scholarly journals Measuring α-FPUT Cores and Tails

Physics ◽  
2021 ◽  
Vol 3 (4) ◽  
pp. 879-887
Author(s):  
Sergej Flach
Keyword(s):  
Normal Mode ◽  
Normal Modes ◽  
Numerical Data ◽  
One Dimensional ◽  
The Core ◽  
Long Time ◽  
Good Agreement

Almost 70 years ago, the Fermi–Pasta–Ulam–Tsingou (FPUT) paradox was formulated in, observed in, and reported using normal modes of a nonlinear, one-dimensional, non-integrable string. Let us recap the paradox. One normal mode is excited, which drives three or four more normal modes in the core. Then, that is it for quite a long time. So why are many normal modes staying weakly excited in the tail? Furthermore, how many? A quantitative, analytical answer to the latter question is given here using resonances and secular avalanches A comparison with the previous numerical data is made and extremely good agreement is found.

scholarly journals Some Improvements in a Gas Turbine Stator-Rotor Systems Core-Swirl Ratio Correlation

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
R. Da Soghe ◽  
B. Facchini ◽  
L. Innocenti ◽  
M. Micio
Keyword(s):  
Swirl Ratio ◽  
Rotating Fluid ◽  
One Dimensional ◽  
Rotor Systems ◽  
Solid Body Rotation ◽  
The Core ◽  
Turbine Stator ◽  
Experimental Correlation ◽  
Ratio Correlation ◽  
Good Agreement

The present work concerns the turbulent flow inside a rotor-stator cavity with superimposed throughflow. The authors focused their analysis on a simple two-faced disk cavity, without shrouds, with interdisk-spacing sufficiently large so that the boundary layers developed on each disk are separated and the flow is turbulent. In such a system, the solid body rotation of the core predicted by Batchelor can develop. The evolution of the core-swirl ratio of the rotating fluid with an outward throughflow is studied by applying a classical experimental correlation, inserted in a one-dimensional (1D) in-house developed code. Results are compared to those predicted by CFD computations. Due to the discrepancies revealed, the authors provided a correction of the experimental correlation, based on CFD computation. Results thus obtained are finally in good agreement with CFD predictions.

Vibration of an elastic strip with varying curvature

1992 ◽  
Vol 339 (1655) ◽  
pp. 587-625 ◽  
Keyword(s):  
Total Internal Reflection ◽  
Normal Modes ◽  
Mode Shapes ◽  
Elastic Strip ◽  
Interesting Phenomenon ◽  
One Dimensional ◽  
End Conditions ◽  
The One ◽  
Fixed End ◽  
Good Agreement

The vibrational behaviour of an elastic strip with varying curvature is investigated. The case of vibration which is predominantly transverse is considered, and it is shown that when the strip is S-shaped, certain of the normal modes may be confined to the vicinity of the inflection point of the S by a process of total internal reflection from points where the curvature reaches critical values. This confinement can produce modes with extraordinarily low damping factors. Asymptotic analysis is compared with experimental measurements on a strip in several S-shaped configurations, and very good agreement is demonstrated for modal frequencies and shapes. Mathematically, the lower modes turn out to be analogous to those of the one-dimensional harmonic oscillator in quantum mechanics. This mode confinement behaviour occurs for all waveguide branches except the lowest, ‘bending beam ’, branch. In this particular case, wave propagation is insensitive to curvature. However, an interesting phenomenon associated with curvature is found : the successive mode shapes do not display the normal alternation of symmetry and antisymmetry with respect to the centre of the strip. The effect is shown to result from the constraint on axial movement produced by fixed end conditions. For the geometry of the experiments, this constraint raises the frequencies of antisymmetric modes in a characteristic way while leaving the symmetric modes unaltered, thus changing the mode sequence. Theory is developed which gives reasonable quantitive agreement with the observations.

scholarly journals Stability Boundaries in Laterally-Coupled Pairs of Semiconductor Lasers

Photonics ◽  
2019 ◽  
Vol 6 (2) ◽  
pp. 74
Author(s):  
Martin Vaughan ◽  
Hadi Susanto ◽  
Nianqiang Li ◽  
Ian Henning ◽  
Mike Adams
Keyword(s):  
Semiconductor Lasers ◽  
Normal Mode ◽  
Dynamic Behaviour ◽  
Normal Modes ◽  
Stability Boundaries ◽  
Pumping Rate ◽  
One Dimensional ◽  
Coupled Mode ◽  
Normal Mode Theory ◽  
Laser Separation

The dynamic behaviour of coupled pairs of semiconductor lasers is studied using normal-mode theory, applied to one-dimensional (slab) and two-dimensional (circular cylindrical) real index confined structures. It is shown that regions of stable behaviour depend not only on pumping rate and laser separation, but also on the degree of guidance in the structures. Comparison of results between normal-mode and coupled-mode theories for these structures leads to the tentative conclusion that the accuracy of the latter is determined by the strength of self-overlap and cross-overlap of the symmetric and antisymmetric normal modes in the two lasers.

scholarly journals ESTUDIO EXPERIMENTAL Y TEÓRICO DE LA PROPAGACIÓN DE ONDAS A TRAVÉS DE ESTRUCTURAS PERIÓDICAS

Anales AFA ◽  
2010 ◽  
pp. 14-18
Author(s):  
A. Dolinko ◽  
B. J. Gómez ◽  
C. E. Repetto ◽  
C. R. Stia ◽  
R. Welti
Keyword(s):  
Band Gap ◽  
Periodic System ◽  
Normal Modes ◽  
Simple Device ◽  
Impedance Method ◽  
Simple Version ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Theoretical Results ◽  
Good Agreement

In this work, the acoustic band-gap of a one-dimensional and locally periodic system is studied by using a simple version of the impedance method. The system consists of a duct with modulated section. The normal modes and the transmission coefficients are calculated for a system with two or more repeated structures. It is shown that very selective bands are obtained at specific frequencies after a convenient choice of the periods of repetition. A very good agreement is found between theoretical results and the corresponding experimental ones obtained by using a simple device.

scholarly journals Forced oscillations of the string under conditions of ‘sonic vacuum’

2018 ◽  
Vol 376 (2127) ◽  
pp. 20170135 ◽  
Author(s):  
V. V. Sminrov ◽  
L. I. Manevitch
Keyword(s):  
Normal Mode ◽  
Energy Flow ◽  
Nonlinear Oscillations ◽  
Normal Modes ◽  
Numerical Data ◽  
Nonlinear Normal Modes ◽  
Theoretical Explanation ◽  
Forced Oscillations ◽  
Nonlinear Normal Mode ◽  
Nonlinear Normal

We present the results of analytical study of the significant regularities which are inherent to forced nonlinear oscillations of a string with uniformly distributed discrete masses, without its preliminary stretching. It was found recently that a corresponding autonomous system admits a series of nonlinear normal modes with a lot of possible intermodal resonances and that similar synchronized solutions can exist in the presence of a periodic external field also. The paper is devoted to theoretical explanation of numerical data relating to one of possible scenarios of intermodal interaction which was numerically revealed earlier. This is unidirectional energy flow from unstable nonlinear normal mode to nonlinear normal modes with higher wavenumbers under the conditions of sonic vacuum. The mechanism of such a scenario has not yet been clarified contrary to alternative mechanisms consisting in almost simultaneous energy flow to all nonlinear normal modes with breaking the above-mentioned conditions of sonic vacuum. We begin with a description of single-mode manifolds and then show that consideration of arbitrary double mode manifolds is sufficient for solution of the problem. Because of this, the two-modal equations of motion can be reduced to a linear equation which describes a perturbation of initially excited nonlinear normal mode of the forced system in the conditions of sonic vacuum. We have found analytical representation (in the parametric space) of the thresholds for all possible energy transfers corresponding to unidirectional energy flow from unstable nonlinear normal modes. The analytical results are in a good agreement with previous numerical calculations.This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.

scholarly journals An Unsuspected Boundary-Induced Temporal Computational Mode in a Two-Time-Level Discretization

2005 ◽  
Vol 133 (3) ◽  
pp. 712-720 ◽  
Author(s):  
Andrew Staniforth ◽  
Nigel Wood
Keyword(s):  
Dispersion Relation ◽  
Normal Mode ◽  
Normal Modes ◽  
Time Level ◽  
One Dimensional ◽  
Temporal Discretization ◽  
Acoustic Equations ◽  
Continuous Equation ◽  
The One ◽  
Bounded System

Abstract Normal-mode analyses are applied to various discrete forms of the one-dimensional, linearized, vertical acoustic equations in a height-based coordinate. First, the temporally discrete, spatially continuous equations are considered and the normal modes for a bounded system are compared to those of an unbounded system. Despite the use of a two-time-level discretization, a computational mode is found in the bounded case that is absent in the unbounded case. Second, the complete temporally and spatially discrete bounded system is considered and the normal modes and associated dispersion relation are derived. No computational modes are found. However, under certain limiting conditions, the temporal discretization leads to a distortion of the physical modes so that they resemble the computational mode of the spatially continuous bounded system. Implications for analyses based on spatially continuous equation sets are discussed.

Non-Normal Effects on Salt Finger Growth

2005 ◽  
Vol 35 (5) ◽  
pp. 616-627 ◽  
Author(s):  
Ian Eisenman
Keyword(s):  
Normal Mode ◽  
Stability Theory ◽  
Normal Modes ◽  
Growth Dynamics ◽  
Normal Growth ◽  
Initial Growth ◽  
Transient Effects ◽  
Salt Fingers ◽  
Long Time ◽  
The Difference

Abstract Salt fingers, which occur because of the difference in diffusivities of salt and heat in water, may play an important role in ocean mixing and circulation. Previous studies have suggested the long-time dominance of initially fastest growing finger perturbations. Finger growth has been theoretically derived in terms of the normal modes of the idealized system, which include a growing mode and a pair of decaying internal wave modes. Because these normal modes are not orthogonal, however, transient effects can occur related to the interaction between the modes, as explained by the generalized stability theory of non-normal growth. Initial growth of a perturbation that is not along a normal mode can be faster than the leading normal mode. In this study, the effects of non-normal growth on salt finger formation are investigated. It is shown that some salt finger perturbations that are a superposition of the growing mode and the decaying modes initially grow faster than pure growing normal mode perturbations. These non-normal effects are found to be significant for up to 10 or more e-folding times of the growing normal mode. The generalization of the standard idealized salt finger growth dynamics to include non-normal effects is found to lead to fastest-growing fingers that agree less well with observed fully developed salt fingers than the fastest-growing normal mode previously investigated.

Effect of leakage and blockage on the acoustic behavior of particle filters

2019 ◽  
Vol 67 (6) ◽  
pp. 483-492
Author(s):  
Seonghyeon Baek ◽  
Iljae Lee
Keyword(s):  
Transfer Matrix ◽  
Particle Filters ◽  
Acoustic Analysis ◽  
Transmission Loss ◽  
One Dimensional ◽  
Filter System ◽  
The Difference ◽  
The One ◽  
Analytical Approaches ◽  
Good Agreement

The effects of leakage and blockage on the acoustic performance of particle filters have been examined by using one-dimensional acoustic analysis and experimental methods. First, the transfer matrix of a filter system connected to inlet and outlet pipes with conical sections is measured using a two-load method. Then, the transfer matrix of a particle filter only is extracted from the experiments by applying inverse matrices of the conical sections. In the analytical approaches, the one-dimensional acoustic model for the leakage between the filter and the housing is developed. The predicted transmission loss shows a good agreement with the experimental results. Compared to the baseline, the leakage between the filter and housing increases transmission loss at a certain frequency and its harmonics. In addition, the transmission loss for the system with a partially blocked filter is measured. The blockage of the filter also increases the transmission loss at higher frequencies. For the simplicity of experiments to identify the leakage and blockage, the reflection coefficients at the inlet of the filter system have been measured using two different downstream conditions: open pipe and highly absorptive terminations. The experiments show that with highly absorptive terminations, it is easier to see the difference between the baseline and the defects.

PHOTOINDUCED NONLINEAR OCTUPOLAR POLARIZATION: TRANSIENT AND PERMANENT REGIMES

1996 ◽  
Vol 05 (04) ◽  
pp. 653-670 ◽  
Author(s):  
CÉLINE FIORINI ◽  
JEAN-MICHEL NUNZI ◽  
FABRICE CHARRA ◽  
IFOR D.W. SAMUEL ◽  
JOSEPH ZYSS
Keyword(s):  
Theoretical Analysis ◽  
Second Harmonic ◽  
Experimental Results ◽  
Polar Field ◽  
Rotational Spectrum ◽  
Dual Frequency ◽  
One Dimensional ◽  
Ethyl Violet ◽  
Disperse Red 1 ◽  
Good Agreement

An original poling method using purely optical means and based on a dual-frequency interference process is presented. We show that the coherent superposition of two beams at fundamental and second-harmonic frequencies results in a polar field with an irreducible rotational spectrum containing both a vector and an octupolar component. This enables the method to be applied even to molecules without a permanent dipole such as octupolar molecules. After a theoretical analysis of the process, we describe different experiments aiming at light-induced noncentrosymmetry performed respectively on one-dimensional Disperse Red 1 and octupolar Ethyl Violet molecules. Macroscopic octupolar patterning of the induced order is demonstrated in both transient and permanent regimes. Experimental results show good agreement with theory.

The Deformation of an Erythrocyte Under the Radiation Pressure by Optical Stretch

2006 ◽  
Vol 128 (6) ◽  
pp. 830-836 ◽  
Author(s):  
Yong-Ping Liu ◽  
Chuan Li ◽  
Kuo-Kang Liu ◽  
Alvin C. K. Lai
Keyword(s):  
Radiation Pressure ◽  
Experimental Situation ◽  
Numerical Data ◽  
Shear Stiffness ◽  
Cell Deformation ◽  
Membrane Properties ◽  
Optimization Approach ◽  
Bending Modulus ◽  
Average Shear ◽  
Good Agreement

In this paper, the mechanical properties of erythrocytes were studied numerically based upon the mechanical model originally developed by Pamplona and Calladine (ASME J. Biomech. Eng., 115, p. 149, 1993) for liposomes. The case under study is the erythrocyte stretched by a pair of laser beams in opposite directions within buffer solutions. The study aims to elucidate the effect of radiation pressure from the optical laser because up to now little is known about its influence on the cell deformation. Following an earlier study by Guck et al. (Phys. Rev. Lett., 84, p. 5451, 2000; Biophys. J., 81, p. 767, 2001), the empirical results of the radiation pressure were introduced and imposed on the cell surface to simulate the real experimental situation. In addition, an algorithm is specially designed to implement the simulation. For better understanding of the radiation pressure on the cell deformation, a large number of simulations were conducted for different properties of cell membrane. Results are first discussed parametrically and then evaluated by comparing with the experimental data reported by Guck et al. An optimization approach through minimizing the errors between experimental and numerical data is used to determine the optimal values of membrane properties. The results showed that an average shear stiffness around 4.611×10-6Nm−1, when the nondimensional ratio of shear modulus to bending modulus ranges from 10 to 300. These values are in a good agreement with those reported in literature.

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