5,118 research outputs found
An onboard deorbit target line computation technique
The design concept and results of a target line generator software package, which was developed to provide the onboard entry interface range, were documented. This generator, which was eventually reduced to one linear equation, was developed to the point that it provides autonomous landing site relocation capability, negligible core storage, and acceptable performance for the cases tested
Function spaces for liquid crystals
We consider the relationship between three continuum liquid crystal theories:
Oseen-Frank, Ericksen and Landau-de Gennes. It is known that the function space
is an important part of the mathematical model and by considering various
function space choices for the order parameters , , and ,
we establish connections between the variational formulations of these
theories. We use these results to derive a version of the Oseen-Frank theory
using special functions of bounded variation. This proposed model can describe
both orientable and non-orientable defects. Finally we study a number of
frustrated nematic and cholesteric liquid crystal systems and show that the
model predicts the existence of point and surface discontinuities in the
director
Analysis of local minima for constrained minimization problems
We consider vectorial problems in the calculus of variations with an
additional pointwise constraint. Our admissible mappings satisfy , where
is a manifold embedded in Euclidean space. The main results of the paper all
formulate necessary or sufficient conditions for a given mapping to
be a weak or strong local minimizer. Our methods involve using projection
mappings in order to build on existing, unconstrained, local minimizer results.
We apply our results to a liquid crystal variational problem to quantify the
stability of the unwound cholesteric state under frustrated boundary
conditions
A Topological Separation Condition for Fractal Attractors
We consider finite systems of contractive homeomorphisms of a complete metric
space, which are non-redundant on every level. In general this separation
condition is weaker than the strong open set condition and is not equivalent to
the weak separation property. We prove that this separation condition is
equivalent to the strong Markov property (see definition below). We also show
that the set of -tuples of contractive homeomorphisms, which are
non-redundant on every level, is a set in the topology of pointwise
convergence of every component mapping with an additional requirement that the
supremum of contraction coefficients of mappings be strictly less than one. We
give several sufficient conditions for this separation property. For every
fixed -tuple of invertible contraction matrices from a certain
class, we obtain density results for -tuples of fixed points which define
-tuples of mappings non-redundant on every level.Comment: 19 page
Distribution of periodic points of polynomial diffeomorphisms of C^2
This paper deals with the dynamics of a simple family of holomorphic
diffeomorphisms of \C^2: the polynomial automorphisms. This family of maps
has been studied by a number of authors. We refer to [BLS] for a general
introduction to this class of dynamical systems. An interesting object from the
point of view of potential theory is the equilibrium measure of the set
of points with bounded orbits. In [BLS] is also characterized
dynamically as the unique measure of maximal entropy. Thus is also an
equilibrium measure from the point of view of the thermodynamical formalism. In
the present paper we give another dynamical interpretation of as the
limit distribution of the periodic points of
Wermer examples and currents
In this paper we give the first examples of positive closed currents in
with continuous potentials, vanishing self-intersection, and
which are not laminar. More precisely, they are supported on sets "without
analytic structure". The result is mostly interesting when the potential has
regularity close to , because laminarity is expected to hold in that case.
We actually construct examples which are for all .Comment: Minor modifications. Final version, to appear in GAF
Alien Registration- Bedford, Mildred J. (Bar Harbor, Hancock County)
https://digitalmaine.com/alien_docs/19929/thumbnail.jp
Matrix Big Brunch
Following the holographic description of linear dilaton null Cosmologies with
a Big Bang in terms of Matrix String Theory put forward by Craps, Sethi and
Verlinde, we propose an extended background describing a Universe including
both Big Bang and Big Crunch singularities. This belongs to a class of exact
string backgrounds and is perturbative in the string coupling far away from the
singularities, both of which can be resolved using Matrix String Theory. We
provide a simple theory capable of describing the complete evolution of this
closed Universe.Comment: 15 pages, no figures. References adde
Global minimisers of cholesteric liquid crystal systems
In this paper we examine the modelling and minimisation of cholesteric liquid
crystals systems within the Oseen-Frank theory. We focus on a cuboid domain
with the frustrated boundary conditions and . With general elastic constants, we find the unique global
minimisers amongst functions of one variable and prove that these are global
minimisers of the entire problem if the cholesteric pitch is sufficiently long.
Finally we show that our analysis easily translates over the study the global
stability of the constant state with unfrustrated
boundary conditions.Comment: Version 2: Acknowledgements added and some small English errors
correcte
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