Shell models of two-dimensional Coulomb crystals: Assessment and comparison with the three-dimensional case

2012 ◽  
Vol 136 (11) ◽  
pp. 114306 ◽  
Author(s):  
Jerzy Cioslowski ◽  
Joanna Albin
Keyword(s):  
Three Dimensional ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Shell Models ◽  
Coulomb Crystals

Three-dimensional disturbances to a mixing layer in the nonlinear critical-layer regime

1995 ◽  
Vol 291 ◽  
pp. 57-81 ◽  
Author(s):  
S. M. Churilov ◽  
I. G. Shukhman
Keyword(s):  
Travelling Waves ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Critical Layer ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
New Type ◽  
Two Stages

We consider the nonlinear spatial evolution in the streamwise direction of slightly three-dimensional disturbances in the form of oblique travelling waves (with spanwise wavenumber kz much less than the streamwise one kx) in a mixing layer vx = u(y) at large Reynolds numbers. A study is made of the transition (with the growth of amplitude) to the regime of a nonlinear critical layer (CL) from regimes of a viscous CL and an unsteady CL, which we have investigated earlier (Churilov & Shukhman 1994). We have found a new type of transition to the nonlinear CL regime that has no analogy in the two-dimensional case, namely the transition from a stage of ‘explosive’ development. A nonlinear evolution equation is obtained which describes the development of disturbances in a regime of a quasi-steady nonlinear CL. We show that unlike the two-dimensional case there are two stages of disturbance growth after transition. In the first stage (immediately after transition) the amplitude A increases as x. Later, at the second stage, the ‘classical’ law A ∼ x2/3 is reached, which is usual for two-dimensional disturbances. It is demonstrated that with the growth of kz the region of three-dimensional behaviour is expanded, in particular the amplitude threshold of transition to the nonlinear CL regime from a stage of ‘explosive’ development rises and therefore in the ‘strongly three-dimensional’ limit kz = O(kx) such a transition cannot be realized in the framework of weakly nonlinear theory.

On the Hydrodynamic Interaction Between Ship and Free-Surface Motions on Vessels With Moonpools

2019 ◽  
Author(s):  
Senthuran Ravinthrakumar ◽  
Trygve Kristiansen ◽  
Babak Ommani
Keyword(s):  
Free Surface ◽  
Flow Separation ◽  
Coupling Effect ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Navier Stokes ◽  
Linear Potential ◽  
Two Dimensional ◽  
Sloshing Mode ◽  
Vessel Motion

Abstract Coupling between moonpool resonance and vessel motion is investigated in two-dimensional and quasi three-dimensional settings, where the models are studied in forced heave and in freely floating conditions. The two-dimensional setups are with a recess, while the quasi three-dimensional setups are without recess. One configuration with recess is presented for the two-dimensional case, while three different moonpool sizes (without recess) are tested for the quasi three-dimensional setup. A large number of forcing periods, and three wave steepnesses are tested. Boundary Element Method (BEM) and Viscous BEM (VBEM) time-domain codes based on linear potential flow theory, and a Navier–Stokes solver with linear free-surface and body-boundary conditions, are implemented to investigate resonant motion of the free-surface and the model. Damping due to flow separation from the sharp corners of the moonpool inlets is shown to matter for both vessel motions and moonpool response around the piston mode. In general, the CFD simulations compare well with the experimental results. BEM over-predicts the response significantly at resonance. VBEM provides improved results compared to the BEM, but still over-predicts the response. In the two-dimensional study there are significant coupling effects between heave, pitch and moonpool responses. In the quasi three-dimensional tests, the coupling effect is reduced significantly as the moonpool dimensions relative to the displaced volume of the ship is reduced. The first sloshing mode is investigated in the two-dimensional case. The studies show that damping due to flow separation is dominant. The vessel motions are unaffected by the moonpool response around the first sloshing mode.

Pipe Response Under Concentrated Lateral Loads and External Pressure

2005 ◽  
Author(s):  
Spyros A. Karamanos ◽  
Charis Eleftheriadis
Keyword(s):  
Three Dimensional ◽  
External Pressure ◽  
Absorption Capacity ◽  
Pressure Effects ◽  
Analytical Models ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Lateral Loads ◽  
Offshore Pipelines ◽  
Different Levels

The present paper examines the denting deformation of offshore pipelines and tubular members (D/t≤50) subjected to lateral (transverse) quasi-static loading in the presence of uniform external pressure. Particular emphasis is given on pressure effects on the ultimate lateral load of tubes and on their energy absorption capacity. Pipe segments are modeled with shell finite elements, accounting for geometric and material nonlinearities, and give very good predictions compared with test data from non-pressurized pipes. Lateral loading between two rigid plates, a two-dimensional case, is examined first. Three-dimensional case, are also analyzed, where the load is applied either through a pair of opposite wedge-shaped denting tools or a single spherical denting tool. Load-deflection curves for different levels of external pressure are presented, which indicate that pressure has significant influence on pipe response and strength. Finally, simplified analytical models are proposed for the two-dimensional and three-dimensional load configurations, which yield closed-form expressions, compare fairly well with the finite element results and illustrate some important features of pipeline response in a clear and elegant manner.

On: “Inversion of gravity profiles by use of a Backus‐Gilbert approach” by William R. Green (GEOPHYSICS, October 1975, p. 763–772).

Geophysics ◽  
1976 ◽  
Vol 41 (4) ◽  
pp. 777-777
Author(s):  
Ramesh Chander
Keyword(s):  
Gravity Anomaly ◽  
Total Mass ◽  
Gravity Data ◽  
Unit Length ◽  
Three Dimensional ◽  
Density Model ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Mass Excess ◽  
Seminal Paper

An important possible constraint on a density model obtained from inversion of gravity data has been overlooked in the seminal paper by Green. The computed density model should be such that the corresponding total mass excess or deficit per unit length in a two‐dimensional case, or total mass excess or deficit in a three‐dimensional case, should be comparable to the value obtained by applying Gauss’s theorem to the observed gravity anomaly data (Grant and West, 1965, p. 227–28 and p. 232).

Three-dimensional ray tracing and the method of principal curvature for geometric spreading

1983 ◽  
Vol 73 (3) ◽  
pp. 765-780
Author(s):  
Jia-Ju Lee ◽  
Charles A. Langston
Keyword(s):  
Principal Curvature ◽  
Three Dimensional ◽  
Seismic Energy ◽  
Front Surface ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Ray Method ◽  
P Waves ◽  
Curved Boundaries ◽  
Wave Source

abstract A three-dimensional ray method is used to compute three components of ground motion for complex structures involving curved boundaries. The method of principal curvature is developed to compute geometrical spreading of rays. This method, commonly used in electromagnetic wave propagation problems, employs phase matching at model interfaces and analysis of the wave front surface metric as the ray propagates throughout the model. It is an elegant way to examine the characteristics of three-dimensional caustics. Results computed for a two-dimensional canonical basin model with a plane SH-wave source are compared and are found to be in good agreement with those previously obtained by other independent numerical methods. Relaxing the restriction that the incident wave be perpendicular to the basin symmetry axis gives rise to large amplitude vertical and radial motions for incident SH waves and large tangential motions for incident P waves. As in the two-dimensional case, seismic energy is geometrically focused in the central region of the basin but strong later arrivals from the curved boundaries are not well developed in the three-dimensional case. The method is of direct use in analyzing three-dimensional crustal structure from off-azimuth P to S and S to P conversions.

Exact, Hierarchical Solutions for Localized Loadings in Isotropic, Laminated, and Sandwich Shells

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
E. Carrera ◽  
G. Giunta
Keyword(s):  
Three Dimensional ◽  
Bending Moment ◽  
Two Dimensional ◽  
Application Area ◽  
Spherical Shells ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
Transverse Pressure ◽  
Shell Models ◽  
Stress And Deformation

This paper presents closed form solutions for simply supported cylindrical and spherical shells subjected to uniform localized distributions of transverse pressure and bending moment. These distributions have been expanded in terms of Fourier’s series for which Navier type “exact” solutions have been found for the governing differential equations of the employed shell theories. Shells made of isotropic materials, composites laminates, and sandwich have been analyzed. Carrera’s unified formulation has been adopted in order to implement a large variety of two-dimensional theories. Classical, refined, zigzag, layerwise, and mixed theories are compared in order to evaluate the stress and deformation variables. Conclusions are drawn with respect to the accuracy of the various theories for the considered loadings and layouts. The importance of the refined shell models in order to describe accurately the three-dimensional stress state in the neighborhood of the localized loading application area is outlined.

FINDING SIMPLICES CONTAINING THE ORIGIN IN TWO AND THREE DIMENSIONS

2011 ◽  
Vol 21 (05) ◽  
pp. 495-506 ◽  
Author(s):  
KHALED ELBASSIONI ◽  
AMR ELMASRY ◽  
KAZUHISA MAKINO
Keyword(s):  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Line Segments

We show that finding the simplices containing a fixed given point among those defined on a set of n points can be done in O(n + k) time for the two-dimensional case, and in O(n2 + k) time for the three-dimensional case, where k is the number of these simplices. As a byproduct, we give an alternative (to the algorithm in Ref. 4) O(n log r) algorithm that finds the red-blue boundary for n bichromatic points on the line, where r is the size of this boundary. Another byproduct is an O(n2 + t) algorithm that finds the intersections of line segments having two red endpoints with those having two blue endpoints defined on a set of n bichromatic points in the plane, where t is the number of these intersections.

Release of a viscous power-law fluid over an inviscid ocean

2012 ◽  
Vol 700 ◽  
pp. 63-76 ◽  
Author(s):  
Samuel S. Pegler ◽  
John R. Lister ◽  
M. Grae Worster
Keyword(s):  
Power Law ◽  
Large Time ◽  
Three Dimensional ◽  
Shear Thinning ◽  
Capillary Forces ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Power Law Fluid ◽  
Initial Shape ◽  
Algebraic Decay

AbstractWe consider the two- and three-dimensional spreading of a finite volume of viscous power-law fluid released over a denser inviscid fluid and subject to gravitational and capillary forces. In the case of gravity-driven spreading, with a power-law fluid having strain rate proportional to stress to the power $n$, there are similarity solutions with the extent of the current being proportional to ${t}^{1/ n} $ in the two-dimensional case and ${t}^{1/ 2n} $ in the three-dimensional case. Perturbations from these asymptotic states are shown to retain their initial shape but to decay relatively as ${t}^{\ensuremath{-} 1} $ in the two-dimensional case and ${t}^{\ensuremath{-} 3/ (n+ 3)} $ in the three-dimensional case. The former is independent of $n$, whereas the latter gives a slower rate of relative decay for fluids that are more shear-thinning. In cases where the layer is subject to a constraining surface tension, we determine the evolution of the layer towards a static state of uniform thickness in which the gravitational and capillary forces balance. The asymptotic form of this convergence is shown to depend strongly on $n$, with rapid finite-time algebraic decay in shear-thickening cases, large-time exponential decay in the Newtonian case and slow large-time algebraic decay in shear-thinning cases.

scholarly journals L-Fuzzy Sets and Isomorphic Lattices: Are All the “New” Results Really New? †

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 146 ◽  
Author(s):  
Erich Klement ◽  
Radko Mesiar
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Pythagorean Fuzzy Sets ◽  
Truth Values ◽  
Isomorphic Type

We review several generalizations of the concept of fuzzy sets with two- or three-dimensional lattices of truth values and study their relationship. It turns out that, in the two-dimensional case, several of the lattices of truth values considered here are pairwise isomorphic, and so are the corresponding families of fuzzy sets. Therefore, each result for one of these types of fuzzy sets can be directly rewritten for each (isomorphic) type of fuzzy set. Finally we also discuss some questionable notations, in particular, those of “intuitionistic” and “Pythagorean” fuzzy sets.

scholarly journals Stability analysis of three-dimensional breather solitons in a Bose–Einstein condensate

2005 ◽  
Vol 461 (2063) ◽  
pp. 3561-3574 ◽  
Author(s):  
M Matuszewski ◽  
E Infeld ◽  
G Rowlands ◽  
M Trippenbach
Keyword(s):  
Three Dimensional ◽  
Einstein Condensate ◽  
Dimensional Case ◽  
Two Dimensional ◽  
One Dimensional ◽  
Stability Properties ◽  
Bose Einstein Condensate ◽  
The Stability ◽  
Bose Einstein ◽  
Dimensional Soliton

We investigated the stability properties of breather soliton trains in a three-dimensional Bose–Einstein condensate (BEC) with Feshbach-resonance management of the scattering length. This is done so as to generate both attractive and repulsive interaction. The condensate is confined only by a one-dimensional optical lattice and we consider strong, moderate and weak confinement. By strong confinement we mean a situation in which a quasi two-dimensional soliton is created. Moderate confinement admits a fully three-dimensional soliton. Weak confinement allows individual solitons to interact. Stability properties are investigated by several theoretical methods such as a variational analysis, treatment of motion in effective potential wells, and collapse dynamics. Armed with all the information forthcoming from these methods, we then undertake a numerical calculation. Our theoretical predictions are fully confirmed, perhaps to a higher degree than expected. We compare regions of stability in parameter space obtained from a fully three-dimensional analysis with those from a quasi two-dimensional treatment, when the dynamics in one direction are frozen. We find that in the three-dimensional case the stability region splits into two parts. However, as we tighten the confinement, one of the islands of stability moves toward higher frequencies and the lower frequency region becomes more and more like that for the quasi two-dimensional case. We demonstrate these solutions in direct numerical simulations and, importantly, suggest a way of creating robust three-dimensional solitons in experiments in a BEC in a one-dimensional lattice.

Sign in / Sign up

Export Citation Format

Share Document