5,019 research outputs found
A numerical method for computing unsteady 2-D boundary layer flows
A numerical method for computing unsteady two-dimensional boundary layers in incompressible laminar and turbulent flows is described and applied to a single airfoil changing its incidence angle in time. The solution procedure adopts a first order panel method with a simple wake model to solve for the inviscid part of the flow, and an implicit finite difference method for the viscous part of the flow. Both procedures integrate in time in a step-by-step fashion, in the course of which each step involves the solution of the elliptic Laplace equation and the solution of the parabolic boundary layer equations. The Reynolds shear stress term of the boundary layer equations is modeled by an algebraic eddy viscosity closure. The location of transition is predicted by an empirical data correlation originating from Michel. Since transition and turbulence modeling are key factors in the prediction of viscous flows, their accuracy will be of dominant influence to the overall results
Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential
We address a two-dimensional nonlinear elliptic problem with a
finite-amplitude periodic potential. For a class of separable symmetric
potentials, we study the bifurcation of the first band gap in the spectrum of
the linear Schr\"{o}dinger operator and the relevant coupled-mode equations to
describe this bifurcation. The coupled-mode equations are derived by the
rigorous analysis based on the Fourier--Bloch decomposition and the Implicit
Function Theorem in the space of bounded continuous functions vanishing at
infinity. Persistence of reversible localized solutions, called gap solitons,
beyond the coupled-mode equations is proved under a non-degeneracy assumption
on the kernel of the linearization operator. Various branches of reversible
localized solutions are classified numerically in the framework of the
coupled-mode equations and convergence of the approximation error is verified.
Error estimates on the time-dependent solutions of the Gross--Pitaevskii
equation and the coupled-mode equations are obtained for a finite-time
interval.Comment: 32 pages, 16 figure
Periodic Travelling Waves in Dimer Granular Chains
We study bifurcations of periodic travelling waves in granular dimer chains
from the anti-continuum limit, when the mass ratio between the light and heavy
beads is zero. We show that every limiting periodic wave is uniquely continued
with respect to the mass ratio parameter and the periodic waves with the
wavelength larger than a certain critical value are spectrally stable.
Numerical computations are developed to study how this solution family is
continued to the limit of equal mass ratio between the beads, where periodic
travelling waves of granular monomer chains exist
Synchronization of Nonlinear Circuits in Dynamic Electrical Networks with General Topologies
Sufficient conditions are derived for global asymptotic synchronization in a
system of identical nonlinear electrical circuits coupled through linear
time-invariant (LTI) electrical networks. In particular, the conditions we
derive apply to settings where: i) the nonlinear circuits are composed of a
parallel combination of passive LTI circuit elements and a nonlinear
voltage-dependent current source with finite gain; and ii) a collection of
these circuits are coupled through either uniform or homogeneous LTI electrical
networks. Uniform electrical networks have identical per-unit-length
impedances. Homogeneous electrical networks are characterized by having the
same effective impedance between any two terminals with the others open
circuited. Synchronization in these networks is guaranteed by ensuring the
stability of an equivalent coordinate-transformed differential system that
emphasizes signal differences. The applicability of the synchronization
conditions to this broad class of networks follows from leveraging recent
results on structural and spectral properties of Kron reduction---a
model-reduction procedure that isolates the interactions of the nonlinear
circuits in the network. The validity of the analytical results is demonstrated
with simulations in networks of coupled Chua's circuits
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