Two-dimensional Setting Research Articles

Dynamic Optical Localization of a Mobile Robot Using Kalman Filtering-Based Position Prediction

Autonomous mobile robots operating in areas with poor GPS and wireless coverage (e.g., underwater) must rely on alternative localization and communication approaches. In this article, we present an light-emitting diode (LED) based system that achieves simultaneous localization and communication (SLAC), where the line-of-sight (LOS) requirement for communication is exploited to extract the relative bearing of the communicating parties for localization. By using Kalman filtering to obtain the mobile robot's predicted position, the system is able to reduce the overhead of establishing the LOS and, therefore, significantly improve on the quality of the localization. The proposed design of the optical localization system is presented and its effectiveness is demonstrated with extensive simulation and experimentation in a two-dimensional setting, consisting of a mobile robot and two stationary base nodes.

Multiwavelet-based mesh adaptivity with Discontinuous Galerkin schemes: Exploring 2D shallow water problems

In Gerhard et al. (2015a) a new class of adaptive Discontinuous Galerkin schemes has been introduced for shallow water equations, including the particular necessary properties, such as well-balancing and wetting-drying treatments. The adaptivity strategy is based on multiresolution analysis using multiwavelets in order to encode information across different mesh resolution levels. In this work, we follow-up on the previous proof-of-concept to thoroughly explore the performance, capabilities and weaknesses of the adaptive numerical scheme in the two-dimensional shallow water setting, under complex and realistic problems. To do so, we simulate three well-known and frequently used experimental benchmark tests in the context of flood modelling, ranging from laboratory to field scale. The real and complex topographies result in complex flow fields which pose a greater challenge to the adaptive numerical scheme and are computationally more ambitious, thus requiring a parallelised version of the aforementioned scheme. The benchmark tests allow to examine in depth the resulting adaptive meshes and the hydrodynamic performance of the scheme. We show that the scheme presented by Gerhard et al. (2015a) is accurate, i.e., allows to capture simultaneously large and very small flow structures, is robust, i.e., local grid refinement is controlled by just one parmeter that is auotmatically chosen and is more efficient in terms of the adaptive meshes than other shallow-water adaptive schemes achieving higher resolution with less cells.

Finite dimensional attractors for binary mixtures of viscoelastic bodies

We consider a class of semilinear problems for binary mixtures in the presence of viscoelastic dissipation. This paper aims to study the existence and properties of long-time dynamics in a two-dimensional setting. More precisely, we first prove the existence of a finite-dimensional global attractor that exhibits additional regularity in higher topology. Secondly, we show that the dynamical system has a generalized fractal exponential attractor.

Time periodic Navier\u2013Stokes equations in a thin tube structure

The time periodic Navier–Stokes equations are considered in the three-dimensional and two-dimensional settings with Dirichlet boundary conditions in thin tube structures. These structures are finite union of thin cylinders (thin rectangles in the case of dimension two), where the small parameter ε is the ratio of the hight and the diameter of the cylinders. We consider the case of finite or big coefficient before the time derivative. This setting is motivated by hemodynamical applications. Theorems of existence and uniqueness of a solution are proved. Complete asymptotic expansion of a solution is constructed and justified by estimates of the difference of the exact solution and truncated series of the expansion in norms taking into account the first and second derivatives with respect to the space variables and the first derivative in time. The method of asymptotic partial decomposition of the domain is justified for the time periodic problem.

A method of generating alveolar organoids using human pluripotent stem cells.

The lung consists of branched structures that are anatomically, developmentally and functionally divided into airway and alveolar regions. Each region contributes to lung-specific functions involving a defense system and gas exchange, and their dysfunction can cause fatal lung diseases. In the alveolar region, the cuboidal alveolar type 2 (AT2) cells account for 90% of the alveolar epithelial cells and serve as the tissue stem cells secreting pulmonary surfactant, and flattened alveolar type I (AT1) cells cover most of the alveolar surface directly contributing to gas exchange adjacent to capillary vessels. It has been difficult to culture alveolar epithelial cells in vitro, as the lineage-specific features of those cells are rapidly lost in a conventional two-dimensional culture setting. The culture of alveolar organoids (AOs) is an emerging technique that can help maintain the features of alveolar epithelial cells in vitro, and their application to human disease modeling is eagerly awaited. We herein describe our method of generating and culturing alveolar epithelial cells and AOs derived from human induced pluripotent stem cells (iPSCs). iPSCs derived from lung disease patients, including those with rare genetic diseases, will make help elucidate the disease mechanism and hopefully identify therapeutic targets.

Boundedness in a two-dimensional Keller–Segel–Navier–Stokes system involving a rapidly diffusing repulsive signal

This paper is concerned with the Keller–Segel–Navier–Stokes system $$\begin{aligned} \left\{ \begin{array}{lcll} n_t + u\cdot \nabla n &{}=&{} \Delta n + \nabla \cdot (n\nabla c), \qquad &{} x\in \Omega , \ t>0, \\ u\cdot \nabla c &{}=&{} \Delta c -c+n, \qquad &{} x\in \Omega , \ t>0, \\ u_t + (u\cdot \nabla ) u &{}=&{} \Delta u + \nabla P + n\nabla \Phi , \qquad \nabla \cdot u=0, \qquad &{} x\in \Omega , \ t>0, \end{array} \right. \qquad \qquad (\star ) \end{aligned}$$with a given smooth gravitational potential $$\Phi $$. It is shown that for all suitably regular initial data, a corresponding no-flux/no-flux/Dirichlet initial boundary value problem posed in a smoothly bounded planar domain admits a uniquely determined global classical solution (n, c, u, P) which has the additional property that n remains uniformly bounded. This partially goes beyond a recent result asserting global classical solvability, but without any boundedness information, in a related slightly more complex variant of ($$\star $$) accounting for parabolic evolution of the quantity c. In particular, the obtained outcome therefore provides further evidence indicating that the considered fluid interaction does not substantially reduce a certain explosion-avoiding character of the Keller–Segel-type chemorepulsion mechanisms, as known to form an essential feature of corresponding fluid-free analogues. The reasoning at its core relies on the use of a quasi-Lyapunov inequality which operates at regularity levels that seem rather unusual in this and related contexts, but which in the considered two-dimensional setting can be seen to serve as a starting point sufficient for a bootstrap-type series of arguments, finally providing global boundedness.

The influence of surface inhomogeneity on the overcharge and lithium plating of graphite electrodes

We seek to clarify phenomena involved in the overcharge of a graphite electrode in a lithium ion battery, including lithium (Li) plating. In Baker and Verbrugge (2019 J. Electrochem. Soc.), we developed a set of equations that can be used to treat Li plating and subsequent electro-dissolution, and we analyzed how the equation system behaved for a particle of graphite, a fundamental unit of the negative (porous) electrode in lithium ion cells. In this work, we employ the same governing equations, but we render them in a two-dimensional setting to examine the graphite-electrolyte interface, allowing us to clarify phenomena involved in Li plating over graphitic electrode elements in the absence of complicating factors associated with the architecture of a porous electrode. For a variety of reasons described in the Introduction of this work, the surface of graphite is nonuniform in terms of reaction rates for Li insertion and plating, and we show that when the electrode is subjected to constant-current charging, as is commonly employed, such nonuniformities lead to early Li plating over the highly reactive surfaces. These observations underscore the importance of maintaining a uniform electrode surface, especially when the cell is to be subjected to high rates of charge.

The Stokes Limit in a Three-Dimensional Chemotaxis-Navier–Stokes System

We consider initial-boundary value problems for the $\kappa$-dependent family of chemotaxis-(Navier--)Stokes systems \begin{align*} \left\{ \begin{array}{r@{\,}c@{\,}c@{\ }l@{\quad}l@{\quad}l@{\,}c} n_{t}&+&u\cdot\!\nabla n&=\Delta n-\nabla\!\cdot(n\nabla c),\ &x\in\Omega,& t>0,\\ c_{t}&+&u\cdot\!\nabla c&=\Delta c-cn,\ &x\in\Omega,& t>0,\\ u_{t}&+&\kappa(u\cdot\nabla)u&=\Delta u+\nabla P+n\nabla\phi,\ &x\in\Omega,& t>0,\\ &&\nabla\cdot u&=0,\ &x\in\Omega,& t>0, \end{array}\right. \end{align*} in a bounded domain $\Omega\subset\mathbb{R}^3$ with smooth boundary and given potential function $\phi\in C^{1+\beta}(\overline{\Omega})$ for some $\beta>0$. It is known that for fixed $\kappa\in\mathbb{R}$ an associated initial-boundary value problem possesses at least one global weak solution $(n^{(\kappa)},c^{(\kappa)},u^{(\kappa)})$, which after some waiting time becomes a classical solution of the system. In this work we will show that upon letting $\kappa\to0$ the solutions $(n^{(\kappa)},c^{(\kappa)},u^{(\kappa)})$ converge towards a weak solution of the Stokes variant $(\kappa=0)$ of the systems above with respect to the strong topology in certain Lebesgue and Sobolev spaces. We thereby extend the recently obtained result on the Stokes limit process for classical solutions in the two-dimensional setting to the more intricate three-dimensional case.

A finite volume method for the simulation of elastoviscoplastic flows and its application to the lid-driven cavity case

We propose a Finite Volume Method for the simulation of elastoviscoplastic (EVP) flows, modelled after the extension to the Herschel-Bulkley model by Saramito [J. Non-Newton. Fluid Mech. 158 (2009) 154–161]. The method is applicable to cell-centred grids of arbitrary geometry by the introduction of new stabilisation techniques of the “momentum interpolation” and “both sides diffusion” types, for pressure and velocity, respectively. Adaptive time stepping is employed. The method is used to perform benchmark simulations of lid-driven cavity flow, which also serve to explore certain aspects of this EVP constitutive equation in a two-dimensional setting. The model parameters are chosen so as to represent Carbopol, and simulations are performed for different lid velocities and with either slip or no-slip wall boundaries. The results are compared against those obtained with the classic Herschel-Bulkley model. It is noticed that different initial conditions for stress lead to different steady states. Furthermore, we investigate the cessation of the flow, once the lid is suddenly halted; it is found that, contrary to the classic Herschel-Bulkley predictions, the EVP flow does not cease in finite time. Rather, the flow decays very slowly while the material oscillates as kinetic energy is converted to elastic energy and vice versa. Flow decay is much faster under slip conditions due to the friction between the material and the walls.

A global existence of classical solutions to the two-dimensional kinetic-fluid model for flocking with large initial data

We present a two-dimensional coupled system for flocking particle-compressible fluid interactions, and study its global solvability for the proposed coupled system. For particle and fluid dynamics, we employ the kinetic Cucker-Smale-Fokker-Planck (CS-FP) model for flocking particle part, and the isentropic compressible Navier-Stokes (N-S) equations for the fluid part, respectively, and these separate systems are coupled through the drag force. For the global solvability of the coupled system, we present a sufficient framework for the global existence of classical solutions with large initial data which can contain vacuum using the weighted energy method. We extend an earlier global solvability result [20] in the one-dimensional setting to the two-dimensional setting.

A Two-Dimensional Experimental and Numerical Study of Moonpools With Recess

Abstract Moonpool resonance is investigated in a two-dimensional setting in terms of regular, forced heave motions of a model with moonpool with different rectangular-shaped recess configurations. A recess is a reduced draft zone in the moonpool. Dedicated experiments were carried out. The model consisted of two boxes of 40 cm width each, with a distance of 20 cm between them. Recess configurations varying between 5 cm and 10 cm in length and 5 cm in height were tested. Different drafts were also tested. A large number of forcing periods and five forcing amplitudes were tested. A time-domain boundary element method (BEM) code based on the linear potential flow theory was implemented to investigate the resonance periods, mode shapes, as well as the moonpool response as predicted by the (linear) potential flow theory. Dominant physical effects were discussed, in particular damping due to flow separation from the sharp corners of the moonpool inlet and recess. The effect of the recess on the piston-mode behavior is discussed. The nondimensional moonpool response suggests strong viscous damping at the piston-mode resonance. The viscous BEM (VBEM) simulations demonstrate improvement over inviscid BEM, although further improvement of the method is needed. The VBEM simulations are, in general, in good agreement with the experiments. For the largest recess case, some discrepancies are observed in the amplitude-dependent response amplitude operators (RAOs). The piston-mode shapes are clearly different from the near flat free-surface elevation for a moonpool without recess, consistent with the recently published theory.

Determining radially symmetric potential from near-field scattering data

In this study, we consider an inverse medium scattering problem in two-dimensional setting, which is motivated from a nondestructive method for testing optical fibers. We intend to reconstruct the index of refractive, so-called scattering potential from the measurement of near-field scattering data, assuming the potential is radially symmetric. We propose numerical algorithms to reconstruct the potentials based on Frechet derivative using Neumann series and demonstrate the performance of our proposed algorithms.

Correlations, dynamics, and interferometry of anyons in the lowest Landau level

In this article, we present a systematic study of quantum statistics and dynamics of a pair of anyons in the lowerst Landau level (LLL), of direct relevance to quasiparticle excitations in the quantum Hall bulk. We develop the formalism for such a two-dimensional setting of two charged particles subject to a transverse field, including fractional angular momentum states and the related algebra stemming from the anyonic boundary condition, coherent state descriptions of localized anyons, and bunching features associated with such anyons. We analyze the dynamic motion of the anyons in a harmonic trap, emphasizing phase factors emerging from exchange statistics. We then describe non-equilibrium dynamics upon the application of a saddle potential, elaborating on its role as a squeezing operator acting on LLL coherent states, and its action as a beam splitter for anyons. Employing these potential landscapes as building blocks, we analyze anyon dynamics in a quantum Hall bulk interferometer. We discuss parallels between the presented LLL setting and other realms, extensively in the context of quantum optics, whose formalism we heavily borrow from, and briefly in that of black hole phenomena.

Tissue Regeneration from Mechanical Stretching of Cell-Cell Adhesion.

Cell-cell adhesion complexes are macromolecular adhesive organelles that integrate cells into tissues. This mechanochemical coupling in cell-cell adhesion is required for a large number of cell behaviors, and perturbations of the cell-cell adhesion structure or related mechanotransduction pathways can lead to critical pathological conditions such as skin and heart diseases, arthritis, and cancer. Mechanical stretching has been a widely used method to stimulate the mechanotransduction process originating from the cell-cell adhesion and cell-extracellular matrix (ECM) complexes. These studies aimed to reveal the biophysical processes governing cell proliferation, wound healing, gene expression regulation, and cell differentiation in various tissues, including cardiac, muscle, vascular, and bone. This review explores techniques in mechanical stretching in two-dimensional settings with different stretching regimens on different cell types. The mechanotransduction responses from these different cell types will be discussed with an emphasis on their biophysical transformations during mechanical stretching and the cross talk between the cell-cell and cell-ECM adhesion complexes. Therapeutic aspects of mechanical stretching are reviewed considering these cellular responses after the application of mechanical forces, with a focus on wound healing and tissue regeneration. Impact Statement Mechanical stretching has been proposed as a therapeutic option for tissue regeneration and wound healing. It has been accepted that mechanotransduction processes elicited by mechanical stretching govern cellular response and behavior, and these studies have predominantly focused on the cell-extracellular matrix (ECM) sites. This review serves the mechanobiology community by shifting the focus of mechanical stretching effects from cell-ECM adhesions to the less examined cell-cell adhesions, which we believe play an equally important role in orchestrating the response pathways.

Numerical Modeling of the Behavior of a Destructive Rain Flood on a Mountain River

The objective of this study was to provide the most accurate presentation of the behavior of a disastrous rain flood, which had resulted in destruction of a dam, casualties, and significant material damage. The problems set were solved by methods of numerical modeling in the two-dimensional setting applying the STREAM 2D CUDA software package. To calculate the rain flood, a catchment model of the Durso River was developed on a triangular non-uniform mesh, adapted to the river channel and the main inflows. To ensure direct numerical modeling of the dam’s destruction, a model was developed, which included the water area of the reservoir, the dam, composed of non-homogeneous earth material, and a downstream section of the river from the dam to the river mouth. The main results of the study were: the hydrograph of the water discharge of the rain flood, calculated by the actual precipitation data; a description of the washout of the earth dam composed of non-homogeneous materials, resulting from water spill over the dam crest, and a desctiption of the downstream spread of the breach wave.

A high-order discontinuous Galerkin approach to the elasto-acoustic problem

We address the spatial discretization of an evolution problem arising from the coupling of elastic and acoustic wave propagation phenomena by employing a discontinuous Galerkin scheme on polygonal and polyhedral meshes. The coupled nature of the problem is ascribed to suitable transmission conditions imposed at the interface between the solid (elastic) and fluid (acoustic) domains. We state and prove a well-posedness result for the strong formulation of the problem, present a stability analysis for the semi-discrete formulation, and finally prove an a priorihp-version error estimate for the resulting formulation in a suitable (mesh-dependent) energy norm. We also discuss the time integration scheme employed to obtain the fully discrete system. The convergence results are validated by numerical experiments carried out in a two-dimensional setting.

The invisibility via anomalous localized resonance of a source for electromagnetic waves

We investigate the invisibility via anomalous localized resonance of a general source in anisotropic media for electromagnetic waves. To this end, we first introduce the concept of doubly complementary media in the electromagnetic setting. These are media consisting of negative-index metamaterials in a shell and positive-index materials in its complement for which the shell is complementary to a part of the core and a part of the exterior of the core–shell structure. We then provide criteria for establishing the invisibility of a source in these media. We show that (i) a source is invisible if the power is blown up; (ii) a source is invisible if it is sufficiently close to the plasmonic shell structure, and it is visible if it is far from this plasmonic structure; (iii) if the plasmonic structure is complementary to an annulus of constant isotropic medium, there is a critical length that characterizes the cloaking phenomena, as first observed in the two-dimensional acoustic quasistatic setting by Milton and Nicorovici.

Wrinkling to crinkling transitions and curvature localization in a magnetoelastic film bonded to a non-magnetic substrate

This work studies experimentally and numerically the post-bifurcation response of a magnetorheological elastomer (MRE) film bonded to a soft non-magnetic (passive) substrate. The film-substrate system is subjected to a combination of an axial mechanical pre-compression and a transverse magnetic field. The non-trivial interaction of the two fields leads to a decrease of the critical magnetic field with applied pre-compression, while the observed wrinkling patterns evolve into crinkles, a bifurcation mode that is defined by the accompanied curvature localization and strong shearing of the side faces of the wrinkled geometry. Using a magneto-elastic variational formulation in a two-dimensional finite element numerical setting, we find that the crinkling is an intrinsic feature of magnetoelasticity and its presence is directly associated with the repulsive magnetic forces of the neighboring wrinkled-crinkled faces. As a result, the presence of the magnetic field prohibits the formation of creases and folds. In an effort to obtain a good quantitative agreement between the numerical and the experimental results, we also introduce an approximate way to model the friction of the lateral film-substrate faces. This analysis reveals the strong effects of friction upon the magneto-mechanical wrinkling modes.

Quasi-Optimal Correlation Algorithm for Measuring the Parameters of Surface Microrelief

Proposed a method for measuring parameters of micro-surface machine parts optoelectronic and computer facilities, based on the computation of two-dimensional settings of the autocorrelation function, based on the binary image of the investigated microrelief using kvazioptimalnogo correlation algorithm. Found to be the most informative characterization of the studied surfaces, micro precision components reliably distinguished from each other with a given probability, is the average amplitude of the variable component of the autocorrelation function. Shows the results of determining the parameters of microrelief surface of runner blade GTM using quasi-optimal correlation algorithms.

Continuous bulk and interface description of topological insulators

We analyze the topological properties of systems of Dirac equations in the presence of heterogeneities to model transport in topological insulators. The topology is described by means of indices of Fredholm operators. We describe bulk and interface topological invariants first for two-dimensional materials, which find practical applications, and then in arbitrary dimensions. In the two-dimensional setting, we relate the interface invariant to a physical observable describing asymmetric current along the interface.