1,439 research outputs found
Singular normal form for the Painlev\'e equation P1
We show that there exists a rational change of coordinates of Painlev\'e's P1
equation and of the elliptic equation after which these
two equations become analytically equivalent in a region in the complex phase
space where and are unbounded. The region of equivalence comprises all
singularities of solutions of P1 (i.e. outside the region of equivalence,
solutions are analytic). The Painlev\'e property of P1 (that the only movable
singularities are poles) follows as a corollary. Conversely, we argue that the
Painlev\'e property is crucial in reducing P1, in a singular regime, to an
equation integrable by quadratures
Orthogonality of Jacobi and Laguerre polynomials for general parameters via the Hadamard finite part
Orthogonality of the Jacobi and of Laguerre polynomials, P_n^(a,b) and
L_n^(a), is established for a,b complex (a,b not negative integers and a+b
different from -2,-3,...) using the Hadamard finite part of the integral which
gives their orthogonality in the classical cases. Riemann-Hilbert problems that
these polynomials satisfy are found.
The results are formally similar to the ones in the classical case (when the
real parts of a,b are greater than -1)Comment: 14 page
Evaluation of Human and Anthropomorphic Test Device Finite Element Models under Spaceflight Loading Conditions
In an effort to develop occupant protection standards for future multipurpose crew vehicles, the National Aeronautics and Space Administration (NASA) has looked to evaluate the test device for human occupant restraint with the modification kit (THORK) anthropomorphic test device (ATD) in relevant impact test scenarios. With the allowance and support of the National Highway Traffic Safety Administration, NASA has performed a series of sled impact tests on the latest developed THORK ATD. These tests were performed to match test conditions from human volunteer data previously collected by the U.S. Air Force. The objective of this study was to evaluate the THORK finite element (FE) model and the Total HUman Model for Safety (THUMS) FE model with respect to the tests performed. These models were evaluated in spinal and frontal impacts against kinematic and kinetic data recorded in ATD and human testing. Methods: The FE simulations were developed based on recorded pretest ATD/human position and sled acceleration pulses measured during testing. Predicted responses by both human and ATD models were compared to test data recorded under the same impact conditions. The kinematic responses of the models were quantitatively evaluated using the ISOmetric curve rating system. In addition, ATD injury criteria and human stress/strain data were calculated to evaluate the risk of injury predicted by the ATD and human model, respectively. Results: Preliminary results show wellcorrelated response between both FE models and their physical counterparts. In addition, predicted ATD injury criteria and human model stress/strain values are shown to positively relate. Kinematic comparison between human and ATD models indicates promising biofidelic response, although a slightly stiffer response is observed within the ATD. Conclusion: As a compliment to ATD testing, numerical simulation provides efficient means to assess vehicle safety throughout the design process and further improve the design of physical ATDs. The assessment of the THORK and THUMS FE models in a spaceflight testing condition is an essential first step to implementing these models in the computational evaluation of spacecraft occupant safety. Promising results suggest future use of these models in the aerospace field
Semiclassical low energy scattering for one-dimensional Schr\"odinger operators with exponentially decaying potentials
We consider semiclassical Schr\"odinger operators on the real line of the
form with
small. The potential is assumed to be smooth, positive and exponentially
decaying towards infinity. We establish semiclassical global representations of
Jost solutions with error terms that are uniformly
controlled for small and , and construct the scattering matrix as
well as the semiclassical spectral measure associated to . This is
crucial in order to obtain decay bounds for the corresponding wave and
Schr\"odinger flows. As an application we consider the wave equation on a
Schwarzschild background for large angular momenta where the role of the
small parameter is played by . It follows from the results
in this paper and \cite{DSS2}, that the decay bounds obtained in \cite{DSS1},
\cite{DS} for individual angular momenta can be summed to yield the
sharp decay for data without symmetry assumptions.Comment: 44 pages, minor modifications in order to match the published
version, will appear in Annales Henri Poincar
The big and intricate dreams of little organelles: Embracing complexity in the study of membrane traffic
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138421/1/tra12497_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138421/2/tra12497-sup-0001-EditorialProcess.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138421/3/tra12497.pd
Effects of boundary conditions on irreversible dynamics
We present a simple one-dimensional Ising-type spin system on which we define
a completely asymmetric Markovian single spin-flip dynamics. We study the
system at a very low, yet non-zero, temperature and we show that for empty
boundary conditions the Gibbs measure is stationary for such dynamics, while
introducing in a single site a condition the stationary measure changes
drastically, with macroscopical effects. We achieve this result defining an
absolutely convergent series expansion of the stationary measure around the
zero temperature system. Interesting combinatorial identities are involved in
the proofs
On the Time-Dependent Analysis of Gamow Decay
Gamow's explanation of the exponential decay law uses complex "eigenvalues"
and exponentially growing "eigenfunctions". This raises the question, how
Gamow's description fits into the quantum mechanical description of nature,
which is based on real eigenvalues and square integrable wave functions.
Observing that the time evolution of any wave function is given by its
expansion in generalized eigenfunctions, we shall answer this question in the
most straightforward manner, which at the same time is accessible to graduate
students and specialists. Moreover the presentation can well be used in physics
lectures to students.Comment: 10 pages, 4 figures; heuristic argument simplified, different example
discussed, calculation of decay rate adde
Decay versus survival of a localized state subjected to harmonic forcing: exact results
We investigate the survival probability of a localized 1-d quantum particle
subjected to a time dependent potential of the form with
or . The particle is
initially in a bound state produced by the binding potential . We
prove that this probability goes to zero as for almost all values
of , , and . The decay is initially exponential followed by a
law if is not close to resonances and is small; otherwise
the exponential disappears and Fermi's golden rule fails. For exceptional sets
of parameters and the survival probability never decays to zero,
corresponding to the Floquet operator having a bound state. We show similar
behavior even in the absence of a binding potential: permitting a free particle
to be trapped by harmonically oscillating delta function potential
A quantitative central limit theorem for linear statistics of random matrix eigenvalues
It is known that the fluctuations of suitable linear statistics of Haar
distributed elements of the compact classical groups satisfy a central limit
theorem. We show that if the corresponding test functions are sufficiently
smooth, a rate of convergence of order almost can be obtained using a
quantitative multivariate CLT for traces of powers that was recently proven
using Stein's method of exchangeable pairs.Comment: Title modified; main result stated under slightly weaker conditions;
accepted for publication in the Journal of Theoretical Probabilit
On the spectral properties of L_{+-} in three dimensions
This paper is part of the radial asymptotic stability analysis of the ground
state soliton for either the cubic nonlinear Schrodinger or Klein-Gordon
equations in three dimensions. We demonstrate by a rigorous method that the
linearized scalar operators which arise in this setting, traditionally denoted
by L_{+-}, satisfy the gap property, at least over the radial functions. This
means that the interval (0,1] does not contain any eigenvalues of L_{+-} and
that the threshold 1 is neither an eigenvalue nor a resonance. The gap property
is required in order to prove scattering to the ground states for solutions
starting on the center-stable manifold associated with these states. This paper
therefore provides the final installment in the proof of this scattering
property for the cubic Klein-Gordon and Schrodinger equations in the radial
case, see the recent theory of Nakanishi and the third author, as well as the
earlier work of the third author and Beceanu on NLS. The method developed here
is quite general, and applicable to other spectral problems which arise in the
theory of nonlinear equations
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