Related papers: Geometric Design and Stability of Power Networks

In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…

We give a new proof of the existence of nontrivial quasimeromorphic mappings on a smooth Riemannian manifold, using solely the intrinsic geometry of the manifold.

In the conventional formulation of general relativity, gravity is represented by the metric curvature of Riemannian geometry. There are also alternative formulations in flat affine geometries, wherein the gravitational dynamics is instead…

We propose a new mathematical model for $n-k$-dimensional non-linear correlations with intrinsic scatter in $n$-dimensional data. The model is based on Riemannian geometry, and is naturally symmetric with respect to the measured variables…

We isolate a geometric mechanism that complements the dynamical suppression of macroscopic interference: In a high-dimensional Hilbert space, almost all state vectors are nearly orthogonal, accommodating an exponentially large reservoir of…

After an introductory chapter on the quantum supersymmetric string, in which particular attention will be devoted to the techniques via which phenomenologically viable models can be obtained from the ultraviolet microscopic degrees of…

In this paper we show how a gravitational field generated by a given energy-momentum distribution (for all realistic cases) can be represented by distinct geometrical structures (Lorentzian, teleparallel and non null nonmetricity…

In this paper, the power flow in electrical systems is modelled in the time domain by using Geometric Algebra and the Hilbert Transform. The use of this mathematical framework overcomes some of the limitations shown by the existing…

I describe the manifestation of the non-Euclidean geometry in the behavior of collective observables of some complex physical systems. Specifically, I consider the formation of equilibrium shapes of plants and statistics of sparse random…

Networks of disparate phenomena-- be it the global ecology, human social institutions, within the human brain, or in micro-scale protein interactions-- exhibit broadly consistent architectural features. To explain this, we propose a new…

Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…

Motivated by numerical schemes for large scale geophysical flow, we consider the rotating shallow water and Boussinesq equations on the whole space with horizontal kinetic energy backscatter source terms built from negative viscosity and…

We propose a neural network framework to preclude the need to define or observe incompletely or inaccurately defined states of a material in order to describe its response. The neural network design is based on the classical Coleman-Gurtin…

A introductory review to emergent noncommutative gravity within Yang-Mills Matrix models is presented. Space-time is described as a noncommutative brane solution of the matrix model, i.e. as submanifold of \R^D. Fields and matter on the…

The conservation laws of continuum mechanic written in an Eulerian frame make no difference between fluids and solids except in the expression of the stress tensors, usually with Newton's hypothesis for the fluids and Helmholtz potentials…

In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…

Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and…

A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the…

We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we…

We propose an end-to-end framework based on a Graph Neural Network (GNN) to balance the power flows in energy grids. The balancing is framed as a supervised vertex regression task, where the GNN is trained to predict the current and power…