KNOTTED PERIODIC SOLUTIONS OF A LINEAR NONAUTONOMOUS SYSTEM AND SOME RELATED THREE-DIMENSIONAL FLOWS

2012 ◽  
Vol 22 (11) ◽  
pp. 1250280
Author(s):  
JIBIN LI ◽  
XIAOHUA ZHAO
Keyword(s):  
Phase Space ◽  
Periodic Solutions ◽  
Periodic Orbits ◽  
Autonomous Systems ◽  
Three Dimensional ◽  
Distinct Type ◽  
Frequency Parameter ◽  
Bounded Region ◽  
Nonautonomous Systems ◽  
Dimensional Phase Space

This paper considers a three-dimensional linear nonautonomous systems. It shows that for every integer frequency parameter value, this system has a distinct type of knotted periodic solutions, which lie in a bounded region of R3. Exact explicit parametric representations of the knotted periodic solutions are given. By using these parametric representations, two series of three-dimensional flows are constructed, such that these three-dimensional autonomous systems have knotted periodic orbits in the three-dimensional phase space.

Superconductivity and the existence of Nambu's three-dimensional phase space mechanics

1984 ◽  
Vol 104 (2) ◽  
pp. 106-108 ◽  
Author(s):  
Reinaldo Angulo ◽  
Simón Codriansky ◽  
Carlos A. Gonzalez-Bernardo ◽  
Andrés J. Kalnay ◽  
Freddy Perez-M ◽  
...  
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Dimensional Phase Space ◽  
Space Mechanics

scholarly journals Constraining cluster masses from the stacked phase space distribution at large radii

2019 ◽  
Vol 489 (1) ◽  
pp. 1344-1356
Author(s):  
Akinari Hamabata ◽  
Masamune Oguri ◽  
Takahiro Nishimichi
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Space Distribution ◽  
Line Of Sight ◽  
Mass Dependence ◽  
Mass Measurements ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
Transverse Distance ◽  
Hubble Flow

Abstract Velocity dispersions have been employed as a method to measure masses of clusters. To complement this conventional method, we explore the possibility of constraining cluster masses from the stacked phase space distribution of galaxies at larger radii, where infall velocities are expected to have a sensitivity to cluster masses. First, we construct a two-component model of the three-dimensional phase space distribution of haloes surrounding clusters up to 50 $\, h^{-1}$ Mpc from cluster centres based on N-body simulations. We confirm that the three-dimensional phase space distribution shows a clear cluster mass dependence up to the largest scale examined. We then calculate the probability distribution function of pairwise line-of-sight velocities between clusters and haloes by projecting the three-dimensional phase space distribution along the line of sight with the effect of the Hubble flow. We find that this projected phase space distribution, which can directly be compared with observations, shows a complex mass dependence due to the interplay between infall velocities and the Hubble flow. Using this model, we estimate the accuracy of dynamical mass measurements from the projected phase space distribution at the transverse distance from cluster centres larger than $2\, h^{-1}$ Mpc. We estimate that, by using 1.5 × 105 spectroscopic galaxies, we can constrain the mean cluster masses with an accuracy of 14.5 per cent if we fully take account of the systematic error coming from the inaccuracy of our model. This can be improved down to 5.7 per cent by improving the accuracy of the model.

scholarly journals Time evolution of companies towards a stable scaling curve obtained from flow diagrams in three-dimensional phase space

2019 ◽  
Vol 21 (4) ◽  
pp. 043038
Author(s):  
Yuh Kobayashi ◽  
Hideki Takayasu ◽  
Shlomo Havlin ◽  
Misako Takayasu
Keyword(s):  
Phase Space ◽  
Time Evolution ◽  
Three Dimensional ◽  
Dimensional Phase Space ◽  
Flow Diagrams

scholarly journals CANONICAL TRANSFORMATIONS IN THREE-DIMENSIONAL PHASE-SPACE

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4769-4788 ◽  
Author(s):  
TEKİN DERELİ ◽  
ADNAN TEĞMEN ◽  
TUĞRUL HAKİOĞLU
Keyword(s):  
Phase Space ◽  
Canonical Transformation ◽  
Generating Functions ◽  
General Framework ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Canonical Transformations ◽  
Dimensional Phase Space ◽  
Nambu Bracket ◽  
Definition Of

Canonical transformation in a three-dimensional phase-space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed based on canonoid transformations. It is shown that generating functions, transformed Hamilton functions and the transformation itself for given generating functions can be determined by solving Pfaffian differential equations corresponding to that quantities. Types of the generating functions are introduced and all of them are listed. Infinitesimal canonical transformations are also discussed. Finally, we show that the decomposition of canonical transformations is also possible in three-dimensional phase space as in the usual two-dimensional one.

scholarly journals Features of pulsed synchronization of an autooscillatory system with a three-dimensional phase space

2006 ◽  
Vol 32 (4) ◽  
pp. 343-346 ◽  
Author(s):  
A. P. Kuznetsov ◽  
N. V. Stankevich ◽  
L. V. Tyuryukina
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Dimensional Phase Space

scholarly journals Complexity of a Microblogging Social Network in the Framework of Modern Nonlinear Science

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Andrey Dmitriev ◽  
Vasily Kornilov ◽  
Svetlana Maltseva
Keyword(s):  
Dynamical System ◽  
Social Network ◽  
Phase Space ◽  
Adiabatic Approximation ◽  
Three Dimensional ◽  
Evolutionary Model ◽  
Random Dynamical System ◽  
New Paradigm ◽  
Dimensional Phase Space ◽  
Nonlinear Science

Recent developments in nonlinear science have caused the formation of a new paradigm called the paradigm of complexity. The self-organized criticality theory constitutes the foundation of this paradigm. To estimate the complexity of a microblogging social network, we used one of the conceptual schemes of the paradigm, namely, the system of key signs of complexity of the external manifestations of the system irrespective of its internal structure. Our research revealed all the key signs of complexity of the time series of a number of microposts. We offer a new model of a microblogging social network as a nonlinear random dynamical system with additive noise in three-dimensional phase space. Implementations of this model in the adiabatic approximation possess all the key signs of complexity, making the model a reasonable evolutionary model for a microblogging social network. The use of adiabatic approximation allows us to model a microblogging social network as a nonlinear random dynamical system with multiplicative noise with the power-law in one-dimensional phase space.

scholarly journals Building CX peanut-shaped disk galaxy profiles

2018 ◽  
Vol 612 ◽  
pp. A114 ◽  
Author(s):  
P. A. Patsis ◽  
M. Harsoula
Keyword(s):  
Phase Space ◽  
Periodic Orbits ◽  
Three Dimensional ◽  
Resonance Region ◽  
Space Structure ◽  
Jacobi Constant ◽  
Dynamical Mechanism ◽  
Standard Case ◽  
New Model ◽  
Stable Periodic

Context. We present and discuss the orbital content of a rather unusual rotating barred galaxy model, in which the three-dimensional (3D) family, bifurcating from x1 at the 2:1 vertical resonance with the known “frown-smile” side-on morphology, is unstable. Aims. Our goal is to study the differences that occur in the phase space structure at the vertical 2:1 resonance region in this case, with respect to the known, well studied, standard case, in which the families with the frown-smile profiles are stable and support an X-shaped morphology. Methods. The potential used in the study originates in a frozen snapshot of an N-body simulation in which a fast bar has evolved. We follow the evolution of the vertical stability of the central family of periodic orbits as a function of the energy (Jacobi constant) and we investigate the phase space content by means of spaces of section. Results. The two bifurcating families at the vertical 2:1 resonance region of the new model change their stability with respect to that of most studied analytic potentials. The structure in the side-on view that is directly supported by the trapping of quasi-periodic orbits around 3D stable periodic orbits has now an infinity symbol (i.e. ∞-type) profile. However, the available sticky orbits can reinforce other types of side-on morphologies as well. Conclusions. In the new model, the dynamical mechanism of trapping quasi-periodic orbits around the 3D stable periodic orbits that build the peanut, supports the ∞-type profile. The same mechanism in the standard case supports the X shape with the frown-smile orbits. Nevertheless, in both cases (i.e. in the new and in the standard model) a combination of 3D quasi-periodic orbits around the stable x1 family with sticky orbits can support a profile reminiscent of the shape of the orbits of the 3D unstable family existing in each model.

Phase Space Interpretation and Stability Analysis of a Self Excited, Friction Damped Turbine Airfoil

1997 ◽  
Author(s):  
E. Pesheck ◽  
C. Pierre
Keyword(s):  
Stability Analysis ◽  
Phase Space ◽  
Asymptotic Methods ◽  
Three Dimensional ◽  
Space Representation ◽  
Free Response ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Dimensional Phase Space ◽  
Phase Space Representation

Abstract The free response motion of a self excited, friction damped, single-degree of freedom, turbine airfoil model is determined utilizing both exact and asymptotic methods. A three-dimensional phase space representation is used to examine the system’s global stability, and to further intuitive understanding of the system dynamics. Conclusions are reached regarding the validity and application of stability predictions through comparison of approximate and exact solutions.

Sign in / Sign up

Export Citation Format

Share Document