1,721,058 research outputs found
Non-stationary flows of asymptotically Newtonian fluids
No full textWe study nonlinear parabolic Stokes systems with an asymptotically linear structure. This refers to the slow flow of a non-Newtonian fluid with Newtonian behavior for large shear rates. We show that the symmetric gradient of the velocity field is locally bounded in space-time
On the existence of weak solutions for the steady Baldwin-Lomax model and generalizations
Full text linkIn this paper we consider the steady Baldwin-Lomax model, which is a rotational model proposed to describe turbulent flows at statistical equilibrium. The Baldwin-Lomax model is specifically designed to address the problem of a turbulent motion taking place in a bounded domain, with Dirichlet boundary conditions at solid boundaries. The main features of this model are the degeneracy of the operator at the boundary and a formulation in velocity/vorticity variables. The principal part of the operator is non-linear and it is degenerate, due to the presence (as a coefficient) of a power of the distance from the boundary: This fact makes the existence theory naturally set in the framework of appropriate weighted-Sobolev spaces
Convergence Analysis for a Finite Element Approximation of a Steady Model for Electrorheological Fluids
Full text linkIn this paper we study the finite element approximation of systems of p(.)-Stokes type, where p(.) is not a constant but a function. We derive (in some cases optimal) error estimates for finite element approximation of the velocity and for the pressure in a suitable functional setting
The stochastic compressible Navier-Stokes system on the whole space and some singular limits
Full text linkFirstly, we show the existence of at least one non-trivial solution to the stochastically
forced compressible Navier–Stokes system defined on the whole Euclidean space.
This solution is deterministically weak in the usual sense of distributions but also
weak in the sense of probability, the latter meaning that the underlying probability
space, as well as the stochastic driving force, are also unknowns.
Secondly, we study various asymptotic results for the above mentioned system when
the microscopic time and space variables are rescaled appropriately. Different rescaling leads to various singular versions of this system with coefficients which either
blow up or dissipate when they are made small. Subsequently, we are able to show
that any family of the solutions constructed above parametrised by the singular
coefficients converges to solutions of other fluid dynamic models like the incompressible Navier–Stokes system and the compressible Euler system with corresponding stochastic forcing terms. Crucially, we also consider the case when rotation in
the fluid is taken into account
Convergence rates of the numerical approximation of stochastic Navier-Stokes equations in 2D and 3D
Full text linkFinite-element algorithms for the space-time discretisation of the stochastic Navier-Stokes equations with periodic boundary conditions are considered, in two and three
dimensions. The stochastic forcing is represented by an operator on a Hilbert space,
growing linearly with respect to the velocity, acting on the differential of a cylindrical
Wiener process. Convergence rates for the error between the exact and approximate
solutions are proved in terms of the L
∞
t L
2
x ∩ L
2
tW1,2
x
-norm, with respect to convergence in probability. For the two-dimensional space-time algorithm, convergence
rates from Carelli and Prohl (SIAM J Numer Anal 50(5):2467–2496, 2012) are improved from linear in space and (almost) 1
4
in time to linear in space and (almost)
1
2
in time. This improvement is due to a decomposition of the pressure function
into deterministic and stochastic parts; the resulting stochastic term is a martingale which allows the use of the Burkholder-Davis-Gundy inequality to obtain an
improved error estimate of the convergence rates. Similar convergence rates are
proved for the three-dimensional space-time algorithm although holding only up to
some stopping time, providing the first result regarding convergence rates for local
strong solutions for the stochastic Navier-Stokes equations in three dimensions
Dissipative solutions to the stochastic Euler equations
Full text linkWe study the three-dimensional incompressible Euler system subject to stochastic forcing. We develop a concept of dissipative martingale solutions, where the nonlinear terms
are described by general Young measures. We construct these solutions as the vanishing
limit of solutions to the corresponding stochastic Navier-Stokes equations. This requires
a refined stochastic compactness method incorporating the generalised Young measures.
As a main novelty, our solutions satisfy a form of the energy inequality which gives rise
to the weak-strong uniqueness result (pathwise and in law). A dissipative solution coincides (pathwise and in law) with a strong solution as soon as the later exists.
Furthermore, we extend our results to the compressible Euler system. Here we introduce the concept of stochastic measure-valued solutions to the compressible Euler system describing the motion of a temperature-dependent inviscid fluid subject to stochastic
forcing, where the nonlinear terms are described by defect measures. These solutions
are weak in the probabilistic sense (probability space is not given a ‘priori’, but part of
the solution) and analytical sense (derivatives only exists in the sense distributions). In
particular, we show that existence and weak-strong principle (i.e. a weak measure-valued
solution coincides with a strong solution provided the later exists), hold true provided
they satisfy some form of energy balance. Finally, we show the existence of Markov selection to the associated martingale problem
Quantitative propagation of chaos of McKean-Vlasov equations via the master equation
Full text linkMcKean-Vlasov stochastic differential equations (MVSDEs) are ubiquitous in kinetic theory
and in controlled games with a large number of players. They have been intensively studied
since McKean, as they pave a way to probabilistic representations for many important nonlinear/
nonlocal PDEs. Classically, their simulation involves using standard particle systems,
which replace the evolving law in MVSDEs by the evolving empirical measure of the particles.
However, this type of simulation is costly in terms of computational complexity, due to the
interaction between the particles.
Apart from classical techniques in stochastic analysis, the approach in this thesis relies
heavily on the calculus on Wasserstein space, presented by P. Lions in his course at Collège de
France. An important object in our study, is a PDE written on the product space of the space
of time horizon and the Wasserstein space, which is a generalisation of the classical Feynman-
Kac PDE. This PDE, namely the master equation, provides a new insight into the study of
mean-field limits of particles and consequently allows us to solve many problems on MVSDEs
that are very difficult/impossible to solve by classical techniques.
The layout of the thesis is as follows. We start by a recap on classical results of MVSDEs
(Chapter 2), followed by a full exposition of Wasserstein calculus on the results that we need
(Chapter 3). Chapters 4 and 5 propose approximating systems to MVSDEs (as alternatives to
the classical particle system) via Romberg extrapolation and Antithetic Multi-level Monte-Carlo
estimation respectively, which are less costly in terms of computational complexity. Finally, in
Chapter 6, we explore the converse: given a standard particle system, we hope to find an
alternative mean-field limit that gives a better approximation to the standard particle system
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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