One and Two-Parameter Bifurcations to Divergence and Flutter in the Three-Dimensional Motions of a Fluid Conveying Viscoelastic Tube with D4-Symmetry

1995 ◽  
pp. 161-178
Author(s):  
A. Steindl ◽  
H. Troger
Keyword(s):  
Three Dimensional ◽  
Viscoelastic Tube ◽  
Two Parameter

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.

scholarly journals The Yamada Model for a Self-Pulsing Laser: Bifurcation Structure for Nonidentical Decay Times of Gain and Absorber

2020 ◽  
Vol 30 (14) ◽  
pp. 2030039
Author(s):  
Robert Otupiri ◽  
Bernd Krauskopf ◽  
Neil G. R. Broderick
Keyword(s):  
Three Dimensional ◽  
Equation Model ◽  
Decay Rates ◽  
Phase Portraits ◽  
Stable Phase ◽  
Bifurcation Structure ◽  
Decay Times ◽  
Comprehensive Picture ◽  
Two Parameter ◽  
Parameter Bifurcation

We consider self-pulsing in lasers with a gain section and an absorber section via a mechanism known as [Formula: see text]-switching, as described mathematically by the Yamada ordinary differential equation model for the gain, the absorber and the laser intensity. More specifically, we are interested in the case that gain and absorber decay on different time-scales. We present an overall bifurcation structure by showing how the two-parameter bifurcation diagram in the plane of pump strength versus decay rate of the gain changes with the ratio between the two decay rates. In total, there are ten cases BI to BX of qualitatively different two-parameter bifurcation diagrams, which we present with an explanation of the transitions between them. Moroever, we show for each of the associated eleven cases of structurally stable phase portraits (in open regions of the parameter space) a three-dimensional representation of the organization of phase space by the two-dimensional manifolds of saddle equilibria and saddle periodic orbits. The overall bifurcation structure provides a comprehensive picture of the observable dynamics, including multistability and excitability, which we expect to be of relevance for experimental work on [Formula: see text]-switching lasers with different kinds of saturable absorbers.

scholarly journals Moffatt-type flows in a trihedral cone

2013 ◽  
Vol 725 ◽  
pp. 446-461 ◽  
Author(s):  
Julian F. Scott
Keyword(s):  
Linear Combination ◽  
Particle Motion ◽  
Particle Trajectory ◽  
Three Dimensional ◽  
Parameter Family ◽  
The Other ◽  
Transient Phase ◽  
Primary Flow ◽  
Special Cases ◽  
Two Parameter

AbstractThe three-dimensional analogue of Moffatt eddies is derived for a corner formed by the intersection of three orthogonal planes. The complex exponents of the first few modes are determined and the flows resulting from the primary modes (those which decay least rapidly as the apex is approached and, hence, should dominate the near-apex flow) examined in detail. There are two independent primary modes, one symmetric, the other antisymmetric, with respect to reflection in one of the symmetry planes of the cone. Any linear combination of these modes yields a possible primary flow. Thus, there is not one, but a two-parameter family of such flows. The particle-trajectory equations are integrated numerically to determine the streamlines of primary flows. Three special cases in which the flow is antisymmetric under reflection lead to closed streamlines. However, for all other cases, the streamlines are not closed and quasi-periodic limiting trajectories are approached when the trajectory equations are integrated either forwards or backwards in time. A generic streamline follows the backward-time trajectory in from infinity, undergoes a transient phase in which particle motion is no longer quasi-periodic, before being thrown back out to infinity along the forward-time trajectory.

Physiological Interaction, Its Mathematical Expression

Weed Science ◽  
1980 ◽  
Vol 28 (5) ◽  
pp. 573-579 ◽  
Author(s):  
Robert E. Drury
Keyword(s):  
Three Dimensional ◽  
Mathematical Expression ◽  
Continuous Functions ◽  
Fresh Weight ◽  
Regression Estimate ◽  
Independent Variables ◽  
Algebraic Expressions ◽  
Independent Variable ◽  
Two Parameter ◽  
Two Independent Variables

The concept of interaction arises in the context of continuous functions. Verbally, it is the action of one independent variable on the action of another, and vice versa, on a dependent variable. Quantitatively, it is the second partial derivative of a function with respect to two independent variables. Misconceptions have arisen from attempts to understand action and interaction in discrete terms. The algebraic expressions for the actions of diuron and phorate on the fresh weight of oats and their interaction were determined from the regression polynomial and plotted in three-dimensional graphs. Three other mutually incompatible methods of assessing interaction, namely, the Colby (with its modification, regression estimate), the two-parameter, and the topographical methods were evaluated.

ON THE STRUCTURE OF THE SOLUTIONS OF A TWO-PARAMETER FAMILY OF THREE-DIMENSIONAL ORDINARY DIFFERENTIAL EQUATIONS

2003 ◽  
Vol 13 (05) ◽  
pp. 1287-1298 ◽  
Author(s):  
SERKAN T. IMPRAM ◽  
RUSSELL JOHNSON ◽  
RAFFAELLA PAVANI
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Wide Range ◽  
Two Parameters ◽  
Two Parameter ◽  
Autonomous Ordinary Differential Equation

We analyze the global structure of the solutions of a three-dimensional, autonomous ordinary differential equation which depends on two parameters. We use graphical, heuristic, and rigorous arguments to show that as the parameters vary, a wide range of dynamical behavior is displayed.

Global and local hard X-ray tomography of a centimeter-size tumor vessel tree

2011 ◽  
Vol 19 (1) ◽  
pp. 114-125 ◽  
Author(s):  
Sabrina Lang ◽  
Marco Dominietto ◽  
Philippe Cattin ◽  
Alexandra Ulmann-Schuler ◽  
Timm Weitkamp ◽  
...  
Keyword(s):  
Spatial Resolution ◽  
Three Dimensional ◽  
Local Geometry ◽  
Absorption Coefficients ◽  
X Ray ◽  
Local Tomography ◽  
Histogram Matching ◽  
X Ray Absorption ◽  
Two Parameter ◽  
Tomography Data

The visualization of the vascular network in tumors down to the smallest vessels requires high spatial resolution and reasonable contrast. Stained corrosion casts of the microvasculature network guarantee superior X-ray absorption contrast and highest reproduction fidelity. Tomography of a centimeter-size tumor, however, is unfeasible at the spatial resolution needed to reveal the smallest vessels. Therefore, local tomography has been performed to visualize the smallest capillaries within the region of interest. These three-dimensional data show the detailed morphology, but the reconstructed absorption coefficients obtained in local tomography differ substantially from the absorption coefficients retrieved from the less detailed global tomography data. This paper deals with the adaptation of local tomography data using the global data and considers two-parameter histogram matching of the radiographs, sinogram extension, and multi-parameter cupping correction. It is demonstrated that two-parameter histogram matching of the radiographs already provides reasonable agreement. The change of the lens in front of the detector's camera, however, significantly affects the obtained local X-ray absorption coefficients in the tomograms predominantly owing to the dissimilar point-spread functions of the two configurations used, and much less to the fact that one of the data sets was acquired in a local geometry.

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