Condensation Transition in Polydisperse Hard Rods

We study a mass transport model, where spherical particles diffusing on a ring can stochastically exchange volume $v$, with the constraint of a fixed total volume $V=\sum_{i=1}^N v_i$, $N$ being the total number of particles. The particles, referred to as $p$-spheres, have a linear size that behaves as $v_i^{1/p}$ and our model thus represents a gas of polydisperse hard rods with variable diameters $v_i^{1/p}$. We show that our model admits a factorized steady state distribution which provides the size distribution that minimizes the free energy of a polydisperse hard rod system, under the constraints of fixed $N$ and $V$. Complementary approaches (explicit construction of the steady state distribution on the one hand ; density functional theory on the other hand) completely and consistently specify the behaviour of the system. A real space condensation transition is shown to take place for $p>1$: beyond a critical density a macroscopic aggregate is formed and coexists with a critical fluid phase. Our work establishes the bridge between stochastic mass transport approaches and the optimal polydispersity of hard sphere fluids studied in previous articles

Making a national atlas of population by computer

This paper describes the conceptual and practical problems encountered and solved in producing a multi-colour atlas of population characteristics in Great Britain. The atlas itself is in A4 format; it consists of some thirty-four maps of Great Britain in four colours and the same number of regional maps, together with descriptive text. All maps were plotted on a laser plotter with a resolution of 127 microns. The paper describes how mapping of ratios, such as percentages, was found to be highly misleading and describes the novel probability mapping solution adopted, based on the signed chi-square statistic. In addition, the rationale for selecting the class intervals and for selecting colour schemes is described

Condensation for a fixed number of independent random variables

A family of m independent identically distributed random variables indexed by a chemical potential \phi\in[0,\gamma] represents piles of particles. As \phi increases to \gamma, the mean number of particles per site converges to a maximal density \rho_c<\infty. The distribution of particles conditioned on the total number of particles equal to n does not depend on \phi (canonical ensemble). For fixed m, as n goes to infinity the canonical ensemble measure behave as follows: removing the site with the maximal number of particles, the distribution of particles in the remaining sites converges to the grand canonical measure with density \rho_c; the remaining particles concentrate (condensate) on a single site.Comment: 6 page

Kinetic pathways of multi-phase surfactant systems

The relaxation following a temperature quench of two-phase (lamellar and sponge phase) and three-phase (lamellar, sponge and micellar phase) samples, has been studied in an SDS/octanol/brine system. In the three-phase case we have observed samples that are initially mainly sponge phase with lamellar and micellar phase on the top and bottom respectively. Upon decreasing temperature most of the volume of the sponge phase is replaced by lamellar phase. During the equilibriation we have observed three regimes of behaviour within the sponge phase: (i) disruption in the sponge texture, then (ii) after the sponge phase homogenises there is a lamellar nucleation regime and finally (iii) a bizarre plume connects the lamellar phase with the micellar phase. The relaxation of the two-phase sample proceeds instead in two stages. First lamellar drops nucleate in the sponge phase forming a onion `gel' structure. Over time the lamellar structure compacts while equilibriating into a two phase lamellar/sponge phase sample. We offer possible explanatioins for some of these observations in the context of a general theory for phase kinetics in systems with one fast and one slow variable.Comment: 1 textfile, 20 figures (jpg), to appear in PR

SLS Materials Development Method for Rapid Manufacturing

As soon as SFF technology development began to make Rapid Prototyping possible the interest in Rapid Manufacturing (RM) began to grow. The advantages in terms of functional integration, elimination of tooling and fixtures and mass customization make a compelling case for RM, leading some in the field to call it the next industrial revolution. Yet without the materials properties necessary to provide the function and variety currently available from mass production methods, the application of RM will remain limited. Developing new materials for the SLS process, one immediate step toward a larger portfolio of RM materials, is very challenging. The formation of high quality SLS parts relies on appropriate powder characteristics, thermal cycles and sintering behavior. Based on a brief examination of the key factors in SLS processing and a research project to develop a new binder material for Silicon Carbide composites, a systematic materials development method is proposed in this paper. The method provides guidance for introducing new SLS materials, support for educating new SLS users and researchers and direction for several future research projects.Mechanical Engineerin

Rapid Manufacturing of Silicon Carbide Composites

From the earliest days of SFF technology development, a viable technique for the direct manufacture of fully-functional parts has been a major technology goal. While direct metal methods have been demonstrated for a variety of metals including aluminum, steel and titanium, they have not reached wide commercial application due to processing speed, final material properties and surface finish. In this paper the development of an SLS-based rapid manufacturing (RM) platform is reviewed. The core of this platform is a thermosetting binder system for preform parts in contrast to the thermoplastic materials currently available for SLS. The preforms may include metal and/or ceramic powders. A variety of fully functional parts can be prepared from different combinations of materials and post processing steps including binder pyrolysis, free-standing alloy infiltration, room temperature polymer infiltration and machining. The main issues of these steps are reviewed followed by a discussion about the support of RM. This paper is an intermediate report additional materials, applications, process models and product design strategies will be incorporated into the project in the next year.Mechanical Engineerin

Validity, reliability, acceptability, and utility of the Social Inclusion Questionnaire User Experience (SInQUE): a clinical tool to facilitate social inclusion amongst people with severe mental health problems.

BACKGROUND: Individuals with severe mental health problems are at risk of social exclusion, which may complicate their recovery. Mental health and social care staff have, until now, had no valid or reliable way of assessing their clients' social inclusion. The Social Inclusion Questionnaire User Experience (SInQUE) was developed to address this. It assesses five domains: social integration; productivity; consumption; access to services; and political engagement, in the year prior to first psychiatric admission (T1) and the year prior to interview (T2) from which a total score at each time point can be calculated. AIMS: To establish the validity, reliability, and acceptability of the SInQUE in individuals with a broad range of psychiatric diagnoses receiving care from community mental health services and its utility for mental health staff. METHOD: Participants were 192 mental health service users with psychosis, personality disorder, or common mental disorder (e.g., depression, anxiety) who completed the SInQUE alongside other validated outcome measures. Test-retest reliability was assessed in a sub-sample of 30 participants and inter-rater reliability was assessed in 11 participants. SInQUE ratings of 28 participants were compared with those of a sibling with no experience of mental illness to account for shared socio-cultural factors. Acceptability and utility of the tool were assessed using completion rates and focus groups with staff. RESULTS: The SInQUE demonstrated acceptable convergent validity. The total score and the Social Integration domain score were strongly correlated with quality of life, both in the full sample and in the three diagnostic groups. Discriminant validity and test-retest reliability were established across all domains, although the test-retest reliability on scores for the Service Access and Political Engagement domains prior to first admission to hospital (T1) was lower than other domains. Inter-rater reliability was excellent for all domains at T1 and T2. CONCLUSIONS: The component of the SInQUE that assesses current social inclusion has good psychometric properties and can be recommended for use by mental health staff

Kinetics of viral self-assembly: the role of ss RNA antenna

A big class of viruses self-assemble from a large number of identical capsid proteins with long flexible N-terminal tails and ss RNA. We study the role of the strong Coulomb interaction of positive N-terminal tails with ss RNA in the kinetics of the in vitro virus self-assembly. Capsid proteins stick to unassembled chain of ss RNA (which we call "antenna") and slide on it towards the assembly site. We show that at excess of capsid proteins such one-dimensional diffusion accelerates self-assembly more than ten times. On the other hand at excess of ss RNA, antenna slows self-assembly down. Several experiments are proposed to verify the role of ss RNA antenna.Comment: 4 pages, 3 figures, several experiments are proposed, a new idea of experiment is adde

The VLT-FLAMES survey of massive stars: rotation and nitrogen enrichment as the key to understanding massive star evolution

Rotation has become an important element in evolutionary models of massive stars, specifically via the prediction of rotational mixing. Here, we study a sample of stars, including rapid rotators, to constrain such models and use nitrogen enrichments as a probe of the mixing process. Chemical compositions (C, N, O, Mg and Si) have been estimated for 135 early B-type stars in the Large Magellanic Cloud with projected rotational velocities up to ~300km/s using a non-LTE TLUSTY model atmosphere grid. Evolutionary models, including rotational mixing, have been generated attempting to reproduce these observations by adjusting the overshooting and rotational mixing parameters and produce reasonable agreement with 60% of our core hydrogen burning sample. We find (excluding known binaries) a significant population of highly nitrogen enriched intrinsic slow rotators vsini less than 50km/s incompatible with our models ~20% of the sample). Furthermore, while we find fast rotators with enrichments in agreement with the models, the observation of evolved (log g less than 3.7dex) fast rotators that are relatively unenriched (a further ~20% of the sample) challenges the concept of rotational mixing. We also find that 70% of our blue supergiant sample cannot have evolved directly from the hydrogen burning main-sequence. We are left with a picture where invoking binarity and perhaps fossil magnetic fields are required to understand the surface properties of a population of massive main sequence stars.Comment: ApJL. 10 pages, 1 figure. Updated to match accepted versio