Search results for "algebraic topology"
showing 10 items of 306 documents
Convergence of Markov Chains
2020
We consider a Markov chain X with invariant distribution π and investigate conditions under which the distribution of X n converges to π as n→∞. Essentially it is necessary and sufficient that the state space of the chain cannot be decomposed into subspaces that the chain does not leave, or that are visited by the chain periodically; e.g., only for odd n or only for even n.
Browder's theorems through localized SVEP
2005
A bounded linear operator T ∈ L(X) on aBanach space X is said to satisfy “Browder’s theorem” if the Browder spectrum coincides with the Weyl spectrum. T ∈ L(X) is said to satisfy “a-Browder’s theorem” if the upper semi-Browder spectrum coincides with the approximate point Weyl spectrum. In this note we give several characterizations of operators satisfying these theorems. Most of these characterizations are obtained by using a localized version of the single-valued extension property of T. In the last part we shall give some characterizations of operators for which “Weyl’s theorem” holds.
Complex Formation between Polyelectrolytes and Oppositely Charged Oligoelectrolytes
2016
We study the complex formation between one long polyanion chain and many short oligocation chains by computer simulations. We employ a coarse-grained bead-spring model for the polyelectrolyte chains, and model explicitly the small salt ions. We systematically vary the concentration and the length of the oligocation, and examine how the oligocations affects the chain conformation, the static structure factor, the radial and axial distribution of various charged species, and the number of bound ions in the complex. At low oligocation concentration, the polyanion has an extended structure. Upon increasing the oligocation concentration, the polyanion chain collapses and forms a compact globule,…
Topology-based goodness-of-fit tests for sliced spatial data
2023
In materials science and many other application domains, 3D information can often only be extrapolated by taking 2D slices. In topological data analysis, persistence vineyards have emerged as a powerful tool to take into account topological features stretching over several slices. In the present paper, we illustrate how persistence vineyards can be used to design rigorous statistical hypothesis tests for 3D microstructure models based on data from 2D slices. More precisely, by establishing the asymptotic normality of suitable longitudinal and cross-sectional summary statistics, we devise goodness-of-fit tests that become asymptotically exact in large sampling windows. We illustrate the test…
Coarse to fine : toward an intelligent 3D acquisition system
2015
International audience; The 3D acquisition-compression-processing chain is , most of the time , sequenced into independent stages. As resulting , a large amount of 3D points are acquired whatever the geometry of the object and the processing to be done in further steps. It appears , particularly in mechanical part 3D modeling and in CAD , that the acquisition of such an amount of data is not always mandatory. We propose a method aiming at minimizing the number of 3D points to be acquired with respect to the local geometry of the part and therefore to compress the cloud of points during the acquisition stage. The method we propose is based on a new coarse to fine approach in which from a coa…
Chiralities of nodal points along high symmetry lines with screw rotation symmetry
2021
Screw rotations in nonsymmorphic space group symmetries induce the presence of hourglass and accordion shape band structures along screw invariant lines whenever spin-orbit coupling is nonnegligible. These structures induce topological enforced Weyl points on the band intersections. In this work we show that the chirality of each Weyl point is related to the representations of the cyclic group on the bands that form the intersection. To achieve this, we calculate the Picard group of isomorphism classes of complex line bundles over the 2-dimensional sphere with cyclic group action, and we show how the chirality (Chern number) relates to the eigenvalues of the rotation action on the rotation …
Reptation and constraint release
1991
Abstract The reptation and constraint release models are discussed by considering three recent experimental examples: (1) the diffusion of hydrogenated polybutadiene in matrices of molecular weights raning between 1 ⩽ Mw / Me ⩽ 253; (2) the diffusion of polystyrene (PS) chains in matrices of star branched PS; (3) the diffusion of very long PS chains in chemically cross-linked PS-networks. It is concluded that the reptation and constraint release models are applicable, but ‘constraint release’ should be understood in a wider sense allowing for non-reptative removal of barriers to lateral chain motion. The analysis of the third example proves that lateral modes of motion have a negligible inf…
Excitation Spectrum of a Linear Chain of Paramagnetic Atoms with Spin-Phonon Interaction
1967
The low-lying energy levels of a paramagnetic chain in the presence of spin-phonon interaction have been investigated. It is shown that there is no gap in the one-particle excitation spectrum.
Mechanical and optical properties of continuously spun fibres of a main-chain smectic A elastomer
2012
Oriented smectic liquid crystal elastomer fibres are prepared with a special wet-spinning technique. The continuous spinning process in principle allows the preparation of fibres with arbitrary length. In comparison to ordinary rubbers, they have unique mechanical properties that qualify them as potential candidates for mechanical actuator applications. We demonstrate that these fibres show a remarkable contraction and extension at the transition from the ordered smectic to the disordered isotropic phase. We characterise their most relevant physical properties, viz. the thermally driven shape changes, stress–strain relations and optical birefringence, by optical and mechanical measurements.
Making Floryr–Huggins Practical: Thermodynamics of Polymer-Containing Mixtures
2010
The theoretical part of this article demonstrates how the original Flory–Huggins theory can be extended to describe the thermodynamic behavior of polymer-containing mixtures quantitatively. This progress is achieved by accounting for two features of macromolecules that the original approach ignores: the effects of chain connectivity in the case of dilute solutions, and the ability of polymer coils to change their spatial extension in response to alterations in their molecular environment. In the general case, this approach leads to composition-dependent interaction parameters, which can for most binary systems be described by means of two physically meaningful parameters; systems involving …