7,590 research outputs found
Kinematic dynamo action in a sphere. I. Effects of differential rotation and meridional circulation on solutions with axial dipole symmetry
A sphere containing electrically conducting fluid can generate a magnetic field by dynamo action, provided the flow is sufficiently complicated and vigorous. The dynamo mechanism is thought to sustain magnetic fields in planets and stars. The kinematic dynamo problem tests steady flows for magnetic instability, but rather few dynamos have been found so far because of severe numerical difficulties. Dynamo action might, therefore, be quite unusual, at least for large-scale steady flows. We address this question by testing a two-parameter class of flows for dynamo generation of magnetic fields containing an axial dipole. The class of flows includes two completely different types of known dynamos, one dominated by differential rotation (D) and one with none. We find that 36% of the flows in seven distinct zones in parameter space act as dynamos, while the remaining 64% either fail to generate this type of magnetic field or generate fields that are too small in scale to be resolved by our numerical method. The two previously known dynamo types lie in the same zone, and it is therefore possible to change the flow continuously from one to the other without losing dynamo action. Differential rotation is found to promote large-scale axisymmetric toroidal magnetic fields, while meridional circulation (M) promotes large-scale axisymmetric poloidal fields concentrated at high latitudes near the axis. Magnetic fields resembling that of the Earth are generated by D > 0, corresponding to westward flow at the surface, and M of either sign but not zero. Very few oscillatory solutions are found
Optimal design of chemoepitaxial guideposts for directed self-assembly of block copolymer systems using an inexact-Newton algorithm
Directed self-assembly (DSA) of block-copolymers (BCPs) is one of the most
promising developments in the cost-effective production of nanoscale devices.
The process makes use of the natural tendency for BCP mixtures to form
nanoscale structures upon phase separation. The phase separation can be
directed through the use of chemically patterned substrates to promote the
formation of morphologies that are essential to the production of semiconductor
devices. Moreover, the design of substrate pattern can formulated as an
optimization problem for which we seek optimal substrate designs that
effectively produce given target morphologies.
In this paper, we adopt a phase field model given by a nonlocal
Cahn--Hilliard partial differential equation (PDE) based on the minimization of
the Ohta--Kawasaki free energy, and present an efficient PDE-constrained
optimization framework for the optimal design problem. The design variables are
the locations of circular- or strip-shaped guiding posts that are used to model
the substrate chemical pattern. To solve the ensuing optimization problem, we
propose a variant of an inexact Newton conjugate gradient algorithm tailored to
this problem. We demonstrate the effectiveness of our computational strategy on
numerical examples that span a range of target morphologies. Owing to our
second-order optimizer and fast state solver, the numerical results demonstrate
five orders of magnitude reduction in computational cost over previous work.
The efficiency of our framework and the fast convergence of our optimization
algorithm enable us to rapidly solve the optimal design problem in not only
two, but also three spatial dimensions.Comment: 35 Pages, 17 Figure
Packing ellipsoids with overlap
The problem of packing ellipsoids of different sizes and shapes into an
ellipsoidal container so as to minimize a measure of overlap between ellipsoids
is considered. A bilevel optimization formulation is given, together with an
algorithm for the general case and a simpler algorithm for the special case in
which all ellipsoids are in fact spheres. Convergence results are proved and
computational experience is described and illustrated. The motivating
application - chromosome organization in the human cell nucleus - is discussed
briefly, and some illustrative results are presented
- …