12,671 research outputs found
Stability of jammed packings I: the rigidity length scale
In 2005, Wyart et al. (Europhys. Lett., 72 (2005) 486) showed that the low
frequency vibrational properties of jammed amorphous sphere packings can be
understood in terms of a length scale, called l*, that diverges as the system
becomes marginally unstable. Despite the tremendous success of this theory, it
has been difficult to connect the counting argument that defines l* to other
length scales that diverge near the jamming transition. We present an alternate
derivation of l* based on the onset of rigidity. This phenomenological approach
reveals the physical mechanism underlying the length scale and is relevant to a
range of systems for which the original argument breaks down. It also allows us
to present the first direct numerical measurement of l*.Comment: 8 pages, 5 figure
Découpages et inégalités systoliques pour les surfaces hyperboliques à bord
Résumé: Semi-eutactic and perfect surfaces are hyperbolic surfaces which have particular variational properties related to the systole (Bavard, J. Reine. Angew. Math. 482, 93-120, 1997). We focus on these surfaces, and build a systolic cutting procedure to divide them into pieces of Euler-Poincaré characteristic 0, then we give bounds for the systole. We are mainly concerned with bordered surface
Validity of the scaling functional approach for polymer interfaces as a variational theory
We discuss the soundness of the scaling functional (SF) approach proposed by
Aubouy Guiselin and Raphael (Macromolecules 29, 7261 (1996)) to describe
polymeric interfaces. In particular, we demonstrate that this approach is a
variational theory. We emphasis the role of SF theory as an important link
between ground-state theories suitable to describe adsorbed layers, and
"classical" theories for polymer brushes.Comment: 8 pages, 1 figure, to be published in Phys. Rev.
Inversion mechanism for the transport current in type-II superconductors
The longitudinal transport problem (the current is applied parallel to some
bias magnetic field) in type-II superconductors is analyzed theoretically.
Based on analytical results for simplified configurations, and relying on
numerical studies for general scenarios, it is shown that a remarkable
inversion of the current flow in a surface layer may be predicted under a wide
set of experimental conditions. Strongly inhomogeneous current density
profiles, characterized by enhanced transport toward the center and reduced, or
even negative, values at the periphery of the conductor, are expected when the
physical mechanisms of flux depinning and consumption (via line cutting) are
recalled. A number of striking collateral effects, such as local and global
paramagnetic behavior, are predicted. Our geometrical description of the
macroscopic material laws allows a pictorial interpretation of the physical
phenomena underlying the transport backflow.Comment: 8 pages, 6 figures (Best quality pictures are available by author's
contact
Vector magnetic hysteresis of hard superconductors
Critical state problems which incorporate more than one component for the
magnetization vector of hard superconductors are investigated. The theory is
based on the minimization of a cost functional
which weighs the changes of the magnetic field vector within the sample. We
show that Bean's simplest prescription of choosing the correct sign for the
critical current density in one dimensional problems is just a particular
case of finding the components of the vector . is
determined by minimizing under the constraint , with a bounded set. Upon the selection of
different sets we discuss existing crossed field measurements and
predict new observable features. It is shown that a complex behavior in the
magnetization curves may be controlled by a single external parameter, i.e.:
the maximum value of the applied magnetic field .Comment: 10 pages, 9 figures, accepted in Phys. Rev.
Variational approach to relaxed topological optimization: closed form solutions for structural problems in a sequential pseudo-time framework
The work explores a specific scenario for structural computational optimization based on the following elements: (a) a relaxed optimization setting considering the ersatz (bi-material) approximation, (b) a treatment based on a non-smoothed characteristic function field as a topological design variable, (c) the consistent derivation of a relaxed topological derivative whose determination is simple, general and efficient, (d) formulation of the overall increasing cost function topological sensitivity as a suitable optimality criterion, and (e) consideration of a pseudo-time framework for the problem solution, ruled by the problem constraint evolution.
In this setting, it is shown that the optimization problem can be analytically solved in a variational framework, leading to, nonlinear, closed-form algebraic solutions for the characteristic function, which are then solved, in every time-step, via fixed point methods based on a pseudo-energy cutting algorithm combined with the exact fulfillment of the constraint, at every iteration of the non-linear algorithm, via a bisection method. The issue of the ill-posedness (mesh dependency) of the topological solution, is then easily solved via a Laplacian smoothing of that pseudo-energy.
In the aforementioned context, a number of (3D) topological structural optimization benchmarks are solved, and the solutions obtained with the explored closed-form solution method, are analyzed, and compared, with their solution through an alternative level set method. Although the obtained results, in terms of the cost function and topology designs, are very similar in both methods, the associated computational cost is about five times smaller in the closed-form solution method this possibly being one of its advantages. Some comments, about the possible application of the method to other topological optimization problems, as well as envisaged modifications of the explored method to improve its performance close the workPeer ReviewedPostprint (author's final draft
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