Topological Stability of the Hippocampal Spatial Map and Synaptic Transience

Photo-alignment is a versatile tool to pattern the alignment at the confining substrates in a liquid crystal (LC) cell. Arbitrary alignment patterns can be created by using projection with a spatial light modulator (SLM) for the illumination. We demonstrate that a careful design of the alignment patterns allows the stabilization of topological solitons in nematic liquid crystal (NLC) cells, without the need for chirality or strong confinement. The created LC configurations are stabilized by the anchoring conditions imposed at the substrates. The photo-aligned background at both substrates is uniformly planar aligned, and ring-shaped regions with a 180° azimuthal rotation are patterned with an opposite sense of rotation at the top and bottom substrate. A disclination-free structure containing a closed ring of vertically oriented directors is formed when the patterned rings at the top and bottom substrate overlap. Thanks to the topological stability, a vertical director orientation in the bulk is observed even when the centra of both patterned rings are shifted over relatively large distances. The combination of numerical simulations with experimental measurements allows identification of the 3D director configuration in the bulk. A finite element (FE) Q-tensor simulation model is applied to find the equilibrium director configuration and optical simulations are used to confirm the correspondence with experimental microscopy measurements. The created LC configurations offer opportunities in the field of optical devices, light guiding and switching, particle trapping and studies of topological LC structures.

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Predicting relative topological stability of mobile users in a P2P mobile cloud

SN Applied Sciences ◽

10.1007/s42452-020-03584-3 ◽

2020 ◽

Vol 2 (11) ◽

Author(s):

Pijush Kanti Dutta Pramanik ◽

Gautam Bandyopadhyay ◽

Prasenjit Choudhury

Keyword(s):

Mobile Users ◽

Mobile Cloud ◽

Topological Stability

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THE GEOMETRY OF TOPOLOGICAL STABILITY (LMS Monographs (N.S.) 9)

Bulletin of the London Mathematical Society ◽

10.1112/s0024609398264745 ◽

1998 ◽

Vol 30 (6) ◽

pp. 664-666

Author(s):

John N. Mather

Keyword(s):

Topological Stability

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Dynamics of G-processes

Stochastics and Dynamics ◽

10.1142/s0219493720500379 ◽

2020 ◽

Vol 20 (01) ◽

pp. 2050037

Author(s):

W. Jung ◽

K. Lee ◽

C.A. Morales

Keyword(s):

Dynamical Systems ◽

Group Structure ◽

Global Solutions ◽

Topological Stability ◽

Natural Group ◽

Shadowing Property ◽

Infinite Dimensional ◽

Mathematical Sciences ◽

The Relationship

A G-process is briefly a process ([A. N. Carvalho, J. A. Langa and J. C. Robinson, Attractors for Infinite-Dimensional Non-Autonomous Dynamical Systems, Applied Mathematical Sciences, Vol. 182 (Springer, 2013)], [C. M. Dafermos, An invariance principle for compact processes, J. Differential Equations 9 (1971) 239–252], [P. E. Kloeden and M. Rasmussen, Nonautonomous Dynamical Systems, Mathematical Surveys and Monographs, Vol. 176 (Amer. Math. Soc., 2011)]) for which the role of evolution parameter is played by a general topological group [Formula: see text]. These processes are broad enough to include the [Formula: see text]-actions (characterized as autonomous [Formula: see text]-processes) and the two-parameter flows (where [Formula: see text]). We endow the space of [Formula: see text]-processes with a natural group structure. We introduce the notions of orbit, pseudo-orbit and shadowing property for [Formula: see text]-processes and analyze the relationship with the [Formula: see text]-processes group structure. We study the equicontinuous [Formula: see text]-processes and use it to construct nonautonomous [Formula: see text]-processes with the shadowing property. We study the global solutions of the [Formula: see text]-processes and the corresponding global shadowing property. We study the expansivity (global and pullback) of the [Formula: see text]-processes. We prove that there are nonautonomous expansive [Formula: see text]-processes and characterize the existence of expansive equicontinuous [Formula: see text]-processes. We define the topological stability for [Formula: see text]-processes and prove that every expansive [Formula: see text]-process with the shadowing property is topologically stable. Examples of nonautonomous topologically stable [Formula: see text]-processes are given.

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Topological Stability of 2-D Vanishing Grains

MRS Proceedings ◽

10.1557/proc-278-391 ◽

1992 ◽

Vol 278 ◽

Author(s):

V. E. Fradkov ◽

M. E. Glicksman ◽

J. Nordberg ◽

M. Palmer ◽

K. Rajan

Keyword(s):

Computer Simulation ◽

Grain Boundary ◽

Grain Growth ◽

Triple Junctions ◽

Polycrystalline Films ◽

Topological Stability ◽

Von Neumann ◽

Small Grains ◽

The Mean ◽

Boundary Model

AbstractGrain growth in polycrystals occurs by decreasing the total number of grains as a result of the disappearance of small ones. That is why the both the kinetic and topological details of shrinking of small grains are important.In 2-D, “uniform boundary model” assumptions imply the von Neumann-Mullins law, and all grains having less than 6 neighbors tend to shrink. The mean topological class ef vanishing grains was found experimentally to be about 4.3. This result suggests that most vanishing grains are either 4- or 5-sided, not transforming to 3-sided ones.Shrinking of 4- and 5-sided 2-D grains was studied experimentally on transparent, pure SCN, (succinonitrile) polycrystalline films and by direct computer simulation of grain boundary capillary motion together with triple junctions. It was found that the grains which are much smaller than their neighbors are topologically stable.

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Metal complexes of dissymmetric arsines. Stereochemistry, topological stability, and spectra of cobalt(III) complexes containing a linear quadridenate tetra-tert-arsine ligand

Journal of the American Chemical Society ◽

10.1021/ja00806a012 ◽

1973 ◽

Vol 95 (25) ◽

pp. 8269-8280 ◽

Cited By ~ 33

Author(s):

B. Bosnich ◽

W. G. Jackson ◽

S. B. Wild

Keyword(s):

Metal Complexes ◽

Topological Stability

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Topologically stable solutions in an O(4) Yang–Mills, Higgs system

Canadian Journal of Physics ◽

10.1139/p80-037 ◽

1980 ◽

Vol 58 (2) ◽

pp. 247-248

Author(s):

Gerry McKeon

Keyword(s):

Field Equations ◽

Topological Stability ◽

Yang Mills ◽

Euclidean Field ◽

Stable Solutions

The classical Euclidean field equations for an O(4) Yang–Mills, Higgs system are considered, under the postulate of invariance under combined space and gauge rotations. The topological stability of the solutions is discussed.

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