1,084 research outputs found
A Novel Approach for Ellipsoidal Outer-Approximation of the Intersection Region of Ellipses in the Plane
In this paper, a novel technique for tight outer-approximation of the
intersection region of a finite number of ellipses in 2-dimensional (2D) space
is proposed. First, the vertices of a tight polygon that contains the convex
intersection of the ellipses are found in an efficient manner. To do so, the
intersection points of the ellipses that fall on the boundary of the
intersection region are determined, and a set of points is generated on the
elliptic arcs connecting every two neighbouring intersection points. By finding
the tangent lines to the ellipses at the extended set of points, a set of
half-planes is obtained, whose intersection forms a polygon. To find the
polygon more efficiently, the points are given an order and the intersection of
the half-planes corresponding to every two neighbouring points is calculated.
If the polygon is convex and bounded, these calculated points together with the
initially obtained intersection points will form its vertices. If the polygon
is non-convex or unbounded, we can detect this situation and then generate
additional discrete points only on the elliptical arc segment causing the
issue, and restart the algorithm to obtain a bounded and convex polygon.
Finally, the smallest area ellipse that contains the vertices of the polygon is
obtained by solving a convex optimization problem. Through numerical
experiments, it is illustrated that the proposed technique returns a tighter
outer-approximation of the intersection of multiple ellipses, compared to
conventional techniques, with only slightly higher computational cost
Feynman Rules in the Type III Natural Flavour-Conserving Two-Higgs Doublet Model
We consider a two Higgs-doublet model with symmetry, which implies a
rather than 0 relative phase between the vacuum expectation
values . The corresponding Feynman rules are derived
accordingly and the transformation of the Higgs fields from the weak to the
mass eigenstates includes not only an angle rotation but also a phase
transformation. In this model, both doublets couple to the same type of
fermions and the flavour-changing neutral currents are naturally suppressed. We
also demonstrate that the Type III natural flavour-conserving model is valid at
tree-level even when an explicit symmetry breaking perturbation is
introduced to get a reasonable CKM matrix. In the special case , as the ratio runs from 0 to ,
the dominant Yukawa coupling will change from the first two generations to the
third generation. In the Feynman rules, we also find that the charged Higgs
currents are explicitly left-right asymmetric. The ratios between the left- and
right-handed currents for the quarks in the same generations are estimated.Comment: 16 pages (figures not included), NCKU-HEP/93-1
Lattice Calculation of Point-to-Point Hadron Current Correlation
Point-to-point correlation functions of hadron currents in the QCD vacuum are
calculated on a lattice and analyzed using dispersion relations, providing
physical information down to small spatial separations. Qualitative agreement
with phenomenological results is obtained in channels for which experimental
data are available, and these correlation functions are shown to be useful in
exploring approximations based on sum rules and interacting instantons.Comment: 11 page
Exact Solution of Two-Species Ballistic Annihilation with General Pair-Reaction Probability
The reaction process is modelled for ballistic reactants on an
infinite line with particle velocities and and initially
segregated conditions, i.e. all A particles to the left and all B particles to
the right of the origin. Previous, models of ballistic annihilation have
particles that always react on contact, i.e. pair-reaction probability .
The evolution of such systems are wholly determined by the initial distribution
of particles and therefore do not have a stochastic dynamics. However, in this
paper the generalisation is made to , allowing particles to pass through
each other without necessarily reacting. In this way, the A and B particle
domains overlap to form a fluctuating, finite-sized reaction zone where the
product C is created. Fluctuations are also included in the currents of A and B
particles entering the overlap region, thereby inducing a stochastic motion of
the reaction zone as a whole. These two types of fluctuations, in the reactions
and particle currents, are characterised by the `intrinsic reaction rate', seen
in a single system, and the `extrinsic reaction rate', seen in an average over
many systems. The intrinsic and extrinsic behaviours are examined and compared
to the case of isotropically diffusing reactants.Comment: 22 pages, 2 figures, typos correcte
Renormalization Group Study of the A+B->0 Diffusion-Limited Reaction
The diffusion-limited reaction, with equal initial densities
, is studied by means of a field-theoretic renormalization
group formulation of the problem. For dimension an effective theory is
derived, from which the density and correlation functions can be calculated. We
find the density decays in time as a,b \sim C\sqrt{\D}(Dt)^{-d/4} for , with \D = n_0-C^\prime n_0^{d/2} + \dots, where is a universal
constant, and is non-universal. The calculation is extended to the
case of unequal diffusion constants , resulting in a new
amplitude but the same exponent. For a controlled calculation is not
possible, but a heuristic argument is presented that the results above give at
least the leading term in an expansion. Finally, we address
reaction zones formed in the steady-state by opposing currents of and
particles, and derive scaling properties.Comment: 17 pages, REVTeX, 13 compressed figures, included with epsf. Eq.
(6.12) corrected, and a moderate rewriting of the introduction. Accepted for
publication in J. Stat. Phy
Kinetics of A+B--->0 with Driven Diffusive Motion
We study the kinetics of two-species annihilation, A+B--->0, when all
particles undergo strictly biased motion in the same direction and with an
excluded volume repulsion between same species particles. It was recently shown
that the density in this system decays as t^{-1/3}, compared to t^{-1/4}
density decay in A+B--->0 with isotropic diffusion and either with or without
the hard-core repulsion. We suggest a relatively simple explanation for this
t^{-1/3} decay based on the Burgers equation. Related properties associated
with the asymptotic distribution of reactants can also be accounted for within
this Burgers equation description.Comment: 11 pages, plain Tex, 8 figures. Hardcopy of figures available on
request from S
Diffusion-Limited Annihilation with Initially Separated Reactants
A diffusion-limited annihilation process, A+B->0, with species initially
separated in space is investigated. A heuristic argument suggests the form of
the reaction rate in dimensions less or equal to the upper critical dimension
. Using this reaction rate we find that the width of the reaction front
grows as in one dimension and as in two
dimensions.Comment: 9 pages, Plain Te
Fracture of disordered solids in compression as a critical phenomenon: I. Statistical mechanics formalism
This is the first of a series of three articles that treats fracture
localization as a critical phenomenon. This first article establishes a
statistical mechanics based on ensemble averages when fluctuations through time
play no role in defining the ensemble. Ensembles are obtained by dividing a
huge rock sample into many mesoscopic volumes. Because rocks are a disordered
collection of grains in cohesive contact, we expect that once shear strain is
applied and cracks begin to arrive in the system, the mesoscopic volumes will
have a wide distribution of different crack states. These mesoscopic volumes
are the members of our ensembles. We determine the probability of observing a
mesoscopic volume to be in a given crack state by maximizing Shannon's measure
of the emergent crack disorder subject to constraints coming from the
energy-balance of brittle fracture. The laws of thermodynamics, the partition
function, and the quantification of temperature are obtained for such cracking
systems.Comment: 11 pages, 2 figure
The equation of state for two flavor QCD at N_t=6
We calculate the two flavor equation of state for QCD on lattices with
lattice spacing a=(6T)^{-1} and find that cutoff effects are substantially
reduced compared to an earlier study using a=(4T)^{-1}. However, it is likely
that significant cutoff effects remain. We fit the lattice data to expected
forms of the free energy density for a second order phase transition at
zero-quark-mass, which allows us to extrapolate the equation of state to m_q=0
and to extract the speed of sound. We find that the equation of state depends
weakly on the quark mass for small quark mass.Comment: 24 pages, latex, 11 postscipt figure
Hadron Mass Predictions of the Valence Approximation to Lattice QCD
We evaluate the infinite volume, continuum limits of eight hadron mass ratios
predicted by lattice QCD with Wilson quarks in the valence (quenched)
approximation. Each predicted ratio differs from the corresponding observed
value by less than 6\%.Comment: 13 pages of Latex + 2 PostScript files attached, IBM/HET 92-
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