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

Strong effect of weak diffusion on scalar turbulence at large scales

Passive scalar turbulence forced steadily is characterized by the velocity correlation scale, $L$, injection scale, $l$, and diffusive scale, $r_d$. The scales are well separated if the diffusivity is small, $r_d\ll l,L$, and one normally says that effects of diffusion are confined to smaller scales, $r\ll r_d$. However, if the velocity is single scale one finds that a weak dependence of the scalar correlations on the molecular diffusivity persists to even larger scales, e.g. $l\gg r\gg r_d$ \cite{95BCKL}. We consider the case of $L\gg l$ and report a counter-intuitive result -- the emergence of a new range of large scales, $L\gg r\gg l^2/r_d$, where the diffusivity shows a strong effect on scalar correlations.Comment: 4 pages, 1 figure, submitted to Physics of Fluid

Solving the two-center nuclear shell-model problem with arbitrarily-orientated deformed potentials

A general new technique to solve the two-center problem with arbitrarily-orientated deformed realistic potentials is demonstrated, which is based on the powerful potential separable expansion method. As an example, molecular single-particle spectra for $^{12}$C + $^{12}$C $\to$ $^{24}$Mg are calculated using deformed Woods-Saxon potentials. These clearly show that non-axial symmetric configurations play a crucial role in molecular resonances observed in reaction processes for this system at low energy

Transverse Instabilities of Coasting Beams with Space Charge

Transverse beam stability is strongly affected by the beam space charge. Usually it is analyzed with the rigid-beam model. However this model is only valid when a bare (not affected by the space charge) tune spread is small compared to the space charge tune shift. This condition specifies a relatively small area of parameters which, however, is the most interesting for practical applications. The Landau damping rate and the beam Schottky spectra are computed assuming that validity condition is satisfied. The results are applied to a round Gaussian beam. The stability thresholds are described by simple fits for the cases of chromatic and octupole tune spreads.Comment: 6 pages, 2 figures, accepted by Phys. Rev. ST - Accel. Beam

The effect of electron surface scattering on fine metal particle electromagnetic radiation absorption

The magnetic dipole absorption cross section of a spherically shaped metal particle was calculated in terms of kinetic approach. The particle considered was placed in the field of a plane electromagnetic wave. The model of boundary conditions was investigated taking into account the dependence of the reflectivity coefficient both on the surface roughness parameter and on the electron incidence angle. The results obtained were compared with theoretical computation results for a model of combined diffusion-specular boundary conditions of Fuchs.Comment: 9 pages, 5 figure

The physical limits of communication

It has been well-known since the pioneering work of Claude Shannon in the 1940s that a message transmitted with optimal efficiency over a channel of limited bandwidth is indistinguishable from random noise to a receiver who is unfamiliar with the language in which the message is written. In this letter we demonstrate an equivalent result about electromagnetic transmissions. We show that when electromagnetic radiation is used as the transmission medium, the most information-efficient format for a given message is indistinguishable from black-body radiation to a receiver who is unfamiliar with that format. The characteristic temperature of the radiation is set by the amount of energy used to make the transmission. If information is not encoded in the direction of the radiation, but only its timing, energy or polarization, then the most efficient format has the form of a one-dimensional black-body spectrum which is easily distinguished from the three-dimensional case.Comment: 9 pages, 1 postscript figure, typeset in LaTeX using the RevTeX macro packag

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

Estimates in Beurling--Helson type theorems. Multidimensional case

We consider the spaces $A_p(\mathbb T^m)$ of functions $f$ on the $m$ -dimensional torus $\mathbb T^m$ such that the sequence of the Fourier coefficients $\hat{f}=\{\hat{f}(k), ~k \in \mathbb Z^m\}$ belongs to $l^p(\mathbb Z^m), ~1\leq p<2$. The norm on $A_p(\mathbb T^m)$ is defined by $\|f\|_{A_p(\mathbb T^m)}=\|\hat{f}\|_{l^p(\mathbb Z^m)}$. We study the rate of growth of the norms $\|e^{i\lambda\varphi}\|_{A_p(\mathbb T^m)}$ as $|\lambda|\rightarrow \infty, ~\lambda\in\mathbb R,$ for $C^1$ -smooth real functions $\varphi$ on $\mathbb T^m$ (the one-dimensional case was investigated by the author earlier). The lower estimates that we obtain have direct analogues for the spaces $A_p(\mathbb R^m)$