1,211 research outputs found
Saari's homographic conjecture for planar equal-mass three-body problem in Newton gravity
Saari's homographic conjecture in N-body problem under the Newton gravity is
the following; configurational measure \mu=\sqrt{I}U, which is the product of
square root of the moment of inertia I=(\sum m_k)^{-1}\sum m_i m_j r_{ij}^2 and
the potential function U=\sum m_i m_j/r_{ij}, is constant if and only if the
motion is homographic. Where m_k represents mass of body k and r_{ij}
represents distance between bodies i and j. We prove this conjecture for planar
equal-mass three-body problem.
In this work, we use three sets of shape variables. In the first step, we use
\zeta=3q_3/(2(q_2-q_1)) where q_k \in \mathbb{C} represents position of body k.
Using r_1=r_{23}/r_{12} and r_2=r_{31}/r_{12} in intermediate step, we finally
use \mu itself and \rho=I^{3/2}/(r_{12}r_{23}r_{31}). The shape variables \mu
and \rho make our proof simple
Puzzles in physics
I discuss some puzzles observed in exclusive meson decays, concentrating
on the large difference between the direct CP asymmetries in the and modes, the large
branching ratio, and the large deviation of the mixing-induced CP asymmetries
in the penguins from those in the trees.Comment: 6 pages, 1 figure, talk presented at the 9th Workshop on High Energy
Physics Phenomenology, Bhubaneswar, Orissa, India, Jan. 3-14, 2006; reference
adde
Factorization theorems, effective field theory, and nonleptonic heavy meson decays
The nonleptonic heavy meson decays
and are studied based on the three-scale perturbative QCD
factorization theorem developed recently. In this formalism the
Bauer-Stech-Wirbel parameters a_1 and a_2 are treated as the Wilson
coefficients, whose evolution from the W boson mass down to the characteristic
scale of the decay processes is determined by effective field theory. The
evolution from the characteristic scale to a lower hadronic scale is formulated
by the Sudakov resummation. The scale-setting ambiguity, which exists in the
conventional approach to nonleptonic heavy meson decays, is moderated.
Nonfactorizable and nonspectator contributions are taken into account as part
of the hard decay subamplitudes. Our formalism is applicable to both bottom and
charm decays, and predictions, including those for the ratios R and R_L
associated with the decays, are consistent with
experimental data.Comment: 39 pages, latex, 5 figures, revised version with some correction
Perturbative QCD factorization of and
We prove factorization theorem for the processes and
to leading twist in the covariant gauge by means of the
Ward identity. Soft divergences cancel and collinear divergences are grouped
into a pion wave function defined by a nonlocal matrix element. The gauge
invariance and universality of the pion wave function are confirmed. The proof
is then extended to the exclusive meson decays and
in the heavy quark limit. It is shown that a light-cone
meson wave function, though absorbing soft dynamics, can be defined in an
appropriate frame. Factorization of the decay in
space, being parton transverse momenta, is briefly discussed. We comment
on the extraction of the leading-twist pion wave function from experimental
data.Comment: 21 pages in Latex file, version to appear in Phys. Rev.
Physical Insights of Low Thermal Expansion Coefficient Electrode Stress Effect on Hafnia-Based Switching Speed
In this report, we investigate the effect of low coefficient of thermal
expansion (CTE) metals on the operating speed of hafnium-based oxide
capacitance. We found that the cooling process of low CTE metals during rapid
thermal annealing (RTA) generates in-plane tensile stresses in the film, This
facilitates an increase in the volume fraction of the o-phase and significantly
improves the domain switching speed. However, no significant benefit was
observed at electric fields less than 1 MV/cm. This is because at low voltage
operation, the defective resistance (dead layer) within the interface prevents
electron migration and the increased RC delay. Minimizing interface defects
will be an important key to extending endurance and retention
Infiltration of meteoric water in the South Tibetan Detachment (Mount Everest, Himalaya): When and why?
Publisher's version/PDF must be used in Institutional Repository 6 months after publication
The strong thirteen spheres problem
The thirteen spheres problem is asking if 13 equal size nonoverlapping
spheres in three dimensions can touch another sphere of the same size. This
problem was the subject of the famous discussion between Isaac Newton and David
Gregory in 1694. The problem was solved by Schutte and van der Waerden only in
1953.
A natural extension of this problem is the strong thirteen spheres problem
(or the Tammes problem for 13 points) which asks to find an arrangement and the
maximum radius of 13 equal size nonoverlapping spheres touching the unit
sphere. In the paper we give a solution of this long-standing open problem in
geometry. Our computer-assisted proof is based on a enumeration of the
so-called irreducible graphs.Comment: Modified lemma 2, 16 pages, 12 figures. Uploaded program packag
Trigonometry of spacetimes: a new self-dual approach to a curvature/signature (in)dependent trigonometry
A new method to obtain trigonometry for the real spaces of constant curvature
and metric of any (even degenerate) signature is presented. The method
encapsulates trigonometry for all these spaces into a single basic
trigonometric group equation. This brings to its logical end the idea of an
absolute trigonometry, and provides equations which hold true for the nine
two-dimensional spaces of constant curvature and any signature. This family of
spaces includes both relativistic and non-relativistic homogeneous spacetimes;
therefore a complete discussion of trigonometry in the six de Sitter,
minkowskian, Newton--Hooke and galilean spacetimes follow as particular
instances of the general approach. Any equation previously known for the three
classical riemannian spaces also has a version for the remaining six
spacetimes; in most cases these equations are new. Distinctive traits of the
method are universality and self-duality: every equation is meaningful for the
nine spaces at once, and displays explicitly invariance under a duality
transformation relating the nine spaces. The derivation of the single basic
trigonometric equation at group level, its translation to a set of equations
(cosine, sine and dual cosine laws) and the natural apparition of angular and
lateral excesses, area and coarea are explicitly discussed in detail. The
exposition also aims to introduce the main ideas of this direct group
theoretical way to trigonometry, and may well provide a path to systematically
study trigonometry for any homogeneous symmetric space.Comment: 51 pages, LaTe
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