Asymptotic estimate for the counting problems corresponding to the dynamical system on some decorated graphs

2017 ◽  
Vol 38 (5) ◽  
pp. 1697-1708 ◽  
Author(s):  
V. L. CHERNYSHEV ◽  
A. A. TOLCHENNIKOV
Keyword(s):  
Dynamical System ◽  
Wave Packet ◽  
General Theorem ◽  
Three Dimensional ◽  
Initial Time ◽  
Dimensional Torus ◽  
Counting Problems ◽  
One Dimensional ◽  
Moving Points ◽  
Narrow Wave

We study a topological space obtained from a graph via replacing vertices with smooth Riemannian manifolds, that is, a decorated graph. We consider the following dynamical system on decorated graphs. Suppose that, at the initial time, we have a narrow wave packet on a one-dimensional edge. It can be thought of as a point moving along the edge. When a packet arrives at the point of gluing, the expanding wavefront begins to spread on the Riemannian manifold. At the same time, there is a partial reflection of the wave packet. When the wavefront that propagates on the surface comes to another point of gluing, it generates a reflected wavefront and a wave packet on an edge. We study the number of Gaussian packets, that is, moving points on one-dimensional edges as time goes to infinity. We prove the asymptotic estimations for this number for the following decorated graphs: a cylinder with an interval, a two-dimensional torus with an interval and a three-dimensional torus with an interval. Also we prove a general theorem about a manifold with an interval and apply it to the case of a uniformly secure manifold.

scholarly journals Spatiotemporal dynamics in a diffusive Holling-Tanner model near codimension-two bifurcations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Daifeng Duan ◽  
Ben Niu ◽  
Junjie Wei
Keyword(s):  
Generation Time ◽  
Three Dimensional ◽  
Spatiotemporal Patterns ◽  
Hopf Bifurcations ◽  
Dimensional Torus ◽  
Periodic Oscillations ◽  
One Dimensional ◽  
Codimension Two ◽  
Spatially Inhomogeneous ◽  
Delayed System

<p style='text-indent:20px;'>We investigate spatiotemporal patterns near the Turing-Hopf and double Hopf bifurcations in a diffusive Holling-Tanner model on a one- dimensional spatial domain. Local and global stability of the positive constant steady state for the non-delayed system is studied. Introducing the generation time delay in prey growth, we discuss the existence of Turing-Hopf and double Hopf bifurcations and give the explicit dynamical classification near these bifurcation points. Finally, we obtain the complicated dynamics, including periodic oscillations, quasi-periodic oscillations on a three-dimensional torus, the coexistence of two stable nonconstant steady states, the coexistence of two spatially inhomogeneous periodic solutions, and strange attractors.</p>

scholarly journals THE WZW MODEL AS A DYNAMICAL SYSTEM ON AFFINE LIE GROUPS

1996 ◽  
Vol 11 (12) ◽  
pp. 2167-2212 ◽  
Author(s):  
K. CLUBOK ◽  
M.B. HALPERN
Keyword(s):  
Field Theory ◽  
Dynamical System ◽  
Mechanical System ◽  
Lie Groups ◽  
Lie Group ◽  
Three Dimensional ◽  
Group Element ◽  
Affine Group ◽  
Two Dimensional ◽  
One Dimensional

Working directly on affine Lie groups, we construct several new formulations of the WZW model. In one formulation WZW is expressed as a one-dimensional mechanical system whose variables are coordinates on the affine Lie group. When written in terms of the affine group element, this formulation exhibits a two-dimensional WZW term. In another formulation WZW is written as a two-dimensional field theory, with a three-dimensional WZW term, whose fields are coordinates on the affine group. On the basis of these equivalent formulations, we develop a translation dictionary in which the new formulations on the affine Lie group are understood as mode formulations of the conventional WZW formulation on the Lie group. Using this dictionary, we also express WZW as a three-dimensional field theory on the Lie group with a four-dimensional WZW term.

scholarly journals Shape of a sound wave in a weakly-perturbed Bose gas

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Oleksandr Marchukov ◽  
Artem Volosniev
Keyword(s):  
Wave Packet ◽  
Sound Wave ◽  
Light Propagation ◽  
Three Dimensional ◽  
Bose Gas ◽  
Pitaevskii Equation ◽  
Spherically Symmetric ◽  
One Dimensional ◽  
Optical Media ◽  
Symmetric Perturbation

We employ the Gross-Pitaevskii equation to study acoustic emission generated in a uniform Bose gas by a static impurity. The impurity excites a sound-wave packet, which propagates through the gas. We calculate the shape of this wave packet in the limit of long wavelengths, and argue that it is possible to extract properties of the impurity by observing this shape. We illustrate here this possibility for a Bose gas with a trapped impurity atom – an example of a relevant experimental setup. Presented results are general for all one-dimensional systems described by the nonlinear Schr"{o}dinger equation and can also be used in nonatomic systems, e.g., to analyze light propagation in nonlinear optical media. Finally, we calculate the shape of the sound-wave packet for a three-dimensional Bose gas assuming a spherically symmetric perturbation.

Structure and function of neural networks in the retina

1988 ◽  
Vol 46 ◽  
pp. 26-27
Author(s):  
Peter Sterling
Keyword(s):  
Ganglion Cells ◽  
Three Dimensional ◽  
Structure And Function ◽  
Synaptic Connections ◽  
Visual Axis ◽  
One Dimensional ◽  
Cat Retina ◽  
Ultrathin Sections ◽  
And Function ◽  
Insight Into

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

Sign in / Sign up

Export Citation Format

Share Document