scholarly journals Evolution of a narrow-band spectrum of random surface gravity waves

2003 ◽  
Vol 478 ◽  
pp. 1-10 ◽  
Author(s):  
KRISTIAN B. DYSTHE ◽  
KARSTEN TRULSEN ◽  
HARALD E. KROGSTAD ◽  
HERVÉ SOCQUET-JUGLARD
Keyword(s):  
Three Dimensional ◽  
Low Frequency ◽  
Three Dimensions ◽  
Band Spectrum ◽  
Nls Equation ◽  
Random Surface ◽  
Narrow Bandwidth ◽  
Quasi Stationary State ◽  
The Stability ◽  
Three Dimensional Simulations

Numerical simulations of the evolution of gravity wave spectra of fairly narrow bandwidth have been performed both for two and three dimensions. Simulations using the nonlinear Schrödinger (NLS) equation approximately verify the stability criteria of Alber (1978) in the two-dimensional but not in the three-dimensional case. Using a modified NLS equation (Trulsen et al. 2000) the spectra ‘relax’ towards a quasi-stationary state on a timescale (ε2ω0)−1. In this state the low-frequency face is steepened and the spectral peak is downshifted. The three-dimensional simulations show a power-law behaviour ω−4 on the high-frequency side of the (angularly integrated) spectrum.

scholarly journals Dynamics of gravity–capillary solitary waves in deep water

2012 ◽  
Vol 708 ◽  
pp. 480-501 ◽  
Author(s):  
Zhan Wang ◽  
Paul A. Milewski
Keyword(s):  
Solitary Waves ◽  
Water Waves ◽  
Periodic Structures ◽  
Time Integration ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Full Potential ◽  
Numerical Time Integration ◽  
The Stability ◽  
Nonlinear Focusing

AbstractThe dynamics of solitary gravity–capillary water waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time-dependent solutions, we simplify the full potential flow problem by using surface variables and taking a particular cubic truncation possessing a Hamiltonian with desirable properties. This approximation agrees remarkably well with the full equations for the bifurcation curves, wave profiles and the dynamics of solitary waves for a two-dimensional fluid domain, and with higher-order truncations in three dimensions. Fully localized solitary waves are then computed in the three-dimensional problem and the stability and interaction of both line and localized solitary waves are investigated via numerical time integration of the equations. There are many solitary wave branches, indexed by their finite energy as their amplitude tends to zero. The dynamics of the solitary waves is complex, involving nonlinear focusing of wavepackets, quasi-elastic collisions, and the generation of propagating, spatially localized, time-periodic structures akin to breathers.

Stability and Robustness of a 3D Slip Model for Walking Using Lateral Leg Placement Control

2012 ◽  
Author(s):  
Dominik Budday ◽  
Fabian Bauer ◽  
Justin Seipel
Keyword(s):  
Humanoid Robot ◽  
Performance Test ◽  
Control Mechanism ◽  
Sagittal Plane ◽  
Control Strategies ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Slip Model ◽  
The Stability

The SLIP model has shown a way to easily represent the center of mass dynamics of human walking and running. For 2D motions in the sagittal plane, the model shows self-stabilizing effects that can be very useful when designing a humanoid robot. However, this self-stability could not be found in three-dimensional running, but simple control strategies achieved stabilization of running in three dimensions. Yet, 3D walking with SLIP has not been analyzed to the same extent. In this paper we show that three-dimensional humanoid SLIP walking is also unstable, but can be stabilized using the same strategy that has been successful for running. It is shown that this approach leads to the desired periodic solutions. Furthermore, the influence of different parameters on stability and robustness is examined. Using a performance test to simulate the transition from an upright position to periodic walking we show that the stability is robust. With a comparison of common models for humanoid walking and running it is shown that the simple control mechanism is able to achieve stable solutions for all models, providing a very general approach to this problem. The derived results point out preferable parameters to increase robustness promising the possibility of successfully realizing a humanoid walking robot based on 3D SLIP.

scholarly journals A Systematic Study of the Fracturing of Ronne - Filchner Ice Shelf, Antarctica, Using Multisource Satellite Data from 2001 to 2016

2017 ◽  
Author(s):  
Rongxing Li ◽  
Haifeng Xiao ◽  
Shijie Liu ◽  
Xiaohua Tong
Keyword(s):  
Satellite Data ◽  
Three Dimensional ◽  
Remote Sensing Data ◽  
Three Dimensions ◽  
Landsat 8 ◽  
Ice Shelf ◽  
Sar Imagery ◽  
The Stability ◽  
Fracture Mapping ◽  
New Framework

Abstract. We propose a new framework of systematic fracture mapping and major calving event prediction for the large ice shelves in Antarctica using multisource satellite data, including optical imagery, SAR imagery, altimetric data, and stereo mapping imagery. The new framework is implemented and applied for a comprehensive study of the fracturing of Ronne-Filchner Ice Shelf (RFIS), the second largest ice shelf in Antarctica, using a long time dataset dating back to 1957. New remote sensing data that have been made available in the past decade, including Landsat 8, WV-2, ZY-3 and others, greatly enhance our abilities to detect new fractures and monitor large rifts in three dimensions. Two large rifts, Rifts 1 and 2, were newly detected and are comparable to the Grand Chasm that caused a major calving event in the region in 1986. Three-dimensional rift models generated from quasi real-time stereo ZY-3 images revealed important topographic information about the large rifts that can be used to improve the reliability of ice shelf modeling and support enhanced analyses of ice shelf stability. Based on the results of the 2D and 3D fracture mapping, the spatial and temporal analyses of the overall fracture changes and large rift evolutions, i.e., the level of fracturing in RFIS, were slightly increased, particularly at the front of the ice sheet. The overall fracture observations do not seem to suggest immediate significant impacts on the stability of the shelf. However, the most active regional fracturing activities occurred at the front of Filchner Ice Shelf (FIS). A potential upcoming major calving event of FIS is estimated to occur in 2051. The stability of the ice shelf, particularly with regard to the developments of Rifts 1 and 2, should be closely monitored.

Experiments on nonlinear gravity–capillary waves

1999 ◽  
Vol 380 ◽  
pp. 205-232 ◽  
Author(s):  
LEV SHEMER ◽  
MELAD CHAMESSE
Keyword(s):  
Narrow Band ◽  
Numerical Study ◽  
Three Dimensional ◽  
Capillary Waves ◽  
Carrier Wave ◽  
Nls Equation ◽  
Zakharov Equation ◽  
The Stability ◽  
Nonlinear Gravity

Benjamin–Feir instability of nonlinear gravity–capillary waves is studied experimentally. The experimental results are compared with computations performed for values of wavelength and steepness identical to those employed in the experiments. The theoretical approach is based on the Zakharov nonlinear equation which is modified here to incorporate weak viscous dissipation. Experiments are performed in a wave ume which has an accurately controlled wavemaker for generation of the carrier wave, as well as an additional independent conical wavemaker for generation of controlled three-dimensional disturbances. The approach adopted in the present experimental investigation allows therefore the determination of the actual boundaries of the instability domain, and not just the most unstable disturbances. Instantaneous surface elevation measurements are performed with capacitance-type wave gauges. Multipoint measurements make it possible to determine the angular dependence of the amplitude of the forced and unforced disturbances, as well as their variation along the tank. The limits of the instability domains obtained experimentally for each set of carrier wave parameters agree favourably with those computed numerically using the model equation. The numerical study shows that application of the Zakharov equation, which is free of the narrow-band approximation adopted in the derivation of the nonlinear Schrödinger (NLS) equation, may lead to qualitatively different results regarding the stability of nonlinear gravity–capillary waves. The present experiments support the results of the numerical investigation.

Propagation of Low Frequency Elastic Disturbances in a Three-Dimensional Composite Material

1975 ◽  
Vol 42 (1) ◽  
pp. 159-164 ◽  
Author(s):  
W. Kohn
Keyword(s):  
Secular Equation ◽  
Displacement Vector ◽  
Three Dimensional ◽  
Low Frequency ◽  
Three Dimensions ◽  
Low Frequencies ◽  
One Dimensional ◽  
Coupled Partial Differential Equations ◽  
Constant Coefficients ◽  
The Mean

This paper is a generalization to three dimensions of an earlier study for one-dimensional composites. We show here that in the limit of low frequencies the displacement vector ui(r,t) can be written in the form ui (r,t) = (∂ij + vijl (r) ∂/∂xl + …) Uj (r,t). Here Uj (r,t) is a slowly varying vector function of r and t which describes the mean displacement of each cell of the composite. Its components satisfy a set of three coupled partial differential equations with constant coefficients. These coefficients are obtainable from the three-by-three secular equation which yields the low-lying normal mode frequencies, ω(k). Information about local strains is contained in the function vijl(r), which is characteristic of static deformations, and is discussed in detail. Among applications of this method is the structure of the head of a pulse propagating in an arbitrary direction.

scholarly journals Explicit iterative computation of diffusive vapour field in the 3-D snow matrix: preliminary results for low flux metamorphism

2008 ◽  
Vol 48 ◽  
pp. 13-18 ◽  
Author(s):  
Jean-Bruno Brzoska ◽  
Frédéric Flin ◽  
Jean Barckicke
Keyword(s):  
Three Dimensional ◽  
Computation Time ◽  
Three Dimensions ◽  
Data Mapping ◽  
Preliminary Results ◽  
Iterative Computation ◽  
Reaction Coefficient ◽  
Vapour Diffusion ◽  
Grain Packing ◽  
Three Dimensional Simulations

AbstractThe metamorphism of seasonal snow is classically considered as limited by vapour diffusion in the pore phase. To account for the lack of knowledge of the ice–vapour reaction coefficient near 0°C, the assumption of a reaction-limited metamorphism was first tested in three-dimensional simulations at low and very low temperature gradients; however, the validity of such results is difficult to verify experimentally. By a reasoned use of traditional iterative schemes, vapour diffusion is now simulated in three dimensions on tomographic snow data, mapping the gradient of vapour pressure near the grains. Repeating this process may provide a way to simulate the isothermal metamorphism without grain packing at a reasonable expense of computation time. Preliminary results are compared with existing computations made within the reaction-limited hypothesis.

scholarly journals Three-dimensional simulations of the Rayleigh–Taylor instability during the deceleration phase

1994 ◽  
Vol 12 (2) ◽  
pp. 163-183 ◽  
Author(s):  
R.P.J. Town ◽  
B.J. Jones ◽  
J.D. Findlay ◽  
A.R. Bell
Keyword(s):  
Inertial Confinement Fusion ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Taylor Instability ◽  
Three Dimensions ◽  
Inertial Confinement ◽  
Deceleration Phase ◽  
Confinement Fusion ◽  
Rayleigh Taylor Instability ◽  
Three Dimensional Simulations

The growth of the Rayleigh-Taylor instability in three dimensions is ex amined during the deceleration phase of an inertial confinement fusion implosion. A detailed discussion of the three-dimensional hydrocode, PLATO, is presented. A review of previous calculations is given, concentrating on theshape of the R-T instability in three dimensions. Results of the growth rate during the linear phase, the saturation amplitude, and the nonlinear evolution are presented.

Structural Failure Mechanisms of Common Flexor Tendon Repairs

Hand Surgery ◽  
2015 ◽  
Vol 20 (03) ◽  
pp. 369-379 ◽  
Author(s):  
Tim Sebastian Peltz ◽  
Roger Haddad ◽  
Peter James Scougall ◽  
Sean Nicklin ◽  
Mark Peter Gianoutsos ◽  
...  
Keyword(s):  
Failure Mechanisms ◽  
Biomechanical Testing ◽  
Tendon Repair ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Biomechanical Stability ◽  
Repair Method ◽  
Before And After ◽  
The Stability ◽  
Repair Techniques

Background: This study investigated the exact failure mechanisms of the most commonly used conventional tendon repair techniques. A new method, radiographing repair constructs in antero-posterior and lateral projections before and after tensioning was used. This allowed to precisely analyse failure mechanisms in regards to geometrical changes in all three dimensions. Additionally the biomechanical stability focusing on gapping was tested. Methods: Sheep fore limb deep flexor tendons were harvested and divided in eight groups of ten tendons. Three common variants of the Kessler repair method and four common 4-strand repair techniques were tested. Additionally a new modification of the Adelaide repair was tested. Results: Biomechanical testing showed no significant differences in gapping for the three tested 2-strand Kessler repair groups. Once a double Kessler or 4-strand Kessler repair was performed the stability of the repair improved significantly. Further significant improvements in biomechanical stability could be achieved by using cross locks in the repair like in the Adelaide repair method. Qualitative analysis using radiographs showed that all Kessler repair variants unfolded via rotations around the transverse suturing component, no matter which variant was used. Conclusions: Additional to the commonly described constriction of the repair construct, the rotating deformation is the main reason for repair site gapping in Kessler tendon repair methods. The term “locking” in a Kessler repair is misleading. The cruciate repairs tended to loose grip and drag (cheese-wire) through the tendon and therefore lead to gapping. The most stable repair constructs in all three dimensions were the Adelaide repair and its interlocking modification. This is due to the superior anchoring qualities of its cross locks and three dimensional stability.

Spatial Distribution of Gravity-Dependent Gain Changes in the Vestibuloocular Reflex

2005 ◽  
Vol 93 (6) ◽  
pp. 3693-3698 ◽  
Author(s):  
Sergei B. Yakushin ◽  
Yongqing Xiang ◽  
Theodore Raphan ◽  
Bernard Cohen
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Head Tilt ◽  
Fundamental Property ◽  
Head Position ◽  
Three Dimensions ◽  
Vestibuloocular Reflex ◽  
Gain Adaptation ◽  
The Stability ◽  
Three Dimensional Space

This study determined whether dependence of angular vestibuloocular reflex (aVOR) gain adaptation on gravity is a fundamental property in three dimensions. Horizontal aVOR gains were adaptively increased or decreased in two cynomolgus monkeys in upright, side down, prone, and supine positions, and aVOR gains were tested in darkness by yaw rotation with the head in a wide variety of orientations. Horizontal aVOR gain changes peaked at the head position in which the adaptation took place and gradually decreased as the head moved away from this position in any direction. The gain changes were plotted as a function of head tilt and fit with a sinusoid plus a bias to obtain the gravity-dependent (amplitude) and gravity-independent (bias) components. Peak-to-peak gravity-dependent gain changes in planes containing the position of adaptation and the magnitude of the gravity-independent components were both ∼25%. We assumed that gain changes over three-dimensional space could be described by a sinusoid the amplitude of which also varied sinusoidally. Using gain changes obtained from the head position in which the gains were adapted, a three-dimensional surface was generated that was qualitatively similar to a surface obtained from the experimental data. This extends previous findings on vertical aVOR gain adaptation in one plane and introduces a conceptual framework for understanding plasticity in three dimensions: aVOR gain changes are composed of two components, one of which depends on head position relative to gravity. It is likely that this gravitational dependence optimizes the stability of retinal images during movement in three-dimensional space.

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