Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?

A wide variety of techniques have been developed to homogenize transport equations in multiscale and multiphase systems. This has yielded a rich and diverse field, but has also resulted in the emergence of isolated scientific communities and disconnected bodies of literature. Here, our goal is to bridge the gap between formal multiscale asymptotics and the volume averaging theory. We illustrate the methodologies via a simple example application describing a parabolic transport problem and, in so doing, compare their respective advantages/disadvantages from a practical point of view. This paper is also intended as a pedagogical guide and may be viewed as a tutorial for graduate students as we provide historical context, detail subtle points with great care, and reference many fundamental works

Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?

A wide variety of techniques have been developed to homogenize transport equations in multiscale and multiphase systems. This has yielded a rich and diverse field, but has also resulted in the emergence of isolated scientific communities and disconnected bodies of literature. Here, our goal is to bridge the gap between formal multiscale asymptotics and the volume averaging theory. We illustrate the methodologies via a simple example application describing a parabolic transport problem and, in so doing, compare their respective advantages/disadvantages from a practical point of view. This paper is also intended as a pedagogical guide and may be viewed as a tutorial for graduate students as we provide historical context, detail subtle points with great care, and reference many fundamental works

Rheology of frictional grains

Diese Arbeit behandelt die Beschreibung des Fließens und des Blockierens von granularer Materie. Granulare Materie kann einen Verfestigungsübergang durchlaufen. Dieser wird Jamming genannt und ist maßgeblich durch vorliegende Spannungen sowie die Packungsdichte der Körner, welche das Granulat bilden, bestimmt. Die Rheologie dichter granularer Medien ist zusätzlich zu Spannung und Packungsdichte stark durch Reibung zwischen den Körnern beeinflusst. Wir zeigen mittels numerischer Simulationen und analytischer Betrachtungen, wie Reibung Jamming qualitativ verändert. Reibungsfreies Jamming ist ein kontinuierlicher Phasenübergang mit einem kritischen Punkt bei verschwindender Spannung. Reibungsbehaftetes Jamming ist ein diskontinuierlicher Phasenübergang mit einem kritischen Punkt bei endlicher Spannung. Der kritische Punkt bei endlicher Spannung führt zu bemerkenswertem Verhalten: Oberhalb der kri- tischen Packungsdichte gibt es ein Intervall an Packungsdichten, innerhalb dessen große oder kleine Spannungen zum Fließen führen, mittlere Spannungen hingegen führen zum Blockieren des Mediums. Das Fließverhalten nahe Jamming ist stark durch die Systemgröße beeinflusst: Es gibt eine kritische Systemgröße, oberhalb derer zeitabhängiger Fluss entsteht. Dieser zeitabhängige Fluss wird durch die Ausbildung von großskaligen Strukturen im Spannungsfeld erklärt. Sowohl die großskaligen Strukuren als auch der damit einhergehende zeitabhängige Fluss sind neuartige Phänomene im Fluss von trockenen Granulaten und durch Rei- bung hervorgerufen.This thesis deals with the description of flow and arrest of granular matter. Granular matter can undergo a rigidity transition — called jamming — that is mainly controlled by the applied stresses and the packing fraction of the grains that constitute the medium. In addition to stress and packing fraction, interparticle friction greatly affects the rheology of granular matter. Using numerical simulations and analytical modeling, we show how novel behavior in dense flow and jamming regimes arises in the presence of friction. In particular, frictionless jamming is continuous with a critical point at zero stress. In contrast, frictional jamming is shown to exhibit a discontinuous phase transition with a critical point at finite stress. The fact that the critical point resides at finite stress gives rise to remarkable flow behavior, called reentrant flow. Explicitly, there is an interval of packing fractions above the critical packing fraction in which large or low stress leads to flow but intermediate stress jams the medium. The behavior close to jamming depends substantially on the system size, i.e., there is a critical system size above which unsteady flow emerges. Unsteady flow is rationalized by large-scale structures in the stress fields. Both, the large-scale structures and the accompanied unsteady flow, are novel phenomena regarding the flow of dry granular matter and can be attributed to interparticle friction

Proceedings of FORM 2022. Construction The Formation of Living Environment

This study examines the integration of building information modelling (BIM) technologies in operation & maintenance stage in the system of managing real estate that helps to reduce transaction costs. The approach and method are based on Digital Twin technology and Model Based System Engineering (MBSE) approach. The results of the development of a service for digital facility management and digital expertise are presented. The connection between physical and digital objects is conceptualized

The 2nd International Conference on Mathematical Modelling in Applied Sciences, ICMMAS’19, Belgorod, Russia, August 20-24, 2019 : book of abstracts

The proposed Scientific Program of the conference is including plenary lectures, contributed oral talks, poster sessions and listeners. Five suggested special sessions / mini-symposium are also considered by the scientific committe

Estimation of Thalamocortical and Intracortical Network Models from Joint Thalamic Single-Electrode and Cortical Laminar-Electrode Recordings in the Rat Barrel System

A new method is presented for extraction of population firing-rate models for both thalamocortical and intracortical signal transfer based on stimulus-evoked data from simultaneous thalamic single-electrode and cortical recordings using linear (laminar) multielectrodes in the rat barrel system. Time-dependent population firing rates for granular (layer 4), supragranular (layer 2/3), and infragranular (layer 5) populations in a barrel column and the thalamic population in the homologous barreloid are extracted from the high-frequency portion (multi-unit activity; MUA) of the recorded extracellular signals. These extracted firing rates are in turn used to identify population firing-rate models formulated as integral equations with exponentially decaying coupling kernels, allowing for straightforward transformation to the more common firing-rate formulation in terms of differential equations. Optimal model structures and model parameters are identified by minimizing the deviation between model firing rates and the experimentally extracted population firing rates. For the thalamocortical transfer, the experimental data favor a model with fast feedforward excitation from thalamus to the layer-4 laminar population combined with a slower inhibitory process due to feedforward and/or recurrent connections and mixed linear-parabolic activation functions. The extracted firing rates of the various cortical laminar populations are found to exhibit strong temporal correlations for the present experimental paradigm, and simple feedforward population firing-rate models combined with linear or mixed linear-parabolic activation function are found to provide excellent fits to the data. The identified thalamocortical and intracortical network models are thus found to be qualitatively very different. While the thalamocortical circuit is optimally stimulated by rapid changes in the thalamic firing rate, the intracortical circuits are low-pass and respond most strongly to slowly varying inputs from the cortical layer-4 population