1,240 research outputs found
Approximate method for predicting the permanent set in a beam in vacuo and in water subject to a shock wave
An approximate method to compute the maximum deformation and permanent set of a beam subjected to shock wave laoding in vacuo and in water was investigated. The method equates the maximum kinetic energy of the beam (and water) to the elastic plastic work done by a static uniform load applied to a beam. Results for the water case indicate that the plastic deformation is controlled by the kinetic energy of the water. The simplified approach can result in significant savings in computer time or it can expediently be used as a check of results from a more rigorous approach. The accuracy of the method is demonstrated by various examples of beams with simple support and clamped support boundary conditions
Existence and Uniqueness of Tri-tronqu\'ee Solutions of the second Painlev\'e hierarchy
The first five classical Painlev\'e equations are known to have solutions
described by divergent asymptotic power series near infinity. Here we prove
that such solutions also exist for the infinite hierarchy of equations
associated with the second Painlev\'e equation. Moreover we prove that these
are unique in certain sectors near infinity.Comment: 13 pages, Late
The Current Density Distribution in a Segmented-in-Series SOFC,â
A common tubular solid oxide fuel cell (SOFC) design consists of segmented-in-serie
Vector-soliton collision dynamics in nonlinear optical fibers
We consider the interactions of two identical, orthogonally polarized vector
solitons in a nonlinear optical fiber with two polarization directions,
described by a coupled pair of nonlinear Schroedinger equations. We study a
low-dimensional model system of Hamiltonian ODE derived by Ueda and Kath and
also studied by Tan and Yang. We derive a further simplified model which has
similar dynamics but is more amenable to analysis. Sufficiently fast solitons
move by each other without much interaction, but below a critical velocity the
solitons may be captured. In certain bands of initial velocities the solitons
are initially captured, but separate after passing each other twice, a
phenomenon known as the two-bounce or two-pass resonance. We derive an analytic
formula for the critical velocity. Using matched asymptotic expansions for
separatrix crossing, we determine the location of these "resonance windows."
Numerical simulations of the ODE models show they compare quite well with the
asymptotic theory.Comment: 32 pages, submitted to Physical Review
Hard loss of stability in Painlev\'e-2 equation
A special asymptotic solution of the Painlev\'e-2 equation with small
parameter is studied. This solution has a critical point corresponding to
a bifurcation phenomenon. When the constructed solution varies slowly
and when the solution oscillates very fast. We investigate the
transitional layer in detail and obtain a smooth asymptotic solution, using a
sequence of scaling and matching procedures
Statistical Inference in a Directed Network Model with Covariates
Networks are often characterized by node heterogeneity for which nodes
exhibit different degrees of interaction and link homophily for which nodes
sharing common features tend to associate with each other. In this paper, we
propose a new directed network model to capture the former via node-specific
parametrization and the latter by incorporating covariates. In particular, this
model quantifies the extent of heterogeneity in terms of outgoingness and
incomingness of each node by different parameters, thus allowing the number of
heterogeneity parameters to be twice the number of nodes. We study the maximum
likelihood estimation of the model and establish the uniform consistency and
asymptotic normality of the resulting estimators. Numerical studies demonstrate
our theoretical findings and a data analysis confirms the usefulness of our
model.Comment: 29 pages. minor revisio
Data Science Issues in Understanding Protein-RNA Interactions
An interplay of experimental and computational methods is required to achieve a comprehensive understanding of proteinâRNA interactions. UV crosslinking and immunoprecipitation (CLIP) identifies endogenous interactions by sequencing RNA fragments that copurify with a selected RNA-binding protein under stringent conditions. Here we focus on approaches for the analysis of the resulting data and appraise the methods for peak calling, visualization, analysis, and computational modeling of proteinâRNA binding sites. We advocate that the sensitivity and specificity of data be assessed in combination for computational quality control. Moreover, we demonstrate the value of analyzing sequence motif enrichment in peaks assigned from CLIP data and of visualizing RNA maps, which examine the positional distribution of peaks around regulated landmarks in transcripts. We use these to assess how variations in CLIP data quality and in different peak calling methods affect the insights into regulatory mechanisms. We conclude by discussing future opportunities for the computational analysis of proteinâRNA interaction experiments
Theoretical approach to two-dimensional traffic flow models
In this paper we present a theoretical analysis of a recently proposed
two-dimensional Cellular Automata model for traffic flow in cities with the
novel ingredient of turning capability. Numerical simulations of this model
show that there is a transition between a freely moving phase with high
velocity to a jammed state with low velocity. We study the dynamics of such a
model starting with the microscopic evolution equation, which will serve as a
basis for further analysis. It is shown that a kinetic approach, based on the
Boltzmann assumption, is able to provide a reasonably good description of the
jamming transition. We further introduce a space-time continuous
phenomenological model leading to a couple of partial differential equations
whose preliminary results agree rather well with the numerical simulations.Comment: 15 pages, REVTeX 3.0, 7 uuencoded figures upon request to
[email protected]
Sex-specific mortality forecasting for UK countries: a coherent approach
This paper introduces a gender specific model for the joint mortality projection of three countries (England and Wales combined, Scotland, and Northern Ireland) of the United Kingdom. The model, called 2-tier Augmented Common Factor model, extends the classical Lee and Carter [26] and Li and Lee [32] models, with a common time factor for the whole UK population, a sex specific period factor for males and females, and a specific time factor for each country within each gender. As death counts in each subpopulation are modelled directly, a Poisson framework is used. Our results show that the 2-tier ACF model improves the in-sample fitting compared to the use of independent LC models for each subpopulation or of independent Li and Lee models for each couple of genders within each country. Mortality projections also show that the 2-tier ACF model produces coherent forecasts for the two genders within each country and different countries within each gender, thus avoiding the divergence issues arising when independent projections are used. The 2-tier ACF is further extended to include a cohort term to take into account the faster improvements of the UK âgolden generationâ
Quasi-linear Stokes phenomenon for the Painlev\'e first equation
Using the Riemann-Hilbert approach, the -function corresponding to the
solution of the first Painleve equation, , with the asymptotic
behavior as is constructed. The
exponentially small jump in the dominant solution and the coefficient
asymptotics in the power-like expansion to the latter are found.Comment: version accepted for publicatio
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