Related papers: A quantitative second order minimality criterion f…

This paper is devoted to study of the limiting behaviour of an elastic material with periodically distributed rigid inclusions of size {\epsilon}, as the small parameter {\epsilon} goes to zero. We address here the case with inclusions of…

We study an array of coupled optical cavities in presence of two-photon driving and dissipation. The system displays a critical behavior similar to that of a quantum Ising model at finite temperature. Using the corner-space renormalization…

Adaptive Finite Element Method (adaptivity) is known to be an effective numerical tool for some ill-posed problems. The key advantage of the adaptivity is the image improvement with local mesh refinements. A rigorous proof of this property…

Using a rigorous method of matched asymptotic expansions, I derive the equation of motion of a small, compact body in an external vacuum spacetime through second order in the body's mass (neglecting effects of internal structure). The…

A class of causal variational principles on a compact manifold is introduced and analyzed both numerically and analytically. It is proved under general assumptions that the support of a minimizing measure is either completely timelike, or…

There is described a spacetime formulation of both nonrelativistic and relativistic elasticity. Specific attention is devoted to the causal structure of the theories and the availability of local existence theorems for the initial-value…

Motivated by the study of an important data set for understanding the large-scale structure of the universe, this work considers the estimation of the reduced second moment function, or K-function, of a stationary point process observed…

We propose the notions of uniform local weak o-minimality and $*$-local weak o-minimality. Local monotonicity theorems hold in definably complete locally o-minimal structures and uniformly locally o-minimal structures of the second kind. In…

By using some deep tools from microlocal analysis, the authors of the papers (Ann. of Math., 165 (2007), 567--591, J. Amer. Math. Soc., 23 (2010), 655--691; Invent. Math., 178 (2009), 119--171; Duke Math. J., 158(2011), 83--120) have…

We prove an a priori estimate for the second derivatives of local minimizers of integral functionals of calculus of variation with convex integrand with respect to the gradient variable, assuming that the function that measures the…

A geometrical interpretation of the $G$-structures associated to elastic material bodies is given. In addition, characterizations of their integrability are obtained. Since the lack of integrability is a geometrical measure of the lack of…

This paper derives an a posteriori error estimator for the nonlinear first-order optimality conditions associated with the electrically and flexoelectrically coupled Frank-Oseen model of liquid crystals, building on previous results for…

In order to extract physical parameters from the waveform of an extreme-mass-ratio binary, one requires a second-order--accurate description of the motion of the smaller of the two objects in the binary. Using a method of matched asymptotic…

We formulate a cut finite element method for linear elasticity based on higher order elements on a fixed background mesh. Key to the method is a stabilization term which provides control of the jumps in the derivatives of the finite element…

We propose an optimal method exploiting second order quantum phase transitions to perform high precision measurements of the control parameter at criticality. Our approach accesses the high fidelity susceptibility via the measurement of…

Second order linear non-autonomous differential equations with negative stiffness are considered. Using Chetaev-like (Lyapunov-like) functions, necessary (sufficient) conditions are found for the solutions to be bounded for all initial…

In complex crystals close to melting or at finite temperatures, different types of defects are ubiquitous and their role becomes relevant in the mechanical response of these solids. Conventional elasticity theory fails to provide a…

Quantum metrology fundamentally relies upon the efficient management of quantum uncertainties. We show that, under equilibrium conditions, the management of quantum noise becomes extremely flexible around the quantum critical point of a…

Second order systems whose drift is defined by the gradient of a given potential are considered, and minimization of the $L^1$-norm of the control is addressed. An analysis of the extremal flow emphasizes the role of singular trajectories…

In this paper we propose a penalized Crouzeix-Raviart element method for eigenvalue problems of second order elliptic operators. The key idea is to add a penalty term to tune the local approximation property and the global continuity…