scholarly journals Coupled-Oscillators

1993 ◽  
Vol 134 ◽  
pp. 333-341
Author(s):  
Y. Tanaka
Keyword(s):  
Coupled Oscillators ◽  
Phase Locking ◽  
Period Doubling ◽  
Second Order ◽  
Coupling Constants ◽  
Stellar Structure ◽  
Radial Pulsation ◽  
Third Order ◽  
Period Ratio ◽  
Dissipation Term

AbstractModal coupling oscillation models for the stellar radial pulsation and coupled-oscillators are reviewed. Coupled-oscillators with the second-order and third-order terms seemed to behave non-systematically. Using the equation by Schwarzschild and Savedoff (1949) with the dissipation term of van del Pol’s type which is third-order, we demonstrate the effect of each term. The effects can be understood by the terms of the nonlinear dynamics, which is recently developing, that is. phase-locking, quasi-periodicity, period doubling, and chaos. As the problem of stellar pulsation, especially of double-mode cepheids on the period-ratio, we examine the dependence on the stellar structure from which the coupling constants in the second-order terms are derived. Eigen functions for adiabatic pulsations had been used for the calculation of the constants. It is noted that only two set of the constants are available, that is, for the polytrope model with n = 3 and a cepheid model without convection. Some examples of nonlinear dynamical effects will be shown.It is shown that if the constants were suitable values, the period-ratio of double-mode cepheids is probably realized. The possibility is briefly suggested.

Bulk Contributions Modulate the Sum-Frequency Generation Spectra of Interfacial Water on Model Sea-Spray Aerosols

2018 ◽  
Author(s):  
Sandeep K. Reddy ◽  
Raphael Thiraux ◽  
Bethany A. Wellen Rudd ◽  
Lu Lin ◽  
Tehseen Adel ◽  
...  
Keyword(s):  
Single Layer ◽  
Sum Frequency Generation ◽  
Second Order ◽  
Interfacial Structure ◽  
Sea Spray ◽  
Third Order ◽  
Systematic Analysis ◽  
Sum Frequency ◽  
Structure Of Water ◽  
Frequency Generation

Vibrational sum-frequency generation (vSFG) spectroscopy is used to determine the molecular structure of water at the interface of palmitic acid monolayers. Both measured and calculated spectra display speci c features due to third-order contributions to the vSFG response which are associated with nite interfacial electric potentials. We demonstrate that theoretical modeling enables to separate the third-order contributions, thus allowing for a systematic analysis of the strictly surface-sensitive, second-order component of the vSFG response. This study provides fundamental, molecular-level insights into the interfacial structure of water in a neutral surfactant system with relevance to single layer bio-membranes and environmentally relevant sea-spray aerosols. These results emphasize the key role that computer simulations can play in interpreting vSFG spectra and revealing microscopic details of water at complex interfaces, which can be difficult to extract from experiments due to the mixing of second-order, surface-sensitive and third-order, bulk-dependent contributions to the vSFG response.

Evidence for general base catalysis by protic solvents in a kinetic study of alcoholyses and hydrolyses of 1-(phenoxycarbonyl)pyridinium ions under both solvolytic and non-solvolytic conditions

2009 ◽  
Vol 74 (1) ◽  
pp. 43-55 ◽  
Author(s):  
Dennis N. Kevill ◽  
Byoung-Chun Park ◽  
Jin Burm Kyong
Keyword(s):  
Second Order ◽  
Base Catalysis ◽  
Substitution Reactions ◽  
Third Order ◽  
Methoxy Derivative ◽  
First Order ◽  
General Base ◽  
Protic Solvents ◽  
Kinetics Of ◽  
Pyridinium Ions

The kinetics of nucleophilic substitution reactions of 1-(phenoxycarbonyl)pyridinium ions, prepared with the essentially non-nucleophilic/non-basic fluoroborate as the counterion, have been studied using up to 1.60 M methanol in acetonitrile as solvent and under solvolytic conditions in 2,2,2-trifluoroethan-1-ol (TFE) and its mixtures with water. Under the non- solvolytic conditions, the parent and three pyridine-ring-substituted derivatives were studied. Both second-order (first-order in methanol) and third-order (second-order in methanol) kinetic contributions were observed. In the solvolysis studies, since solvent ionizing power values were almost constant over the range of aqueous TFE studied, a Grunwald–Winstein equation treatment of the specific rates of solvolysis for the parent and the 4-methoxy derivative could be carried out in terms of variations in solvent nucleophilicity, and an appreciable sensitivity to changes in solvent nucleophilicity was found.

Investigation of zirconium nanowire by elastic, thermal and ultrasonic analysis

2020 ◽  
Vol 75 (12) ◽  
pp. 1077-1084
Author(s):  
Bhawan Jyoti ◽  
Shakti Pratap Singh ◽  
Mohit Gupta ◽  
Sudhanshu Tripathi ◽  
Devraj Singh ◽  
...  
Keyword(s):  
Ultrasonic Attenuation ◽  
Thermal Relaxation ◽  
Coupling Constants ◽  
Physical Parameters ◽  
Third Order ◽  
Jones Potential ◽  
Acoustic Coupling ◽  
Anisotropic Factor ◽  
Third Order Elastic Constants ◽  
Ultrasonic Analysis

AbstractThe elastic, thermal and ultrasonic properties of zirconium nanowire (Zr-NW) have been investigated at room temperature. The second and third order elastic constants (SOECs and TOECs) of Zr-NW have been figured out using the Lennard–Jones Potential model. SOECs have been used to find out the Young’s modulus, bulk modulus, shear modulus, Poisson’s ratio, Pugh’s ratio, Zener anisotropic factor and ultrasonic velocities. Further these associated parameters of Zr-NW have been utilized for the evaluation of the Grüneisen parameters, thermal conductivity, thermal relaxation time, acoustic coupling constants and ultrasonic attenuation. On the basis of the above analyzed properties of Zr-NW, some characteristics features of the chosen nanowire connected with ultrasonic and thermo-physical parameters have been discussed.

Panicle, spikelet, and floret development in orchardgrass (Dactylis glomerata)

1993 ◽  
Vol 71 (4) ◽  
pp. 523-532 ◽  
Author(s):  
Joanna Fraser ◽  
Eric G. Kokko
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Unique Feature ◽  
Dactylis Glomerata ◽  
Bilateral Symmetry ◽  
Second Order ◽  
Third Order ◽  
First Order ◽  
Lateral Branches ◽  
Scanning Electron

The initial stages of panicle, spikelet, and floret development in field-grown 'Kay' orchardgrass were examined using scanning electron microscopy. Spikelets arose from a complex multilevelled sequence of initiation from branch apices. Spikelets developed indirectly in a two-tiered progression: (i) an acropetal and basipetal sequence of first order, second-order, and third-order inflorescence apices, and (ii) an acropetal development within subclusters of higher-order lateral branch inflorescence apices. The panicle had the unique feature of dorsiventrality as well as bilateral symmetry. The basal apex from first-order, second-order, or third-order apices developed on the same side of the main axis as the first-order apex. The two glumes subtending each spikelet primordium developed alternately and acropetally. Development and initiation of florets within spikelets was basipetal within the panicle, basipetal within clusters and subclusters of spikelets on lateral branches, and acropetal within spikelets. Within florets, paleas developed later than lemmas. Key words: Dactylis glomerata, cocksfoot, scanning electron microscopy, development, panicle.

COMPLEX DYNAMICS AND FAST-SLOW SCALE INSTABILITY IN CURRENT-MODE CONTROLLED BUCK CONVERTER WITH CONSTANT CURRENT LOAD

2013 ◽  
Vol 23 (04) ◽  
pp. 1350062 ◽  
Author(s):  
GUOHUA ZHOU ◽  
BOCHENG BAO ◽  
JIANPING XU
Keyword(s):  
Complex Dynamics ◽  
Period Doubling ◽  
Current Mode ◽  
Input Voltage ◽  
Second Order ◽  
Buck Converter ◽  
Constant Current ◽  
Current Load ◽  
Time Model ◽  
Conduction Mode

The complex dynamics and coexisting fast-slow scale instability in current-mode controlled buck converter with constant current load (CCL), operating in both continuous conduction mode (CCM) and discontinuous conduction mode (DCM), are investigated in this paper. Via cycle-by-cycle computer simulation and experimental measurement of current-mode controlled buck converter with CCL, it is found that a unique fast-slow scale instability exists in the second-order switching converter. It is also found that a unique period-doubling accompanied by Neimark–Sacker bifurcation exists in this simple second-order converter, which is different from period-doubling or Neimark–Sacker bifurcations reported previously. Based on a nonlinear discrete-time model and the corresponding Jacobian, the effects of CCL and input voltage on the dynamics of current-mode controlled buck converter are investigated and verified theoretically. Fixed point analysis for slow-scale low-frequency oscillation is also given to verify the dynamics and the coexisting fast-slow scale instability.

Second Order Averaging Study of an Autoparametric System

1993 ◽  
Author(s):  
Bappaditya Banerjee ◽  
Anil K. Bajaj ◽  
Patricia Davies
Keyword(s):  
Dynamical Behavior ◽  
Period Doubling ◽  
Nonlinear Effects ◽  
Single Mode ◽  
Pitchfork Bifurcation ◽  
Second Order ◽  
System Response ◽  
Response Curves ◽  
Vibratory System ◽  
First Order

Abstract The autoparametric vibratory system consisting of a primary spring-mass-dashpot system coupled with a damped simple pendulum serves as an useful example of two degree-of-freedom nonlinear systems that exhibit complex dynamic behavior. It exhibits 1:2 internal resonance and amplitude modulated chaos under harmonic forcing conditions. First-order averaging studies of this system using AUTO and KAOS have yielded useful information about the amplitude dynamics of this system. Response curves of the system indicate saturation and the pitchfork bifurcation sets are found to be symmetric. The period-doubling route to chaotic solutions is observed. However questions about the range of the small parameter ε (a function of the forcing amplitude) for which the solutions are valid cannot be answered by a first-order study. Some observed dynamical behavior, like saturation, may not persist when higher-order nonlinear effects are taken into account. Second-order averaging of the system, using Mathematica (Maeder, 1991; Wolfram, 1991) is undertaken to address these questions. Loss of saturation is observed in the steady-state amplitude responses. The breaking of symmetry in the various bifurcation sets becomes apparent as a consequence of ε appearing in the averaged equations. The dynamics of the system is found to be very sensitive to damping, with extremely complicated behavior arising for low values of damping. For large ε second-order averaging predicts additional Pitchfork and Hopf bifurcation points in the single-mode response.

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