A multi-moment vortex method for 2D viscous fluids

In this paper we introduce simplified, exact, combinatorial formulas that arise in the vortex interaction model found in [33]. These combinatorial formulas allow for the efficient implementation and development of a new multi-moment vortex method (MMVM) using a Hermite expansion to simulate 2D vorticity. The method naturally allows the particles to deform and become highly anisotropic as they evolve without the added cost of computing the non-local Biot–Savart integral. We present three examples using MMVM. We first focus our attention on the implementation of a single particle, large number of Hermite moments case, in the context of quadrupole perturbations of the Lamb–Oseen vortex. At smaller perturbation values, we show the method captures the shear diffusion mechanism and the rapid relaxation (on Re^1/3 time scale) to an axisymmetric state. We then present two more examples of the full multi-moment vortex method and discuss the results in the context of classic vortex methods. We perform numerical tests of convergence of the single particle method and show that at least in simple cases the method exhibits the exponential convergence typical of spectral methods. Lastly, we numerically investigate the spatial accuracy improvement from the inclusion of higher Hermite moments in the full MMVM.     

Bayesian knowledge base tuning

For a knowledge-based system that fails to provide the correct answer, it is important to be able to tune the system while minimizing overall change in the knowledge-base. There are a variety of reasons why the answer is incorrect ranging from incorrect knowledge to information vagueness to incompleteness. Still, in all these situations, it is typically the case that most of the knowledge in the system is likely to be correct as specified by the expert (s) and/or knowledge engineer (s). In this paper, we propose a method to identify the possible changes by understanding the contribution of parameters on the outputs of concern. Our approach is based on Bayesian Knowledge Bases for modeling uncertainties. We start with single parameter changes and then extend to multiple parameters. In order to identify the optimal solution that can minimize the change to the model as specified by the domain experts, we define and evaluate the sensitivity values of the results with respect to the parameters. We discuss the computational complexities of determining the solution and show that the problem of multiple parameters changes can be transformed into Linear Programming problems, and thus, efficiently solvable. Our work can also be applied towards validating the knowledge base such that the updated model can satisfy all test-cases collected from the domain experts.     

Synthesis of 7-Alkoxyquinolines,Coumarins, and Resorufins

Synthesis of the title compounds by treatment of the sodium salts of 7-quinolinol, 7-hydroxycoumarin, and resorufin with alkyl halides is described.     

Addendum to: Capillary Floating and The Billiard Ball Problem

We compare the results of our earlier paper on the floating in neutral equilibrium at arbitrary orientation in the sense of Finn-Young with the literature on its counterpart in the sense of Archimedes. We add a few remarks of personal and social-historical character.     

A universality theorem for ratios of random characteristic polynomials

We consider asymptotics of ratios of random characteristic polynomials associated with orthogonal polynomial ensembles. Under some natural conditions on the measure in the definition of the orthogonal polynomial ensemble we establish a universality limit for these ratios.     

Early Abortion and Personal Ontology

We are beings endowed with “personal capacities”—the capacity for reason, for a concept of self, perhaps more. Among ontologically salient views about what else we are, I focus on the “Big Three.” According to animalism, we are animals that have psychological properties only contingently. According to psychologistic materialism, we are material beings; according to substance dualism, we are either immaterial beings or composites of immaterial and material ones; but according to both psychologistic materialism and substance dualism, we essentially have some psychological properties. I argue that—contrary to what has been argued and is natural to think—none of the Big Three yields different assignments of moral status to early fetuses from any of the others, and consequently the moral status of early abortion doesn’t depend on which (if any) of these views of personal ontology is correct.