Related papers: Geometric Design and Stability of Power Networks
Over the past few years, we developed a mathematically rigorous method to study the dynamical processes associated to nonlinear Forchheimer flows for slightly compressible fluids. We have proved the existence of a geometric transformation…
In this work, we are interested in tree-shaped networks of freely vibrating beams which are geometrically exact (GEB) -- in the sense that large motions (deflections, rotations) are accounted for in addition to shearing -- and linked by…
We define a formal Riemannian metric on a given conformal class of metrics on a closed Riemann surface. We show interesting formal properties for this metric, in particular the curvature is nonpositive and the Liouville energy is…
We examine the hypothesis that space-time is a product of a continuous four-dimensional manifold times a finite space. A new tensorial notation is developed to present the various constructs of noncommutative geometry. In particular, this…
Nematic polymeric networks are (heat and light) activable materials, which combine the features of rubber and nematic liquid crystals. When only the stretching energy of a thin sheet of nematic polymeric network is minimized, the intrinsic…
Effects of geometric constraints on a steady flow potential are described by an elliptic-hyperbolic generalization of the harmonic map equations. Sufficient conditions are given for global triviality.
Quadratic flows have the unique property of uniform strain and are commonly used in turbulence modeling and hydrodynamic analysis. While previous application focused on two-dimensional homogeneous fluid, this study examines the geometric…
Starting from an axiomatic perspective, \emph{fluctuation geometry} is developed as a counterpart approach of inference geometry. This approach is inspired on the existence of a notable analogy between the general theorems of…
We show that real multiplex networks are unexpectedly robust against targeted attacks on high degree nodes, and that hidden interlayer geometric correlations predict this robustness. Without geometric correlations, multiplexes exhibit an…
A gaussian distribution of binding energies, but conditioned to exploit generally available information on packing in liquids, provides a statistical-thermodynamic theory of liquid water that is structurally non-committal, molecularly…
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…
A remarkable feature of static granular matter is the distribution of force along intricate networks. Even regular inter-particle contact networks produce wildly inhomogeneous force networks where certain "chains" of particles carry forces…
Real networks are finite metric spaces. Yet the geometry induced by shortest path distances in a network is definitely not its only geometry. Other forms of network geometry are the geometry of latent spaces underlying many networks, and…
Effective analysis in neuroscience benefits significantly from robust conceptual frameworks. Traditional metrics of interbrain synchrony in social neuroscience typically depend on fixed, correlation-based approaches, restricting their…
The application of graph neural networks (GNNs) to the domain of electrical power grids has high potential impact on smart grid monitoring. Even though there is a natural correspondence of power flow to message-passing in GNNs, their…
We present the formalism of phenomenological thermodynamics in terms of the even-dimensional symplectic geometry, and argue that it catches its geometric essence in a more profound and clearer way than the popular odd-dimensional contact…
Security assessment of large-scale, strongly nonlinear power grids containing thousands to millions of interacting components is a computationally expensive task. Targeting at reducing the computational cost, this paper introduces a…
Using the square-root map p-->\sqrt{p} a probability density function p can be represented as a point of the unit sphere S in the Hilbert space of square-integrable functions. If the density function depends smoothly on a set of parameters,…
It is developed a Riemannian reformulation of classical statistical mechanics for systems in thermodynamic equilibrium, which arises as a natural extension of Ruppeiner geometry of thermodynamics. The present proposal leads to interpret…
An increasingly common viewpoint is that protein dynamics data sets reside in a non-linear subspace of low conformational energy. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The…