4,151 research outputs found
Motion of discrete interfaces in low-contrast periodic media
No full textWe study the motion of discrete interfaces driven by ferromagnetic interactions in a two-dimensional low-contrast periodic environment, by coupling the minimizing movements approach by Almgren, Taylor and Wang and a discrete-to-continuum analysis. As in a recent paper by Braides and Scilla dealing with high-contrast periodic media, we give an example showing that in general the effective motion does not depend only on the Γ-limit, but also on geometrical features that are not detected in the static description. We show that there exists a critical value δ ̃ of the contrast parameter δ above which the discrete motion is constrained and coincides with the high-contrast case. If δ<δ ̃ we have a new pinning threshold and a new effective velocity both depending on δ. We also consider the case of non-uniform inclusions distributed into periodic uniform layers
Variational problems with percolation: rigid spin systems
No full textIn this paper we describe the asymptotic behavior of rigid spin lattice energies by exhibiting a continuous interfacial limit energy as scaling to zero the lattice spacing. The limit is not trivial below a percolation threshold: it can be characterized by two phases separated by an interface. The macroscopic surface tension at this interface is defined through a first-passage percolation formula, related to the chemical distance on the lattice Z^2. We also show a continuity result, that is the homogenization of rigid spin system is a limit case of the elliptic random homogenization
Stochastic weighted variational inequalities in non-pivot Hilbert spaces with applications to a transportation model
No full textA class of stochastic weighted variational inequalities in non-pivot Hilbert spaces is proposed. Existence and continuity results are proved. These theoretical results play a prominent role in order to introduce a new weighted transportation model with uncertainty. Moreover, they allow to establish the equivalence between the random weighted equilibrium principle and a suitable stochastic weighted variational inequality. At the end, a numerical model is discussed
Relaxation of nonlinear elastic energies related to Orlicz-Sobolev nematic elastomers
No full textWe compute the relaxation of the total energy related to a variational model for nematic elastomers, involving a nonlinear elastic mechanical energy depending on the orientation of the molecules of the nematic elastomer, and a nematic Oseen--Frank energy in the deformed configuration. The main assumptions are that the quasiconvexification of the mechanical term is polyconvex and that the deformation belongs to an Orlicz-Sobolev space with an integrability just above the space dimension minus one, and does not present cavitation. We benefit from the fine properties of orientation-preserving maps satisfying that regularity requirement proven in cite{HS} and extend the result of cite{MCOl} to Orlicz spaces with a suitable growth condition at infinity
Partial regularity for steady double phase fluids
No full textWe study partial Holder regularity for nonlinear elliptic systems in divergence form with double-phase growth, modeling double-phase non-Newtonian fluids in the stationary case
Nucleation and backward motion of discrete interfaces
No full textWe use a discrete approximation of the motion by crystalline curvature to define an evolution of sets from a single point (nucleation) following a criterion of "maximization" of the perimeter, formally giving a backward version of the motion by crystalline curvature. This evolution depends on the approximation chosen
Motion of discrete interfaces in periodic media
No full textWe study the motion of discrete interfaces driven by ferromagnetic interactions in a two-dimensional periodic environment by coupling the minimizing movements approach by Almgren, Taylor and Wang and a discrete-to-continuous analysis. The case of a homogeneous environment has been recently treated by Braides, Gelli and Novaga, showing that the effective continuous motion is a flat motion related to the crystalline perimeter obtained by Gamma-convergence from the ferromagnetic energies, with an additional discontinuous dependence on the curvature, giving in particular a pinning threshold. In this paper we give an example showing that in general the motion does not depend only on the Gamma-limit, but also on geometrical features that are not detected in the static description. In particular we show how the pinning threshold is influenced by the microstructure and that the effective motion is described by a new homogenized velocity
Integral representation and -convergence for free-discontinuity problems with -growth
No full textAn integral representation result for free-discontinuity energies defined on
the space of generalized special functions of bounded variation with variable exponent is proved, under the assumption of log-H\"older continuity for the variable exponent . Our analysis is based on a variable exponent version of the global method for relaxation devised in \cite{BFLM} for a constant exponent. %Under the assumption of local log-H\"older continuity for the variable exponent ,
We prove -convergence of sequences of energies of the same type, we identify the limit integrands in terms of asymptotic cell formulas and prove a non-interaction property between bulk and surface contributions
The notions of inertial balanced viscosity and inertial virtual viscosity solution for rate-independent systems
No full textThe notion of inertial balanced viscosity (IBV) solution to rate-independent evolutionary processes is introduced. Such solutions are characterized by an energy balance where a suitable, rate-dependent, dissipation cost is optimized at jump times. The cost is reminiscent of the limit effect of small inertial terms. Therefore, this notion proves to be a suitable one to describe the asymptotic behavior of evolutions of mechanical systems with rate-independent dissipation in the limit of vanishing inertia and viscosity. It is indeed proved, in finite dimension, that these evolutions converge to IBV solutions. If the viscosity operator is neglected, or has a nontrivial kernel, the weaker notion of inertial virtual viscosity (IVV) solutions is introduced, and the analogous convergence result holds. Again in a finite-dimensional context, it is also shown that IBV and IVV solutions can be obtained via a natural extension of the minimizing movements algorithm, where the limit effect of inertial terms is taken into account
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