Related papers: Attraction-Based Computation of Hyperbolic Lagrang…
The nonlinear convection terms in the governing equations of compressible fluid flows are hyperbolic in nature and are nontrivial for modelling and numerical simulation. Many numerical methods have been developed in the last few decades for…
A fundamental way to study 3-manifolds is through the geometric lens, one of the most prominent geometries being the hyperbolic one. We focus on the computation of a complete hyperbolic structure on a connected orientable hyperbolic…
Lagrangian Neural Networks (LNNs) can learn arbitrary Lagrangians from trajectory data, but their unusual optimization objective leads to significant training instabilities that limit their application to complex systems. We propose several…
Persistent Lagrangian transport patterns at the ocean surface are revealed from Lagrangian Coherent Structures (LCSs) computed from daily climatological surface current velocities in the northwestern Gulf of Mexico (NWGoM). The velocities…
Semi-Lagrangian schemes have proven to be very efficient to model advection problems. However most semi-Lagrangian schemes are not conservative. Here, a systematic method is introduced in order to enforce the conservative property on a…
Learning generalizable self-supervised graph representations for downstream tasks is challenging. To this end, Contrastive Learning (CL) has emerged as a leading approach. The embeddings of CL are arranged on a hypersphere where similarity…
This preliminary report studies immersed surfaces of constant mean curvature in $H^3$ through their {\it adjusted Gauss maps} (as harmonic maps in $S^2$) and their {\it adjusted frames} in SU(2). Lawson's correspondence between Euclidean…
Deterministic and probabilistic tools from nonlinear dynamics are used to assess enduring near-surface Lagrangian aspects of the Malvinas Current. The deterministic tools are applied on a multi-year record of velocities derived from…
In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in…
We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…
We explore the mechanisms of heat transfer in a turbulent constant heat flux-driven Rayleigh-B\'enard convection flow, which exhibits a hierarchy of flow structures from granules to supergranules. Our computational framework makes use of…
Collision detection plays a key role in the simulation of interacting rigid bodies. However, owing to its computational complexity current methods typically prioritize either maximizing processing speed or fidelity to real-world behaviors.…
The paper deals with topical issues of modern mathematical theory of dynamical chaos and its applications. At present, it is customary to assume that dynamical chaos in finitedimensional smooth systems can exist in three different forms.…
Computational studies of basic models of strongly-correlated electron systems can provide guidance in the search for new materials as well as insight into the physical mechanisms responsible for their properties. Here, we illustrate this by…
We establish some statistical properties of the hyperbolic times for a class of nonuniformly expanding dynamical systems. The maps arise as factors of area preserving maps of the unit square via a geometric Baker's map type construction,…
In this paper, a Line based Compressive Sensing (LCS) scheme is discussed and proposed for low power visual applications, in which image acquisition is performed in a line-by-line manner at the encoder side using same measurement operator.…
A new statistical technique for constructing linear latent structure (LLS) models from available data, supported by well established theoretical results and an efficient algorithm, is presented. The method reduces the problem of estimating…
In this paper we found a Lagrangian representation and corresponding Hamiltonian structure for the constant astigmatism equation. Utilizing this Hamiltonian structure and extra conservation law densities we construct a first evolution…
We present high-resolution direct numerical simulations of turbulent three-dimensional Rayleigh-Benard convection with a focus on the Lagrangian properties of the flow. The volume is a Cartesian slab with an aspect ratio of four bounded by…
We suggest a new approach to the study of relatively hyperbolic groups based on relative isoperimetric inequalities. Various geometric, algebraic, and algorithmic properties are discussed.