Instantaneous Kinematics of a Tangent-Plane in Two-Parameter Space Motion

1994 ◽  
Vol 116 (1) ◽  
pp. 210-214
Author(s):  
D. P. Sathyadev ◽  
A. H. Soni
Keyword(s):  
Parameter Space ◽  
Tangent Plane ◽  
Plane Motion ◽  
Parameter Family ◽  
Spherical Image ◽  
Space Motion ◽  
Two Parameter

A tangent-plane undergoing two-parameter motion envelopes a surface called the tangent-plane envelope. Such surfaces can be considered as the envelope of a two-parameter family of planes or ∞2 family of planes. The properties of the tangent-plane motion are characterized through the properties of the spherical image of the normal to the surface it envelopes. This paper presents a methodology to locate a family of planes that envelope surfaces with similar characteristics.

scholarly journals Triality and the consistent reductions on AdS3 × S3

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Camille Eloy ◽  
Gabriel Larios ◽  
Henning Samtleben
Keyword(s):  
Field Theory ◽  
Nonlinear Dynamics ◽  
Parameter Space ◽  
Three Dimensional ◽  
Parameter Family ◽  
Duality Group ◽  
Consistent Truncations ◽  
Two Parameter ◽  
Kaluza Klein

Abstract We study compactifications on AdS3×S3 and deformations thereof. We exploit the triality symmetry of the underlying duality group SO(4,4) of three-dimensional supergravity in order to construct and relate new consistent truncations. For non-chiral D = 6, $$ \mathcal{N} $$ N 6d = (1, 1) supergravity, we find two different consistent truncations to three-dimensional supergravity, retaining different subsets of Kaluza-Klein modes, thereby offering access to different subsectors of the full nonlinear dynamics. As an application, we construct a two-parameter family of AdS3 × M3 backgrounds on squashed spheres preserving U(1)2 isometries. For generic value of the parameters, these solutions break all supersymmetries, yet they remain perturbatively stable within a non-vanishing region in parameter space. They also contain a one-parameter family of $$ \mathcal{N} $$ N = (0, 4) supersymmetric AdS3 × M3 backgrounds on squashed spheres with U(2) isometries. Using techniques from exceptional field theory, we determine the full Kaluza-Klein spectrum around these backgrounds.

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

scholarly journals Bifurcations of Oscillatory and Rotational Solutions of Double Pendulum with Parametric Vertical Excitation

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Michal Marszal ◽  
Krzysztof Jankowski ◽  
Przemyslaw Perlikowski ◽  
Tomasz Kapitaniak
Keyword(s):  
Periodic Solutions ◽  
Parameter Space ◽  
Double Pendulum ◽  
Bifurcation Diagrams ◽  
Kinematic Excitation ◽  
Vertical Excitation ◽  
Two Parameter ◽  
Domain Of Periodic Solutions

This paper investigates dynamics of double pendulum subjected to vertical parametric kinematic excitation. It includes detailed bifurcation diagrams in two-parameter space (excitation’s frequency and amplitude) for both oscillations and rotations in the domain of periodic solutions.

Pseudoedge: A Hierarchical Skeletal Modeler for the Design of Structural Components

1991 ◽  
Author(s):  
David L. Bonner ◽  
Mark J. Jakiela ◽  
Masaki Watanabe
Keyword(s):  
Parameter Space ◽  
Local Control ◽  
Tangent Plane ◽  
Design Model ◽  
Shape Features ◽  
Structural Components ◽  
General Shape ◽  
Isolated Singularities ◽  
Traditional Design ◽  
Global And Local

Abstract A new design model for the creation of mechanical components has been developed. In this model, the shape is expressed by its areas of prominence or maximum curvature, for which we use the term pseudoedges. In terms of traditional design, these represent both fillet, chamfer and intersection lines, and more general shape features. The pseudoedges of the model combine with a skeletal shape that is used as a starting form, thereby creating a hierarchy of geometric dependencies that affords both global and local control. The surface is represented by a quilt of parametric Bezier patches, with tangent plane continuity everywhere and only certain isolated singularities. Considerable degrees of deformation are possible, with predictable control and at small computational expense; there is no need for computation of intersections or parameter space trimming of patches.

Sign in / Sign up

Export Citation Format

Share Document