Lagrangian coherent structures (LCSs) are distinguished surfaces of trajectories in a dynamical system that exert a major influence on nearby trajectories...

bodies Lagrangian coordinates, a way of describing the motions of particles of a solid or fluid in continuum mechanics Lagrangian coherent structure, distinguished...

splitting into substructures or interacting with other coherent structures. Lagrangian coherent structures (LCSs) are influential material surfaces that create...

of scanner used on the Space Shuttle Lagrangian coherent structure, in fluid mechanics, a type of flow structure Learning classifier system, machine learning...

counterexamples to instability at the center manifold, called Lagrangian coherent structures. The entire unforced rigid body dynamics of a ball is a center...

simulation Hagen–Poiseuille equation Kelvin–Helmholtz instability Lagrangian coherent structure Turbulence kinetic energy Mesocyclones Navier–Stokes existence...

limit of Lagrangian coherent structures (LCSs). Such influence can be of different types, but OECSs invariably create a short-term coherent trajectory...

non-autonomous dynamical systems are known as Lagrangian Coherent Structures. Hyperbolic set Lagrangian coherent structure Spectral submanifold Hirsh M.W., Pugh...

manifold Inertial manifold Normally hyperbolic invariant manifold Lagrangian coherent structure Abraham, Ralph; Marsden, Jerrold E. (1978). Foundations of Mechanics...

algorithms. Invariant manifold Nonlinear dimensionality reduction Lagrangian coherent structure Jain, Shobhit; Haller, George (2022). "How to compute invariant...

complicated examples of coherent sheaves, analogous to building a coherent sheaf using the torsion filtration. As a simple example, a Lagrangian multisection (a...

fabc are the structure constants of SU(3). Repeated indices i,j,a are implicitly summed over following Einstein notation. This Lagrangian is invariant...

manifold. Roughly speaking, they are what mathematicians call special Lagrangian submanifolds. This means, among other things, that they have half the...

Center manifold Hyperbolic fixed point Hyperbolic set Hyperbolic Lagrangian coherent structures Fenichel, N (1972). "Persistence and Smoothness of Invariant...

equality between the Lagrangian Floer homology of Lagrangians in a Calabi–Yau manifold X {\displaystyle X} and the Ext groups of coherent sheaves on the mirror...

and renormalization prescriptions were as much part of the model as the Lagrangian density, especially when they relied on the powerful but mathematically...

energy spectrum exhibited by the total flow, and corresponded to coherent structures (vortex tubes), while the incoherent parts of the flow composed homogeneous...

vacuum states. The dynamical effects of the vacuum are captured in the Lagrangian formalism through the presence of a θ-term which in quantum chromodynamics...

Fourier–Mukai transform ΦK is a functor between derived categories of coherent sheaves D(X) → D(Y) for schemes X and Y, which is, in a sense, an integral...

mathematical structure of local canonical quantum field theory ... In quantum field theories, Feynman diagrams are obtained from a Lagrangian by Feynman...

Springer. pp. 1–53. arXiv:math/0401021. Auroux, Denis (2009). "Special Lagrangian fibrations, wall-crossing, and mirror symmetry". Surveys in Differential...

implied by this anomaly also breaks CP symmetry. In summary, the QCD Lagrangian has the following symmetries: Poincaré symmetry and CPT invariance SU(3)...

characteristic variety cut out by the symbols, which in the good case is a Lagrangian submanifold of the cotangent bundle of maximal dimension (involutive systems)...

Control, Vol.101, September 1979, pp. 187–192. Book, W.J., "Recursive Lagrangian Dynamics of Flexible Manipulator Arms Via Transformation Matrices", Carnegie-Mellon...

data point. To preserve the topological structure of the point sets, the GMM centroids are forced to move coherently as a group. The expectation maximization...

conditions come in the form of Lagrangian submanifolds of Y with some additional structure (often called a brane structure). In the B-model, the boundary...

advantage is that it is in practice easier to guess the correct form of the Lagrangian of a theory, which naturally enters the path integrals (for interactions...

does not specify the stochastic Lagrangian L {\displaystyle L} . This Lagrangian can be obtained from a classical Lagrangian using a standard procedure. Here...

Calabi–Yau manifolds, which string theorists predict should have the structure of Lagrangian fibrations through the SYZ conjecture, and the development of Gromov–Witten...

Goldstein Lagrangian mechanics Lagrangian analysis Lagrangian and Eulerian specification of the flow field Lagrangian coherent structures Lagrangian mechanics...