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.

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.

Weir flows and waterfalls

1991 ◽  
Vol 230 ◽  
pp. 525-539 ◽  
Author(s):  
Frédéric Dias ◽  
E. O. Tuck
Keyword(s):  
Vertical Wall ◽  
Finite Depth ◽  
Free Surface Flows ◽  
Parameter Family ◽  
The Other ◽  
Two Dimensional ◽  
Surface Flows ◽  
Supercritical Solutions ◽  
Subcritical Solutions ◽  
Two Parameter

Two-dimensional free-surface flows, which are uniform far upstream in a channel of finite depth that ends suddenly, are computed numerically. The ending is in the form of a vertical wall, which may force the flow upward before it falls down forever as a jet under the effect of gravity. Both subcritical and supercritical solutions are presented. The subcritical solutions are a one-parameter family of solutions, the single parameter being the ratio between the height of the wall and the height of the uniform flow far upstream. On the other hand, the supercritical solutions are a two-parameter family of solutions, the second parameter being the Froude number. Moreover, for some combinations of the parameters, it is shown that the solution is not unique.

Singularities of line congruences

2003 ◽  
Vol 133 (6) ◽  
pp. 1341-1359 ◽  
Author(s):  
Shyuichi Izumiya ◽  
Kentaro Saji ◽  
Nobuko Takeuchi
Keyword(s):  
Three Dimensional ◽  
Parameter Family ◽  
General Line ◽  
Line Congruence ◽  
Lagrangian Singularities ◽  
Generic Singularities ◽  
Two Parameter

A line congruence is a two-parameter family of lines in R3. In this paper we study singularities of line congruences. We show that generic singularities of general line congruences are the same as those of stable mappings between three-dimensional manifolds. Moreover, we also study singularities of normal congruences and equiaffine normal congruences from the viewpoint of the theory of Lagrangian singularities.

Practical Mobility Conditions for RSSR Mechanism

1992 ◽  
Author(s):  
Kyeong-Won Lee ◽  
Young-Jin Seo ◽  
Yong-San Yoon
Keyword(s):  
Necessary Conditions ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Analytic Form ◽  
The Other ◽  
Design Stage ◽  
Deviation Angle ◽  
Detail Design ◽  
Special Cases ◽  
Necessary And Sufficient

Abstract In this study, two sets of mobility conditions for a RSSR mechanism are developed to ensure the crank motion in the three dimensional four-bar mechanism. First set of the mobility conditions is the Grashof-type necessary conditions expressed only in terms of link lengths. The other set of the mobility conditions provides the necessary and sufficient conditions in analytic form accounting for the constraint of the deviation angle. For some special cases, the equations are simplified. The first set of equations may be useful in the initial design stage while the second set may be used for the final detail design. An example of mechanism is taken for the comparison of the analyses results.

PHASE HOLONOMY OF THE VACUUM IN THREE-DIMENSIONAL GAUGE THEORIES

1992 ◽  
Vol 07 (20) ◽  
pp. 4937-4948
Author(s):  
ROBERT LINK
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Gauge Theories ◽  
Magnetic Monopole ◽  
Three Dimensional ◽  
Parameter Family ◽  
Two Parameter ◽  
Dirac Hamiltonian

The phase two-form of Berry in the neighborhood of a degeneracy of the Fock vacuum of a semisimple, nonabelian, second-quantized, relativistic fermion-background gauge field Hamiltonian is shown to be that of the Dirac magnetic monopole—thus extending a result of Berry to field theory. The Dirac Hamiltonian for an SU(2) fermion on the two-sphere is solved in a particular two-parameter family of background instanton gauge potentials as an explicit illustrative example.

scholarly journals Notes on hyperloops in $$ \mathcal{N} $$ = 4 Chern-Simons-matter theories

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Nadav Drukker ◽  
Marcia Tenser ◽  
Diego Trancanelli
Keyword(s):  
Moduli Spaces ◽  
Three Dimensional ◽  
Discrete Data ◽  
Parameter Family ◽  
Wilson Loops ◽  
Matter Theory ◽  
M Theory ◽  
Chern Simons ◽  
Two Parameter ◽  
Matter Fields

Abstract We present new circular Wilson loops in three-dimensional $$ \mathcal{N} $$ N = 4 quiver Chern-Simons-matter theory on S3. At any given node of the quiver, a two-parameter family of operators can be obtained by opportunely deforming the 1/4 BPS Gaiotto-Yin loop. Including then adjacent nodes, the coupling to the bifundamental matter fields allows to enlarge this family and to construct loop operators based on superconnections. We discuss their classification, which depends on both discrete data and continuous parameters subject to an identification. The resulting moduli spaces are conical manifolds, similar to the conifold of the 1/6 BPS loops of the ABJ(M) theory.

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.

Three-Dimensional Reconstruction of Two Forms of the Chaperonin GRO EL

1990 ◽  
Vol 48 (1) ◽  
pp. 258-259
Author(s):  
J.L. Carrascosa ◽  
G. Abella ◽  
S. Marco ◽  
M. Muyal ◽  
J.M. Carazo
Keyword(s):  
Three Dimensional ◽  
The Other ◽  
Two Dimensional ◽  
Series Method ◽  
Three Dimensional Reconstruction ◽  
Structural Components ◽  
E Coli ◽  
Dimensional Reconstruction ◽  
Morphogenetic Factors ◽  
Tilt Series

Chaperonins are a class of proteins characterized by their role as morphogenetic factors. They trantsiently interact with the structural components of certain biological aggregates (viruses, enzymes etc), promoting their correct folding, assembly and, eventually transport. The groEL factor from E. coli is a conspicuous member of the chaperonins, as it promotes the assembly and morphogenesis of bacterial oligomers and/viral structures.We have studied groEL-like factors from two different bacteria:E. coli and B.subtilis. These factors share common morphological features , showing two different views: one is 6-fold, while the other shows 7 morphological units. There is also a correlation between the presence of a dominant 6-fold view and the fact of both bacteria been grown at low temperature (32°C), while the 7-fold is the main view at higher temperatures (42°C). As the two-dimensional projections of groEL were difficult to interprete, we studied their three-dimensional reconstruction by the random conical tilt series method from negatively stained particles.

An Efficient Multiple Description Coding for Multi-View Video Based on the Correlation of Spatial Polyphase Transformed Subsequences

2019 ◽  
Vol 63 (5) ◽  
pp. 50401-1-50401-7 ◽  
Author(s):  
Jing Chen ◽  
Jie Liao ◽  
Huanqiang Zeng ◽  
Canhui Cai ◽  
Kai-Kuang Ma
Keyword(s):  
Video Transmission ◽  
Video Sequence ◽  
Three Dimensional ◽  
The Other ◽  
Multiple Description Coding ◽  
Multiple Description ◽  
Prediction Mode ◽  
Gradient Based ◽  
Directional Interpolation ◽  
Description Coding

Abstract For a robust three-dimensional video transmission through error prone channels, an efficient multiple description coding for multi-view video based on the correlation of spatial polyphase transformed subsequences (CSPT_MDC_MVC) is proposed in this article. The input multi-view video sequence is first separated into four subsequences by spatial polyphase transform and then grouped into two descriptions. With the correlation of macroblocks in corresponding subsequence positions, these subsequences should not be coded in completely the same way. In each description, one subsequence is directly coded by the Joint Multi-view Video Coding (JMVC) encoder and the other subsequence is classified into four sets. According to the classification, the indirectly coding subsequence selectively employed the prediction mode and the prediction vector of the counter directly coding subsequence, which reduces the bitrate consumption and the coding complexity of multiple description coding for multi-view video. On the decoder side, the gradient-based directional interpolation is employed to improve the side reconstructed quality. The effectiveness and robustness of the proposed algorithm is verified by experiments in the JMVC coding platform.

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