scholarly journals Stability of nonlinear waves and patterns and related topics

2018 ◽  
Vol 376 (2117) ◽  
pp. 20180001
Author(s):  
Anna Ghazaryan ◽  
Stephane Lafortune ◽  
Vahagn Manukian
Keyword(s):  
Coherent Structures ◽  
Nonlinear Waves ◽  
Dynamic Properties ◽  
Travelling Waves ◽  
Complex Structure ◽  
Nonlinear Partial Differential Equations ◽  
Theme Issue ◽  
Hybrid Techniques ◽  
Wave Trains ◽  
The Waves

Periodic and localized travelling waves such as wave trains, pulses, fronts and patterns of more complex structure often occur in natural and experimentally built systems. In mathematics, these objects are realized as solutions of nonlinear partial differential equations. The existence, dynamic properties and bifurcations of those solutions are of interest. In particular, their stability is important for applications, as the waves that are observable are usually stable. When the waves are unstable, further investigation is warranted of the way the instability is exhibited, i.e. the nature of the instability, and also coherent structures that appear as a result of an instability of travelling waves. A variety of analytical, numerical and hybrid techniques are used to study travelling waves and their properties. This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’.

scholarly journals An energy-based stability criterion for solitary travelling waves in Hamiltonian lattices

2018 ◽  
Vol 376 (2117) ◽  
pp. 20170192 ◽  
Author(s):  
Haitao Xu ◽  
Jesús Cuevas-Maraver ◽  
Panayotis G. Kevrekidis ◽  
Anna Vainchtein
Keyword(s):  
Nonlinear Waves ◽  
Travelling Waves ◽  
Travelling Wave ◽  
Point Of View ◽  
Floquet Multiplier ◽  
Theme Issue ◽  
Future Directions ◽  
Infinite Dimensional ◽  
The Stability ◽  
Delay Differential

In this work, we revisit a criterion, originally proposed in Friesecke & Pego (Friesecke & Pego 2004 Nonlinearity 17 , 207–227. ( doi:10.1088/0951715/17/1/013 )), for the stability of solitary travelling waves in Hamiltonian, infinite-dimensional lattice dynamical systems. We discuss the implications of this criterion from the point of view of stability theory, both at the level of the spectral analysis of the advance-delay differential equations in the co-travelling frame, as well as at that of the Floquet problem arising when considering the travelling wave as a periodic orbit modulo shift. We establish the correspondence of these perspectives for the pertinent eigenvalue and Floquet multiplier and provide explicit expressions for their dependence on the velocity of the travelling wave in the vicinity of the critical point. Numerical results are used to corroborate the relevant predictions in two different models, where the stability may change twice. Some extensions, generalizations and future directions of this investigation are also discussed. This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’.

The generation of waves by wind

1952 ◽  
Vol 215 (1122) ◽  
pp. 299-328 ◽  
Keyword(s):  
Ocean Waves ◽  
Irish Sea ◽  
North Coast ◽  
Empirical Relationships ◽  
The North ◽  
Component Wave ◽  
Wave Trains ◽  
The Irish Sea ◽  
The Waves ◽  
Group Velocities

This paper describes an investigation of the height and length of ocean waves and swell in relation to the strength, extent and duration of the wind in the generating area, and the subsequent travel of the swell through calm and disturbed water. The investigation is based on records of waves made on the north coast of Cornwall, in the Irish Sea and in Lough Neagh. It is a practical continuation of the work of Barber & Ursell (1948), who showed that the waves leaving the generating area behave as a continuous spectrum of component wave trains which travel independently with the group velocities appropriate to their periods. The spectral distribution of energy in the storm area is considered, and the relative amplitudes of the different components are deduced empirically under various wind conditions. The results indicate that the wave characteristics become practically independent of fetch after 200 to 300 miles, and that in the equilibrium condition the steepness of the highest waves is inversely proportional to the square root of the wind speed. Some theoretical foundation can be found for the form of the empirical relationships if it is assumed that the wind acts on each wave component independently, and that the sheltering coefficient used by Jeffreys is proportional to the wave steepness. The results provide a basis for making reasonably accurate predictions of waves and swell from meteorological charts and forecasts.

scholarly journals Surface microtopography modulates sealing zone development in osteoclasts cultured on bone

2017 ◽  
Vol 14 (127) ◽  
pp. 20160958 ◽  
Author(s):  
Michal Shemesh ◽  
Lia Addadi ◽  
Benjamin Geiger
Keyword(s):  
Dynamic Properties ◽  
Complex Structure ◽  
Chemical Properties ◽  
Bone Diseases ◽  
Bone Homeostasis ◽  
Native Bone ◽  
Surface Microtopography ◽  
Significant Enrichment ◽  
Sealing Zone ◽  
Physical And Chemical

Bone homeostasis is continuously regulated by the coordinated action of bone-resorbing osteoclasts and bone-forming osteoblasts. Imbalance between these two cell populations leads to pathological bone diseases such as osteoporosis and osteopetrosis. Osteoclast functionality relies on the formation of sealing zone (SZ) rings that define the resorption lacuna. It is commonly assumed that the structure and dynamic properties of the SZ depend on the physical and chemical properties of the substrate. Considering the unique complex structure of native bone, elucidation of the relevant parameters affecting SZ formation and stability is challenging. In this study, we examined in detail the dynamic response of the SZ to the microtopography of devitalized bone surfaces, taken from the same area in cattle femur. We show that there is a significant enrichment in large and stable SZs (diameter larger than 14 µm; lifespan of hours) in cells cultured on rough bone surfaces, compared with small and fast turning over SZ rings (diameter below 7 µm; lifespan approx. 7 min) formed on smooth bone surfaces. Based on these results, we propose that the surface roughness of the physiologically relevant substrate of osteoclasts, namely bone, affects primarily the local stability of growing SZs.

Study on Dynamic Properties of the Intake Tower with Finite Element Method

2014 ◽  
Vol 501-504 ◽  
pp. 1888-1891 ◽  
Author(s):  
Cheng Lin Gong ◽  
Hua Liu ◽  
Jian Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Properties ◽  
Complex Structure ◽  
Hollow Structure ◽  
Complex Loading ◽  
Thin Wall ◽  
Finite Element Software ◽  
Complex Boundary ◽  
Tower Foundation

Intake tower is a complex structure, which has complex boundary conditions and has complex loading situation. Intake tower is made up of reinforced concrete ,which is thin-wall hollow structure. It builds in the near the shore in the reservoir, its top bridge connects to the banks of the river, The tower is in the water and is under pressure, intake towers safety is very important under the action of earthquake. Based on the large finite element software ANSYS, the dynamic properties of the intake tower is studied, and the intake tower+ foundation is also studied. The research conclusions can be used as reference for engineering design.

scholarly journals Evolutionary trade-offs and the structure of polymorphisms

2018 ◽  
Vol 373 (1747) ◽  
pp. 20170105 ◽  
Author(s):  
Hila Sheftel ◽  
Pablo Szekely ◽  
Avi Mayo ◽  
Guy Sella ◽  
Uri Alon
Keyword(s):  
High Frequency ◽  
Cell Biology ◽  
Pareto Front ◽  
Complex Structure ◽  
Self Organization ◽  
Theme Issue ◽  
Single Task ◽  
Trade Offs ◽  
Simple Geometry ◽  
Multiple Tasks

Populations of organisms show genetic differences called polymorphisms. Understanding the effects of polymorphisms is important for biology and medicine. Here, we ask which polymorphisms occur at high frequency when organisms evolve under trade-offs between multiple tasks. Multiple tasks present a problem, because it is not possible to be optimal at all tasks simultaneously and hence compromises are necessary. Recent work indicates that trade-offs lead to a simple geometry of phenotypes in the space of traits: phenotypes fall on the Pareto front, which is shaped as a polytope: a line, triangle, tetrahedron etc. The vertices of these polytopes are the optimal phenotypes for a single task. Up to now, work on this Pareto approach has not considered its genetic underpinnings. Here, we address this by asking how the polymorphism structure of a population is affected by evolution under trade-offs. We simulate a multi-task selection scenario, in which the population evolves to the Pareto front: the line segment between two archetypes or the triangle between three archetypes. We find that polymorphisms that become prevalent in the population have pleiotropic phenotypic effects that align with the Pareto front. Similarly, epistatic effects between prevalent polymorphisms are parallel to the front. Alignment with the front occurs also for asexual mating. Alignment is reduced when drift or linkage is strong, and is replaced by a more complex structure in which many perpendicular allele effects cancel out. Aligned polymorphism structure allows mating to produce offspring that stand a good chance of being optimal multi-taskers in at least one of the locales available to the species. This article is part of the theme issue ‘Self-organization in cell biology’.

Experimental investigation on the evolution of the modulation instability with dissipation

2012 ◽  
Vol 711 ◽  
pp. 101-121 ◽  
Author(s):  
Y. Ma ◽  
G. Dong ◽  
M. Perlin ◽  
X. Ma ◽  
G. Wang
Keyword(s):  
Experimental Investigation ◽  
Modulational Instability ◽  
Experimental Results ◽  
Damping Term ◽  
Wave Flume ◽  
Perturbation Frequency ◽  
Linear Damping ◽  
Wave Trains ◽  
Momentum Integral ◽  
The Waves

AbstractAn experimental investigation focusing on the effect of dissipation on the evolution of the Benjamin–Feir instability is reported. A series of wave trains with added sidebands, and varying initial steepness, perturbed amplitudes and frequencies, are physically generated in a long wave flume. The experimental results directly confirm the stabilization theory of Segur et al. (J. Fluid Mech., vol. 539, 2005, pp. 229–271), i.e. dissipation can stabilize the Benjamin–Feir instability. Furthermore, the experiments reveal that the effect of dissipation on modulational instability depends strongly on the perturbation frequency. It is found that the effect of dissipation on the growth rates of the sidebands for the waves with higher perturbation frequencies is more evident than on those of waves with lower perturbation frequencies. In addition, numerical simulations based on Dysthe’s equation with a linear damping term included, which is estimated from the experimental data, can predict the experimental results well if the momentum integral of the wave trains is conserved during evolution.

scholarly journals ‘Perpetual First Generation’: A Strategy for a New Minority – People Originating from Turkey in France

2016 ◽  
Vol 24 (3) ◽  
pp. 405-416
Author(s):  
Samim Akgönül
Keyword(s):  
First Generation ◽  
Dynamic Properties ◽  
Complex Structure ◽  
Turkish People ◽  
Definition Of ◽  
Minority People

To investigate the identity attributes of Turkish people living in France it is necessary to consider ‘Turkish identity’, determine the stage of their identity building, and understand the role religion plays in this quest for identity. Considering the complex structure of Ottoman society and the multiple and dynamic properties of loyalty criteria, it is difficult to ascertain the definition of ‘Turkishness’ even in Turkey. It is probably not necessary to explain that this is even more difficult for Turks who are in the minority.

A falling film down a slippery inclined plane

2011 ◽  
Vol 684 ◽  
pp. 353-383 ◽  
Author(s):  
A. Samanta ◽  
C. Ruyer-Quil ◽  
B. Goyeau
Keyword(s):  
Travelling Waves ◽  
Falling Film ◽  
Inclined Plane ◽  
Local Flow ◽  
Navier Slip ◽  
Averaged Equations ◽  
Gravity Driven ◽  
The Waves ◽  
Navier Slip Condition ◽  
Good Agreement

AbstractA gravity-driven film flow on a slippery inclined plane is considered within the framework of long-wave and boundary layer approximations. Two coupled depth-averaged equations are derived in terms of the local flow rate $q(x, t)$ and the film thickness $h(x, t)$. Linear stability analysis of the averaged equations shows good agreement with the Orr–Sommerfeld analysis. The effect of a slip at the wall on the primary instability has been found to be non-trivial. Close to the instability onset, the effect is destabilising whereas it becomes stabilising at larger values of the Reynolds number. Nonlinear travelling waves are amplified by the presence of the slip. Comparisons to direct numerical simulations show a remarkable agreement for all tested values of parameters. The averaged equations capture satisfactorily the speed, shape and velocity distribution in the waves. The Navier slip condition is observed to significantly enhance the backflow phenomenon in the capillary region of the solitary waves with a possible effect on heat and mass transfer.

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