scholarly journals Non-Linear Behaviors of Transient Periodic Plasma Dynamics in a Multifractal Paradigm

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1356
Author(s):  
Stefan-Andrei Irimiciuc ◽  
Alexandra Saviuc ◽  
Florin Tudose-Sandu-Ville ◽  
Stefan Toma ◽  
Florin Nedeff ◽  
...  
Keyword(s):  
Period Doubling ◽  
Nonlinear Behavior ◽  
Structural Units ◽  
Plasma Dynamics ◽  
Oscillatory Dynamics ◽  
Damped Oscillations ◽  
Hidden Symmetry ◽  
Non Linear ◽  
Transient Plasma ◽  
Newtonian Behavior

In a multifractal paradigm of motion, nonlinear behavior of transient periodic plasmas, such as Schrodinger and hydrodynamic-type regimes, at various scale resolutions are represented. In a stationary case of Schrodinger-type regimes, the functionality of “hidden symmetry” of the group SL (2R) is implied though Riccati–Gauge different “synchronization modes” among period plasmas’ structural units. These modes, expressed in the form of period doubling, damped oscillations, quasi-periodicity, intermittences, etc., mimic the various non-linear behaviors of the transient plasma dynamics similar to chaos transitions scenarios. In the hydrodynamic regime, the non-Newtonian behavior of the transient plasma dynamics can be corelated with the viscous tension tensor of the multifractal type. The predictions given by our theoretical model are confronted with experimental data depicting electronic and ionic oscillatory dynamics seen by implementing the Langmuir probe technique on transient plasmas generated by ns-laser ablation of nickel and manganese targets.

ISUM: Its Birth, Growth and Future

2016 ◽  
Author(s):  
Sherif Rashed
Keyword(s):  
Nonlinear Behavior ◽  
Impact Loads ◽  
Coarse Mesh ◽  
Structural Units ◽  
Large Size ◽  
Linear Behavior ◽  
Large Ship ◽  
Non Linear ◽  
Recent Developments ◽  
Future Potential

ISUM (The Idealized Structural Unit Method) was born in 1972 to efficiently and accurately analyze the behavior of large size structures up to and beyond their ultimate strength. In this method a structure is divided into large elements, basically its structural units (members). Geometric and material non-linear behavior inside the element is formulated and expressed at a limited number of nodal points at the element boundaries. In this way a large structure can be modeled using a coarse mesh while still being able to consider the nonlinear behavior until the collapse of the structure. Several ISUM elements have been formulated and used to analyze the non-linear behavior of large ship structures. In further developments, more elements with more accurate formulations have been developed and more types of structures have been analyzed using this method. The same ISUM concept has been applied to the analysis of welding deformation of large welded structures and to failure analysis of structural and mechanical components subjected to impact loads. In this paper, the basic ISUM concept is outlined, and several elements are presented. Examples of applications to ships and marine structures are presented demonstrating the effectiveness of the method. Recent developments are also reviewed and future potential is explored.

scholarly journals Polymer Dynamics Through Group Invariance of SL(2R) - Type in a Fractal Paradigm

2020 ◽  
Vol 57 (1) ◽  
pp. 167-174
Author(s):  
Constantin Placinta ◽  
Tudor Cristian Petrescu ◽  
Vlad Ghizdovat ◽  
Stefan Andrei Irimiciuc ◽  
Decebal Vasincu ◽  
...  
Keyword(s):  
Large Class ◽  
Present Model ◽  
Period Doubling ◽  
Invariant Function ◽  
Polymer Dynamics ◽  
Advanced Materials ◽  
Structural Units ◽  
Damped Oscillations ◽  
Group Invariance ◽  
Joint Invariant

We analyze polymer dynamics in a fractal paradigm. Then, it is shown that polymer dynamics in the form of Schrödinger - type regimes imply synchronization processes of the polymers� structural units, through joint invariant function of two simultaneous isomorphic groups of SL(2R) - type, as solutions of Stoka equations. In this context, period doubling, damped oscillations, self - modulation and chaotic regimes emerge as natural behaviors in the polymer dynamics. The present model can also be applied to a large class of materials, such as biomaterials, biocomposites and other advanced materials.

Miraculous Agitations: On the Uses of Chaotic, Non-Linear and Emergent Behavior in Acoustic Vibrating Physical Systems

2012 ◽  
Vol 22 ◽  
pp. 35-40 ◽  
Author(s):  
Daniel Wilson
Keyword(s):  
Music Composition ◽  
Nonlinear Behavior ◽  
Qualitative Approach ◽  
Emergent Behavior ◽  
New Music ◽  
Physical Systems ◽  
Non Linear ◽  
Subjective Phenomenon

“Miraculous agitation” denotes an acoustic marvel: a striking sound emerging from vibrating physical systems. A somewhat subjective phenomenon, acoustic marvels are typified by expressive or harmonic richness, and their production is reliant on delicate interrelationships between objects under vibration, often involving chaotic or nonlinear behavior. In some cases it is even possible to observe emergent behavior. Significantly, acoustic marvels may commonly strike the auditor as seeming to be “of electronic origin,” thus pointing toward postelectronic electroacoustic techniques. This paper takes a qualitative approach to the examination of such acoustic marvels and their possible applications in new music composition.

Nonlinear Dynamic Analysis on Planetary Gears-Rotor System in Geared Turbofan Engines

2019 ◽  
Vol 29 (06) ◽  
pp. 1950076 ◽  
Author(s):  
Lanlan Hou ◽  
Shuqian Cao
Keyword(s):  
Nonlinear Dynamic Analysis ◽  
Period Doubling ◽  
Nonlinear Behavior ◽  
Rotor System ◽  
Chaotic Motions ◽  
Planetary Gears ◽  
Gear Noise ◽  
Turbofan Engines ◽  
Vibration Responses ◽  
Nonlinear Analytical Model

Rotor fatigue and gear noise triggered by nonlinear vibration are the key concerns in Geared Turbofan (GTF) engine which features a new configuration by introducing planetary gears into low-pressure compressor. A nonlinear analytical model of the GTF planetary gears-rotor system is developed, where the torsional effect of rotor and pivotal parameters from gears are incorporated. The nonlinear behavior of the model can be obtained by focusing on the relative torsional vibration responses between gear and rotor. The torsional nonlinear responses are illustrated with bifurcation diagrams, the largest Lyapunov exponents (LLE), Poincaré maps, phase diagrams and spectrum waterfall. Numerical results reveal that the gears-rotor system exhibits abundant torsional nonlinear behaviors, including multiperiodic, quasi-periodic, and chaotic motions. Furthermore, the roads to chaos via quasi-periodicity, period-doubling scenario, mutation and intermittence are demonstrated. The ring gear stiffness at a low value can propel the system into chaos. The damping may complicate the motion, i.e. the system may enter chaos with increasing damping. These results provide an understanding of undesirable torsional dynamic motion for the GTF engine rotor system and therefore serve as a useful reference for engineers in designing and controlling such system.

scholarly journals Bubble Dynamics in Soft and Biological Matter

2019 ◽  
Vol 51 (1) ◽  
pp. 331-355 ◽  
Author(s):  
Benjamin Dollet ◽  
Philippe Marmottant ◽  
Valeria Garbin
Keyword(s):  
Viscoelastic Medium ◽  
Bubble Dynamics ◽  
Nonlinear Behavior ◽  
Bubble Surface ◽  
Solid Particles ◽  
Advanced Materials ◽  
Viscoelastic Layer ◽  
Future Research ◽  
Oscillatory Dynamics ◽  
Biological Matter

Bubbles are present in a large variety of emerging applications, from advanced materials to biology and medicine, as either laser-generated or acoustically driven bubbles. In these applications, the bubbles undergo oscillatory dynamics and collapse inside—or near—soft and biological materials. The presence of a soft, viscoelastic medium strongly affects the bubble dynamics, both its linear resonance properties and its nonlinear behavior. Surfactant molecules or solid particles adsorbed on a bubble surface can also modify the bubble dynamics through the rheological properties of the interfacial layer. Furthermore, the interaction of bubbles with biological cells and tissues is highly dependent on the mechanical properties of these soft deformable media. This review covers recent developments in bubble dynamics in soft and biological matter for different confinement conditions: bubbles in a viscoelastic medium, coated by a viscoelastic layer, or in the vicinity of soft confinement or objects. The review surveys current work in the field and illustrates open questions for future research.

Non-Linear Description of Floating Ring Bearings Rotordynamics

2005 ◽  
Author(s):  
S. E. Di´az ◽  
R. Castro
Keyword(s):  
Design Process ◽  
Period Doubling ◽  
Trial And Error ◽  
Flexible Rotor ◽  
Manufacturing Costs ◽  
Numerical Characterization ◽  
Linear Description ◽  
Non Linear ◽  
Shaft Flexibility

Floating ring bearings are commonly used in automotive turbochargers for their low manufacturing costs. However, the strong non-linearity of this configuration prevents the use of traditional rotordynamic techniques to describe their behaivior, thus relegating its design process to a costly trial and error process. A numerical characterization of this non-linearity is hereby presented for a flexible rotor supported on two FRBs. Non-linear techniques such as Poincare´ and Bifurcation maps, along with traditional rotordynamic techniques, show ranges of periodic, quasiperiodic, and chaotic motion, being the most stable ones related to high unbalance and/or low speeds, though in some cases the periodicity of the motion is reestablished at higher speeds. In all cases chaos is reached through a period doubling route. Shaft flexibility is shown to retard the occurrence of chaos, while excitation of conical motion seems to favor it.

Nonlinear physical properties of some nonconventional semiconducting Bi–Pb–Ba–O glasses

1998 ◽  
Vol 13 (8) ◽  
pp. 2328-2333
Author(s):  
D. K. Modak ◽  
G. Banerjee ◽  
M. Karar ◽  
M. Sadhukhan ◽  
A. K. Bera ◽  
...  
Keyword(s):  
Glass Matrix ◽  
Glass Network ◽  
Nonlinear Behavior ◽  
Local Instability ◽  
Temperature Dependent ◽  
Structural Units ◽  
Local Ordering ◽  
Fast Quenching ◽  
Heat Capacity Anomaly ◽  
Glass Compositions

Semiconducting Bi1−xPbxBaO3−δ (or BPB) glasses with x = 0 to 0.8 have been prepared by fast quenching from the melt. Interesting anomalies in the temperature-dependent polaronic conductivity and dielectric constant have been observed in all these glass compositions at temperatures, Tp, varying from 310 to 330 K (depending on Pb concentration). This nonlinear behavior is considered to be associated with the local ordering or the displacements of the BiO3 type pyramidal structural units present in the glass matrix (observed from the infrared spectra of these glasses). This type of ordering/displacement gives rise to a local instability in the glass network structure which is also supported by the observed heat capacity anomaly around the same temperatures Tp.

PENDULUM TRACED CURVES AND DAMPED OSCILLATIONS IN THE PLANE

2007 ◽  
Vol 16 (10) ◽  
pp. 1451-1457
Author(s):  
LOUIS H. KAUFFMAN
Keyword(s):  
Linear Model ◽  
Damped Oscillations ◽  
Non Linear

This paper studies a non-linear model for the damped oscillations of a pendulum.

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