1,061 research outputs found
The Vortex-Wave equation with a single vortex as the limit of the Euler equation
In this article we consider the physical justification of the Vortex-Wave
equation introduced by Marchioro and Pulvirenti in the case of a single point
vortex moving in an ambient vorticity. We consider a sequence of solutions for
the Euler equation in the plane corresponding to initial data consisting of an
ambient vorticity in and a sequence of concentrated blobs
which approach the Dirac distribution. We introduce a notion of a weak solution
of the Vortex-Wave equation in terms of velocity (or primitive variables) and
then show, for a subsequence of the blobs, the solutions of the Euler equation
converge in velocity to a weak solution of the Vortex-Wave equation.Comment: 24 pages, to appea
McKenzie Based Approach For Screening Lumbar Spine In A Patient With A Hamstring Strain: A Case Report
Research presentation slides:
Background and Purpose: The leading cause of musculoskeletal (MSK) disorders globally is low back pain (LBP). Historically, research efforts have been focused on the pathoanatomical causes of LBP. However, recent evidence found a high prevalence of structural abnormalities in the lumbar spine using magnetic resonance imaging (MRI) in asymptomatic patients and it is common that spinal pathology is the true culprit for patients referred to physical therapy (PT) with extremity diagnoses. Therefore, research has shifted to focus on classification systems to group patients based on subjective responses to specific movement patterns. The purpose of this case report was to outline the implementation a classification system, the McKenzie Mechanical Diagnosis and Treatment (MDT) method and discuss its potential in screening for spinal involvement in lower extremity (LE) PT referrals.Case Description: The patient was a 47-year-old male referred to PT by his primary care provider with a diagnosis of a hamstring strain. He received PT twice a week consisting of education, LE strengthening, directional preference exercises, manual therapy, and a home-exercise program.Outcomes: Proper sub-group classification of posterior derangement syndrome was achieved through the McKenzie algorithm. Centralization of pain was achieved, and the patient’s pain levels decreased from 3/10 to 1/10 based on the Numeric Pain Rating Scale (NPRS). The patient improved his lumbar range of motion (ROM) and global hip strength resulting in functional improvement.Discussion: Lower extremity pain masking the presence of LBP is common. This case report demonstrated that MDT may be effective at ruling out spinal involvement in LE PT referrals by addressing this hypothesis first. In doing so, MDT prevents the waste of healthcare resources by avoiding mis-directed treatments.https://dune.une.edu/pt_studcrpres/1007/thumbnail.jp
A Simple Proof of Inequalities of Integrals of Composite Functions
In this paper we give a simple proof of inequalities of integrals of
functions which are the composition of nonnegative continous convex functions
on a vector space and vector-valued functions in a weakly compact
subset of a Banach vector space generated by -spaces for Also, the same inequalities hold if these vector-valued functions
are in a weakly* compact subset of a Banach vector space generated by
-spaces instead
Weak-strong uniqueness of solutions to entropy-dissipating reaction-diffusion equations
We establish a weak-strong uniqueness principle for solutions to
entropy-dissipating reaction-diffusion equations: As long as a strong solution
to the reaction-diffusion equation exists, any weak solution and even any
renormalized solution must coincide with this strong solution. Our assumptions
on the reaction rates are just the entropy condition and local Lipschitz
continuity; in particular, we do not impose any growth restrictions on the
reaction rates. Therefore, our result applies to any single reversible reaction
with mass-action kinetics as well as to systems of reversible reactions with
mass-action kinetics satisfying the detailed balance condition. Renormalized
solutions are known to exist globally in time for reaction-diffusion equations
with entropy-dissipating reaction rates; in contrast, the global-in-time
existence of weak solutions is in general still an open problem - even for
smooth data - , thereby motivating the study of renormalized solutions. The key
ingredient of our result is a careful adjustment of the usual relative entropy
functional, whose evolution cannot be controlled properly for weak solutions or
renormalized solutions.Comment: 32 page
A kinetic model for coagulation-fragmentation
The aim of this paper is to show an existence theorem for a kinetic model of
coagulation-fragmentation with initial data satisfying the natural physical
bounds, and assumptions of finite number of particles and finite -norm. We
use the notion of renormalized solutions introduced dy DiPerna and Lions,
because of the lack of \textit{a priori} estimates. The proof is based on
weak-compactness methods in , allowed by -norms propagation.Comment: 36 page
On massless electron limit for a multispecies kinetic system with external magnetic field
We consider a three-dimensional kinetic model for a two species plasma
consisting of electrons and ions confined by an external nonconstant magnetic
field. Then we derive a kinetic-fluid model when the mass ratio tends
to zero. Each species initially obeys a Vlasov-type equation and the
electrostatic coupling follows from a Poisson equation. In our modeling, ions
are assumed non-collisional while a Fokker-Planck collision operator is taken
into account in the electron equation. As the mass ratio tends to zero we show
convergence to a new system where the macroscopic electron density satisfies an
anisotropic drift-diffusion equation. To achieve this task, we overcome some
specific technical issues of our model such as the strong effect of the
magnetic field on electrons and the lack of regularity at the limit. With
methods usually adapted to diffusion limit of collisional kinetic equations and
including renormalized solutions, relative entropy dissipation and velocity
averages, we establish the rigorous derivation of the limit model
Young Measures Generated by Ideal Incompressible Fluid Flows
In their seminal paper "Oscillations and concentrations in weak solutions of
the incompressible fluid equations", R. DiPerna and A. Majda introduced the
notion of measure-valued solution for the incompressible Euler equations in
order to capture complex phenomena present in limits of approximate solutions,
such as persistence of oscillation and development of concentrations.
Furthermore, they gave several explicit examples exhibiting such phenomena. In
this paper we show that any measure-valued solution can be generated by a
sequence of exact weak solutions. In particular this gives rise to a very
large, arguably too large, set of weak solutions of the incompressible Euler
equations.Comment: 35 pages. Final revised version. To appear in Arch. Ration. Mech.
Ana
Vanishing viscosity limit for an expanding domain in space
We study the limiting behavior of viscous incompressible flows when the fluid
domain is allowed to expand as the viscosity vanishes. We describe precise
conditions under which the limiting flow satisfies the full space Euler
equations. The argument is based on truncation and on energy estimates,
following the structure of the proof of Kato's criterion for the vanishing
viscosity limit. This work complements previous work by the authors, see
[Kelliher, Comm. Math. Phys. 278 (2008), 753-773] and [arXiv:0801.4935v1].Comment: 23 pages, submitted for publicatio
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