61 research outputs found
Diffusion coefficients and constraints on hadronic inhomogeneities in the early universe
Hadronic inhomogeneities are formed after the quark hadron phase transition.
The nature of the phase transition dictates the nature of the inhomogeneities
formed. Recently some scenarios of inhomogeneities have been discussed where
the strange quarks are in excess over the up and down quarks. The hadronization
of these quarks will give rise to a large density of hyperons and kaons in
addition to the protons and neutrons which are formed after the phase
transition. These unstable hyperons decay into pions, muons and their
respective neutrinos. Hence the plasma during this period consists of neutrons,
protons, electrons, muons and neutrinos. Due to the decay of the hyperons, the
muon component of the inhomogeneities will be very high. We study the diffusion
of neutrons and protons in the presence of a large number of muons immediately
after the quark hadron phase transition. We find that the presence of the muons
enhances the diffusion coefficient of the neutrons/protons. As the diffusion
coefficient is enhanced, the inhomogeneities will decay faster in the regions
where the muon density is higher. Hence smaller muon rich inhomogeneities will
be completely wiped out. The decay of the hyperons will also generate muon
neutrinos. Since the big bang nucleosynthesis provides constraints on the
neutrino degeneracies, we revisit the effect of non zero degeneracies on the
primordial elements.Comment: 20 pages 7 figures Revised version accepted for publication in
European Journal of Physics
Minimum-Weight Edge Discriminator in Hypergraphs
In this paper we introduce the concept of minimum-weight edge-discriminators
in hypergraphs, and study its various properties. For a hypergraph , a function is said to be an {\it edge-discriminator} on if
, for all hyperedges , and
, for every two
distinct hyperedges . An {\it optimal
edge-discriminator} on , to be denoted by , is
an edge-discriminator on satisfying , where
the minimum is taken over all edge-discriminators on . We prove
that any hypergraph , with , satisfies ,
and equality holds if and only if the elements of are mutually
disjoint. For -uniform hypergraphs , it
follows from results on Sidon sequences that , and
the bound is attained up to a constant factor by the complete -uniform
hypergraph. Next, we construct optimal edge-discriminators for some special
hypergraphs, which include paths, cycles, and complete -partite hypergraphs.
Finally, we show that no optimal edge-discriminator on any hypergraph , with , satisfies
, which, in turn,
raises many other interesting combinatorial questions.Comment: 22 pages, 5 figure
Quantification of uncertainty in a stereoscopic particle image velocimetry measurement
In Stereoscopic Particle Image Velocimetry (Stereo-PIV), the three velocity components are obtained by illuminating a planar region in the flow field and recording the region of interest using two cameras at an angle. Calibration, planar velocity estimation, and velocity reconstruction are the three essential steps involved in the process. Earlier efforts to quantify the accuracy in a Stereo-PIV measurement process have shown higher error in out of plane motion. However, a detailed analysis of the measurement uncertainty involved in a Stereo-PIV calibration-based reconstruction process has yet to be presented. This analysis provides a detailed framework to specify the uncertainty in the coefficients of the calibration mapping function and the uncertainty involved in self-calibration step for correction of the registration error. Using Taylor series expansion for uncertainty propagation the contribution of the calibration step uncertainties are combined with planar field uncertainties to predict the overall uncertainty in the reconstructed velocity components. The analysis is tested using simulated random field images and experimental vortex ring images. The results emphasize the sensitivity and interdependence of the individual uncertainties involved in each step of a Stereo-PIV measurement process
Volumetric Particle Tracking Velocimetry (PTV) Uncertainty Quantification
We introduce the first comprehensive approach to determine the uncertainty in
volumetric Particle Tracking Velocimetry (PTV) measurements. Volumetric PTV is
a state-of-the-art non-invasive flow measurement technique, which measures the
velocity field by recording successive snapshots of the tracer particle motion
using a multi-camera set-up. The measurement chain involves reconstructing the
three-dimensional particle positions by a triangulation process using the
calibrated camera mapping functions. The non-linear combination of the
elemental error sources during the iterative self-calibration correction and
particle reconstruction steps increases the complexity of the task. Here, we
first estimate the uncertainty in the particle image location, which we model
as a combination of the particle position estimation uncertainty and the
reprojection error uncertainty. The latter is obtained by a gaussian fit to the
histogram of disparity estimates within a sub-volume. Next, we determine the
uncertainty in the camera calibration coefficients. As a final step the
previous two uncertainties are combined using an uncertainty propagation
through the volumetric reconstruction process. The uncertainty in the velocity
vector is directly obtained as a function of the reconstructed particle
position uncertainty. The framework is tested with synthetic vortex ring
images. The results show good agreement between the predicted and the expected
RMS uncertainty values. The prediction is consistent for seeding densities
tested in the range of 0.01 to 0.1 particles per pixel. Finally, the
methodology is also successfully validated for an experimental test case of
laminar pipe flow velocity profile measurement where the predicted uncertainty
is within 17% of the RMS error value
A New Spatio-Temporal Model Exploiting Hamiltonian Equations
The solutions of Hamiltonian equations are known to describe the underlying
phase space of the mechanical system. In Bayesian Statistics, the only place,
where the properties of solutions to the Hamiltonian equations are successfully
applied, is Hamiltonian Monte Carlo. In this article, we propose a novel
spatio-temporal model using a strategic modification of the Hamiltonian
equations, incorporating appropriate stochasticity via Gaussian processes. The
resultant sptaio-temporal process, continuously varying with time, turns out to
be nonparametric, nonstationary, nonseparable and no-Gaussian. Besides, the
lagged correlations tend to zero as the spatio-temporal lag tends to infinity.
We investigate the theoretical properties of the new spatio-temporal process,
along with its continuity and smoothness properties. Considering the Bayesian
paradigm, we derive methods for complete Bayesian inference using MCMC
techniques. Applications of our new model and methods to two simulation
experiments and two real data sets revealed encouraging performance
Minimum-Weight Edge Discriminators in Hypergraphs
In this paper we introduce the notion of minimum-weight edge-discriminators in hypergraphs, and study their various properties. For a hypergraph H = (V , E), a function λ : V → Z+∪{0} is said to be an edge-discriminator on H if ∑v∈Eiλ(v)\u3e0, for all hyperedges Ei ∈ E and ∑v∈Eiλ(v) ≠ ∑v∈Ejλ(v), for every two distinct hyperedges Ei,Ej, ∈ E. An optimal edge-discriminator on H, to be denoted by λH, is an edge-discriminator on H satisfying ∑v∈VλH(v) = minλ ∑v∈Vλ(v), where the minimum is taken over all edge-discriminators on H. We prove that any hypergraph H = (V , E), with |E| = m, satisfies ∑v∈VλH(v) ≤ m(m+1)/2, and the equality holds if and only if the elements of E are mutually disjoint. For r-uniform hypergraphs H = (V,E), it follows from earlier results on Sidon sequences that ∑v∈VλH(v) ≤ |V|r+1+o(|V|r+1), and the bound is attained up to a constant factor by the complete r-uniform hypergraph. Finally, we show that no optimal edge-discriminator on any hypergraph H = (V,E), with |E| = m (≥3), satisfies ∑v∈VλH(v) = m(m+1)/2−1. This shows that all integer values between m and m(m+1)/2 cannot be the weight of an optimal edge-discriminator of a hypergraph, and this raises many other interesting combinatorial questions
Simulated Annealing Approach onto VLSI Circuit Partitioning
Decompositions of inter-connected components, to achieve modular independence, poses the major problem in VLSI circuit partitioning. This problem is intractable in nature, Solutions of these problems in computational science is possible through appropriate heuristics. Reduction of the cost that occurs due to interconnectivity between several VLSI components is referred to in this paper. Modification of results derived by classical iterative procedures with probabilistic methods is attempted. Verification has been done on ISCAS-85 benchmark circuits. The proposed design tool shows remarkable improvement results in comparison to the traditional one when applied to the standard benchmark circuits like ISCAS-85
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