638 research outputs found
Nonlinear stabilization via system immersion and manifold invariance: Survey and new results
Published versio
Refining Finite-Time Lyapunov Exponent Ridges and the Challenges of Classifying Them
While more rigorous and sophisticated methods for identifying Lagrangian based coherent structures exist, the finite-time Lyapunov exponent (FTLE) field remains a straightforward and popular method for gaining some insight into transport by complex, time-dependent two-dimensional flows. In light of its enduring appeal, and in support of good practice, we begin by investigating the effects of discretization and noise on two numerical approaches for calculating the FTLE field. A practical method to extract and refine FTLE ridges in two-dimensional flows, which builds on previous methods, is then presented. Seeking to better ascertain the role of a FTLE ridge in flow transport, we adapt an existing classification scheme and provide a thorough treatment of the challenges of classifying the types of deformation represented by a FTLE ridge. As a practical demonstration, the methods are applied to an ocean surface velocity field data set generated by a numerical model. (C) 2015 AIP Publishing LLC.ONR N000141210665Center for Nonlinear Dynamic
Null Energy Condition Violation and Classical Stability in the Bianchi I Metric
The stability of isotropic cosmological solutions in the Bianchi I model is
considered. We prove that the stability of isotropic solutions in the Bianchi I
metric for a positive Hubble parameter follows from their stability in the
Friedmann-Robertson-Walker metric. This result is applied to models inspired by
string field theory, which violate the null energy condition. Examples of
stable isotropic solutions are presented. We also consider the k-essence model
and analyse the stability of solutions of the form .Comment: 27 pages, references added, accepted for publication in Phys. Rev.
Conceptual inconsistencies in finite-dimensional quantum and classical mechanics
Utilizing operational dynamic modeling [Phys. Rev. Lett. 109, 190403 (2012);
arXiv:1105.4014], we demonstrate that any finite-dimensional representation of
quantum and classical dynamics violates the Ehrenfest theorems. Other
peculiarities are also revealed, including the nonexistence of the free
particle and ambiguity in defining potential forces. Non-Hermitian mechanics is
shown to have the same problems. This work compromises a popular belief that
finite-dimensional mechanics is a straightforward discretization of the
corresponding infinite-dimensional formulation.Comment: 5 pages, 2 figure
Stability of Simple Periodic Orbits and Chaos in a Fermi -- Pasta -- Ulam Lattice
We investigate the connection between local and global dynamics in the Fermi
-- Pasta -- Ulam (FPU) -- model from the point of view of stability of
its simplest periodic orbits (SPOs). In particular, we show that there is a
relatively high mode of the linear lattice, having one
particle fixed every two oppositely moving ones (called SPO2 here), which can
be exactly continued to the nonlinear case for and whose
first destabilization, , as the energy (or ) increases for {\it
any} fixed , practically {\it coincides} with the onset of a ``weak'' form
of chaos preceding the break down of FPU recurrences, as predicted recently in
a similar study of the continuation of a very low () mode of the
corresponding linear chain. This energy threshold per particle behaves like
. We also follow exactly the properties of
another SPO (with ) in which fixed and moving particles are
interchanged (called SPO1 here) and which destabilizes at higher energies than
SPO2, since . We find that, immediately after
their first destabilization, these SPOs have different (positive) Lyapunov
spectra in their vicinity. However, as the energy increases further (at fixed
), these spectra converge to {\it the same} exponentially decreasing
function, thus providing strong evidence that the chaotic regions around SPO1
and SPO2 have ``merged'' and large scale chaos has spread throughout the
lattice.Comment: Physical Review E, 18 pages, 6 figure
-Breathers in finite lattices: nonlinearity and weak disorder
Nonlinearity and disorder are the recognized ingredients of the lattice
vibrational dynamics, the factors that could be diminished, but never excluded.
We generalize the concept of -breathers -- periodic orbits in nonlinear
lattices, exponentially localized in the reciprocal linear mode space -- to the
case of weak disorder, taking the Fermi-Pasta-Ulan chain as an example. We
show, that these nonlinear vibrational modes remain exponentially localized
near the central mode and stable, provided the disorder is sufficiently small.
The instability threshold depends sensitively on a particular realization of
disorder and can be modified by specifically designed impurities. Basing on it,
an approach to controlling the energy flow between the modes is proposed. The
relevance to other model lattices and experimental miniature arrays is
discussed.Comment: 4 pages, 3 figure
Optimization of the extent of surgical treatment in patients with stage I in cervical cancer
The study included 26 patients with FIGO stage Ia1–Ib1 cervical cancer who underwent fertility-sparing surgery (transabdominaltrachelectomy). To visualize sentinel lymph nodes, lymphoscintigraphy with injection of 99mTc-labelled nanocolloid was performed the day before surgery. Intraoperative identification of sentinel lymph nodes using hand-held gamma probe was carried out to determine the radioactive counts over the draining lymph node basin. The sentinel lymph node detection in cervical cancer patients contributes to the accurate clinical assessment of the pelvic lymph node status, precise staging of the disease and tailoring of surgical treatment to individual patient
q-Breathers and the Fermi-Pasta-Ulam Problem
The Fermi-Pasta-Ulam (FPU) paradox consists of the nonequipartition of energy
among normal modes of a weakly anharmonic atomic chain model. In the harmonic
limit each normal mode corresponds to a periodic orbit in phase space and is
characterized by its wave number . We continue normal modes from the
harmonic limit into the FPU parameter regime and obtain persistence of these
periodic orbits, termed here -Breathers (QB). They are characterized by time
periodicity, exponential localization in the -space of normal modes and
linear stability up to a size-dependent threshold amplitude. Trajectories
computed in the original FPU setting are perturbations around these exact QB
solutions. The QB concept is applicable to other nonlinear lattices as well.Comment: 4 pages, 4 figure
Optimization of the extent of surgical treatment in patients with stage I in cervical cancer
The study included 26 patients with FIGO stage Ia1–Ib1 cervical cancer who underwent fertility-sparing surgery (transabdominaltrachelectomy). To visualize sentinel lymph nodes, lymphoscintigraphy with injection of 99mTc-labelled nanocolloid was performed the day before surgery. Intraoperative identification of sentinel lymph nodes using hand-held gamma probe was carried out to determine the radioactive counts over the draining lymph node basin. The sentinel lymph node detection in cervical cancer patients contributes to the accurate clinical assessment of the pelvic lymph node status, precise staging of the disease and tailoring of surgical treatment to individual patient
Numerical integration of variational equations
We present and compare different numerical schemes for the integration of the
variational equations of autonomous Hamiltonian systems whose kinetic energy is
quadratic in the generalized momenta and whose potential is a function of the
generalized positions. We apply these techniques to Hamiltonian systems of
various degrees of freedom, and investigate their efficiency in accurately
reproducing well-known properties of chaos indicators like the Lyapunov
Characteristic Exponents (LCEs) and the Generalized Alignment Indices (GALIs).
We find that the best numerical performance is exhibited by the
\textit{`tangent map (TM) method'}, a scheme based on symplectic integration
techniques which proves to be optimal in speed and accuracy. According to this
method, a symplectic integrator is used to approximate the solution of the
Hamilton's equations of motion by the repeated action of a symplectic map ,
while the corresponding tangent map , is used for the integration of the
variational equations. A simple and systematic technique to construct is
also presented.Comment: 27 pages, 11 figures, to appear in Phys. Rev.
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