Solitary and shock waves in discrete double power-law materials

A novel strongly nonlinear laminar metamaterial supporting new types of solitary and shock waves with impact energy mitigating capabilities is presented. It consists of steel plates with intermittent polymer toroidal rings acting as strongly nonlinear springs with large allowable strain. Their force-displacement relationship is described by the addition of two power-law relationships resulting in a solitary wave speed and width depending on the amplitude. This double nonlinearity allows splitting of an initial impulse into two separate strongly nonlinear solitary wave trains. Solitary and shock waves are observed experimentally and analyzed numerically in an assembly with Teflon o-rings.Comment: 14 pages, 6 figure

Momentum distribution in heavy deformed nuclei: role of effective mass

The impact of nuclear deformation on the momentum distributions (MD) of occupied proton states in $^{238}$U is studied with a phenomenological Woods-Saxon (WS) shell model and the self-consistent Skyrme-Hartree-Fock (SHF) scheme. Four Skyrme parameterizations (SkT6, SkM*, SLy6, SkI3) with different effective masses are used. The calculations reveal significant deformation effects in the low-momentum domain of $K^{\pi}=1/2^{\pm}$ states, mainly of those lying near the Fermi surface. For other states, the deformation effect on MD is rather small and may be neglected. The most remarkable result is that the very different Skyrme parameterizations and the WS potential give about identical MD. This means that the value of effective mass, being crucial for the description of the spectra, is not important for the spatial shape of the wave functions and thus for the MD. In general, it seems that, for the description of MD at $0\le k \le 300$ MeV/c, one may use any single-particle scheme (phenomenological or self-consistent) fitted properly to the global ground state properties.Comment: 14 pages, 6 figure

Role of the rho meson in the description of pion electroproduction experiments at JLab

We study the p(e,e' pi+)n reaction in the framework of an effective Lagrangian approach including nucleon, pi and rho meson degrees of freedom and show the importance of the rho-meson t-pole contribution to sigmaT, the transverse part of cross section. We test two different field representations of the rho meson, vector and tensor, and find that the tensor representation of the rho meson is more reliable in the description of the existing data. In particular, we show that the rho-meson t-pole contribution, including the interference with an effective non-local contact term, sufficiently improves the description of the recent JLab data at invariant mass W less 2.2 GeV and Q2 less 2.5 GeV2/c2. A ``soft'' variant of the strong piNN and rhoNN form factors is also found to be compatible with these data. On the basis of the successful description of both the sigmaL and sigmaT parts of the cross section we discuss the importance of taking into account the sigmaT data when extracting the charge pion form factor Fpi from sigmaL.Comment: 23 pages, 6 figures, accepted for publication in Phys. Rev.

Shock Wave Structure in a Strongly Nonlinear Granular Lattice with Viscous Dissipation

The shock wave structure in a one-dimensional lattice (e.g. granular chain) with a power law dependence of force on displacement between particles with viscous dissipation is considered and compared to the corresponding long wave approximation. A dissipative term depending on the relative velocity between neighboring particles is included in the discrete model to investigate its influence on the shape of steady shock profiles. The critical viscosity coefficient is obtained from the long-wave approximation for arbitrary values of the exponent n and denotes the transition from an oscillatory to a monotonic shock profile in stronly nonlinear systems. The expression for the critical viscosity coefficient converges to the known equation for the critical viscosity in the weakly nonlinear case. Values of viscosity based on this expression are comparable to the values obtained in the numerical analysis of a discrete particle lattice with a Herzian contact interaction corresponding to n = 3/2. An initial disturbance in a discrete system approaches a stationary shock profile after traveling a short distance that is comparable to the width of the leading pulse of a stationary shock front. The shock front width is minimized when the viscosity is equal to its critical value.Comment: 20 pages, 6 figure

Is it possible to assign physical meaning to field theory with higher derivatives?

To overcome the difficulties with the energy indefiniteness in field theories with higher derivatives, it is supposed to use the mechanical analogy, the Timoshenko theory of the transverse flexural vibrations of beams or rods well known in mechanical engineering. It enables one to introduce the notion of a "mechanical" energy in such field models that is wittingly positive definite. This approach can be applied at least to the higher derivative models which effectively describe the extended localized solutions in usual first order field theories (vortex solutions in Higgs models and so on). Any problems with a negative norm ghost states and unitarity violation do not arise here.Comment: 16 pp, LaTeX, JINR E2-93-19

Scissors modes in triaxial metal clusters

We study the scissors mode (orbital M1 excitations) in small Na clusters, triaxial metal clusters ${\rm Na}_{12}$ and ${\rm Na}_{16}$ and the close-to-spherical ${{\rm Na}_9}^+$, all described in DFT with detailed ionic background. The scissors modes built on spin-saturated ground and spin-polarized isomeric states are analyzed in virtue of both macroscopic collective and microscopic shell-model treatments. It is shown that the mutual destruction of Coulomb and the exchange-correlation parts of the residual interaction makes the collective shift small and the net effect can depend on details of the actual excited state. The crosstalk with dipole and spin-dipole modes is studied in detail. In particular, a strong crosstalk with spin-dipole negative-parity mode is found in the case of spin-polarized states. Triaxiality and ionic structure considerably complicate the scissors response, mainly at expense of stronger fragmentation of the strength. Nevertheless, even in these complicated cases the scissors mode is mainly determined by the global deformation. The detailed ionic structure destroys the spherical symmetry and can cause finite M1 response (transverse optical mode) even in clusters with zero global deformation. But its strength turns out to be much smaller than for the genuine scissors modes in deformed systems.Comment: 17 pages, 5 figure

STIRAP transport of Bose-Einstein condensate in triple-well trap

The irreversible transport of multi-component Bose-Einstein condensate (BEC) is investigated within the Stimulated Adiabatic Raman Passage (STIRAP) scheme. A general formalism for a single BEC in M-well trap is derived and analogy between multi-photon and tunneling processes is demonstrated. STIRAP transport of BEC in a cyclic triple-well trap is explored for various values of detuning and interaction between BEC atoms. It is shown that STIRAP provides a complete population transfer at zero detuning and interaction and persists at their modest values. The detuning is found not to be obligatory. The possibility of non-adiabatic transport with intuitive order of couplings is demonstrated. Evolution of the condensate phases and generation of dynamical and geometric phases are inspected. It is shown that STIRAP allows to generate the unconventional geometrical phase which is now of a keen interest in quantum computing.Comment: 9 pages, 6 figures. To be published in Laser Physics (v. 19, n.4, 2009

The Adiabatic Transport of Bose-Einstein Condensates in a Double-Well Trap: Case a Small Nonlinearity

A complete adiabatic transport of Bose-Einstein condensate in a double-well trap is investigated within the Landau-Zener (LZ) and Gaussian Landau-Zener (GLZ) schemes for the case of a small nonlinearity, when the atomic interaction is weaker than the coupling. The schemes use the constant (LZ) and time-dependent Gaussian (GLZ) couplings. The mean field calculations show that LZ and GLZ suggest essentially different transport dynamics. Significant deviations from the case of a strong coupling are discussed.Comment: 6 pages, 3 figures, to be published in Laser Physic

Quark mass correction to the string potential

A consistent method for calculating the interquark potential generated by the relativistic string with massive ends is proposed. In this approach the interquark potential in the model of the Nambu--Goto string with point--like masses at its ends is calculated. At first the calculation is done in the one--loop approximation and then the variational estimation is performed. The quark mass correction results in decreasing the critical distance (deconfinement radius). When quark mass decreases the critical distance also decreases. For obtaining a finite result under summation over eigenfrequencies of the Nambu--Goto string with massive ends a suitable mode--by--mode subtraction is proposed. This renormalization procedure proves to be completely unique. In the framework of the developed approach the one--loop interquark potential in the model of the relativistic string with rigidity is also calculated.Comment: 34 pages, LATE

Properties of odd nuclei and the impact of time-odd mean fields: A systematic Skyrme-Hartree-Fock analysis

We present a systematic analysis of the description of odd nuclei by the Skyrme-Hartree-Fock approach augmented with pairing in BCS approximation and blocking of the odd nucleon. Current and spin densities in the Skyrme functional produce time-odd mean fields (TOMF) for odd nuclei. Their effect on basic properties (binding energies, odd-even staggering, separation energies and spectra) is investigated for the three Skyrme parameterizations SkI3, SLy6, and SV-bas. About 1300 spherical and axially-deformed odd nuclei with 16 < Z < 92 are considered. The calculations demonstrate that the TOMF effect is generally small, although not fully negligible. The influence of the Skyrme parameterization and the consistency of the calculations are much more important. With a proper choice of the parameterization, a good description of binding energies and their differences is obtained, comparable to that for even nuclei. The description of low-energy excitation spectra of odd nuclei is of varying quality depending on the nucleus