27,829 research outputs found
Approximation of 2D Euler Equations by the Second-Grade Fluid Equations with Dirichlet Boundary Conditions
The second-grade fluid equations are a model for viscoelastic fluids, with
two parameters: , corresponding to the elastic response, and , corresponding to viscosity. Formally setting these parameters to
reduces the equations to the incompressible Euler equations of ideal fluid
flow. In this article we study the limits of solutions of
the second-grade fluid system, in a smooth, bounded, two-dimensional domain
with no-slip boundary conditions. This class of problems interpolates between
the Euler- model (), for which the authors recently proved
convergence to the solution of the incompressible Euler equations, and the
Navier-Stokes case (), for which the vanishing viscosity limit is
an important open problem. We prove three results. First, we establish
convergence of the solutions of the second-grade model to those of the Euler
equations provided , as , extending
the main result in [19]. Second, we prove equivalence between convergence (of
the second-grade fluid equations to the Euler equations) and vanishing of the
energy dissipation in a suitably thin region near the boundary, in the
asymptotic regime ,
as . This amounts to a convergence criterion similar to the
well-known Kato criterion for the vanishing viscosity limit of the
Navier-Stokes equations to the Euler equations. Finally, we obtain an extension
of Kato's classical criterion to the second-grade fluid model, valid if , as . The proof of all these results
relies on energy estimates and boundary correctors, following the original idea
by Kato.Comment: 20pages,1figur
Convergence of the 2D Euler- to Euler equations in the Dirichlet case: indifference to boundary layers
In this article we consider the Euler- system as a regularization of
the incompressible Euler equations in a smooth, two-dimensional, bounded
domain. For the limiting Euler system we consider the usual non-penetration
boundary condition, while, for the Euler- regularization, we use
velocity vanishing at the boundary. We also assume that the initial velocities
for the Euler- system approximate, in a suitable sense, as the
regularization parameter , the initial velocity for the limiting
Euler system. For small values of , this situation leads to a boundary
layer, which is the main concern of this work. Our main result is that, under
appropriate regularity assumptions, and despite the presence of this boundary
layer, the solutions of the Euler- system converge, as ,
to the corresponding solution of the Euler equations, in in space,
uniformly in time. We also present an example involving parallel flows, in
order to illustrate the indifference to the boundary layer of the limit, which underlies our work.Comment: 22page
Discrete Dynamical Systems: A Brief Survey
Dynamical system is a mathematical formalization for any fixed rule that is described in time dependent fashion. The time can be measured by either of the number systems - integers, real numbers, complex numbers. A discrete dynamical system is a dynamical system whose state evolves over a state space in discrete time steps according to a fixed rule. This brief survey paper is concerned with the part of the work done by José Sousa Ramos [2] and some of his research students. We present the general theory of discrete dynamical systems and present results from applications to geometry, graph theory and synchronization
MCMC Bayesian Estimation in FIEGARCH Models
Bayesian inference for fractionally integrated exponential generalized
autoregressive conditional heteroskedastic (FIEGARCH) models using Markov Chain
Monte Carlo (MCMC) methods is described. A simulation study is presented to
access the performance of the procedure, under the presence of long-memory in
the volatility. Samples from FIEGARCH processes are obtained upon considering
the generalized error distribution (GED) for the innovation process. Different
values for the tail-thickness parameter \nu are considered covering both
scenarios, innovation processes with lighter (\nu2) tails
than the Gaussian distribution (\nu=2). A sensitivity analysis is performed by
considering different prior density functions and by integrating (or not) the
knowledge on the true parameter values to select the hyperparameter values
Effective response theory for zero energy Majorana bound states in three spatial dimensions
We propose a gravitational response theory for point defects (hedgehogs)
binding Majorana zero modes in (3+1)-dimensional superconductors. Starting in
4+1 dimensions, where the point defect is extended into a line, a coupling of
the bulk defect texture with the gravitational field is introduced.
Diffeomorphism invariance then leads to an Kac-Moody current running
along the defect line. The Kac-Moody algebra accounts for the
non-Abelian nature of the zero modes in 3+1 dimensions. It is then shown to
also encode the angular momentum density which permeates throughout the bulk
between hedgehog-anti-hedgehog pairs.Comment: 7 pages, 3 figure
Sanitizing the fortress: protection of ant brood and nest material by worker antibiotics
Social groups are at particular risk for parasite infection, which is heightened in eusocial insects by the low genetic diversity of individuals within a colony. To combat this, adult ants have evolved a suite of defenses to protect each other, including the production of antimicrobial secretions. However, it is the brood in a colony that are most vulnerable to parasites because their individual defenses are limited, and the nest material in which ants live is also likely to be prone to colonization by potential parasites. Here, we investigate in two ant species whether adult workers use their antimicrobial secretions not only to protect each other but also to sanitize the vulnerable brood and nest material. We find that, in both leaf-cutting ants and weaver ants, the survival of the brood was reduced and the sporulation of parasitic fungi from them increased, when the workers nursing them lacked functional antimicrobial-producing glands. This was the case for both larvae that were experimentally treated with a fungal parasite (Metarhizium) and control larvae which developed infections of an opportunistic fungal parasite (Aspergillus). Similarly, fungi were more likely to grow on the nest material of both ant species if the glands of attending workers were blocked. The results show that the defense of brood and sanitization of nest material are important functions of the antimicrobial secretions of adult ants and that ubiquitous, opportunistic fungi may be a more important driver of the evolution of these defenses than rarer, specialist parasites
- …