Classical drop phase diagram and correlations in phase space

2003 ◽  
Vol 723 (1-2) ◽  
pp. 229-248 ◽  
Author(s):  
A. Chernomoretz ◽  
P. Balenzuela ◽  
C.O. Dorso
Keyword(s):  
Phase Diagram ◽  
Phase Space ◽  
Drop Phase

Nonlinear dynamics of forced transitional jets: periodic and chaotic attractors

1994 ◽  
Vol 263 ◽  
pp. 93-132 ◽  
Author(s):  
George Broze ◽  
Fazle Hussain
Keyword(s):  
Phase Diagram ◽  
Phase Space ◽  
Lyapunov Exponent ◽  
Conceptual Model ◽  
Chaotic Attractor ◽  
Excitation Frequency ◽  
Chaotic Attractors ◽  
Largest Lyapunov Exponent ◽  
Open Flow ◽  
Vortex Pairing

Conclusive experimental evidence is presented for the existence of a low-dimensional temporal dynamical system in an open flow, namely the near field of an axisymmetric, subsonic free jet. An initially laminar jet (4 cm air jet in the Reynolds number range 1.1 × 104 [Lt ] ReD × 9.1 × 104) with a top-hat profile was studied using single-frequency, longitudinal, bulk excitation. Two non-dimensional control parameters – forcing frequency StD (≡fexD/Ue, where fez is the excitation frequency, D is the jet exit diameter and Ue is the exit velocity) and forcing amplitude af (≡ u’f/Ue, where u’f is the jet exit r.m.s. longitudinal velocity fluctuation at the excitation frequency) – were varied over the ranges 10-4 < af < 0.3 and 0.3 < StD < 3.0 in order to construct a phase diagram. Periodic and chaotic states were found over large domains of the parameter space. The periodic attractors correspond to stable pairing (SP) and stable double pairing (SDP) of rolled-up vortices. One chaotic attractor, near SP in the parameter space, results from nearly periodic modulations of pairing (NPMP) of vortices. At large scales (i.e. approximately the size of the attractor) in phase space, NPMP exhibits approximately quasi-periodic behaviour, including modulation sidebands around ½fex in u-spectra, large closed loops in its Poincaré sections, correlation dimension v ∼ 2 and largest Lyapunov exponent λ1 ∼ 0. But investigations at smaller scales (i.e. distances greater than, but of the order of, trajectory separation) in phase space reveal chaos, as shown by v > 2 and λ1 > 0. The other chaotic attractor, near SDP, results from nearly periodic modulations of the first vortex pairing but chaotic modulations of the second pairing and has a broadband spectrum, a dimension 2.5 [Lt ] v [Lt ] 3 and the largest Lyapunov exponent 0.2 [Lt ] λ1 [Lt ] 0.7 bits per orbit (depending on measurement locations in physical and parameter spaces).A definition that distinguishes between physically and dynamically open flows is proposed and justified by our experimental results. The most important conclusion of this study is that a physically open flow, even one that is apparently dynamically open due to convective instability, can exhibit dynamically closed behaviour as a result of feedback. A conceptual model for transitional jets is proposed based on twodimensional instabilities, subharmonic resonance and feedback from downstream vortical structures to the nozzle lip. Feedback was quantified and shown to affect the exit fundamental–subharmonic phase difference ϕ – a crucial variable in subharmonic resonance and, hence, vortex pairing. The effect of feedback, the sensitivity of pairings to ϕ, the phase diagram, and the documented periodic and chaotic attractors demonstrate the validity of the proposed conceptual model.

scholarly journals Feature selection by higher criticism thresholding achieves the optimal phase diagram

2009 ◽  
Vol 367 (1906) ◽  
pp. 4449-4470 ◽  
Author(s):  
David Donoho ◽  
Jiashun Jin
Keyword(s):  
Phase Diagram ◽  
Phase Space ◽  
Order Statistic ◽  
Small Sample Size ◽  
Forthcoming Paper ◽  
Small Sample ◽  
Classification Error ◽  
Two Dimensional ◽  
Higher Criticism ◽  
The Ideal

We consider two-class linear classification in a high-dimensional, small-sample-size setting. Only a small fraction of the features are useful, these being unknown to us, and each useful feature contributes weakly to the classification decision. This was called the rare/weak (RW) model in our previous study ( Donoho, D. & Jin, J. 2008 Proc. Natl Acad. Sci. USA 105 , 14 790–14 795). We select features by thresholding feature Z -scores. The threshold is set by higher criticism (HC). For 1≤ i ≤ N , let π i denote the p -value associated with the i th Z -score and π ( i ) denote the i th order statistic of the collection of p -values. The HC threshold (HCT) is the order statistic of the Z -score corresponding to index i maximizing . The ideal threshold optimizes the classification error. In that previous study, we showed that HCT was numerically close to the ideal threshold. We formalize an asymptotic framework for studying the RW model, considering a sequence of problems with increasingly many features and relatively fewer observations. We show that, along this sequence, the limiting performance of ideal HCT is essentially just as good as the limiting performance of ideal thresholding. Our results describe two-dimensional phase space , a two-dimensional diagram with coordinates quantifying ‘rare’ and ‘weak’ in the RW model. The phase space can be partitioned into two regions—one where ideal threshold classification is successful, and one where the features are so weak and so rare that it must fail. Surprisingly, the regions where ideal HCT succeeds and fails make exactly the same partition of the phase diagram. Other threshold methods, such as false (feature) discovery rate (FDR) threshold selection, are successful in a substantially smaller region of the phase space than either HCT or ideal thresholding. The FDR and local FDR of the ideal and HC threshold selectors have surprising phase diagrams, which are also described. Results showing the asymptotic equivalence of HCT with ideal HCT can be found in a forthcoming paper ( Donoho, D. & Jin, J. In preparation ).

scholarly journals From Color-Avoiding to Color-Favored Percolation in Diluted Lattices

2020 ◽  
Vol 12 (8) ◽  
pp. 139
Author(s):  
Michele Giusfredi ◽  
Franco Bagnoli
Keyword(s):  
Phase Diagram ◽  
Phase Space ◽  
Paradoxical Effect ◽  
Critical Problem ◽  
Self Organized ◽  
Convex Formulations ◽  
Asymptotic Phase

We study the problem of color-avoiding and color-favored percolation in a network, i.e., the problem of finding a path that avoids a certain number of colors, associated with vulnerabilities of nodes or links, or is attracted by them. We investigate here regular (mainly directed) lattices with a fractions of links removed (hence the term “diluted”). We show that this problem can be formulated as a self-organized critical problem, in which the asymptotic phase space can be obtained in one simulation. The method is particularly effective for certain “convex” formulations, but can be extended to arbitrary problems using multi-bit coding. We obtain the phase diagram for some problem related to color-avoiding percolation on directed models. We also show that the interference among colors induces a paradoxical effect in which color-favored percolation is permitted where standard percolation for a single color is impossible.

Phase diagram of a growing succinonitrile crystal in supercooling-anisotropy phase space

1987 ◽  
Vol 36 (9) ◽  
pp. 4555-4558 ◽  
Author(s):  
H. Honjo ◽  
S. Ohta ◽  
M. Matsushita
Keyword(s):  
Phase Diagram ◽  
Phase Space

scholarly journals EXTENDED PHASE DIAGRAM OF THE LORENZ MODEL

2007 ◽  
Vol 17 (09) ◽  
pp. 3013-3033 ◽  
Author(s):  
H. R. DULLIN ◽  
S. SCHMIDT ◽  
P. H. RICHTER ◽  
S. K. GROSSMANN
Keyword(s):  
Phase Diagram ◽  
Phase Space ◽  
Rayleigh Number ◽  
Airy Function ◽  
Periodic Pattern ◽  
Airy Functions ◽  
Lorenz Equations ◽  
Lorenz Model ◽  
Extended Phase ◽  
Full Phase Space

The parameter dependence of the various attractive solutions of the three variable nonlinear Lorenz equations is studied as a function of r, the normalized Rayleigh number, and of σ, the Prandtl number. Previous work, either for fixed σ and all r or along σ ∝ r and [Formula: see text], is extended to the entire (r, σ) parameter plane. An onion-like periodic pattern is found which is due to the alternating stability of symmetric and nonsymmetric periodic orbits. This periodic pattern is explained by considering non-trivial limits of large r and σ and thus interpolating between the above mentioned cases. The mathematical analysis uses Airy functions as introduced in previous work, but instead of concentrating on the Lorenz map we analyze the trajectories in full phase space. The periodicity of the Airy function allows to calculate analytically the periodic onion structure in the (r, σ)-plane. Previous observations about sequences of bifurcations are confirmed, and more details regarding their symmetry are reported.

scholarly journals Phase Diagram-Based Sensing with Adaptive Waveform Design and Recurrent States Quantification for the Instantaneous Frequency Law Tracking

Sensors ◽  
2019 ◽  
Vol 19 (11) ◽  
pp. 2434 ◽  
Author(s):  
Angela Digulescu ◽  
Cornel Ioana ◽  
Alexandru Serbanescu
Keyword(s):  
Phase Diagram ◽  
Phase Space ◽  
Instantaneous Frequency ◽  
High Speed ◽  
Time Of Flight ◽  
Waveform Design ◽  
Accurate Estimation ◽  
Active Sensing ◽  
Representation Space ◽  
Time Frequency

Monitoring highly dynamic environments is a difficult task when the changes within the systems require high speed monitoring systems. An active sensing system has to solve the problem of overlapped responses coming from different parts of the surveyed environment. Thus, the need of a new representation space which separates the overlapped responses, is mandatory. This paper describes two new concepts for high speed active sensing systems. On the emitter side, we propose a phase-space-based waveform design that presents a unique shape in the phase space, which can be easily converted into a real signal. We call it phase space lobe. The instantaneous frequency (IF) law of the emitted signal is found inside the time series. The main advantage of this new concept is its capability to generate several distinct signals, non-orthogonal in the time/frequency domain but orthogonal within the representation space, namely the phase diagram. On the receiver side, the IF law information is estimated in the phase diagram representation domain by quantifying the recurrent states of the system. This waveform design technique gives the possibility to develop the high speed sensing methods, adapted for monitoring complex dynamic phenomena In our paper, as an applicative context, we consider the problem of estimating the time of flight in an dynamic acoustic environment. In this context, we show through experimental trials that our approach provides three times more accurate estimation of time of flight than spectrogram based technique. This very good accuracy comes from the capability of our approach to generate separable IF law components as well as from the quantification in phase diagram, both of them being the key element of our approach for high speed sensing.

scholarly journals Privacy-Preserving Data Sharing in High Dimensional Regression and Classification Settings

2012 ◽  
Vol 4 (1) ◽  
Author(s):  
Stephen E. Fienberg ◽  
Jiashun Jin
Keyword(s):  
Phase Diagram ◽  
Phase Space ◽  
Data Sharing ◽  
High Dimensional Data ◽  
Privacy Preserving ◽  
High Dimensional ◽  
Statistical Research ◽  
Higher Criticism ◽  
Dimensional Phase Space ◽  
Privacy Violation

We focus on the problem of multi-party data sharing in high dimensional data settings where the number of measured features (or the dimension) p is frequently much larger than the number of subjects (or the sample size) n, the so-called p >> n scenario that has been the focus of much recent statistical research. Here, we consider data sharing for two interconnected problems in high dimensional data analysis, namely the feature selection and classification. We characterize the notions of ``cautious", ``regular", and ``generous" data sharing in terms of their privacy-preserving implications for the parties and their share of data, with focus on the ``feature privacy" rather than the ``sample privacy", though the violation of the former may lead to the latter. We evaluate the data sharing methods using {\it phase diagram} from the statistical literature on multiplicity and Higher Criticism thresholding. In the two-dimensional phase space calibrated by the signal sparsity and signal strength, a phase diagram is a partition of the phase space and contains three distinguished regions, where we have no (feature)-privacy violation, relatively rare privacy violations, and an overwhelming amount of privacy violation.

A HYBRID MONTE CARLO STUDY OF THE SU-SCHRIEFFER-HEEGER MODEL

1994 ◽  
Vol 05 (03) ◽  
pp. 459-481 ◽  
Author(s):  
MARCIA G. DO AMARAL ◽  
C. ARAGÃO DE CARVALHO
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Phase Space ◽  
Chemical Potential ◽  
Monte Carlo Study ◽  
Fermion Mass ◽  
Coupling Constant ◽  
Hybrid Monte Carlo ◽  
Expectation Value ◽  
Fermionic Fields

We study, using the Hybrid Monte Carlo Method, the behavior of the spinless SuSchrieffer-Heeger model that describes conducting polymers, as a function of the Yukawa coupling constant, the fermion mass and the chemical potential, which simulates doping. We measure the expectation value of the bosonic fields, φ, and of the fermionic fields, [Formula: see text], in the phase space of all parameters. We exhibit the phase diagram of the theory and look for the presence of solitons, polarons and bipolarons in the configurations generated.

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