Related papers: A beam that can only bend on the Cantor set
We study the spectrum of the Dirac hamiltonian in one space dimension for a single electron in the electrostatic potential of a point nucleus, in the Born-Oppenheimer approximation where the nucleus is assumed fixed at the origin. The…
We consider a pair of artificial atoms with different ground state energies. By means of finite element calculations we predict that the ground state energies can be tuned into resonance if the artificial atoms are placed into a flexible…
Elastic waves scattering off a periodic single and double array of thin cylindrical defects is considered for isotropic materials. An analytical expression for the scattering matrix is obtained by means of the Lippmann-Schwinger formalism…
We consider low energy configurations for the Heitmann-Radin sticky discs functional, in the limit of diverging number of discs. More precisely, we renormalize the Heitmann-Radin potential by subtracting the minimal energy per particle,…
This paper is a survey devoted to the study of probability and infinite ergodic invariant measures for aperiodic homeomorphisms of a Cantor set. We focus mostly on the cases when a homeomorphism has either a unique ergodic invariant measure…
We propose theoretical and numerical analyses of smart bending deformation of a dielectric-elastic bilayer in response to a voltage, based on the nonlinear theory of electro-elasticity and the associated linearized incremental field theory.…
We consider a few-boson system confined to one dimension with a single distinguishable particle of lesser mass. All particle interactions are modeled with $\delta$-functions, but due to the mass imbalance the problem is nonintegrable.…
Some issues that arise when modeling elastic energy for binary alloys are discussed within the context of a Keating model and density functional calculations. The Keating model is based on atomistic modeling of elastic interactions in…
Proposed low energy beta beam facilities would be capable of producing intense beams of neutrinos (anti-neutrinos) with well defined spectra. We present analytic expressions and numerical results which accurately show how the total neutrino…
Linear collider designs foresee some bends of about 5-10 mrad. The spin precession angle of one TeV electrons on 10 mrad bend is 23.2 rad and it changes proportional to the energy. Measurement of the spin direction using Compton scattering…
In this paper we discuss the motion of a beam in interaction with fluids. We allow the beam to move freely in all coordinate directions. We consider the case of a beam situated in between two different fluids as well as the case where the…
In this paper, we review recent development in the theory of resonant inelastic light (Raman) scattering in one-dimensional electron systems. The particular systems we have in mind are electron doped GaAs based semiconductor quantum wire…
Considerable attention has been given to the study of the arithmetic sum of two planar sets. We focus on understanding the measure and dimension of $A+\Gamma:=\left\{a+v:a\in A, v\in \Gamma \right\}$ when $A\subset \mathbb{R}^2$ and…
We consider a thin elastic strip of thickness h and we show that stationary points of the nonlinear elastic energy (per unit height) whose energy is of order h^2 converge to stationary points of the Euler-Bernoulli functional. The proof…
The fractal properties of the energy spectra of quantum systems are discussed in connection with the paper by S\'aiz and Mart\'inez [Phys. Rev. E 54, 2431 (1996)]. It is shown that for discrete energy levels the Hausdorff--Basicovitch…
We constrain the primordial fluctuation spectrum P(k) by using the new data on the Cosmic Microwave Background (CMB) from the Boomerang and MAXIMA experiments. Our study is based on slow-roll inflationary models, and we consider the…
We study the exact Hausdorff and packing dimensions of the $prime$ $Cantor$ $set$, $\Lambda_P$, which comprises the irrationals whose continued fraction entries are prime numbers. We prove that the Hausdorff measure of the prime Cantor set…
We discuss effects of reflective scattering for hadron and heavy nuclei collisions at the LHC and asymptotical energies. It is shown that the reflective scattering might lead to decreasing matter density with energy beyond the LHC energies.…
A beam line for electrons with energies in the range of 1 to 45 GeV, low contamination of hadrons and muons and high intensity up to 10^6 per accelerator spill at 27 GeV was setup at U70 accelerator in Protvino, Russia. A beam tagging…
We evaluate, by means of variational calculations, the bound state energy E_B of a pair of charges located on the surface of a cylinder, interacting via Coulomb potential - e^2 / r . The trial wave function involves three variational…