257 research outputs found
Geometric analysis of noisy perturbations to nonholonomic constraints
We propose two types of stochastic extensions of nonholonomic constraints for
mechanical systems. Our approach relies on a stochastic extension of the
Lagrange-d'Alembert framework. We consider in details the case of invariant
nonholonomic systems on the group of rotations and on the special Euclidean
group. Based on this, we then develop two types of stochastic deformations of
the Suslov problem and study the possibility of extending to the stochastic
case the preservation of some of its integrals of motion such as the Kharlamova
or Clebsch-Tisserand integrals
Vascular plants on the islands and peninsulas of Maloe More (Lake Baikal): patterns of diversity and species turnover
Unique biota of the Lake Baikal region face many threats due to increasing human activities. We documented spatial patterns in diversity of vascular plants, explored effects of natural (bird colonies) and human-induced (tourism) disturbances on species richness of semi-desert and steppe-desert plant communities of 12 islands and 4 peninsulas, and estimated species turnover within a 30-year period. Floras of surveyed islands/peninsulas contained 9 to 143 species; species area relationship followed the power law model. Species richness did not change between 1979 and 2009, but the proportion of ruderal species doubled during this period. Mean relative turnover rate was 1.17% of species per year. The islands with large bird colonies had lower species richness than the islands with small or no colonies. Imposing restrictions on tourist visitation to at least three islands (Zamogoj, Khubyn and Khunuk) is a feasible way to conserve substantial part of regional biodiversity
Thalhammerite, Pd9Ag2Bi2S4, a New Mineral from the Talnakh and Oktyabrsk Deposits, Noril'sk Region, Russia
This is an Open Access publicatiomThe file attached is the Published/publisher’s pdf version of the article
Multi-scale polarisation phenomena
Multi-scale methods that separate different time or spatial scales are among the most powerful techniques in physics, especially in applications that study nonlinear systems with noise. When the time scales (noise and perturbation) are of the same order, the scales separation becomes impossible. Thus, the multi-scale approach has to be modified to characterise a variety of noise-induced phenomena. Here, based on stochastic modelling and analytical study, we demonstrate in terms of the fluctuation-induced phenomena and Hurst R/S analysis metrics that the matching scales of random birefringence and pump–signal states of polarisation interaction in a fibre Raman amplifier results in a new random birefringence-mediated phenomenon, which is similar to stochastic anti-resonance. The observed phenomenon, apart from the fundamental interest, provides a base for advancing multi-scale methods with application to different coupled nonlinear systems ranging from lasers (multimode, mode-locked, random, etc.) to nanostructures (light-mediated conformation of molecules and chemical reactions, Brownian motors, etc.)
Anholonomic frames in constrained dynamics
We demonstrate the usefulness of anholonomic frames in the contexts of
nonholonomic and vakonomic systems. We take a consistently
differential-geometric approach. As an application, we investigate the
conditions under which the dynamics of the two systems will be consistent. A
few illustrative examples confirm the results.Comment: 33 pages, to appear in `Dynamical Systems. An international journal.
On the Equivalence Between Type I Liouville Dynamical Systems in the Plane and the Sphere
ProducciĂłn CientĂficaSeparable Hamiltonian systems either in sphero-conical coordinates on an S2 sphere or in elliptic coordinates on a R2 plane are described in a unified way. A back and forth route connecting these Liouville Type I separable systems is unveiled. It is shown how the gnomonic projection and its inverse map allow us to pass from a Liouville Type I separable system with a spherical configuration space
to its Liouville Type I partners where the configuration space is a plane and back. Several selected spherical separable systems and their planar cousins are discussed in a classical context
Position-dependent mass systems: Classical and quantum pictures
Extended abstract of "Algebraic approach to position-dependent mass systems
in both classical and quantum pictures", a series of three lectures delivered
by the author in the VIII School on Geometry and Physics, 24 June-8 June 2019,
organized by the Department of Mathematical Physics of the University of
Bialystok, in Bialowieza, Poland (http://wgmp.uwb.edu.pl/wgmp38/part_s.html)Comment: 12 pages, no figure
Atomic transition frequencies, isotope shifts, and sensitivity to variation of the fine structure constant for studies of quasar absorption spectra
Theories unifying gravity with other interactions suggest spatial and
temporal variation of fundamental "constants" in the Universe. A change in the
fine structure constant, alpha, could be detected via shifts in the frequencies
of atomic transitions in quasar absorption systems. Recent studies using 140
absorption systems from the Keck telescope and 153 from the Very Large
Telescope, suggest that alpha varies spatially. That is, in one direction on
the sky alpha seems to have been smaller at the time of absorption, while in
the opposite direction it seems to have been larger.
To continue this study we need accurate laboratory measurements of atomic
transition frequencies. The aim of this paper is to provide a compilation of
transitions of importance to the search for alpha variation. They are E1
transitions to the ground state in several different atoms and ions, with
wavelengths ranging from around 900 - 6000 A, and require an accuracy of better
than 10^{-4} A. We discuss isotope shift measurements that are needed in order
to resolve systematic effects in the study. The coefficients of sensitivity to
alpha-variation (q) are also presented.Comment: Includes updated version of the "alpha line" lis
Complex Estimation of Strength Properties of Functional Materials on the Basis of the Analysis of Grain-Phase Structure Parameters
The technique allows analysis using grain-phase structure of the functional material to evaluate its performance, particularly strength properties. The technique is based on the use of linguistic variable in the process of comprehensive evaluation. An example of estimating the strength properties of steel reinforcement, subject to special heat treatment to obtain the desired grain-phase structure
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