1,659 research outputs found

### Propagation of surface initiated rolling contact fatigue cracks in bearing Steel

Surface initiated rolling contact fatigue, leading to a surface failure known as pitting, is a life limiting failure mode in many modern machine elements, particularly rolling element bearings. Most research on rolling contact fatigue considers total life to pitting. Instead, this work studies the growth of rolling contact fatigue cracks before they develop into surface pits in an attempt to better understand crack propagation mechanisms. A triple-contact disc machine was used to perform pitting experiments on bearing steel samples under closely controlled contact conditions in mixed lubrication regime. Crack growth across the specimen surface is monitored and crack propagation rates extracted. The morphology of the generated cracks is observed by preparing sections of cracked specimens at the end of the test. It was found that crack initiation occurred very early in total life, which was attributed to high asperity stresses due to mixed lubrication regime. Total life to pitting was dominated by crack propagation. Results provide direct evidence of two distinct stages of crack growth in rolling contact fatigue: stage 1, within which cracks grow at a slow and relatively steady rate, consumed most of the total life; and stage 2, reached at a critical crack length, within which the propagation rate rapidly increases. Contact pressure and crack size were shown to be the main parameters controlling the propagation rate. Results show that crack propagation under rolling contact fatigue follows similar trends to those known to occur in classical fatigue. A log-log plot of measured crack growth rates against the product of maximum contact pressure and the square root of crack length, a parameter describing the applied stress intensity, produces a straight line for stage 2 propagation. This provides the first evidence that growth of hereby-identified stage 2 rolling contact fatigue cracks can be described by a Paris-type power law, where the rate of crack growth across the surface is proportional to the contact pressure raised to a power of approximately 7.5

### On the variational noncommutative Poisson geometry

We outline the notions and concepts of the calculus of variational
multivectors within the Poisson formalism over the spaces of infinite jets of
mappings from commutative (non)graded smooth manifolds to the factors of
noncommutative associative algebras over the equivalence under cyclic
permutations of the letters in the associative words. We state the basic
properties of the variational Schouten bracket and derive an interesting
criterion for (non)commutative differential operators to be Hamiltonian (and
thus determine the (non)commutative Poisson structures). We place the
noncommutative jet-bundle construction at hand in the context of the quantum
string theory.Comment: Proc. Int. workshop SQS'11 `Supersymmetry and Quantum Symmetries'
(July 18-23, 2011; JINR Dubna, Russia), 4 page

### An integrable shallow water equation with peaked solitons

We derive a new completely integrable dispersive shallow water equation that
is biHamiltonian and thus possesses an infinite number of conservation laws in
involution. The equation is obtained by using an asymptotic expansion directly
in the Hamiltonian for Euler's equations in the shallow water regime. The
soliton solution for this equation has a limiting form that has a discontinuity
in the first derivative at its peak.Comment: LaTeX file. Figure available from authors upon reques

### Weak Transversality and Partially Invariant Solutions

New exact solutions are obtained for several nonlinear physical equations,
namely the Navier-Stokes and Euler systems, an isentropic compressible fluid
system and a vector nonlinear Schroedinger equation. The solution methods make
use of the symmetry group of the system in situations when the standard Lie
method of symmetry reduction is not applicable.Comment: 23 pages, preprint CRM-284

### Non-classical symmetries and the singular manifold method: A further two examples

This paper discusses two equations with the conditional Painleve property.
The usefulness of the singular manifold method as a tool for determining the
non-classical symmetries that reduce the equations to ordinary differential
equations with the Painleve property is confirmed once moreComment: 9 pages (latex), to appear in Journal of Physics

### Rational Approximate Symmetries of KdV Equation

We construct one-parameter deformation of the Dorfman Hamiltonian operator
for the Riemann hierarchy using the quasi-Miura transformation from topological
field theory. In this way, one can get the approximately rational symmetries of
KdV equation and then investigate its bi-Hamiltonian structure.Comment: 14 pages, no figure

### Jet Bundles in Quantum Field Theory: The BRST-BV method

The geometric interpretation of the Batalin-Vilkovisky antibracket as the
Schouten bracket of functional multivectors is examined in detail. The
identification is achieved by the process of repeated contraction of even
functional multivectors with fermionic functional 1-forms. The classical master
equation may then be considered as a generalisation of the Jacobi identity for
Poisson brackets, and the cohomology of a nilpotent even functional multivector
is identified with the BRST cohomology. As an example, the BRST-BV formulation
of gauge fixing in theories with gauge symmetries is reformulated in the jet
bundle formalism. (Hopefully this version will be TeXable)Comment: 26 page

### Bi-Hamiltonian structures for integrable systems on regular time scales

A construction of the bi-Hamiltonian structures for integrable systems on
regular time scales is presented. The trace functional on an algebra of
$\delta$-pseudo-differential operators, valid on an arbitrary regular time
scale, is introduced. The linear Poisson tensors and the related Hamiltonians
are derived. The quadratic Poisson tensors is given by the use of the recursion
operators of the Lax hierarchies. The theory is illustrated by
$\Delta$-differential counterparts of Ablowitz-Kaup-Newell-Segur and Kaup-Broer
hierarchies.Comment: 18 page

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