2,175 research outputs found
Chaotic quasi-collision trajectories in the 3-centre problem
We study a particular kind of chaotic dynamics for the planar 3-centre
problem on small negative energy level sets. We know that chaotic motions
exist, if we make the assumption that one of the centres is far away from the
other two (see Bolotin and Negrini, J. Diff. Eq. 190 (2003), 539--558): this
result has been obtained by the use of the Poincar\'e-Melnikov theory. Here we
change the assumption on the third centre: we do not make any hypothesis on its
position, and we obtain a perturbation of the 2-centre problem by assuming its
intensity to be very small. Then, for a dense subset of possible positions of
the perturbing centre on the real plane, we prove the existence of uniformly
hyperbolic invariant sets of periodic and chaotic almost collision orbits by
the use of a general result of Bolotin and MacKay (see Cel. Mech. & Dyn. Astr.
77 (2000), 49--75). To apply it, we must preliminarily construct chains of
collision arcs in a proper way. We succeed in doing that by the classical
regularisation of the 2-centre problem and the use of the periodic orbits of
the regularised problem passing through the third centre.Comment: 22 pages, 6 figure
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: “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
Distributed computing system with dual independent communications paths between computers and employing split tokens
This is a distributed computing system providing flexible fault tolerance; ease of software design and concurrency specification; and dynamic balance of the loads. The system comprises a plurality of computers each having a first input/output interface and a second input/output interface for interfacing to communications networks each second input/output interface including a bypass for bypassing the associated computer. A global communications network interconnects the first input/output interfaces for providing each computer the ability to broadcast messages simultaneously to the remainder of the computers. A meshwork communications network interconnects the second input/output interfaces providing each computer with the ability to establish a communications link with another of the computers bypassing the remainder of computers. Each computer is controlled by a resident copy of a common operating system. Communications between respective ones of computers is by means of split tokens each having a moving first portion which is sent from computer to computer and a resident second portion which is disposed in the memory of at least one of computer and wherein the location of the second portion is part of the first portion. The split tokens represent both functions to be executed by the computers and data to be employed in the execution of the functions. The first input/output interfaces each include logic for detecting a collision between messages and for terminating the broadcasting of a message whereby collisions between messages are detected and avoided
Three-dimensional modular electronic interconnection system
A three-dimensional connection system uses a plurality of printed wiring boards with connectors completely around the printed wiring boards, and connected by an elastomeric interface connector. The device includes internal space to allow room for circuitry. The device is formed by stacking an electronics module, an elastomeric interface board on the electronics module such that the interface board's exterior makes electrical connection with the connectors around the perimeter of the interface board, but the internal portion is open to allow room for the electrical devices on the printed wiring board. A plurality of these devices are stacked between a top stiffener and a bottom device, and held into place by alignment elements
Anisotropic magnetoresistance in nanocontacts
We present ab initio calculations of the evolution of anisotropic
magnetoresistance (AMR) in Ni nanocontacts from the ballistic to the tunnel
regime. We find an extraordinary enhancement of AMR, compared to bulk, in two
scenarios. In systems without localized states, like chemically pure break
junctions, large AMR only occurs if the orbital polarization of the current is
large, regardless of the anisotropy of the density of states. In systems that
display localized states close to the Fermi energy, like a single electron
transistor with ferromagnetic electrodes, large AMR is related to the variation
of the Fermi energy as a function of the magnetization direction.Comment: 7 pages, 4 figures; revised for publication, new figures in greyscal
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
Persistence of homoclinic orbits for billiards and twist maps
We consider the billiard motion inside a C2-small perturbation of a ndimensional
ellipsoid Q with a unique major axis. The diameter of the ellipsoid Q is a
hyperbolic two-periodic trajectory whose stable and unstable invariant manifolds are
doubled, so that there is a n-dimensional invariant set W of homoclinic orbits for the
unperturbed billiard map. The set W is a stratified set with a complicated structure.
For the perturbed billiard map the set W generically breaks down into isolated
homoclinic orbits. We provide lower bounds for the number of primary homoclinic
orbits of the perturbed billiard which are close to unperturbed homoclinic orbits in
certain strata of W.
The lower bound for the number of persisting primary homoclinic billiard orbits
is deduced from a more general lower bound for exact perturbations of twist maps
possessing a manifold of homoclinic orbits
Stark shift and electric-field-induced dissociation of excitons in monolayer MoS2 and hBN/MoS2 heterostructures
Efficient conversion of photons into electrical current in two-dimensional
semiconductors requires, as a first step, the dissociation of the strongly
bound excitons into free electrons and holes. Here we calculate the
dissociation rates and energy shift of excitons in monolayer MoS2 as a
function of an applied in-plane electric field. The dissociation rates are
obtained as the inverse lifetime of the resonant states of a two-dimensional
hydrogenic Hamiltonian which describes the exciton within the Mott-Wannier
model. The resonances are computed using complex scaling, and the effective
masses and screened electron-hole interaction defining the hydrogenic
Hamiltonian are computed from first principles. For field strengths above 0.1
V/nm the dissociation lifetime is shorter than 1 ps, which is below the
lifetime associated with competing decay mechanisms. Interestingly,
encapsulation of the MoS2 layer in just two layers of hexagonal boron nitride
(hBN), enhances the dissociation rate by around one order of magnitude due to
the increased screening. This shows that dielectric engineering is an
effective way to control exciton lifetimes in two-dimensional materials
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