Metastability and Dynamics of Discrete Topological Singularities in Two Dimensions: A Γ-Convergence Approach

2014 ◽  
Vol 214 (1) ◽  
pp. 269-330 ◽  
Author(s):  
Roberto Alicandro ◽  
Lucia De Luca ◽  
Adriana Garroni ◽  
Marcello Ponsiglione
Keyword(s):  
Two Dimensions ◽  
Γ Convergence ◽  
Topological Singularities

Low energy configurations of topological singularities in two dimensions: A Γ-convergence analysis of dipoles

2019 ◽  
Vol 22 (03) ◽  
pp. 1950019
Author(s):  
Lucia De Luca ◽  
Marcello Ponsiglione
Keyword(s):  
Convergence Analysis ◽  
Two Dimensions ◽  
Low Energy ◽  
Ginzburg Landau ◽  
Energy Plus ◽  
Γ Convergence ◽  
Flat Norm ◽  
Topological Singularities ◽  
Energy Configurations ◽  
Small Zero

This paper deals with the variational analysis of topological singularities in two dimensions. We consider two canonical zero-temperature models: the core radius approach and the Ginzburg–Landau energy. Denoting by [Formula: see text] the length scale parameter in such models, we focus on the [Formula: see text] energy regime. It is well known that, for configurations whose energy is bounded by [Formula: see text], the vorticity measures can be decoupled into the sum of a finite number of Dirac masses, each one of them carrying [Formula: see text] energy, plus a measure supported on small zero-average sets. Loosely speaking, on such sets the vorticity measure is close, with respect to the flat norm, to zero-average clusters of positive and negative masses. Here, we perform a compactness and [Formula: see text]-convergence analysis accounting also for the presence of such clusters of dipoles (on the range scale [Formula: see text], for [Formula: see text]), which vanish in the flat convergence and whose energy contribution has, so far, been neglected. Our results refine and contain as a particular case the classical [Formula: see text]-convergence analysis for vortices, extending it also to low energy configurations consisting of just clusters of dipoles, and whose energy is of order [Formula: see text] with [Formula: see text].

scholarly journals A phase-field approximation of the Steiner problem in dimension two

2019 ◽  
Vol 12 (2) ◽  
pp. 157-179 ◽  
Author(s):  
Antonin Chambolle ◽  
Luca Alberto Davide Ferrari ◽  
Benoit Merlet
Keyword(s):  
Phase Field ◽  
Transportation Problem ◽  
Numerical Approximation ◽  
Unit Length ◽  
Field Approximation ◽  
Two Dimensions ◽  
Steiner Problem ◽  
Limit Case ◽  
Fixed Parameter ◽  
Γ Convergence

AbstractIn this paper we consider the branched transportation problem in two dimensions associated with a cost per unit length of the form {1+\beta\,\theta}, where θ denotes the amount of transported mass and {\beta>0} is a fixed parameter (notice that the limit case {\beta=0} corresponds to the classical Steiner problem). Motivated by the numerical approximation of this problem, we introduce a family of functionals ({\{\mathcal{F}_{\varepsilon}\}_{\varepsilon>0}}) which approximate the above branched transport energy. We justify rigorously the approximation by establishing the equicoercivity and the Γ-convergence of {\{\mathcal{F}_{\varepsilon}\}} as {\varepsilon\downarrow 0}. Our functionals are modeled on the Ambrosio–Tortorelli functional and are easy to optimize in practice. We present numerical evidences of the efficiency of the method.

Michell truss type theories as a Γ-limit of optimal design in linear elasticity

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Heiner Olbermann
Keyword(s):  
Optimal Design ◽  
Linear Elasticity ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Michell Trusses ◽  
Design Problems ◽  
Michell Truss ◽  
Applied Forces ◽  
Γ Convergence

AbstractWe show how to derive (variants of) Michell truss theory in two and three dimensions rigorously as the vanishing weight limit of optimal design problems in linear elasticity in the sense of Γ-convergence. We improve our results from [H. Olbermann, Michell trusses in two dimensions as a Γ-limit of optimal design problems in linear elasticity, Calc. Var. Partial Differential Equations 56 2017, 6, Article ID 166] in that our treatment here includes the three-dimensional case and that we allow for more general boundary conditions and applied forces.

scholarly journals Anatomy of a Periodically Driven p-Wave Superconductor

2016 ◽  
Vol 71 (10) ◽  
pp. 883-895 ◽  
Author(s):  
Erhai Zhao
Keyword(s):  
Two Dimensions ◽  
P Wave ◽  
Edge States ◽  
Many Body ◽  
Simple Description ◽  
Periodically Driven ◽  
Topological Superconductors ◽  
Many Body Systems ◽  
Isolated Point ◽  
Topological Singularities

AbstractThe topological properties of periodically driven many-body systems often have no static analogs and defy a simple description based on the effective Hamiltonian. To explore the emergent edge modes in driven p-wave superconductors in two dimensions, we analysed a toy model of Kitaev chains (one-dimensional spinless p-wave superconductors with Majorana edge states) coupled by time-periodic hopping. We showed that with proper driving, the coupled Kitaev chains can turn into a fully gapped superconductor, which is analogous to the px+ipy state but has two, rather than one, chiral edge modes. A different driving protocol turns it into a gapless superconductor with isolated point nodes and completely flat edge states at quasienergy ω=0 or π/T, with T as the driving period. The time evolution operator U(kx, ky, t) of the toy model is computed exactly to yield the phase bands. And the “topological singularities” of the phase bands are exhausted and compared to those of a periodically driven Hofstadter model, which features counter-propagating chiral edge modes. These examples demonstrate the unique edge states in driven superconducting systems and suggest driving as a potentially fruitful route to engineer new topological superconductors.

The tangled web of agency

2018 ◽  
Vol 41 ◽  
Author(s):  
Alain Pe-Curto ◽  
Julien A. Deonna ◽  
David Sander
Keyword(s):  
Two Dimensions ◽  
Bad Company

AbstractWe characterize Doris's anti-reflectivist, collaborativist, valuational theory along two dimensions. The first dimension is socialentanglement, according to which cognition, agency, and selves are socially embedded. The second dimension isdisentanglement, the valuational element of the theory that licenses the anchoring of agency and responsibility in distinct actors. We then present an issue for the account: theproblem of bad company.

A transmission electron microscopic study of structural transitions in fast ionic conductors

1987 ◽  
Vol 45 ◽  
pp. 156-157
Author(s):  
R. B. Queenan ◽  
P. K. Davies
Keyword(s):  
Optical Properties ◽  
Ionic Conduction ◽  
Recent Observation ◽  
Ionic Conductivities ◽  
Sodium Aluminate ◽  
Two Dimensions ◽  
Ionic Conductors ◽  
Electron Microscopic ◽  
Transmission Electron ◽  
Trivalent Cations

Na ß“-alumina (Na1.67Mg67Al10.33O17) is a non-stoichiometric sodium aluminate which exhibits fast ionic conduction of the Na+ ions in two dimensions. The Na+ ions can be exchanged with a variety of mono-, di-, and trivalent cations. The resulting exchanged materials also show high ionic conductivities.Considerable interest in the Na+-Nd3+-ß“-aluminas has been generated as a result of the recent observation of lasing in the pulsed and cw modes. A recent TEM investigation on a 100% exchanged Nd ß“-alumina sample found evidence for the intergrowth of two different structure types. Microdiffraction revealed an ordered phase coexisting with an apparently disordered phase, in which the cations are completely randomized in two dimensions. If an order-disorder transition is present then the cooling rates would be expected to affect the microstructures of these materials which may in turn affect the optical properties. The purpose of this work was to investigate the affect of thermal treatments upon the micro-structural and optical properties of these materials.

Laser Scanning Confocal Microscopy and Three-Dimesnsional Reconstruction of the Mitotic Spindles of Unequally Dividing Embryonic Cells

1990 ◽  
Vol 48 (3) ◽  
pp. 166-167
Author(s):  
J. Holy ◽  
G. Schatten
Keyword(s):  
Confocal Microscopy ◽  
Mitotic Spindle ◽  
Laser Scanning ◽  
Three Dimensional ◽  
Laser Scanning Confocal Microscopy ◽  
Two Dimensions ◽  
Embryonic Cells ◽  
Mitotic Spindles ◽  
Cleavage Division ◽  
Scanning Confocal Microscopy

One of the classic limitations of light microscopy has been the fact that three dimensional biological events could only be visualized in two dimensions. Recently, this shortcoming has been overcome by combining the technologies of laser scanning confocal microscopy (LSCM) and computer processing of microscopical data by volume rendering methods. We have employed these techniques to examine morphogenetic events characterizing early development of sea urchin embryos. Specifically, the fourth cleavage division was examined because it is at this point that the first morphological signs of cell differentiation appear, manifested in the production of macromeres and micromeres by unequally dividing vegetal blastomeres.The mitotic spindle within vegetal blastomeres undergoing unequal cleavage are highly polarized and develop specialized, flattened asters toward the micromere pole. In order to reconstruct the three-dimensional features of these spindles, both isolated spindles and intact, extracted embryos were fluorescently labeled with antibodies directed against either centrosomes or tubulin.

Instrumental and Ideological Union Commitment: Longitudinal Assessment of Construct Validity

2001 ◽  
Vol 17 (2) ◽  
pp. 98-111 ◽  
Author(s):  
Anders Sjöberg ◽  
Magnus Sverke
Keyword(s):  
Construct Validity ◽  
Temporal Stability ◽  
Strong Support ◽  
Internal Consistency Reliability ◽  
Measurement Model ◽  
Two Dimensions ◽  
Model Parameters ◽  
Longitudinal Assessment ◽  
Union Commitment ◽  
Union Participation

Summary: Previous research has identified instrumentality and ideology as important aspects of member attachment to labor unions. The present study evaluated the construct validity of a scale designed to reflect the two dimensions of instrumental and ideological union commitment using a sample of 1170 Swedish blue-collar union members. Longitudinal data were used to test seven propositions referring to the dimensionality, internal consistency reliability, and temporal stability of the scale as well as postulated group differences in union participation to which the scale should be sensitive. Support for the hypothesized factor structure of the scale and for adequate reliabilities of the dimensions was obtained and was also replicated 18 months later. Tests for equality of measurement model parameters and test-retest correlations indicated support for the temporal stability of the scale. In addition, the results were consistent with most of the predicted differences between groups characterized by different patterns of change/stability in union participation status. The study provides strong support for the construct validity of the scale and indicates that it can be used in future theory testing on instrumental and ideological union commitment.

The Prediction of Problem-Solving Assessed Via Microworlds

2016 ◽  
Vol 32 (4) ◽  
pp. 298-306 ◽  
Author(s):  
Samuel Greiff ◽  
Katarina Krkovic ◽  
Jarkko Hautamäki
Keyword(s):  
Working Memory ◽  
Problem Solving ◽  
Complex Problem ◽  
Two Dimensions ◽  
Assessment Instruments ◽  
Complex Problem Solving ◽  
Visual Spatial ◽  
Rule Knowledge ◽  
Rule Application ◽  
Fluid Reasoning

Abstract. In this study, we explored the network of relations between fluid reasoning, working memory, and the two dimensions of complex problem solving, rule knowledge and rule application. In doing so, we replicated the recent study by Bühner, Kröner, and Ziegler (2008) and the structural relations investigated therein [ Bühner, Kröner, & Ziegler, (2008) . Working memory, visual-spatial intelligence and their relationship to problem-solving. Intelligence, 36, 672–680]. However, in the present study, we used different assessment instruments by employing assessments of figural, numerical, and verbal fluid reasoning, an assessment of numerical working memory, and a complex problem solving assessment using the MicroDYN approach. In a sample of N = 2,029 Finnish sixth-grade students of which 328 students took the numerical working memory assessment, the findings diverged substantially from the results reported by Bühner et al. Importantly, in the present study, fluid reasoning was the main source of variation for rule knowledge and rule application, and working memory contributed only a little added value. Albeit generally in line with previously conducted research on the relation between complex problem solving and other cognitive abilities, these findings directly contrast the results of Bühner et al. (2008) who reported that only working memory was a source of variation in complex problem solving, whereas fluid reasoning was not. Explanations for the different patterns of results are sought, and implications for the use of assessment instruments and for research on interindividual differences in complex problem solving are discussed.

Sign in / Sign up

Export Citation Format

Share Document