Phase behavior of parallel hard cylinders

We test the performance of a recently proposed fundamental measure density functional of aligned hard cylinders by calculating the phase diagram of a monodisperse fluid of these particles. We consider all possible liquid crystalline symmetries, namely nematic, smectic and columnar, as well as the crystalline phase. For this purpose we introduce a Gaussian parameterization of the density profile and use it to minimize numerically the functional. We also determine, from the analytic expression for the structure factor of the uniform fluid, the bifurcation points from the nematic to the smectic and columnar phases. The equation of state, as obtained from functional minimization, is compared to the available Monte Carlo simulation. The agreement is is very good, nearly perfect in the description of the inhomogeneous phases. The columnar phase is found to be metastable with respect to the smectic or crystal phases, its free energy though being very close to that of the stable phases. This result justifies the observation of a window of stability of the columnar phase in some simulations, which disappears as the size of the system increases. The only important deviation between theory and simulations shows up in the location of the nematic-smectic transition. This is the common drawback of any fundamental measure functional of describing the uniform phase just with the accuracy of scaled particle theory.Comment: 17 pages, 5 figure

The Role of Selectivity in Hierarchical Social Systems

We consider a selection process and a hierarchical institution in a dynamic model as in Harrington [3], where agents are "climbing the pyramid" in a rank-order contest based on the "up or out" policy. Agents are ranked according to the quality of their performances in a particular environment that they face in groups, and a fraction of the highest ranked agents are promoted. The size of this fraction characterizes the selectivity of the process, and we distinguish between local and global selectivity. We study the role of the degree of local and global selectivity in the dynamic process where agents' types differ in their expected performances. Surprisingly, we find that an increase in the selectivity of the process can be detrimental to the agents with the highest expected performances. In fact, it does not matter how small the expected performance of a particular type of agent is. If the degree of selectivity is high enough, that type of agent will survive. However, if the selectivity decreases, the only survivor is the agent with the highest expected performance.Social hierarchy, Selection, Selectivity, Promotion

An Unexpected Role of Local Selectivity in Social Promotion

A selection process and a hierarchical promotion system in a dynamic model are considered as in Harrington (1998) and Garcia-Martinez (2010), where agents are "climbing the pyramid" in a rank-order contest based on the "up or out" policy. The population at any level of the hierarchy is matched in groups of n agents, and each group faces a particular environment. Agents are ranked according to the quality of their performances in each particular environment. The top k performing agents from each group are promoted. The fraction (k/n) characterizes the local selectivity of the process. The role of the degree of local selectivity in the dynamic process where agents' types differ in their expected performances is studied. For low selectivity, the selection process is not strong enough to overcome the inertia of the initial population. If selectivity increases, only the best-performing type of agent will survive. If the selectivity is increased far enough, the worst-performing type also survives, and the proportion for which they account at equilibrium increases as selectivity increases. Therefore, surprisingly, no matter how low the expected success rate of a type is, if the selection process has a high enough level of selectivity, agents of that type survive in the long run: Too much selectivity is always harmful to the best-performing type.Social hierarchy; Selection; Selectivity; Promotion

Phase diagrams of Zwanzig models: The effect of polydispersity

The first goal of this article is to study the validity of the Zwanzig model for liquid crystals to predict transitions to inhomogeneous phases (like smectic and columnar) and the way polydispersity affects these transitions. The second goal is to analyze the extension of the Zwanzig model to a binary mixture of rods and plates. The mixture is symmetric in that all particles have equal volume and length-to-breadth ratio, $\kappa$. The phase diagram containing the homogeneous phases as well as the spinodals of the transitions to inhomogeneous phases is determined for the cases $\kappa=5$ and 15 in order to compare with previous results obtained in the Onsager approximation. We then study the effect of polydispersity on these phase diagrams, emphasizing the enhancement of the stability of the biaxial nematic phase it induces.Comment: 11 pages, 12 figure

The space of solutions to the Hessian one equation in the finitely punctured plane

We construct the space of solutions to the elliptic Monge-Ampere equation det(D^2 u)=1 in the plane R^2 with n points removed. We show that, modulo equiaffine transformations and for n>1, this space can be seen as an open subset of R^{3n-4}, where the coordinates are described by the conformal equivalence classes of once punctured bounded domains in the complex plane of connectivity n-1. This approach actually provides a constructive procedure that recovers all such solutions to the Monge-Ampere equation, and generalizes a theorem by K. Jorgens.Comment: 14 pages, 3 figure

International survey of integrated financial sector supervision

Despite the intense debate on the advantages and disadvantages of adopting integrated supervision that has taken place in recent years, little is known about the experiences of countries that have adopted it and the obstacles and challenges they have faced to implement it. In an attempt to shed light on this area, the authors present the results of a survey conducted in a group of 15 countries that have adopted integrated supervision. After a brief review of the literature on integrated supervision, the authors examine four topics: 1) The reasons cited by this group of countries for establishing an integrated supervisory agency. 2) The scope of regulatory and supervisory powers of these agencies. 3) The progress of these agencies in harmonizing their regulatory and supervisory practices across the intermediaries they supervise. 4) The practical problems faced by policymakers in adopting integrated supervision. The survey revealed that the group of integrated supervisory agencies is not as homogeneous as it seems. Important differences arise with regard to the scope of regulatory and supervisory powers the agencies have been given. In fact, contrary to popular belief, less than 50 percent of the agencies can be categorized as mega-supervisors. Another finding is that in most countries progress toward the harmonization of prudential regulation andsupervision across financial intermediaries remains limited. Interestingly, the survey revealed that practically all countries believe they have achieved a higher degree of harmonization in the regulation and supervision of banks and securities companies than between banks and insurance firms. The survey also identified some practical problems faced by this group of countries in establishing their unified supervisory agencies. The authors discuss these problems, along with the practical lessons and recommendations provided by the 15 agencies to other countries considering integrated supervision, in the final section of the paper.Banks&Banking Reform,Insurance&Risk Mitigation,Housing Finance,Payment Systems&Infrastructure,Financial Intermediation,Banks&Banking Reform,Insurance&Risk Mitigation,Financial Intermediation,Housing Finance,Environmental Economics&Policies