Kronecker delta

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Moments, Intermittency, and Growth Indices for Nonlinear Stochastic PDE's with Rough Initial Conditions

Le Chen

In this thesis, we study several stochastic partial differential equations (SPDE’s) in the spatial domain R, driven by multiplicative space-time white noise. We are interested in how rough and unbounded initial data affect the random field solution and the ...

EPFL2013

Global simulations of tokamak microturbulence: finite beta effects and collisions

Laurent Villard, Stephan Brunner, Trach-Minh Tran, Alberto Bottino, Sébastien Jolliet, Ben McMillan, Thibaut Vernay

In this paper, we present global nonlinear gyrokinetic simulations including finite beta effects and collisions in tokamak geometry. Global electromagnetic simulations using conventional delta-f particle in cell methods are very demanding, with respect to ...

Institute of Physics2011

Reservoir optimization in recurrent neural networks using properties of Kronecker product

Martin Hasler, Ali Ajdari Rad, Mahdi Jalili

Recurrent neural networks based on reservoir computing are increasingly being used in many applications. Optimization of the topological structure of the reservoir and the internal connection weights for a given task is one of the most important problems i ...

2010

Analytical Footprints: Compact Representation of Elementary Singularities in Wavelet Bases

Michaël Unser, Dimitri Nestor Alice Van De Ville, Thierry Blu

We introduce a family of elementary singularities that are point-Holder alpha-regular. These singularities are self-similar and are the Green functions of fractional derivative operators; i.e., by suitable fractional differentiation, one retrieves a Dirac ...

Institute of Electrical and Electronics Engineers2010

Universal constraints on conformal operator dimensions

Alessandro Vichi

We continue the study of model-independent constraints on the unitary conformal field theories (CFTs) in four dimensions, initiated in [R. Rattazzi, V. S. Rychkov, E. Tonni, and A. Vichi, J. High Energy Phys. 12 (2008) 031]. Our main result is an improved ...

American Physical Society2009

On the definition of a kinetic equilibrium in global gyrokinetic simulations

Olivier Sauter, Laurent Villard, Trach-Minh Tran, Alberto Bottino, Sébastien Jolliet, Paolo Angelino

Nonlinear electrostatic global gyrokinetic simulations of collisionless ion temperature gradient (ITG) turbulence and ExB zonal flows in axisymmetric toroidal plasmas are examined for different choices of the initial distribution function. Using a local Ma ...

American Institute of Physics2006

Nonlinear Circuit Analysis using Multivariate Volterra Operators

The work introduces a mathematical framework and a corresponding implementable algorithm to automatically perform Volterra analysis of weakly nonlinear circuits. The analysis is based on the general composition rule for multivariate Volterra operators. The ...

2011

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