Some Results on Superpatterns for Preferential Arrangements

A {\it superpattern} is a string of characters of length $n$ that contains as a subsequence, and in a sense that depends on the context, all the smaller strings of length $k$ in a certain class. We prove structural and probabilistic results on superpatterns for {\em preferential arrangements}, including (i) a theorem that demonstrates that a string is a superpattern for all preferential arrangements if and only if it is a superpattern for all permutations; and (ii) a result that is reminiscent of a still unresolved conjecture of Alon on the smallest permutation on $[n]$ that contains all $k$-permutations with high probability.Comment: 13 page

Intrinsic Reduced Attitude Formation with Ring Inter-Agent Graph

This paper investigates the reduced attitude formation control problem for a group of rigid-body agents using feedback based on relative attitude information. Under both undirected and directed cycle graph topologies, it is shown that reversing the sign of a classic consensus protocol yields asymptotical convergence to formations whose shape depends on the parity of the group size. Specifically, in the case of even parity the reduced attitudes converge asymptotically to a pair of antipodal points and distribute equidistantly on a great circle in the case of odd parity. Moreover, when the inter-agent graph is an undirected ring, the desired formation is shown to be achieved from almost all initial states

Best and worst case permutations for random online domination of the path

We study a randomized algorithm for graph domination, by which, according to a uniformly chosen permutation, vertices are revealed and added to the dominating set if not already dominated. We determine the expected size of the dominating set produced by the algorithm for the path graph $P_n$ and use this to derive the expected size for some related families of graphs. We then provide a much-refined analysis of the worst and best cases of this algorithm on $P_n$ and enumerate the permutations for which the algorithm has the worst-possible performance and best-possible performance. The case of dominating the path graph has connections to previous work of Bouwer and Star, and of Gessel on greedily coloring the path.Comment: 13 pages, 1 figur

The Total Acquisition Number of the Randomly Weighted Path

There exists a significant body of work on determining the acquisition number $a_t(G)$ of various graphs when the vertices of those graphs are each initially assigned a unit weight. We determine properties of the acquisition number of the path, star, complete, complete bipartite, cycle, and wheel graphs for variations on this initial weighting scheme, with the majority of our work focusing on the expected acquisition number of randomly weighted graphs. In particular, we bound the expected acquisition number $E(a_t(P_n))$ of the $n$-path when $n$ distinguishable "units" of integral weight, or chips, are randomly distributed across its vertices between $0.242n$ and $0.375n$. With computer support, we improve it by showing that $E(a_t(P_n))$ lies between $0.29523n$ and $0.29576n$. We then use subadditivity to show that the limiting ratio $\lim E(a_t(P_n))/n$ exists, and simulations reveal more exactly what the limiting value equals. The Hoeffding-Azuma inequality is used to prove that the acquisition number is tightly concentrated around its expected value. Additionally, in a different context, we offer a non-optimal acquisition protocol algorithm for the randomly weighted path and exactly compute the expected size of the resultant residual set.Comment: 19 page

The Number of Seymour Vertices in Random Tournaments and Digraphs

Seymour's distance two conjecture states that in any digraph there exists a vertex (a "Seymour vertex") that has at least as many neighbors at distance two as it does at distance one. We explore the validity of probabilistic statements along lines suggested by Seymour's conjecture, proving that almost surely there are a "large" number of Seymour vertices in random tournaments and "even more" in general random digraphs.Comment: 14 page

Heat transfer characteristic analysis of negative pressure type EGR valve based on CFD

The negative pressure valve EGR bears thermal load for a long period, thus its heat transfer characteristics have an important impact on the stability of the engine. The fluid solid coupling method was employed to analyze the contact heat transfer between the inner cavity of the valve and the cooling water as well as the high temperature gas based on CFD. As a result, the characteristics of the internal fluid velocity field, pressure field and temperature field were obtained. Besides, the heat transfer capability of the valve was also improved by adding the annular cooling water channel. The test results showed that the calculation method has a high calculation accuracy providing an important basis for the optimization design of valves

Distributed Algorithm for Continuous-type Bayesian Nash Equilibrium in Subnetwork Zero-sum Games

In this paper, we consider a continuous-type Bayesian Nash equilibrium (BNE) seeking problem in subnetwork zero-sum games, which is a generalization of deterministic subnetwork zero-sum games and discrete-type Bayesian zero-sum games. In this continuous-type model, because the feasible strategy set is composed of infinite-dimensional functions and is not compact, it is hard to seek a BNE in a non-compact set and convey such complex strategies in network communication. To this end, we design two steps to overcome the above bottleneck. One is a discretization step, where we discretize continuous types and prove that the BNE of the discretized model is an approximate BNE of the continuous model with an explicit error bound. The other one is a communication step, where we adopt a novel compression scheme with a designed sparsification rule and prove that agents can obtain unbiased estimations through compressed communication. Based on the above two steps, we propose a distributed communication-efficient algorithm to practicably seek an approximate BNE, and further provide an explicit error bound and an $O(\ln T/\sqrt{T})$ convergence rate.Comment: Submitted to SIAM Journal on Control and Optimizatio

Application of in situ full-field measurement in the transmission electron microscope: Mechanical property extraction from amorphous to crystalline materials

This thesis work develops an innovative experimental approach that combines the full-field optical measurement methods of digital image correlation (DIC) and particle tracking (PT) with an in situ loading experiment in the transmission electron microscope (TEM), and demonstrates how these full-field measurements facilitate the acquisition of microscale mechanical properties in both amorphous and crystalline materials. Central to the DIC technique is the presence of a random speckle pattern on the sample surface which can be tracked to produce measurements of surface strain and displacement during loading. The challenge of developing such a pattern suitable for use in the harsh TEM environment was solved by using a gold nanoparticle deposition technique in which a thin gold film is deposited on the sample and undergoes de-wetting upon annealing to form gold nanoparticle islands–the DIC speckles. The same speckles can also serve as markers particles for PT. The particles were seen to be effective speckles while at the same time not altering sample response. In addition to particle deposition, significant care must be taken in applying the remaining experimental procedures including sample sectioning, focused ion beam milling, TEM loading set up, and application of DIC and PT. As a demonstrator for the method, in situ TEM images were captured during a bending experiment of an amorphous SiO2 beam, and DIC and PT were applied to measure the full-field displacements. Their effectiveness was validated through a comparative analysis of these measurements. The remainder of this effort was devoted to applying the TEM/DIC/PT technique to a variety of problems in both an amorphous and a crystalline material system, SiO2 and magnesium aluminate spinel (MgAl2O4) respectively. The next part of this work delves into the electron beam irradiation induced creep (IIC) behavior of amorphous SiO2 in the TEM environment. Full-field displacements were measured from TEM images during a carefully designed multiple-ramp-loading creep experiment, and creep properties were quantified via 2D FEM parameter optimization, assuming the creep behavior was governed by Norton’s law. By determining Norton’s creep constants, the creep compliance of SiO2 was extracted, and a linear dependence between creep strain rate and stress was found. In the final part of this work, failure of single crystal and bi-crystal magnesium aluminate spinel is investigated. Due to the presence of bend contours on the crystalline sample in the TEM, rendering DIC impractical, in this case PT was used for full-field measurements. One approach in this part of work is to extract opening-dominated fracture toughness through a single-edge notched bending (SENB) test in the TEM, followed by analytical fitting with the asymptotic crack-tip field. In addition, a novel punch compression configuration is proposed to induce local shear bands, enabling an exploration of the shear yielding behavior of single crystal spinel. Through inverse analysis in the FEM, parameters for the tri-linear plasticity model were determined, thus extracting yield stress of spinel. Fracture property disparity between the grain boundary and lattice, and the mode mixity dependence of the grain boundary fracture property, were also studied. By placing a notch aligned with the grain boundary at the top or bottom edge of a bi-crystal beam sample, bending experiments can generate grain boundary failure with different mode mixites. Critical energy release rates and mode mixity indices for each sample were extracted through 3D FEM analysis, validated by PT-FEM comparisons. For opening-dominated fracture, the grain boundary exhibited a lower fracture energy compared to the single crystal lattice, providing partial evidence for nonuniform material strength of the bulk polycrystal spinel. Furthermore, different grain boundary fracture properties were observed for opening- and shear-dominated modes.Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-03-01 without embargo termsThe student, Yiguang Zhang, accepted the attached license on 2023-10-02 at 13:06.The student, Yiguang Zhang, submitted this Dissertation for approval on 2023-10-02 at 13:24.This Dissertation was approved for publication on 2023-10-12 at 15:34.DSpace SAF Submission Ingestion Package generated from Vireo submission #19839 on 2024-03-01 at 13:13:3

A robust-generalized reduced gradient program (R-GRG) : with engineering design optimization applications

This report specifically describes algorithms, programming, and applications of a Robust-Generalized Reduced Gradient (R-GRG) for optimum engineering design. The first part of the report depicts the mathematical principles and implementation of the R-GRG method. The second part describes two engineering applications using RGRG. The mathematical models, usage of R-GRG, and design results are presented. The comparisons with other optimization algorithms are made to test the algorithm and programming of R-GRG. The algorithm and design results indicate R-GRG is an efficient and desirable optimization program for engineering optimization problems. Further improvements of R-GRG are discussed in the conclusion section of this report.Includes bibliographical references (leaves 100-102)California State University, Northridge. Department of Engineering