Modeling and Tuning of Energy Harvesting Device Using Piezoelectric Cantilever Array

Piezoelectric devices have been increasingly investigated as a means of converting ambient vibrations into electrical energy that can be stored and used to power other devices, such as the sensors/actuators, micro-electro-mechanical systems (MEMS) devices, and microprocessor units etc. The objective of this work was to design, fabricate, and test a piezoelectric device to harvest as much power as possible from vibration sources and effectively store the power in a battery.;The main factors determining the amount of collectable power of a single piezoelectric cantilever are its resonant frequency, operation mode and resistive load in the charging circuit. A proof mass was used to adjust the resonant frequency and operation mode of a piezoelectric cantilever by moving the mass along the cantilever. Due to the tiny amount of collected power, a capacitor was suggested in the charging circuit as an intermediate station. To harvest sufficient energy, a piezoelectric cantilever array, which integrates multiple cantilevers in parallel connection, was investigated.;In the past, most prior research has focused on the theoretical analysis of power generation instead of storing generated power in a physical device. In this research, a commercial solid-state battery was used to store the power collected by the proposed piezoelectric cantilever array. The time required to charge the battery up to 80% capacity using a constant power supply was 970 s. It took about 2400 s for the piezoelectric array to complete the same task. Other than harvesting energy from sinusoidal waveforms, a vibration source that emulates a real environment was also studied. In this research the response of a bridge-vehicle system was used as the vibration sources such a scenario is much closer to a real environment compared with typical lab setups

Realizing degree sequences with graphs having nowhere-zero 3-flows

The following open problem was proposed by Archdeacon: Characterize all graphical sequences π such that some realization of π admits a nowhere-zero 3-flow. The purpose of this paper is to resolve this problem and present a complete characterization: A graphical sequence π = (d I,d2,...,dn) with minimum degree at least two has a realization that admits a nowhere-zero 3-flow if and only if π ≠ (34,2), (k,3k), (k2,3k-1), where k is an odd integer. © 2008 Society for Industrial and Applied Mathematics.published_or_final_versio

Totally balanced combinatorial optimization games

Combinatorial optimization games deal with cooperative games for which the value of every subset of players is obtained by solving a combinatorial optimization problem on the resources collectively owned by this subset. A solution of the game is in the core if no subset of players is able to gain advantage by breaking away from this collective decision of all players. The game is totally balanced if and only if the core is non-empty for every induced subgame of it. We study the total balancedness of several combinatorial optimization games in this paper. For a class of the partition game [5], we have a complete characterization for the total balancedness. For the packing and covering games [3], we completely clarify the relationship between the related primal/dual linear programs for the corresponding games to be totally balanced. Our work opens up the question of fully characterizing the combinatorial structures of totally balanced packing and covering games, for which we present some interesting examples: the totally balanced matching, vertex cover, and minimum coloring games.link_to_subscribed_fulltex

Realizing Degree Sequences with Graphs Having Nowhere-Zero 3-Flows

The following open problem was proposed by Archdeacon: Characterize all graphical sequences π such that some realization of π admits a nowhere-zero 3-flow. The purpose of this paper is to resolve this problem and present a complete characterization: A graphical sequence π = (d1, d2, ., dn) with minimum degree at least two has a realization that admits a nowhere-zero 3-flow if and only if π ≠ (34, 2), (k, 3k), (k2, 3k―1), where k is an odd integer

Weighted Modulo Orientations of Graphs

This dissertation focuses on the subject of nowhere-zero flow problems on graphs. Tutte\u27s 5-Flow Conjecture (1954) states that every bridgeless graph admits a nowhere-zero 5-flow, and Tutte\u27s 3-Flow Conjecture (1972) states that every 4-edge-connected graph admits a nowhere-zero 3-flow. Extending Tutte\u27s flows conjectures, Jaeger\u27s Circular Flow Conjecture (1981) says every 4k-edge-connected graph admits a modulo (2k+1)-orientation, that is, an orientation such that the indegree is congruent to outdegree modulo (2k+1) at every vertex. Note that the k=1 case of Circular Flow Conjecture coincides with the 3-Flow Conjecture, and the case of k=2 implies the 5-Flow Conjecture. This work is devoted to providing some partial results on these problems. In Chapter 2, we study the problem of modulo 5-orientation for given multigraphic degree sequences. We prove that a multigraphic degree sequence d=(d1,..., dn) has a realization G with a modulo 5-orientation if and only if di≤1,3 for each i. In addition, we show that every multigraphic sequence d=(d1,..., dn) with min{1≤i≤n}di≥9 has a 9-edge-connected realization that admits a modulo 5-orientation for every possible boundary function. Jaeger conjectured that every 9-edge-connected multigraph admits a modulo 5-orientation, whose truth would imply Tutte\u27s 5-Flow Conjecture. Consequently, this supports the conjecture of Jaeger. In Chapter 3, we show that there are essentially finite many exceptions for graphs with bounded matching numbers not admitting any modulo (2k+1)-orientations for any positive integers t. We additionally characterize all infinite many graphs with bounded matching numbers but without a nowhere-zero 3-flow. This partially supports Jaeger\u27s Circular Flow Conjecture and Tutte\u27s 3-Flow Conjecture. In 2018, Esperet, De Verclos, Le and Thomass introduced the problem of weighted modulo orientations of graphs and indicated that this problem is closely related to modulo orientations of graphs, including Tutte\u27s 3-Flow Conjecture. In Chapter 4 and Chapter 5, utilizing properties of additive bases and contractible configurations, we reduced the Esperet et al\u27s edge-connectivity lower bound for some (signed) graphs families including planar graphs, complete graphs, chordal graphs, series-parallel graphs and bipartite graphs, indicating that much lower edge-connectivity bound still guarantees the existence of such orientations for those graph families. In Chapter 6, we show that the assertion of Jaeger\u27s Circular Flow Conjecture with k=2 holds asymptotically almost surely for random 9-regular graphs

Coloring and constructing (hyper)graphs with restrictions

We consider questions regarding the existence of graphs and hypergraphs with certain coloring properties and other structural properties. In Chapter 2 we consider color-critical graphs that are nearly bipartite and have few edges. We prove a conjecture of Chen, Erdős, Gyárfás, and Schelp concerning the minimum number of edges in a “nearly bipartite” 4-critical graph. In Chapter 3 we consider coloring and list-coloring graphs and hypergraphs with few edges and no small cycles. We prove two main results. If a bipartite graph has maximum average degree at most 2(k−1), then it is colorable from lists of size k; we prove that this is sharp, even with an additional girth requirement. Using the same approach, we also provide a simple construction of graphs with arbitrarily large girth and chromatic number (first proved to exist by Erdős). In Chapter 4 we consider list-coloring the family of kth power graphs. Kostochka and Woodall conjectured that graph squares are chromatic-choosable, as a strengthening of the Total List Coloring Conjecture. Kim and Park disproved this stronger conjecture, and Zhu asked whether graph kth powers are chromatic-choosable for any k. We show that this is not true: we construct families of graphs based on affine planes whose choice number exceeds their chromatic number by a logarithmic factor. In Chapter 5 we consider the existence of uniform hypergraphs with prescribed degrees and codegrees. In Section 5.2, we show that a generalization of the graphic 2-switch is insufficient to connect realizations of a given degree sequence. In Section 5.3, we consider an operation on 3-graphs related to the octahedron that preserves codegrees; this leads to an inductive definition for 2-colorable triangulations of the sphere. In Section 5.4, we discuss the notion of fractional realizations of degree sequences, in particular noting the equivalence of the existence of a realization and the existence of a fractional realization in the graph and multihypergraph cases. In Chapter 6 we consider a question concerning poset dimension. Dorais asked for the maximum guaranteed size of a subposet with dimension at most d of an n-element poset. A lower bound of sqrt(dn) was observed by Goodwillie. We provide a sublinear upper bound

The mixing time of the switch Markov chains: a unified approach

Since 1997 a considerable effort has been spent to study the mixing time of switch Markov chains on the realizations of graphic degree sequences of simple graphs. Several results were proved on rapidly mixing Markov chains on unconstrained, bipartite, and directed sequences, using different mechanisms. The aim of this paper is to unify these approaches. We will illustrate the strength of the unified method by showing that on any $P$-stable family of unconstrained/bipartite/directed degree sequences the switch Markov chain is rapidly mixing. This is a common generalization of every known result that shows the rapid mixing nature of the switch Markov chain on a region of degree sequences. Two applications of this general result will be presented. One is an almost uniform sampler for power-law degree sequences with exponent $\gamma>1+\sqrt{3}$. The other one shows that the switch Markov chain on the degree sequence of an Erd\H{o}s-R\'enyi random graph $G(n,p)$ is asymptotically almost surely rapidly mixing if $p$ is bounded away from 0 and 1 by at least $\frac{5\log n}{n-1}$.Comment: Clarification

Spanning Trails and Spanning Trees

There are two major parts in my dissertation. One is based on spanning trail, the other one is comparing spanning tree packing and covering.;The results of the spanning trail in my dissertation are motivated by Thomassen\u27s Conjecture that every 4-connected line graph is hamiltonian. Harary and Nash-Williams showed that the line graph L( G) is hamiltonian if and only if the graph G has a dominating eulerian subgraph. Also, motivated by the Chinese Postman Problem, Boesch et al. introduced supereulerian graphs which contain spanning closed trails. In the spanning trail part of my dissertation, I proved some results based on supereulerian graphs and, a more general case, spanning trails.;Let alpha(G), alpha\u27(G), kappa( G) and kappa\u27(G) denote the independence number, the matching number, connectivity and edge connectivity of a graph G, respectively. First, we discuss the 3-edge-connected graphs with bounded edge-cuts of size 3, and prove that any 3-edge-connected graph with at most 11 edge cuts of size 3 is supereulerian, which improves Catlin\u27s result. Second, having the idea from Chvatal-Erdos Theorem which states that every graph G with kappa(G) ≥ alpha( G) is hamiltonian, we find families of finite graphs F 1 and F2 such that if a connected graph G satisfies kappa\u27(G) ≥ alpha(G) -- 1 (resp. kappa\u27(G) ≥ 3 and alpha\u27( G) ≤ 7), then G has a spanning closed trail if and only if G is not contractible to a member of F1 (resp. F2). Third, by solving a conjecture posed in [Discrete Math. 306 (2006) 87-98], we prove if G is essentially 4-edge-connected, then for any edge subset X0 ⊆ E(G) with |X0| ≤ 3 and any distinct edges e, e\u27 2 ∈ E(G), G has a spanning ( e, e\u27)-trail containing all edges in X0.;The results on spanning trees in my dissertation concern spanning tree packing and covering. We find a characterization of spanning tree packing and covering based on degree sequence. Let tau(G) be the maximum number of edge-disjoint spanning trees in G, a(G) be the minimum number of spanning trees whose union covers E(G). We prove that, given a graphic sequence d = (d1, d2···dn) (d1 ≥ d2 ≥···≥ dn) and integers k2 ≥ k1 \u3e 0, there exists a simple graph G with degree sequence d satisfying k 1 ≤ tau(G) ≤ a(G) ≤ k2 if and only if dn ≥ k1 and 2k1(n -- 1) ≤ Sigmani =1 di ≤ 2k2( n -- 1 |I| -- 1) + 2Sigma i∈I di, where I = {lcub}i : di \u3c k2{rcub}

Network Characteristics and Dynamics: Reciprocity, Competition and Information Dissemination

Networks are commonly used to study complex systems. This often requires a good understanding of the structural characteristics and evolution dynamics of networks, and also their impacts on a variety of dynamic processes taking place on top of them. In this thesis, we study various aspects of networks characteristics and dynamics, with a focus on reciprocity, competition and information dissemination. We first formulate the maximum reciprocity problem and study its use in the interpretation of reciprocity in real networks. We propose to interpret reciprocity based on its comparison with the maximum possible reciprocity for a network exhibiting the same degrees. We show that the maximum reciprocity problem is NP-hard, and use an upper bound instead of the maximum. We find that this bound is surprisingly close to the empirical reciprocity in a wide range of real networks, and that there is a surprisingly strong linear relationship between the two. We also show that certain small suboptimal motifs called 3-paths are the major cause for suboptimality in real networks. Secondly, we analyze competition dynamics under cumulative advantage, where accumulated resource promotes gathering even more resource. We characterize the tail distributions of duration and intensity for pairwise competition. We show that duration always has a power-law tail irrespective of competitors\u27 fitness, while intensity has either a power-law tail or an exponential tail depending on whether the competitors are equally fit. We observe a struggle-of-the-fitness phenomenon, where a slight different in fitness results in an extremely heavy tail of duration distribution. Lastly, we study the efficiency of information dissemination in social networks with limited budget of attention. We quantify the efficiency of information dissemination for both cooperative and selfish user behaviors in various network topologies. We identify topologies where cooperation plays a critical role in efficient information propagation. We propose an incentive mechanism called plus-one to coax users into cooperation in such cases