7,040 research outputs found
Exponential self-similar mixing and loss of regularity for continuity equations
We consider the mixing behaviour of the solutions of the continuity equation
associated with a divergence-free velocity field. In this announcement we
sketch two explicit examples of exponential decay of the mixing scale of the
solution, in case of Sobolev velocity fields, thus showing the optimality of
known lower bounds. We also describe how to use such examples to construct
solutions to the continuity equation with Sobolev but non-Lipschitz velocity
field exhibiting instantaneous loss of any fractional Sobolev regularity.Comment: 8 pages, 3 figures, statement of Theorem 11 slightly revise
Singular kernels, multiscale decomposition of microstructure, and dislocation models
We consider a model for dislocations in crystals introduced by Koslowski,
Cuiti\~no and Ortiz, which includes elastic interactions via a singular kernel
behaving as the norm of the slip. We obtain a sharp-interface limit
of the model within the framework of -convergence. From an analytical
point of view, our functional is a vector-valued generalization of the one
studied by Alberti, Bouchitt\'e and Seppecher to which their rearrangement
argument no longer applies. Instead we show that the microstructure must be
approximately one-dimensional on most length scales and exploit this property
to derive a sharp lower bound
Exponential self-similar mixing by incompressible flows
We study the problem of the optimal mixing of a passive scalar under the
action of an incompressible flow in two space dimensions. The scalar solves the
continuity equation with a divergence-free velocity field, which satisfies a
bound in the Sobolev space , where and . The mixing properties are given in terms of a characteristic length
scale, called the mixing scale. We consider two notions of mixing scale, one
functional, expressed in terms of the homogeneous Sobolev norm ,
the other geometric, related to rearrangements of sets. We study rates of decay
in time of both scales under self-similar mixing. For the case and (including the case of Lipschitz continuous velocities, and
the case of physical interest of enstrophy-constrained flows), we present
examples of velocity fields and initial configurations for the scalar that
saturate the exponential lower bound, established in previous works, on the
time decay of both scales. We also present several consequences for the
geometry of regular Lagrangian flows associated to Sobolev velocity fields.Comment: To appear in Journal of the American Mathematical Society. Some
results were announced in G. Alberti, G. Crippa, A. L. Mazzucato,
"Exponential self-similar mixing and loss of regularity for continuity
equations", C. R. Math. Acad. Sci. Paris, 352(11):901--906, 2014,
arXiv:1407.2631v
Damage as Gamma-limit of microfractures in anti-plane linearized elasticity
A homogenization result is given for a material having brittle inclusions arranged in a periodic structure.
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According to the relation between the softness parameter and the size of the microstructure, three different limit models are deduced via Gamma-convergence.
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In particular, damage is obtained as limit of periodically distributed
microfractures
A simple abstraction of arrays and maps by program translation
We present an approach for the static analysis of programs handling arrays,
with a Galois connection between the semantics of the array program and
semantics of purely scalar operations. The simplest way to implement it is by
automatic, syntactic transformation of the array program into a scalar program
followed analysis of the scalar program with any static analysis technique
(abstract interpretation, acceleration, predicate abstraction,.. .). The
scalars invariants thus obtained are translated back onto the original program
as universally quantified array invariants. We illustrate our approach on a
variety of examples, leading to the " Dutch flag " algorithm
Coherent transport of atomic wave packets in amplitude-modulated vertical optical lattices
We report on the realization of dynamical control of transport for ultra-cold
Sr88 atoms loaded in an accelerated and amplitude-modulated 1D optical lattice.
We tailor the energy dispersion of traveling wave packets and reversibly switch
between Wannier-Stark localization and driven transport based on coherent
tunneling. Within a Loschmidt-echo scheme where the atomic group velocities are
reversed at once, we demonstrate a novel mirror for matter waves working
independently of the momentum state and discuss possible applications to force
measurements at micrometric scales
Reduction on characteristics for continuous solutions of a scalar balance law
We consider continuous solutions u to the balance equation
∂t u(t, x) + ∂x [f (u(t, x))] = g(t, x) f ∈ C 2 (R), g ∈ L∞ (R) for a bounded source term g. Continuity improves to H ̈lder continuity o when f is uniformly convex, but it is not more regular in general. We discuss the reduction to ODEs on characteristics, mainly based on the joint works [5, 1]. We provide here local regularity results holding in
the region where f (u)f (u) = 0 and only in the simpler case of autonomous sources g = g(x), but for solutions u(t, x) which may depend on time. This corresponds to a local regularity result, in that region, for the system of ODEs
γ(t) = f (u(t, γ(t)))
̇
d
u(t, γ(t)) = g(t, γ(t)).
d
SBV regularity for Hamilton-Jacobi equations in
In this paper we study the regularity of viscosity solutions to the following
Hamilton-Jacobi equations In particular, under the
assumption that the Hamiltonian is uniformly convex, we
prove that and belong to the class .Comment: 15 page
Poblaciones y comunidades de algas bentónicas en la costa catalana
Las poblaciones de algas bentónicas forman comunidades que en unos lugares están poco diferenciadas y en otros constituyen comunidades definidas de un cierto valor indicativo. En este trabajo se comentan diversos perfiles de la costa catalana, confeccionadas según esquemas tomados sobre el terreno y auxiliados por fotografías submarinas.Los perfiles, tomados en varias localidades de la costa, revelan algunos horizontes y facies característicos del Mediterráneo occidental, lo que nos permite a modo de síntesis, tabular según su exposición al oleaje y a la luz, las facies más conspicuas y mejor caracterizadas.The populations of benthic algae form communities which are little differenciated in some spots while in others they constitute definite communities with some indicative value. Several profiles of the catalan coast are treated in this paper they have been drawn in accordance with outlines taken on the ground and with the aid of submarine pictures.The profiles, taken at several spots of the coast, reveal some horizonts and facieswhich are characteristic of the west Mediterranean, this allows us to tabulate the facies more evidents and better characterized according to their exposure to the swell and to the light
Experiences of health communication within the family: Parent and adolescent perspectives
Background: Adolescence is a critical period for the development of health and well-being and is a pivotal time for transition toward independent health decision making. Family health communication patterns, can influence behaviors and attitudes of adolescents. Health literacy is a pre-requisite for acquiring and comprehending health information. However, minimal research exists examining the connection between health literacy and family communication. Purpose: To examine the risk of limited health literacy and explore the experiences of health communication among families. Methods: 9 Adolescents and 8 parents completed demographic questionnaires, the Newest Vital Sign and private semi-structured qualitative interviews. Glazer’s grounded theory approach was used to identify thematic categories and theoretic cores of the qualitative data. Results: Limited health literacy risk was 12.5% for parents and 22/2% for adolescents. Narrow definitions of health, evaluation methods of information, opportunity and interpretation were the identified themes. Conclusions: Results from our study suggest that within families who are not at risk for limited health literacy, health communication is occurring related to topics of interest to adolescents. These conversations persist despite parental perceptions of these conversations being negative. Further research should investigate parent motivation related to health communication and the role that health literacy may play in motivation toward and ability to engage in family health communication
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