scholarly journals Traveling-Standing Water Waves

Fluids ◽  
2021 ◽  
Vol 6 (5) ◽  
pp. 187
Author(s):  
Jon Wilkening
Keyword(s):  
Traveling Waves ◽  
Water Waves ◽  
Shooting Method ◽  
Perturbation Expansion ◽  
Parameter Family ◽  
Amplitude Parameter ◽  
Chebyshev Interpolation ◽  
Horizontal Momentum ◽  
The Given ◽  
Two Parameter

We propose a new two-parameter family of hybrid traveling-standing (TS) water waves in infinite depth that evolve to a spatial translation of their initial condition at a later time. We use the square root of the energy as an amplitude parameter and introduce a traveling parameter that naturally interpolates between pure traveling waves moving in either direction and pure standing waves in one of four natural phase configurations. The problem is formulated as a two-point boundary value problem and a quasi-periodic torus representation is presented that exhibits TS-waves as nonlinear superpositions of counter-propagating traveling waves. We use an overdetermined shooting method to compute nearly 50,000 TS-wave solutions and explore their properties. Examples of waves that periodically form sharp crests with high curvature or dimpled crests with negative curvature are presented. We find that pure traveling waves maximize the magnitude of the horizontal momentum among TS-waves of a given energy. Numerical evidence suggests that the two-parameter family of TS-waves contains many gaps and disconnections where solutions with the given parameters do not exist. Some of these gaps are shown to persist to zero-amplitude in a fourth-order perturbation expansion of the solutions in powers of the amplitude parameter. Analytic formulas for the coefficients of this perturbation expansion are identified using Chebyshev interpolation of solutions computed in quadruple-precision.

Added Moment of Inertia of a Rotating Ship Section

1979 ◽  
Vol 23 (03) ◽  
pp. 171-174
Author(s):  
L. Landweber
Keyword(s):  
Laurent Series ◽  
Parameter Family ◽  
Thickness Ratio ◽  
Moment Of Inertia ◽  
Section Area ◽  
Family Of Curves ◽  
The Given ◽  
Two Parameter

An expression for the added moment of inertia of a rotating ship section, in terms of the coefficients of the Laurent series of the function which maps the given section into a circle, has been derived. The method is applied to the two-parameter family of Lewis forms and the results are presented as a family of curves which gives the coefficient of the added moment of inertia as a function of the thickness ratio and the section-area coefficient of a form. A second application, to a square section, indicates that a sufficiently accurate value of the added moment of inertia can be obtained with little arithmetical work even in a case where the Laurent series is an infinite one.

scholarly journals The holographic conformal manifold of 3d $$ \mathcal{N} $$ = 2 S-fold SCFTs

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Nikolay Bobev ◽  
Friðrik Freyr Gautason ◽  
Jesse van Muiden
Keyword(s):  
String Theory ◽  
Three Dimensional ◽  
Parameter Family ◽  
Global Symmetry ◽  
Maximal Supergravity ◽  
All Solutions ◽  
Operator Spectrum ◽  
Type Iib String Theory ◽  
Two Parameter

Abstract We employ a non-compact gauging of four-dimensional maximal supergravity to construct a two-parameter family of AdS4 J-fold solutions preserving $$ \mathcal{N} $$ N = 2 supersymmetry. All solutions preserve $$ \mathfrak{u} $$ u (1) × $$ \mathfrak{u} $$ u (1) global symmetry and in special limits we recover the previously known $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{u} $$ u (1) invariant $$ \mathcal{N} $$ N = 2 and $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{su} $$ su (2) invariant $$ \mathcal{N} $$ N = 4 J-fold solutions. This family of AdS4 backgrounds can be uplifted to type IIB string theory and is holographically dual to the conformal manifold of a class of three-dimensional S-fold SCFTs obtained from the $$ \mathcal{N} $$ N = 4 T [U(N)] theory of Gaiotto-Witten. We find the spectrum of supergravity excitations of the AdS4 solutions and use it to study how the operator spectrum of the three-dimensional SCFT depends on the exactly marginal couplings.

Dynamics of a two-parameter family of maps of the interval

1986 ◽  
Vol 10 (5) ◽  
pp. 415-423 ◽  
Author(s):  
J.R. Pounder ◽  
Thomas D. Rogers
Keyword(s):  
Parameter Family ◽  
Two Parameter

Large-amplitude unsteady flow in liquid-filled elastic tubes

1967 ◽  
Vol 29 (3) ◽  
pp. 513-538 ◽  
Author(s):  
John H. Olsen ◽  
Ascher H. Shapiro
Keyword(s):  
Water Waves ◽  
Large Amplitude ◽  
Linear Equations ◽  
Perturbation Expansion ◽  
Elastic Tube ◽  
Fluid Viscosity ◽  
Elastic Tubes ◽  
Non Linear ◽  
Laminar And Turbulent Flow ◽  
Large Amplitude Motion

Unsteady, large-amplitude motion of a viscous liquid in a long elastic tube is investigated theoretically and experimentally, in the context of physiological problems of blood flow in the larger arteries. Based on the assumptions of long wavelength and longitudinal tethering, a quasi-one-dimensional model is adopted, in which the tube wall moves only radially, and in which only longitudinal pressure gradients and fluid accelerations are important. The effects of fluid viscosity are treated for both laminar and turbulent flow. The governing non-linear equations are solved analytically in closed form by a perturbation expansion in the amplitude parameter, and, for comparison, by numerical integration of the characteristic curves. The two types of solution are compared with each other and with experimental data. Non-linear effects due to large amplitude motion are found to be not as large as those found in similar problems in gasdynamics and water waves.

CONTINUITY OF ENTROPY FOR A TWO-PARAMETER FAMILY OF BIMODAL MAPS

1995 ◽  
pp. 101-116
Author(s):  
LOUIS BLOCK ◽  
ROZA GALEEVA ◽  
JAMES KEESLING
Keyword(s):  
Parameter Family ◽  
Two Parameter
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