Agreement Problems in Networks with Directed Graphs and Switching Topology

In this paper, we provide tools for convergence and performance analysis of an agreement protocol for a network of integrator agents with directed information flow. Moreover, we analyze algorithmic robustness of this consensus protocol for the case of a network with mobile nodes and switching topology. We establish a connection between the Fiedler eigenvalue of the graph Laplacian and the performance of this agreement protocol. We demostrate that a class of directed graphs, called balanced graphs, have a crucial role in solving average-consensus problems. Based on the properties of balanced graphs, a group disagreement function (i.e. Lyapunov function) is proposed for convergence analysis of this agreement protocol for networks with directed graphs. This group disagreement function is later used for convergence analysis for the agreement problem in networks with switching topology. We provide simulation results that are consistent with our theoretical results and demonstrate the effectiveness of the proposed analytical tools

Consensus problems in networks of agents with switching topology and time-delays

In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results

Many-body Green's function theory for thin ferromagnetic films: exact treatment of the single-ion anisotropy

A theory for the magnetization of ferromagnetic films is formulated within the framework of many-body Green's funtion theory which considers all components of the magnetization. The model Hamiltonian includes a Heisenberg term, an external field, a second- and fourth-order uniaxial single-ion anisotropy, and the magnetic dipole-dipole coupling. The single-ion anisotropy terms can be treated exactly by introducing higher-order Green's functions and subsequently taking advantage of relations between products of spin operators which leads to an automatic closure of the hierarchy of the equations of motion for the Green's functions with respect to the anisotropy terms. This is an improvement on the method of our previous work, which treated the corresponding terms only approximately by decoupling them at the level of the lowest-order Green's functions. RPA-like approximations are used to decouple the exchange terms in both the low-order and higher-order Green's functions. As a first numerical example we apply the theory to a monolayer for spin S=1 in order to demonstrate the superiority of the present treatment of the anisotropy terms over the previous approximate decouplings.Comment: 23 pages, 5 figure

Reply to “Comments on “Consensus and Cooperation in Networked Multi-Agent Systems””

[No abstract

On Steering Swarms

The main contribution of this paper is a novel method allowing an external observer/controller to steer and guide swarms of identical and indistinguishable agents, in spite of the agents' lack of information on absolute location and orientation. Importantly, this is done via simple global broadcast signals, based on the observed average swarm location, with no need to send control signals to any specific agent in the swarm

Perturbative Analysis of Spectral Singularities and Their Optical Realizations

We develop a perturbative method of computing spectral singularities of a Schreodinger operator defined by a general complex potential that vanishes outside a closed interval. These can be realized as zero-width resonances in optical gain media and correspond to a lasing effect that occurs at the threshold gain. Their time-reversed copies yield coherent perfect absorption of light that is also known as an antilaser. We use our general results to establish the exactness of the n-th order perturbation theory for an arbitrary complex potential consisting of n delta-functions, obtain an exact expression for the transfer matrix of these potentials, and examine spectral singularities of complex barrier potentials of arbitrary shape. In the context of optical spectral singularities, these correspond to inhomogeneous gain media.Comment: 13 pages, 2 figures, one table, a reference added, typos correcte

Investigations of carbon nanotube catalyst morphology and behavior with transmission electron microscopy

Carbon nanotubes (CNTs) are materials with significant potential applications due to their desirable mechanical and electronic properties, which can both vary based on their structure. Electronic applications for CNTs are still few and not widely available, mainly due to the difficulty in the control of fabrication. Carbon nanotubes are grown in batches, but despite many years of research from their first discovery in 1991, there are still many unanswered questions regarding how to control the structure of CNTs. This work attempts to bridge some of the gap between question and answer by focusing on the catalyst particle used in common CNT growth procedures. Ostwald ripening studies on iron nanoparticles are performed in an attempt to link catalyst morphology during growth and CNT chirality (the structure aspect of a nanotube that determines its electrical properties). These results suggest that inert gas dynamics play a critical role on the catalyst morphology during CNT growth. A novel method for CNT catalyst activation by substrate manipulation is presented. Results of this study build upon prior knowledge of the role of the chemistry of the substrate supporting CNT catalysts. By bombarding sapphire, a substrate known to not support CNT growth, with an argon ion beam, the substrate is transformed into an active CNT growth support by modifying both the structure and chemistry of the sapphire surface. Finally, catalyst formation is studied with transmission electron microscopy by depositing an iron gradient film in order to identify a potential critical catalyst size and morphology for CNT growth. A relationship between catalyst size and morphology has been identified that adds evidence to the hypothesis that a catalysts activity is determined by its size and ability to properly reduce

Investigations of carbon nanotube catalyst morphology and behavior with transmission electron microscopy

Carbon nanotubes (CNTs) are materials with significant potential applications due to their desirable mechanical and electronic properties, which can both vary based on their structure. Electronic applications for CNTs are still few and not widely available, mainly due to the difficulty in the control of fabrication. Carbon nanotubes are grown in batches, but despite many years of research from their first discovery in 1991, there are still many unanswered questions regarding how to control the structure of CNTs. This work attempts to bridge some of the gap between question and answer by focusing on the catalyst particle used in common CNT growth procedures. Ostwald ripening studies on iron nanoparticles are performed in an attempt to link catalyst morphology during growth and CNT chirality (the structure aspect of a nanotube that determines its electrical properties). These results suggest that inert gas dynamics play a critical role on the catalyst morphology during CNT growth. A novel method for CNT catalyst activation by substrate manipulation is presented. Results of this study build upon prior knowledge of the role of the chemistry of the substrate supporting CNT catalysts. By bombarding sapphire, a substrate known to not support CNT growth, with an argon ion beam, the substrate is transformed into an active CNT growth support by modifying both the structure and chemistry of the sapphire surface. Finally, catalyst formation is studied with transmission electron microscopy by depositing an iron gradient film in order to identify a potential critical catalyst size and morphology for CNT growth. A relationship between catalyst size and morphology has been identified that adds evidence to the hypothesis that a catalysts activity is determined by its size and ability to properly reduce

Induction of triploidy in grass carp Ctenopharyngodon idella Valenciennes, 1844: comparison of cold & heat shocks

Triploidy in grass carp, Ctenopharyngodon idella Valenciennes, 1844, was induced on fertilized eggs to compare cold and heat shocks. Two simplified methods explained for verification of triploidy in grass carp. The cold shock (7 ˚C) was given in three treatments for 30 min starting 2.0, 2.5 and 4.0 min after fertilization. In cold shock, the start point (2.0 min after fertilization) showed the highest rate of triploidy (60.9%). Heat shocks were given at 38 ˚C, 40 ˚C and 42 ˚C, at 4.0 min after fertilization and lasted for 1.0 min. Produced larvae using heat shock 38 ˚C showed 10.8% triploidy, but no signs of triploidy were seen in other heat shock treatments. Verification of triploidy in grass carp was carried out using karyotyping and measurment of erythrocytes surface area and volume in fingerlings. Ratio of erythrocytes dimention and the size of their nuclei in triploids to diploids was 2.35 and 1.80, respectively. Comparison of results obtained from the application of cold and heat shocks indicated that cold shocks are more effective than heat shocks in the induction of triploidy in grass carp