Planar channeling and quasichanneling oscillations in a bent crystal

Particles passing through a crystal under planar channeling experience transverse oscillations in their motion. As channeled particles approach the atomic planes of a crystal, they are likely to be dechanneled. This effect was used in ion-beam analysis with MeV energy. We studied this effect in a bent crystal for positive and negative particles within a wide range of energies in sight of application of such crystals at accelerators. We found the conditions for the appearance or not of channeling oscillations. Indeed a new kind of oscillations, strictly related to the motion of over-barrier particles, i.e. quasichanneling particles, has been predicted. Such oscillations, named planar quasichanneling oscillations, possess a different nature than channeling oscillations. Through computer simulation, we studied this effect and provided a theoretical interpretation for them. We show that channeling oscillations can be observed only for positive particles while quasichanneling oscillations can exist for particles with either sign. The conditions for experimental observation of channeling and quasichanneling oscillations at existing accelerators with available crystal has been found and optimized.Comment: 25 pages, 11 figure

Prediction of the Material Composition of the VVER-type Reactor Burned Pellet with Use of Neutron-Physical Codes

The purpose of neutron-physical calculations is typically isotopic composition of the fuel elements. However, in solving materials science problems related to nuclear fuel, researchers are usually interested in elemental composition of the fuel pellets, because the chemical and thermal physic properties are the same for differentisotopes of one chemical element. Nevertheless, for modeling of the elemental composition one should perform calculation of the isotopic composition and carry out the summation over all isotopes of a given chemical element. The development of computational tools allows the use of improved methods and codes, which held the consequent solution of tasks of heat conduction, neutron transport, and kinetics ofnuclides transformation. Thus the calculations take into account the dependence of the thermal conductivity from the changing isotopic composition and fuel burnup. This allows to perform neutron-physical and thermal-physical calculations of the reactor with detailed temperature distribution, taking into account temperature dependence of thermal conductivity and other characteristics. This approach was applied to calculations of the fuel pellet of the VVER type reactor and calculation of its elemental composition. Keywords: materials science, elemental composition, fuel pellet

Space-Time Complexity in Hamiltonian Dynamics

New notions of the complexity function C(epsilon;t,s) and entropy function S(epsilon;t,s) are introduced to describe systems with nonzero or zero Lyapunov exponents or systems that exhibit strong intermittent behavior with ``flights'', trappings, weak mixing, etc. The important part of the new notions is the first appearance of epsilon-separation of initially close trajectories. The complexity function is similar to the propagator p(t0,x0;t,x) with a replacement of x by the natural lengths s of trajectories, and its introduction does not assume of the space-time independence in the process of evolution of the system. A special stress is done on the choice of variables and the replacement t by eta=ln(t), s by xi=ln(s) makes it possible to consider time-algebraic and space-algebraic complexity and some mixed cases. It is shown that for typical cases the entropy function S(epsilon;xi,eta) possesses invariants (alpha,beta) that describe the fractal dimensions of the space-time structures of trajectories. The invariants (alpha,beta) can be linked to the transport properties of the system, from one side, and to the Riemann invariants for simple waves, from the other side. This analog provides a new meaning for the transport exponent mu that can be considered as the speed of a Riemann wave in the log-phase space of the log-space-time variables. Some other applications of new notions are considered and numerical examples are presented.Comment: 27 pages, 6 figure

Topological properties of punctual Hilbert schemes of almost-complex fourfolds (I)

In this article, we study topological properties of Voisin's punctual Hilbert schemes of an almost-complex fourfold $X$. In this setting, we compute their Betti numbers and construct Nakajima operators. We also define tautological bundles associated with any complex bundle on $X$, which are shown to be canonical in $K$-theory

Experimental evidence of planar channeling in a periodically bent crystal

The usage of a Crystalline Undulator (CU) has been identified as a promising solution for generating powerful and monochromatic $\gamma$-rays. A CU was fabricated at SSL through the grooving method, i.e., by the manufacturing of a series of periodical grooves on the major surfaces of a crystal. The CU was extensively characterized both morphologically via optical interferometry at SSL and structurally via X-ray diffraction at ESRF. Then, it was finally tested for channeling with a 400 GeV/c proton beam at CERN. The experimental results were compared to Monte Carlo simulations. Evidence of planar channeling in the CU was firmly observed. Finally, the emission spectrum of the positron beam interacting with the CU was simulated for possible usage in currently existing facilities

Universal microscopic correlation functions for products of independent Ginibre matrices

We consider the product of n complex non-Hermitian, independent random matrices, each of size NxN with independent identically distributed Gaussian entries (Ginibre matrices). The joint probability distribution of the complex eigenvalues of the product matrix is found to be given by a determinantal point process as in the case of a single Ginibre matrix, but with a more complicated weight given by a Meijer G-function depending on n. Using the method of orthogonal polynomials we compute all eigenvalue density correlation functions exactly for finite N and fixed n. They are given by the determinant of the corresponding kernel which we construct explicitly. In the large-N limit at fixed n we first determine the microscopic correlation functions in the bulk and at the edge of the spectrum. After unfolding they are identical to that of the Ginibre ensemble with n=1 and thus universal. In contrast the microscopic correlations we find at the origin differ for each n>1 and generalise the known Bessel-law in the complex plane for n=2 to a new hypergeometric kernel 0_F_n-1.Comment: 20 pages, v2 published version: typos corrected and references adde

Predictability in the large: an extension of the concept of Lyapunov exponent

We investigate the predictability problem in dynamical systems with many degrees of freedom and a wide spectrum of temporal scales. In particular, we study the case of $3D$ turbulence at high Reynolds numbers by introducing a finite-size Lyapunov exponent which measures the growth rate of finite-size perturbations. For sufficiently small perturbations this quantity coincides with the usual Lyapunov exponent. When the perturbation is still small compared to large-scale fluctuations, but large compared to fluctuations at the smallest dynamically active scales, the finite-size Lyapunov exponent is inversely proportional to the square of the perturbation size. Our results are supported by numerical experiments on shell models. We find that intermittency corrections do not change the scaling law of predictability. We also discuss the relation between finite-size Lyapunov exponent and information entropy.Comment: 4 pages, 2 Postscript figures (included), RevTeX 3.0, files packed with uufile

Experimental Parameters for a Cerium 144 Based Intense Electron Antineutrino Generator Experiment at Very Short Baselines

The standard three-neutrino oscillation paradigm, associated with small squared mass splittings $\ll 0.1\ \mathrm{eV^2}$, has been successfully built up over the last 15 years using solar, atmospheric, long baseline accelerator and reactor neutrino experiments. However, this well-established picture might suffer from anomalous results reported at very short baselines in some of these experiments. If not experimental artifacts, such results could possibly be interpreted as the existence of at least an additional fourth sterile neutrino species, mixing with the known active flavors with an associated mass splitting $\ll 0.1\ \mathrm{eV^2}$, and being insensitive to standard weak interactions. Precision measurements at very short baselines (5 to 15 m) with intense MeV electronic antineutrino emitters can be used to probe these anomalies. In this article, the expected antineutrino signal and backgrounds of a generic experiment which consists of deploying an intense beta minus radioactive source inside or in the vicinity of a large liquid scintillator detector are studied. The technical challenges to perform such an experiment are identified, along with quantifying the possible source and detector induced systematics, and their impact on the sensitivity to the observation of neutrino oscillations at short baselines.Comment: 21 pages, 27 figures, generated with pdflatex, accepted for publication in Phys. Rev.