1,145 research outputs found
Quasi-BiHamiltonian Systems and Separability
Two quasi--biHamiltonian systems with three and four degrees of freedom are
presented. These systems are shown to be separable in terms of Nijenhuis
coordinates. Moreover the most general Pfaffian quasi-biHamiltonian system with
an arbitrary number of degrees of freedom is constructed (in terms of Nijenhuis
coordinates) and its separability is proved.Comment: 10 pages, AMS-LaTeX 1.1, to appear in J. Phys. A: Math. Gen. (May
1997
Applications of Information Theory to Analysis of Neural Data
Information theory is a practical and theoretical framework developed for the
study of communication over noisy channels. Its probabilistic basis and
capacity to relate statistical structure to function make it ideally suited for
studying information flow in the nervous system. It has a number of useful
properties: it is a general measure sensitive to any relationship, not only
linear effects; it has meaningful units which in many cases allow direct
comparison between different experiments; and it can be used to study how much
information can be gained by observing neural responses in single trials,
rather than in averages over multiple trials. A variety of information
theoretic quantities are commonly used in neuroscience - (see entry
"Definitions of Information-Theoretic Quantities"). In this entry we review
some applications of information theory in neuroscience to study encoding of
information in both single neurons and neuronal populations.Comment: 8 pages, 2 figure
Data-driven modeling for drop size distributions
The prediction of the drop size distribution (DSD) resulting from liquid atomization is key to the optimization of multiphase flows from gas-turbine propulsion through agriculture to healthcare. Obtaining high-fidelity data of liquid atomization, either experimentally or numerically, is expensive, which makes the exploration of the design space difficult. First, to tackle these challenges, we propose a framework to predict the DSD of a liquid spray based on data as a function of the spray angle, the Reynolds number, and the Weber number. Second, to guide the design of liquid atomizers, the model accurately predicts the volume of fluid contained in drops of specific sizes while providing uncertainty estimation. To do so, we propose a Gaussian process regression (GPR) model, which infers the DSD and its uncertainty form the knowledge of its integrals and of its first moment, i.e., the mean drop diameter. Third, we deploy multiple GPR models to estimate these quantities at arbitrary points of the design space from data obtained from a large number of numerical simulations of a flat fan spray. The kernel used for reconstructing the DSD incorporates prior physical knowledge, which enables the prediction of sharply peaked and heavy-tailed distributions. Fourth, we compare our method with a benchmark approach, which estimates the DSD by interpolating the frequency polygon of the binned drops with a GPR. We show that our integral approach is significantly more accurate, especially in the tail of the distribution (i.e., large, rare drops), and it reduces the bias of the density estimator by up to 10 times. Finally, we discuss physical aspects of the model's predictions and interpret them against experimental results from the literature. This work opens opportunities for modeling drop size distribution in multiphase flows from data
The quasi-bi-Hamiltonian formulation of the Lagrange top
Starting from the tri-Hamiltonian formulation of the Lagrange top in a
six-dimensional phase space, we discuss the possible reductions of the Poisson
tensors, the vector field and its Hamiltonian functions on a four-dimensional
space. We show that the vector field of the Lagrange top possesses, on the
reduced phase space, a quasi-bi-Hamiltonian formulation, which provides a set
of separation variables for the corresponding Hamilton-Jacobi equation.Comment: 12 pages, no figures, LaTeX, to appear in J. Phys. A: Math. Gen.
(March 2002
Flat Pencils of Symplectic Connections and Hamiltonian Operators of Degree 2
Bi-Hamiltonian structures involving Hamiltonian operators of degree 2 are
studied. Firstly, pairs of degree 2 operators are considered in terms of an
algebra structure on the space of 1-forms, related to so-called Fermionic
Novikov algebras. Then, degree 2 operators are considered as deformations of
hydrodynamic type Poisson brackets.Comment: 20 page
Reduction of bihamiltonian systems and separation of variables: an example from the Boussinesq hierarchy
We discuss the Boussinesq system with stationary, within a general
framework for the analysis of stationary flows of n-Gel'fand-Dickey
hierarchies. We show how a careful use of its bihamiltonian structure can be
used to provide a set of separation coordinates for the corresponding
Hamilton--Jacobi equations.Comment: 20 pages, LaTeX2e, report to NEEDS in Leeds (1998), to be published
in Theor. Math. Phy
Effective method for Blind Adaptive CD Compensation and Estimation in a DSP-based Coherent Optical Systems
A blind adaptive chromatic dispersion compensation and estimation algorithm is proposed
and experimentally validated. The method is based on a Frequency Domain Equalizer, a
Time Domain Equalizer and an Optical Performance Monitoring in a loop configuration
Quantum deformations of associative algebras and integrable systems
Quantum deformations of the structure constants for a class of associative
noncommutative algebras are studied. It is shown that these deformations are
governed by the quantum central systems which has a geometrical meaning of
vanishing Riemann curvature tensor for Christoffel symbols identified with the
structure constants. A subclass of isoassociative quantum deformations is
described by the oriented associativity equation and, in particular, by the
WDVV equation. It is demonstrated that a wider class of weakly (non)associative
quantum deformations is connected with the integrable soliton equations too. In
particular, such deformations for the three-dimensional and
infinite-dimensional algebras are described by the Boussinesq equation and KP
hierarchy, respectively.Comment: Numeration of the formulas is correcte
Quantization with maximally degenerate Poisson brackets: The harmonic oscillator!
Nambu's construction of multi-linear brackets for super-integrable systems
can be thought of as degenerate Poisson brackets with a maximal set of Casimirs
in their kernel. By introducing privileged coordinates in phase space these
degenerate Poisson brackets are brought to the form of Heisenberg's equations.
We propose a definition for constructing quantum operators for classical
functions which enables us to turn the maximally degenerate Poisson brackets
into operators. They pose a set of eigenvalue problems for a new state vector.
The requirement of the single valuedness of this eigenfunction leads to
quantization. The example of the harmonic oscillator is used to illustrate this
general procedure for quantizing a class of maximally super-integrable systems
Tectonic Regime as a Control Factor for Crustal Fault Zone (CFZ) Geothermal Reservoir in an Amagmatic System: A 3D Dynamic Numerical Modeling Approach
Crustal fault zones provide interesting geological targets for high-temperature geothermal energy source in naturally deep-fractured basement areas. Field and laboratory studies have shown the ability of these systems to let fluid flow down to the brittle–ductile transition. However, several key questions about exploration still exist, in particular the fundamental effect of tectonic regimes on fluid flow in fractured basement domains. Based on poro-elasticity assumption, we considered an idealized 3D geometry and realistic physical properties. We examined a model with no tectonic regime (benchmark experiment) and a model with different tectonic regimes, namely a compressional, an extensional and a strike-slip tectonic regime. Compared to the benchmark experiment, the results demonstrate that different tectonic regimes cause pressure changes in the fault/basement system. The tectonic-induced pressure changes affect convective patterns, onset of convection as well as the spatial extent of thermal plumes and the intensity of temperature anomalies. Driven by poro-elastic forces, temperature anomalies around vertical faults in a strike-slip tectonic regime have a spatial extent that should be considered in preliminary exploratory phases
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