Shilnikov Lemma for a nondegenerate critical manifold of a Hamiltonian system

We prove an analog of Shilnikov Lemma for a normally hyperbolic symplectic critical manifold $M\subset H^{-1}(0)$ of a Hamiltonian system. Using this result, trajectories with small energy $H=\mu>0$ shadowing chains of homoclinic orbits to $M$ are represented as extremals of a discrete variational problem, and their existence is proved. This paper is motivated by applications to the Poincar\'e second species solutions of the 3 body problem with 2 masses small of order $\mu$. As $\mu\to 0$, double collisions of small bodies correspond to a symplectic critical manifold of the regularized Hamiltonian system

UNION COUNTRIES AND THE RUSSIAN FEDERATION

The article is aimed at the consideration of the problems occurring in the field of economic and legal integration of fundamental principles concerning the innovations, the innovation process and the types of innovations. The priority of economy innovation development and the suffi cient legal regulation of this process in the global community is determinated in the article. The basic notions of Innovation law such as: “innovation”, “innovative activity”, “innovation process” are carefully examined and analyzed in detail. The authors have classified the innovation types on various grounds. They came to the conclusion, that there is the necessity to establish a common understanding of the above mentioned notions, to develop the integrated mechanisms to stimulate innovative activity of all innovation process participants. The dominating method of research is a comparative analysis of the basic notions, economic prerequisites and Innovation law

Symbolic dynamics for the NN-centre problem at negative energies

We consider the planar $N$-centre problem, with homogeneous potentials of degree -\a<0, \a \in [1,2). We prove the existence of infinitely many collisions-free periodic solutions with negative and small energy, for any distribution of the centres inside a compact set. The proof is based upon topological, variational and geometric arguments. The existence result allows to characterize the associated dynamical system with a symbolic dynamics, where the symbols are the partitions of the $N$ centres in two non-empty sets

UNION COUNTRIES AND THE RUSSIAN FEDERATION

The article is aimed at the consideration of the problems occurring in the field of economic and legal integration of fundamental principles concerning the innovations, the innovation process and the types of innovations. The priority of economy innovation development and the suffi cient legal regulation of this process in the global community is determinated in the article. The basic notions of Innovation law such as: “innovation”, “innovative activity”, “innovation process” are carefully examined and analyzed in detail. The authors have classified the innovation types on various grounds. They came to the conclusion, that there is the necessity to establish a common understanding of the above mentioned notions, to develop the integrated mechanisms to stimulate innovative activity of all innovation process participants. The dominating method of research is a comparative analysis of the basic notions, economic prerequisites and Innovation law

Theoretical backgrounds of durability analysis by normalized equivalent stress functionals

Generalized durability diagrams and their properties are considered for a material under a multiaxial loading given by an arbitrary function of time. Material strength and durability under such loading are described in terms of durability, safety factor and normalized equivalent stress. Relations between these functionals are analysed. We discuss some material properties including time and load stability, self-degradation (ageing), and monotonic damaging. Phenomenological strength conditions are presented in terms of the normalized equivalent stress. It is shown that the damage based durability analysis is reduced to a particular case of such strength conditions. Examples of the reduction are presented for some known durability models. The approach is applicable to the strength and durability description at creep and impact loading and their combination

How close can one approach the Dirac point in graphene experimentally?

The above question is frequently asked by theorists who are interested in graphene as a model system, especially in context of relativistic quantum physics. We offer an experimental answer by describing electron transport in suspended devices with carrier mobilities of several 10^6 cm^2V^-1s^-1 and with the onset of Landau quantization occurring in fields below 5 mT. The observed charge inhomogeneity is as low as \approx10^8 cm^-2, allowing a neutral state with a few charge carriers per entire micron-scale device. Above liquid helium temperatures, the electronic properties of such devices are intrinsic, being governed by thermal excitations only. This yields that the Dirac point can be approached within 1 meV, a limit currently set by the remaining charge inhomogeneity. No sign of an insulating state is observed down to 1 K, which establishes the upper limit on a possible bandgap

The Non-Trapping Degree of Scattering

We consider classical potential scattering. If no orbit is trapped at energy E, the Hamiltonian dynamics defines an integer-valued topological degree. This can be calculated explicitly and be used for symbolic dynamics of multi-obstacle scattering. If the potential is bounded, then in the non-trapping case the boundary of Hill's Region is empty or homeomorphic to a sphere. We consider classical potential scattering. If at energy E no orbit is trapped, the Hamiltonian dynamics defines an integer-valued topological degree deg(E) < 2. This is calculated explicitly for all potentials, and exactly the integers < 2 are shown to occur for suitable potentials. The non-trapping condition is restrictive in the sense that for a bounded potential it is shown to imply that the boundary of Hill's Region in configuration space is either empty or homeomorphic to a sphere. However, in many situations one can decompose a potential into a sum of non-trapping potentials with non-trivial degree and embed symbolic dynamics of multi-obstacle scattering. This comprises a large number of earlier results, obtained by different authors on multi-obstacle scattering.Comment: 25 pages, 1 figure Revised and enlarged version, containing more detailed proofs and remark

Electronic structure, magnetic and optical properties of intermetallic compounds R2Fe17 (R=Pr,Gd)

In this paper we report comprehensive experimental and theoretical investigation of magnetic and electronic properties of the intermetallic compounds Pr2Fe17 and Gd2Fe17. For the first time electronic structure of these two systems was probed by optical measurements in the spectral range of 0.22-15 micrometers. On top of that charge carriers parameters (plasma frequency and relaxation frequency) and optical conductivity s(w) were determined. Self-consistent spin-resolved bandstructure calculations within the conventional LSDA+U method were performed. Theoretical interpetation of the experimental s(w) dispersions indicates transitions between 3d and 4p states of Fe ions to be the biggest ones. Qualitatively the line shape of the theoretical optical conductivity coincides well with our experimental data. Calculated by LSDA+U method magnetic moments per formula unit are found to be in good agreement with observed experimental values of saturation magnetization.Comment: 16 pages, 5 figures, 1 tabl

Theory-assisted determination of nano-rippling and impurities in atomic resolution images of angle-mismatched bilayer graphene

Ripples and impurity atoms are universally present in 2D materials, limiting carrier mobility, creating pseudo–magnetic fields, or affecting the electronic and magnetic properties. Scanning transmission electron microscopy (STEM) generally provides picometer-level precision in the determination of the location of atoms or atomic 'columns' in the in-image plane (xy plane). However, precise atomic positions in the z-direction as well as the presence of certain impurities are difficult to detect. Furthermore, images containing moiré patterns such as those in angle-mismatched bilayer graphene compound the problem by limiting the determination of atomic positions in the xy plane. Here, we introduce a reconstructive approach for the analysis of STEM images of twisted bilayers that combines the accessible xy coordinates of atomic positions in a STEM image with density-functional-theory calculations. The approach allows us to determine all three coordinates of all atomic positions in the bilayer and establishes the presence and identity of impurities. The deduced strain-induced rippling in a twisted bilayer graphene sample is consistent with the continuum model of elasticity. We also find that the moiré pattern induces undulations in the z direction that are approximately an order of magnitude smaller than the strain-induced rippling. A single substitutional impurity, identified as nitrogen, is detected. The present reconstructive approach can, therefore, distinguish between moiré and strain-induced effects and allows for the full reconstruction of 3D positions and atomic identities

Screening and interlayer coupling in multilayer graphene field-effect transistors

With the motivation of improving the performance and reliability of aggressively scaled nano-patterned graphene field-effect transistors, we present the first systematic experimental study on charge and current distribution in multilayer graphene field-effect transistors. We find a very particular thickness dependence for Ion, Ioff, and the Ion/Ioff ratio, and propose a resistor network model including screening and interlayer coupling to explain the experimental findings. In particular, our model does not invoke modification of the linear energy-band structure of graphene for the multilayer case. Noise reduction in nano-scale few-layer graphene transistors is experimentally demonstrated and can be understood within this model as well.Comment: 13 pages, 4 figures, 20 reference