendix added, improved tex

The nonabelian Liouville-Arnold integrability by quadratures problem: a symplectic approach

A symplectic theory approach is devised for solving the problem of algebraic-analytical construction of integral submanifold imbeddings for integrable (via the nonabelian Liouville-Arnold theorem) Hamiltonian systems on canonically symplectic phase spaces

Delayed Apoptotic Cell Clearance and Lupus-like Autoimmunity in Mice Lacking the c-mer Membrane Tyrosine Kinase

Mice lacking the membrane tyrosine kinase c-mer have been shown to have altered macro-phage cytokine production and defective phagocytosis of apoptotic cells despite normal phagocytosis of other particles. We show here that c-mer–deficient mice have impaired clearance of infused apoptotic cells and that they develop progressive lupus-like autoimmunity, with antibodies to chromatin, DNA, and IgG. The autoimmunity appears to be driven by endogenous antigens, with little polyclonal B cell activation. These mice should be an excellent model for studying the role of apoptotic debris as an immunogenic stimulus for systemic autoimmunity

p-wave phase shift and scattering length of 6^6Li

We have calculated the p-wave phase shifts and scattering length of $^6$Li. For this we solve the $p$ partial wave Schr\"odinger equation and analyze the validity of adopting the semiclassical solution to evaluate the constant factors in the solution. Unlike in the $s$ wave case, the semiclassical solution does not provide unique value of the constants. We suggest an approximate analytic solution, which provides reliable results in special cases. Further more, we also use the variable phase method to evaluate the phase shifts. The p-wave scattering lengths of $^{132}$Cs and $^{134}$Cs are calculated to validate the schemes followed. Based on our calculations, the value of the $p$ wave scattering length of $^6$Li is $-45a_o$.Comment: 10 figure