333 research outputs found
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
Understanding Anomalous Transport in Intermittent Maps: From Continuous Time Random Walks to Fractals
We show that the generalized diffusion coefficient of a subdiffusive
intermittent map is a fractal function of control parameters. A modified
continuous time random walk theory yields its coarse functional form and
correctly describes a dynamical phase transition from normal to anomalous
diffusion marked by strong suppression of diffusion. Similarly, the probability
density of moving particles is governed by a time-fractional diffusion equation
on coarse scales while exhibiting a specific fine structure. Approximations
beyond stochastic theory are derived from a generalized Taylor-Green-Kubo
formula.Comment: 4 pages, 3 eps figure
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
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
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 (),
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 . 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
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 – 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.
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 цього при виводі 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 параметри – тобто розв'язувати задачі 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.
 
ANALYSIS OF THE MORTALITY STRUCTURE IN HEMODIALYSIS PATIENTS
Studies of the mortality structure in patients receiving hemodialysis (HD) remain relevant and are the basis for developing measures and recommendations directed to increase the lifetime of patients.
Aim. The aim was to study the assessment of death causes in patients who received programmed hemodialysis, based on the demographic and gender characteristics, the duration of dialysis treatment.
Methods. Mortality causes in 137 patients who received programmed hemodialysis from 2007 to 2011 years in Kyiv City Scientific and Practical Center of Nephrology an Dialysis were analyzed.
Results. The leading cause of death was cardiovascular complications, but their decreasing has been observed since 2008. Fatality rate in young and middle- aged women with cardiovascular diseases (CVD) was almost two times higher than that of men. At the same time CVD is a predominant cause of men’s death at the age older than 44. Cerebrovascular complications were permanently in the second place of the mortality structure. About 30% of deaths occurred during the first 90 days of HD treatment, 72,5% of them were among males.
Conclusion. Gender characteristics influence the structure of death causes in patients received programmed hemodialysis depending on age
Construction of uricase-overproducing strains of Hansenula polymorpha and its application as biological recognition element in microbial urate biosensor
<p>Abstract</p> <p>Background</p> <p>The detection and quantification of uric acid in human physiological fluids is of great importance in the diagnosis and therapy of patients suffering from a range of disorders associated with altered purine metabolism, most notably gout and hyperuricaemia. The fabrication of cheap and reliable urate-selective amperometric biosensors is a challenging task.</p> <p>Results</p> <p>A urate-selective microbial biosensor was developed using cells of the recombinant thermotolerant methylotrophic yeast <it>Hansenula polymorpha </it>as biorecognition element. The construction of uricase (UOX) producing yeast by over-expression of the uricase gene of <it>H. polymorpha </it>is described. Following a preliminary screening of the transformants with increased UOX activity in permeabilized yeast cells the optimal cultivation conditions for maximal UOX yield namely a 40-fold increase in UOX activity were determined.</p> <p>The UOX producing cells were coupled to horseradish peroxidase and immobilized on graphite electrodes by physical entrapment behind a dialysis membrane. A high urate selectivity with a detection limit of about 8 μM was found.</p> <p>Conclusion</p> <p>A strain of <it>H. polymorpha </it>overproducing UOX was constructed. A cheap urate selective microbial biosensor was developed.</p
Strong asymptotics for Jacobi polynomials with varying nonstandard parameters
Strong asymptotics on the whole complex plane of a sequence of monic Jacobi
polynomials is studied, assuming that with and satisfying , , . 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 of a certain quadratic differential according to the
equilibrium measure on in an external field. However, when either
, or are geometrically close to ,
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
Ladder operators and differential equations for multiple orthogonal polynomials
In this paper, we obtain the ladder operators and associated compatibility
conditions for the type I and the type II multiple orthogonal polynomials.
These ladder equations extend known results for orthogonal polynomials and can
be used to derive the differential equations satisfied by multiple orthogonal
polynomials. Our approach is based on Riemann-Hilbert problems and the
Christoffel-Darboux formula for multiple orthogonal polynomials, and the
nearest-neighbor recurrence relations. As an illustration, we give several
explicit examples involving multiple Hermite and Laguerre polynomials, and
multiple orthogonal polynomials with exponential weights and cubic potentials.Comment: 28 page
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