Quantifying Dimensional Accuracy of a Mask Projection Micro Stereolithography System

Mask Projection Microstereolithography is capable for fabricating true three-dimensional microparts and hence, holds promise as a potential micro-fabrication process for micro-machine components. In this paper, the Mask Projection Micro-Stereolithography (MPµSLA) system developed at the Rapid Prototyping and Manufacturing Institute at Georgia Institute of Technology is presented. The dimensional accuracy of the system is improved by reducing its process planning errors. To this effect, the MPµSLA process is mathematically modeled. In this paper, the irradiance received by the resin surface is modeled as a function of the imaging system parameters and the pattern displayed on the dynamic mask. The resin used in the system is characterized to experimentally determine its working curve. This work enables us to compute the dimensions of a single layer cured using our system. The analytical model is validated by curing test layers on the system. The model computes layer dimensions within 5% error.Mechanical Engineerin

Jupiter: New estimates of mean zonal flow at the cloud level

In order to reexamine the magnitude differences of the Jovian atmosphere's jets, as determined by Voyager 1 and 2 images, a novel approach is used to ascertain the zonal mean east-west component of motion. This technique is based on digital pattern matching, and is applied on pairs of mapped images to yield a profile of the mean zonal component that reproduces the exact locations of the easterly and westerly jets between + and 60 deg latitude. Results were obtained for all of the Voyager 1 and 2 cylindrical mosaics; the correlation coefficient between Voyagers 1 and 2 in mean zonal flow between + and - 60 deg latitude, determined from violet filter mosaics, is 0.998

Compensation Zone Approach to Avoid Z Errors in Mask Projection Stereolithography Builds

Print-through results in unwanted polymerization occurring beneath a part cured using Mask Projection Stereolithography (MPSLA) and thus creates error in its Z dimension. In this paper, the "Compensation zone approach" is proposed to avoid this error. This approach entails modifying the geometry of the part to be cured. A volume (Compensation zone) is subtracted from underneath the CAD model in order to compensate for the increase in the Z dimension that would occur due to Print-through. Three process variables have been identified: Thickness of Compensation zone, Thickness of every layer and Exposure distribution across every image used to cure a layer. Analytical relations have been formulated between these process variables in order to obtain dimensionally accurate parts. The Compensation zone approach is demonstrated on an example problem.Mechanical Engineerin

Optimal Embedding of Functions for In-Network Computation: Complexity Analysis and Algorithms

We consider optimal distributed computation of a given function of distributed data. The input (data) nodes and the sink node that receives the function form a connected network that is described by an undirected weighted network graph. The algorithm to compute the given function is described by a weighted directed acyclic graph and is called the computation graph. An embedding defines the computation communication sequence that obtains the function at the sink. Two kinds of optimal embeddings are sought, the embedding that---(1)~minimizes delay in obtaining function at sink, and (2)~minimizes cost of one instance of computation of function. This abstraction is motivated by three applications---in-network computation over sensor networks, operator placement in distributed databases, and module placement in distributed computing. We first show that obtaining minimum-delay and minimum-cost embeddings are both NP-complete problems and that cost minimization is actually MAX SNP-hard. Next, we consider specific forms of the computation graph for which polynomial time solutions are possible. When the computation graph is a tree, a polynomial time algorithm to obtain the minimum delay embedding is described. Next, for the case when the function is described by a layered graph we describe an algorithm that obtains the minimum cost embedding in polynomial time. This algorithm can also be used to obtain an approximation for delay minimization. We then consider bounded treewidth computation graphs and give an algorithm to obtain the minimum cost embedding in polynomial time

Streaming algorithms for language recognition problems

We study the complexity of the following problems in the streaming model. Membership testing for \DLIN We show that every language in \DLIN\ can be recognised by a randomized one-pass $O(\log n)$ space algorithm with inverse polynomial one-sided error, and by a deterministic p-pass $O(n/p)$ space algorithm. We show that these algorithms are optimal. Membership testing for \LL$(k)$ For languages generated by \LL$(k)$ grammars with a bound of $r$ on the number of nonterminals at any stage in the left-most derivation, we show that membership can be tested by a randomized one-pass $O(r\log n)$ space algorithm with inverse polynomial (in $n$) one-sided error. Membership testing for \DCFL We show that randomized algorithms as efficient as the ones described above for \DLIN\ and \LL(k) (which are subclasses of \DCFL) cannot exist for all of \DCFL: there is a language in \VPL\ (a subclass of \DCFL) for which any randomized p-pass algorithm with error bounded by $\epsilon < 1/2$ must use $\Omega(n/p)$ space. Degree sequence problem We study the problem of determining, given a sequence $d_1, d_2,..., d_n$ and a graph $G$, whether the degree sequence of $G$ is precisely $d_1, d_2,..., d_n$. We give a randomized one-pass $O(\log n)$ space algorithm with inverse polynomial one-sided error probability. We show that our algorithms are optimal. Our randomized algorithms are based on the recent work of Magniez et al. \cite{MMN09}; our lower bounds are obtained by considering related communication complexity problems