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Conic Nonholonomic Constraints on Surfaces and Control Systems
This paper addresses the equivalence problem of conic submanifolds in the tangent bundle of a smooth 2-dimensional manifold. Those are given by a...
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Morrey’s Conjecture for the Planar Volumetric-Isochoric Split: Least Rank-One Convex Energy Functions
We consider Morrey’s open question whether rank-one convexity already implies quasiconvexity in the planar case. For some specific families of...
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Fenchel Conjugate via Busemann Function on Hadamard Manifolds
In this paper we introduce a Fenchel-type conjugate, given as the supremum of convex functions, via Busemann functions. It is known that Busemann...
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Energy Resource Coordination
The last application of networked dynamical systems comes from the power systems. Consider a power network of a large number of distributed energy...
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General-Affine Invariants of Plane Curves and Space Curves
We present a fundamental theory of curves in the affine plane and the affine space, equipped with the general-affine groups GA(2) = GL(2, ℝ) ⋉ ℝ 2 and...
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Action versus energy ground states in nonlinear Schrödinger equations
We investigate the relations between normalized critical points of the nonlinear Schrödinger energy functional and critical points of the...
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Uniformization by Energy
We did not prove that the energy functional EJ achieves its minimum. So the Uniformization Theorem does not follow yet.
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Singularity of Energy Measures on a Class of Inhomogeneous Sierpinski Gaskets
We study energy measures of canonical Dirichlet forms on inhomogeneous Sierpinski gaskets. We prove that the energy measures and suitable reference...
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Energy dissipation admissibility condition for conservation law systems admitting singular solutions
The main goal of the paper is to define and use a condition sufficient to choose a unique solution to conservation law systems with a singular...
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Metric Affine Spaces
This paper is a review of some directions in the study of special classes of metric affince spaces, i.e., spaces endowed with a (pseudo)Riemannian...
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Symplectic cohomology rings of affine varieties in the topological limit
We construct a multiplicative spectral sequence converging to the symplectic cohomology ring of any affine variety X , with first page built out of...
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A Positivity Preserving, Energy Stable Finite Difference Scheme for the Flory-Huggins-Cahn-Hilliard-Navier-Stokes System
In this paper, we propose and analyze a finite difference numerical scheme for the Cahn-Hilliard-Navier-Stokes system, with logarithmic Flory-Huggins...
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An Extended Range of Energy Stable Flux Reconstruction Methods on Triangles
We present an extended range of stable flux reconstruction (FR) methods on triangles through the development and application of the...
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A column generation algorithm for solving energy system planning problems
Energy system optimization models are typically large models which combine sub-models which range from linear to very nonlinear. Column generation...
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Model order reduction for gas and energy networks
To counter the volatile nature of renewable energy sources, gas networks take a vital role. But, to ensure fulfillment of contracts under these...
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Cavity Volume and Free Energy in Many-Body Systems
Within this work, we derive and analyse an expression for the free energy of a single-species system in the thermodynamic limit in terms of a...
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ReLU neural networks of polynomial size for exact maximum flow computation
This paper studies the expressive power of artificial neural networks with rectified linear units. In order to study them as a model of real-valued ...
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Perspective on the description of viscoelastic flows via continuum elastic dumbbell models
Non-Newtonian fluid mechanics and computational rheology widely exploit elastic dumbbell models such as Oldroyd-B and FENE-P for a continuum...
