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We investigate a quasicontinuum method by means of analytical tools. More precisely, we compare a discrete-to-continuum analysis of an atomistic one-dimensional model problem with a corresponding quasicontinuum model. We consider next and…

Analysis of PDEs · Mathematics 2014-11-12 Mathias Schäffner , Anja Schlömerkemper

A new energy functional for pure traction problems in elasticity has been deduced in [23] as the variational limit of nonlinear elastic energy functional for a material body subject to an equilibrated force field: a sort of Gamma limit with…

Optimization and Control · Mathematics 2019-07-01 Francesco Maddalena , Danilo Percivale , Franco Tomarelli

The Cahn--Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In recent years, several types of dynamic boundary conditions have been proposed in order to account for possible short-range…

Analysis of PDEs · Mathematics 2023-07-28 Chun Liu , Hao Wu

Phase separation in the Hubbard model is investigated with the dynamical cluster approximation. We find that it is present in the paramagnetic solution for values of filling smaller than one and at finite temperature when a positive…

Strongly Correlated Electrons · Physics 2007-05-23 A. Macridin , M. Jarrell , Th. Maier

We propose a first rigorous homogenisation procedure in image-segmentation models by analysing the relative impact of (possibly random) fine-scale oscillations and phase-field regularisations for a family of elliptic functionals of Ambrosio…

Analysis of PDEs · Mathematics 2026-05-12 Francesco Colasanto , Matteo Focardi , Caterina Ida Zeppieri

We derive the non-retarded energy shift of a neutral atom for two different geometries. For an atom close to a cylindrical wire we find an integral representation for the energy shift, give asymptotic expressions, and interpolate…

Quantum Physics · Physics 2009-12-07 Claudia Eberlein , Robert Zietal

Waves propagating through a bounded plasma can rearrange the densities of states in the six-dimensional velocity-configuration phase space. Depending on the rearrangement, the wave energy can either increase or decrease, with the difference…

Plasma Physics · Physics 2015-10-28 Michael J. Hay , Jeremy Schiff , Nathaniel J. Fisch

The energy spectrum of two short-range interacting particles in a harmonic potential trap has previously been related to free-space scattering phase shifts. But the existing formula for this purpose is exact only in the limit of an…

Nuclear Theory · Physics 2020-05-20 Xilin Zhang

We consider second order phase field functionals, in the continuum setting, and their discretization with isogeometric tensor product B-splines. We prove that these functionals, continuum and discrete, $\Gamma$-converge to a brittle…

Numerical Analysis · Mathematics 2020-03-18 Matteo Negri

This article is concerned with the problem of minimising the Willmore energy in the class of \emph{connected} surfaces with prescribed area which are confined to a small container. We propose a phase field approximation based on De Giorgi's…

Analysis of PDEs · Mathematics 2016-10-28 Patrick W. Dondl , Antoine Lemenant , Stephan Wojtowytsch

In this paper a we derive by means of $\Gamma$-convergence a macroscopic strain-gradient plasticity from a semi-discrete model for dislocations in an infinite cylindrical crystal. In contrast to existing work, we consider an energy with…

Analysis of PDEs · Mathematics 2018-06-14 Janusz Ginster

This work is devoted to the analysis of convergence of an alternate (staggered) minimization algorithm in the framework of phase field models of fracture. The energy of the system is characterized by a nonlinear splitting of tensile and…

Analysis of PDEs · Mathematics 2020-08-26 Stefano Almi

In the present work, the evolution of damage in periodic composite materials is investigated through a novel finite element-based multiscale computational approach. The methodology is developed by means of the original combination of…

Numerical Analysis · Mathematics 2019-08-09 Francesca Fantoni , Andrea Bacigalupo , Marco Paggi , Josè Reinoso

Phase field models have emerged as a powerful and flexible framework for simulating complex interface-driven phenomena across a wide range of scientific and engineering applications. In fracture mechanics, the phase field…

Numerical Analysis · Mathematics 2025-06-23 Md Mamun Miah , Ryuhei Wakida , Masato Kimura

This article is devoted to the study of certain models for phase transitions involving nonlocal energies. A first part is concerned with to the asymptotic analysis of a system of fractional elliptic equations of Allen-Cahn type as a…

Analysis of PDEs · Mathematics 2025-06-26 Thomas Gabard , Vincent Millot

In traditional phase-field modeling of multiphase materials, a significant challenge arises from the non-local nature of fracture energy regularization, where interfacial toughness is inherently coupled with the properties of the…

Computational Physics · Physics 2026-04-14 Ye-Hang Qin , Ye Feng

In this paper, we derive the time-fractional Cahn-Hilliard equation from continuum mixture theory with a modification of Fick's law of diffusion. This model describes the process of phase separation with nonlocal memory effects. We analyze…

Analysis of PDEs · Mathematics 2022-10-10 Marvin Fritz , Mabel L. Rajendran , Barbara Wohlmuth

We show that the energy of a perturbed system can be fully recovered from the unperturbed system's electron density. We derive an alchemical integral transform by parametrizing space in terms of transmutations, the chain rule and…

Chemical Physics · Physics 2022-10-28 Simon León Krug , Guido Falk von Rudorff , O. Anatole von Lilienfeld

A new method of accessing information on the symmetry free energy from yields of fragments produced in Fermi-energy heavy-ion collisions is proposed. Furthermore, by means of quantum fluctuation analysis techniques, correlations between…

We consider a nonlinear, frame indifferent Griffith model for nonsimple brittle materials where the elastic energy also depends on the second gradient of the deformations. In the framework of free discontinuity and gradient discontinuity…

Analysis of PDEs · Mathematics 2019-09-25 Manuel Friedrich