9,362 research outputs found
Phase-field modeling of microstructural pattern formation during directional solidification of peritectic alloys without morphological instability
During the directional solidification of peritectic alloys, two stable solid
phases (parent and peritectic) grow competitively into a metastable liquid
phase of larger impurity content than either solid phase. When the parent or
both solid phases are morphologically unstable, i.e., for a small temperature
gradient/growth rate ratio (), one solid phase usually outgrows and
covers the other phase, leading to a cellular-dendritic array structure closely
analogous to the one formed during monophase solidification of a dilute binary
alloy. In contrast, when is large enough for both phases to be
morphologically stable, the formation of the microstructurebecomes controlled
by a subtle interplay between the nucleation and growth of the two solid
phases. The structures that have been observed in this regime (in small samples
where convection effect are suppressed) include alternate layers (bands) of the
parent and peritectic phases perpendicular to the growth direction, which are
formed by alternate nucleation and lateral spreading of one phase onto the
other as proposed in a recent model [R. Trivedi, Metall. Mater. Trans. A 26, 1
(1995)], as well as partially filled bands (islands), where the peritectic
phase does not fully cover the parent phase which grows continuously. We
develop a phase-field model of peritectic solidification that incorporates
nucleation processes in order to explore the formation of these structures.
Simulations of this model shed light on the morphology transition from islands
to bands, the dynamics of spreading of the peritectic phase on the parent phase
following nucleation, which turns out to be characterized by a remarkably
constant acceleration, and the types of growth morphology that one might expect
to observe in large samples under purely diffusive growth conditions.Comment: Final version, minor revisions, 16 pages, 14 EPS figures, RevTe
Analysis of A Splitting Approach for the Parallel Solution of Linear Systems on GPU Cards
We discuss an approach for solving sparse or dense banded linear systems
on a Graphics Processing Unit (GPU) card. The
matrix is possibly nonsymmetric and
moderately large; i.e., . The ${\it split\ and\
parallelize}{\tt SaP}{\bf A}{\bf A}_ii=1,\ldots,P{\bf A}_i{\tt SaP::GPU}{\tt PARDISO}{\tt SuperLU}{\tt MUMPS}{\tt SaP::GPU}{\tt MKL}{\tt SaP::GPU}{\tt SaP::GPU}$ is publicly available and distributed as
open source under a permissive BSD3 license.Comment: 38 page
On the transition to turbulence of wall-bounded flows in general, and plane Couette flow in particular
The main part of this contribution to the special issue of EJM-B/Fluids
dedicated to Patrick Huerre outlines the problem of the subcritical transition
to turbulence in wall-bounded flows in its historical perspective with emphasis
on plane Couette flow, the flow generated between counter-translating parallel
planes. Subcritical here means discontinuous and direct, with strong
hysteresis. This is due to the existence of nontrivial flow regimes between the
global stability threshold Re_g, the upper bound for unconditional return to
the base flow, and the linear instability threshold Re_c characterized by
unconditional departure from the base flow. The transitional range around Re_g
is first discussed from an empirical viewpoint ({\S}1). The recent
determination of Re_g for pipe flow by Avila et al. (2011) is recalled. Plane
Couette flow is next examined. In laboratory conditions, its transitional range
displays an oblique pattern made of alternately laminar and turbulent bands, up
to a third threshold Re_t beyond which turbulence is uniform. Our current
theoretical understanding of the problem is next reviewed ({\S}2): linear
theory and non-normal amplification of perturbations; nonlinear approaches and
dynamical systems, basin boundaries and chaotic transients in minimal flow
units; spatiotemporal chaos in extended systems and the use of concepts from
statistical physics, spatiotemporal intermittency and directed percolation,
large deviations and extreme values. Two appendices present some recent
personal results obtained in plane Couette flow about patterning from numerical
simulations and modeling attempts.Comment: 35 pages, 7 figures, to appear in Eur. J. Mech B/Fluid
Linearly scaling direct method for accurately inverting sparse banded matrices
In many problems in Computational Physics and Chemistry, one finds a special
kind of sparse matrices, termed "banded matrices". These matrices, which are
defined as having non-zero entries only within a given distance from the main
diagonal, need often to be inverted in order to solve the associated linear
system of equations. In this work, we introduce a new O(n) algorithm for
solving such a system, being n X n the size of the matrix. We produce the
analytical recursive expressions that allow to directly obtain the solution, as
well as the pseudocode for its computer implementation. Moreover, we review the
different options for possibly parallelizing the method, we describe the
extension to deal with matrices that are banded plus a small number of non-zero
entries outside the band, and we use the same ideas to produce a method for
obtaining the full inverse matrix. Finally, we show that the New Algorithm is
competitive, both in accuracy and in numerical efficiency, when compared to a
standard method based in Gaussian elimination. We do this using sets of large
random banded matrices, as well as the ones that appear when one tries to solve
the 1D Poisson equation by finite differences.Comment: 24 pages, 5 figures, submitted to J. Comp. Phy
Phase Coexistence of Complex Fluids in Shear Flow
We present some results of recent calculations of rigid rod-like particles in
shear flow, based on the Doi model. This is an ideal model system for
exhibiting the generic behavior of shear-thinning fluids (polymer solutions,
wormlike micelles, surfactant solutions, liquid crystals) in shear flow. We
present calculations of phase coexistence under shear among weakly-aligned
(paranematic) and strongly-aligned phases, including alignment in the shear
plane and in the vorticity direction (log-rolling). Phase coexistence is
possible, in principle, under conditions of both common shear stress and common
strain rate, corresponding to different orientations of the interface between
phases. We discuss arguments for resolving this degeneracy. Calculation of
phase coexistence relies on the presence of inhomogeneous terms in the
dynamical equations of motion, which select the appropriate pair of coexisting
states. We cast this condition in terms of an equivalent dynamical system, and
explore some aspects of how this differs from equilibrium phase coexistence.Comment: 16 pages, 10 figures, submitted to Faraday Discussion
Describing the Flow Curve of Shear-Banding Fluids Through a Structural Minimal Model
Main characteristics of colloidal systems that develop fluid phases with
different mechanical properties, namely shear-banding fluids, are briefly
reviewed both from experimental and theoretical (modelling) point of view. A
non-monotonic shear stress vs. shear rate constitutive relation is presented.
This relation derives from a phenomenological model of a shear ratedependent
viscosity describing structural changes and involves the possibility of
multivalued shear rates under a given shear stress. In the case of a
stress-dependent viscosity, the same model allows one to predict vorticity
banding. Predictions of this model under controlled stress are discussed,
namely occurrence of a kind of top- and bottom-jumping of the shear rate in
response to stress increasing-decreasing. Applying this model to evaluation of
the flow curve of such colloidal systems is performed. Particular emphasis is
placed on the adequate computation of the shear rate function in cylindrical
Couette cells in order to handle the corresponding flow curve which exhibits
the well-known shear stress plateau. Indeed, as different fluid phases coexist
in the flow domain, measured (torque vs. angular velocity) data cannot be
directly converted into rheometric (shear stress vs. shear rate) functions. As
the lacking non-local terms in the model prevents the direct determination of
the stress-plateau, this value is included as an adjustable parameter. Thus
model predictions satisfactorily match up experimental data of wormlike
micellar solutions from the literature.Comment: 22 pages, 9 fi
Phase Separation of Rigid-Rod Suspensions in Shear Flow
We analyze the behavior of a suspension of rigid rod-like particles in shear
flow using a modified version of the Doi model, and construct diagrams for
phase coexistence under conditions of constant imposed stress and constant
imposed strain rate, among paranematic, flow-aligning nematic, and log-rolling
nematic states. We calculate the effective constitutive relations that would be
measured through the regime of phase separation into shear bands. We calculate
phase coexistence by examining the stability of interfacial steady states and
find a wide range of possible ``phase'' behaviors.Comment: 23 pages 19 figures, revised version to be published in Physical
Review
A bibliography on parallel and vector numerical algorithms
This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also
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