Barrier Grossing Induced by Fractional Gaussian Noise

A problem of the rate of escape of a particle under the influence of the external fractional Gaussian noise is studied by using the method of numerical integration of an overdamped Langevin equation. Considering a truncated harmonic potential, the dependences of the mean escape time on the noise intensity and Hurst index are evaluated, together with the probability density functions for the escape times. It is found that, like the corresponding classical problem with white Gaussian noise, they both obey an exponential law.За допомогою чисельного iнтегрування передемпфованого рiвняння Ланжевена дослiджено задачу про швидкiсть вильоту частинки iз потенцiальної ями пiд дiєю дробового гаусового шуму. На прикладi обрiзаного гармонiчного потенцiалу отримано залежностi середнього часу вильоту вiд iнтенсивностi шуму та показника Херста, а також обчислено функцiї розподiлу часiв вильоту. Зроблено висновок, що, як i у випадку класичної задачi з бiлим гаусовим шумом, цi величини є експоненцiальними функцiями вiдповiдних параметрiв

Calculation of temperature fields in ampoules under the radiation treatment by electrons with energy 10 MeV

To obtain the temperature fields in ampoules under the radiation treatment we use the one-dimensional equations of the thermal conductivity on the coordinates along the axis which is congruent with the direction of the beam. The results of the calculations of temperature fields within the ampoule are discussed for two cases: for the ampoule with the molten fluorides mix between three tested Hastelloy specimens (in section 1); and for the ampoule with exhalations of ftuorides salts (in section 2). These two situations are differed as in the energy losses of electron beam, as well in the mechanism of heat transport, that leads to essentially different temperature fields inside of the ampoule. It is shown that for ampoule with fluoride salts exhalations the stationary temperatures strongly depend from heat transport mechanisms and from layers thickness, that leads to conclusion about necessity to take into account both mechanisms of heat transport (thermal radiation and thermal conductivity) simultaneously.При розрахунках температурних полей в ампулі під випромінюванням електронами нами використовувались одновимірні рівняння теплопровідності із вісью х, яка збігається із напрямком потоку електронів. Одержані коордінатні залежності температури для двох випадків: 1) для ампули із с розплавом солей флюориду між випробуваними зразками Хастелоя; 2) для ампули із парами солей флюориду між шарами ампули.. Показано, що у другому випадку сталий розподіл температури істотно залежить від механизму переносу тепла і товщини шарів, що дозволяє зробити висновок про необхідність одночасно брати до уваги обидва механізми переносу тепла (теплове випромінювання і теплопровідніть шарів).Для вычисления температурных полей в ампуле под облучением электронами нами использовались одномерные уравнения теплопроводности с осью х, совпадающей с направлением потока электронов. Получены координатные зависимости температуры для двух случаев: 1) для ампулы с расплавом солей флюорида между испытуемыми образцами Хастеллоя; 2) для ампулы с парами солей флюорида между образцами Хастеллоя. Показано, что во втором случае установившееся распределение температуры существенно зависит от механизма переноса тепла и от толщины слоев, что позволяет сделать вывод о необходимости принимать во внимание оба механизма переноса тепла одновременно( тепловое излучение и теплопроводность слоев)

A Model for Persistent Levy Motion

We propose the model, which allows us to approximate fractional Levy noise and fractional Levy motion. Our model is based (i) on the Gnedenko limit theorem for an attraction basin of stable probability law, and (ii) on regarding fractional noise as the result of fractional integration/differentiation of a white Levy noise. We investigate self - affine properties of the approximation and conclude that it is suitable for modeling persistent Levy motion with the Levy index between 1 and 2.Comment: 14 pages, REVTeX, 5 figures PostScrip

Enhancement of the Raman Scattering and the Third-Harmonic Generation in Silicon Nanowires

We studied features of Raman scattering and the third-harmonic generation in silicon nanowire (SiNW) ensembles formed by means of chemical etching of crystalline silicon (c-Si) wafers with preliminary deposited silver nanoparticles in hydrofluoric acid. The c-Si wafers of different crystallographic orientations and doping levels were used, which results in variations of the formed nanostructure size and degree of order. For the excitation at 1064 nm the ratio of Raman scattering signals for SiNWs and those for initial c-Si wafer ranges from 2 to 5, whereas for shorter wavelengths the ratio increases for more ordered arrays of SiNWs of greater diameter and decreases for less ordered SiNW structures. The TH signals in SiNW ensembles demonstrate both fall and one- or two-orders-of-magnitude rise in comparison with c-Si depending on the structure of the SiNW ensemble. The obtained results are explained by the effect of partial light localization in SiNW ensembles

Quantitative analysis of morphology of porous silicon nanostructures formed by metal-assisted chemical etching

Morphology features of porous layers consisting of silicon nanowire arrays, which were grown by metal-assisted chemical etching, have been analyzed by means of digital processing of their scanning electron microscopy (SEM) images. Informational-entropic and Fourier analysis have been applied to quantitatively describe the degree of order and chaos in nanostructure distribution in the layers. Self-similarity of the layer morphology has been quantitatively described via its fractal dimensions. The applied approach allows us to distinguish morphological features of as-called "black" (more ordered) and "white" (less ordered) silicon layers characterized by minimal and maximal optical reflection, respectively.This work was partially supported by the Committee of Science of the Ministry of Education and Science of the Republic of Kazakhstan (Grant AP05132854, Grant AP05132738). G.K.M. and V.Yu.T. acknowledge the support of the Comprehensive Program of NRNU “MEPhI”

Fluctuation-driven directed transport in the presence of Levy flights

Numerical evidence of directed transport driven by symmetric Levy noise in time-independent ratchet potentials in the absence of an external tilting force is presented. The results are based on the numerical solution of the fractional Fokker-Planck equation in a periodic potential and the corresponding Langevin equation with Levy noise. The Levy noise drives the system out of thermodynamic equilibrium and an up-hill net current is generated. For small values of the noise intensity there is an optimal value of the Levy noise index yielding the maximum current. The direction and magnitude of the current can be manipulated by changing the Levy noise asymmetry and the potential asymmetry

Density and potential fluctuations in the edge plasma of the Uragan-3m torsatron

Ion saturation current and floating potential fluctuations are recorded by movable array of 4 Langmuir probes near the boundary of the confinement region in the l = 3/m = 9 Uragan-3M torsatron with an RF produced and heated plasma. On the basis of these data main spectral and time characteristics of the low frequency electrostatic turbulence have been derived. The existence of the radial electric field shear and reversal of poloidal phase velocity of the fluctuations at the plasma boundary have been confirmed. The time function of the turbulent E×B particle flux contains intermittent bursts with the amplitude multiply exceeding the average flux. Up to 70% of the total fluctuating flux is carried in these bursts

Translationally invariant calculations of form factors, nucleon densities and momentum distributions for finite nuclei with short-range correlations included

Relying upon our previous treatment of the density matrices for nuclei (in general, nonrelativistic self-bound finite systems) we are studying a combined effect of center-of-mass motion and short-range nucleon-nucleon correlations on the nucleon density and momentum distributions in light nuclei ($^{4}He$ and $^{16}O$). Their intrinsic ground-state wave functions are constructed in the so-called fixed center-of-mass approximation, starting with mean-field Slater determinants modified by some correlator (e.g., after Jastrow or Villars). We develop the formalism based upon the Cartesian or boson representation, in which the coordinate and momentum operators are linear combinations of the creation and annihilation operators for oscillatory quanta in the three different space directions, and get the own "Tassie-Barker" factors for each distribution and point out other model-independent results. After this separation of the center-of-mass motion effects we propose additional analytic means in order to simplify the subsequent calculations (e.g., within the Jastrow approach or the unitary correlation operator method). The charge form factors, densities and momentum distributions of $^{4}He$ and $^{16}O$ evaluated by using the well known cluster expansions are compared with data, our exact (numerical) results and microscopic calculations.Comment: 19 pages, 6 figure