A parabolic local problem with exponential decay of the resonance error for numerical homogenization

This paper aims at an accurate and efficient computation of effective quantities, e.g. the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods are based on a micro–macro-coupling, where the macromodel describes the coarse scale behavior, and the micromodel is solved only locally to upscale the effective quantities, which are missing in the macromodel. The fact that the microproblems are solved over small domains within the entire macroscopic domain, implies imposing artificial boundary conditions on the boundary of the microscopic domains. A naive treatment of these artificial boundary conditions leads to a first-order error in [Formula: see text], where [Formula: see text] represents the characteristic length of the small scale oscillations and [Formula: see text] is the size of microdomain. This error dominates all other errors originating from the discretization of the macro and the microproblems, and its reduction is a main issue in today’s engineering multiscale computations. The objective of this work is to analyze a parabolic approach, first announced in A. Abdulle, D. Arjmand, E. Paganoni, C. R. Acad. Sci. Paris, Ser. I, 2019, for computing the homogenized coefficients with arbitrarily high convergence rates in [Formula: see text]. The analysis covers the setting of periodic microstructure, and numerical simulations are provided to verify the theoretical findings for more general settings, e.g. non-periodic microstructures.

Quantum Mechatronics

Mechatronics systems, a macroscopic domain, aim at producing highly efficient engineering platforms, with applications in a variety of industries and situations. On the other hand, quantum technologies, a microscopic domain, are emerging as a promising avenue to speed up computations and perform more efficient sensing. Recently, these two fields have started to merge in a novel area: quantum mechatronics. In this review article, we describe some developments produced so far in this respect, including early steps into quantum robotics, macroscopic actuators via quantum effects, as well as educational initiatives in quantum mechatronics.

Quenching an active swarm: Effects of light exposure on collective motility in swarmingSerratia marcescenscolonies

Swarming colonies of the light responsive bacteriaSerratia marcescensgrown on agar exhibit robust fluctuating large-scale collective flows that include arrayed vortices, jets, and sinuous streamers. We study the immobilization and quenching of these large-scale flows when the moving swarm is exposed to light with a substantial ultra-violet component. We map the response to light in terms of two independent parameters - the light intensity and duration of exposure and identify the conditions under which mobility is affected significantly. For small exposure times and/or low intensities, we find collective mobility to be negligibly affected. Increasing exposure times and/or intensity to higher values temporarily suppresses collective mobility. Terminating exposure allows bacteria regain motility and eventually reestablish large scale flows. For long exposure times or at high intensities, exposed bacteria become paralyzed, with macroscopic speeds eventually reducing to zero. In this process, they form highly aligned, jammed domains. Individual domains eventually coalesce into a large macroscopic domain with mean radial extent growing as the square root of exposure time. Post exposure, active bacteria dislodge exposed bacteria from these jammed configurations; initial dissolution rates are found to be strongly dependent on duration of exposure suggesting that caging effects are substantial at higher exposure times. Based on our experimental observations, we propose a minimal Brownian dynamics model to examine the escape of exposed bacteria from the region of exposure. Our results complement studies on planktonic bacteria and inform models for pattern formation in gradated illumination.

Statistical Physics and Thermodynamics

Statistical physics and thermodynamics describe the behaviour of systems on the macroscopic scale. Their methods are applicable to a wide range of phenomena: from heat engines to chemical reactions, from the interior of stars to the melting of ice. Indeed, the laws of thermodynamics are among the most universal ones of all laws of physics. Yet this subject can prove difficult to grasp. Many view thermodynamics as merely a collection of ad hoc recipes, or are confused by unfamiliar novel concepts, such as the entropy, which have little in common with the theories to which students have got accustomed in other areas of physics. This text provides a concise yet thorough introduction to the key concepts which underlie statistical physics and thermodynamics. It begins with a review of classical probability theory and quantum theory, as well as a careful discussion of the notions of information and entropy, prior to embarking on the development of statistical physics proper. The crucial steps leading from the microscopic to the macroscopic domain are rendered transparent. In particular, the laws of thermodynamics are shown to emerge as natural consequences of the statistical framework. While the emphasis is on clarifying the basic concepts, the text also contains many applications and classroom-tested exercises, covering all major topics of a standard course on statistical physics and thermodynamics. The text is suited both for a one-semester course at the advanced undergraduate or beginning graduate level and as a self-contained tutorial guide for students in physics, chemistry, and engineering.

A quantitative method to determine preservice chemistry teachers' perceptions of chemical representations

Chemical representations serve as a cornerstone to guide the teaching of chemistry concepts. The influence that a chemical representation has on instruction is largely dependent on how well the viewer interprets the information in the representation. Teachers serve as a guide to the students as they point out and make connections between the features present in a chemical representation. To influence how well the teacher serves as a guide it is important to develop teachers' pedagogical content knowledge as it relates to visualizations. As a first step towards developing this area of teaching expertise it is crucial to develop an understanding of how preservice chemistry teachers perceive a variety of chemical representations. To this end, this paper presents a novel card-sorting methodology that utilizes Johnstone's triangle as a continuum to determine how chemistry preservice teachers perceive representations relative to the presence of each of the three representational levels: macroscopic, submicroscopic, and symbolic. This study has determined that this methodology is both valid and reliable among a group of chemistry preservice teachers. The participants were able to effectively detect the presence or absence of the macroscopic domain. However, there was greater variance when the symbolic and submicroscopic levels were present. In addition, variance among the participants’ responses also increased dramatically when multiple levels were present in one representation. This was largely a result of what key features the participant focused on while viewing the card. The variance results of this study, along with the accompanying rationales for the placement of the cards, serve to inform the development of practices to further foster preservice chemistry teachers’ pedagogical-visual-content-knowledge (PVCK).

Multiscale models of compact bone

This work is concerned about multiscale models of compact bone. We focus on the lacuna–canalicular system. The interstitial fluid and the ions in it are regarded as solvent and others are treated as solute. The system has the characteristic of solvation process as well as non-equilibrium dynamics. The differential geometry theory of surfaces is adopted. We use this theory to separate the macroscopic domain of solvent from the microscopic domain of solute. We also use it to couple continuum and discrete descriptions. The energy functionals are constructed and then the variational principle is applied to the energy functionals so as to derive desirable governing equations. We consider both long-range polar interactions and short-range nonpolar interactions. The solution of governing equations leads to the minimization of the total energy.