123 research outputs found
Counting Berg partitions
We call a Markov partition of a two dimensional hyperbolic toral automorphism
a Berg partition if it contains just two rectangles. We describe all Berg
partitions for a given hyperbolic toral automorphism. In particular there are
exactly (k + n + l + m)/2 nonequivalent Berg partitions with the same
connectivity matrix (k, l, m, n)
Well-posed infinite horizon variational problems on a compact manifold
We give an effective sufficient condition for a variational problem with
infinite horizon on a compact Riemannian manifold M to admit a smooth optimal
synthesis, i. e. a smooth dynamical system on M whose positive
semi-trajectories are solutions to the problem. To realize the synthesis we
construct a well-projected to M invariant Lagrange submanifold of the
extremals' flow in the cotangent bundle T*M. The construction uses the
curvature of the flow in the cotangent bundle and some ideas of hyperbolic
dynamics
Fluctuation Theorem, non linear response and the regularity of time reversal symmetry
The Gallavotti - Cohen Fluctuation Theorem (FT) implies an infinite set of
identities between correlation functions that can be seen as a generalization
of Green Kubo formula to the nonlinear regime. As an application, we discuss a
perturbative check of the FT relation through these identities for a simple
Anosov reversible system; we find that the lack of differentiability of the
time reversal symmetry implies a violation of the Gallavotti - Cohen
fluctuation relation. Finally, a brief comparison with Lebowitz - Spohn FT is
reported.Comment: 7 page
Classification of biological micro-objects using optical coherence tomography: in silico study
We report on the development of a technique for differentiating between biological micro-objects using a rigorous, full-wave model of OCT image formation. We model an existing experimental prototype which uses OCT to interrogate a microfluidic chip containing the blood cells. A full-wave model is required since the technique uses light back-scattered by a scattering substrate, rather than by the cells directly. The light back-scattered by the substrate is perturbed upon propagation through the cells, which flow between the substrate and imaging system’s objective lens. We present the key elements of the 3D, Maxwell equation-based computational model, the key findings of the computational study and a comparison with experimental results
Track billiards
We study a class of planar billiards having the remarkable property that
their phase space consists up to a set of zero measure of two invariant sets
formed by orbits moving in opposite directions. The tables of these billiards
are tubular neighborhoods of differentiable Jordan curves that are unions of
finitely many segments and arcs of circles. We prove that under proper
conditions on the segments and the arcs, the billiards considered have non-zero
Lyapunov exponents almost everywhere. These results are then extended to a
similar class of of 3-dimensional billiards. Finally, we find that for some
subclasses of track billiards, the mechanism generating hyperbolicity is not
the defocusing one that requires every infinitesimal beam of parallel rays to
defocus after every reflection off of the focusing boundary.Comment: 7 figure
Hyperbolic outer billiards : a first example
We present the first example of a hyperbolic outer billiard. More precisely
we construct a one parameter family of examples which in some sense correspond
to the Bunimovich billiards.Comment: 11 pages, 8 figures, to appear in Nonlinearit
Linear stability in billiards with potential
A general formula for the linearized Poincar\'e map of a billiard with a
potential is derived. The stability of periodic orbits is given by the trace of
a product of matrices describing the piecewise free motion between reflections
and the contributions from the reflections alone. For the case without
potential this gives well known formulas. Four billiards with potentials for
which the free motion is integrable are treated as examples: The linear
gravitational potential, the constant magnetic field, the harmonic potential,
and a billiard in a rotating frame of reference, imitating the restricted three
body problem. The linear stability of periodic orbits with period one and two
is analyzed with the help of stability diagrams, showing the essential
parameter dependence of the residue of the periodic orbits for these examples.Comment: 22 pages, LaTex, 4 Figure
Entropy production in Gaussian thermostats
We show that an arbitrary Anosov Gaussian thermostat on a surface is
dissipative unless the external field has a global potential
Optical Coherence Tomography (OCT) for examination of artworks
Chapter in the book: Bastidas D., Cano E. (eds) Advanced Characterization Techniques, Diagnostic Tools and Evaluation Methods in Heritage Science. Springer, Cham, 2018, pp 49-59 , doi: 10.1007/978-3-319-75316-4, Authors’version after embargo periodOptical coherence tomography is a fast, non-invasive technique of structural analysis utilising near-infrared radiation. Examples of using OCT, for obtaining cross-sectional images of objects of craftsmanship and an easel painting have been shown. Issues regarding the technique of execution and destruction phenomena were resolved non-invasively. In some cases, the secondary alterations can be identified and localised within the object’s structure which helps in authentication of the artwork
Frame-independence of the Inhomogeneous Mixmaster Chaos via Misner-Chitre'-like variables
We outline the covariant nature,with respect to the choice of a reference
frame, of the chaos characterizing the generic cosmological solution near the
initial singularity, i.e. the so-called inhomogeneous Mixmaster model. Our
analysis is based on a "gauge" independent ADM-reduction of the dynamics to the
physical degrees of freedom. The out coming picture shows how the inhomogeneous
Mixmaster model is isomorphic point by point in space to a billiard on a
Lobachevsky plane. Indeed, the existence of an asymptotic (energy-like)
constant of the motion allows to construct the Jacobi metric associated to the
geodesic flow and to calculate a non-zero Lyapunov exponent in each space
point. The chaos covariance emerges from the independence of our scheme with
respect to the form of the lapse function and the shift vector; the origin of
this result relies on the dynamical decoupling of the space-points which takes
place near the singularity, due to the asymptotic approach of the potential
term to infinite walls. At the ground of the obtained dynamical scheme is the
choice of Misner-Chitre' like variables which allows to fix the billiard
potential walls.Comment: 8 pages,2 figures, to appear on Phys Rev
- …