4,346 research outputs found
G2 Bézier-Like Cubic as the S-Transition and C-Spiral Curves and Its Application in Designing a Spur Gear Tooth
Many of the researchers or designers are mostly used the involute curves (known as one of the approximation curves) to design the profile of gears. This study intends to develop the transition (S transition and C spiral) curves using Bézier–like cubic curve function with G2 (curvature) continuity as the degree of smoothness. Method of designing the transition curves is adapted by using circle to circle templates. While the transition curves are completely finished, it will be applied in redesigning the profile of spur gear. The mathematical proofs and simple models are also shown
Complex Curve of the Two Matrix Model and its Tau-function
We study the hermitean and normal two matrix models in planar approximation
for an arbitrary number of eigenvalue supports. Its planar graph interpretation
is given. The study reveals a general structure of the underlying analytic
complex curve, different from the hyperelliptic curve of the one matrix model.
The matrix model quantities are expressed through the periods of meromorphic
generating differential on this curve and the partition function of the
multiple support solution, as a function of filling numbers and coefficients of
the matrix potential, is shown to be the quasiclassical tau-function. The
relation to softly broken N=1 supersymmetric Yang-Mills theories is discussed.
A general class of solvable multimatrix models with tree-like interactions is
considered.Comment: 36 pages, 10 figures, TeX; final version appeared in special issue of
J.Phys. A on Random Matrix Theor
INTEGRATING SPUR GEAR TEETH DESIGN AND ITS ANALYSIS WITH G2 PARAMETRIC BÉZIER-LIKE CUBIC TRANSITION AND SPIRAL CURVES
An involute curve (or known as an approximated curve) is mostly used in designing the gear teeth (profile) especially in spur gear. Conversely, this study has the intention to redesign the spur gear teeth using the transition (S transition and C spiral) curves (also known as the exact curves) with curvature continuity (G2) as the degree of smoothness. Method of designing the transition curves is adapted from the circle to circle templates. The applicability of the new teeth model with the chosen
material, Stainless Steel Grade 304 is determined using Linear Static Analysis, Fatigue Analysis and Design Efficiency (DE). Several concepts and the related examples are shown throughout this study
Orbitally Degenerate Spin-1 Model for Insulating V2O3
Motivated by recent neutron, X-ray absorption and resonant scattering
experiments, we revisit the electronic structure of V2O3. We propose a model in
which S=1 V3+ ions are coupled in the vertical V-V pairs forming two-fold
orbitally degenerate configurations with S=2. Ferro-orbital ordering of the V-V
pairs gives a description which is consistent with all experiments in the
antiferromagnetic insulating phase.Comment: 4 pages, including three figure
A Victorian Age Proof of the Four Color Theorem
In this paper we have investigated some old issues concerning four color map
problem. We have given a general method for constructing counter-examples to
Kempe's proof of the four color theorem and then show that all counterexamples
can be rule out by re-constructing special 2-colored two paths decomposition in
the form of a double-spiral chain of the maximal planar graph. In the second
part of the paper we have given an algorithmic proof of the four color theorem
which is based only on the coloring faces (regions) of a cubic planar maps. Our
algorithmic proof has been given in three steps. The first two steps are the
maximal mono-chromatic and then maximal dichromatic coloring of the faces in
such a way that the resulting uncolored (white) regions of the incomplete
two-colored map induce no odd-cycles so that in the (final) third step four
coloring of the map has been obtained almost trivially.Comment: 27 pages, 18 figures, revised versio
Geometric approach to chaos in the classical dynamics of abelian lattice gauge theory
A Riemannian geometrization of dynamics is used to study chaoticity in the
classical Hamiltonian dynamics of a U(1) lattice gauge theory. This approach
allows one to obtain analytical estimates of the largest Lyapunov exponent in
terms of time averages of geometric quantities. These estimates are compared
with the results of numerical simulations, and turn out to be very close to the
values extrapolated for very large lattice sizes even when the geometric
quantities are computed using small lattices. The scaling of the Lyapunov
exponent with the energy density is found to be well described by a quadratic
power law.Comment: REVTeX, 9 pages, 4 PostScript figures include
- …