Waves at liquid surfaces: coupled oscillators and mode mixing

1991 ◽  
Vol 433 (1889) ◽  
pp. 663-678 ◽  
Keyword(s):  
Surface Waves ◽  
Linear Theory ◽  
Coupled Oscillators ◽  
Degrees Of Freedom ◽  
Physical Reality ◽  
Critical Value ◽  
Surface Element ◽  
Surface Viscosity ◽  
Frame Work ◽  
Mode Mixing

The dispersion of surface waves on liquids has been reconsidered in the frame work of currently established linear theory. Mixed excitations, which are neither capillary nor dilational in nature, can occur due to the coupling between the lossy oscillator formed by the vertical and horizontal motions of a surface element. The results emphasize that the capillary and dilational waves are only approximately transverse and longitudinal in nature and that it cannot, in general, be correct to neglect the coupling between these degrees of freedom. In the present case mode mixing only occurs when a particular surface viscosity - that affecting shear normal to the surface - exceeds a critical value. Experimentally accessible tests of the predicted mode mixing are proposed, which would further test the physical reality of the surface viscosity involved.

scholarly journals TWO MODELS OF NONSMOOTH DYNAMICAL SYSTEMS

2011 ◽  
Vol 21 (10) ◽  
pp. 2853-2860 ◽  
Author(s):  
MADELEINE PASCAL
Keyword(s):  
Dry Friction ◽  
Coupled Oscillators ◽  
Degrees Of Freedom ◽  
Analytical Form ◽  
Critical Value ◽  
Form Solution ◽  
Nonsmooth Systems ◽  
The Stability ◽  
Close Form ◽  
Nonsmooth Dynamical Systems

Two examples of nonsmooth systems are considered. The first one is a two degrees of freedom oscillator in the presence of a stop. A discontinuity appears when the system position reaches a critical value. The second example consists of coupled oscillators excited by dry friction. In this case, the discontinuity occurs when the system's velocities take a critical value. For both examples, the dynamical system can be partitioned into different configurations limited by a set of boundaries. Within each configuration, the dynamical model is linear and the close form solution is known. Periodic orbits, including several transitions between the various configurations of the system, are found in analytical form. The stability of these orbits is investigated by using the Poincaré map modeling.

Large Deflections of a Simply Supported Beam Subjected to Moment at One End

1984 ◽  
Vol 51 (3) ◽  
pp. 519-525 ◽  
Author(s):  
P. Seide
Keyword(s):  
Linear Theory ◽  
Bending Moment ◽  
Critical Value ◽  
The Other ◽  
Large Deflections ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Elastica Theory ◽  
Angle Of Rotation

The large deflections of a simply supported beam, one end of which is free to move horizontally while the other is subjected to a moment, are investigated by means of inextensional elastica theory. The linear theory is found to be valid for relatively large angles of rotation of the loaded end. The beam becomes transitionally unstable, however, at a critical value of the bending moment parameter MIL/EI equal to 5.284. If the angle of rotation is controlled, the beam is found to become unstable when the rotation is 222.65 deg.

scholarly journals Моды волновода с пороговой нелинейностью

2020 ◽  
Vol 46 (16) ◽  
pp. 43
Author(s):  
С.Е. Савотченко
Keyword(s):  
Dielectric Constant ◽  
Optical Properties ◽  
Surface Waves ◽  
Nonlinear Optical ◽  
Layer Structure ◽  
Finite Thickness ◽  
Critical Value ◽  
Field Structure ◽  
Finite Width ◽  
Border Regions

A three-layer structure consisting of a nonlinear optical medium with a stepwise change in the dielectric constant inside which there is a dielectric layer of finite thickness is considered. The surface waves of two types of symmetry with a special field structure can propagate along the layers. Domains of finite width with different optical properties in the border regions in a nonlinear medium are formed. The formation of domains, as well as the existence of surface waves, occurs at interlayer thicknesses not exceeding a certain critical value.

scholarly journals Entanglement in massive coupled oscillators

2011 ◽  
Vol 11 (3&4) ◽  
pp. 278-299
Author(s):  
Nathan L. Harshman ◽  
William F. Flynn
Keyword(s):  
Coupled Oscillators ◽  
Coherent States ◽  
Degrees Of Freedom ◽  
Classical Model ◽  
Reduced Density Matrix ◽  
One Dimension ◽  
Atomic Position ◽  
Pure States ◽  
Non Gaussian ◽  
Reduced Density

This article investigates entanglement of the motional states of massive coupled oscillators. The specific realization of an idealized diatomic molecule in one-dimension is considered, but the techniques developed apply to any massive particles with two degrees of freedom and a quadratic Hamiltonian. We present two methods, one analytic and one approximate, to calculate the interatomic entanglement for Gaussian and non-Gaussian pure states as measured by the purity of the reduced density matrix. The cases of free and trapped molecules and hetero- and homonuclear molecules are treated. In general, when the trap frequency and the molecular frequency are very different, and when the atomic masses are equal, the atoms are highly-entangled for molecular coherent states and number states. Surprisingly, while the interatomic entanglement can be quite large even for molecular coherent states, the covariance of atomic position and momentum observables can be entirely explained by a classical model with appropriately chosen statistical uncertainty.

scholarly journals Transition mechanism for a periodic bar-and-joint framework with limited degrees of freedom controlled by uniaxial load and internal stiffness

2018 ◽  
Vol 5 (6) ◽  
pp. 180139 ◽  
Author(s):  
H. Tanaka ◽  
K. Hamada ◽  
Y. Shibutani
Keyword(s):  
Exact Solution ◽  
Transition State ◽  
Nonlinear Elasticity ◽  
External Force ◽  
Degrees Of Freedom ◽  
Critical Value ◽  
Uniaxial Load ◽  
Transition Mechanism ◽  
Two Systems ◽  
Load Displacement

A specific periodic bar-and-joint framework with limited degrees of freedom is shown to have a transition mechanism when subjected to an external force. The static nonlinear elasticity of this framework under a uniaxial load is modelled with the two angular variables specifying the rotation and distortion of the linked square components. Numerically exploring the equilibrium paths then reveals a transition state of the structure at a critical value of the internal stiffness. A simplified formulation of the model with weak nonlinear terms yields an exact solution of its transition state. Load–displacement behaviour and stability for the two systems with or without approximation are analysed and compared.

Surface waves on water of non-uniform depth

1958 ◽  
Vol 4 (6) ◽  
pp. 607-614 ◽  
Author(s):  
Joseph B. Keller
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Linear Theory ◽  
Gravity Waves ◽  
Geometrical Optics ◽  
Surface Wave Propagation ◽  
Special Cases

Gravity waves occur on the surface of a liquid such as water, and the manner in which they propagate depends upon its depth. Although this dependence is described in principle by the equations of the ‘exact linear theory’ of surface waves, these equations have not been solved except in some special cases. Therefore, oceanographers have been unable to use the theory to describe surface wave propagation in water whose depth varies in a general way. Instead they have employed a simplified geometrical optics theory for this purpose (see, for example, Sverdrup & Munk (1944)). It has been used very successfully, and consequently various attempts, only partially successful, have been made to deduce it from the exact linear theory. It is the purpose of this article to present a derivation which appears to be satisfactory and which also yields corrections to the geometrical optics theory.

Localized Modes in Periodic Systems With Nonlinear Disorders

1997 ◽  
Vol 64 (4) ◽  
pp. 940-945 ◽  
Author(s):  
C. W. Cai ◽  
H. C. Chan ◽  
Y. K. Cheung
Keyword(s):  
Degrees Of Freedom ◽  
Maximum Amplitude ◽  
Critical Value ◽  
Periodic Systems ◽  
Algebraic Equations ◽  
Localized Modes ◽  
Transformation Technique ◽  
Nonlinear Algebraic Equations ◽  
Coupling Stiffness ◽  
Localized Mode

The localized modes of periodic systems with infinite degrees-of-freedom and having one or two nonlinear disorders are examined by using the Lindstedt-Poincare (L-P) method. The set of nonlinear algebraic equations with infinite number of variables is derived and solved exactly by the U-transformation technique. It is shown that the localized modes exist for any amount of the ratio between the linear coupling stiffness kc and the coefficient γ of the nonlinear disordered term, and the nonsymmetric localized mode in the periodic system with two nonlinear disorders occurs as the ratio kc/γ, decreasing to a critical value depending on the maximum amplitude.

DIGITAL ORIGIN OF COSMIC INFLATION

2010 ◽  
Vol 25 (18) ◽  
pp. 1483-1489
Author(s):  
CHUNG-HSIEN CHOU ◽  
HOI-LAI YU
Keyword(s):  
Degrees Of Freedom ◽  
Dynamical Evolution ◽  
Critical Value ◽  
Cosmic Inflation ◽  
The Past ◽  
Physical Universe ◽  
Communication Time ◽  
Hubble Radius ◽  
Time Required ◽  
The Universe

Assuming our physical universe processes and registers information to determine its dynamical evolution, one can put serious constraints on the cosmology that our universe can bear, in particular, the origin of cosmic inflation. The universe evolves to gain her computation capacity which is linear in time t. On the other hand, the growth in content of degrees of freedom (i.e. by integrating in more galaxies) is as t3/2 through expansion. When the in flux of degrees of freedom of the universe grows beyond some value, the computation capacity of the universe becomes insufficient to determine its evolution, the universe fixes its Hubble radius and inflates away its degrees of freedom within its horizon to regain dynamical evolution. The length of inflation is determined by the communication time required by the universe to become aware of the dropping in the degrees of freedom below some critical value by inflation and is proportional to its Hubble radius. We predict that there can be multiple cosmic inflations. The next inflation era will stop after inflating for a period of 1019 sec if the past inflation period of our universe was 10-33 sec.

Finite Temperature Quasicontinuum Methods

1998 ◽  
Vol 538 ◽  
Author(s):  
Vivek Shenoy ◽  
Vijay Shenoy ◽  
Rob Phillips
Keyword(s):  
Free Energy ◽  
Energy Minimization ◽  
Finite Temperature ◽  
Degrees Of Freedom ◽  
Elastic Moduli ◽  
Dislocation Core ◽  
Minimization Method ◽  
Free Energy Minimization ◽  
Minimization Technique ◽  
Frame Work

AbstractIn this paper we extend the quasi-continuum method to study equilibrium properties of defects at finite temperatures. We present a derivation of an effective energy function to perform Monte Carlo simulations in a mixed atomistic and continuum setting. It is shown that the free energy minimization technique can be easily incorporated into the quasi-continuum frame work, permitting a reduction of the full set of atomistic degrees of freedom even in the finite temperature setting. The validity of the proposed methods is demonstrated by computing the thermal expansion and the temperature dependence of the elastic moduli for Cu. We also employ the quasi-continuum free energy minimization method to study the finite temperarure structure of a dislocation core in Al.

Diffusive Interaction Leading to Dephasing of Coupled Neural Oscillators

1997 ◽  
Vol 07 (04) ◽  
pp. 869-876 ◽  
Author(s):  
Seung Kee Han ◽  
Christian Kurrer ◽  
Yoshiki Kuramoto
Keyword(s):  
Asymptotic Behavior ◽  
Phase Velocity ◽  
Limit Cycle ◽  
Coupled Oscillators ◽  
Control Parameter ◽  
Critical Value ◽  
Homoclinic Bifurcation ◽  
Neural Oscillators ◽  
Diffusive Coupling ◽  
Synchronization Of Oscillators

It is usually believed that strong diffusive coupling in one of the dynamical variables is well-suited for imposing synchronization of oscillators. But it was recently shown that weak diffusive coupling, counter-intuitively, can lead to dephasing of coupled neural oscillators. In this paper, we investigate how diffusively coupled oscillators become dephasing. For this we study a system of coupled neural oscillators on a limit cycle generated through a homoclinic bifurcation. We examine the asymptotic behavior of diffusive coupling as the control parameter approaches the critical value for which the homoclinic bifurcation occurs. In this study, we show that the gradient of phase velocity near the limit cycle is essential in generating dephasing through diffusive interaction.

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