Equilibrium clusters in suspensions of colloids interacting via potentials with a local minimum

In simple colloidal suspensions, clusters are various multimers that result from colloid self-association and exist in equilibrium with monomers.There are two types of potentials that are known to produce clusters: a) potentials that result from the competition between short-range attraction and long-range repulsion and are characterized by a global minimum and a repulsive tail and b) purely repulsive potentials which have a soft shoulder. Using computer simulations, we demonstrate in this work that potentials with a local minimum and a repulsive tail, not belonging to either of the known types, are also capable of generating clusters. A detailed comparative analysis shows that the new type of cluster-forming potential serves as a bridge between the other two. The new clusters are expanded in shape and their assembly is driven by entropy, like in the purely repulsive systems but only at low density. At high density, clusters are collapsed and stabilized by energy, in common with the systems with competing attractive and repulsive interactions.Comment: 12 pages, 7 figure

Supervisor Localization of Discrete-Event Systems based on State Tree Structures

Recently we developed supervisor localization, a top-down approach to distributed control of discrete-event systems in the Ramadge-Wonham supervisory control framework. Its essence is the decomposition of monolithic (global) control action into local control strategies for the individual agents. In this paper, we establish a counterpart supervisor localization theory in the framework of State Tree Structures, known to be efficient for control design of very large systems. In the new framework, we introduce the new concepts of local state tracker, local control function, and state-based local-global control equivalence. As before, we prove that the collective localized control behavior is identical to the monolithic optimal (i.e. maximally permissive) and nonblocking controlled behavior. In addition, we propose a new and more efficient localization algorithm which exploits BDD computation. Finally we demonstrate our localization approach on a model for a complex semiconductor manufacturing system

Optimization of Dimples in Microchannel Heat Sink with Impinging Jets—Part B: the Influences of Dimple Height and Arrangement

The combination of a microchannel heat sink with impinging jets and dimples (MHSIJD) can effectively improve the flow and heat transfer performance on the cooling surface of electronic devices with very high heat fluxes. Based on the previous work by analysing the effect of dimple radius on the overall performance of MHSIJD, the effects of dimple height and arrangement were numerically analysed. The velocity distribution, pressure drop, and thermal performance of MHSIJD under various dimple heights and arrangements were presented. The results showed that: MHSIJD with higher dimples had better overall performance with dimple radius being fixed; creating a mismatch between the impinging hole and dimple can solve the issue caused by the drift phenomenon; the mismatch between the impinging hole and dimple did not exhibit better overall performance than a well-matched design

Exact Outage Performance Analysis of Multiuser Multi-relay Spectrum Sharing Cognitive Networks

In this paper, we investigate the outage performance of dual-hop multiuser multi-relay cognitive radio networks under spectrum sharing constraints. Using an efficient relay-destination selection scheme, the exact and asymptotic closed-form expressions for the outage probability are derived. From these expressions it is indicated that the achieved diversity order is only determined by the number of secondary user (SU) relays and destinations, and equals to M+N (where M and N are the number of destination nodes and relay nodes, respectively). Further, we find that the coding gain of the SU network will be affected by the interference threshold $bar I$ at the primary user (PU) receiver. Specifically, as the increases of the interference threshold, the coding gain of the considered network approaches to that of the multiuser multi-relay system in the non-cognitive network. Finally, our study is corroborated by representative numerical examples

Two-peaked and flat-top perfect bright solitons in epsilon-near-zero nonlinear metamaterials: novel Kerr self-trapping mechanisms

We analytically investigate transverse magnetic (TM) spatial bright solitons, as exact solutions of Maxwell's equations, propagating through nonlinear metamaterials whose linear dielectric permittivity is very close to zero and whose effective nonlinear Kerr parameters can be tailored to achieve values not available in standard materials. Exploiting the fact that, in the considered medium, linear and nonlinear polarization can be comparable at feasible and realistic optical intensities, we identify two novel self-trapping mechanisms able to support two-peaked and flat-top solitons, respectively. Specifically, these two novel mechanisms are based on the occurrence of critical points at which the effective nonlinear permittivity vanishes, the two mechanisms differing in the way the compensation between linear and nonlinear polarization is achieved through the non-standard values of the nonlinear parameters.Comment: 7 pages, 4 figure

Optimal Timing of Cartel Formation Under Uncertainty

Understanding how business cartels form and expand is foundational for developing sound deterrence strategies. Past work (i.e. Connor, 2005) has relied on net present value (NPV) methods to evaluate the streams of costs and benefits of forming or joining a cartel. While NPV adequately measure the expected value of future streams of benefits and costs, higher moments of the distribution are also important in understanding agent behavior. Thus, in the presence of uncertainty about future streams and litigation costs, NPV may miss important dimensions that shape the issue. The decision to form or join a cartel is, at least, partially irreversible, because it exposes the firm or its involved managers to litigation on all previous returns and even after the cartel is dissolved. In this study, we rely on the aforementioned irreversible and uncertain nature of cartel participation and returns to develop a real-options framework that examines the optimal decision rules regarding the timing of cartel formation. This leads to suggestions for improved policy tools for antitrust agencies. In our model, all firms outside of a cartel essentially hold the option to form or join a cartel at some point in the future. The option is exercised the day the cartel is formed and has no cash value before that. The payoffs that firms give up by not immediately forming a cartel are weighed against uncertain and partially irreversible forming decision nature. Under the assumption of stochastic market demand, we find a threshold level of demand beyond which the cartel is formed. This threshold is analytically calculated as a function of a number of parameters. We then illustrate the conditions that determine the optimal timing decision of cartel formation by conducting comparative dynamics analysis. The timing of cartel formation is analyzed in both domestic and international settings. The qualitative results are obtained by comparative dynamics analysis and the quantitative results by numerical analysis. The results obtained in this study will assist in the development and improvement of guidelines to deter the formation of cartels by antitrust agencies in both developed and developing nations. In the first scenario of domestic cartel formation, at the beginning of each period, firms will choose to compete when the sunk costs related to a cartel operation are too high, current period demand is too low, and/or the expected duration of collusion is too short. Obviously, the possibilities of cartel formation increase when sunk costs go down, demand increases, or relationships with firms improve the prospects for a longer cartel arrangement. The value of waiting increases with a) increased uncertainty of market demand, b) increase irreversibility, and c) increased number of firms and d) a higher discount rate. We study the effect of demand uncertainty on the expected social welfare of cartel formation. The simulation results suggest that the expected social welfare under uncertainty could be higher than that under certainty. In a second scenario, we study the formation of international cartels. The model considers two markets with demand uncertainty that is either correlated or uncorrelated. The demand shocks in each market are assumed to follow geometric Brownian motion. We calculate the threshold value of demand faced by the cartel and obtain the rules guiding a firm's decision to form an international cartel. The comparative dynamics results obtained in the previous domestic scenario still apply. The simulation results suggest that cartel formation is most likely to occur between firms that come from countries with highly correlated markets and similar expected demand growth.Cartel Joining Behavior, Real Options Theory, International Cartels, Industrial Organization, K21, L00, L12,