131 research outputs found
SENSITIVITY OF STRESSES TO THE FORCES ACTING ON THE CAST PARTS OF FREIGHT-CAR BOGIE
Purpose. To determine the effect of the force components acting in the axle box and the central spring suspension on the stresses occurring in the solebar of the three-piece bogie. Methodology. To assess the effect of the forces acting on the solebar on the stresses in it, we developed a finite element model of the solebar. After that, we carried out an assessment of its stress-strain state under loading conditions corresponding to the І and ІІІ design modes. According to the results obtained, we determined the stress concentration points in the construction, which are selected as check ones for further studies. Also, as checkpoints we took the points corresponding to the sensor locations when estimating the stresses in the solebar during the tests. At the next stage, we applied unit loads in sequence at the interaction points of the solebar with the boxes and the central spring group. To obtain a more accurate result, the unit forces were balanced by the corresponding forces and moments of inertia. With each loading variant, tensors of stresses arising from the action of unit loads were obtained at checkpoints. On the basis of the stress tensors obtained, we determined the corresponding equivalent stresses - the sensitivity coefficients. Findings. The paper determines the stress sensitivity coefficients in the three-piece bogie solebar to external loads acting on the solebar from the side of axle box and central spring group. Based on the results of the assessment of the coefficients obtained, we determined the forces having the greatest influence on individual sections of the solebar. We estimated the possibility of using the obtained results in optimizing the parameters of the bogie spring suspension to increase the strength and durability of the solebar. Originality. For the first time, the effect of individual components of the forces acting on the solebar on the stresses in it has been estimated. Practical value. The obtained result can be used in the design and optimization of three-piece bogies, to improve the solebar durability. The stress tensors obtained can be used to estimate the effect of complex loading on the solebar strength and durability
STABILITY OF MOTION OF RAILWAY VEHICLES DESCRIBED WITH LAGRANGE EQUATIONS OF THE FIRST KIND
Purpose. The article aims to estimate the stability of the railway vehicle motion, whose oscillations are described by Lagrange equations of the first kind under the assumption that there are no nonlinearities with discontinuities of the right-hand sides. Methodology. The study is based on the Lyapunov’s stability method of linear approximation. The equations of motion are compiled in a matrix form. The creep forces are calculated in accordance with the Kalker linear theory. Sequential differentiations of the constraint equations reduced the equation system index from 2 to 0. The coefficient matrix eigenvalues of the system obtained in such a way are found by means of the QR-algorithm. In accordance with Lyapunov's criterion of stability in the linear approximation, the motion is stable if the real part of all eigenvalues is negative. The presence of «superfluous» degrees of freedom, which the mechanical system does not have (in whose motion equations there are left only independent coordinates) is not trivial. Herewith the eigenvalues and eigenvectors correspond to these degrees of freedom and have no relation to the stability. In order to find a rule that allows excluding them, we considered several models of a bogie, with rigid and elastic constraints of high rigidity at the nodes. In the limiting case of high rigidities, the results for a system without rigid constraints must coincide with the results for a system with rigid constraints. Findings. We carried out the analysis and compared the frequencies (with decrements) and the vibration modes of a three-piece bogie with and without constraints. When analysing the stability of the system with constraints, only those eigenvalues are of interest whose eigenvectors do not break the constraints. The values of these numbers are limits for the eigenvalues of the system, in which rigid constraints are replaced by elastic elements of high rigidity, which allows us to leave the Lyapunov’s criterion unchanged. Originality consists in the adaptation of Lyapunov's stability method of linear approximation to the case when the equations of railway vehicle motion are written in the form of differential-algebraic Lagrange equations of the first kind. Practical value. This written form of the equation of motion makes it possible to simplify the stability study by avoiding the selection of a set of independent generalized coordinates with the subsequent elimination of dependent ones and allows for the coefficient matrix calculation in an easily algorithmized way. Information on the vehicle stability is vitally important, since the truck design must necessarily exclude the loss of stability in the operational speed range
On insertion-deletion systems over relational words
We introduce a new notion of a relational word as a finite totally ordered
set of positions endowed with three binary relations that describe which
positions are labeled by equal data, by unequal data and those having an
undefined relation between their labels. We define the operations of insertion
and deletion on relational words generalizing corresponding operations on
strings. We prove that the transitive and reflexive closure of these operations
has a decidable membership problem for the case of short insertion-deletion
rules (of size two/three and three/two). At the same time, we show that in the
general case such systems can produce a coding of any recursively enumerable
language leading to undecidabilty of reachability questions.Comment: 24 pages, 8 figure
Knot Theory: from Fox 3-colorings of links to Yang-Baxter homology and Khovanov homology
This paper is an extended account of my "Introductory Plenary talk at Knots
in Hellas 2016" conference We start from the short introduction to Knot Theory
from the historical perspective, starting from Heraclas text (the first century
AD), mentioning R.Llull (1232-1315), A.Kircher (1602-1680), Leibniz idea of
Geometria Situs (1679), and J.B.Listing (student of Gauss) work of 1847. We
spend some space on Ralph H. Fox (1913-1973) elementary introduction to diagram
colorings (1956). In the second section we describe how Fox work was
generalized to distributive colorings (racks and quandles) and eventually in
the work of Jones and Turaev to link invariants via Yang-Baxter operators, here
the importance of statistical mechanics to topology will be mentioned. Finally
we describe recent developments which started with Mikhail Khovanov work on
categorification of the Jones polynomial. By analogy to Khovanov homology we
build homology of distributive structures (including homology of Fox colorings)
and generalize it to homology of Yang-Baxter operators. We speculate, with
supporting evidence, on co-cycle invariants of knots coming from Yang-Baxter
homology. Here the work of Fenn-Rourke-Sanderson (geometric realization of
pre-cubic sets of link diagrams) and Carter-Kamada-Saito (co-cycle invariants
of links) will be discussed and expanded.
Dedicated to Lou Kauffman for his 70th birthday.Comment: 35 pages, 31 figures, for Knots in Hellas II Proceedings, Springer,
part of the series Proceedings in Mathematics & Statistics (PROMS
Barrier and internal wave contributions to the quantum probability density and flux in light heavy-ion elastic scattering
We investigate the properties of the optical model wave function for light
heavy-ion systems where absorption is incomplete, such as Ca
and O around 30 MeV incident energy. Strong focusing effects
are predicted to occur well inside the nucleus, where the probability density
can reach values much higher than that of the incident wave. This focusing is
shown to be correlated with the presence at back angles of a strong enhancement
in the elastic cross section, the so-called ALAS (anomalous large angle
scattering) phenomenon; this is substantiated by calculations of the quantum
probability flux and of classical trajectories. To clarify this mechanism, we
decompose the scattering wave function and the associated probability flux into
their barrier and internal wave contributions within a fully quantal
calculation. Finally, a calculation of the divergence of the quantum flux shows
that when absorption is incomplete, the focal region gives a sizeable
contribution to nonelastic processes.Comment: 16 pages, 15 figures. RevTeX file. To appear in Phys. Rev. C. The
figures are only available via anonynous FTP on
ftp://umhsp02.umh.ac.be/pub/ftp_pnt/figscat
Chern-Simons Theory in the Temporal Gauge and Knot Invariants through the Universal Quantum R-Matrix
In temporal gauge A_{0}=0 the 3d Chern-Simons theory acquires quadratic
action and an ultralocal propagator. This directly implies a 2d R-matrix
representation for the correlators of Wilson lines (knot invariants), where
only the crossing points of the contours projection on the xy plane contribute.
Though the theory is quadratic, P-exponents remain non-trivial operators and
R-factors are easier to guess then derive. We show that the topological
invariants arise if additional flag structure (xy plane and an y line in it) is
introduced, R is the universal quantum R-matrix and turning points contribute
the "enhancement" factors q^{\rho}.Comment: 27 pages, 17 figure
The Architectural Design Rules of Solar Systems based on the New Perspective
On the basis of the Lunar Laser Ranging Data released by NASA on the Silver
Jubilee Celebration of Man Landing on Moon on 21st July 1969-1994, theoretical
formulation of Earth-Moon tidal interaction was carried out and Planetary
Satellite Dynamics was established. It was found that this mathematical
analysis could as well be applied to Star and Planets system and since every
star could potentially contain an extra-solar system, hence we have a large
ensemble of exoplanets to test our new perspective on the birth and evolution
of solar systems. Till date 403 exoplanets have been discovered in 390
extra-solar systems. I have taken 12 single planet systems, 4 Brown Dwarf -
Star systems and 2 Brown Dwarf pairs. Following architectural design rules are
corroborated through this study of exoplanets. All planets are born at inner
Clarke Orbit what we refer to as inner geo-synchronous orbit in case of
Earth-Moon System. By any perturbative force such as cosmic particles or
radiation pressure, the planet gets tipped long of aG1 or short of aG1. Here
aG1 is inner Clarke Orbit. The exoplanet can either be launched on death spiral
as CLOSE HOT JUPITERS or can be launched on an expanding spiral path as the
planets in our Solar System are. It was also found that if the exo-planet are
significant fraction of the host star then those exo-planets rapidly migrate
from aG1 to aG2 and have very short Time Constant of Evolution as Brown Dwarfs
have. This vindicates our basic premise that planets are always born at inner
Clarke Orbit. This study vindicates the design rules which had been postulated
at 35th COSPAR Scientific Assembly in 2004 at Paris, France, under the title
,New Perspective on the Birth & Evolution of Solar Systems.Comment: This paper has been reported to Earth,Moon and Planets Journal as
MOON-S-09-0007
Quantum Holonomy in Three-dimensional General Covariant Field Theory and Link Invariant
We consider quantum holonomy of some three-dimensional general covariant
non-Abelian field theory in Landau gauge and confirm a previous result
partially proven. We show that quantum holonomy retains metric independence
after explicit gauge fixing and hence possesses the topological property of a
link invariant. We examine the generalized quantum holonomy defined on a
multi-component link and discuss its relation to a polynomial for the link.Comment: RevTex, 12 pages. The metric independence of path integral measure is
justified and the case of multi-component link is discussed in detail. To be
published in Physical Review
A peculiar class of debris disks from Herschel/DUNES - A steep fall off in the far infrared
Aims. We present photometric data of debris disks around HIP 103389 (HD
199260), HIP 107350 (HN Peg, HD206860), and HIP 114948 (HD 219482), obtained in
the context of our Herschel Open Time Key Program DUNES (DUst around NEarby
Stars). Methods. We used Herschel/PACS to detect the thermal emission of the
three debris disks with a 3 sigma sensitivity of a few mJy at 100 um and 160
um. In addition, we obtained Herschel/PACS photometric data at 70 um for HIP
103389. Two different approaches are applied to reduce the Herschel data to
investigate the impact of data reduction on the photometry. We fit analytical
models to the available spectral energy distribution (SED) data. Results. The
SEDs of the three disks potentially exhibit an unusually steep decrease at
wavelengths > 70 um. We investigate the significance of the peculiar shape of
these SEDs and the impact on models of the disks provided it is real. Our
modeling reveals that such a steep decrease of the SEDs in the long wavelength
regime is inconsistent with a power-law exponent of the grain size distribution
-3.5 expected from a standard equilibrium collisional cascade. In contrast, a
very distinct range of grain sizes is implied to dominate the thermal emission
of such disks. However, we demonstrate that the understanding of the data of
faint sources obtained with Herschel is still incomplete and that the
significance of our results depends on the version of the data reduction
pipeline used. Conclusions. A new mechanism to produce the dust in the
presented debris disks, deviations from the conditions required for a standard
equilibrium collisional cascade (grain size exponent of -3.5), and/or
significantly different dust properties would be necessary to explain the
potentially steep SED shape of the three debris disks presented. (abridged)Comment: 14 pages, 4 figures, accepted by A&
The Computational Complexity of Knot and Link Problems
We consider the problem of deciding whether a polygonal knot in 3-dimensional
Euclidean space is unknotted, capable of being continuously deformed without
self-intersection so that it lies in a plane. We show that this problem, {\sc
unknotting problem} is in {\bf NP}. We also consider the problem, {\sc
unknotting problem} of determining whether two or more such polygons can be
split, or continuously deformed without self-intersection so that they occupy
both sides of a plane without intersecting it. We show that it also is in NP.
Finally, we show that the problem of determining the genus of a polygonal knot
(a generalization of the problem of determining whether it is unknotted) is in
{\bf PSPACE}. We also give exponential worst-case running time bounds for
deterministic algorithms to solve each of these problems. These algorithms are
based on the use of normal surfaces and decision procedures due to W. Haken,
with recent extensions by W. Jaco and J. L. Tollefson.Comment: 32 pages, 1 figur
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