Existence and regularity of minimizers in elliptic free boundary problems have been extensively studied in the literature. We initiate the corresponding study of higher critical points by considering a superlinear free boundary problem related to plasma confinement. The associated energy functional is nondifferentiable, and therefore standard variational methods cannot be used directly to prove...

In this paper we prove the existence of weak solutions for the thin film equation with prescribed non zero contact angle and for a large class of mobility coefficients, in dimension 1. The existence of weak solutions for this degenerate parabolic fourth order free boundary problem was proved by F. Otto in [35] when the mobility coefficient is given by f(u) = u, using a particular gradient flow ...

We study zero-temperature Ising Glauber Dynamics, on 2D slabs of thickness k ≥ 2. In this model, ±1-valued spins at integer sites update according to majority vote dynamics with two opinions. We show that all spins reaches a final state (that is, the system fixates) for k = 2 under free boundary conditions and for k = 2 or 3 under periodic boundary conditions. For thicker slabs there are sites ...

Sets of non-intersecting, monotonic lattice paths, or xed routings, provide a common representation for several combinatorial problems and have been the key element for designing sampling algorithms. Markov chain algorithms based on routings have led to eecient samplers for tilings, Eulerian orientations 8] and triangulations 9], while an algorithm which successively calculates ratios of determ...

We analyse the homogeneous instabilities in a nematic liquid crystal subjected to plane steady Couette or Poiseuille flow in the case when the director is prealigned perpendicular to the flow plane taking into account weak anchoring at the confining surfaces. The critical shear rate decreases for decreasing anchoring strength and goes to zero in the limit of torque-free boundary conditions. For...

Fritz John and Kuhn-Tucker type necessary optimality conditions for a Pareto optimal (efficient) solution of a multiobjective control problem are obtained by first reducing the multiobjective control problem to a system of single objective control problems, and then using already established optimality conditions. As an application of Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir ...

Data race free (DRF) programs constitute an important class of concurrent programs. In this paper we provide a framework for designing and proving the correctness of data flow analyses that target this class of programs, and which are in the same spirit as the “sync-CFG” analysis originally proposed in [9]. To achieve this, we first propose a novel concrete semantics for DRF programs called L-D...

2014 We study non linearities in the thermal instability induced by heating a nematic liquid crystal from below. First a model with free-free boundary conditions is studied. Critical behaviour of the free-free model is analysed. Properties above the threshold are determined with use of perturbation analysis. One shows that the first expansion coefficient R(1) of the critical number vanishes. On...

Active contours are used extensively in vision for more than two decades, primarily for applications such as image segmentation and object detection. The vast majority of active contours models make use of closed curves and the few that employ open curves rely on either fixed boundary conditions or no boundary conditions at all. In this paper we discuss a new class of open active contours with ...

In this paper, we study a multi-symplectic scheme for three dimensional Maxwell’s equations in a simple medium. This is a system of PDEs with multi-symplectic structures. We prove that this multi-symplectic scheme preserves the discrete version of local and global energy conservation law and the discrete divergence. Furthermore, we extend the discussion to several dispersion properties of the m...