Related papers: Phase-field approximation of functionals defined o…
We study the properties of convex functionals which have been proposed for the simulation of charged molecular systems within the Poisson-Boltzmann approximation. We consider the extent to which the functionals reproduce the true…
A novel numerical approach to analyze the mechanical behavior within composite materials including the inelastic regime up to final failure is presented. Therefore, a second-gradient theory is combined with phase-field methods to fracture.…
This paper addresses the asymptotics of functionals with linear growth depending on the Riesz $s$-fractional gradient on piecewise constant functions. We consider a general class of varying energy densities and, as $s\to 1$, we characterize…
In this work we derive by Gamma-convergence techniques a model for brittle fracture linearly elastic plates. Precisely, we start from a brittle linearly elastic thin film with positive thickness $\rho$ and study the limit as $\rho$ tends to…
This paper is devoted to the robust approximation with a variational phase field approach of multiphase mean curvature flows with possibly highly contrasted mobilities. The case of harmonically additive mobilities has been addressed…
The phase-field approach to fracture has been proven to be a mathematically sound and easy to implement method for computing crack propagation with arbitrary crack paths. Hereby crack growth is driven by energy minimization resulting in a…
This paper presents an analytical formula that closely approximates the fully nonlinear power spectrum of matter fluctuations for redshift $z\approx 5$ to 0 over a wide range of cosmologically interesting flat models with varying matter…
Koopmans-compliant functionals provide an orbital-density-dependent framework for an accurate evaluation of spectral properties; they are obtained by imposing a generalized piecewise-linearity condition on the total energy of the system…
We propose a consistent approach to the definition of electric, magnetic, and toroidal multipole moments. Electric and magnetic fields are split into potential, vortex, and radiative terms, with the latter ones dropped off in the…
In this paper, we consider the boundedness of fractional type multilinear commutators generated by fractional integral with rough variable kernel and local Campanato functions on both generalized local (central) Morrey spaces and…
A field theory is presented for predicting damage and fracture in quasi-brittle materials. The approach taken here is new and blends a non-local constitutive law with a two-point phase field. In this formulation, the material displacement…
A phase field model for ductile fracture considering Hencky strain and finite J2 plasticity is presented using the nonlocal operator method. A variational derivation of J2 plasticity at finite strain with a phase field model is performed.…
Modern density functional approximations achieve moderate accuracy at low computational cost for many electronic structure calculations. Some background is given relating the gradient expansion of density functional theory to the WKB…
This paper presents an efficient approach to image segmentation that approximates the piecewise-smooth (PS) functional in [12] with explicit solutions. By rendering some rational constraints on the initial conditions and the final solutions…
Using principles of asymptotic analysis, we derive the exact leading corrections to the Thomas-Fermi kinetic energy approximation for Kohn-Sham electrons for slabs. This asymptotic expansion approximation includes crucial quantum…
Numerical simulations of brittle fracture using phase-field approaches often employ a discrete approximation framework that applies the same order of interpolation for the displacement and phase-field variables. Most common is to use linear…
We present an asymptotically exact solution of a local copper-oxide model abstracted from the multi-band models. The phase diagram is obtained through the renormalization-group analysis of the partition function. In the strong coupling…
A prolate $\gamma$-rigid version of the Bohr-Mottelson Hamiltonian with a quartic anharmonic oscillator potential in $\beta$ collective shape variable is used to describe the spectra for a variety of vibrational-like nuclei. Speculating the…
This paper develops a functional-analytic framework for approximating the push-forward induced by an analytic map from finitely many samples. Instead of working directly with the map, we study the push-forward on the space of locally…
In exact density functional theory (DFT) the total ground-state energy is a series of linear segments between integer electron points, a condition known as "piecewise linearity". Deviation from this condition is indicative of poor…