466 research outputs found
Piecewise-linear maps with heterogeneous chaos
Chaotic dynamics can be quite heterogeneous in the sense that in some regions
the dynamics are unstable in more directions than in other regions. When
trajectories wander between these regions, the dynamics is complicated. We say
a chaotic invariant set is heterogeneous when arbitrarily close to each point
of the set there are different periodic points with different numbers of
unstable dimensions. We call such dynamics heterogeneous chaos (or
hetero-chaos), While we believe it is common for physical systems to be
hetero-chaotic, few explicit examples have been proved to be hetero-chaotic.
Here we present two more explicit dynamical systems that are particularly
simple and tractable with computer. It will give more intuition as to how
complex even simple systems can be. Our maps have one dense set of periodic
points whose orbits are 1D unstable and another dense set of periodic points
whose orbits are 2D unstable. Moreover, they are ergodic relative to the
Lebesgue measure.Comment: 16 pages, 9 figure
Hausdorff dimension of heteroclinic intersections for some partially hyperbolic sets
We introduce a -open set of diffeomorphisms of which have
two transitive hyperbolic sets, one is of index 1 (the dimension of the
unstable subbundle) and the other is of index 2. We prove that: the unstable
set of the first hyperbolic set and the stable set of the second are of
Hausdorff dimension nearly 2; the intersection of these unstable and stable
sets contains a set of Hausdorff dimension nearly 1.Comment: 28 pages, 8 figure
The dynamics of the heterochaos baker maps
The heterochaos baker maps are piecewise affine maps of the unit square or
cube introduced by Saiki et al. (2018), to provide a hands-on, elementary
understanding of complicated phenomena in systems of large degrees of freedom.
We review recent progress on a dynamical systems theory of the heterochaos
baker maps, and present new results on properties of measures of maximal
entropy and the underlying Lebesgue measure. We address several conjectures and
questions that may illuminate new aspects of heterochaos and inspire future
research.Comment: 37 pages, 10 figure
Quantum noise in ideal operational amplifiers
We consider a model of quantum measurement built on an ideal operational
amplifier operating in the limit of infinite gain, infinite input impedance and
null output impedance and with a feddback loop. We evaluate the intensity and
voltage noises which have to be added to the classical amplification equations
in order to fulfill the requirements of quantum mechanics. We give a
description of this measurement device as a quantum network scattering quantum
fluctuations from input to output ports.Comment: 4 pages, 2 figures, RevTe
Fluctuation-dissipation theorem and quantum tunneling with dissipation at finite temperature
A reformulation of the fluctuation-dissipation theorem of Callen and Welton
is presented in such a manner that the basic idea of Feynman-Vernon and
Caldeira -Leggett of using an infinite number of oscillators to simulate the
dissipative medium is realized manifestly without actually introducing
oscillators. If one assumes the existence of a well defined dissipative
coefficient which little depends on the temperature in the energy
region we are interested in, the spontanous and induced emissions as well as
induced absorption of these effective oscillators with correct Bose
distribution automatically appears.
Combined with a dispersion relation, we reproduce the tunneling formula in
the presence of dissipation at finite temperature without referring to an
explicit model Lagrangian. The fluctuation-dissipation theorem of Callen-Welton
is also generalized to the fermionic dissipation (or fluctuation) which allows
a transparent physical interpretation in terms of second quantized fermionic
oscillators. This fermionic version of fluctuation-dissipation theorem may
become relevant in the analyses of, for example, fermion radiation from a black
hole and also supersymmetry at the early universe.Comment: 19 pages. Phys. Rev. E (in press
Ulam type stability problems for alternative homomorphisms
We introduce an alternative homomorphism with respect to binary operations and investigate the Ulam type stability problem for such a mapping. The obtained results apply to Ulam type stability problems for several important functional equations.ArticleJOURNAL OF INEQUALITIES AND APPLICATIONS. 2014:228 (2014)journal articl
A note on alpha-vacua and interacting field theory in de Sitter space
We set up a consistent renormalizable perturbation theory of a scalar field
in a nontrivial alpha vacuum in de Sitter space. Although one representation of
the effective action involves non-local interactions between anti-podal points,
we show the theory leads to causal physics, and we prove a spectral theorem for
the interacting two-point function. We construct the renormalized stress energy
tensor and show this develops no imaginary part at leading order in the
interactions, consistent with stability.Comment: 22 pages, 2 figures, latex. v4 some clarifications, some typos fixe
Black Hole Thermodynamics in Horava Lifshitz Gravity and the Related Geometry
Recently, Hoava proposed a non-relativistic renormalizable theory
of gravity which is essentially a field theoretic model for a UV complete
theory of gravity and reduces to Einstein gravity with a non-vanishing
cosmological constant in IR. Also the theory admits a Lifshitz scale-invariance
in time and space with broken Lorentz symmetry at short scale. On the other
hand, at large distances higher derivative terms do not contribute and the
theory coincides with general relativity. Subsequently, Cai and his
collaborators and then Catiuo et al have obtained black hole solutions in this
gravity theory and studied the thermodynamic properties of the black hole
solution. In the present paper, we have investigated the black hole
thermodynamic for two choices of the entropy function - a classical and a
topological in nature. Finally, it is examined whether a phase transition is
possible or not.Comment: 8 figure
Long-range attraction between particles in dusty plasma and partial surface tension of dusty phase boundary
Effective potential of a charged dusty particle moving in homogeneous plasma
has a negative part that provides attraction between similarly charged dusty
particles. A depth of this potential well is great enough to ensure both
stability of crystal structure of dusty plasma and sizable value of surface
tension of a boundary surface of dusty region. The latter depends on the
orientation of the surface relative to the counter-ion flow, namely, it is
maximal and positive for the surface normal to the flow and minimal and
negative for the surface along the flow. For the most cases of dusty plasma in
a gas discharge, a value of the first of them is more than sufficient to ensure
stability of lenticular dusty phase void oriented across the counter-ion flow.Comment: LATEX, REVTEX4, 7 pages, 6 figure
VERTICAL AND HORIZONTAL FORCES DURING CUTIING IN BASKETBALL UNDER DIFFERENT CONDITIONS
The purpose of this study is to evaluate ground reaction force responses in professional basketball athletes while executing this sport's typical cutting maneuver with and without ankle bracing: taping, aircast-type orthosis and basketball shoes. Eight athletes were dynamically analyzed during a basketball cutting maneuver with a force platform. We collected vertical and medial-lateral forces under these three conditions and analyzed force peaks of foot contact with the ground and propulsion and growth gradient for these forces. Results show that bracing did not significantly change Fymax1 and GCFymax1; significantly reduced Fymax2 and GG Fymax2. With respect to the medial-lateral component, there were no significant differences in relation to force magnitudes between the three study conditions. However, GG Fzmax1 was significantly greater for the sport shoe condition than for the taping condition. Bracing decreased ground reaction force at some instances, but increased in others
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