New Approach to Nonlinear Dynamics of Fullerenes and Fullerites

New type of nonlinear (anharmonic) excitations -- bushes of vibrational modes -- in physical systems with point or space symmetry are discussed. All infrared active and Raman active bushes for C60 fulerene are found by means of special group-theoretical methods.Comment: LaTeX, 8 pages, to be published in Fizika Tverdogo Tela, 200

Stability of Nonlinear Normal Modes in the FPU-β\beta Chain in the Thermodynamic Limit

All possible symmetry-determined nonlinear normal modes (also called by simple periodic orbits, one-mode solutions etc.) in both hard and soft Fermi-Pasta-Ulam-$\beta$ chains are discussed. A general method for studying their stability in the thermodynamic limit, as well as its application for each of the above nonlinear normal modes are presented

Could One Find Petroleum Using Neutrino Oscillations in Matter?

In neutrino physics, it is now widely believed that neutrino oscillations are influenced by the presence of matter, modifying the energy spectrum produced by a neutrino beam traversing the Earth. Here, we will discuss the reverse problem, i.e. what could be learned about the Earth's interior from a single neutrino baseline energy spectrum, especially about the Earth's mantle. We will use a statistical analysis with a low-energy neutrino beam under very optimistic assumptions. At the end, we will note that it is hard to find petroleum with such a method, though it is not too far away from technical feasibility.Comment: 6 pages, 4 figures, EPL LaTeX. Final version to be published in Europhys. Let

Organization of Communication with the Unmanned Aerial Vehicle in a Combined Data Transmission Network

Communication with UAV (Unmanned Aerial Vehicle) can be organized using terrestrial radio (high efficiency, but limited in terms of service area) and satellite (global coverage area, but large delay in propagation of radio signals) communication networks. Their integration will ensure high efficiency and reliability of information interaction with UAV. The task of dynamic control of information flows to ensure the specified characteristics is relevant. The article analyzes the algorithm for managing information flows when a communication session with UAV is performed through that segment of the network (terrestrial or satellite one), which at the moment will provide the maximum efficiency of information delivery. A mathematical model of information exchange in this integrated communication network as a queuing network with Poisson incoming traffic and exponential distribution of the volume of transmitted information has been developed. Ratios are obtained for calculating the average network delay depending on the ratio between throughputs of satellite and terrestrial segments of integration of the communication network. The proposed model allows selecting the required bandwidth of satellite and terrestrial segments of communication networks, where the specified requirements for the speed of information delivery are provided. The use of dynamic flow control can significantly increase the efficiency of information exchange with UAV

Delocalized nonlinear vibrational modes in graphene: second harmonic generation and negative pressure

With the help of molecular dynamics simulations, delocalized nonlinear vibrational modes (DNVM) in graphene are analyzed. Such modes are dictated by the lattice symmetry, they are exact solutions to the atomic equations of motion, regardless the employed interatomic potential and for any mode amplitude (though for large amplitudes they are typically unstable). In this study, only one‐ and two‐component DNVM are analyzed, they are reducible to the dynamical systems with one and two degrees of freedom, respectively. There exist 4 one‐component and 12 two‐component DNVM with in‐plane atomic displacements. Any two‐component mode includes one of the one‐component modes. If the amplitudes of the modes constituting a two‐component mode are properly chosen, periodic in time vibrations are observed for the two degrees of freedom at frequencies ω and 2ω, that is, second harmonic generation takes place. For particular DNVM, the higher harmonic can have frequency nearly two times larger than the maximal frequency of the phonon spectrum of graphene. Excitation of some of DNVM results in the appearance of negative in‐plane pressure in graphene. This counterintuitive result is explained by the rotational motion of carbon hexagons. Our results contribute to the understanding of nonlinear dynamics of the graphene lattice

Discrete Symmetry and Stability in Hamiltonian Dynamics

In this tutorial we address the existence and stability of periodic and quasiperiodic orbits in N degree of freedom Hamiltonian systems and their connection with discrete symmetries. Of primary importance in our study are the nonlinear normal modes (NNMs), i.e periodic solutions which represent continuations of the system's linear normal modes in the nonlinear regime. We examine the existence of such solutions and discuss different methods for constructing them and studying their stability under fixed and periodic boundary conditions. In the periodic case, we employ group theoretical concepts to identify a special type of NNMs called one-dimensional "bushes". We describe how to use linear combinations such NNMs to construct s(>1)-dimensional bushes of quasiperiodic orbits, for a wide variety of Hamiltonian systems and exploit the symmetries of the linearized equations to simplify the study of their destabilization. Applying this theory to the Fermi Pasta Ulam (FPU) chain, we review a number of interesting results, which have appeared in the recent literature. We then turn to an analytical and numerical construction of quasiperiodic orbits, which does not depend on the symmetries or boundary conditions. We demonstrate that the well-known "paradox" of FPU recurrences may be explained in terms of the exponential localization of the energies Eq of NNM's excited at the low part of the frequency spectrum, i.e. q=1,2,3,.... Thus, we show that the stability of these low-dimensional manifolds called q-tori is related to the persistence or FPU recurrences at low energies. Finally, we discuss a novel approach to the stability of orbits of conservative systems, the GALIk, k=2,...,2N, by means of which one can determine accurately and efficiently the destabilization of q-tori, leading to the breakdown of recurrences and the equipartition of energy, at high values of the total energy E.Comment: 50 pages, 13 figure

The Maximum Energy and Spectra of Cosmic Rays Accelerated in Active Galactic Nuclei

We computed the energy spectra of the incident (on an air shower array) ultrahigh-energy (E > 4x10^19 eV) cosmic rays (CRs) that were accelerated in nearby Seyfert nuclei at redshifts z<= 0.0092 and in BL Lac objects. For our calculations, we took the distribution of these sources over the sky from catalogs of active galactic nuclei. In accordance with the possible particle acceleration mechanisms, the initial CR spectrum was assumed to be monoenergetic for BL Lac's and a power law for Seyfert nuclei. The CR energy losses in intergalactic space were computed by the Monte Carlo method. The artificial proton statistic was 10^5 for each case considered. The computed spectra of the particles incident on an air shower array agree with the measurements, which indirectly confirms the adopted acceleration models. At energies E>=10^20 eV, the spectrum of the protons from nearby Seyfert nuclei that reached an air shower array closely matches the spectrum of the particles from BL Lac's. BL Lac's are, on average, several hundred Mpc away. Therefore, it is hard to tell whether a blackbody cutoff exists or not by analyzing the shape of the measured spectrum at E>= 5x10^19 eV.Comment: 14 pages, 5 fig. To be Published in Astronomy Letters, 2004, v.30, #1

Critical Review of Theoretical Models for Anomalous Effects (Cold Fusion) in Deuterated Metals

We briefly summarize the reported anomalous effects in deuterated metals at ambient temperature, commonly known as "Cold Fusion" (CF), with an emphasis on important experiments as well as the theoretical basis for the opposition to interpreting them as cold fusion. Then we critically examine more than 25 theoretical models for CF, including unusual nuclear and exotic chemical hypotheses. We conclude that they do not explain the data.Comment: 51 pages, 4 Figure