Quasichemical theory and the description of associating fluids relative to a reference: Multiple bonding of a single site solute

We derive an expression for the chemical potential of an associating solute in a solvent relative to the value in a reference fluid using the quasichemical organization of the potential distribution theorem. The fraction of times the solute is not associated with the solvent, the monomer fraction, is expressed in terms of (a) the statistics of occupancy of the solvent around the solute in the reference fluid and (b) the Widom factors that arise because of turning on solute-solvent association. Assuming pair-additivity, we expand the Widom factor into a product of Mayer f-functions and the resulting expression is rearranged to reveal a form of the monomer fraction that is analogous to that used within the statistical associating fluid theory (SAFT). The present formulation avoids all graph-theoretic arguments and provides a fresh, more intuitive, perspective on Wertheim's theory and SAFT. Importantly, multi-body effects are transparently incorporated into the very foundations of the theory. We illustrate the generality of the present approach by considering examples of multiple solvent association to a colloid solute with bonding domains that range from a small patch on the sphere, a Janus particle, and a solute whose entire surface is available for association

Mini-grand canonical ensemble: chemical potential in the solvation shell

Quantifying the statistics of occupancy of solvent molecules in the vicinity of solutes is central to our understanding of solvation phenomena. Number fluctuations in small `solvation shells' around solutes cannot be described within the macroscopic grand canonical framework using a single chemical potential that represents the solvent `bath'. In this communication, we hypothesize that molecular-sized observation volumes such as solvation shells are best described by coupling the solvation shell with a mixture of particle baths each with its own chemical potential. We confirm our hypotheses by studying the enhanced fluctuations in the occupancy statistics of hard sphere solvent particles around a distinguished hard sphere solute particle. Connections with established theories of solvation are also discussed

On the number of matroids

We consider the problem of determining $m_n$, the number of matroids on $n$ elements. The best known lower bound on $m_n$ is due to Knuth (1974) who showed that $\log \log m_n$ is at least $n-3/2\log n-1$. On the other hand, Piff (1973) showed that $\log\log m_n\leq n-\log n+\log\log n +O(1)$, and it has been conjectured since that the right answer is perhaps closer to Knuth's bound. We show that this is indeed the case, and prove an upper bound on $\log\log m_n$ that is within an additive $1+o(1)$ term of Knuth's lower bound. Our proof is based on using some structural properties of non-bases in a matroid together with some properties of independent sets in the Johnson graph to give a compressed representation of matroids.Comment: Final version, 17 page

An entropy argument for counting matroids

We show how a direct application of Shearers' Lemma gives an almost optimum bound on the number of matroids on $n$ elements.Comment: Short note, 4 page

Pion-less effective field theory for atomic nuclei and lattice nuclei

We compute the medium-mass nuclei $^{16}$O and $^{40}$Ca using pionless effective field theory (EFT) at next-to-leading order (NLO). The low-energy coefficients of the EFT Hamiltonian are adjusted to experimantal data for nuclei with mass numbers $A=2$ and $3$, or alternatively to results from lattice quantum chromodynamics (QCD) at an unphysical pion mass of 806 MeV. The EFT is implemented through a discrete variable representation in the harmonic oscillator basis. This approach ensures rapid convergence with respect to the size of the model space and facilitates the computation of medium-mass nuclei. At NLO the nuclei $^{16}$O and $^{40}$Ca are bound with respect to decay into alpha particles. Binding energies per nucleon are 9-10 MeV and 30-40 MeV at pion masses of 140 MeV and 806 MeV, respectively.Comment: 26 page

On the Mixtures of Weibull and Pareto (IV) Distribution: An Alternative to Pareto Distribution

Finite mixture models have provided a reasonable tool to model various types of observed phenomena, specially those which are random in nature. In this article, a finite mixture of Weibull and Pareto (IV) distribution is considered and studied. Some structural properties of the resulting model are discussed including estimation of the model parameters via expectation maximization (EM) algorithm. A real-life data application exhibits the fact that in certain situations, this mixture model might be a better alternative than the rival popular models

System Support for Bandwidth Management and Content Adaptation in Internet Applications

This paper describes the implementation and evaluation of an operating system module, the Congestion Manager (CM), which provides integrated network flow management and exports a convenient programming interface that allows applications to be notified of, and adapt to, changing network conditions. We describe the API by which applications interface with the CM, and the architectural considerations that factored into the design. To evaluate the architecture and API, we describe our implementations of TCP; a streaming layered audio/video application; and an interactive audio application using the CM, and show that they achieve adaptive behavior without incurring much end-system overhead. All flows including TCP benefit from the sharing of congestion information, and applications are able to incorporate new functionality such as congestion control and adaptive behavior.Comment: 14 pages, appeared in OSDI 200