672 research outputs found
Quantum & Classical Eigenfunctions in Calogero & Sutherland Systems
An interesting observation was reported by Corrigan-Sasaki that all the
frequencies of small oscillations around equilibrium are " quantised" for
Calogero and Sutherland (C-S) systems, typical integrable multi-particle
dynamics. We present an analytic proof by applying recent results of
Loris-Sasaki. Explicit forms of `classical' and quantum eigenfunctions are
presented for C-S systems based on any root systems.Comment: LaTeX2e 37 pages, references added, typo corrected, a few paragraphs
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Affine Toda-Sutherland Systems
A cross between two well-known integrable multi-particle dynamics, an affine
Toda molecule and a Sutherland system, is introduced for any affine root
system. Though it is not completely integrable but partially integrable, or
quasi exactly solvable, it inherits many remarkable properties from the
parents. The equilibrium position is algebraic, i.e. proportional to the Weyl
vector. The frequencies of small oscillations near equilibrium are proportional
to the affine Toda masses, which are essential ingredients of the exact
factorisable S-matrices of affine Toda field theories. Some lower lying
frequencies are integer times a coupling constant for which the corresponding
exact quantum eigenvalues and eigenfunctions are obtained. An affine
Toda-Calogero system, with a corresponding rational potential, is also
discussed.Comment: LaTeX2e 22 pages with amsfonts and graphicx, 5 eps figure
A Dynamical Study of the Non-Star Forming Translucent Molecular Cloud MBM16: Evidence for Shear Driven Turbulence in the Interstellar Medium
We present the results of a velocity correlation study of the high latitude
cloud MBM16 using a fully sampled CO map, supplemented by new CO
data. We find a correlation length of 0.4 pc. This is similar in size to the
formaldehyde clumps described in our previous study. We associate this
correlated motion with coherent structures within the turbulent flow. Such
structures are generated by free shear flows. Their presence in this non-star
forming cloud indicates that kinetic energy is being supplied to the internal
turbulence by an external shear flow. Such large scale driving over long times
is a possible solution to the dissipation problem for molecular cloud
turbulence.Comment: Uses AAS aasms4.sty macros. Accepted for publication in Ap
Elastic-Net Regularization: Error estimates and Active Set Methods
This paper investigates theoretical properties and efficient numerical
algorithms for the so-called elastic-net regularization originating from
statistics, which enforces simultaneously l^1 and l^2 regularization. The
stability of the minimizer and its consistency are studied, and convergence
rates for both a priori and a posteriori parameter choice rules are
established. Two iterative numerical algorithms of active set type are
proposed, and their convergence properties are discussed. Numerical results are
presented to illustrate the features of the functional and algorithms
Some results on the eigenfunctions of the quantum trigonometric Calogero-Sutherland model related to the Lie algebra E6
The quantum trigonometric Calogero-Sutherland models related to Lie algebras
admit a parametrization in which the dynamical variables are the characters of
the fundamental representations of the algebra. We develop here this approach
for the case of the exceptional Lie algebra E6.Comment: 17 pages, no figure
On the performance of algorithms for the minimization of -penalized functionals
The problem of assessing the performance of algorithms used for the
minimization of an -penalized least-squares functional, for a range of
penalty parameters, is investigated. A criterion that uses the idea of
`approximation isochrones' is introduced. Five different iterative minimization
algorithms are tested and compared, as well as two warm-start strategies. Both
well-conditioned and ill-conditioned problems are used in the comparison, and
the contrast between these two categories is highlighted.Comment: 18 pages, 10 figures; v3: expanded version with an additional
synthetic test problem
The Escherichia coli RnlA–RnlB toxin–antitoxin complex: production, characterization and crystallization
The Escherichia coli rnlAB operon encodes a toxin–antitoxin module that is involved in protection against infection by bacteriophage T4. The full-length RnlA–RnlB toxin–antitoxin complex as well as the toxin RnlA were purified to homogeneity and crystallized. When the affinity tag is placed on RnlA, RnlB is largely lost during purification and the resulting crystals exclusively comprise RnlA. A homogeneous preparation of RnlA–RnlB containing stoichiometric amounts of both proteins could only be obtained using a His tag placed C-terminal to RnlB. Native mass spectrometry and SAXS indicate a 1:1 stoichiometry for this RnlA–RnlB complex. Crystals of the RnlA–RnlB complex belonged to space group C2, with unit-cell parameters a = 243.32, b = 133.58, c = 55.64 Å, β = 95.11°, and diffracted to 2.6 Å resolution. The presence of both proteins in the crystals was confirmed and the asymmetric unit is likely to contain a heterotetramer with RnlA2:RnlB2 stoichiometry
Accelerating gradient projection methods for -constrained signal recovery by steplength selection rules
We propose a new gradient projection algorithm that compares favorably with
the fastest algorithms available to date for -constrained sparse
recovery from noisy data, both in the compressed sensing and inverse problem
frameworks. The method exploits a line-search along the feasible direction and
an adaptive steplength selection based on recent strategies for the alternation
of the well-known Barzilai-Borwein rules. The convergence of the proposed
approach is discussed and a computational study on both well-conditioned and
ill-conditioned problems is carried out for performance evaluations in
comparison with five other algorithms proposed in the literature.Comment: 11 pages, 4 figure
Polynomials Associated with Equilibria of Affine Toda-Sutherland Systems
An affine Toda-Sutherland system is a quasi-exactly solvable multi-particle
dynamics based on an affine simple root system. It is a `cross' between two
well-known integrable multi-particle dynamics, an affine Toda molecule and a
Sutherland system. Polynomials describing the equilibrium positions of affine
Toda-Sutherland systems are determined for all affine simple root systems.Comment: 9 page
Linear waves in sheared flows. Lower bound of the vorticity growth and propagation discontinuities in the parameters space
This study provides sufficient conditions for the temporal monotonic decay of
enstrophy for two-dimensional perturbations traveling in the incompressible,
viscous, plane Poiseuille and Couette flows. Extension of J. L. Synge's
procedure (1938) to the initial-value problem allowed us to find the region of
the wavenumber-Reynolds number map where the enstrophy of any initial
disturbance cannot grow. This region is wider than the kinetic energy's one. We
also show that the parameters space is split in two regions with clearly
distinct propagation and dispersion properties
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