The 2nd order renormalization group flow for non-linear sigma models in 2 dimensions

We show that for two dimensional manifolds M with negative Euler characteristic there exists subsets of the space of smooth Riemannian metrics which are invariant and either parabolic or backwards-parabolic for the 2nd order RG flow. We also show that solutions exists globally on these sets. Finally, we establish the existence of an eternal solution that has both a UV and IR limit, and passes through regions where the flow is parabolic and backwards-parabolic

To the modification of methods of nuclear chronometry in astrophysics and geophysics

In practically all known till now methods of nuclear chronometry there were usually taken into account the life-times of only fundamental states of $\alpha$-radioactive nuclei. But in the processes of nuclear synthesis in stars and under the influence of the constant cosmic radiation on surfaces of planets the excitations of the $\alpha$-radioactive nuclei are going on. Between them there are the states with the excited $\alpha$-particles inside the parent nuclei and so with much smaller life-times. And inside the large masses of stellar, terrestrial and meteoric substances the transitions between different internal conditions of radioactive nuclei are accompanied by infinite chains of the $\gamma$-radiations with the subsequent $\gamma$-absorptions, the further $\gamma$-radiations etc. For the description of the $\alpha$-decay evolution with considering of such excited states and multiple $\gamma$-radiations and $\gamma$-absorptions inside stars and under the influence of the cosmic radiation on the earth surface we present the quantum-mechanical approach, which is based on the generalized Krylov-Fock theorem. Some simple estimations are also presented. They bring to the conclusion that the usual (non-corrected) "nuclear clocks" do really indicate not to realistic values but to the \emph{upper limits} of the durations of the $\alpha$-decay stellar and planet processes.Comment: 6 pages, Standard LaTeX v.2

Unitarity of the tree approximation to the Glauber AA amplitude for large A

The nucleus-nucleus Glauber amplitude in the tree approximation is studied for heavy participant nuclei. It is shown that, contrary to previous published results, it is not unitary for realistic values of nucleon-nucleon cross-sections.Comment: 15 pages, 1 figure, 1 table. Submitted to Yad. Fi

Non-affine geometrization can lead to nonphysical instabilities

Geometrization of dynamics consists of representing trajectories by geodesics on a configuration space with a suitably defined metric. Previously, efforts were made to show that the analysis of dynamical stability can also be carried out within geometrical frameworks, by measuring the broadening rate of a bundle of geodesics. Two known formalisms are via Jacobi and Eisenhart metrics. We find that this geometrical analysis measures the actual stability when the length of any geodesic is proportional to the corresponding time interval. We prove that the Jacobi metric is not always an appropriate parametrization by showing that it predicts chaotic behavior for a system of harmonic oscillators. Furthermore, we show, by explicit calculation, that the correspondence between dynamical- and geometrical-spread is ill-defined for the Jacobi metric. We find that the Eisenhart dynamics corresponds to the actual tangent dynamics and is therefore an appropriate geometrization scheme.Comment: Featured on the Cover of the Journal. 9 pages, 6 figures: http://iopscience.iop.org/1751-8121/48/7/07510

Scattering of Rayleigh waves by a groove of arbitrary depth

The scattering of Rayieigh waves by a two-dimensional groove formed on the surface of an aluminum sample is investigated experimentally. A complete set of measurements of the scattered-field parameters, including the elastic characteristics of the scattered longitudinal and shear bulk waves and the reflection and transmission coefficients of the Rayleigh surface waves, is carried out for a broad range of groove depths

Towards a feasible implementation of quantum neural networks using quantum dots

We propose an implementation of quantum neural networks using an array of quantum dots with dipole-dipole interactions. We demonstrate that this implementation is both feasible and versatile by studying it within the framework of GaAs based quantum dot qubits coupled to a reservoir of acoustic phonons. Using numerically exact Feynman integral calculations, we have found that the quantum coherence in our neural networks survive for over a hundred ps even at liquid nitrogen temperatures (77 K), which is three orders of magnitude higher than current implementations which are based on SQUID-based systems operating at temperatures in the mK range.Comment: revtex, 5 pages, 2 eps figure

Theoretical prediction of ground vibrations from heavy military vehicles

The demand for reliable autonomous systems capable to detect and identify heavy military vehicles becomes an issue of paramount importance in the current complicated and delicate political climate. It is expected that such autonomous systems would alleviate some of the burden placed on UN peace keeping forces, who currently must patrol areas systematically to identify and monitor military activity. A promising method of detection and identification that influenced increasing levels of recent investment is the one using the information extracted from ground vibration spectra generated by heavy military vehicles, often termed as their seismic signatures. This paper presents the results of the theoretical investigation of ground vibrations generated by heavy military vehicles, such as tanks and armed personnel carriers. Initially, vehicle models of different degrees of complexity are considered - to identify the resulting dynamic forces applied to the ground. Then the obtained analytical expressions for vehicle dynamic forces are used for calculations of generated ground vibrations (primarily Rayleigh surface waves) using Green’s function method. A comparison of the obtained theoretical results with published experimental data shows their good agreement

Calculation of ground vibration spectra from heavy military vehicles

The demand for reliable autonomous systems capable to detect and identify heavy military vehicles becomes an important issue for UN peacekeeping forces in the current delicate political climate. A promising method of detection and identification is the one using the information extracted from ground vibration spectra generated by heavy military vehicles, often termed as their seismic signatures. This paper presents the results of the theoretical investigation of ground vibration spectra generated by heavy military vehicles, such as tanks and armed personnel carriers. A simple quarter car model is considered to identify the resulting dynamic forces applied from a vehicle to the ground. Then the obtained analytical expressions for vehicle dynamic forces are used for calculations of generated ground vibrations, predominantly Rayleigh surface waves, using Green’s function method. A comparison of the obtained theoretical results with published experimental data shows that analytical techniques based on the simplified quarter car vehicle model are capable of producing ground vibration spectra of heavy military vehicles that reproduce basic properties of experimental spectra