2,559 research outputs found
Shape optimization of pressurized air bearings
Use of externally pressurized air bearings allows for the design of mechanical systems requiring extreme precision in positioning. One application is the fine control for the positioning of mirrors in large-scale optical telescopes. Other examples come from applications in robotics and computer hard-drive manufacturing. Pressurized bearings maintain a finite separation between mechanical components by virtue of the presence of a pressurized flow of air through the gap between the components. An everyday example is an air hockey table, where a puck is levitated above the table by an array of vertical jets of air. Using pressurized bearings there is no contact between âmoving partsâ and hence there is no friction and no wear of sensitive components.
This workshop project is focused on the problem of designing optimal static air bearings subject to given engineering constraints. Recent numerical computations of this problem, done at IBM by Robert and Hendriks, suggest that near-optimal designs can have unexpected complicated and intricate structures. We will use analytical approaches to shed some light on this situation and to offer some guides for the design process.
In Section 2 the design problem is stated and formulated as an optimization problem for an elliptic boundary value problem.
In Section 3 the general problem is specialized to bearings with rectangular bases.
Section 4 addresses the solutions of this problem that can be obtained using variational formulations of the problem.
Analysis showing the sensitive dependence to perturbations (in numerical computations or manufacturing constraints) of near-optimal designs is given in Section 5.
In Section 6, a restricted class of âgroove networkâ designs motivated by the original results of Robert and Hendriks is examined.
Finally, in Section 7, we consider the design problem for circular axisymmetric air bearings
Linked Gaussian Process Emulation for Systems of Computer Models Using Matérn Kernels and Adaptive Design
The state-of-the-art linked Gaussian process offers a way to build analytical
emulators for systems of computer models. We generalize the closed form
expressions for the linked Gaussian process under the squared exponential
kernel to a class of Mat\'ern kernels, that are essential in advanced
applications. An iterative procedure to construct linked Gaussian processes as
surrogate models for any feed-forward systems of computer models is presented
and illustrated on a feed-back coupled satellite system. We also introduce an
adaptive design algorithm that could increase the approximation accuracy of
linked Gaussian process surrogates with reduced computational costs on running
expensive computer systems, by allocating runs and refining emulators of
individual sub-models based on their heterogeneous functional complexity
Some results on partial difference sets and partial geometries
This thesis shows results on 3 different problems involving partial difference sets (PDS) in abelian groups, and uses PDS to study partial geometries with an abelian Singer group. First, the last two undetermined cases of PDS on abelian groups with k †100, both of order 216, were shown not to exist. Second, new parameter bounds for k and â were found for PDS on abelian groups of order p^n , p an odd prime, n odd. A parameter search on p^5 in particular was conducted, and only 5 possible such cases remain for p \u3c 250. Lastly, the existence of rigid type partial geometries with an abelian Singer group are examined; existence is left undetermined for 11 cases with α †200. This final study led to the determination of nonexistence for an infinite class of cases which impose a negative Latin type PDS
A graph partition problem
Given a graph on vertices, for which is it possible to partition
the edge set of the -fold complete graph into copies of ? We show
that there is an integer , which we call the \emph{partition modulus of
}, such that the set of values of for which such a partition
exists consists of all but finitely many multiples of . Trivial
divisibility conditions derived from give an integer which divides
; we call the quotient the \emph{partition index of }. It
seems that most graphs have partition index equal to , but we give two
infinite families of graphs for which this is not true. We also compute
for various graphs, and outline some connections between our problem and the
existence of designs of various types
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