53 research outputs found
Analytic model for a frictional shallow-water undular bore
We use the integrable Kaup-Boussinesq shallow water system, modified by a
small viscous term, to model the formation of an undular bore with a steady
profile. The description is made in terms of the corresponding integrable
Whitham system, also appropriately modified by friction. This is derived in
Riemann variables using a modified finite-gap integration technique for the
AKNS scheme. The Whitham system is then reduced to a simple first-order
differential equation which is integrated numerically to obtain an asymptotic
profile of the undular bore, with the local oscillatory structure described by
the periodic solution of the unperturbed Kaup-Boussinesq system. This solution
of the Whitham equations is shown to be consistent with certain jump conditions
following directly from conservation laws for the original system. A comparison
is made with the recently studied dissipationless case for the same system,
where the undular bore is unsteady.Comment: 24 page
Unsteady undular bores in fully nonlinear shallow-water theory
We consider unsteady undular bores for a pair of coupled equations of
Boussinesq-type which contain the familiar fully nonlinear dissipationless
shallow-water dynamics and the leading-order fully nonlinear dispersive terms.
This system contains one horizontal space dimension and time and can be
systematically derived from the full Euler equations for irrotational flows
with a free surface using a standard long-wave asymptotic expansion.
In this context the system was first derived by Su and Gardner. It coincides
with the one-dimensional flat-bottom reduction of the Green-Naghdi system and,
additionally, has recently found a number of fluid dynamics applications other
than the present context of shallow-water gravity waves. We then use the
Whitham modulation theory for a one-phase periodic travelling wave to obtain an
asymptotic analytical description of an undular bore in the Su-Gardner system
for a full range of "depth" ratios across the bore. The positions of the
leading and trailing edges of the undular bore and the amplitude of the leading
solitary wave of the bore are found as functions of this "depth ratio". The
formation of a partial undular bore with a rapidly-varying finite-amplitude
trailing wave front is predicted for ``depth ratios'' across the bore exceeding
1.43. The analytical results from the modulation theory are shown to be in
excellent agreement with full numerical solutions for the development of an
undular bore in the Su-Gardner system.Comment: Revised version accepted for publication in Phys. Fluids, 51 pages, 9
figure
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
Resolution of a shock in hyperbolic systems modified by weak dispersion
We present a way to deal with dispersion-dominated ``shock-type'' transition
in the absence of completely integrable structure for the systems that one may
characterize as strictly hyperbolic regularized by a small amount of
dispersion. The analysis is performed by assuming that, the dispersive shock
transition between two different constant states can be modelled by an
expansion fan solution of the associated modulation (Whitham) system for the
short-wavelength nonlinear oscillations in the transition region (the so-called
Gurevich -- Pitaevskii problem). We consider as single-wave so bi-directional
systems. The main mathematical assumption is that of hyperbolicity of the
Whitham system for the solutions of our interest. By using general properties
of the Whitham averaging for a certain class of nonlinear dispersive systems
and specific features of the Cauchy data prescription on characteristics we
derive a set of transition conditions for the dispersive shock, actually
bypassing full integration of the modulation equations. Along with model KdV
and mKdV examples, we consider a non-integrable system describing fully
nonlinear ion-acoustic waves in collisionless plasma. In all cases our
transition conditions are in complete agreement with previous analytical and
numerical results.Comment: 56 pages, 5 figures. Misprints corrected. References adde
Biomedical informatics and translational medicine
Biomedical informatics involves a core set of methodologies that can provide a foundation for crossing the "translational barriers" associated with translational medicine. To this end, the fundamental aspects of biomedical informatics (e.g., bioinformatics, imaging informatics, clinical informatics, and public health informatics) may be essential in helping improve the ability to bring basic research findings to the bedside, evaluate the efficacy of interventions across communities, and enable the assessment of the eventual impact of translational medicine innovations on health policies. Here, a brief description is provided for a selection of key biomedical informatics topics (Decision Support, Natural Language Processing, Standards, Information Retrieval, and Electronic Health Records) and their relevance to translational medicine. Based on contributions and advancements in each of these topic areas, the article proposes that biomedical informatics practitioners ("biomedical informaticians") can be essential members of translational medicine teams
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