25,138 research outputs found
Adaptive meshless refinement schemes for RBF-PUM collocation
In this paper we present an adaptive discretization technique for solving
elliptic partial differential equations via a collocation radial basis function
partition of unity method. In particular, we propose a new adaptive scheme
based on the construction of an error indicator and a refinement algorithm,
which used together turn out to be ad-hoc strategies within this framework. The
performance of the adaptive meshless refinement scheme is assessed by numerical
tests
Efficient computation of partition of unity interpolants through a block-based searching technique
In this paper we propose a new efficient interpolation tool, extremely
suitable for large scattered data sets. The partition of unity method is used
and performed by blending Radial Basis Functions (RBFs) as local approximants
and using locally supported weight functions. In particular we present a new
space-partitioning data structure based on a partition of the underlying
generic domain in blocks. This approach allows us to examine only a reduced
number of blocks in the search process of the nearest neighbour points, leading
to an optimized searching routine. Complexity analysis and numerical
experiments in two- and three-dimensional interpolation support our findings.
Some applications to geometric modelling are also considered. Moreover, the
associated software package written in \textsc{Matlab} is here discussed and
made available to the scientific community
Quantum erasure in the presence of a thermal bath: the effects of system-environment microscopic correlations
We investigate the role of the environment in a quantum erasure setup in the
cavity quantum electrodynamics domain. Two slightly different schemes are
analyzed. We show that the effects of the environment vary when a scheme is
exchanged for another. This can be used to estimate the macroscopic parameters
related to the system-environment microscopic correlations.Comment: 10 pages, 2 figure
RBF approximation of large datasets by partition of unity and local stabilization
We present an algorithm to approximate large dataset by Radial Basis Function
(RBF) techniques. The method couples a fast domain decomposition procedure with a
localized stabilization method. The resulting algorithm can efficiently deal with large
problems and it is robust with respect to the typical instability of kernel methods
Partition of unity interpolation using stable kernel-based techniques
In this paper we propose a new stable and accurate approximation technique
which is extremely effective for interpolating large scattered data sets. The
Partition of Unity (PU) method is performed considering Radial Basis Functions
(RBFs) as local approximants and using locally supported weights. In
particular, the approach consists in computing, for each PU subdomain, a stable
basis. Such technique, taking advantage of the local scheme, leads to a
significant benefit in terms of stability, especially for flat kernels.
Furthermore, an optimized searching procedure is applied to build the local
stable bases, thus rendering the method more efficient
Control of state and state entanglement with a single auxiliary subsystem
We present a strategy to control the evolution of a quantum system. The novel
aspect of this protocol is the use of a \emph{single auxiliary subsystem}. Two
applications are given, one which allows for state preservation and another
which controls the degree of entanglement of a given initial state
Multi-path entanglement of two photons
We present a novel optical device based on an integrated system of
micro-lenses and single mode optical fibers. It allows to collect and direct
into many modes two photons generated by spontaneous parametric down
conversion. By this device multiqubit entangled states and/or multilevel
qu-it states of two photons, encoded in the longitudinal momentum degree of
freedom, are created. The multi-path photon entanglement realized by this
device is expected to find important applications in modern quantum information
technology.Comment: 4 pages, 3 figures, revtex, revised versio
Atomic detection in microwave cavity experiments: a dynamical model
We construct a model for the detection of one atom maser in the context of
cavity Quantum Electrodynamics (QED) used to study coherence properties of
superpositions of electromagnetic modes. Analytic expressions for the atomic
ionization are obtained, considering the imperfections of the measurement
process due to the probabilistic nature of the interactions between the
ionization field and the atoms. Limited efficiency and false counting rates are
considered in a dynamical context, and consequent results on the information
about the state of the cavity modes are obtained.Comment: 12 pages, 1 figur
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