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We present some long-range interaction models for phase coexistence which have recently appeared in the literature, recalling also their relation to classical interface and capillarity problems. In this note, the main focus will be on the…
We study the limit behavior of Cahn--Hilliard-type functionals in which the derivative is replaced by higher-order fractional derivatives and modulated by an oscillating factor. Depending on the ratio between the oscillation scale and the…
We establish a Harnack inequality for weak solutions of nonlocal equations in a disconnected region. The inequality compares the value of a solution on one connected component with its value on another, capturing a purely nonlocal…
We study the rate of convergence of some nonlocal functionals recently considered by Bourgain, Brezis and Mironescu. In particular we establish the $\Gamma$-convergence of the corresponding rate functionals, suitably rescaled, to a limit…
We derive a family of inequalities involving different phase-space distributions of a quantum state which have to be fulfilled by any classical state. The violation of these inequalities is a clear signature of nonclassicality. Our approach…
For $s\in (0,1)$ we introduce a notion of fractional $s$-mass on $(n-2)$-dimensional closed, orientable surfaces in $\R^n$. Moreover, we prove its $\Gamma$-convergence, with respect to the flat topology, and pointwise convergence to the…
In this paper, the effect of weak nonlinearities in 1D locally resonant metamaterials is investigated via the method of multiple scales. Commonly employed to the investigate the effect of weakly nonlinear interactions on the free wave…
In this paper we study two different ways of coupling a local operator with a nonlocal one in such a way that the resulting equation is related to an energy functional. In the first strategy the coupling is given via source terms in the…
We study the asymptotic behavior of the fractional Allen--Cahn energy functional in bounded domains with prescribed Dirichlet boundary conditions. When the fractional power $s \in (0,\frac12)$, we establish establish the first-order…
We study problems in which a local model is coupled with a nonlocal one. We propose two energies: both of them are based on the same classical weighted $H^1$-semi norm to model the local part, while two different weighted $H^s$-semi norms,…
We investigate a highly-nonlocal generalization of the Lindhard function, given by the jellium-with-gap model. We find a band-gap-dependent gradient expansion of the kinetic energy, which performs noticeably well for large atoms. Using the…
Nonlocal (spatial-dispersion) effects in multilayered metamaterials composed of periodic stacks of alternating, deeply subwavelength dielectric layers are known to be negligibly weak. Counterintuitively, under certain critical conditions,…
Semi-local density functional approximations are widely used. None of them can capture the long-range van der Waals (vdW) attraction between separated subsystems, but they differ remarkably in the extent to which they capture…
We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces are equipped with a seminorm depending on finite differences…
The key feature of nonlocal kinetic energy functionals is their ability to reduce to the Thomas-Fermi functional in the regions of high density and to the von Weizs\"acker functional in the region of low density/high density gradient. This…
We construct a meta-generalized-gradient approximation which properly balances the nonlocality contributions to the exchange and correlation at the semilocal level. This non-empirical functional shows good accuracy for a broad palette of…
We show that certain free energy functionals that are not convex with respect to the usual convex structure on their domain of definition, are strictly convex in the sense of displacement convexity under a natural change of variables. We…
We obtain a compactness result for $\Gamma$-convergence of integral functionals defined on $\mathcal{A}$-free vector fields. This is used to study homogenization problems for these functionals without periodicity assumptions. More…
We study the duality of quasilocal energy and charges with non-orthogonal boundaries in the (2+1)-dimensional low-energy string theory. Quasilocal quantities shown in the previous work and some new variables arisen from considering the…
In this article, we establish weighted strong and weak type inequalities for non-commutative square functions that naturally arise in the analysis of differences between ball averages and martingale sequences within the framework of group…