scholarly journals Two-dimensional Riemannian and Lorentzian geometries from second-order ODE’s

2004 ◽  
Vol 45 (11) ◽  
pp. 4186-4190 ◽  
Author(s):  
Emanuel Gallo
Keyword(s):  
Second Order ◽  
Two Dimensional

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

Numerical Simulation of Die Swell of Second-Order Fluids Using Smoothed Particle Hydrodynamics

2010 ◽  
Author(s):  
Samir Hassan Sadek ◽  
Mehmet Yildiz
Keyword(s):  
Free Surface ◽  
Smoothed Particle Hydrodynamics ◽  
Second Order ◽  
Rheological Parameters ◽  
Die Swell ◽  
Two Dimensional ◽  
Polymeric Fluid ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Second Order Fluids

This work presents the development of both weakly compressible and incompressible Smoothed Particle Hydrodynamics (SPH) models for simulating two-dimensional transient viscoelastic free surface flow which has extensive applications in polymer processing industries. As an illustration with industrial significance, we have chosen to model the extrudate swell of a second-order polymeric fluid. The extrudate or die swell is a phenomenon that takes place during the extrusion of polymeric fluids. When a polymeric fluid is forced through a die to give a polymer its desired shape, due to its viscoelastic non-Newtonian nature, it shows a tendency to swell or contract at the die exit depending on its rheological parameters. The die swell phenomenon is a typical example of a free surface problem where the free surface is formed at the die exit after the polymeric fluid has been extruded. The swelling process leads to an undesired increase in the dimensions of the extrudate. To be able to obtain a near-net shape product, the flow in the extrusion process should be well-understood to shed some light on the important process parameters behind the swelling phenomenon. To this end, a systematic study has been carried out to compare constitutive models proposed in literature for second-order fluids in terms of their ability to capture the physics behind the swelling phenomenon. The effect of various process and rheological parameters on the die swell such as the extrusion velocity, normal stress coefficients, and Reynolds and Deborah numbers have also been investigated. The models developed here can predict both swelling and contraction of the extrudate successfully. The die swell problem was solved for a wide range of Deborah numbers and for two different Re numbers. The numerical model was validated through the solution of fully developed Newtonian and Non-Newtonian viscoelastic flows in a two-dimensional channel, and the results of these two benchmark problems were compared with analytic solutions, and good agreements were obtained.

TWO-DIMENSIONAL NONLINEAR OPTICS SPECTROSCOPY: SIMULATIONS AND EXPERIMENTAL DEMONSTRATION

1996 ◽  
Vol 05 (03) ◽  
pp. 465-476 ◽  
Author(s):  
L. LEPETIT ◽  
G. CHÉRIAUX ◽  
M. JOFFRE
Keyword(s):  
Fourier Transform ◽  
Nonlinear Response ◽  
Two Dimensions ◽  
Second Order ◽  
Phase Matching ◽  
Two Dimensional ◽  
Experimental Demonstration ◽  
Spectral Interferometry ◽  
Dimensional Measurement ◽  
A New Technique

We propose a new technique, using femtosecond Fourier-transform spectral interferometry, to measure the second-order nonlinear response of a material in two dimensions of frequency. We show numerically the specific and unique information obtained from such a two-dimensional measurement. The technique is demonstrated by measuring the second-order phase-matching map of two non-resonant nonlinear crystals.

scholarly journals Characterizing sand ripples at equilibrium phases

2013 ◽  
Vol 61 (4) ◽  
pp. 293-298 ◽  
Author(s):  
Jie Qin ◽  
Deyu Zhong ◽  
Guangqian Wang
Keyword(s):  
Time Series ◽  
Random Fields ◽  
Morphological Characteristics ◽  
Structure Functions ◽  
Second Order ◽  
Order Structure ◽  
Two Dimensional ◽  
Sand Ripples ◽  
Digital Elevation ◽  
Equilibrium Phases

Abstract Morphological characteristics of ripples are analyzed considering bed surfaces as two dimensional random fields of bed elevations. Two equilibrium phases are analyzed with respect to successive development of ripples based on digital elevation models. The key findings relate to the shape of the two dimensional second-order structure functions and multiscaling behavior revealed by higher-order structure functions. Our results suggest that (1) the two dimensional second-order structure functions can be used to differentiate the two equilibrium phases of ripples; and (2) in contrast to the elevational time series of ripples that exhibit significant multiscaling behavior, the DEMs of ripples at both equilibrium phases do not exhibit multiscaling behavior.

Diffraction by a half plane perpendicular to the distinguished axis of a gyrotropic medium (oblique incidence)

1981 ◽  
Vol 59 (3) ◽  
pp. 403-424 ◽  
Author(s):  
S. Przeździecki ◽  
R. A. Hurd
Keyword(s):  
Half Plane ◽  
Fourier Transforms ◽  
Boundary Value ◽  
Diffraction Problem ◽  
Closed Form Solution ◽  
Second Order ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Electromagnetic Plane Wave

An exact, closed form solution is found for the following half plane diffraction problem. (I) The medium surrounding the half plane is gyrotropic. (II) The scattering half plane is perfectly conducting and oriented perpendicular to the distinguished axis of the medium. (III) The direction of propagation of the incident electromagnetic plane wave is arbitrary (skew) with respect to the edge of the half plane. The result presented is a generalization of a solution for the same problem with incidence normal to the edge of the half plane (two-dimensional case).The fundamental, distinctive feature of the problem is that it constitutes a boundary value problem for a system of two coupled second order partial differential equations. All previously solved electromagnetic diffraction problems reduced to boundary value problems for either one or two uncoupled second order equations. (Exception: the two-dimensional case of the present problem.) The problem is formulated in terms of the (generalized) scalar Hertz potentials and leads to a set of two coupled Wiener–Hopf equations. This set, previously thought insoluble by quadratures, yields to the Wiener–Hopf–Hilbert method.The three-dimensional solution is synthesized from appropriate solutions to two-dimensional problems. Peculiar waves of ghost potentials, which correspond to zero electromagnetic fields play an essential role in this synthesis. The problem is two-moded: that is, superpositions of both ordinary and extraordinary waves are necessary for the spectral representation of the solution. An important simplifying feature of the problem is that the coupling of the modes is purely due to edge diffraction, there being no reflection coupling. The solution is simple in that the Fourier transforms of the potentials are just algebraic functions. Basic properties of the solution are briefly discussed.

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