Stability of Single-Wave-Form Solutions in the Underdamped Frenkel–Kontorova Model

2008 ◽  
Vol 40 (3) ◽  
pp. 952-967 ◽  
Author(s):  
Wen-Xin Qin ◽  
Chun-Lan Xu ◽  
Xin Ma
Keyword(s):  
Wave Form ◽  
Single Wave ◽  
Kontorova Model

Climatology of the Sierra Nevada Mountain-Wave Events

2008 ◽  
Vol 136 (2) ◽  
pp. 757-768 ◽  
Author(s):  
Vanda Grubišić ◽  
Brian J. Billings
Keyword(s):  
Sierra Nevada ◽  
Cloud Formation ◽  
Wave Form ◽  
Mountain Range ◽  
Mountain Wave ◽  
Single Wave ◽  
Sierra Nevada Mountain ◽  
Lee Waves ◽  
Lee Wave ◽  
Wave Trains

Abstract This note presents a satellite-based climatology of the Sierra Nevada mountain-wave events. The data presented were obtained by detailed visual inspection of visible satellite imagery to detect mountain lee-wave clouds based on their location, shape, and texture. Consequently, this climatology includes only mountain-wave events during which sufficient moisture was present in the incoming airstream and whose amplitude was large enough to lead to cloud formation atop mountain-wave crests. The climatology is based on data from two mountain-wave seasons in the 1999–2001 period. Mountain-wave events are classified in two types according to cloud type as lee-wave trains and single wave clouds. The frequency of occurrence of these two wave types is examined as a function of the month of occurrence (October–May) and region of formation (north, middle, south, or the entire Sierra Nevada range). Results indicate that the maximum number of mountain-wave events in the lee of the Sierra Nevada occurs in the month of April. For several months, including January and May, frequency of wave events displays substantial interannual variability. Overall, trapped lee waves appear to be more common, in particular in the lee of the northern sierra. A single wave cloud on the lee side of the mountain range was found to be a more common wave form in the southern Sierra Nevada. The average wavelength of the Sierra Nevada lee waves was found to lie between 10 and 15 km, with a minimum at 4 km and a maximum at 32 km.

scholarly journals Analysis of Simulated Radar Altimetric Wave Forms for Polar Ice and Snow Surfaces (Abstract)

1987 ◽  
Vol 9 ◽  
pp. 241-241
Author(s):  
Eva Novotny
Keyword(s):  
Sea Ice ◽  
Leading Edge ◽  
Wave Form ◽  
Polar Regions ◽  
Radar Altimeter ◽  
Single Wave ◽  
Height Determination ◽  
Wave Forms ◽  
Imaging Instrument ◽  
Ice Floes

The radar altimeter of the satellite Seasat has proved that ice and snow surfaces in the polar regions can return meaningful signals if the terrain is not excessively rugged or sloping. Because the use of the leading edge of the wave forms for height determination entails inherent uncertainties and, at best, provides only a single datum per wave form, the entire wave forms should be studied. Excesses or deficiencies in amplitude at various ranges within a single wave form, and the changes that occur in successive wave forms, can be analysed to yield information on the geometric and scattering properties of features observed by the altimeter.Results from computer simulations are presented, showing how (1) a margin of sea ice (sinusoidal in the model) can be mapped, (2) the boundaries of two isolated ice floes can be outlined, (3) sea-ice concentrations can be derived within annuli about the nadir of an individual footprint, and (4) for land ice, the elevations of topographic features, together with the general slope of the ground, can be determined if an imaging instrument that operates simultaneously with the altimeter provides the outlines of these features. In examples (1) and (2), it is assumed that the ice is contiguous wherever that is possible, to permit the analytical reconstruction of the ice margin or individual ice floes in the presence of the inevitable ambiguity in the position of any feature with respect to the two sides of the satellite track. Example (4) requires that the altimeter record correctly records the strongest signals returned by ice-packs. This condition is not fulfilled by any existing radar altimeter, but it may be achieved in the next generation of these instruments. In additional examples of information from entire wave forms, the effects of crevasses and sastrugi in reducing or re-distributing the energy of the returned signals are also illustrated.Full details of these analyses and results will be published at a later date.

scholarly journals Analysis of Simulated Radar Altimetric Wave Forms for Polar Ice and Snow Surfaces (Abstract)

1987 ◽  
Vol 9 ◽  
pp. 241
Author(s):  
Eva Novotny
Keyword(s):  
Sea Ice ◽  
Leading Edge ◽  
Wave Form ◽  
Polar Regions ◽  
Radar Altimeter ◽  
Single Wave ◽  
Height Determination ◽  
Wave Forms ◽  
Imaging Instrument ◽  
Ice Floes

The radar altimeter of the satellite Seasat has proved that ice and snow surfaces in the polar regions can return meaningful signals if the terrain is not excessively rugged or sloping. Because the use of the leading edge of the wave forms for height determination entails inherent uncertainties and, at best, provides only a single datum per wave form, the entire wave forms should be studied. Excesses or deficiencies in amplitude at various ranges within a single wave form, and the changes that occur in successive wave forms, can be analysed to yield information on the geometric and scattering properties of features observed by the altimeter. Results from computer simulations are presented, showing how (1) a margin of sea ice (sinusoidal in the model) can be mapped, (2) the boundaries of two isolated ice floes can be outlined, (3) sea-ice concentrations can be derived within annuli about the nadir of an individual footprint, and (4) for land ice, the elevations of topographic features, together with the general slope of the ground, can be determined if an imaging instrument that operates simultaneously with the altimeter provides the outlines of these features. In examples (1) and (2), it is assumed that the ice is contiguous wherever that is possible, to permit the analytical reconstruction of the ice margin or individual ice floes in the presence of the inevitable ambiguity in the position of any feature with respect to the two sides of the satellite track. Example (4) requires that the altimeter record correctly records the strongest signals returned by ice-packs. This condition is not fulfilled by any existing radar altimeter, but it may be achieved in the next generation of these instruments. In additional examples of information from entire wave forms, the effects of crevasses and sastrugi in reducing or re-distributing the energy of the returned signals are also illustrated. Full details of these analyses and results will be published at a later date.

Multi-Wave Vibration Caused by Flutter Instability and Nonlinear Tip-Shroud Friction

2020 ◽  
Vol 142 (2) ◽  
Author(s):  
Johann Gross ◽  
Malte Krack
Keyword(s):  
Initial Conditions ◽  
Theoretical Work ◽  
Wave Form ◽  
Nonlinear Phenomenon ◽  
Limit States ◽  
Single Wave ◽  
Nonlinear Dynamical ◽  
Strongly Nonlinear ◽  
Recent Theoretical Work ◽  
Intimate Relation

Abstract Measurements revealed the contribution of multiple traveling waves to the flutter vibrations of bladed disks. Saturated flutter vibration, whether in this multi-wave or in its better-understood single-wave form, is a nonlinear phenomenon. However, it is still not understood of what physical origin the relevant nonlinearities are, and under what conditions single-wave or multi-wave flutter vibration occurs. Recent theoretical work suggests that multi-wave flutter vibration can be explained by strongly nonlinear frictional interblade coupling. The verity of this hypothesis is strictly limited by the simplicity of the considered model, namely, a cyclic chain of seven oscillators with frictional coupling and rather unrealistic aeroelastic behavior. In this work, it is demonstrated that nonlinear dynamical contact interactions at tip-shrouds are a likely cause for the observed multi-wave flutter vibration. To this end, a more realistic structural turbine blade row model with a more realistic aeroelastic behavior is considered. Some insight into its intriguing dynamics, dependence of limit states on initial conditions, and eigenvalue placement is provided. For instance, it is shown that there is an intimate relation between internal combination resonance conditions of certain traveling wave modes and the spectral content of single- and multi-wave flutter oscillations.

scholarly journals Modelling the COVID-19 Fatality Rate in England and its Regions

2021 ◽  
Author(s):  
Nigel Saunders
Keyword(s):  
Peak Height ◽  
Positive Test ◽  
Wave Form ◽  
Fatality Rate ◽  
Final State ◽  
Single Wave ◽  
Start Date ◽  
Its Regions ◽  
Cumulative Curve ◽  
The Waves

AbstractA model to account for the fatality rate in England and its regions is proposed. It follows the clear observation that, rather than two connected waves, there have been many waves of infections and fatalities in the regions of England of various magnitudes, usually overlapping. The waves are self-limiting, in that clear peaks are seen, particularly in reported positive test rates. The present model considers fatalities as the data reported are more reliable than positive test rates, particularly so during the first wave when so little testing was done.The model considers the observed waves are essentially similar in form and can be modelled using a single wave form, whose final state is only dependent on its peak height and start date. The basic wave form was modelled using the observed fatality rates for London, which unlike the other regions, exhibited almost completely as a single wave in the “first wave”. Its form matches rather well with the “Do Nothing” model reported by Imperial College on 16th March 2020, but reduced substantially from its expected peak.There are, essentially, only two adjustable parameters used in the model, the start date of the relevant wave and its height. The modelled fatalities for each wave are summated per day and a cumulative curve is matched to that reported. The minimal number of adjustable parameters, alongside the fact that the waves invariably overlap, provides highly stringent conditions on the fitting process.Results are presented for each region for both the “first” and “second’ waves. High levels of accuracy are obtained with R2 values approaching 100% against the ideal fit for both waves. It can also be seen there are fundamental differences between the underlying behaviour of the “first” and “second” waves.

Multi-Wave Vibration Caused by Flutter Instability and Nonlinear Tip Shroud Friction

2019 ◽  
Author(s):  
Johann Gross ◽  
Malte Krack
Keyword(s):  
Initial Conditions ◽  
Theoretical Work ◽  
Wave Form ◽  
Nonlinear Phenomenon ◽  
Limit States ◽  
Single Wave ◽  
Nonlinear Dynamical ◽  
Strongly Nonlinear ◽  
Recent Theoretical Work ◽  
Intimate Relation

Abstract Measurements revealed the contribution of multiple traveling waves to the flutter vibrations of bladed disks. Saturated flutter vibration, whether in this multi-wave or in its better-understood single-wave form, is a nonlinear phenomenon. However, it is still not understood of what physical origin the relevant nonlinearities are, and under what conditions single-wave or multi-wave flutter vibration occurs. Recent theoretical work suggests that multi-wave flutter vibration can be explained by strongly nonlinear frictional inter-blade coupling. The verity of this hypothesis is strictly limited by the simplicity of the considered model, namely a cyclic chain of seven oscillators with frictional coupling and rather unrealistic aeroelastic behavior. In the present work, it is demonstrated that nonlinear dynamical contact interactions at tip shrouds are a likely cause for the observed multi-wave flutter vibration. To this end, a more realistic structural turbine blade row model with a more realistic aeroelastic behavior is considered. Some insight into its intriguing dynamics, dependence of limit states on initial conditions and eigenvalue placement is provided. For instance, it is shown that there is an intimate relation between internal combination resonance conditions of certain traveling wave modes and the spectral content of single- and multi-wave flutter oscillations.

The observation of solutions in Ni3Nb

1988 ◽  
Vol 46 ◽  
pp. 540-541
Author(s):  
Z.M. Wang ◽  
J.P. Zhang
Keyword(s):  
Electron Microscopy ◽  
High Resolution ◽  
Phase Modulation ◽  
High Resolution Electron Microscopy ◽  
Antiphase Domain ◽  
Boundary Area ◽  
Matrix Type ◽  
Resolution Electron ◽  
Domain Boundaries ◽  
Kontorova Model

High resolution electron microscopy reveals that antiphase domain boundaries in β-Ni3Nb have a hexagonal unit cell with lattice parameters ah=aβ and ch=bβ, where aβ and bβ are of the orthogonal β matrix. (See Figure 1.) Some of these boundaries can creep “upstairs” leaving an incoherent area, as shown in region P. When the stepped boundaries meet each other, they do not lose their own character. Our consideration in this work is to estimate the influnce of the natural misfit δ{(ab-aβ)/aβ≠0}. Defining the displacement field at the boundary as a phase modulation Φ(x), following the Frenkel-Kontorova model [2], we consider the boundary area to be made up of a two unit chain, the upper portion of which can move and the lower portion of the β matrix type, assumed to be fixed. (See the schematic pattern in Figure 2(a)).

Visual-Neural Correlate of Speechreading Ability in Normal-Hearing Adults

1982 ◽  
Vol 25 (4) ◽  
pp. 521-527 ◽  
Author(s):  
David C. Shepherd
Keyword(s):  
Normal Hearing ◽  
Wave Form ◽  
Firing Time ◽  
Neural Firing ◽  
Neural Correlate ◽  
Retest Reliability ◽  
Repeated Word ◽  
Negative Peak ◽  
The Stability ◽  
Test Retest Reliability

In 1977, Shepherd and colleagues reported significant correlations (–.90, –.91) between speechreading scores and the latency of a selected negative peak (VN 130 measure) on the averaged visual electroencephalic wave form. The primary purpose of this current study was to examine the stability, or repeatability, of this relation between these cognitive and neurophysiologic measures over a period of several months and thus support its test-retest reliability. Repeated speechreading word and sentence scores were gathered during three test-retest sessions from each of 20 normal-hearing adults. An average of 56 days occurred from the end of one to the beginning of another speechreading sessions. During each of four other test-retest sessions, averaged visual electroencephalic responses (AVER s ) were evoked from each subject. An average of 49 clays intervened between AVER sessions. Product-moment correlations computed among repeated word scores and VN l30 measures ranged from –.61 to –.89. Based on these findings, it was concluded that the VN l30 measure of visual neural firing time is a reliable correlate of speech-reading in normal-hearing adults.

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