Augusto Visintin

Bio: Augusto Visintin is an academic researcher from University of Trento. The author has contributed to research in topics: Hysteresis & Stefan problem. The author has an hindex of 30, co-authored 116 publications receiving 4300 citations. Previous affiliations of Augusto Visintin include Nuclear Regulatory Commission & University of Pavia.

Differential models of hysteresis

Abstract: Reader's Guide.- Historical Notes.- I. Genesis of Hysteresis.- II. Rheological and Circuital Models.- III. Plays, Stops and Prandtl-Ishlinski? Models.- IV. The Preisach Model.- V. The Duhem Model.- VI. Discontinuous Hysteresis.- VII. P.D.E. Models of Elasto-Plasticity.- VIII. Hysteresis and Semigroups.- IX. Quasilinear P.D.E.s with Memory.- X. Semilinear P.D.E.s with Memory.- XI. P.D.E.s with Discontinuous Hysteresis.- XII. Some Tools.- Conclusion.

Models of Phase Transitions

Abstract: Part I Some nonlinear PDEs: models and PDEs a class of quasilinear parabolic PDEs doubly-nonlinear parabolic PDEs. Part 2 Phase transitions: the Stefan problem generalizations of the Stefan problem.

On Landau-Lifshitz’ equations for ferromagnetism

Abstract: According to the classical theory of Weiβ, on a microscopic scale a ferromagnetic body is magnetically saturated (|M| =M 0: constant) and is composed by uniformly magnetized regions separated by thin transition layers. At equilibrium this corresponds to the minimization of the magnetic energy functional under the above constraint; this problem has at least one solutionM of classH 1, which in general is not unique. The evolution is governed by Landau-Lifshitz’ equations $$\begin{gathered} \frac{{\partial M}}{{\partial t}} = \lambda _1 M \times H^e = \lambda _2 M \times \left( {M \times H^e } \right) \left( {\lambda _1 ,\lambda _2 : constant; \lambda _2 > 0} \right) \hfill \\ H^e = - \frac{{\partial e_{mag} \left( M \right)}}{{\partial M}} \left( {e_{mag} : density of magnetic energy} \right) \hfill \\ \end{gathered} $$ ; these are coupled with Maxwell’s equations. An existence result based on the energy estimate and some complementary properties are proved for the corresponding variational formulation. Finally the magnetostrictive effect is included.

Strong convergence results related to strict convexity

Abstract: Let Ωbe endowed with a σ—, complete measure and let weakly in . If u(x) is an external point of the closed convex hull of a.e. in Ω, then strongly in cannot oscillate around u(x). Other strong convergence results are proved. Applications to the solution of nonlinear partial differential equaitons and of minimization problems are given.

Gradient Flows: In Metric Spaces and in the Space of Probability Measures

Abstract: Notation.- Notation.- Gradient Flow in Metric Spaces.- Curves and Gradients in Metric Spaces.- Existence of Curves of Maximal Slope and their Variational Approximation.- Proofs of the Convergence Theorems.- Uniqueness, Generation of Contraction Semigroups, Error Estimates.- Gradient Flow in the Space of Probability Measures.- Preliminary Results on Measure Theory.- The Optimal Transportation Problem.- The Wasserstein Distance and its Behaviour along Geodesics.- Absolutely Continuous Curves in p(X) and the Continuity Equation.- Convex Functionals in p(X).- Metric Slope and Subdifferential Calculus in (X).- Gradient Flows and Curves of Maximal Slope in p(X).

Controlled growth of tetrapod-branched inorganic nanocrystals

Abstract: Nanoscale materials are currently being exploited as active components in a wide range of technological applications in various fields, such as composite materials1,2, chemical sensing3, biomedicine4,5,6, optoelectronics7,8,9 and nanoelectronics10,11,12. Colloidal nanocrystals are promising candidates in these fields, due to their ease of fabrication and processibility. Even more applications and new functional materials might emerge if nanocrystals could be synthesized in shapes of higher complexity than the ones produced by current methods (spheres, rods, discs)13,14,15,16,17,18,19. Here, we demonstrate that polytypism, or the existence of two or more crystal structures in different domains of the same crystal, coupled with the manipulation of surface energy at the nanoscale, can be exploited to produce branched inorganic nanostructures controllably. For the case of CdTe, we designed a high yield, reproducible synthesis of soluble, tetrapod-shaped nanocrystals through which we can independently control the width and length of the four arms.

The inverse mean curvature flow and the Riemannian Penrose Inequality

Abstract: Let M be an asymptotically flat 3-manifold of nonnegative scalar curvature. The Riemannian Penrose Inequality states that the area of an outermost minimal surface N in M is bounded by the ADM mass m according to the formula |N |≤ 16πm 2 . We develop a theory of weak solutions of the inverse mean curvature flow, and employ it to prove this inequality for each connected component of N using Geroch’s monotonicity formula for the ADM mass. Our method also proves positivity of Bartnik’s gravitational capacity by computing a positive lower bound for the mass purely in terms of local geometry.