Autonomous Oscillations, Bifurcations, and Chaotic Response of Moored Vessels

1988 ◽  
Vol 32 (03) ◽  
pp. 220-228
Author(s):  
Fotis A. Papoulias ◽  
Michael M. Bernitsas
Keyword(s):  
Phase Space ◽  
Rational Design ◽  
Single Point ◽  
State Equations ◽  
Dimensional Phase Space ◽  
Stability And Instability ◽  
Analysis Of Stability ◽  
Wave Drift Forces ◽  
Parameter Values ◽  
Selection Of

The dynamic behavior of single-point mooring (SPM) systems under time-independent external excitation is analyzed. The time evolution of the corresponding dynamical system is described in a six-dimensional phase space. Bifurcation sequences of state equations are studied and parameter values at which the response of the SPM changes radically are identified. Analysis of stability and instability domains of the system reveals regions of operationally hazardous response. It is shown that an SPM system under time-independent environmental excitation may not stay in a position of static equilibrium. It may start oscillating either periodically or even in a random way depending on the dimension of the attracting set in the phase space, which in general may be noninteger. This explains the large-amplitude slow motions of SPM systems, in the horizontal plane, occasionally observed in practice and often attributed to time-dependent excitation from wave drift forces. Based on these results, rational design decisions can be made for selection of the principal SPM geometric parameters in order to improve the system operability.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

scholarly journals Geometric particle-in-cell methods for the Vlasov–Maxwell equations with spin effects

2021 ◽  
Vol 87 (3) ◽  
Author(s):  
Nicolas Crouseilles ◽  
Paul-Antoine Hervieux ◽  
Yingzhe Li ◽  
Giovanni Manfredi ◽  
Yajuan Sun
Keyword(s):  
Phase Space ◽  
Maxwell Equations ◽  
Stimulated Raman Scattering ◽  
Extended Phase ◽  
Five Dimensions ◽  
Particle In Cell ◽  
Spin Effects ◽  
Dimensional Phase Space ◽  
Spin Polarized ◽  
Underdense Plasma

We propose a numerical scheme to solve the semiclassical Vlasov–Maxwell equations for electrons with spin. The electron gas is described by a distribution function $f(t,{\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$ that evolves in an extended 9-dimensional phase space $({\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$ , where $\boldsymbol s$ represents the spin vector. Using suitable approximations and symmetries, the extended phase space can be reduced to five dimensions: $(x,{{p_x}}, {\boldsymbol s})$ . It can be shown that the spin Vlasov–Maxwell equations enjoy a Hamiltonian structure that motivates the use of the recently developed geometric particle-in-cell (PIC) methods. Here, the geometric PIC approach is generalized to the case of electrons with spin. Total energy conservation is very well satisfied, with a relative error below $0.05\,\%$ . As a relevant example, we study the stimulated Raman scattering of an electromagnetic wave interacting with an underdense plasma, where the electrons are partially or fully spin polarized. It is shown that the Raman instability is very effective in destroying the electron polarization.

scholarly journals Stability and Instability in the Lysogenic State of Phage Lambda

2010 ◽  
Vol 192 (22) ◽  
pp. 6064-6076 ◽  
Author(s):  
John W. Little ◽  
Christine B. Michalowski
Keyword(s):  
Intrinsic Rate ◽  
Growth Conditions ◽  
Emergent Properties ◽  
Regulatory Circuits ◽  
Stability And Instability ◽  
Natural Range ◽  
Analysis Of Stability ◽  
Stable Association ◽  
The Stability ◽  
Gene Regulatory Circuits

ABSTRACT Complex gene regulatory circuits exhibit emergent properties that are difficult to predict from the behavior of the components. One such property is the stability of regulatory states. Here we analyze the stability of the lysogenic state of phage λ. In this state, the virus maintains a stable association with the host, and the lytic functions of the virus are repressed by the viral CI repressor. This state readily switches to the lytic pathway when the host SOS system is induced. A low level of SOS-dependent switching occurs without an overt stimulus. We found that the intrinsic rate of switching to the lytic pathway, measured in a host lacking the SOS response, was almost undetectably low, probably less than 10−8/generation. We surmise that this low rate has not been selected directly during evolution but results from optimizing the rate of switching in a wild-type host over the natural range of SOS-inducing conditions. We also analyzed a mutant, λprm240, in which the promoter controlling CI expression was weakened, rendering lysogens unstable. Strikingly, the intrinsic stability of λprm240 lysogens depended markedly on the growth conditions; lysogens grown in minimal medium were nearly stable but switched at high rates when grown in rich medium. These effects on stability likely reflect corresponding effects on the strength of the prm240 promoter, measured in an uncoupled assay system. Several derivatives of λprm240 with altered stabilities were characterized. This mutant and its derivatives afford a model system for further analysis of stability.

scholarly journals Dynamical properties and extremes of Northern Hemisphere climate fields over the past 60 years

2017 ◽  
Vol 24 (4) ◽  
pp. 713-725 ◽  
Author(s):  
Davide Faranda ◽  
Gabriele Messori ◽  
M. Carmen Alvarez-Castro ◽  
Pascal Yiou
Keyword(s):  
Phase Space ◽  
Sea Level ◽  
Northern Hemisphere ◽  
Atmospheric Dynamics ◽  
Complex Nature ◽  
Human Welfare ◽  
Sea Level Pressure ◽  
Level Pressure ◽  
Dimensional Phase Space ◽  
Dynamical Properties

Abstract. Atmospheric dynamics are described by a set of partial differential equations yielding an infinite-dimensional phase space. However, the actual trajectories followed by the system appear to be constrained to a finite-dimensional phase space, i.e. a strange attractor. The dynamical properties of this attractor are difficult to determine due to the complex nature of atmospheric motions. A first step to simplify the problem is to focus on observables which affect – or are linked to phenomena which affect – human welfare and activities, such as sea-level pressure, 2 m temperature, and precipitation frequency. We make use of recent advances in dynamical systems theory to estimate two instantaneous dynamical properties of the above fields for the Northern Hemisphere: local dimension and persistence. We then use these metrics to characterize the seasonality of the different fields and their interplay. We further analyse the large-scale anomaly patterns corresponding to phase-space extremes – namely time steps at which the fields display extremes in their instantaneous dynamical properties. The analysis is based on the NCEP/NCAR reanalysis data, over the period 1948–2013. The results show that (i) despite the high dimensionality of atmospheric dynamics, the Northern Hemisphere sea-level pressure and temperature fields can on average be described by roughly 20 degrees of freedom; (ii) the precipitation field has a higher dimensionality; and (iii) the seasonal forcing modulates the variability of the dynamical indicators and affects the occurrence of phase-space extremes. We further identify a number of robust correlations between the dynamical properties of the different variables.

scholarly journals Selection of Pairings Reaching Evenly Across the Data (SPREAD): A simple algorithm to design maximally informative fully crossed mating experiments

2014 ◽  
Author(s):  
Kolea Zimmerman ◽  
Daniel Levitis ◽  
Ethan Addicott ◽  
Anne Pringle
Keyword(s):  
Nearest Neighbor ◽  
Simple Algorithm ◽  
Two Dimensional ◽  
Neighbor Distance ◽  
Crossing Experiments ◽  
The Mean ◽  
Parameter Values ◽  
Selection Of ◽  
Novel Algorithm ◽  
Trait Space

We present a novel algorithm for the design of crossing experiments. The algorithm identifies a set of individuals (a ?crossing-set?) from a larger pool of potential crossing-sets by maximizing the diversity of traits of interest, for example, maximizing the range of genetic and geographic distances between individuals included in the crossing-set. To calculate diversity, we use the mean nearest neighbor distance of crosses plotted in trait space. We implement our algorithm on a real dataset ofNeurospora crassastrains, using the genetic and geographic distances between potential crosses as a two-dimensional trait space. In simulated mating experiments, crossing-sets selected by our algorithm provide better estimates of underlying parameter values than randomly chosen crossing-sets.

scholarly journals Effects of Vegetation and Topography on the Boundary Layer Structure above the Amazon Forest

2020 ◽  
Vol 77 (8) ◽  
pp. 2941-2957
Author(s):  
Marcelo Chamecki ◽  
Livia S. Freire ◽  
Nelson L. Dias ◽  
Bicheng Chen ◽  
Cléo Quaresma Dias-Junior ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Phase Space ◽  
Vertical Structure ◽  
Layer Structure ◽  
Roughness Sublayer ◽  
Large Contribution ◽  
Amazon Forest ◽  
Two Dimensional ◽  
Dimensional Phase Space ◽  
Field Campaigns

Abstract Observational data from two field campaigns in the Amazon forest were used to study the vertical structure of turbulence above the forest. The analysis was performed using the reduced turbulent kinetic energy (TKE) budget and its associated two-dimensional phase space. Results revealed the existence of two regions within the roughness sublayer in which the TKE budget cannot be explained by the canonical flat-terrain TKE budgets in the canopy roughness sublayer or in the lower portion of the convective ABL. Data analysis also suggested that deviations from horizontal homogeneity have a large contribution to the TKE budget. Results from LES of a model canopy over idealized topography presented similar features, leading to the conclusion that flow distortions caused by topography are responsible for the observed features in the TKE budget. These results support the conclusion that the boundary layer above the Amazon forest is strongly impacted by the gentle topography underneath.

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 PROPERTIES OF THE INVARIANT DISK PACKING IN A MODEL BANDPASS SIGMA–DELTA MODULATOR

2003 ◽  
Vol 13 (03) ◽  
pp. 631-641 ◽  
Author(s):  
PETER ASHWIN ◽  
XIN-CHU FU ◽  
JONATHAN DEANE
Keyword(s):  
Phase Space ◽  
Analytic Functions ◽  
Parameter Family ◽  
Sigma Delta Modulator ◽  
Sigma Delta ◽  
Disk Packing ◽  
Piecewise Isometries ◽  
Map Operations ◽  
Countably Infinite ◽  
Parameter Values

In this paper we discuss the packing properties of invariant disks defined by periodic behavior of a model for a bandpass Σ–Δ modulator. The periodically coded regions form a packing of the forward invariant phase space by invariant disks. For this one-parameter family of PWIs, by introducing codings underlying the map operations we give explicit expressions for the centers of the disks by analytic functions of the parameters, and then show that tangencies between disks in the packings are very rare; more precisely they occur on parameter values that are at most countably infinite. We indicate how similar results can be obtained for other plane maps that are piecewise isometries.

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