Theoretical analysis of the high-order irradiance moments of light waves observed in turbulent air

1982 ◽  
Vol 72 (6) ◽  
pp. 760 ◽  
Author(s):  
Shigeo Ito ◽  
K. Furutsu
Keyword(s):  
Theoretical Analysis ◽  
High Order ◽  
Light Waves

scholarly journals Phyllotaxis instability – exploring the depths of first available space

2011 ◽  
Vol 80 (4) ◽  
pp. 279-284 ◽  
Author(s):  
Marcin Szpak ◽  
Beata Zagórska-Marek
Keyword(s):  
Theoretical Analysis ◽  
Computer Simulations ◽  
Dominant Role ◽  
High Order ◽  
The Other ◽  
Phyllotactic Pattern ◽  
Low Order

The theoretical analysis of the consequences of the phyllotactic pattern being propagated according to the first available space rule has revealed that all monojugate patterns, with the exception of the main Fibonacci pattern, should become developmentally unstable in their low expressions. This fact explains why the main Fibonacci pattern plays the dominant role among other patterns of spiral phyllotaxis. The probability that the pattern becomes unstable varies for different patterns, which likely makes them more or less frequent, and thus easier or more difficult to encounter in nature. The unstable pattern inevitably transforms into another, as the computer simulations show. Theoretically predicted instability of low order phyllotaxis may be treated as one of the causes of natural ontogenetic transitions, occurring in plants. This, however, still does not explain why in nature some patterns with high order of phyllotaxis also change, quite readily one into the other, in shoot apical meristem’s ontogeny.

Nonlinear resonant interactions of interfacial waves in horizontal stratified channel flows

2013 ◽  
Vol 717 ◽  
pp. 612-642 ◽  
Author(s):  
Bryce K. Campbell ◽  
Yuming Liu
Keyword(s):  
Theoretical Analysis ◽  
Evolution Equations ◽  
Multiple Scales ◽  
High Order ◽  
Base Flow ◽  
Interfacial Instability ◽  
Unstable Wave ◽  
Interfacial Waves ◽  
Resonant Interactions ◽  
Long Wave

AbstractWe consider the problem of nonlinear resonant interactions of interfacial waves with the presence of a linear interfacial instability in an inviscid two-fluid stratified flow through a horizontal channel. The resonant triad consists of a (linearly) unstable wave and two stable waves, one of which has a wavelength that can be much longer than that of the unstable component. Of special interest is the development of the long wave by energy transfer from the base flow due to the coupled effect of nonlinear resonance and interfacial instability. By use of the method of multiple scales, we derive the interaction equations which govern the time evolution of the amplitudes of the interacting waves including the effect of interfacial instability. The solution of the evolution equations shows that depending on the flow conditions, the (stable) long wave can achieve a bi-exponential growth rate through the resonant interaction with the unstable wave. Moreover, the unstable wave can grow unboundedly even when the nonlinear self-interaction effect is included, as do the stable waves in the associated resonant triad. For the verification of the theoretical analysis and the practical application involving a broadbanded spectrum of waves, we develop an effective direct simulation method, based on a high-order pseudo-spectral approach, which accounts for nonlinear interactions of interfacial waves up to an arbitrary high order. The direct numerical simulations compare well with the theoretical analysis for all of the characteristic flows considered, and agree qualitatively with the experimental observation of slug development near the entrance of two-phase flow into a pipe.

scholarly journals GENERATION OF POLARIZATION SQUEEZED LIGHT IN PPNC

2003 ◽  
Vol 01 (03) ◽  
pp. 403-416 ◽  
Author(s):  
V. G. DMITRIEV ◽  
R. SINGH
Keyword(s):  
Theoretical Analysis ◽  
Quantum State ◽  
Nonlinear Crystal ◽  
Stokes Parameters ◽  
Periodically Poled ◽  
Squeezed Light ◽  
Light Waves ◽  
State Evolution

Theoretical analysis is presented on quantum state evolution of polarization light waves at frequencies ωo and ωe in a periodically poled nonlinear crystal (PPNC). It is shown that the variances of all the four Stokes parameters can be squeezed.

Theoretical analysis of high order harmonic generation from bulk crystals

2013 ◽  
Author(s):  
Giulio Vampa ◽  
Chris R. McDonald ◽  
Gianfranco Orlando ◽  
Dennis D. Klug ◽  
Paul B. Corkum ◽  
...  
Keyword(s):  
Theoretical Analysis ◽  
Harmonic Generation ◽  
High Order ◽  
Bulk Crystals ◽  
High Order Harmonic Generation ◽  
High Order Harmonic

scholarly journals Consensus Control of Time-Varying Delayed Multiagent Systems with High-Order Iterative Learning Control

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Xiongfeng Deng ◽  
Xiuxia Sun ◽  
Ri Liu ◽  
Shuguang Liu
Keyword(s):  
Theoretical Analysis ◽  
Multiagent Systems ◽  
Iterative Learning Control ◽  
Learning Control ◽  
Iterative Learning ◽  
High Order ◽  
Time Varying ◽  
Tracking Errors ◽  
Consensus Control ◽  
Control Protocol

We address the consensus control problem of time-varying delayed multiagent systems with directed communication topology. The model of each agent includes time-varying nonlinear dynamic and external disturbance, where the time-varying nonlinear term satisfies the global Lipschitz condition and the disturbance term satisfies norm-bounded condition. An improved control protocol, that is, a high-order iterative learning control scheme, is applied to cope with consensus tracking problem, where the desired trajectory is generated by a virtual leader agent. Through theoretical analysis, the improved control protocol guarantees that the tracking errors converge asymptotically to a sufficiently small interval under the given convergence conditions. Furthermore, the bounds of initial state difference and disturbances tend to zero; the bound of tracking errors also tends to zero. In the end, some cases are provided to illustrate the effectiveness of the theoretical analysis.

Theoretical Analysis and Engineering Implications for the High Order Term Solutions of the Mode II Type Creep Crack

2017 ◽  
Author(s):  
Yanwei Dai ◽  
Yinghua Liu ◽  
Yuh J. Chao
Keyword(s):  
Theoretical Analysis ◽  
Plane Strain ◽  
Order Term ◽  
Crack Tip ◽  
High Order ◽  
High Order Term ◽  
Mode I ◽  
Mode Ii ◽  
Mode I Crack ◽  
Creep Crack

The high order term (HOT) solutions of crack tip field should be taken into account in engineering applications due to their potential influences on the fracture toughness as well as the crack growth rate. Towards this end, the high order asymptotic analysis of mode II crack in a power-law creeping material under the plane strain condition is presented theoretically in this paper. By comparing among the three order term solution, HRR field and finite element calculations, it can be found that the proposed three order term solution is able to characterize the full field of mode II creep crack tip accurately. The high order term solution of mode II creep crack relies on the creep exponent, which is different from that of mode I crack case. There are two independent terms among these three terms of asymptotic solution for mode II creep crack, which indicates that there exists the constraint effect for the plane strain mode II creep crack though the effect of high order term may not be as significant as the mode I crack case. Based on the theoretical analysis, a modified time-dependent failure assessment diagram (TDFAD) for mode II creep crack is proposed by considering the high order term solution.

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