1,186 research outputs found
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 of a Hamiltonian system. Using this
result, trajectories with small energy shadowing chains of homoclinic
orbits to 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 . As , 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: âinnovationâ, âinnovative activityâ, âinnovation processâ 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 -centre problem at negative energies
We consider the planar -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 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: âinnovationâ, âinnovative activityâ, âinnovation processâ 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 pseudoâmagnetic 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 moirĂ© 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 moirĂ© 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 moirĂ© and strain-induced effects and allows for the full reconstruction of 3D positions and atomic identities
Impact of gigahertz and terahertz transport regimes on spin propagation and conversion in the antiferromagnet IrMn
Control over spin transport in antiferromagnetic systems is essential for future spintronic applications with operational speeds extending to ultrafast time scales. Here, we study the transition from the gigahertz (GHz) to terahertz (THz) regime of spin transport and spin-to-charge current conversion (S2C) in the prototypical antiferromagnet IrMn by employing spin pumping and THz spectroscopy techniques. We reveal a factor of 4 shorter characteristic propagation lengths of the spin current at THz frequencies (âŒ0.5ânm) as compared to GHz experiments (âŒ2ânm). This observation may be attributed to different transport regimes. The conclusion is supported by extraction of sub-picosecond temporal dynamics of the THz spin current. We identify no relevant impact of the magnetic order parameter on S2C signals and no scalable magnonic transport in THz experiments. A significant role of the S2C originating from interfaces between IrMn and magnetic or non-magnetic metals is observed, which is much more pronounced in the THz regime and opens the door for optimization of the spin control at ultrafast time scales
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