Upscaling of dislocation walls in finite domains

We wish to understand the macroscopic plastic behaviour of metals by upscaling the micro-mechanics of dislocations. We consider a highly simplified dislocation network, which allows our microscopic model to be a one dimensional particle system, in which the interactions between the particles (dislocation walls) are singular and non-local. As a first step towards treating realistic geometries, we focus on finite-size effects rather than considering an infinite domain as typically discussed in the literature. We derive effective equations for the dislocation density by means of \Gamma-convergence on the space of probability measures. Our analysis yields a classification of macroscopic models, in which the size of the domain plays a key role

Quantification of coarse-graining error in Langevin and overdamped Langevin dynamics

In molecular dynamics and sampling of high dimensional Gibbs measures coarse-graining is an important technique to reduce the dimensionality of the problem. We will study and quantify the coarse-graining error between the coarse-grained dynamics and an effective dynamics. The effective dynamics is a Markov process on the coarse-grained state space obtained by a closure procedure from the coarse-grained coefficients. We obtain error estimates both in relative entropy and Wasserstein distance, for both Langevin and overdamped Langevin dynamics. The approach allows for vectorial coarse-graining maps. Hereby, the quality of the chosen coarse-graining is measured by certain functional inequalities encoding the scale separation of the Gibbs measure. The method is based on error estimates between solutions of (kinetic) Fokker-Planck equations in terms of large-deviation rate functionals

A consistent treatment of link and writhe for open rods, and their relation to end rotation

We combine and extend the work of Alexander & Antman \cite{alexander.82} and Fuller \cite{fuller.71,fuller.78} to give a framework within which precise definitions can be given of topological and geometrical quantities characterising the contortion of open rods undergoing large deformations under end loading. We use these definitions to examine the extension of known results for closed rods to open rods. In particular, we formulate the analogue of the celebrated formula $Lk=Tw+Wr$ (link equals twist plus writhe) for open rods and propose an end rotation, through which the applied end moment does work, in the form of an integral over the length of the rod. The results serve to promote the variational analysis of boundary-value problems for rods undergoing large deformations.Comment: 17 pages, 4 figure

Three flow regimes of viscous jet falling onto a moving surface

A stationary viscous jet falling from an oriented nozzle onto a moving surface is studied, both theoretically and experimentally. We distinguish three flow regimes and classify them by the convexity of the jet shape (concave, vertical and convex). The fluid is modeled as a Newtonian fluid, and the model for the flow includes viscous effects, inertia and gravity. By studying the characteristics of the conservation of momentum for a dynamic jet, the boundary conditions for each flow regime are derived, and the flow regimes are characterized in terms of the process and material parameters. The model is solved by a transformation into an algebraic equation. We make a comparison between the model and experiments, and obtain qualitative agreement

Falling of a viscous jet onto a moving surface

We analyze the stationary flow of a jet of Newtonian fluid that is drawn by gravity onto a moving surface. The situation is modeled by a third-order ODE on a domain of unknown length and with an additional integral condition; by solving part of the equation explicitly we can reformulate the problem as a first-order ODE, again with an integral constraint. We show that there are two flow regimes, and characterize the associated regions in the three-dimensional parameter space in terms of an easily calculable quantity. In a qualitative sense the results from the model are found to correspond with experimental observations.Comment: 16 pages, 11 figure

A generalization of Onsager's reciprocity relations to gradient flows with nonlinear mobility

Onsager's 1931 `reciprocity relations' result connects microscopic time-reversibility with a symmetry property of corresponding macroscopic evolution equations. Among the many consequences is a variational characterization of the macroscopic evolution equation as a gradient-flow, steepest-ascent, or maximal-entropy-production equation. Onsager's original theorem is limited to close-to-equilibrium situations, with a Gaussian invariant measure and a linear macroscopic evolution. In this paper we generalize this result beyond these limitations, and show how the microscopic time-reversibility leads to natural generalized symmetry conditions, which take the form of generalized gradient flows

A subarcsecond resolution near-infrared study of Seyfert and `normal' galaxies: II. Morphology

We present a detailed study of the bar fraction in the CfA sample of Seyfert galaxies, and in a carefully selected control sample of non-active galaxies, to investigate the relation between the presence of bars and of nuclear activity. To avoid the problems related to bar classification in the RC3, e.g., subjectivity, low resolution and contamination by dust, we have developed an objective bar classification method, which we conservatively apply to our new sub-arcsecond resolution near-infrared imaging data set (Peletier et al. 1999). We are able to use stringent criteria based on radial profiles of ellipticity and major axis position angle to determine the presence of a bar and its axial ratio. Concentrating on non-interacting galaxies in our sample for which morphological information can be obtained, we find that Seyfert hosts are barred more often (79% +/- 7.5%) than the non-active galaxies in our control sample (59% +/- 9%), a result which is at the 2.5 sigma significance level. The fraction of non-axisymmetric hosts becomes even larger when interacting galaxies are taken into account. We discuss the implications of this result for the fueling of central activity by large-scale bars. This paper improves on previous work by means of imaging at higher spatial resolution and by the use of a set of stringent criteria for bar presence, and confirms that the use of NIR is superior to optical imaging for detection of bars in disk galaxies.Comment: Latex, 3 figures, includes aaspptwo.sty, accepted for publication in the Astrophysical Journa

On microscopic origins of generalized gradient structures

Classical gradient systems have a linear relation between rates and driving forces. In generalized gradient systems we allow for arbitrary relations derived from general non-quadratic dissipation potentials. This paper describes two natural origins for these structures. A first microscopic origin of generalized gradient structures is given by the theory of large-deviation principles. While Markovian diffusion processes lead to classical gradient structures, Poissonian jump processes give rise to cosh-type dissipation potentials. A second origin arises via a new form of convergence, that we call EDP-convergence. Even when starting with classical gradient systems, where the dissipation potential is a quadratic functional of the rate, we may obtain a generalized gradient system in the evolutionary Gamma-limit. As examples we treat (i) the limit of a diffusion equation having a thin layer of low diffusivity, which leads to a membrane model, and (ii) the limit of diffusion over a high barrier, which gives a reaction-diffusion system

Multilayered folding with voids

In the deformation of layered materials such as geological strata, or stacks of paper, mechanical properties compete with the geometry of layering. Smooth, rounded corners lead to voids between the layers, while close packing of the layers results in geometrically-induced curvature singularities. When voids are penalized by external pressure, the system is forced to trade off these competing effects, leading to sometimes striking periodic patterns. In this paper we construct a simple model of geometrically nonlinear multi-layered structures under axial loading and pressure confinement, with non-interpenetration conditions separating the layers. Energy minimizers are characterized as solutions of a set of fourth-order nonlinear differential equations with contact-force Lagrange multipliers, or equivalently of a fourth-order free-boundary problem. We numerically investigate the solutions of this free boundary problem, and compare them with the periodic solutions observed experimentally

Non-equilibrium thermodynamical principles for chemical reactions with mass-action kinetics

We study stochastic interacting particle systems that model chemical reaction networks on the micro scale, converging to the macroscopic Reaction Rate Equation. One abstraction level higher, we study the ensemble of such particle systems, converging to the corresponding Liouville transport equation. For both systems, we calculate the corresponding large deviations and show that under the condition of detailed balance, the large deviations induce a non-linear relation between thermodynamic fluxes and free energy driving force