Analysis of a moving mask approximation for martensitic transformations

In this work we introduce a moving mask approximation to describe the dynamics of austenite to martensite phase transitions at a continuum level. In this framework, we prove a new type of Hadamard jump condition, from which we deduce that the deformation gradient must be of the form $\mathsf{1} +\mathbf{a}\otimes \mathbf{n}$ a.e. in the martensite phase. This is useful to better understand the complex microstructures and the formation of curved interfaces between phases in new ultra-low hysteresis alloys such as Zn45Au30Cu25, and provides a selection mechanism for physically-relevant energy-minimising microstructures. In particular, we use the new type of Hadamard jump condition to deduce a rigidity theorem for the two well problem. The latter provides more insight on the cofactor conditions, particular conditions of supercompatibility between phases believed to influence reversibility of martensitic transformations

On the nonlocal Cahn-Hilliard-Brinkman and Cahn-Hilliard-Hele-Shaw systems

The phase separation of an isothermal incompressible binary fluid in a porous medium can be described by the so-called Brinkman equation coupled with a convective Cahn-Hilliard (CH) equation. The former governs the average fluid velocity $\mathbf{u}$, while the latter rules evolution of $\varphi$, the difference of the (relative) concentrations of the two phases. The two equations are known as the Cahn-Hilliard-Brinkman (CHB) system. In particular, the Brinkman equation is a Stokes-like equation with a forcing term (Korteweg force) which is proportional to $\mu\nabla\varphi$, where $\mu$ is the chemical potential. When the viscosity vanishes, then the system becomes the Cahn-Hilliard-Hele-Shaw (CHHS) system. Both systems have been studied from the theoretical and the numerical viewpoints. However, theoretical results on the CHHS system are still rather incomplete. For instance, uniqueness of weak solutions is unknown even in 2D. Here we replace the usual CH equation with its physically more relevant nonlocal version. This choice allows us to prove more about the corresponding nonlocal CHHS system. More precisely, we first study well-posedness for the CHB system, endowed with no-slip and no-flux boundary conditions. Then, existence of a weak solution to the CHHS system is obtained as a limit of solutions to the CHB system. Stronger assumptions on the initial datum allow us to prove uniqueness for the CHHS system. Further regularity properties are obtained by assuming additional, though reasonable, assumptions on the interaction kernel. By exploiting these properties, we provide an estimate for the difference between the solution to the CHB system and the one to the CHHS system with respect to viscosity

Convective nonlocal Cahn-Hilliard equations with reaction terms

We introduce and analyze the nonlocal variants of two Cahn-Hilliard type equations with reaction terms. The first one is the so-called Cahn-Hilliard-Oono equation which models, for instance, pattern formation in diblock-copolymers as well as in binary alloys with induced reaction and type-I superconductors. The second one is the Cahn-Hilliard type equation introduced by Bertozzi et al. to describe image inpainting. Here we take a free energy functional which accounts for nonlocal interactions. Our choice is motivated by the work of Giacomin and Lebowitz who showed that the rigorous physical derivation of the Cahn-Hilliard equation leads to consider nonlocal functionals. The equations also have a transport term with a given velocity field and are subject to a homogenous Neumann boundary condition for the chemical potential, i.e., the first variation of the free energy functional. We first establish the well-posedness of the corresponding initial and boundary value problems in a weak setting. Then we consider such problems as dynamical systems and we show that they have bounded absorbing sets and global attractors

Extreme Right and Populism: A Frame Analysis of Extreme Right Wing Discourses in Italy and Germany. IHS Political Science Series No. 121, July 2010

This paper addresses the interactions between the extreme right and populism, looking at right wing discourses in Italy and Germany, focusing on different types of extreme right organizations (political parties, violent subcultural/young right wing groups, and political movements), and adopting a social movement perspective. Through a frame analysis conducted on several types of organizational documents (newspapers, websites, online guest books and forums, and other forms of publications), covering a period from 2000-2006, for a total of 4000 frames, it explores empirically the aspect of the conceptualization of the populism by the extreme right, showing the bridging of the appeal to the people with some traditional frames of the extreme right, such as nativism and authoritarianism, and stressing how the central populist frames (the people versus the elite) are linked to the extreme right definition of the 'us' and the 'them', when developing diagnoses, prognoses and motivations to action. A political opportunity and discursive approach will be useful in explaining the different configurations of populist frames depending on country and organizational type

Procedural Due Process Under the District of Columbia Historic Protection Act

This article is part of the District of Columbia Survey

Cycles of Protest and the Consolidation of Democracy

Outcomes of democratization paths have been addressed within literature on democratic consolidation as well as on revolution. These approaches have however never been linked with social movement theory that, I argue in this article, can provide new lenses to explain how movements’ characteristics at the time of transition might have an impact on the quality of ensuing democracy. As the same time, looking at effects of social movements in terms of democratization can help broadening social movement studies, that have rarely addressed this type of effects. I am in particular interested in linking reflections (and empirical evidence) on effects of social movements to the typology on paths towards democratization that I have developed in other works. Looking especially at Central Eastern Europe post-1989, I single out the different characteristics of contentious politics in countries that underwent, respectively, eventful democratization, participated pacts and troubled democratization. Protest event analysis as constituted the empirical basis for the analysi

A model for the evolution of highly reversible martensitic transformations

In this work we introduce a new system of partial differential equations as a simplified model for the evolution of reversible martensitic transformations under thermal cycling in low hysteresis alloys. The model is developed in the context of nonlinear continuum mechanics, where the developed theory is mostly static, and cannot capture the influence of dynamics on martensitic microstructures. First, we prove existence of weak solutions; secondly, we study the physically relevant limit when the interface energy density vanishes, and the elastic constants tend to infinity. The limit problem provides a framework for the moving mask approximation recently introduced by the author. In the last section we study the limit equations in a one-dimensional setting. After closing the equations with a constitutive relation between the phase interface velocity and the temperature of the one-dimensional sample, the equations become a two-phase Stefan problem with a kinetic condition at the free boundary. Under some further assumptions, we show that the phase interface reaches the domain boundary in finite time

Cycles of Protest and the Consolidation of Democracy

Outcomes of democratization paths have been addressed within literature on democratic consolidation as well as on revolution. These approaches have however never been linked with social movement theory that, I argue in this article, can provide new lenses to explain how movements’ characteristics at the time of transition might have an impact on the quality of ensuing democracy. As the same time, looking at effects of social movements in terms of democratization can help broadening social movement studies, that have rarely addressed this type of effects. I am in particular interested in linking reflections (and empirical evidence) on effects of social movements to the typology on paths towards democratization that I have developed in other works. Looking especially at Central Eastern Europe post-1989, I single out the different characteristics of contentious politics in countries that underwent, respectively, eventful democratization, participated pacts and troubled democratization. Protest event analysis as constituted the empirical basis for the analysi