Fractionation effects in phase equilibria of polydisperse hard sphere colloids

The equilibrium phase behaviour of hard spheres with size polydispersity is studied theoretically. We solve numerically the exact phase equilibrium equations that result from accurate free energy expressions for the fluid and solid phases, while accounting fully for size fractionation between coexisting phases. Fluids up to the largest polydispersities that we can study (around 14%) can phase separate by splitting off a solid with a much narrower size distribution. This shows that experimentally observed terminal polydispersities above which phase separation no longer occurs must be due to non-equilibrium effects. We find no evidence of re-entrant melting; instead, sufficiently compressed solids phase separate into two or more solid phases. Under appropriate conditions, coexistence of multiple solids with a fluid phase is also predicted. The solids have smaller polydispersities than the parent phase as expected, while the reverse is true for the fluid phase, which contains predominantly smaller particles but also residual amounts of the larger ones. The properties of the coexisting phases are studied in detail; mean diameter, polydispersity and volume fraction of the phases all reveal marked fractionation. We also propose a method for constructing quantities that optimally distinguish between the coexisting phases, using Principal Component Analysis in the space of density distributions. We conclude by comparing our predictions to perturbative theories for near-monodisperse systems and to Monte Carlo simulations at imposed chemical potential distribution, and find excellent agreement.Comment: 21 pages, 23 figures, 2 table

A recurrent neural network with ever changing synapses

A recurrent neural network with noisy input is studied analytically, on the basis of a Discrete Time Master Equation. The latter is derived from a biologically realizable learning rule for the weights of the connections. In a numerical study it is found that the fixed points of the dynamics of the net are time dependent, implying that the representation in the brain of a fixed piece of information (e.g., a word to be recognized) is not fixed in time.Comment: 17 pages, LaTeX, 4 figure

Derivation of Hebb's rule

On the basis of the general form for the energy needed to adapt the connection strengths of a network in which learning takes place, a local learning rule is found for the changes of the weights. This biologically realizable learning rule turns out to comply with Hebb's neuro-physiological postulate, but is not of the form of any of the learning rules proposed in the literature. It is shown that, if a finite set of the same patterns is presented over and over again to the network, the weights of the synapses converge to finite values. Furthermore, it is proved that the final values found in this biologically realizable limit are the same as those found via a mathematical approach to the problem of finding the weights of a partially connected neural network that can store a collection of patterns. The mathematical solution is obtained via a modified version of the so-called method of the pseudo-inverse, and has the inverse of a reduced correlation matrix, rather than the usual correlation matrix, as its basic ingredient. Thus, a biological network might realize the final results of the mathematician by the energetically economic rule for the adaption of the synapses found in this article.Comment: 29 pages, LaTeX, 3 figure

Phase separation in mixtures of colloids and long ideal polymer coils

Colloidal suspensions with free polymer coils which are larger than the colloidal particles are considered. The polymer-colloid interaction is modeled by an extension of the Asakura-Oosawa model. Phase separation occurs into dilute and dense fluid phases of colloidal particles when polymer is added. The critical density of this transition tends to zero as the size of the polymer coils diverges.Comment: 5 pages, 3 figure

Validation of a New Predictive Risk Model: Measuring the Impact of the Major Modifiable Risks of Death for Patients and Populations

Background: Modifiable risks account for a large fraction of disease and death, but clinicians and patients lack tools to identify high risk populations or compare the possible benefit of different interventions. Methods: We used data on the distribution of exposure to 12 major behavioral and biometric risk factors inthe US population, mortality rates by cause, and estimates of the proportional hazards of risk factor exposure from published systematic reviews to develop a risk prediction model that estimates an adult\u27s 10 year mortality risk compared to a population with optimum risk factors. We compared predicted risk to observed mortality in 8,241 respondents in NHANES 1988-1994 and NHANES 1999-2004 with linked mortality data up to the end of 2006

Concept for a Large Scalable Space Telescope: In-Space Assembly

We present a conceptual design for a scalable (10-50 meter segmented filled-aperture) space observatory operating at UV-optical-near infrared wavelengths. This telescope is designed for assembly in space by robots, astronauts or a combination of the two, as envisioned in NASA s Vision for Space Exploration. Our operations concept for this-space telescope provides for assembly and check-out in an Earth Moon L2 (EML2) orbit, and transport to a Sun-Earth L2 (SEL2) orbit for science operations and routine servicing, with return to EML2 for major servicing. We have developed and analyzed initial designs for the optical, structural, thermal and attitude control systems for a 30-m aperture space telescope. We further describe how the separate components are packaged for launch by heavy lift vehicle(s) and the approach for the robot assembly of the telescope from these components

Stream Microbial Communities Show Resistance to Pharmaceutical Exposure

Residues of pharmaceuticals are increasingly detected in surface waters throughout the world. In four streams in Baltimore, Maryland, USA, we detected analgesics, stimulants, antihistamines, and antibiotics using passive organic samplers. We exposed biofilm communities in these streams to the common drugs caffeine, cimetidine, ciprofloxacin, and diphenhydramine. Respiration rates in the least urban stream were suppressed when exposed to these drugs, but biofilm functioning in the most urban stream was resistant to drug exposure. Exposure to the antibiotic ciprofloxacin altered bacterial community composition at all sites, with the greatest change occurring in the most urban stream. These results indicated that continuous exposure to drugs in urban streams may select for sub‐populations of highly resistant bacteria that maintain community function in response to urban contaminants

Urban stream microbial communities show resistance to pharmaceutical exposure

Residues of pharmaceuticals are increasingly detected in surface waters throughout the world. In four streams in Baltimore, Maryland, USA, we detected analgesics, stimulants, antihistamines, and antibiotics using passive organic samplers. We exposed biofilm communities in these streams to the common drugs caffeine, cimetidine, ciprofloxacin, and diphenhydramine. Respiration rates in the least urban stream were suppressed when exposed to these drugs, but biofilm functioning in the most urban stream was resistant to drug exposure. Exposure to the antibiotic ciprofloxacin altered bacterial community composition at all sites, with the greatest change occurring in the most urban stream. These results indicated that continuous exposure to drugs in urban streams may select for sub-populations of highly resistant bacteria that maintain community function in response to urban contaminants

Mode-coupling theory for multiple-time correlation functions of tagged particle densities and dynamical filters designed for glassy systems

The theoretical framework for higher-order correlation functions involving multiple times and multiple points in a classical, many-body system developed by Van Zon and Schofield [Phys. Rev. E 65, 011106 (2002)] is extended here to include tagged particle densities. Such densities have found an intriguing application as proposed measures of dynamical heterogeneities in structural glasses. The theoretical formalism is based upon projection operator techniques which are used to isolate the slow time evolution of dynamical variables by expanding the slowly-evolving component of arbitrary variables in an infinite basis composed of the products of slow variables of the system. The resulting formally exact mode-coupling expressions for multiple-point and multiple-time correlation functions are made tractable by applying the so-called N-ordering method. This theory is used to derive for moderate densities the leading mode coupling expressions for indicators of relaxation type and domain relaxation, which use dynamical filters that lead to multiple-time correlations of a tagged particle density. The mode coupling expressions for higher order correlation functions are also succesfully tested against simulations of a hard sphere fluid at relatively low density.Comment: 15 pages, 2 figure