293 research outputs found
Nonlinear dynamical systems and classical orthogonal polynomials
It is demonstrated that nonlinear dynamical systems with analytic
nonlinearities can be brought down to the abstract Schr\"odinger equation in
Hilbert space with boson Hamiltonian. The Fourier coefficients of the expansion
of solutions to the Schr\"odinger equation in the particular occupation number
representation are expressed by means of the classical orthogonal polynomials.
The introduced formalism amounts a generalization of the classical methods for
linearization of nonlinear differential equations such as the Carleman
embedding technique and Koopman approach.Comment: 21 pages latex, uses revte
Chaotic saddles in nonlinear modulational interactions in a plasma
A nonlinear model of modulational processes in the subsonic regime involving
a linearly unstable wave and two linearly damped waves with different damping
rates in a plasma is studied numerically. We compute the maximum Lyapunov
exponent as a function of the damping rates in a two-parameter space, and
identify shrimp-shaped self-similar structures in the parameter space. By
varying the damping rate of the low-frequency wave, we construct bifurcation
diagrams and focus on a saddle-node bifurcation and an interior crisis
associated with a periodic window. We detect chaotic saddles and their stable
and unstable manifolds, and demonstrate how the connection between two chaotic
saddles via coupling unstable periodic orbits can result in a crisis-induced
intermittency. The relevance of this work for the understanding of modulational
processes observed in plasmas and fluids is discussed.Comment: Physics of Plasmas, in pres
A Geometrical Method of Decoupling
The computation of tunes and matched beam distributions are essential steps
in the analysis of circular accelerators. If certain symmetries - like midplane
symmetrie - are present, then it is possible to treat the betatron motion in
the horizontal, the vertical plane and (under certain circumstances) the
longitudinal motion separately using the well-known Courant-Snyder theory, or
to apply transformations that have been described previously as for instance
the method of Teng and Edwards. In a preceeding paper it has been shown that
this method requires a modification for the treatment of isochronous cyclotrons
with non-negligible space charge forces. Unfortunately the modification was
numerically not as stable as desired and it was still unclear, if the extension
would work for all thinkable cases. Hence a systematic derivation of a more
general treatment seemed advisable.
In a second paper the author suggested the use of real Dirac matrices as
basic tools to coupled linear optics and gave a straightforward recipe to
decouple positive definite Hamiltonians with imaginary eigenvalues. In this
article this method is generalized and simplified in order to formulate a
straightforward method to decouple Hamiltonian matrices with eigenvalues on the
real and the imaginary axis. It is shown that this algebraic decoupling is
closely related to a geometric "decoupling" by the orthogonalization of the
vectors , and , that were introduced with the
so-called "electromechanical equivalence". We present a structure-preserving
block-diagonalization of symplectic or Hamiltonian matrices, respectively. When
used iteratively, the decoupling algorithm can also be applied to n-dimensional
systems and requires iterations to converge to a given
precision.Comment: 13 pages, 1 figur
Comment on the Shiner-Davison-Landsberg Measure
The complexity measure from Shiner et al. [Physical Review E 59, 1999, 1459-1464] (henceforth abbreviated as SDL-measure) has recently been the subject of a fierce debate. We discuss the properties and shortcomings of this measure, from the point of view of our recently constructed fundamental, statistical mechanics-based measures of complexity Cs(γ,β) [Stoop et al., J. Stat. Phys. 114, 2004, 1127-1137]. We show explicitly, what the shortcomings of the SDL-measure are: It is over-universal, and the implemented temperature dependence is trivial. We also show how the original SDL-approach can be modified to rule out these points of critique. Results of this modification are shown for the logistic parabol
Entrustable Professional Activities (EPAs) for Global Health
Purpose As global health education and training shift toward competency-based approaches, academic institutions and organizations must define appropriate assessment strategies for use across health professions. The authors aim to develop entrustable professional activities (EPAs) for global health to apply across academic and workplace settings. Method In 2019, the authors invited 55 global health experts from medicine, nursing, pharmacy, and public health to participate in a multiround, online Delphi process; 30 (55%) agreed. Experts averaged 17 years of global health experience, and 12 (40%) were from low-to middle-income countries. In round one, participants listed essential global health activities. The authors used in vivo coding for round one responses to develop initial EPA statements. In subsequent rounds, participants used 5-point Likert-Type scales to evaluate EPA statements for importance and relevance to global health across health professions. The authors elevated statements that were rated 4 (important/relevant to most) or 5 (very important/relevant to all) by a minimum of 70% of participants (decided a priori) to the final round, during which participants evaluated whether each statement represented an observable unit of work that could be assigned to a trainee. Descriptive statistics were used for quantitative data analysis. The authors used participant comments to categorize EPA statements into role domains. Results Twenty-Two EPA statements reached at least 70% consensus. The authors categorized these into 5 role domains: partnership developer, capacity builder, data analyzer, equity advocate, and health promoter. Statements in the equity advocate and partnership developer domains had the highest agreement for importance and relevance. Several statements achieved 100% agreement as a unit of work but achieved lower levels of agreement regarding their observability. Conclusions EPAs for global health may be useful to academic institutions and other organizations to guide the assessment of trainees within education and training programs across health professions
Global Experiential and Didactic Education Opportunities at US Colleges and Schools of Pharmacy
Objective. To assess the characteristics of global experiential and didactic education offerings in the pharmacy curricula
Lyapunov exponent and natural invariant density determination of chaotic maps: An iterative maximum entropy ansatz
We apply the maximum entropy principle to construct the natural invariant
density and Lyapunov exponent of one-dimensional chaotic maps. Using a novel
function reconstruction technique that is based on the solution of Hausdorff
moment problem via maximizing Shannon entropy, we estimate the invariant
density and the Lyapunov exponent of nonlinear maps in one-dimension from a
knowledge of finite number of moments. The accuracy and the stability of the
algorithm are illustrated by comparing our results to a number of nonlinear
maps for which the exact analytical results are available. Furthermore, we also
consider a very complex example for which no exact analytical result for
invariant density is available. A comparison of our results to those available
in the literature is also discussed.Comment: 16 pages including 6 figure
Function reconstruction as a classical moment problem: A maximum entropy approach
We present a systematic study of the reconstruction of a non-negative
function via maximum entropy approach utilizing the information contained in a
finite number of moments of the function. For testing the efficacy of the
approach, we reconstruct a set of functions using an iterative entropy
optimization scheme, and study the convergence profile as the number of moments
is increased. We consider a wide variety of functions that include a
distribution with a sharp discontinuity, a rapidly oscillatory function, a
distribution with singularities, and finally a distribution with several spikes
and fine structure. The last example is important in the context of the
determination of the natural density of the logistic map. The convergence of
the method is studied by comparing the moments of the approximated functions
with the exact ones. Furthermore, by varying the number of moments and
iterations, we examine to what extent the features of the functions, such as
the divergence behavior at singular points within the interval, is reproduced.
The proximity of the reconstructed maximum entropy solution to the exact
solution is examined via Kullback-Leibler divergence and variation measures for
different number of moments.Comment: 20 pages, 17 figure
Painlev\'{e} test of coupled Gross-Pitaevskii equations
Painlev\'{e} test of the coupled Gross-Pitaevskii equations has been carried
out with the result that the coupled equations pass the P-test only if a
special relation containing system parameters (masses, scattering lengths) is
satisfied. Computer algebra is applied to evaluate j=4 compatibility condition
for admissible external potentials. Appearance of an arbitrary real potential
embedded in the external potentials is shown to be the consequence of the
coupling. Connection with recent experiments related to stability of
two-component Bose-Einstein condensates of Rb atoms is discussed.Comment: 13 pages, no figure
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