18,465 research outputs found
Microstructural enrichment functions based on stochastic Wang tilings
This paper presents an approach to constructing microstructural enrichment
functions to local fields in non-periodic heterogeneous materials with
applications in Partition of Unity and Hybrid Finite Element schemes. It is
based on a concept of aperiodic tilings by the Wang tiles, designed to produce
microstructures morphologically similar to original media and enrichment
functions that satisfy the underlying governing equations. An appealing feature
of this approach is that the enrichment functions are defined only on a small
set of square tiles and extended to larger domains by an inexpensive stochastic
tiling algorithm in a non-periodic manner. Feasibility of the proposed
methodology is demonstrated on constructions of stress enrichment functions for
two-dimensional mono-disperse particulate media.Comment: 27 pages, 12 figures; v2: completely re-written after the first
revie
Positive trigonometric polynomials for strong stability of difference equations
We follow a polynomial approach to analyse strong stability of linear
difference equations with rationally independent delays. Upon application of
the Hermite stability criterion on the discrete-time homogeneous characteristic
polynomial, assessing strong stability amounts to deciding positive
definiteness of a multivariate trigonometric polynomial matrix. This latter
problem is addressed with a converging hierarchy of linear matrix inequalities
(LMIs). Numerical experiments indicate that certificates of strong stability
can be obtained at a reasonable computational cost for state dimension and
number of delays not exceeding 4 or 5
All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1
We construct all solvable Lie algebras with a specific n-dimensional
nilradical n_(n,2) (of degree of nilpotency (n-1) and with an (n-2)-dimensional
maximal Abelian ideal). We find that for given n such a solvable algebra is
unique up to isomorphisms. Using the method of moving frames we construct a
basis for the Casimir invariants of the nilradical n_(n,2). We also construct a
basis for the generalized Casimir invariants of its solvable extension s_(n+1)
consisting entirely of rational functions of the chosen invariants of the
nilradical.Comment: 19 pages; added references, changes mainly in introduction and
conclusions, typos corrected; submitted to J. Phys. A, version to be
publishe
Linear representation of energy-dependent Hamiltonians
Effective (i.e., subspace-constrained) Hamiltonians become, by construction,
energy-dependent while all the energy-dependent forces prove non-linear because
the energy itself is merely an eigenvalue of the Hamiltonian H. One of the most
natural resolutions of such a puzzle is proposed via an introduction of teh two
separate linear representatives of the respective right and left action of
H=H(E). Both the new energy-independent operators are non-Hermitian so that the
formalism admits a natural extension to non-Hermitian initial H(E)s.Comment: 14 pages - first half of the material to be presented during 2nd
International Workshop on Pseudo-Hermitian Hamiltonians in June (cf.
http://www.ujf.cas.cz/PTsymmetry
Identification of observables in quantum toboggans
Quantum systems with real energies generated by an apparently non-Hermitian
Hamiltonian may re-acquire the consistent probabilistic interpretation via an
ad hoc metric which specifies the set of observables in the updated Hilbert
space of states. The recipe is extended here to quantum toboggans. In the first
step the tobogganic integration path is rectified and the Schroedinger equation
is given the generalized eigenvalue-problem form. In the second step the
general double-series representation of the eligible metric operators is
derived.Comment: 25 p
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