244,381 research outputs found
A Novel Approach to Elastodynamics: II. The Three-Dimensional Case
A new approach was recently introduced by the authors for constructing
analytic solutions of the linear PDEs describing elastodynamics. Here, this
approach is applied to the case of a homogeneous isotropic half-space body
satisfying arbitrary initial conditions and Lamb's boundary conditions. A
particular case of this problem, namely the case of homogeneous initial
conditions and normal point load boundary conditions, was first solved by Lamb
using the Fourier-Laplace transform. The general problem solved here can also
be analysed via the Fourier transform, but in this case, the solution
representation involves transforms of \textit{unknown} boundary values; this
necessitates the formulation and solution of a cumbersome auxiliary problem,
which expresses the unknown boundary values in terms of the Laplace transform
of the given boundary data. The new approach, which is applicable to arbitrary
initial and boundary conditions, bypasses the above auxiliary problem and
expresses the solutions directly in terms of the given initial and boundary
conditions
On a Novel Class of Integrable ODEs Related to the Painlev\'e Equations
One of the authors has recently introduced the concept of conjugate
Hamiltonian systems: the solution of the equation where is a
given Hamiltonian containing explicitly, yields the function ,
which defines a new Hamiltonian system with Hamiltonian and independent
variable By employing this construction and by using the fact that the
classical Painlev\'e equations are Hamiltonian systems, it is straightforward
to associate with each Painlev\'e equation two new integrable ODEs. Here, we
investigate the conjugate Painlev\'e II equations. In particular, for these
novel integrable ODEs, we present a Lax pair formulation, as well as a class of
implicit solutions. We also construct conjugate equations associated with
Painlev\'e I and Painlev\'e IV equations.Comment: This paper is dedicated to Professor T. Bountis on the occasion of
his 60th birthday with appreciation of his important contributions to
"Nonlinear Science
Optimal and efficient crossover designs for comparing test treatments with a control treatment
This paper deals exclusively with crossover designs for the purpose of
comparing t test treatments with a control treatment when the number of periods
is no larger than t+1. Among other results it specifies sufficient conditions
for a crossover design to be simultaneously A-optimal and MV-optimal in a very
large and appealing class of crossover designs. It is expected that these
optimal designs are highly efficient in the entire class of crossover designs.
Some computationally useful tools are given and used to build assorted small
optimal and efficient crossover designs. The model robustness of these newly
discovered crossover designs is discussed.Comment: Published at http://dx.doi.org/10.1214/009053604000000887 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Inverse Spin Hall Effect Driven by Spin Motive Force
The spin Hall effect is a phenomenon that an electric field induces a spin
Hall current. In this Letter, we examine the inverse effect that, in a
ferromagnetic conductor, a charge Hall current is induced by a spin motive
force, or a spin-dependent effective ` electric' field ,
arising from the time variation of magnetization texture. By considering
skew-scattering and side-jump processes due to spin-orbit interaction at
impurities, we obtain the Hall current density as , where is the local spin direction and
is the spin Hall conductivity. The Hall angle due to the spin
motive force is enhanced by a factor of compared to the conventional
anomalous Hall effect due to the ordinary electric field, where is the spin
polarization of the current. The Hall voltage is estimated for a field-driven
domain wall oscillation in a ferromagnetic nanowire.Comment: 4 pages, 3 figures, the title has been change
Asymmetric vortex solitons in nonlinear periodic lattices
We reveal the existence of asymmetric vortex solitons in ideally symmetric
periodic lattices, and show how such nonlinear localized structures describing
elementary circular flows can be analyzed systematically using the
energy-balance relations. We present the examples of rhomboid, rectangular, and
triangular vortex solitons on a square lattice, and also describe novel
coherent states where the populations of clockwise and anti-clockwise vortex
modes change periodically due to a nonlinearity-induced momentum exchange
through the lattice. Asymmetric vortex solitons are expected to exist in
different nonlinear lattice systems including optically-induced photonic
lattices, nonlinear photonic crystals, and Bose-Einstein condensates in optical
lattices.Comment: 4 pages, 5 figure
Estimation of causal effects using instrumental variables with nonignorable missing covariates: Application to effect of type of delivery NICU on premature infants
Understanding how effective high-level NICUs (neonatal intensive care units
that have the capacity for sustained mechanical assisted ventilation and high
volume) are compared to low-level NICUs is important and valuable for both
individual mothers and for public policy decisions. The goal of this paper is
to estimate the effect on mortality of premature babies being delivered in a
high-level NICU vs. a low-level NICU through an observational study where there
are unmeasured confounders as well as nonignorable missing covariates. We
consider the use of excess travel time as an instrumental variable (IV) to
control for unmeasured confounders. In order for an IV to be valid, we must
condition on confounders of the IV---outcome relationship, for example, month
prenatal care started must be conditioned on for excess travel time to be a
valid IV. However, sometimes month prenatal care started is missing, and the
missingness may be nonignorable because it is related to the not fully measured
mother's/infant's risk of complications. We develop a method to estimate the
causal effect of a treatment using an IV when there are nonignorable missing
covariates as in our data, where we allow the missingness to depend on the
fully observed outcome as well as the partially observed compliance class,
which is a proxy for the unmeasured risk of complications. A simulation study
shows that under our nonignorable missingness assumption, the commonly used
estimation methods, complete-case analysis and multiple imputation by chained
equations assuming missingness at random, provide biased estimates, while our
method provides approximately unbiased estimates. We apply our method to the
NICU study and find evidence that high-level NICUs significantly reduce deaths
for babies of small gestational age, whereas for almost mature babies like 37
weeks, the level of NICUs makes little difference. A sensitivity analysis is
conducted to assess the sensitivity of our conclusions to key assumptions about
the missing covariates. The method we develop in this paper may be useful for
many observational studies facing similar issues of unmeasured confounders and
nonignorable missing data as ours.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS699 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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