Chaotic and turbulent behavior of unstable one-dimensional nonlinear dispersive waves

2000 ◽  
Vol 41 (6) ◽  
pp. 4125-4153 ◽  
Author(s):  
David Cai ◽  
David W. McLaughlin
Keyword(s):  
Dispersive Waves ◽  
One Dimensional

Implementation of fictitious absorbing layers with deceleration effects for one-dimensional Schrödinger equations

2020 ◽  
Vol 86 (5) ◽  
Author(s):  
Hitoshi Kanai ◽  
Tomo Tatsuno
Keyword(s):  
Absorbing Boundary Conditions ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Wave Reflections ◽  
Absorbing Boundary ◽  
Dispersive Waves ◽  
One Dimensional ◽  
Phase Velocities ◽  
Absorbing Layer ◽  
And Performance

Absorbing boundary conditions or layers are used in simulations to reduce or eliminate wave reflections from the boundary; one of the most widely used absorbing layers is Berenger's perfectly matched layer (PML). In this paper, PML is extended to a compound absorbing layer which has multiple effects of damping and deceleration, and is applied to linear and nonlinear Schrödinger equations. The deceleration extends the time to damp out the modes with higher phase velocities, leading to remarkably reduced total reflection for dispersive waves. By invoking the two effects independently, the flexibility and performance are enhanced. Since this method is based on the WKB formalism, it requires an absorbing layer of a moderate size.

Resonant interactions between waves. The case of discrete oscillations

1964 ◽  
Vol 20 (3) ◽  
pp. 457-479 ◽  
Author(s):  
F. P. Bretherton
Keyword(s):  
Initial Conditions ◽  
Wave Number ◽  
Quadratic Term ◽  
Mathematical Basis ◽  
Dispersive Waves ◽  
One Dimensional ◽  
Resonant Interactions ◽  
Expansion Procedure ◽  
Wave Numbers ◽  
Time Invariant

The mathematical basis for resonance is investigated using a model equation describing one-dimensional dispersive waves interacting weakly through a quadratic term. If suitable time-invariant boundary conditions are imposed, possible oscillations of infinitesimal amplitude are restricted to a discrete set of wave-numbers. An asymptotic expansion valid for small amplitude shows that oscillations of different wave-number interact primarily in independent resonant trios. Energy is redistributed between members of a trio over a characteristic time inversely proportional to the amplitude of the oscillations in a periodic manner. The period depends on the initial conditions but is in general finite. Cubic interactions through resonant quartets are also discussed. The methods used are valid for a fairly wide class of equations describing weakly non-linear dispersive waves, but the expansion procedure used here fails for a continuous spectrum.

scholarly journals VALIDATION OF A DOUBLE-LAYER BOUSSINESQ-TYPE MODEL FOR HIGHLY NONLINEAR AND DISPERSIVE WAVES

2011 ◽  
Vol 1 (32) ◽  
pp. 14
Author(s):  
Florent Chazel ◽  
Michel Benoit ◽  
Alexandre Ern
Keyword(s):  
Laboratory Experiments ◽  
Irregular Waves ◽  
Type Model ◽  
Breaking Wave ◽  
Test Cases ◽  
Regular Waves ◽  
Dispersive Waves ◽  
One Dimensional ◽  
Highly Nonlinear ◽  
Nonlinearity Dispersion

A two-layer Boussinesq-type mathematical model has been recently introduced by the authors with the goal of modeling highly nonlinear and dispersive waves (Chazel et al. 2009). The analysis of this model has previously shown that it possesses excellent linear properties, up to kh = 10 at least, for dispersion, shoaling coefficient and vertical profile of orbital velocities. In the present work a numerical one-dimensional (1DH) version of model is developed based on a finite difference technique for meshing the spatial domain. It is then applied and verified against a set of three one-dimensional (1DH) test-cases for which either numerical or experimental reference results are available: i. nonlinear and dispersive regular waves of permanent form; ii. propagation of regular waves on a trapezoidal bar (laboratory experiments by Dingemans (1994)); iii. shoaling and propagation of irregular waves on a barred beach profile (laboratory experiments by Becq-Girard et al. (1999)). The test-cases considered in this study confirm the very good capabilities of the model to reproduce either exact solutions, high-precision numerical simulations and experimental measurements in a variety of non-breaking wave conditions and types of bottom profiles. Nonlinearity, dispersion and bathymetric effects are well accounted for by the model, which appears to possess a rather wide domain of validity while maintaining a reasonable level of complexity.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Electron-Mirror Microscopic Aspects of Ferroelectric Domains of BaTiO3 And Ca2Sr (C2H5CO2)6

1970 ◽  
Vol 28 ◽  
pp. 478-479
Author(s):  
Teruo Someya ◽  
Jinzo Kobayashi
Keyword(s):  
Surface Layer ◽  
Electric Fields ◽  
Quantitative Study ◽  
Recent Progress ◽  
Ferroelectric Domain ◽  
Resolving Power ◽  
Surface Pattern ◽  
Crystal Surfaces ◽  
One Dimensional ◽  
Ferroelectric Domains

Recent progress in the electron-mirror microscopy (EMM), e.g., an improvement of its resolving power together with an increase of the magnification makes it useful for investigating the ferroelectric domain physics. English has recently observed the domain texture in the surface layer of BaTiO3. The present authors ) have developed a theory by which one can evaluate small one-dimensional electric fields and/or topographic step heights in the crystal surfaces from their EMM pictures. This theory was applied to a quantitative study of the surface pattern of BaTiO3).

Structure and function of neural networks in the retina

1988 ◽  
Vol 46 ◽  
pp. 26-27
Author(s):  
Peter Sterling
Keyword(s):  
Ganglion Cells ◽  
Three Dimensional ◽  
Structure And Function ◽  
Synaptic Connections ◽  
Visual Axis ◽  
One Dimensional ◽  
Cat Retina ◽  
Ultrathin Sections ◽  
And Function ◽  
Insight Into

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.

Intergrowth of modulated structures in high Tc Bi-Sr-Ca-Cu-O superconductors

1990 ◽  
Vol 48 (4) ◽  
pp. 76-77
Author(s):  
A.Q. He ◽  
G.W. Qiao ◽  
J. Zhu ◽  
H.Q. Ye
Keyword(s):  
Twin Structure ◽  
Modulated Structure ◽  
High Tc ◽  
One Dimensional ◽  
Lattice Constants ◽  
Superconducting Phases ◽  
Modulated Structures ◽  
Layer Structures

Since the first discovery of high Tc Bi-Sr-Ca-Cu-O superconductor by Maeda et al, many EM works have been done on it. The results show that the superconducting phases have a type of ordered layer structures similar to that in Y-Ba-Cu-O system formulated in Bi2Sr2Can−1CunO2n+4 (n=1,2,3) (simply called 22(n-1) phase) with lattice constants of a=0.358, b=0.382nm but the length of c being different according to the different value of n in the formulate. Unlike the twin structure observed in the Y-Ba-Cu-O system, there is an incommensurate modulated structure in the superconducting phases of Bi system superconductors. Modulated wavelengths of both 1.3 and 2.7 nm have been observed in the 2212 phase. This communication mainly presents the intergrowth of these two kinds of one-dimensional modulated structures in 2212 phase.

Electronic structure studies of conducting polymers by electron energy-loss spectroscopy

1996 ◽  
Vol 54 ◽  
pp. 160-161
Author(s):  
J. Fink
Keyword(s):  
Electronic Structure ◽  
Conducting Polymers ◽  
Conjugated Polymers ◽  
Electron Acceptors ◽  
Electron Donors ◽  
Light Emitting ◽  
One Dimensional ◽  
New Class ◽  
Electrical Conductivities ◽  
Electron Energy Loss

Conducting polymers comprises a new class of materials achieving electrical conductivities which rival those of the best metals. The parent compounds (conjugated polymers) are quasi-one-dimensional semiconductors. These polymers can be doped by electron acceptors or electron donors. The prototype of these materials is polyacetylene (PA). There are various other conjugated polymers such as polyparaphenylene, polyphenylenevinylene, polypoyrrole or polythiophene. The doped systems, i.e. the conducting polymers, have intersting potential technological applications such as replacement of conventional metals in electronic shielding and antistatic equipment, rechargable batteries, and flexible light emitting diodes.Although these systems have been investigated almost 20 years, the electronic structure of the doped metallic systems is not clear and even the reason for the gap in undoped semiconducting systems is under discussion.

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