Chaos Induced Transition

1997 ◽  
Vol 07 (04) ◽  
pp. 855-867 ◽  
Author(s):  
Toshihiro Shimizu ◽  
Nozomi Morioka
Keyword(s):  
Stationary Distribution ◽  
Logistic Map ◽  
Period Doubling ◽  
Bifurcation Parameter ◽  
Proposed Model ◽  
Linear Harmonic Oscillator ◽  
Small Change ◽  
Intermittent Chaos ◽  
Theoretical Results ◽  
Good Agreement

To study the coherent nature of chaos, two models are proposed. Model 1 is a simple nonlinear system [Formula: see text] and Model 2 is a linear harmonic oscillator [Formula: see text], which are driven by a chaotic force f(t). The chaotic force f(t) is defined by [Formula: see text] for nτ < t ≤ (n + 1)τ(n = 0, 1, 2, …), where yn+1 is a chaotic sequence of a map F(y; r) with the bifurcation parameter r: yn+1 = F(yn; r) (-0.5 ≤ yn ≤ 0.5) and ŷn = yn - < y0>. In Model 1 the relaxation process of this system and the τ- and r-dependence of the stationary distribution of x are discussed. It is shown that the small change of the bifurcation parameter r causes the drastic change of the stationary distribution. In Model 2, resonance phenomena are investigated near the period 3 window of the logistic map, in particular, in the intermittent chaos region and the period doubling region. The theoretical results are shown to be in a good agreement with numerical ones, which have been done for the logistic map as F(y; r).

scholarly journals Dependence of Thermal Shock Crack on Specimen Width for Ceramic Materials

2016 ◽  
Vol 08 (03) ◽  
pp. 1650042
Author(s):  
Xianghong Xu ◽  
Wenjun Yuan ◽  
Cheng Tian
Keyword(s):  
Size Effect ◽  
Thermal Shock ◽  
Crack Depth ◽  
Ceramic Materials ◽  
Elastic Strip ◽  
Modified Model ◽  
Specimen Width ◽  
Proposed Model ◽  
Theoretical Results ◽  
Good Agreement

Knowledge of size effect of thermal shock properties of ceramics is a prerequisite in engineering applications. In the present study, the size effect of the cracking in the ceramic materials subjected to water quenching has been experimentally conducted. Based on the Rizk model, the equivalent specimen width of the elastic strip with cracks is introduced and modified to describe the effect of cracks on the deformation of the elastic strip underwater quenching. It is found that the simulation obtained from the proposed modified model is in good agreement with the experimental results. And the reasons for the size effect of crack depth and crack growth into the compressive region are well analyzed by theoretical results. The proposed model is expected to provide a powerful tool to characterize and predict the size effect on thermal shock crack of ceramic materials.

Analysis of snake rolling force and torque with changes of thickness depending on unequal roll radii based on pure aluminum experiments

2016 ◽  
Vol 231 (1) ◽  
pp. 161-174 ◽  
Author(s):  
HY Wang ◽  
ZH Wang ◽  
DH Zhang ◽  
DW Zhao
Keyword(s):  
Rolling Force ◽  
Pure Aluminum ◽  
Speed Ratio ◽  
Roll Speed ◽  
Equivalent Radius ◽  
Roll Torque ◽  
Offset Distance ◽  
Proposed Model ◽  
Theoretical Results ◽  
Good Agreement

An analytical model, in which unequal radii are replaced with an equivalent radius, is creatively proposed to predict the rolling force and roll torque in general case of snake rolling. With the model, the effects of roll radius ratio, roll speed ratio, offset distance between rolls, reduction and friction coefficient on rolling forces in hot snake rolling of aluminum alloy are obtained. Also, the thicknesses of slab are investigated in different zones, which firstly propose the changes of thickness during snake rolling. Owing to the good agreement with the results measured in experiments and calculated by finite element method and other traditional models, those calculated by the proposed model are verified. The proposed model can be used to predict more accurate theoretical results for snake rolling force and torque.

Period-Doubling and Neimark–Sacker Bifurcations of a Beddington Host-Parasitoid Model with a Host Refuge Effect

2020 ◽  
Vol 30 (16) ◽  
pp. 2050254
Author(s):  
Senada Kalabušić ◽  
Džana Drino ◽  
Esmir Pilav
Keyword(s):  
Growth Rate ◽  
Steady State ◽  
Numerical Simulations ◽  
Period Doubling ◽  
Host Population ◽  
Bifurcation Parameter ◽  
Intrinsic Growth Rate ◽  
Refuge Effect ◽  
Text Model ◽  
Theoretical Results

In this paper, we explore the dynamics of a certain class of Beddington host-parasitoid models, where in each generation a constant portion of hosts is safe from attack by parasitoids, and the Ricker equation governs the host population. Using the intrinsic growth rate of the host population that is not safe from parasitoids as a bifurcation parameter, we prove that the system can either undergo a period-doubling or a Neimark–Sacker bifurcation when the unique interior steady state loses its stability. Then, we apply the new theory to the following well-known cases: May’s model, [Formula: see text]-model, Hassel and Varley (HV)-model, parasitoid-parasitoid (PP) model and [Formula: see text] model. We use numerical simulations to confirm our theoretical results.

Investigating the Nonlinear Optical Response of Pepper Oil under Low Power Irradiation with Continuous Wave Visible Laser Beam

2020 ◽  
pp. 131-138
Keyword(s):  
Refractive Index ◽  
Nonlinear Refractive Index ◽  
Nonlinear Optical ◽  
Continuous Wave ◽  
Diffraction Integral ◽  
Visible Laser ◽  
Limiting Property ◽  
Kirchhoff Diffraction Integral ◽  
Theoretical Results ◽  
Good Agreement

The nonlinear optical properties of pepper oil are studied by diffraction ring patterns and Z-scan techniques with continuous wave beam from solid state laser at 473 nm wavelength. The nonlinear refractive index of the sample is calculated by both techniques. The sample show high nonlinear refractive index. Based on Fresnel-Kirchhoff diffraction integral, the far-field intensity distributions of ring patterns have been calculated. It is found that the experimental results are in good agreement with the theoretical results. Also the optical limiting property of pepper oil is reported. The results obtained in this study prove that the pepper oil has applications in nonlinear optical devices.

scholarly journals Compact Modelling of Electrical, Optical and Thermal Properties of Multi-Colour Power LEDs Operating on a Common PCB

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1286
Author(s):  
Krzysztof Górecki ◽  
Przemysław Ptak
Keyword(s):  
Integrated Circuits ◽  
Optical Model ◽  
Printed Circuit Board ◽  
Circuit Board ◽  
Junction Temperature ◽  
Optical Parameters ◽  
Spice Simulation ◽  
Light Emitting ◽  
Proposed Model ◽  
Good Agreement

This paper concerns the problem of modelling electrical, thermal and optical properties of multi-colour power light-emitting diodes (LEDs) situated on a common PCB (Printed Circuit Board). A new form of electro-thermo-optical model of such power LEDs is proposed in the form of a subcircuit for SPICE (Simulation Program with Integrated Circuits Emphasis). With the use of this model, the currents and voltages of the considered devices, their junction temperature and selected radiometric parameters can be calculated, taking into account self-heating phenomena in each LED and mutual thermal couplings between each pair of the considered devices. The form of the formulated model is described, and a manner of parameter estimation is also proposed. The correctness and usefulness of the proposed model are verified experimentally for six power LEDs emitting light of different colours and mounted on an experimental PCB prepared by the producer of the investigated devices. Verification was performed for the investigated diodes operating alone and together. Good agreement between the results of measurements and computations was obtained. It was also proved that the main thermal and optical parameters of the investigated LEDs depend on a dominant wavelength of the emitted light.

Studies of local structures for Cu2+ centers in M2Zn(SO4)2·6H2O (M = NH4 and Rb) crystals

2021 ◽  
Vol 76 (4) ◽  
pp. 299-304
Author(s):  
Fu Chen ◽  
Jian-Rong Yang ◽  
Zi-Fa Zhou
Keyword(s):  
Crystal Field ◽  
Elongation Ratio ◽  
Paramagnetic Resonance ◽  
Local Structures ◽  
Epr Parameters ◽  
Structure Constants ◽  
Crystal Field Parameters ◽  
Electron Paramagnetic ◽  
Theoretical Results ◽  
Good Agreement

Abstract The electron paramagnetic resonance (EPR) parameters (g factor g i , and hyperfine structure constants A i , with i = x, y, z) and local structures for Cu2+ centers in M2Zn(SO4)2·6H2O (M = NH4 and Rb) are theoretically investigated using the high order perturbation formulas of these EPR parameters for a 3d 9 ion under orthorhombically elongated octahedra. In the calculations, contribution to these EPR parameters due to the admixture of d-orbitals in the ground state wave function of the Cu2+ ion are taken into account based on the cluster approach, and the required crystal-field parameters are estimated from the superposition model which enables correlation of the crystal-field parameters and hence the studied EPR parameters with the local structures of the Cu2+ centers. Based on the calculations, the Cu–H2O bonds are found to suffer the axial elongation ratio δ of about 3 and 2.9% along the z-axis, meanwhile, the planar bond lengths may experience variation ratio τ (≈3.8 and 1%) along x- and y-axis for Cu2+ center in (NH4)2Zn(SO4)2·6H2O and Rb2Zn(SO4)2·6H2O, respectively. The theoretical results show good agreement with the observed values.

Static and Dynamic Structure of Molecular Monomers and Dimers of the Rare-earth Fluorides

2001 ◽  
Vol 56 (5) ◽  
pp. 381-385
Author(s):  
Z. Akdeniz ◽  
M . Gaune-Escard ◽  
M. P. Tosi
Keyword(s):  
Rare Earth ◽  
Bond Length ◽  
Geometrical Structure ◽  
Vibrational Mode ◽  
Dynamic Structure ◽  
Molecular Shape ◽  
Proposed Model ◽  
Infrared Studies ◽  
Charged Clusters ◽  
Good Agreement

Abstract We determine a model of the ionic interactions in RF3 compounds, where R is a rare-earth element in the series from La to Lu, by an analysis of data on the bond length and the vibrational mode frequencies of the PrF3, GdF3 and HoF3 molecular monomers. All RF3 monomers are predicted to have a pyramidal shape, displaying a progressive flattening of the molecular shape in parallel with the lanthanide contraction of the bond length. The vibrational frequencies of all monomers are calculated, the results being in good agreement with the data from infrared studies of matrix-isolated molecules. We also evaluate the geometrical structure and the vibrational spectrum of the La2F6 and Ce2F6 dimers, as a further test of the proposed model. -PACS 36.40.Wa (Charged clusters)

On the Flow Fields of Inertial Impactors

1974 ◽  
Vol 96 (4) ◽  
pp. 394-400 ◽  
Author(s):  
V. A. Marple ◽  
B. Y. H. Liu ◽  
K. T. Whitby
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Relaxation Method ◽  
Water Model ◽  
Navier Stokes ◽  
Visualization Technique ◽  
Navier Stokes Equations ◽  
Theoretical Results ◽  
Plate Distance ◽  
Good Agreement

The flow field in an inertial impactor was studied experimentally with a water model by means of a flow visualization technique. The influence of such parameters as Reynolds number and jet-to-plate distance on the flow field was determined. The Navier-Stokes equations describing the laminar flow field in the impactor were solved numerically by means of a finite difference relaxation method. The theoretical results were found to be in good agreement with the empirical observations made with the water model.

scholarly journals Rate Equation Modelling of Nonlinear Dynamics in Directly Modulated Multiple Quantum Well Laser Diodes

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 355-360 ◽  
Author(s):  
Stephen Bennett ◽  
Christopher M. Snowden ◽  
Stavros Iezekiel
Keyword(s):  
Nonlinear Dynamics ◽  
Quantum Well ◽  
Multiple Quantum Well ◽  
Period Doubling ◽  
Rate Equations ◽  
Multiple Quantum ◽  
Quantum Well Laser ◽  
Wide Range ◽  
Multiple Quantum Well Laser ◽  
Good Agreement

A theoretical (using rate equations) and experimental study of the nonlinear dynamics of a distributed feedback multiple quantum well laser diode is presented. The analysis is performed under direct modulation. Period doubling and period tripling are identified in both the measurements and simulations. Period doubling is found over a wide range of modulation frequencies in the laser. Computational results using rate equations show good agreement with the experimental results.

Explanation of the Influence of Inflow Air Content on the Lift of Cavitating Hydrofoils

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Eduard Amromin
Keyword(s):  
Experimental Data ◽  
Theoretical Study ◽  
Lift Coefficient ◽  
Cavity Surface ◽  
Air Bubbles ◽  
Incoming Flow ◽  
Fluid Density ◽  
Air Content ◽  
Theoretical Results ◽  
Good Agreement

According to several known experiments, an increase of the incoming flow air content can increase the hydrofoil lift coefficient. The presented theoretical study shows that such increase is associated with the decrease of the fluid density at the cavity surface. This decrease is caused by entrainment of air bubbles to the cavity from the surrounding flow. The theoretical results based on such explanation are in a good agreement with the earlier published experimental data for NACA0015.

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