Mixing of fermion fields of opposite parities and baryon resonances

We consider a loop mixing of two fermion fields of opposite parities whereas the parity is conserved in a Lagrangian. Such kind of mixing is specific for fermions and has no analogy in boson case. Possible applications of this effect may be related with physics of baryon resonances. The obtained matrix propagator defines a pair of unitary partial amplitudes which describe the production of resonances of spin $J$ and different parity ${1/2}^{\pm}$ or ${3/2}^{\pm}$. The use of our amplitudes for joint description of $\pi N$ partial waves $P_{13}$ and $D_{13}$ shows that the discussed effect is clearly seen in these partial waves as the specific form of interference between resonance and background. Another interesting application of this effect may be a pair of partial waves $S_{11}$ and $P_{11}$ where the picture is more complicated due to presence of several resonance states.Comment: 22 pages, 6 figures, more detailed comparison with \pi N PW

Is constant needle motion during soft tissue filler injections a safer procedure?:A theoretical mathematical model for evaluating patient safety

BackgroundThe safety rationale behind the constant needle motion injection technique is based on the assumption that due to the constant needle motion and simultaneous soft tissue filler material administration a smaller amount of product per area may be injected into an artery if an artery within the range of the moving needle is inadvertently entered.ObjectiveTo perform mathematical calculations for determining the probability for causing intra-arterial product administration when constantly moving the needle during facial aesthetic soft tissue filler injections.MethodsThis study was designed as a theoretical investigation into the probabilities for causing adverse events due to intravascular injection of soft tissue filler material when constantly moving a 27-G needle during facial soft tissue filler administration.ResultsIt was revealed that with a higher number of conducted injection passes a greater soft tissue area can be covered by the needle. The odds of encountering an artery within the covered soft tissue volume and the odds of injecting any volume greater than zero into the arterial blood stream increases with the number of performed injection passes. This increase is greatest between 1 and 10 performed injection passes.ConclusionThis model demonstrates that the constant needle motion technique increases the probability of encountering an artery within the treatment area and thus increases the odds for intra-arterial product administration. The constant needle motion technique does not increase safety but rather may increase the odds of causing intra-arterial product administration with the respective adverse consequences for the patient

Meromorphic Approximants to Complex Cauchy Transforms with Polar Singularities

We study AAK-type meromorphic approximants to functions $F$, where $F$ is a sum of a rational function $R$ and a Cauchy transform of a complex measure $\lambda$ with compact regular support included in $(-1,1)$, whose argument has bounded variation on the support. The approximation is understood in $L^p$-norm of the unit circle, $p\geq2$. We obtain that the counting measures of poles of the approximants converge to the Green equilibrium distribution on the support of $\lambda$ relative to the unit disk, that the approximants themselves converge in capacity to $F$, and that the poles of $R$ attract at least as many poles of the approximants as their multiplicity and not much more.Comment: 39 pages, 4 figure

Fractional Kinetics for Relaxation and Superdiffusion in Magnetic Field

We propose fractional Fokker-Planck equation for the kinetic description of relaxation and superdiffusion processes in constant magnetic and random electric fields. We assume that the random electric field acting on a test charged particle is isotropic and possesses non-Gaussian Levy stable statistics. These assumptions provide us with a straightforward possibility to consider formation of anomalous stationary states and superdiffusion processes, both properties are inherent to strongly non-equilibrium plasmas of solar systems and thermonuclear devices. We solve fractional kinetic equations, study the properties of the solution, and compare analytical results with those of numerical simulation based on the solution of the Langevin equations with the noise source having Levy stable probability density. We found, in particular, that the stationary states are essentially non-Maxwellian ones and, at the diffusion stage of relaxation, the characteristic displacement of a particle grows superdiffusively with time and is inversely proportional to the magnetic field.Comment: 15 pages, LaTeX, 5 figures PostScrip

Strong asymptotics for Jacobi polynomials with varying nonstandard parameters

Strong asymptotics on the whole complex plane of a sequence of monic Jacobi polynomials $P_n^{(\alpha_n, \beta_n)}$ is studied, assuming that $$\lim_{n\to\infty} \frac{\alpha_n}{n}=A, \qquad \lim_{n\to\infty} \frac{\beta _n}{n}=B,$$ with $A$ and $B$ satisfying $A > -1$, $B>-1$, $A+B < -1$. The asymptotic analysis is based on the non-Hermitian orthogonality of these polynomials, and uses the Deift/Zhou steepest descent analysis for matrix Riemann-Hilbert problems. As a corollary, asymptotic zero behavior is derived. We show that in a generic case the zeros distribute on the set of critical trajectories $\Gamma$ of a certain quadratic differential according to the equilibrium measure on $\Gamma$ in an external field. However, when either $\alpha_n$, $\beta_n$ or $\alpha_n+\beta_n$ are geometrically close to $\Z$, part of the zeros accumulate along a different trajectory of the same quadratic differential.Comment: 31 pages, 12 figures. Some references added. To appear in Journal D'Analyse Mathematiqu

Kramers escape driven by fractional Brownian motion

We investigate the Kramers escape from a potential well of a test particle driven by fractional Gaussian noise with Hurst exponent 0<H<1. From a numerical analysis we demonstrate the exponential distribution of escape times from the well and analyze in detail the dependence of the mean escape time as function of H and the particle diffusivity D. We observe different behavior for the subdiffusive (antipersistent) and superdiffusive (persistent) domains. In particular we find that the escape becomes increasingly faster for decreasing values of H, consistent with previous findings on the first passage behavior. Approximate analytical calculations are shown to support the numerically observed dependencies.Comment: 14 pages, 16 figures, RevTeX

First passage and arrival time densities for L\'evy flights and the failure of the method of images

We discuss the first passage time problem in the semi-infinite interval, for homogeneous stochastic Markov processes with L{\'e}vy stable jump length distributions $\lambda(x)\sim\ell^{\alpha}/|x|^{1+\alpha}$ ($|x|\gg\ell$), namely, L{\'e}vy flights (LFs). In particular, we demonstrate that the method of images leads to a result, which violates a theorem due to Sparre Andersen, according to which an arbitrary continuous and symmetric jump length distribution produces a first passage time density (FPTD) governed by the universal long-time decay $\sim t^{-3/2}$. Conversely, we show that for LFs the direct definition known from Gaussian processes in fact defines the probability density of first arrival, which for LFs differs from the FPTD. Our findings are corroborated by numerical results.Comment: 8 pages, 3 figures, iopart.cls style, accepted to J. Phys. A (Lett

Linear Relaxation Processes Governed by Fractional Symmetric Kinetic Equations

We get fractional symmetric Fokker - Planck and Einstein - Smoluchowski kinetic equations, which describe evolution of the systems influenced by stochastic forces distributed with stable probability laws. These equations generalize known kinetic equations of the Brownian motion theory and contain symmetric fractional derivatives over velocity and space, respectively. With the help of these equations we study analytically the processes of linear relaxation in a force - free case and for linear oscillator. For a weakly damped oscillator we also get kinetic equation for the distribution in slow variables. Linear relaxation processes are also studied numerically by solving corresponding Langevin equations with the source which is a discrete - time approximation to a white Levy noise. Numerical and analytical results agree quantitatively.Comment: 30 pages, LaTeX, 13 figures PostScrip

КВАЗІСТАТИЧНА ТЕРМОПРУЖНІСТЬ НЕОДНОРІДНИХ ЕЛЕМЕНТІВ МЕХАНІЗМІВ І МАШИН У СУЧАСНИХ ХАРЧОВИХ ТЕХНОЛОГІЯХ

There was suggested the investigation method of the influence of the presented non-stationary environment temperature conditions on the course of physical and mechanical processes in heterogeneous plate and cylinder structures of the working equipment, hardware tools and machinery of modern food production. Following this aim there was formulated a corresponding quasistatic problem of thermoelasticity for inhomogeneous and piecewise homogeneous structures and compound bodies or bodies in the form of basic matrices containing foreign (the through or non-through) inclusions of various shapes and species. These are new problems (mainly three-dimensional) of thermomechanics inhomogeneous structures. Therefore on output of the corresponding Dyugamelya&nbsp;–&nbsp;Neumann's relations there is taken into account that the whole complex of physical-mechanical, thermalphysical and geometric characteristics of the inhomogeneous structure bodies as a single unit (Lame’s coefficients, Young's modulus and shear modulus, Poisson's ratio and the temperature coefficient of linear expansion) are functions of cylindrical coordinates. On the basis of additional hypotheses and assumptions the construction of such layered and composite environment models allows to consider the microstructure of the material and to determine the macroscopic parameters; that is, to solve problems of thermomechanics multicomponent media. Taking into account the hypothesis of immutable rules in the work there were derived examples for the components of the stress tensor and interconnection of differential equations system of second order thermoelasticity in partial derivatives for displacements vector components. &nbsp;Предполагается метод исследования влияния заданых нестационарных температурных режимов внешней среды на физико–механические процессы в неоднородных пластинчатых и цилиндрических структурах для рабочего оборудования механизмов и машин современных пищевых производств. Для этого сформулировано соответствующую квазистатическую задачу термоупругости для  неоднородных структур ,кусочно–однородных и составных тел.,также для тел, а также для тел в виде основных матриц, содержащих инородные (сквозные или несквозные) включения различной формы и вида. Такого рода задачи (преимущественно трехмерные) составляют новое направления термомеханики неоднородных структур. Для этого при выводе соответствующих соотношений Дюгамеля–Неймана учитывается, что целый комплекс теплофизических, физико–механических и геометрических характеристик тела неоднородной структуры, как единого  целого (таких как коэффициенты Ляме, модуль Юнга и модуль сдвига,коэффициент Пуассона и температурный коэффициент линейного расширения) являются функциями цилиндрических координат. Построение таких моделей сложных и композитних сред позволяет, на основании некоторых добавочных гіпотез, учитывать как микроструктуру материала, так и определять макроскопические параметры – тоесть решать задачи термомеханики многокомпонентных сред. С учетом гипотезы неизменных нормалей, в работе выведены соотношения для компонент тензора напряжений и взаимосвязанной системы дифференциальных уравнений термоупругости второго порядка в частных производных для компонент вектора перемещений.Запропоновано метод дослідження впливу заданих нестаціонарних температурних режимів навколишнього середовища на перебіг фізико-механічних процесів у неоднорідних пластинчастих та циліндричних структурах робочого обладнання та устаткування механізмів і машин сучасних харчових виробництв. Для цього сформульовано відповідну квазістатичну задачу термопружності для неоднорідних структур, кусково-однорідних та складених тіл,або тіл у вигляді основних матриць, що містять чужорідні (наскрізні або ненаскрізні) включення різної форми та вигляду. Це нові задачі (переважно трьохвимірні) неоднорідних структур. Для&nbsp; цього&nbsp; при&nbsp; виводі&nbsp; відповідних співвідношень Дюгамеля-Неймана враховано, що весь комплекс фізико-механічних , теплофізичних та геометричних характеристик тіла неоднорідної структури, як єдиного цілого, (коефіцієнти Ляме, модуль Юнга та модуль зсуву, коефіцієнт Пуассона та температурний коефіцієнт лінійного розширення) є функціями циліндричних координат. Побудова таких моделей шаруватих і композитних середовищ,дозволяє на основі додаткових гіпотез і припущень враховувати як мікроструктуру матеріалу, так і визначити макроскопічні&nbsp; параметри&nbsp; – тобто&nbsp; розв'язувати&nbsp; задачі&nbsp; термомеханіки багатокомпонентних середовищ. Із врахуванням гіпотези незмінних нормалей, в роботі виведено вирази для компонентів тензора напружень та взаємозв'язаної системи диференціальних рівнянь термопружності другого порядку у частинних похідних для компонентів вектора переміщень. &nbsp