8,574 research outputs found
Stably non-synchronizable maps of the plane
Pecora and Carroll presented a notion of synchronization where an
(n-1)-dimensional nonautonomous system is constructed from a given
-dimensional dynamical system by imposing the evolution of one coordinate.
They noticed that the resulting dynamics may be contracting even if the
original dynamics are not. It is easy to construct flows or maps such that no
coordinate has synchronizing properties, but this cannot be done in an open set
of linear maps or flows in , . In this paper we give examples of
real analytic homeomorphisms of such that the non-synchronizability is
stable in the sense that in a full neighborhood of the given map, no
homeomorphism is synchronizable
No elliptic islands for the universal area-preserving map
A renormalization approach has been used in \cite{EKW1} and \cite{EKW2} to
prove the existence of a \textit{universal area-preserving map}, a map with
hyperbolic orbits of all binary periods. The existence of a horseshoe, with
positive Hausdorff dimension, in its domain was demonstrated in \cite{GJ1}. In
this paper the coexistence problem is studied, and a computer-aided proof is
given that no elliptic islands with period less than 20 exist in the domain. It
is also shown that less than 1.5% of the measure of the domain consists of
elliptic islands. This is proven by showing that the measure of initial
conditions that escape to infinity is at least 98.5% of the measure of the
domain, and we conjecture that the escaping set has full measure. This is
highly unexpected, since generically it is believed that for conservative
systems hyperbolicity and ellipticity coexist
Macroscopic effects in attosecond pulse generation
We examine how the generation and propagation of high-order harmonics in a
partly ionized gas medium affect their strength and synchronization. The
temporal properties of the resulting attosecond pulses generated in long gas
targets can be significantly influenced by macroscopic effects, in particular
by the intensity in the medium and the degree of ionization. Under some
conditions, the use of gas targets longer than the absorption length can lead
to the generation of self-compressed attosecond pulses. We show this effect
experimentally, using long argon-filled gas cells as generating medium.Comment: 5 pages 4 figure
Development and operation of a pixel segmented liquid-filled linear array for radiotherapy quality assurance
A liquid isooctane (CH) filled ionization linear array for
radiotherapy quality assurance has been designed, built and tested. The
detector consists of 128 pixels, each of them with an area of 1.7 mm
1.7 mm and a gap of 0.5 mm. The small pixel size makes the detector ideal for
high gradient beam profiles like those present in Intensity Modulated Radiation
Therapy (IMRT) and radiosurgery. As read-out electronics we use the X-Ray Data
Acquisition System (XDAS) with the Xchip developed by the CCLRC.
Studies concerning the collection efficiency dependence on the polarization
voltage and on the dose rate have been made in order to optimize the device
operation.
In the first tests we have studied dose rate and energy dependences, and
signal reproducibility. Dose rate dependence was found lower than 2.5 % up to 5
Gy min, and energy dependence lower than 2.1 % up to 20 cm depth in
solid water. Output factors and penumbras for several rectangular fields have
been measured with the linear array and were compared with the results obtained
with a 0.125 cm air ionization chamber and radiographic film,
respectively. Finally, we have acquired profiles for an IMRT field and for a
virtual wedge. These profiles have also been compared with radiographic film
measurements. All the comparisons show a good correspondence. Signal
reproducibility was within a 2% during the test period (around three months).
The device has proved its capability to verify on-line therapy beams with
good spatial resolution and signal to noise ratio.Comment: 16 pages, 12 figures Submitted to Phys. Med. Bio
From Heisenberg matrix mechanics to EBK quantization: theory and first applications
Despite the seminal connection between classical multiply-periodic motion and
Heisenberg matrix mechanics and the massive amount of work done on the
associated problem of semiclassical (EBK) quantization of bound states, we show
that there are, nevertheless, a number of previously unexploited aspects of
this relationship that bear on the quantum-classical correspondence. In
particular, we emphasize a quantum variational principle that implies the
classical variational principle for invariant tori. We also expose the more
indirect connection between commutation relations and quantization of action
variables. With the help of several standard models with one or two degrees of
freedom, we then illustrate how the methods of Heisenberg matrix mechanics
described in this paper may be used to obtain quantum solutions with a modest
increase in effort compared to semiclassical calculations. We also describe and
apply a method for obtaining leading quantum corrections to EBK results.
Finally, we suggest several new or modified applications of EBK quantization.Comment: 37 pages including 3 poscript figures, submitted to Phys. Rev.
The Order of Phase Transitions in Barrier Crossing
A spatially extended classical system with metastable states subject to weak
spatiotemporal noise can exhibit a transition in its activation behavior when
one or more external parameters are varied. Depending on the potential, the
transition can be first or second-order, but there exists no systematic theory
of the relation between the order of the transition and the shape of the
potential barrier. In this paper, we address that question in detail for a
general class of systems whose order parameter is describable by a classical
field that can vary both in space and time, and whose zero-noise dynamics are
governed by a smooth polynomial potential. We show that a quartic potential
barrier can only have second-order transitions, confirming an earlier
conjecture [1]. We then derive, through a combination of analytical and
numerical arguments, both necessary conditions and sufficient conditions to
have a first-order vs. a second-order transition in noise-induced activation
behavior, for a large class of systems with smooth polynomial potentials of
arbitrary order. We find in particular that the order of the transition is
especially sensitive to the potential behavior near the top of the barrier.Comment: 8 pages, 6 figures with extended introduction and discussion; version
accepted for publication by Phys. Rev.
Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
We analyze a large system of globally coupled phase oscillators whose natural
frequencies are bimodally distributed. The dynamics of this system has been the
subject of long-standing interest. In 1984 Kuramoto proposed several
conjectures about its behavior; ten years later, Crawford obtained the first
analytical results by means of a local center manifold calculation.
Nevertheless, many questions have remained open, especially about the
possibility of global bifurcations. Here we derive the system's complete
stability diagram for the special case where the bimodal distribution consists
of two equally weighted Lorentzians. Using an ansatz recently discovered by Ott
and Antonsen, we show that in this case the infinite-dimensional problem
reduces exactly to a flow in four dimensions. Depending on the parameters and
initial conditions, the long-term dynamics evolves to one of three states:
incoherence, where all the oscillators are desynchronized; partial synchrony,
where a macroscopic group of phase-locked oscillators coexists with a sea of
desynchronized ones; and a standing wave state, where two counter-rotating
groups of phase-locked oscillators emerge. Analytical results are presented for
the bifurcation boundaries between these states. Similar results are also
obtained for the case in which the bimodal distribution is given by the sum of
two Gaussians.Comment: 28 pages, 7 figures; submitted to Phys. Rev. E Added comment
The Haroche-Ramsey experiment as a generalized measurement
A number of atomic beam experiments, related to the Ramsey experiment and a
recent experiment by Brune et al., are studied with respect to the question of
complementarity. Three different procedures for obtaining information on the
state of the incoming atom are compared. Positive operator-valued measures are
explicitly calculated. It is demonstrated that, in principle, it is possible to
choose the experimental arrangement so as to admit an interpretation as a joint
non-ideal measurement yielding interference and ``which-way'' information.
Comparison of the different measurements gives insight into the question of
which information is provided by a (generalized) quantum mechanical
measurement. For this purpose the subspaces of Hilbert-Schmidt space, spanned
by the operators of the POVM, are determined for different measurement
arrangements and different values of the parameters.Comment: REVTeX, 22 pages, 5 figure
Temperature Dependence of Exciton Diffusion in Conjugated Polymers
The temperature dependence of the exciton dynamics in a conjugated polymer is studied using time-resolved spectroscopy. Photoluminescence decays were measured in heterostructured samples containing a sharp polymer-fullerene interface, which acts as an exciton quenching wall. Using a 1D diffusion model, the exciton diffusion length and diffusion coefficient were extracted in the temperature range of 4-293 K. The exciton dynamics reveal two temperature regimes: in the range of 4-150 K, the exciton diffusion length (coefficient) of ~3 nm (~1.5 × 10-4 cm2/s) is nearly temperature independent. Increasing the temperature up to 293 K leads to a gradual growth up to 4.5 nm (~3.2 × 10-4 cm2/s). This demonstrates that exciton diffusion in conjugated polymers is governed by two processes: an initial downhill migration toward lower energy states in the inhomogenously broadened density of states, followed by temperature activated hopping. The latter process is switched off below 150 K.
Brunel-Dominated Proton Acceleration with a Few-Cycle Laser Pulse
International audienceExperimental measurements of backward accelerated protons are presented. The beam is produced when an ultrashort (5 fs) laser pulse, delivered by a kHz laser system, with a high temporal contrast (10 8), interacts with a thick solid target. Under these conditions, proton cutoff energy dependence with laser parameters, such as pulse energy, polarization (from p to s), and pulse duration (from 5 to 500 fs), is studied. Theoretical model and two-dimensional particle-in-cell simulations, in good agreement with a large set of experimental results, indicate that proton acceleration is directly driven by Brunel electrons, in contrast to conventional target normal sheath acceleration that relies on electron thermal pressure
- …