Resonant dynamics of an autoparametric system: A study using higher-order averaging

1996 ◽  
Vol 31 (1) ◽  
pp. 21-39 ◽  
Author(s):  
Bappaditya Banerjee ◽  
Anil K. Bajaj ◽  
Patricia Davies
Keyword(s):  
Higher Order ◽  
System A ◽  
Resonant Dynamics

scholarly journals Recovery of the Astrographic Catalogue

1988 ◽  
Vol 133 ◽  
pp. 171-176
Author(s):  
J. Stock ◽  
C. Abad
Keyword(s):  
Higher Order ◽  
Standard System ◽  
System A ◽  
Higher Order Terms ◽  
Fully Automatic ◽  
Overlap Method

An almost fully automatic scheme has been developed which produces final positions in the system determined by the reference catalogue, cross identifications, and approximate magnitudes in a standard system. A plate-overlap method is used which permits inclusion of higher order terms either plate by plate or common to a subset of plates. Magnitude dependent errors are also included. The system has already been applied to more than 500 plates, most of them of the Paris zone, with smaller sets of the Oxford, Potsdam, and Helsingfors zones. The Paris zone yields consistent higher order and magnitude terms over the entire set analyzed so far.

scholarly journals An Algorithm for Higher Order Hopf Normal Forms

1995 ◽  
Vol 2 (4) ◽  
pp. 307-319 ◽  
Author(s):  
A.Y.T. Leung ◽  
T. Ge
Keyword(s):  
Normal Form ◽  
Normal Forms ◽  
Nonlinear Differential Equations ◽  
Higher Order ◽  
Qualitative Behavior ◽  
Van Der Pol ◽  
Normal Form Theory ◽  
System A ◽  
Form Theory ◽  
Cubic System

Normal form theory is important for studying the qualitative behavior of nonlinear oscillators. In some cases, higher order normal forms are required to understand the dynamic behavior near an equilibrium or a periodic orbit. However, the computation of high-order normal forms is usually quite complicated. This article provides an explicit formula for the normalization of nonlinear differential equations. The higher order normal form is given explicitly. Illustrative examples include a cubic system, a quadratic system and a Duffing–Van der Pol system. We use exact arithmetic and find that the undamped Duffing equation can be represented by an exact polynomial differential amplitude equation in a finite number of terms.

scholarly journals Integrability of the Bakirov System: A Zero-Curvature Representation

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
Sergei Sakovich
Keyword(s):  
Higher Order ◽  
Zero Curvature Representation ◽  
System A ◽  
Zero Curvature ◽  
Generalized Symmetry ◽  
Essential Parameter

For the Bakirov system, which is known to possess only one higher-order local generalized symmetry, we explicitly find a zero-curvature representation containing an essential parameter.

scholarly journals Generalized q-Painlevé VI Systems of Type (A2n+1+A1+A1)(1) Arising From Cluster Algebra

2020 ◽  
Author(s):  
Naoto Okubo ◽  
Takao Suzuki
Keyword(s):  
Weyl Group ◽  
Cluster Algebra ◽  
Higher Order ◽  
Root Lattice ◽  
Similarity Reduction ◽  
Birational Transformations ◽  
System A ◽  
Affine Weyl Group ◽  
Painlevé Vi Equation ◽  
Garnier System

Abstract In this article we formulate a group of birational transformations that is isomorphic to an extended affine Weyl group of type $(A_{2n+1}+A_1+A_1)^{(1)}$ with the aid of mutations and permutations of vertices to a mutation-periodic quiver on a torus. This group provides a class of higher order generalizations of Jimbo–Sakai’s $q$-Painlevé VI equation as translations on a root lattice. Then the known three systems are obtained again: the $q$-Garnier system, a similarity reduction of the lattice $q$-UC hierarchy, and a similarity reduction of the $q$-Drinfeld–Sokolov hierarchy.

scholarly journals Thermodynamics and phase transitions of galactic clustering in higher-order modified gravity

2019 ◽  
Vol 28 (01) ◽  
pp. 1950027 ◽  
Author(s):  
Sudhaker Upadhyay ◽  
Behnam Pourhassan ◽  
Salvatore Capozziello
Keyword(s):  
Phase Transition ◽  
Distribution Function ◽  
Modified Gravity ◽  
Probability Distribution Function ◽  
Order Parameter ◽  
Equations Of State ◽  
Higher Order ◽  
Gravitational System ◽  
System A ◽  
Newtonian Dynamics

We study the thermodynamics of galactic clustering under the higher-order corrected Newtonian dynamics. The clustering of galaxies is considered as a gravitational phase transition. In order to study the effects of higher-order correction to the thermodynamics of gravitational system, we compute more exact equations of state. Moreover, we investigate the corrected probability distribution function for such a gravitating system. A relation between order parameter and the critical temperature is also established.

scholarly journals Nonlinear control of photonic higher-order topological bound states in the continuum

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Zhichan Hu ◽  
Domenico Bongiovanni ◽  
Dario Jukić ◽  
Ema Jajtić ◽  
Shiqi Xia ◽  
...  
Keyword(s):  
Bound States ◽  
Higher Order ◽  
Eigenvalue Spectrum ◽  
Proper Action ◽  
Continuum States ◽  
System A ◽  
Self Focusing ◽  
Topological Lattice ◽  
Symmetry Protected ◽  
The Continuum

AbstractHigher-order topological insulators (HOTIs) are recently discovered topological phases, possessing symmetry-protected corner states with fractional charges. An unexpected connection between these states and the seemingly unrelated phenomenon of bound states in the continuum (BICs) was recently unveiled. When nonlinearity is added to the HOTI system, a number of fundamentally important questions arise. For example, how does nonlinearity couple higher-order topological BICs with the rest of the system, including continuum states? In fact, thus far BICs in nonlinear HOTIs have remained unexplored. Here we unveil the interplay of nonlinearity, higher-order topology, and BICs in a photonic platform. We observe topological corner states that are also BICs in a laser-written second-order topological lattice and further demonstrate their nonlinear coupling with edge (but not bulk) modes under the proper action of both self-focusing and defocusing nonlinearities. Theoretically, we calculate the eigenvalue spectrum and analog of the Zak phase in the nonlinear regime, illustrating that a topological BIC can be actively tuned by nonlinearity in such a photonic HOTI. Our studies are applicable to other nonlinear HOTI systems, with promising applications in emerging topology-driven devices.

A Genealogical Charter

Africa ◽  
1952 ◽  
Vol 22 (4) ◽  
pp. 301-315 ◽  
Author(s):  
Laura Bohannan
Keyword(s):  
Social Organization ◽  
Lower Order ◽  
Higher Order ◽  
Northern Nigeria ◽  
Political Structure ◽  
System A ◽  
One To One ◽  
Opening Paragraph

Opening ParagraphThe Tiv of Northern Nigeria, who number some 800,000, believe that they are all descended from one man, Tiv, through some 14 to 17 generations of known ancestors (Fig. 1). These ancestors are constantly named in casual conversation and in discussion of serious affairs. To understand things Tiv one must know Tiv genealogies. By genealogical reference a Tiv traces ties of kinship and marriage, claims a place to live and farm, argues his case in a moot, conducts matters of magic and ritual, and decides against whom he will fight on any given occasion. Genealogies are the key to Tiv social organization. Tiv political structure is based on a lineage system: a system of segmented groups in which each segment (save the maximal) is included in a segment of a higher order but of the same kind, and each segment (save the minimal) includes segments of a lower order but of the same kind. The Tiv system has an almost one to one correlation between lineage and territorial segments. Both are called ‘those of X’, the eponymous ancestor; thus Mbaduku (those of Aduku) describes both the lineage segment (ipaven, pl. uipaven) and the discrete territory which they inhabit (tar, pl. utar).

Use of Higher Order Spectra in Condition Monitoring: Simulation and Experiments

1999 ◽  
Author(s):  
Alessandro Rivola ◽  
Paul R. White
Keyword(s):  
Condition Monitoring ◽  
Vibration Signal ◽  
Health Condition ◽  
Higher Order ◽  
Machine Vibration ◽  
System A ◽  
Straight Beam ◽  
Vibration Signature ◽  
Gaussian Input ◽  
Higher Order Spectra

Abstract In the field of machine condition monitoring one can observe that a link exists between machine vibrations and its health condition, that is, there is a change in the machine vibration signature when machine faults occur. Damages occurring in machine elements are often related to non-linear effects, which may lead to non-linearities in the machine vibration. This paper concerns the study of some systems by means of techniques based on Higher Order Spectra (HOS). These techniques are particularly useful in the situation where only a single measurement sensor is available. If a process is Gaussian then HOS provide no information that cannot be obtained from the second order statistics. On the contrary, HOS give information about a signal’s non-Gaussianity. Since a Gaussian input passing through a linear system leads to a Gaussian output, assuming the signal as an output of a system with a Gaussian input, then HOS make it possible to analyse the structure of the output signal and to provide information related to the non-linearity within the system. A simple model is presented with the aim of showing the effectiveness of the normalised version of polyspectra in detecting different kinds of system non-linearities. HOS are used to interpret the signal structure and the system’s physical characteristics. Moreover, two experimental cases are presented. The HOS are applied to detect the presence of a fatigue crack in a straight beam and to analyse the vibration signal measured on a test bench for rolling element bearings. Both third and fourth order spectra seem to provide a possibility of using HOS as a condition monitoring tool.

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