2,264 research outputs found
An approximate solution of the MHD Falkner-Skan flow by Hermite functions pseudospectral method
Based on a new approximation method, namely pseudospectral method, a solution
for the three order nonlinear ordinary differential laminar boundary layer
Falkner-Skan equation has been obtained on the semi-infinite domain. The
proposed approach is equipped by the orthogonal Hermite functions that have
perfect properties to achieve this goal. This method solves the problem on the
semi-infinite domain without truncating it to a finite domain and transforming
domain of the problem to a finite domain. In addition, this method reduces
solution of the problem to solution of a system of algebraic equations. We also
present the comparison of this work with numerical results and show that the
present method is applicable.Comment: 15 pages, 4 figures; Published online in the journal of
"Communications in Nonlinear Science and Numerical Simulation
Characterization of the microstructure transition during the solidification of metal alloys under the influence of external forces
An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method
In this paper we propose a collocation method for solving some well-known
classes of Lane-Emden type equations which are nonlinear ordinary differential
equations on the semi-infinite domain. They are categorized as singular initial
value problems. The proposed approach is based on a Hermite function
collocation (HFC) method. To illustrate the reliability of the method, some
special cases of the equations are solved as test examples. The new method
reduces the solution of a problem to the solution of a system of algebraic
equations. Hermite functions have prefect properties that make them useful to
achieve this goal. We compare the present work with some well-known results and
show that the new method is efficient and applicable.Comment: 34 pages, 13 figures, Published in "Computer Physics Communications
Centrifugal compressor return channel shape optimization using adjoint method
Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 59-60).This thesis describes the construction of an automated gradient-based optimization process using the adjoint method and its application to centrifugal compressor return channel loss reduction. A proper objective function definition and a generalized geometry parametrization and manipulation algorithm were developed, and the appropriate adjoint equations and boundary conditions were derived for internal flow of an axisymmetric incompressible laminar flow. The adjoint-based gradient calculation was then validated against finite-difference calculations and embedded in a quasi- Newton optimization algorithm. An optimal design was proposed, which achieved an approximately 5% performance improvement compared to the baseline design in an incompressible laminar flow. The geometry was assessed in a compressible turbulent flow at the actual Mach number and Reynolds number and found to yield a 11% performance improvement for an axisymmetric channel with a previously optimized geometry.by Wei Guo.S.M
Growth factor in f(T) gravity
We derive the evolution equation of growth factor for the matter over-dense
perturbation in gravity. For instance, we investigate its behavior in
power law model at small redshift and compare it to the prediction of
CDM and dark energy with the same equation of state in the framework
of Einstein general relativity. We find that the perturbation in gravity
grows slower than that in Einstein general relativity if \p f/\p T>0 due to
the effectively weakened gravity.Comment: 15 pages,1 figure; v2,typos corrected; v3, discussions added,
accepted by JCA
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