Related papers: Quartic Gradient Flow
Four classic criteria used to the classification of complex flows are discussed here. These criteria are useful to identify regions of the flow related to shear, elongation or rigid-body motion. These usual criteria, namely $Q$, $\Delta$,…
We construct the solution to the periodic Cauchy problem of the Schr\"odinger flow on the sphere. Such construction of solutions is formulated explicitly and therefore a geometric algorithm of solving this periodic Cauchy problem follows.…
The acceleration of gradient-based optimization methods is a subject of significant practical and theoretical importance, particularly within machine learning applications. While much attention has been directed towards optimizing within…
This paper considers steady surface waves `riding' a Beltrami flow (a three-dimensional flow with parallel velocity and vorticity fields). It is demonstrated that the hydrodynamic problem can be formulated as two equations for two scalar…
We describe all possible topological structures of typical one-parameter bifurcations of gradient flows on the 2-sphere with holes in the case that the number of singular point of flows is at most six. To describe structures, we separatrix…
Randomly initialized first-order optimization algorithms are the method of choice for solving many high-dimensional nonconvex problems in machine learning, yet general theoretical guarantees cannot rule out convergence to critical points of…
Saddle points constitute a crucial challenge for first-order gradient descent algorithms. In notions of classical machine learning, they are avoided for example by means of stochastic gradient descent methods. In this work, we provide…
Recent observations of hydrostatic structure and virial equilibrium in supersonically turbulent, self-gravitating molecular clouds imply a stability that contrasts with the transcience of turbulent structure. To investigate this…
10 D Euclidean quantum gravity is investigated numerically using the dynamical triangulation approach. It has been found that the behavior of the model is similar to that of the lower dimensional models. However, it turns out that there are…
Aims. Qualitative analysis of key (but yet unappreciated) linear phenomena in stratified hydrodynamic Keplerian flows: (i) the occurrence of a vortex mode, as a consequence of strato-rotational balance, with its transient dynamics; (ii) the…
Active Flux is an extension of the Finite Volume method and additionally incorporates point values located at cell boundaries. This gives rise to a globally continuous approximation of the solution. Originally, the Active Flux method…
We consider the problem of convergence to a saddle point of a concave-convex function via gradient dynamics. Since first introduced by Arrow, Hurwicz and Uzawa in [1] such dynamics have been extensively used in diverse areas, there are,…
Machine learning methods based on normalizing flows have been shown to address important challenges, such as critical slowing-down and topological freezing, in the sampling of gauge field configurations in simple lattice field theories. A…
Gravitational R\'enyi computations have traditionally been described in the language of Euclidean path integrals. In the semiclassical limit, such calculations are governed by Euclidean (or, more generally, complex) saddle-point geometries.…
New spherical scalar modes on the expanding part of Sitter spacetime, eigenfunctions of a conserved Hamiltonian-like operator are found by solving the Klein-Gordon equation in the appropriate coordinate chart, with the help of a time…
The similarities of quantum turbulence with classical hydrodynamics allow quantum fluids to provide essential models of their classical analogue, paving the way for fundamental advances in physics and technology. Recently, experiments on 2D…
We probe flows of soft, viscous spheres near the jamming point, which acts as a critical point for static soft spheres. Starting from energy considerations, we find nontrivial scaling of velocity fluctuations with strain rate. Combining…
We show that a recently discovered fourth order symplectic algorithm, which requires one evaluation of force gradient in addition to three evaluations of the force, when iterated to higher order, yielded algorithms that are far superior to…
The selective frequency damping method was applied to a bent flow. The method was used in an adaptive formulation. The most dangerous frequency was determined by solving an eigenvalue problem. It was found that one of the patterns,…
Hydrodynamics is nowadays understood as an effective field theory that describes the dynamics of the long-wavelength and slow-time fluctuations of an underlying microscopic theory. In this work we extend the relativistic hydrodynamics to…