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Interlaced processes on the circle

Anthony P. Metcalfe, Neil O’Connell, Jon Warren (2009)

Annales de l'I.H.P. Probabilités et statistiques

When two Markov operators commute, it suggests that we can couple two copies of one of the corresponding processes. We explicitly construct a number of couplings of this type for a commuting family of Markov processes on the set of conjugacy classes of the unitary group, using a dynamical rule inspired by the RSK algorithm. Our motivation for doing this is to develop a parallel programme, on the circle, to some recently discovered connections in random matrix theory between reflected and conditioned...

Internal Symmetries and Additional Quantum Numbers for Nanoparticles

V.G. Yarzhemsky (2013)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

Wavefunctions of symmetrical nanoparticles are considered making use of induced representation method. It is shown that when, at the same total symmetry, the order of local symmetry group decreases, additional quantum numbers are required for complete labelling of electron states. It is shown that the labels of irreducible representations of intermediate subgroups can be used for complete classification of states in the case of repeating IRs in symmetry adapted linear combinations. The intermediate...

Invariance principle for the random conductance model with dynamic bounded conductances

Sebastian Andres (2014)

Annales de l'I.H.P. Probabilités et statistiques

We study a continuous time random walk X in an environment of dynamic random conductances in d . We assume that the conductances are stationary ergodic, uniformly bounded and bounded away from zero and polynomially mixing in space and time. We prove a quenched invariance principle for X , and obtain Green’s functions bounds and a local limit theorem. We also discuss a connection to stochastic interface models.

Invariant line integrals in the theory of defective crystals

Gareth P. Parry, Miroslav Šilhavý (2000)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In a continuum theory of crystals with defects, invariant line integrals measure the line defects of the lattice structure. It is shown that the integrands of invariant line integrals can always be taken to have the transformation properties of covariant vector-valued functions.

Isotropy conditions for lattice Boltzmann schemes. Application to D2Q9*

Adeline Augier, Francois Dubois, Benjamin Graille (2012)

ESAIM: Proceedings

In this paper, we recall the linear version of the lattice Boltzmann schemes in the framework proposed by d’Humières. According to the equivalent equations we introduce a definition for a scheme to be isotropic at some order. This definition is chosen such that the equivalent equations are preserved by orthogonal transformations of the frame. The property of isotropy can be read through a group operation and then implies a sequence of relations on...

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