583 research outputs found
Profiles of inflated surfaces
We study the shape of inflated surfaces introduced in \cite{B1} and
\cite{P1}. More precisely, we analyze profiles of surfaces obtained by
inflating a convex polyhedron, or more generally an almost everywhere flat
surface, with a symmetry plane. We show that such profiles are in a
one-parameter family of curves which we describe explicitly as the solutions of
a certain differential equation.Comment: 13 pages, 2 figure
Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems
We propose the integrable (pseudo)spherical generalization of the
four-dimensional anisotropic oscillator with additional nonlinear potential.
Performing its Kustaanheimo-Stiefel transformation we then obtain the
pseudospherical generalization of the MICZ-Kepler system with linear and
potential terms. We also present the generalization of the
parabolic coordinates, in which this system admits the separation of variables.
Finally, we get the spherical analog of the presented MICZ-Kepler-like system.Comment: 7 page
Meat freshness revealed by visible to near-infrared spectroscopy and principal component analysis
Increasing concerns about adulterated meat encouraged industry looking for new non-invasive methods for rapid accurate meat quality assessment. Main meat chromophores (myoglobin, oxy-myoglobin, fat, water, collagen) are characterized by close comparable absorption in visible to near-infrared (NIR) spectral region. Therefore, structural and compositional variations in meat may lead to relative differences in the absorption of light. Utilizing typical fiber-optic probes and integrating sphere, a degradation of pork samples freshness was observed at room temperature referring to the relative changes in absorbance of main meat chromophores. The application of principal component analysis (PCA) used for examination of measured absorbance spectra revealed more detailed sub-stages of freshness, which are not observed by the conventional analysis of the reflectance spectra. The results show a great potential of the combined application of optical-NIR spectroscopy with complementary use of PCA approach for assessing meat quality and monitoring relative absorbance alternation of oxymyoglobin and myoglobin in visible, and fat, water, collagen in NIR spectral ranges
The generalized MIC-Kepler system
This paper deals with dynamical system that generalizes the MIC-Kepler
system. It is shown that the Schr\"{o}dinger equation for this generalized
MIC-Kepler system can be separated in spherical and parabolic coordinates. The
spectral problem in spherical and parabolic coordinates is solved.Comment: 8 page
Purity-bounded uncertainty relations in multidimensional space -- generalized purity
Uncertainty relations for mixed quantum states (precisely, purity-bounded
position-momentum relations, developed by Bastiaans and then by Man'ko and
Dodonov) are studied in general multi-dimensional case. An expression for
family of mixed states at the lower bound of uncertainty relation is obtained.
It is shown, that in case of entropy-bounded uncertainty relations, lower-bound
state is thermal, and a transition from one-dimensional problem to
multi-dimensional one is trivial. Results of numerical calculation of the
relation lower bound for different types of generalized purity are presented.
Analytical expressions for general purity-bounded relations for highly mixed
states are obtained.Comment: 12 pages, 2 figures. draft version, to appear in J. Phys. A Partially
based on a poster "Multidimensional uncertainty relations for states with
given generalized purity" presented on X Intl. Conf. on Quantum Optics'2004
(Minsk, Belarus, May 30 -- June 3, 2004) More actual report is to be
presented on ICSSUR-2005, Besan\c{c}on, France and on EQEC'05, Munich. V. 5:
amended article after referees' remark
A new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow
Modelling incompressible ideal fluids as a finite collection of vortex
filaments is important in physics (super-fluidity, models for the onset of
turbulence) as well as for numerical algorithms used in computer graphics for
the real time simulation of smoke. Here we introduce a time-discrete evolution
equation for arbitrary closed polygons in 3-space that is a discretisation of
the localised induction approximation of filament motion. This discretisation
shares with its continuum limit the property that it is a completely integrable
system. We apply this polygon evolution to a significant improvement of the
numerical algorithms used in Computer Graphics.Comment: 15 pages, 3 figure
3D Oscillator and Coulomb Systems reduced from Kahler spaces
We define the oscillator and Coulomb systems on four-dimensional spaces with
U(2)-invariant Kahler metric and perform their Hamiltonian reduction to the
three-dimensional oscillator and Coulomb systems specified by the presence of
Dirac monopoles. We find the Kahler spaces with conic singularity, where the
oscillator and Coulomb systems on three-dimensional sphere and two-sheet
hyperboloid are originated. Then we construct the superintegrable oscillator
system on three-dimensional sphere and hyperboloid, coupled to monopole, and
find their four-dimensional origins. In the latter case the metric of
configuration space is non-Kahler one. Finally, we extend these results to the
family of Kahler spaces with conic singularities.Comment: To the memory of Professor Valery Ter-Antonyan, 11 page
Quantum oscillator as 1D anyon
It is shown that in one spatial dimension the quantum oscillator is dual to
the charged particle situated in the field described by the superposition of
Coulomb and Calogero-Sutherland potentials.Comment: 9 pages, LaTe
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