Related papers: Discrete knot energies
Distribution grid operation faces new challenges caused by a rising share of renewable energy sources and the introduction of additional types of loads to the grid. With the increasing adoption of distributed generation and emerging…
We analyse the rigidity of discrete energies where at least nearest and next-to-nearest neighbour interactions are taken into account. Our purpose is to show that interactions beyond nearest neighbours have the role of penalising changes of…
We present a brief review of discrete structures in a finite Hilbert space, relevant for the theory of quantum information. Unitary operator bases, mutually unbiased bases, Clifford group and stabilizer states, discrete Wigner function,…
We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the…
We show the importance of properly including the perturbations of the dark energy component in the dynamical dark energy models based on a scalar field and modified gravity theories in order to meet with present and future observational…
Using the method of the "exact discretization" of the Schr\"odinger equation, we propose a particular discretized version of the N=2 Supersymmetric Quantum Mechanics. After defining the corresponding shape invariance condition, we show that…
In this chapter we review recent results concerning localized and extended dissipative solutions of the discrete complex Ginzburg-Landau equation. In particular, we discuss discrete diffraction effects arising both from linear and nonlinear…
One of the most significant research interests in the field of electronics is that on quantum dot, because such materials have electronic properties intermediate between those of bulk semiconductors and those of discrete molecules.…
Energy distributions of decay products carry information on the kinematics of the decay in ways that are at the same time straightforward and quite hidden. I will review these properties and discuss their early historical applications as…
We provide a convincing discretisation of Demoulin's $\Omega$-surfaces along with their specialisations to Guichard and isothermic surfaces with no loss of integrable structure.
In this note we combine the "spin-argument" from [KLR15] and the $n$-dimensional incompatible, one-well rigidity result from [LL16], in order to infer a new proof for the compactness of discrete multi-well energies associated with the…
In this note we study the possibility of obtaining dark energy solution in a D-brane scenario in a warped background that includes brane-position dependent corrections for the non-perturbative superpotential. The volume modulus is…
We establish a physically meaningful representation of a quantum energy density for use in Quantum Monte Carlo calculations. The energy density operator, defined in terms of Hamiltonian components and density operators, returns the correct…
The parabolic-elliptic Keller-Segel equation with sensitivity saturation, because of its pattern formation ability, is a challenge for numerical simulations. We provide two finite-volume schemes whose goals are to preserve, at the discrete…
Compatible Discrete Operator schemes preserve basic properties of the continuous model at the discrete level. They combine discrete differential operators that discretize exactly topological laws and discrete Hodge operators that…
We propose a notion of discrete elastic and area-constrained elastic curves in 2-dimensional space forms. Our definition extends the well-known discrete Euclidean curvature equation to space forms and reflects various geometric properties…
This papers studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs). It presents a new framework using discrete ODEs as a central tool for computation and provides several implicit characterizations…
The energy preserving discrete gradient methods are generalized to finite-dimensional Riemannian manifolds by definition of a discrete approximation to the Riemannian gradient, a retraction, and a coordinate center function. The resulting…
We propose a dynamical (quintessence) model of dark energy in the current universe with a renormalizable (Higgs-like) scalar potential. We prove the viability of our model (after fine tuning) for the certain range of the average scalar…
A novel discrete model (D-model) is presented describing nonlinear wave interactions in systems with small and moderate nonlinearity under narrow frequency band excitation. It integrates in a single theoretical frame two mechanisms of…