scholarly journals Qualitative analysis of the response regimes and triggering mechanism of bistable NES

2021 ◽  
Author(s):  
Zhenhang WU ◽  
Sébastien Seguy ◽  
Manuel Paredes
Keyword(s):  
Energy Levels ◽  
Harmonic Excitation ◽  
Stable Phase ◽  
Excitation Threshold ◽  
Triggering Mechanism ◽  
Numerical Result ◽  
Phase Cycle ◽  
Frequency Domains ◽  
Analytical Result ◽  
Threshold Line

Abstract The main focus of this study is the development of an adapted complex variable method in the vicinity of equilibrium in bistable NES. A simplified chaos trigger model is established to describe the distance between the stable phase cycle and the pseudo-separatrix. An analytical expression can predict the excitation threshold for chaos occurrence. The relative positions between the chaos trigger threshold line and the Slow Invariant Manifold (SIM) structure can express the distribution of response regimes under growing harmonic excitation. This topological structure implies the alternation of the response regime and helps to classify the bistable NES. The experiment compares the analytical result of intra-well oscillation with the numerical result in the frequency domain. The experimental response regimes under different input energy levels and frequency domains have been observed and give ideas to guide the optimal design of a bistable NES. It is shown that the modest bistable NES possesses strong robustness to frequency perturbation.

scholarly journals Basic Constraints for Design Optimization of Cubic and Bistable NES

2021 ◽  
pp. 1-51
Author(s):  
Zhenhang Wu ◽  
Sebastien Seguy ◽  
Manuel Paredes
Keyword(s):  
Multiple Scales ◽  
Energy Levels ◽  
Conservative System ◽  
Harmonic Excitation ◽  
Absorption Efficiency ◽  
Complex Variables ◽  
Maximum Efficiency ◽  
Nonlinear Stiffness ◽  
Optimal Efficiency ◽  
Different Response

Abstract This work mainly concentrates on the optimization of cubic and bistable NES to find the maximum efficiency point under harmonic excitation. The conservative system is considered to reveal the inner property of the damping system. With the application of the multiple scales method and the complex variables method, the threshold of excitation and different response regimes are distinguished under the assumption of 1:1 resonance. The maximum efficiency point of cubic and bistable NES occurs when SMR disappears. The factors that affect the optimal efficiency limit are explored. The result indicates that the maximum absorption efficiency level is mainly determined by the damping parameters. Compared with the cubic case, the bistable case involves more complex regimes in terms of chaos oscillation. The influence of damping parameters on the chaos threshold is discussed to adopt different energy levels. With the help of analytical predictions, the proper nonlinear stiffness is determined for certain harmonic excitation. This work offers some fundamental insights into the optimal design of cubic and bistable NES.

scholarly journals Classification of the 5p5nln'l' LSJ energy levels of Cs excited by 30 eV electrons

2015 ◽  
Vol 55 (2) ◽  
Author(s):  
Gintaras Kerevičius ◽  
Alicija Kupliauskienė
Keyword(s):  
Cross Sections ◽  
Electron Spectrum ◽  
Large Scale ◽  
Energy Levels ◽  
Coupling Scheme ◽  
Excitation Threshold ◽  
Angular Momenta ◽  
Excitation Cross Sections ◽  
Configuration Interaction Calculations

Theoretical investigation of the 5p5 nl(L1S1)n'l' LSJ autoionizing states of Cs was performed by using large scale configuration interaction calculations of energy levels, autoionization probabilities and excitation cross sections obtained in the Dirac–Fock–Slater approximation. Classification of calculated energy levels in the LSJ coupling scheme of angular momenta and simulation of the intensities of ejected Auger electron spectrum were performed. The classified energy levels in the region from the excitation threshold up to 17.365 eV and simulated intensity spectrum were used for identification of the experimental ejected-electron spectrum of Cs excited by 30 eV electrons.

scholarly journals Electron Impact Excitation of Extreme Ultra-Violet Transitions in Xe7+ – Xe10+ Ions

Atoms ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 76
Author(s):  
Aloka Kumar Sahoo ◽  
Lalita Sharma
Keyword(s):  
Electron Impact ◽  
Electron Energy ◽  
Cross Sections ◽  
Energy Levels ◽  
Ultra Violet ◽  
High Energy ◽  
Impact Excitation ◽  
Rate Coefficients ◽  
Electron Impact Excitation ◽  
Excitation Threshold

In the present work, a detailed study on the electron impact excitation of Xe7+, Xe8+, Xe9+ and Xe10+ ions for the dipole allowed (E1) transitions in the EUV range of 8–19 nm is presented. The multi-configuration Dirac–Fock method is used for the atomic structure calculation including the Breit and QED corrections along with the relativistic configuration interaction approach. We have compared our calculated energy levels, wavelengths and transition rates with other reported experimental and theoretical results. Further, the relativistic distorted wave method is used to calculate the cross sections from the excitation threshold to 3000 eV electron energy. For plasma physics applications, we have reported the fitting parameters of these cross sections using two different formulae for low and high energy ranges. The rate coefficients are also obtained using our calculated cross sections and considering the Maxwellian electron energy distribution function in the electron temperature range from 5 eV to 100 eV.

scholarly journals Synchronization Transition and Traffic Congestion in One-Dimensional Traffic Model

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Zhi Xin ◽  
Jian Xu
Keyword(s):  
Reaction Time ◽  
Traffic Congestion ◽  
Kdv Equation ◽  
Density Wave ◽  
Car Following ◽  
Synchronization Transition ◽  
Numerical Result ◽  
Analytical Criterion ◽  
Car Following Model ◽  
Analytical Result

A nonlinear car-following model with driver’s reaction time is studied from the synchronization transition viewpoint. We investigate the traffic congestion from the view of chaos system synchronization transition. Our result shows that the uniform flow corresponds to the complete synchronization and the stop-and-go congested state corresponds to the lag synchronization of the vehicles. An analytical criterion for synchronization manifolds stability is obtained; the analytical result and the numerical result are consistent. The synchronization transition is also trigged by the driver’s reaction time. We analyze the car-following model by the use of the nonlinear analysis method and derive the modified KdV equation describing the kink density wave.

scholarly journals Knots and Numbers in ϕ4 Theory to 7 Loops and Beyond

1995 ◽  
Vol 06 (04) ◽  
pp. 519-524 ◽  
Author(s):  
D.J. BROADHURST ◽  
D. KREIMER
Keyword(s):  
Knot Theory ◽  
Catalan Numbers ◽  
Transcendental Number ◽  
Numerical Result ◽  
Multiple Precision ◽  
Intensive Use ◽  
Satellite Knot ◽  
Analytical Result ◽  
Β Function ◽  
O 10

We evaluate all the primitive divergences contributing to the 7-loop β-function of ɸ4 theory, i.e. all 59 diagrams that are free of subdivergences and hence give scheme-independent contributions. Guided by the association of diagrams with knots, we obtain analytical results for 56 diagrams. The remaining three diagrams, associated with the knots 10124, 10139, and 10152, are evaluated numerically, to 10 sf. Only one satellite knot with 11 crossings is encountered and the transcendental number associated with it is found. Thus we achieve an analytical result for the 6-loop contributions, and a numerical result at 7 loops that is accurate to one part in 1011. The series of ‘zig-zag’ counterterms, [Formula: see text], previously known for n=3, 4, 5, 6 loops, is evaluated to 10 loops, corresponding to 17 crossings, revealing that the n-loop zig-zag term is [Formula: see text], where [Formula: see text] are the Catalan numbers, familiar in knot theory. The investigations reported here entailed intensive use of REDUCE, to generate O(104) lines of code for multiple precision FORTRAN computations, enabled by Bailey’s MPFUN routines, running for O(103) CPUhours on DecAlpha machines.

scholarly journals A Theoretical Model of Corruption Using Modified Lotka Volterra Model: A Perspective of Interactions between Staff and Students

2020 ◽  
pp. 12-25
Author(s):  
Mercy Kawira ◽  
Cyrus Gitonga Ngari ◽  
Stephen Karanja
Keyword(s):  
Real Life ◽  
Real Data ◽  
Political Stability ◽  
Steady States ◽  
Volterra Model ◽  
Numerical Result ◽  
Institutions Of Higher Learning ◽  
Numerical Bifurcation ◽  
Analytical Result ◽  
Life Phenomena

Corruption is the misuse of power or resources for private gain. This undermines economic development, political stability, and government legitimacy, the society fabric, allocation of resources to sectors crucial for development, and encourages and perpetuates other illegal opportunities. Despite Mathematical modeling being a powerful tool in describing real life phenomena it still remains unexploited in the fight of corruption menace. This study uses Lotka Volterra, predator-prey equations to develop a model to describe corruption in institutions of higher learning, use the developed model to determine its equilibria, determine the condition for stability of the equilibria and finally carry out the simulation. The corrupt students and staff act as predators while their non-corrupt counterparts act as prey in the paper. Theory of ordinary differential equations was used to determine steady states and their stability. Mathematica was used for algebraic analysis and Matlab was used for numerical analysis and simulation. Analytical result suggested multiple steady state however numerical result confirmed that the model has four steady states. Numerical bifurcation analysis suggests the possibility of backward of corrupt staff when  is about 39. Numerical simulation points to an increasing trend on corrupt staff and decrease trend on corrupt student. This study concludes that more focus should be put to staff than students in curbing the spread of corruption. Future study should strive to fit this model in real data.

scholarly journals Controlling Optical Bistability in a Five-level Cascade EIT Medium

2016 ◽  
Vol 26 (1) ◽  
pp. 33
Author(s):  
Phan Van Thuan ◽  
Ta Tram Anh ◽  
Le Canh Trung ◽  
Nguyen Tien Dung ◽  
Luong Thi Yen Nga ◽  
...  
Keyword(s):  
Analytical Model ◽  
Optical Bistability ◽  
Electromagnetically Induced Transparency ◽  
Ring Cavity ◽  
Probe Laser ◽  
Switching Threshold ◽  
Numerical Result ◽  
Analytical Result ◽  
Induced Transparency

Optical bistability (OB) of an electromagnetically induced transparency (EIT) medium placed in a conventional unidirectional ring cavity is investigated numerically. The medium is excited by a coupling and probe laser lights via a five-level cascade scheme. It is shown that optical bistabe states with controllable switching threshold intensities and width are established simultaneously in three spectral regions corresponding to EIT windows. The current numerical result is compared to a previous analytical result showing influence of coherence terms neglected in the analytical model.

A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

Characterization of Coherent, Ordered Precipitates in Nickel-Base Alloys

1973 ◽  
Vol 31 ◽  
pp. 144-145
Author(s):  
B. H. Kear ◽  
J. M. Oblak
Keyword(s):  
Stable Phase ◽  
Nickel Base Superalloy ◽  
Alloy 718 ◽  
Commercial Alloy ◽  
Precipitate Morphology ◽  
Continuous Precipitation ◽  
Nickel Base ◽  
Base Superalloy ◽  
Strengthening Precipitate

A nickel-base superalloy is essentially a Ni/Cr solid solution hardened by additions of Al (Ti, Nb, etc.) to precipitate a coherent, ordered phase. In most commercial alloy systems, e.g. B-1900, IN-100 and Mar-M200, the stable precipitate is Ni3 (Al,Ti) γ′, with an LI2structure. In A lloy 901 the normal precipitate is metastable Nis Ti3 γ′ ; the stable phase is a hexagonal Do2 4 structure. In Alloy 718 the strengthening precipitate is metastable γ″, which has a body-centered tetragonal D022 structure.Precipitate MorphologyIn most systems the ordered γ′ phase forms by a continuous precipitation re-action, which gives rise to a uniform intragranular dispersion of precipitate particles. For zero γ/γ′ misfit, the γ′ precipitates assume a spheroidal.

Lorentz microscopy study of magnetic domain walls in Fe-Cr-Co alloys

1978 ◽  
Vol 36 (1) ◽  
pp. 462-463
Author(s):  
Yalcin Belli
Keyword(s):  
Domain Walls ◽  
Magnetic Domain ◽  
Microscopy Study ◽  
Ferromagnetic Phase ◽  
Stable Phase ◽  
Magnetic Domains ◽  
Lorentz Microscopy ◽  
Magnetic Hardening ◽  
Electron Microscopes ◽  
Co Alloys

Fe-Cr-Co alloys have great technological potential to replace Alnico alloys as hard magnets. The relationship between the microstructures and the magnetic properties has been recently established for some of these alloys. The magnetic hardening has been attributed to the decomposition of the high temperature stable phase (α) into an elongated Fe-rich ferromagnetic phase (α1) and a weakly magnetic or non-magnetic Cr-rich phase (α2). The relationships between magnetic domains and domain walls and these different phases are yet to be understood. The TEM has been used to ascertain the mechanism of magnetic hardening for the first time in these alloys. The present paper describes the magnetic domain structure and the magnetization reversal processes in some of these multiphase materials. Microstructures to change properties resulting from, (i) isothermal aging, (ii) thermomagnetic treatment (TMT) and (iii) TMT + stepaging have been chosen for this investigation. The Jem-7A and Philips EM-301 transmission electron microscopes operating at 100 kV have been used for the Lorentz microscopy study of the magnetic domains and their interactions with the finely dispersed precipitate phases.

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