2,431 research outputs found
Classification and stability of simple homoclinic cycles in R^5
The paper presents a complete study of simple homoclinic cycles in R^5. We
find all symmetry groups Gamma such that a Gamma-equivariant dynamical system
in R^5 can possess a simple homoclinic cycle. We introduce a classification of
simple homoclinic cycles in R^n based on the action of the system symmetry
group. For systems in R^5, we list all classes of simple homoclinic cycles. For
each class, we derive necessary and sufficient conditions for asymptotic
stability and fragmentary asymptotic stability in terms of eigenvalues of
linearisation near the steady state involved in the cycle. For any action of
the groups Gamma which can give rise to a simple homoclinic cycle, we list
classes to which the respective homoclinic cycles belong, thus determining
conditions for asymptotic stability of these cycles.Comment: 34 pp., 4 tables, 30 references. Submitted to Nonlinearit
The study of dynamic characteristics of spindle unit with rod blanc
Розроблено динамічну модель шпиндельного вузла токарного автомата з
врахуванням пруткової заготовки. Встановлено максимальні значення динамічної податливості шпиндельного вузла та запропоновано методи її зменщення
методи її зменшенн
Beam self-cleaning in multimode optical fibers and hydrodynamic 2D turbulence
We experimentally demonstrate the conservation of the average mode number in the process of Kerr beam self-cleaning in a graded-index multimode optical fiber, in analogy with wave condensation in hydrodynamic 2D turbulence
Spatial beam self-cleaning and supercontinuum generation with Yb-doped multimode graded-index fiber taper based on accelerating self-imaging and dissipative landscape
We experimentally demonstrate spatial beam self-cleaning and supercontinuum generation in a tapered Ytterbium-doped multimode optical fiber with parabolic core refractive index profile when 1064 nm pulsed beams propagate from wider (122 µm) into smaller (37 µm) diameter. In the passive mode, increasing the input beam peak power above 20 kW leads to a bell-shaped output beam profile. In the active configuration, gain from the pump laser diode permits to combine beam self-cleaning with supercontinuum generation between 520-2600 nm. By taper cut-back, we observed that the dissipative landscape, i.e., a non-monotonic variation of the average beam power along the MMF, leads to modal transitions of self-cleaned beams along the taper length
Dependence of magnetic field generation by thermal convection on the rotation rate: a case study
Dependence of magnetic field generation on the rotation rate is explored by
direct numerical simulation of magnetohydrodynamic convective attractors in a
plane layer of conducting fluid with square periodicity cells for the Taylor
number varied from zero to 2000, for which the convective fluid motion halts
(other parameters of the system are fixed). We observe 5 types of hydrodynamic
(amagnetic) attractors: two families of two-dimensional (i.e. depending on two
spatial variables) rolls parallel to sides of periodicity boxes of different
widths and parallel to the diagonal, travelling waves and three-dimensional
"wavy" rolls. All types of attractors, except for one family of rolls, are
capable of kinematic magnetic field generation. We have found 21 distinct
nonlinear convective MHD attractors (13 steady states and 8 periodic regimes)
and identified bifurcations in which they emerge. In addition, we have observed
a family of periodic, two-frequency quasiperiodic and chaotic regimes, as well
as an incomplete Feigenbaum period doubling sequence of bifurcations of a torus
followed by a chaotic regime and subsequently by a torus with 1/3 of the
cascade frequency. The system is highly symmetric. We have found two novel
global bifurcations reminiscent of the SNIC bifurcation, which are only
possible in the presence of symmetries. The universally accepted paradigm,
whereby an increase of the rotation rate below a certain level is beneficial
for magnetic field generation, while a further increase inhibits it (and halts
the motion of fluid on continuing the increase) remains unaltered, but we
demonstrate that this "large-scale" picture lacks many significant details.Comment: 39 pp., 22 figures (some are low quality), 5 tables. Accepted in
Physica
Finishing treatment of the involute surfaces og the direct gear wheels by the surfaces plastic deformation forming regular micro-projection
Розглянуто існуючі методи поверхневого пластичного зміцнення робочих
поверхонь циліндричних прямозубих коліс. Запрпоновано метод вібраційного обкочування зубчастих колі
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