94 research outputs found
Discrete Breathers
Nonlinear classical Hamiltonian lattices exhibit generic solutions in the
form of discrete breathers. These solutions are time-periodic and (typically
exponentially) localized in space. The lattices exhibit discrete translational
symmetry. Discrete breathers are not confined to certain lattice dimensions.
Necessary ingredients for their occurence are the existence of upper bounds on
the phonon spectrum (of small fluctuations around the groundstate) of the
system as well as the nonlinearity in the differential equations. We will
present existence proofs, formulate necessary existence conditions, and discuss
structural stability of discrete breathers. The following results will be also
discussed: the creation of breathers through tangent bifurcation of band edge
plane waves; dynamical stability; details of the spatial decay; numerical
methods of obtaining breathers; interaction of breathers with phonons and
electrons; movability; influence of the lattice dimension on discrete breather
properties; quantum lattices - quantum breathers. Finally we will formulate a
new conceptual aproach capable of predicting whether discrete breather exist
for a given system or not, without actually solving for the breather. We
discuss potential applications in lattice dynamics of solids (especially
molecular crystals), selective bond excitations in large molecules, dynamical
properties of coupled arrays of Josephson junctions, and localization of
electromagnetic waves in photonic crystals with nonlinear response.Comment: 62 pages, LaTeX, 14 ps figures. Physics Reports, to be published; see
also at http://www.mpipks-dresden.mpg.de/~flach/html/preprints.htm
Acoustic breathers in two-dimensional lattices
The existence of breathers (time-periodic and spatially localized lattice
vibrations) is well established for i) systems without acoustic phonon branches
and ii) systems with acoustic phonons, but also with additional symmetries
preventing the occurence of strains (dc terms) in the breather solution. The
case of coexistence of strains and acoustic phonon branches is solved (for
simple models) only for one-dimensional lattices.
We calculate breather solutions for a two-dimensional lattice with one
acoustic phonon branch. We start from the easy-to-handle case of a system with
homogeneous (anharmonic) interaction potentials. We then easily continue the
zero-strain breather solution into the model sector with additional quadratic
and cubic potential terms with the help of a generalized Newton method. The
lattice size is . The breather continues to exist, but is dressed
with a strain field. In contrast to the ac breather components, which decay
exponentially in space, the strain field (which has dipole symmetry) should
decay like . On our rather small lattice we find an exponent
On the Existence of Localized Excitations in Nonlinear Hamiltonian Lattices
We consider time-periodic nonlinear localized excitations (NLEs) on
one-dimensional translationally invariant Hamiltonian lattices with arbitrary
finite interaction range and arbitrary finite number of degrees of freedom per
unit cell. We analyse a mapping of the Fourier coefficients of the NLE
solution. NLEs correspond to homoclinic points in the phase space of this map.
Using dimensionality properties of separatrix manifolds of the mapping we show
the persistence of NLE solutions under perturbations of the system, provided
NLEs exist for the given system. For a class of nonintegrable Fermi-Pasta-Ulam
chains we rigorously prove the existence of NLE solutions.Comment: 13 pages, LaTeX, 2 figures will be mailed upon request (Phys. Rev. E,
in press
Blind source separation via multinode sparse representation
We consider a problem of blind source separation from a set of instan taneous
linear mixtures, where the mixing matrix is unknown. It was discovered recently, that
exploiting the sparsity of sources in an appro priate representation according to some signal
dictionary, dramatically improves the quality of separation. In this work we use the property
of multiscale transforms, such as wavelet or wavelet packets, to decompose signals into sets
of local features with various degrees of sparsity. We use this intrinsic property for selecting the best (most sparse) subsets of features for further separation. The performance of the algorithm is verified on noise-free and noisy data. Experiments with simulated signals, musical sounds and images demonstrate significant improvement of separation quality over previously reported results
Field exposed water in a nanopore: liquid or vapour?
We study the behavior of ambient temperature water under the combined effects
of nanoscale confinement and applied electric field. Using molecular
simulations we analyze the thermodynamic causes of field-induced expansion at
some, and contraction at other conditions. Repulsion among parallel water
dipoles and mild weakening of interactions between partially aligned water
molecules prove sufficient to destabilize the aqueous liquid phase in isobaric
systems in which all water molecules are permanently exposed to a uniform
electric field. At the same time, simulations reveal comparatively weak
field-induced perturbations of water structure upheld by flexible hydrogen
bonding. In open systems with fixed chemical potential, these perturbations do
not suffice to offset attraction of water into the field; additional water is
typically driven from unperturbed bulk phase to the field-exposed region. In
contrast to recent theoretical predictions in the literature, our analysis and
simulations confirm that classical electrostriction characterizes usual
electrowetting behavior in nanoscale channels and nanoporous materials.Comment: 20 pages, 6 figures + T.O.C. figure, in press in PCC
Representations of solutions of the wave equation based on relativistic wavelets
A representation of solutions of the wave equation with two spatial
coordinates in terms of localized elementary ones is presented. Elementary
solutions are constructed from four solutions with the help of transformations
of the affine Poincar\'e group, i.e., with the help of translations, dilations
in space and time and Lorentz transformations. The representation can be
interpreted in terms of the initial-boundary value problem for the wave
equation in a half-plane. It gives the solution as an integral representation
of two types of solutions: propagating localized solutions running away from
the boundary under different angles and packet-like surface waves running along
the boundary and exponentially decreasing away from the boundary. Properties of
elementary solutions are discussed. A numerical investigation of coefficients
of the decomposition is carried out. An example of the field created by sources
moving along a line with different speeds is considered, and the dependence of
coefficients on speeds of sources is discussed.Comment: submitted to J. Phys. A: Math. Theor., 20 pages, 6 figure
Π―Π΄Π΅ΡΠ½ΡΠ΅ ΠΈΡΠΏΡΡΠ°Π½ΠΈΡ Π½Π° Π‘Π΅ΠΌΠΈΠΏΠ°Π»Π°ΡΠΈΠ½ΡΠΊΠΎΠΌ ΠΏΠΎΠ»ΠΈΠ³ΠΎΠ½Π΅ ΠΈ Π·Π΄ΠΎΡΠΎΠ²ΡΠ΅ Π½Π°ΡΠ΅Π»Π΅Π½ΠΈΡ ΠΠ»ΡΠ°ΠΉΡΠΊΠΎΠ³ΠΎ ΠΊΡΠ°Ρ
The comparative analysis of morbidity, mortality and in validation of the population of Altay region and other regions of West Siberia (Kemerovsky, Novosibirsky, Omsky, Tomsky, Tyumensky) is presented in this paper. It was found that in recent years in spite of a more favorable ecologic situation in this area the level of morbidity (hematological disorders, cardiovascular disorders, urinary diseases), mortality from infectious, parasitic, pulmonary diseases and malignant tumors and invalidisation of the population increased. The main cause of this is supposed to be the consequences of nuclear weapon tests in the atmosphere in 1949-1962 on the testing ground near Semipalatinsk at the border of Altay region. The data on repeated pollutions by the products of nuclear disintegration in Altay region are reported.Π ΡΡΠ°ΡΡΠ΅ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½ ΡΡΠ°Π²Π½ΠΈΡΠ΅Π»ΡΠ½ΡΠΉ Π°Π½Π°Π»ΠΈΠ· ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Π΅ΠΉ Π·Π°Π±ΠΎΠ»Π΅Π²Π°Π΅ΠΌΠΎΡΡΠΈ, ΡΠΌΠ΅ΡΡΠ½ΠΎΡΡΠΈ ΠΈ ΠΈΠ½Π²Π°Π»ΠΈΠ΄ΠΈΠ·Π°ΡΠΈΠΈ Π½Π°ΡΠ΅Π»Π΅Π½ΠΈΡ ΠΠ»ΡΠ°ΠΉΡΠΊΠΎΠ³ΠΎ ΠΊΡΠ°Ρ ΠΈ Π΄ΡΡΠ³ΠΈΡ
ΠΎΠ±Π»Π°ΡΡΠ΅ΠΉ ΠΠ°ΠΏΠ°Π΄Π½ΠΎΠΉ Π‘ΠΈΠ±ΠΈΡΠΈ (ΠΠ΅ΠΌΠ΅ΡΠΎΠ²ΡΠΊΠΎΠΉ, ΠΠΎΠ²ΠΎΡΠΈΠ±ΠΈΡΡΠΊΠΎΠΉ, ΠΠΌΡΠΊΠΎΠΉ, Π’ΠΎΠΌΡΠΊΠΎΠΉ, Π’ΡΠΌΠ΅Π½ΡΠΊΠΎΠΉ). Π£ΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΎ, ΡΡΠΎ Π² ΠΏΠΎΡΠ»Π΅Π΄Π½ΠΈΠ΅ Π³ΠΎΠ΄Ρ ΠΏΡΠΈ Π±ΠΎΠ»Π΅Π΅ Π±Π»Π°Π³ΠΎΠΏΡΠΈΡΡΠ½ΠΎΠΉ ΡΠΊΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΎΠ±ΡΡΠ°Π½ΠΎΠ²ΠΊΠ΅ ΠΎΡΠ½ΠΎΡΠΈΡΠ΅Π»ΡΠ½ΠΎ ΡΡΠ°Π²Π½ΠΈΠ²Π°Π΅ΠΌΡΡ
ΡΠ΅ΡΡΠΈΡΠΎΡΠΈΠΉ Π² ΠΊΡΠ°Π΅ ΠΎΡΠΌΠ΅ΡΠ°Π΅ΡΡΡ Π±ΠΎΠ»Π΅Π΅ Π²ΡΡΠΎΠΊΠΈΠΉ ΡΡΠΎΠ²Π΅Π½Ρ Π·Π°Π±ΠΎΠ»Π΅Π²Π°Π΅ΠΌΠΎΡΡΠΈ (Π±ΠΎΠ»Π΅Π·Π½ΠΈ ΠΊΡΠΎΠ²ΠΈ, ΡΠ΅ΡΠ΄Π΅ΡΠ½ΠΎ-ΡΠΎΡΡΠ΄ΠΈΡΡΠΎΠΉ, ΠΌΠΎΡΠ΅ΠΏΠΎΠ»ΠΎΠ²ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌ), ΡΠΌΠ΅ΡΡΠ½ΠΎΡΡΠΈ (ΠΎΡ ΠΈΠ½ΡΠ΅ΠΊΡΠΈΠΎΠ½Π½ΡΡ
ΠΈ ΠΏΠ°ΡΠ°Π·ΠΈΡΠ°ΡΠ½ΡΡ
Π±ΠΎΠ»Π΅Π·Π½Π΅ΠΉ, Π·Π»ΠΎΠΊΠ°ΡΠ΅ΡΡΠ²Π΅Π½Π½ΡΡ
Π½ΠΎΠ²ΠΎΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΠΉ, Π±ΠΎΠ»Π΅Π·Π½Π΅ΠΉ ΠΎΡΠ³Π°Π½ΠΎΠ² Π΄ΡΡ
Π°Π½ΠΈΡ) ΠΈ ΠΈΠ½Π²Π°Π»ΠΈΠ΄ΠΈΠ·Π°ΡΠΈΠΈ Π½Π°ΡΠ΅Π»Π΅Π½ΠΈΡ. Π ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΠΎΡΠ½ΠΎΠ²Π½ΠΎΠΉ ΠΏΡΠΈΡΠΈΠ½Ρ Π½Π΅Π±Π»Π°Π³ΠΎΠΏΡΠΈΡΡΠ½ΡΡ
ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Π΅ΠΉ Π·Π΄ΠΎΡΠΎΠ²ΡΡ ΠΆΠΈΡΠ΅Π»Π΅ΠΉ ΡΡΠΎΠ³ΠΎ ΡΠ°ΠΉΠΎΠ½Π° ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ ΠΏΠΎΡΠ»Π΅Π΄ΡΡΠ²ΠΈΡ ΡΠ΄Π΅ΡΠ½ΡΡ
ΠΈΡΠΏΡΡΠ°Π½ΠΈΠΉ Π² Π°ΡΠΌΠΎΡΡΠ΅ΡΠ΅ Π² 1949β1962 Π³Π³. Π½Π° Π‘Π΅ΠΌΠΈΠΏΠ°Π»Π°ΡΠΈΠ½ΡΠΊΠΎΠΌ ΠΏΠΎΠ»ΠΈΠ³ΠΎΠ½Π΅, Π½Π°Ρ
ΠΎΠ΄ΡΡΠ΅ΠΌΡΡ Π² Π½Π΅ΠΏΠΎΡΡΠ΅Π΄ΡΡΠ²Π΅Π½Π½ΠΎΠΉ Π±Π»ΠΈΠ·ΠΎΡΡΠΈ ΠΎΡ Π³ΡΠ°Π½ΠΈΡΡ ΠΊΡΠ°Ρ. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ Π΄Π°Π½Π½ΡΠ΅, ΡΠ²ΠΈΠ΄Π΅ΡΠ΅Π»ΡΡΡΠ²ΡΡΡΠΈΠ΅ ΠΎΠ± ΠΈΠΌΠ΅Π²ΡΠ΅ΠΌ ΠΌΠ΅ΡΡΠΎ ΠΌΠ½ΠΎΠ³ΠΎΠΊΡΠ°ΡΠ½ΠΎΠΌ Π·Π°Π³ΡΡΠ·Π½Π΅Π½ΠΈΠΈ ΡΠ΅ΡΡΠΈΡΠΎΡΠΈΠΈ ΠΠ»ΡΠ°ΠΉΡΠΊΠΎΠ³ΠΎ ΠΊΡΠ°Ρ ΠΏΡΠΎΠ΄ΡΠΊΡΠ°ΠΌΠΈ ΡΠ΄Π΅ΡΠ½ΠΎΠ³ΠΎ ΡΠ°ΡΠΏΠ°Π΄Π°
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