On the Fourier transform of the characteristic functions of domains with C1C^1 -smooth boundary

We consider domains $D\subseteq\mathbb R^n$ with $C^1$ -smooth boundary and study the following question: when the Fourier transform $\hat{1_D}$ of the characteristic function $1_D$ belongs to $L^p(\mathbb R^n)$?Comment: added two references; added footnotes on pages 6 and 1

Calculation of The Lifetimes of Thin Stripper Targets Under Bombardment of Intense Pulsed Ions

The problems of stripper target behavior in the nonstationary intense particle beams are considered. The historical sketch of studying of radiation damage failure of carbon targets under ion bombardment is presented. The simple model of evaporation of a target by an intensive pulsing beam is supposed. Stripper foils lifetimes in the nonstationary intense particle can be described by two failure mechanisms: radiation damage accumulation and evaporation of target. At the maximal temperatures less than 2500K the radiation damage are dominated; at temperatures above 2500K the mechanism of evaporation of a foil prevails. The proposed approach has been applied to the discription of behaviour of stripper foils in the BNL linac and SNS conditions.Comment: 12 pages, 5 figure

Size-independent Young's modulus of inverted conical GaAs nanowire resonators

We explore mechanical properties of top down fabricated, singly clamped inverted conical GaAs nanowires. Combining nanowire lengths of 2-9 $\mu$m with foot diameters of 36-935 nm yields fundamental flexural eigenmodes spanning two orders of magnitude from 200 kHz to 42 MHz. We extract a size-independent value of Young's modulus of (45$\pm$3) GPa. With foot diameters down to a few tens of nanometers, the investigated nanowires are promising candidates for ultra-flexible and ultra-sensitive nanomechanical devices

Broad-band chopper for a CW proton linac at Fermilab

Requirements and technical limitations to the bunch-by-bunch chopper for the Fermilab Project X are discussed.Comment: 3 pp. Particle Accelerator, 24th Conference (PAC'11) 2011. 28 Mar - 1 Apr 2011. New York, US

Directed Polymer -- Directed Percolation Transition

We study the relation between the directed polymer and the directed percolation models, for the case of a disordered energy landscape where the energies are taken from bimodal distribution. We find that at the critical concentration of the directed percolation, the directed polymer undergoes a transition from the directed polymer universality class to the directed percolation universality class. We also find that directed percolation clusters affect the characterisrics of the directed polymer below the critical concentration.Comment: LaTeX 2e; 12 pages, 5 figures; in press, will be published in Europhys. Let

Non-intrusive and structure preserving multiscale integration of stiff ODEs, SDEs and Hamiltonian systems with hidden slow dynamics via flow averaging

We introduce a new class of integrators for stiff ODEs as well as SDEs. These integrators are (i) {\it Multiscale}: they are based on flow averaging and so do not fully resolve the fast variables and have a computational cost determined by slow variables (ii) {\it Versatile}: the method is based on averaging the flows of the given dynamical system (which may have hidden slow and fast processes) instead of averaging the instantaneous drift of assumed separated slow and fast processes. This bypasses the need for identifying explicitly (or numerically) the slow or fast variables (iii) {\it Nonintrusive}: A pre-existing numerical scheme resolving the microscopic time scale can be used as a black box and easily turned into one of the integrators in this paper by turning the large coefficients on over a microscopic timescale and off during a mesoscopic timescale (iv) {\it Convergent over two scales}: strongly over slow processes and in the sense of measures over fast ones. We introduce the related notion of two-scale flow convergence and analyze the convergence of these integrators under the induced topology (v) {\it Structure preserving}: for stiff Hamiltonian systems (possibly on manifolds), they can be made to be symplectic, time-reversible, and symmetry preserving (symmetries are group actions that leave the system invariant) in all variables. They are explicit and applicable to arbitrary stiff potentials (that need not be quadratic). Their application to the Fermi-Pasta-Ulam problems shows accuracy and stability over four orders of magnitude of time scales. For stiff Langevin equations, they are symmetry preserving, time-reversible and Boltzmann-Gibbs reversible, quasi-symplectic on all variables and conformally symplectic with isotropic friction.Comment: 69 pages, 21 figure

Observation of Instabilities of Coherent Transverse Ocillations in the Fermilab Booster

The Fermilab Booster - built more than 40 years ago - operates well above the design proton beam intensity of 4x10**12 ppp. Still, the Fermilab neutrino experiments call for even higher intensity of 5.5x10**12 ppp. A multitude of intensity related effects must be overcome in order to meet this goal including suppression of coherent dipole instabilities of transverse oscillations which manifest themselves as a sudden drop in the beam current. In this report we present the results of observation of these instabilities at different tune, coupling and chromaticity settings and discuss possible cures.Comment: 3 pp. 3rd International Particle Accelerator Conference (IPAC 2012) 20-25 May 2012, New Orleans, Louisian

Is \lq\lq Heavy Quark Damping Rate Puzzle'' in Hot QCD Really the Puzzle?

Within the framework of perturbative resummation scheme of Pisarski and Braaten, the decay- or damping-rate of a moving heavy quark (muon) to leading order in weak coupling in hot QCD (QED) is examined. Although, as is well known, the conventionally-defined damping rate diverges logarithmically at the infrared limit, shown is that no such divergence appears in the physically measurable decay rate. The cancellation occurs between the contribution from the \lq\lq real'' decay diagram and the contribution from the diagrams with \lq\lq thermal radiative correction''.Comment: 13pages, OCU-PHYS-15

Scaling and Dissipation in the GOY Shell Model

This is a paper about multi-fractal scaling and dissipation in a shell model of turbulence, called the GOY model. This set of equations describes a one dimensional cascade of energy towards higher wave vectors. When the model is chaotic, the high-wave-vector velocity is a product of roughly independent multipliers, one for each logarithmic momentum shell. The appropriate tool for studying the multifractal properties of this model is shown to be the energy current on each shell rather than the velocity on each shell. Using this quantity, one can obtain better measurements of the deviations from Kolmogorov scaling (in the GOY dynamics) than were available up to now. These deviations are seen to depend upon the details of inertial-range structure of the model and hence are {\em not} universal. However, once the conserved quantities of the model are fixed to have the same scaling structure as energy and helicity, these deviations seem to depend only weakly upon the scale parameter of the model. We analyze the connection between multifractality in the velocity distribution and multifractality in the dissipation. Our arguments suggest that the connection is universal for models of this character, but the model has a different behavior from that of real turbulence. We also predict the scaling behavior of time correlations of shell-velocities, of the dissipation,Comment: Revised Versio

Evaporative Deposition Patterns Revisited: Spatial Dimensions of the Deposit

A model accounting for finite spatial dimensions of the deposit patterns in the evaporating sessile drops of colloidal solution on a plane substrate is proposed. The model is based on the assumption that the solute particles occupy finite volume and hence these dimensions are of the steric origin. Within this model, the geometrical characteristics of the deposition patterns are found as functions of the initial concentration of the solute, the initial geometry of the drop, and the time elapsed from the beginning of the drying process. The model is solved analytically for small initial concentrations of the solute and numerically for arbitrary initial concentrations of the solute. The agreement between our theoretical results and the experimental data is demonstrated, and it is shown that the observed dependence of the deposit dimensions on the experimental parameters can indeed be attributed to the finite dimensions of the solute particles. These results are universal and do not depend on any free or fitting parameters; they are important for understanding the evaporative deposition and may be useful for creating controlled deposition patterns.Comment: 34 pages, 14 figures, LaTeX; submitted to Physical Review