94,020 research outputs found
Lattice-Boltzmann Method for Non-Newtonian Fluid Flows
We study an ad hoc extension of the Lattice-Boltzmann method that allows the
simulation of non-Newtonian fluids described by generalized Newtonian models.
We extensively test the accuracy of the method for the case of shear-thinning
and shear-thickening truncated power-law fluids in the parallel plate geometry,
and show that the relative error compared to analytical solutions decays
approximately linear with the lattice resolution. Finally, we also tested the
method in the reentrant-flow geometry, in which the shear-rate is no-longer a
scalar and the presence of two singular points requires high accuracy in order
to obtain satisfactory resolution in the local stress near these points. In
this geometry, we also found excellent agreement with the solutions obtained by
standard finite-element methods, and the agreement improves with higher lattice
resolution
Folding transitions of the triangular lattice with defects
A recently introduced model describing the folding of the triangular lattice
is generalized allowing for defects in the lattice and written as an Ising
model with nearest-neighbor and plaquette interactions on the honeycomb
lattice. Its phase diagram is determined in the hexagon approximation of the
cluster variation method and the crossover from the pure Ising to the pure
folding model is investigated, obtaining a quite rich structure with several
multicritical points. Our results are in very good agreement with the available
exact ones and extend a previous transfer matrix study.Comment: 16 pages, latex, 5 postscript figure
Gravitational and higher-order form factors of the pion in chiral quark models
The gravitational form factor of the pion is evaluated in two chiral quark
models and confronted to the recent full-QCD lattice data. We find good
agreement for the case of the Spectral Quark Model, which builds in the
vector-meson dominance for the charge form factor. We derive a simple relation
between the gravitational and electromagnetic form factors, holding in the
considered quark models in the chiral limit. The relation implies that the
gravitational mean squared radius is half the electromagnetic one. We also
analyze higher-order quark generalized form factors of the pion, related to
higher moments in the symmetric Bjorken X-variable of the generalized parton
distribution functions, and discuss their perturbative QCD evolution, needed to
relate the quark-model predictions to the lattice data. The values of the
higher-order quark form factors at t=0, computed on the lattice, also agree
with our quark model results within the statistical and method uncertainties.Comment: 12 pages, 4 figures, discussion and references adde
Generalized vector form factors of the pion in a chiral quark model
Generalized vector form factors of the pion, related to the moments of the
generalized parton distribution functions, are evaluated in the
Nambu--Jona-Lasinio model with the Pauli-Villars regularization. The lowest
moments (the electromagnetic and the gravitational form factors) are compared
to recent lattice data, with fair agreement. Predictions for higher-order
moments are also made. Relevant features of the generalized form factors in the
chiral quark models are highlighted and the role of the QCD evolution for the
higher-order GFFs is stressed.Comment: Dedicated to the memory of Manoj K. Banerjee, to appear in a special
issue of the Indian Journal of Physics, 6 pages, 4 figure
First principle electronic, structural, elastic, and optical properties of strontium titanate
We report self-consistent ab-initio electronic, structural, elastic, and
optical properties of cubic SrTiO perovskite. Our non-relativistic
calculations employed a generalized gradient approximation (GGA) potential and
the linear combination of atomic orbitals (LCAO) formalism. The distinctive
feature of our computations stem from solving self-consistently the system of
equations describing the GGA, using the Bagayoko-Zhao-Williams (BZW) method.
Our results are in agreement with experimental ones where the later are
available. In particular, our theoretical, indirect band gap of 3.24 eV, at the
experimental lattice constant of 3.91 \AA{}, is in excellent agreement with
experiment. Our predicted, equilibrium lattice constant is 3.92 \AA{}, with a
corresponding indirect band gap of 3.21 eV and bulk modulus of 183 GPa.Comment: 11 pages, 6 figures,Accepted for publication in AIP Advances (2012
Lattice Agreement in Message Passing Systems
This paper studies the lattice agreement problem and the generalized lattice agreement problem in distributed message passing systems. In the lattice agreement problem, given input values from a lattice, processes have to non-trivially decide output values that lie on a chain. We consider the lattice agreement problem in both synchronous and asynchronous systems. For synchronous lattice agreement, we present two algorithms which run in log(f) and min{O(log^2 h(L)), O(log^2 f)} rounds, respectively, where h(L) denotes the height of the input sublattice L, f < n is the number of crash failures the system can tolerate, and n is the number of processes in the system. These algorithms have significant better round complexity than previously known algorithms. The algorithm by Attiya et al. [Attiya et al. DISC, 1995] takes log(n) synchronous rounds, and the algorithm by Mavronicolasa [Mavronicolasa, 2018] takes min{O(h(L)), O(sqrt(f))} rounds. For asynchronous lattice agreement, we propose an algorithm which has time complexity of 2*min{h(L), f + 1} message delays which improves on the previously known time complexity of O(n) message delays.
The generalized lattice agreement problem defined by Faleiro et al in [Faleiro et al. PODC, 2012] is a generalization of the lattice agreement problem where it is applied for the replicated state machine. We propose an algorithm which guarantees liveness when a majority of the processes are correct in asynchronous systems. Our algorithm requires min{O(h(L)), O(f)} units of time in the worst case which is better than O(n) units of time required by the algorithm in [Faleiro et al. PODC, 2012]
Channel Flow of a Tensorial Shear-Thinning Maxwell Model: Lattice Boltzmann Simulations
We introduce a nonlinear generalized tensorial Maxwell-type constitutive
equation to describe shear-thinning glass-forming fluids, motivated by a recent
microscopic approach to the nonlinear rheology of colloidal suspensions. The
model captures a nonvanishing dynamical yield stress at the glass transition
and incorporates normal-stress differences. A modified lattice-Boltzmann (LB)
simulation scheme is presented that includes non-Newtonian contributions to the
stress tensor and deals with flow-induced pressure differences. We test this
scheme in pressure-driven 2D Poiseuille flow of the nonlinear generalized
Maxwell fluid. In the steady state, comparison with an analytical solution
shows good agreement. The transient dynamics after startup and cessation of the
pressure gradient are studied; the simulation reproduces a finite stopping time
for the cessation flow of the yield-stress fluid in agreement with previous
analytical estimates
Re-examining the electronic structure of germanium: A first-principle study
We report results from an efficient, robust, ab-initio method for
self-consistent calculations of electronic and structural properties of Ge. Our
non-relativistic calculations employed a generalized gradient approximation
(GGA) potential and the linear combination of atomic orbitals (LCAO) formalism.
The distinctive feature of our computations stem from the use of
Bagayoko-Zhao-Williams-Ekuma-Franklin (BZW-EF) method. Our results are in
agreement with experimental ones where the latter are available. In particular,
our theoretical, indirect band gap of 0.65 eV, at the experimental lattice
constant of 5.66 \AA{}, is in excellent agreement with experiment. Our
predicted, equilibrium lattice constant is 5.63 \AA{}, with a corresponding
indirect band gap of 0.65 eV and a bulk modulus of 80 GPa. We also calculated
the effective masses in various directions with respect to the point.Comment: 10 Pages, 3 Figures, and 1 tabl
Effects of site dilution on the magnetic properties of geometrically frustrated antiferromagnets
The effect of site dilution by non magnetic impurities on the susceptibility
of geometrically frustrated antiferromagnets (kagome and pyrochlore lattices)
is discussed in the framework of the Generalized Constant Coupling model, for
both classical and quantum Heisenberg spins. For the classical diluted
pyrochlore lattice, excellent agreement is found when compared with Monte Carlo
data. Results for the quantum case are also presented and discussed.Comment: 5 pages, 3 figure
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