arXiv subjects

Rainer Backofen

Publications and source records attributed to Rainer Backofen.

15 recordsLinked to original sources

arXiv2026

Scalar Truesdell Time Derivative and $(L^{2},H^{-1})$ -- Surface Gradient Flows

We address surface gradient flows which allow for energy dissipation by evolving the surface and a scalar quantity on it, simultaneously. A proper choice of the time derivative and the gauge of surface independence guarantees energy dissipation and ensures conservation of the scalar quantity. The resulting system of partial differential equations couples geometric evolution equations for the evolution of the surface in normal directions, equations for tangential movement and scalar-valued equations on the evolving surface. We discuss the general setting and the special case of surface tension flows and numerically demonstrate the importance of tangential movement on the evolution.

math-ph↗

arXiv2026

Self-organized flows break morphological symmetry in active/passive systems

We consider a phase-separating mixture of active and passive fluids and explore morphological asymmetries of the emerging dominantly bicontinous dynamic emulsion. Two-dimensional numerical simulations reveal that the geometric and topological asymmetries can solely be explained by self-organized flows in the active region. As in inertial turbulence an inverse energy cascade in the active region leads to the formation of condensates. The size of these mesocales vortices is determined by the locally available space in the emulsion. As these condensates accumulate energy they impact the fluctuation of the surrounding interface and thus form a tight coupling between the flow field and the dynamic morphology. While explored for active/passive systems the symmetry-breaking mechanism can be generalized to heterogeneous active systems and proposes a way to control the morphology of various functional soft materials.

cond-mat.soft↗

arXiv2023

Nonequilibrium hyperuniform states in active turbulence

We demonstrate that the complex spatiotemporal structure in active fluids can feature characteristics of hyperuniformity. Using a hydrodynamic model, we show that the transition from hyperuniformity to non-hyperuniformity and anti-hyperuniformity depends on the strength of active forcing and can be related to features of active turbulence without and with scaling characteristics of inertial turbulence. Combined with identified signatures of Levy walks and non-universal diffusion in these systems, this allows for a biological interpretation and the speculation of non-equilibrium hyperuniform states in active fluids as optimal states with respect to robustness and strategies of evasion and foraging.

cond-mat.soft↗

arXiv2022

Magnetically enhanced thin film coarsening by a magnetic XPFC model allowing to decouple magnetic anisotropy and magnetostriction

External magnetic fields provide a macroscopic control mechanism to influence the microstructure of polycrystalline materials. We model the influence of strong magnetic fields on grain growth in thin films with a magnetic extended phase field crystal (XPFC) model. The magneto-structural effects are incorporated into the correlation function in reciprocal space. With this approach magnetic anisotropy, magnetostriction and mobility of grain boundary can be controlled and a variety of geometrical and topological properties consistent with experimental results can be determined.

cond-mat.mtrl-sci↗

arXiv2022

Controlling magnetic anisotropy in amplitude expansion of phase field crystal model

The amplitude expansion for a magnetic phase-field-crystal (magnetic APFC) model enables a convenient coarse-grained description of crystalline structures under the influence of magnetic fields. Considering higher-order magnetic coupling terms, we demonstrate the possibility of tuning the magnetic anisotropy in these models. This allows for reproducing the easy and hard direction of magnetization. Such a result can be achieved without increasing the computational cost, enabling simulations of the manipulation of dislocation networks and microstructures in ferromagnetic materials. As a demonstration, we report on the simulation of the shrinkage of a spherical grain with the magnetic anisotropy of Fe.

cond-mat.mtrl-sci↗

arXiv2022

Magnetic APFC modeling and the influence of magneto-structural interactions on grain shrinkage

We derive the amplitude expansion for a phase-field-crystal (APFC) model that captures the basic physics of magneto-structural interactions. The symmetry breaking due to magnetization is demonstrated, and the characterization of the magnetic anisotropy for a BCC crystal is provided. This model enables a convenient coarse-grained description of crystalline structures, in particular when considering the features of the APFC model combined with numerical methods featuring inhomogeneous spatial resolution. This is shown by addressing the shrinkage of a spherical grain within a matrix, chosen as a prototypical system to demonstrate the influence of different magnetizations. These simulations serve as a proof of concept for the modeling of manipulation of dislocation networks and microstructures in ferromagnetic materials within the APFC model.

cond-mat.mtrl-sci↗

arXiv2019

Magnetically induced/enhanced coarsening in thin films

External magnetic fields influence the microstructure of polycrystalline materials. We explore the influence of strong external magnetic fields on the long time scaling of grain size during coarsening in thin films with an extended phase-field-crystal model. Additionally, the change of various geometrical and topological properties is studied. In a situation which leads to stagnation, an applied external magnetic field can induce further grain growth. The induced driving force due to the magnetic anisotropy defines the magnetic influence of the external magnetic field. Different scaling regimes are identified dependent on the magnetization. At the beginning, the scaling exponent increases with the strength of the magnetization. Later, when the texture becomes dominated by grains preferably aligned with the external magnetic field, the scaling exponent becomes independent of the strength of the magnetization or stagnation occurs. We discuss how the magnetic influence change the effect of retarding or pinning forces, which are known to influence the scaling exponent. We further study the influence of the magnetic field on the grain size distribution (GSD), next neighbor distribution (NND) as well as grain shape and orientation. If possible, we compare our predictions with experimental findings.

cond-mat.mtrl-sci↗

arXiv2018

Defects at grain boundaries: A coarse-grained, three-dimensional description by the amplitude expansion of the phase-field crystal model

We address a three-dimensional, coarse-grained description of dislocation networks at grain boundaries between rotated crystals. The so-called amplitude expansion of the phase-field crystal model is exploited with the aid of finite element method calculations. This approach allows for the description of microscopic features, such as dislocations, while simultaneously being able to describe length scales that are orders of magnitude larger than the lattice spacing. Moreover, it allows for the direct description of extended defects by means of a scalar order parameter. The versatility of this framework is shown by considering both fcc and bcc lattice symmetries and different rotation axes. First, the specific case of planar, twist grain boundaries is illustrated. The details of the method are reported and the consistency of the results with literature is discussed. Then, the dislocation networks forming at the interface between a spherical, rotated crystal embedded in an unrotated crystalline structure, are shown. Although explicitly accounting for dislocations which lead to an anisotropic shrinkage of the rotated grain, the extension of the spherical grain boundary is found to decrease linearly over time in agreement with the classical theory of grain growth and recent atomistic investigations. It is shown that the results obtained for a system with bcc symmetry agree very well with existing results, validating the methodology. Furthermore, fully original results are shown for fcc lattice symmetry, revealing the generality of the reported observations.

cond-mat.mtrl-sci↗

arXiv2017

Convexity splitting in a phase field model for surface diffusion

Convexity splitting like schemes with improved accuracy are proposed for a phase field model for surface diffusion. The schemes are developed to enable large scale simulations in three spatial dimensions describing experimentally observed solid state dewetting phenomena. We introduce a first and a second order unconditionally energy stable scheme and carefully elaborate the loss in accuracy associated with large time steps in such schemes. We then present a family of Rosenbrock convex splitting schemes. We show the existence of a maximal numerical timestep and demonstrate the increase of this maximal numerical time step by at least one order of magnitude using a Rosenbrock method. This scheme is used to study the effect of contact angle on solid state dewetting phenomena.

math.NA↗

arXiv2017

Controlling the energy of defects and interfaces in the amplitude expansion of the phase-field crystal model

One of the major difficulties in employing phase field crystal (PFC) modeling and the associated amplitude (APFC) formulation is the ability to tune model parameters to match experimental quantities. In this work we address the problem of tuning the defect core and interface energies in the APFC formulation. We show that the addition of a single term to the free energy functional can be used to increase the solid-liquid interface and defect energies in a well-controlled fashion, without any major change to other features. The influence of the newly added term is explored in two-dimensional triangular and honeycomb structures as well as bcc and fcc lattices in three dimensions. In addition, a finite element method (FEM) is developed for the model that incorporates a mesh refinement scheme. The combination of the FEM and mesh refinement to simulate amplitude expansion with a new energy term provides a method of controlling microscopic features such as defect and interface energies while simultaneously delivering a coarse-grained examination of the system.

cond-mat.mtrl-sci↗

arXiv2015

Liquid crystalline growth within a phase-field crystal model

By using a phase-field crystal (PFC) model, the liquid-crystal growth of the plastic triangular phase is simulated with emphasis on crystal shape and topological defect formation. The equilibrium shape of a plastic triangular crystal (PTC) grown from a isotropic phase is compared with that grown from a columnar/smectic A (CSA) phase. While the shape of a PTC nucleus in the isotropic phase is almost identical to that of a classical PFC model, the shape of a PTC nucleus in CSA is affected by the orientation of stripes in the CSA phase, and irregular hexagonal, elliptical, octagonal, and rectangular shapes are obtained. Concerning the dynamics of the growth process we analyse the topological structure of the nematic-order, which starts from nucleation of $+\frac{1}{2}$ and $-\frac{1}{2}$ disclination pairs at the PTC growth front and evolves into hexagonal cells consisting of $+1$ vortices surrounded by six satellite $-\frac{1}{2}$ disclinations. It is found that the orientational and the positional order do not evolve simultaneously, the orientational order evolves behind the positional order, leading to a large transition zone, which can span over several lattice spacings.

cond-mat.soft↗

arXiv2013

Grain growth beyond the Mullins model, capturing the complex physics behind universal grain size distributions

Grain growth experiments on thin metallic films have shown the geometric and topological characteristics of the grain structure to be universal and independent of many experimental conditions. The universal size distribution, however, is found to differ both qualitatively and quantitatively from the standard Mullins curvature driven model of grain growth; with the experiments exhibiting an excess of small grains (termed an "ear") and an excess of very large grains (termed a "tail") compared with the model. While a plethora of extensions of the Mullins model have been proposed to explain these characteristics, none have been successful. In this work, large scale simulations of a model that resolves the atomic scale on diffusive time scales, the phase field crystal model, is used to examine the complex phenomena of grain growth. The results are in remarkable agreement with the experimental results, recovering the characteristic "ear" and "tail" features of the experimental grain size distribution. The simulations also indicate that while the geometric and topological characteristics are universal, the dynamic growth exponent is not.

cond-mat.mtrl-sci↗

arXiv2010

Particles on curved surfaces - a dynamic approach by a phase field crystal model

We present a dynamic model to study ordering of particles on arbitrary curved surfaces. Thereby the particles are represented as maxima in a density field and a surface partial differential equation for the density field is solved to the minimal energy configuration. We study annihilation of dislocations within the ordered sytem and premelting along grain boundary scars. The obtained minimal energy configurations on a sphere are compared with existing results and scaling laws are computed for the number of excess dislocations as a function of system size.

cond-mat.mtrl-sci↗

arXiv2010

A phase-field-crystal approach to critical nuclei

We investigate a phase-field-crystal model for homogeneous nucleation. Instead of solving the time evolution of a density field towards equilibrium we use a String Method to identify saddle points in phase space. The saddle points allow to obtain the nucleation barrier and the critical nucleus. The advantage of using the phase-field-crystal model for this task is its ability to resolve atomistic effects. The obtained results indicate different properties of the critical nucleus compared with bulk crystals and show a detailed description of the nucleation process.

cond-mat.stat-mech↗

arXiv2009

Derivation of the phase field crystal model for colloidal solidification

The phase-field crystal model is by now widely used in order to predict crystal nucleation and growth. For colloidal solidification with completely overdamped individual particle motion, we show that the phase-field crystal dynamics can be derived from the microscopic Smoluchowski equation via dynamical density functional theory. The different underlying approximations are discussed. In particular, a variant of the phase-field crystal model is proposed which involves less approximations than the standard phase-field crystal model. We finally test the validity of these phase-field crystal models against dynamical density functional theory. In particular, the velocities of a linear crystal front from the undercooled melt are compared as a function of the undercooling for a two-dimensional colloidal suspension of parallel dipoles. Good agreement is only obtained by a drastic scaling of the free energies in the phase-field crystal model in order to match the bulk freezing transition point.

cond-mat.soft↗