SOME REMARKS ON THE SMARANDACHE FUNCTION

Remarks on a Function in the Number Theory

Transmission enhancement in loss-gain multilayers by resonant suppression of reflection

Using the transfer-matrix approach and solving time-domain differential equations, we analyze the loss compensation mechanism in multilayer systems composed of an absorbing transparent conductive oxide and dielectric doped with an active material. We reveal also another regime with the possibility of enhanced transmission with suppressed reflection originating from the resonant properties of the multilayers. For obliquely incident and evanescent waves, such enhanced transmission under suppressed reflection turns into the reflectionless regime, which is similar to that observed in the PT-symmetric structures, but does not require PT symmetry. We infer that the reflectionless transmission is due to the full loss compensation at the resonant wavelengths of the multilayers.Comment: 12 pages, 10 figure

Camden Childcare Needs Assessment

The Camden Childcare Needs Assessment is a mixed methods study that has sought to consider the childcare needs of parents in the borough, including considering where there is unmet demand, the adequacy of the timing of childcare provision and parental views on the cost and quality of provision. The study aims to contribute to the planning of future childcare in the borough. Aims The Camden Childcare Needs Assessment aims to: - develop a clear and concise picture of the demand for childcare from Camden residents - identify unmet needs in childcare provision in Camden The objective of the project is to enable the Local Authority to plan childcare expansion and support sustainable service development

Effects of confinement on the permanent electric-dipole moment of Xe atoms in liquid Xe

Searches for permanent electric-dipole moments (EDM) of atoms provide important constraints on competing extensions to the standard model of elementary particles. Recently proposed experiment with liquid $^{129}$Xe [M.V. Romalis and M.P. Ledbetter, Phys. Rev. Lett. \textbf{87}, 067601 (2001)] may significantly improve present limits on the EDMs. To interpret experimental data in terms of CP-violating sources, one must relate measured atomic EDM to various model interactions via electronic-structure calculations. Here we study density dependence of atomic EDMs. The analysis is carried out in the framework of the cell model of the liquid coupled with relativistic atomic-structure calculations. We find that compared to an isolated atom, the EDM of an atom of liquid Xe is suppressed by about 40%

Molecular CP-violating magnetic moment

A concept of CP-violating (T,P-odd) permanent molecular magnetic moments $\mu^{CP}$ is introduced. We relate the moments to the electric dipole moment of electron (eEDM) and estimate $\mu^{CP}$ for several diamagnetic polar molecules. The moments exhibit a steep, Z^5, scaling with the nuclear charge Z of the heavier molecular constituent. A measurement of the CP-violating magnetization of a polarized sample of heavy molecules may improve the present limit on eEDM by several orders of magnitude.Comment: 4 pages, no figures, submitted to PR

Coherent radiation of an ultra-relativistic charged particle channeled in a periodically bent crystal

We suggest a new type of the undulator radiation which is generated by an ultra-relativistic particle channeled along a periodically bent crystallographic plane or axis. The electromagnetic radiation arises mainly due to the bending of the particle's trajectory, which follows the shape of the channel. The parameters of this undulator, which totally define the spectrum and the angular distribution of the radiation (both spontaneous and stimulated), depend on the type of the crystal and the crystallographic plane (axis), on the type of a projectile and its energy, and on the shape of the bent channel, and, thus, can be varied significantly by varying these characteristics. As an example, we consider the acoustically induced radiation (AIR) which is generated by ultra-relativistic particles channeled in a crystal which is bent by a transverse acoustic wave. The AIR mechanism allows to make the undulator with the main parameters varying in wide ranges, which are inaccessible in the undulators based on the motion of particles in the periodic magnetic fields and also in the field of the laser radiation. The intensity of AIR can be easily made larger than the intensity of the radiation in a linear crystal and can be varied in a wide range by varying the frequency and the amplitude of the acoustic wave in the crystal. A possibility to generate stimulated emission of high-energy photons (in keV - MeV region) is also discussed.Comment: published in J. Phys. G: Nucl. Part. Phys. 24 (1998) L45-L53, http://www.iop.or

Domain Dynamics in Piezoresponse Force Microscopy: Quantitative Deconvolution and Hysteresis Loop Fine Structure

Domain dynamics in the Piezoresponse Force Spectroscopy (PFS) experiment is studied using the combination of local hysteresis loop acquisition with simultaneous domain imaging. The analytical theory for PFS signal from domain of arbitrary cross-section is developed and used for the analysis of experimental data on Pb(Zr,Ti)O3 polycrystalline films. The results suggest formation of oblate domain at early stage of the domain nucleation and growth, consistent with efficient screening of depolarization field within the material. The fine structure of the hysteresis loop is shown to be related to the observed jumps in the domain geometry during domain wall propagation (nanoscale Barkhausen jumps), indicative of strong domain-defect interactions.Comment: 17 pages, 3 figures, 2 Appendices, to be submmited to Appl. Phys. Let

Fixed Volume Effect on Polar Properties and Phase Diagrams of Ferroelectric Semi-ellipsoidal Nanoparticles

For advanced applications in modern industry it is very important to reduce the volume of ferroelectric nanoparticles without serious deterioration of their polar properties. In many practically important cases fixed volume (rather than fixed size) corresponds to realistic technological conditions of nanoparticles fabrication. The letter is focused on the theoretical study of the behavior of ferroelectric polarization, paramagnetoelectric coefficient and phase diagrams of semi-ellipsoidal nanoparticles with fixed volume V. Our approach combines the Landau-Ginzburg-Devonshire phenomenology, classical electrostatics and elasticity theory. Our results show that the size effects of the phase diagrams and polarization of semi-ellipsoidal BiFeO3 nanoparticles nontrivially depends on V. These findings provide a path to optimize the polar properties of nanoparticles by controlling their phase diagrams at a fixed volume.Comment: 15 pages, 5 figures, we added the section IV. Paramagnetoelectric (PME) coefficient at fixed volume in this version and changed title and abstract accordingl

On Electrostatic Positron Acceleration In The Accretion Flow Onto Neutron Stars

As first shown by Shvartsman (1970), a neutron star accreting close to the Eddington limit must acquire a positive charge in order for electrons and protons to move at the same speed. The resulting electrostatic field may contribute to accelerating positrons produced near the star surface in conjunction with the radiative force. We reconsider the balance between energy gains and losses, including inverse Compton (IC), bremsstrahlung and non--radiative scatterings. It is found that, even accounting for IC losses only, the maximum positron energy never exceeds $\approx 400$ keV. The electrostatic field alone may produce energies $\approx 50$ keV at most. We also show that Coulomb collisions and annihilation with accreting electrons severely limit the number of positrons that escape to infinity.Comment: 9 pages plus 3 postscript figures, to be published in Ap