Amplitude Equations on Unstable Manifolds: singular behavior from neutral modes

1991 ◽  
pp. 97-108 ◽  
Author(s):  
John David Crawford
Keyword(s):  
Singular Behavior ◽  
Amplitude Equations ◽  
Unstable Manifolds

Distinguishing feast-watching from cringe-watching: Planned, social, and attentive binge-watching predicts increased well-being and decreased regret

2021 ◽  
pp. 135485652199918
Author(s):  
Matthew Pittman ◽  
Emil Steiner
Keyword(s):  
General Practice ◽  
Well Being ◽  
Positive Outcomes ◽  
Singular Behavior ◽  
Definition Of ◽  
Anxiety Depression

This study seeks to add nuance to the definition of binge-watching by identifying the subtypes of the general practice that reflect viewer rituals, motives, and outcomes. The two subtypes are (1) the healthy practice of ‘feast-watching’ and (2) the unhealthy practice of ‘cringe-watching’. While binge-watching as a singular behavior has been associated with anxiety, depression, and loneliness, a survey ( N = 800) finds that binge-watching which is solo, accidental, and distracted (cringe-watching) predicts increased regret and decreased well-being. However, binge-watching that is planned, social, and attentive (feast-watching) predicts positive outcomes. These subtypes add much needed organizational clarity to the discussion of binge-watching, which, due to its popularity, has grown into a catchall for extended video consumption.

scholarly journals On the singular behavior of the Stokes drift in layered miscible fluids

Wave Motion ◽  
2021 ◽  
Vol 102 ◽  
pp. 102712
Author(s):  
Jan Erik H. Weber ◽  
Kai H. Christensen
Keyword(s):  
Stokes Drift ◽  
Singular Behavior ◽  
Miscible Fluids

scholarly journals A substrate for brane shells from $$ T\overline{T} $$

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Jeremias Aguilera-Damia ◽  
Louise M. Anderson ◽  
Evan Coleman
Keyword(s):  
Three Dimensional ◽  
Radial Position ◽  
Singular Behavior ◽  
Curvature Singularity ◽  
Closed Timelike Curves ◽  
Finite Radius ◽  
Linear Dilaton ◽  
Singularity Resolution ◽  
New Interpretation ◽  
Single Trace

Abstract A solvable current-current deformation of the worldsheet theory of strings on AdS3 has been recently conjectured to be dual to an irrelevant deformation of the spacetime orbifold CFT, commonly referred to as single-trace $$ T\overline{T} $$ T T ¯ . These deformations give rise to a family of bulk geometries which realize a non-trivial flow towards the UV. For a particular sign of this deformation, the corresponding three-dimensional geometry approaches AdS3 in the interior, but has a curvature singularity at finite radius, beyond which there are closed timelike curves. It has been suggested that this singularity is due to the presence of “negative branes,” which are exotic objects that generically change the metric signature. We propose an alternative UV-completion for geometries displaying a similar singular behavior by cutting and gluing to a regular background which approaches a linear dilaton vacuum in the UV. In the S-dual picture, a singularity resolution mechanism known as the enhançon induces this transition by the formation of a shell of D5-branes at a fixed radial position near the singularity. The solutions involving negative branes gain a new interpretation in this context.

Study on the Geometrical Properties and Existence of Orbit Homoclinic to a Saddle Point in n-Dimensional Autonomous Vector Field with Polynomials

2018 ◽  
Vol 28 (14) ◽  
pp. 1850169
Author(s):  
Lingli Xie
Keyword(s):  
Vector Field ◽  
Saddle Point ◽  
Equilibrium Point ◽  
Necessary Conditions ◽  
Continuous System ◽  
Homoclinic Bifurcation ◽  
Stable And Unstable Manifolds ◽  
Geometrical Properties ◽  
Unstable Manifolds

According to the theory of stable and unstable manifolds of an equilibrium point, we firstly find out some geometrical properties of orbits on the stable and unstable manifolds of a saddle point under some brief conditions of nonlinear terms composed of polynomials for [Formula: see text]-dimensional time continuous system. These properties show that the orbits on stable and unstable manifolds of the saddle point will stay on the corresponding stable and unstable subspaces in the [Formula: see text]-neighborhood of the saddle point. Furthermore, the necessary conditions of existence for orbit homoclinic to a saddle point are exposed. Some examples including homoclinic bifurcation are given to indicate the application of the results. Finally, the conclusions are presented.

PATTERNS, DEFECTS, AND EVOLUTION OF BÉNARD–MARANGONI CELLS

1996 ◽  
Vol 06 (09) ◽  
pp. 1665-1671 ◽  
Author(s):  
J. BRAGARD ◽  
J. PONTES ◽  
M.G. VELARDE
Keyword(s):  
Fluid Layer ◽  
Ambient Air ◽  
Finite Geometry ◽  
Amplitude Equations ◽  
Ginzburg Landau ◽  
Weakly Nonlinear ◽  
Numerical Exploration ◽  
Ginzburg Landau Equations ◽  
Rigid Plane ◽  
Selection Of

We consider a thin fluid layer of infinite horizontal extent, confined below by a rigid plane and open above to the ambient air, with surface tension linearly depending on the temperature. The fluid is heated from below. First we obtain the weakly nonlinear amplitude equations in specific spatial directions. The procedure yields a set of generalized Ginzburg–Landau equations. Then we proceed to the numerical exploration of the solutions of these equations in finite geometry, hence to the selection of cells as a result of competition between the possible different modes of convection.

scholarly journals Hadamard–Perron theorems and effective hyperbolicity

2014 ◽  
Vol 36 (1) ◽  
pp. 23-63 ◽  
Author(s):  
VAUGHN CLIMENHAGA ◽  
YAKOV PESIN
Keyword(s):  
Closing Lemma ◽  
Stable And Unstable Manifolds ◽  
Local Dynamics ◽  
Local Diffeomorphisms ◽  
Finite Amount ◽  
Amount Of Information ◽  
Unstable Manifolds

We prove several new versions of the Hadamard–Perron theorem, which relates infinitesimal dynamics to local dynamics for a sequence of local diffeomorphisms, and in particular establishes the existence of local stable and unstable manifolds. Our results imply the classical Hadamard–Perron theorem in both its uniform and non-uniform versions, but also apply much more generally. We introduce a notion of ‘effective hyperbolicity’ and show that if the rate of effective hyperbolicity is asymptotically positive, then the local manifolds are well behaved with positive asymptotic frequency. By applying effective hyperbolicity to finite-orbit segments, we prove a closing lemma whose conditions can be verified with a finite amount of information.

Burgers turbulence model for a channel flow

1971 ◽  
Vol 47 (2) ◽  
pp. 321-335 ◽  
Author(s):  
Jon Lee
Keyword(s):  
Channel Flow ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Amplitude Equations ◽  
Fourier Amplitude ◽  
Navier Stokes Equations ◽  
Burgers Model ◽  
Model Dynamics

The truncated Burgers models have a unique equilibrium state which is defined continuously for all the Reynolds numbers and attainable from a realizable class of initial disturbances. Hence, they represent a sequence of convergent approximations to the original (untruncated) Burgers problem. We have pointed out that consideration of certain degenerate equilibrium states can lead to the successive turbulence-turbulence transitions and finite-jump transitions that were suggested by Case & Chiu. As a prototype of the Navier–Stokes equations, Burgers model can simulate the initial-value type of numerical integration of the Fourier amplitude equations for a turbulent channel flow. Thus, the Burgers model dynamics display certain idiosyncrasies of the actual channel flow problem described by a truncated set of Fourier amplitude equations, which includes only a modest number of modes due to the limited capability of the computer at hand.

Smooth conjugacy of centre manifolds

1992 ◽  
Vol 120 (1-2) ◽  
pp. 61-77 ◽  
Author(s):  
Almut Burchard ◽  
Bo Deng ◽  
Kening Lu
Keyword(s):  
Differential Equations ◽  
Equilibrium Point ◽  
Ordinary Differential Equations ◽  
Parabolic Equations ◽  
Geometric Theory ◽  
Unstable Manifolds ◽  
Centre Manifolds ◽  
Smooth Conjugacy

SynopsisIn this paper, we prove that for a system of ordinary differential equations of class Cr+1,1, r≧0 and two arbitrary Cr+1, 1 local centre manifolds of a given equilibrium point, the equations when restricted to the centre manifolds are Cr conjugate. The same result is proved for similinear parabolic equations. The method is based on the geometric theory of invariant foliations for centre-stable and centre-unstable manifolds.

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