5,130 research outputs found
Stochastic inviscid shell models: well-posedness and anomalous dissipation
In this paper we study a stochastic version of an inviscid shell model of
turbulence with multiplicative noise. The deterministic counterpart of this
model is quite general and includes inviscid GOY and Sabra shell models of
turbulence. We prove global weak existence and uniqueness of solutions for any
finite energy initial condition. Moreover energy dissipation of the system is
proved in spite of its formal energy conservation.Comment: v2 has updated introductio
Anomalous dissipation in a stochastic inviscid dyadic model
A stochastic version of an inviscid dyadic model of turbulence, with
multiplicative noise, is proved to exhibit energy dissipation in spite of the
formal energy conservation. As a consequence, global regular solutions cannot
exist. After some reductions, the main tool is the escape bahavior at infinity
of a certain birth and death process.Comment: Published in at http://dx.doi.org/10.1214/11-AAP768 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Uniqueness for a Stochastic Inviscid Dyadic Model
For the deterministic dyadic model of turbulence, there are examples of
initial conditions in which have more than one solution. The aim of this
paper is to prove that uniqueness, for all -initial conditions, is
restored when a suitable multiplicative noise is introduced. The noise is
formally energy preserving. Uniqueness is understood in the weak probabilistic
sense.Comment: 13 pages, no figures. Submitted to the Proceedings of the American
Mathematical Societ
Anomalous dissipation in a stochastic inviscid dyadic model
A stochastic version of an inviscid dyadic model of turbulence, with
multiplicative noise, is proved to exhibit energy dissipation in spite of the
formal energy conservation. As a consequence, global regular solutions cannot
exist. After some reductions, the main tool is the escape bahavior at infinity
of a certain birth and death process.Comment: Published in at http://dx.doi.org/10.1214/11-AAP768 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Qualitative stability and synchronicity analysis of power network models in port-Hamiltonian form
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos 28, 101102 (2018) and may be found at https://doi.org/10.1063/1.5054850.In view of highly decentralized and diversified power generation concepts, in particular with renewable energies, the analysis and control of the stability and the synchronization of power networks is an important topic that requires different levels of modeling detail for different tasks. A frequently used qualitative approach relies on simplified nonlinear network models like the Kuramoto model with inertia. The usual formulation in the form of a system of coupled ordinary differential equations is not always adequate. We present a new energy-based formulation of the Kuramoto model with inertia as a polynomial port-Hamiltonian system of differential-algebraic equations, with a quadratic Hamiltonian function including a generalized order parameter. This leads to a robust representation of the system with respect to disturbances: it encodes the underlying physics, such as the dissipation inequality or the deviation from synchronicity, directly in the structure of the equations, and it explicitly displays all possible constraints and allows for robust simulation methods. The model is immersed into a system of model hierarchies that will be helpful for applying adaptive simulations in future works. We illustrate the advantages of the modified modeling approach with analytics and numerical results.
To reach the goal of temperature reduction to limit the climate change, as stipulated at the Paris Conference in 2015, it is necessary to integrate renewable energy sources into the existing power networks. Wind and solar power are the most promising ones, but the integration into the electric power grid remains an enormous challenge due to their variability that requires storage facilities, back-up plants, and accurate control processing. The current approach to describe the dynamics of power grids in terms of simplified nonlinear models, like the Kuramoto model with inertia, may not be appropriate when different control and optimization tasks are needed to be addressed. Under this aspect, we present a new energy-based formulation of the Kuramoto model with inertia that allows for an easy extension if further effects have to be included and higher fidelity is required for qualitative analysis. We illustrate the new modeling approach with analytic results and numerical simulations carried out for a semi-realistic model of the Italian grid and indicate how this approach can be generalized to models of finer granularity.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept
A dyadic model on a tree
We study an infinite system of non-linear differential equations coupled in a
tree-like structure. This system was previously introduced in the literature
and it is the model from which the dyadic shell model of turbulence was
derived. It mimics 3d Euler and Navier-Stokes equations in a rough
approximation of a wavelet decomposition. We prove existence of finite energy
solutions, anomalous dissipation in the inviscid unforced case, existence and
uniqueness of stationary solutions (either conservative or not) in the forced
case
Smooth solutions for the dyadic model
We consider the dyadic model, which is a toy model to test issues of
well-posedness and blow-up for the Navier-Stokes and Euler equations. We prove
well-posedness of positive solutions of the viscous problem in the relevant
scaling range which corresponds to Navier-Stokes. Likewise we prove
well-posedness for the inviscid problem (in a suitable regularity class) when
the parameter corresponds to the strongest transport effect of the
non-linearity
Electric Waterborne Public Transportation in Venice: a Case Study
The paper reports the results of a study for moving the present diesel-based watercraft propulsion technology used for public transportation in Venice city and lagoon to a more efficient and smart electric propulsion technology, in view of its adopted in a near future. Energy generation and storage systems, electrical machines and drives, as well as economic, environmental and social issues are presented and discussed. Some alternative solutions based on hybrid diesel engine and electric and full electric powertrains are compared in terms of weights, costs and payback times. Previews researches on ship propulsion and electric energy storage developed by the University of Padua and preliminary experiences on electric boats carried out in Venice lagoon by the municipal transportation company ACTV and other stakeholders are the starting point for this study. Results can be transferred to other waterborne mobility systems
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