Hierarchical pinning models, quadratic maps and quenched disorder

We consider a hierarchical model of polymer pinning in presence of quenched disorder, introduced by B. Derrida, V. Hakim and J. Vannimenius in 1992, which can be re-interpreted as an infinite dimensional dynamical system with random initial condition (the disorder). It is defined through a recurrence relation for the law of a random variable {R_n}_{n=1,2,...}, which in absence of disorder (i.e., when the initial condition is degenerate) reduces to a particular case of the well-known Logistic Map. The large-n limit of the sequence of random variables 2^{-n} log R_n, a non-random quantity which is naturally interpreted as a free energy, plays a central role in our analysis. The model depends on a parameter alpha>0, related to the geometry of the hierarchical lattice, and has a phase transition in the sense that the free energy is positive if the expectation of R_0 is larger than a certain threshold value, and it is zero otherwise. It was conjectured by Derrida et al. (1992) that disorder is relevant (respectively, irrelevant or marginally relevant) if 1/2<alpha<1 (respectively, alpha<1/2 or alpha=1/2), in the sense that an arbitrarily small amount of randomness in the initial condition modifies the critical point with respect to that of the pure (i.e., non-disordered) model if alpha is larger or equal to 1/2, but not if alpha is smaller than 1/2. Our main result is a proof of these conjectures for the case alpha different from 1/2. We emphasize that for alpha>1/2 we find the correct scaling form (for weak disorder) of the critical point shift.Comment: 26 pages, 2 figures. v3: Theorem 1.6 improved. To appear on Probab. Theory Rel. Field

Phase Segregation Dynamics in Particle Systems with Long Range Interactions I: Macroscopic Limits

We present and discuss the derivation of a nonlinear non-local integro-differential equation for the macroscopic time evolution of the conserved order parameter of a binary alloy undergoing phase segregation. Our model is a d-dimensional lattice gas evolving via Kawasaki exchange dynamics, i.e. a (Poisson) nearest-neighbor exchange process, reversible with respect to the Gibbs measure for a Hamiltonian which includes both short range (local) and long range (nonlocal) interactions. A rigorous derivation is presented in the case in which there is no local interaction. In a subsequent paper (part II), we discuss the phase segregation phenomena in the model. In particular we argue that the phase boundary evolutions, arising as sharp interface limits of the family of equations derived in this paper, are the same as the ones obtained from the corresponding limits for the Cahn-Hilliard equation.Comment: amstex with macros (included in the file), tex twice, 20 page

Fluctuations for the Ginzburg-Landau ∇ϕ\nabla \phi Interface Model on a Bounded Domain

We study the massless field on $D_n = D \cap \tfrac{1}{n} \Z^2$, where $D \subseteq \R^2$ is a bounded domain with smooth boundary, with Hamiltonian \CH(h) = \sum_{x \sim y} \CV(h(x) - h(y)). The interaction \CV is assumed to be symmetric and uniformly convex. This is a general model for a $(2+1)$-dimensional effective interface where $h$ represents the height. We take our boundary conditions to be a continuous perturbation of a macroscopic tilt: $h(x) = n x \cdot u + f(x)$ for $x \in \partial D_n$, $u \in \R^2$, and $f \colon \R^2 \to \R$ continuous. We prove that the fluctuations of linear functionals of $h(x)$ about the tilt converge in the limit to a Gaussian free field on $D$, the standard Gaussian with respect to the weighted Dirichlet inner product $(f,g)_\nabla^\beta = \int_D \sum_i \beta_i \partial_i f_i \partial_i g_i$ for some explicit $\beta = \beta(u)$. In a subsequent article, we will employ the tools developed here to resolve a conjecture of Sheffield that the zero contour lines of $h$ are asymptotically described by $SLE(4)$, a conformally invariant random curve.Comment: 58 page

Oral peptide vaccine against hookworm infection: correlation of antibody titers with protective efficacy

Approximately 0.4 billion individuals worldwide are infected with hookworm. An effective vaccine is needed to not only improve the health of those affected and at high risk, but also to improve economic growth in disease-endemic areas. An ideal anti-hookworm therapeutic strategy for mass administration is a stable and orally administered vaccine. Oral vaccines are advantageous as they negate the need for trained medical staff for administration and do not require strict sterility conditions. Vaccination, therefore, can be carried out at a significantly reduced cost. One of the most promising current antigenic targets for hookworm vaccine development is the aspartic protease digestive enzyme (APR-1). Antibody-mediated neutralization of APR-1 deprives the worm of nourishment, leading to reduced worm burdens in vaccinated hosts. Previously, we demonstrated that, when incorporated into vaccine delivery systems, the APR-1-derived p3 epitope (TSLIAGPKAQVEAIQKYIGAEL) was able to greatly reduce worm burdens (≥90%) in BALB/c mice; however, multiple, large doses of the vaccine were required. Here, we investigated a variety of p3-antigen conjugates to optimize antigen delivery and establish immune response/protective efficacy relationships. We synthesized, purified, and characterized four p3 peptide-based vaccine candidates with: (a) lipidic (lipid core peptide (LCP)); (b) classical polymeric (polymethylacrylate (PMA)); and (c) novel polymeric (polyleucine in a branched or linear arrangement, BL10 or LL10, respectively) groups as self-adjuvanting moieties. BL10 and LL10 induced the highest serum anti-p3 and anti-APR-1 IgG titers. Upon challenge with rodent hookworms, the highest significant reduction in worm burden was observed in mice immunized with LL10 . APR-1-specific serum IgG titers correlated with worm burden reduction. Thus, we provide the first vaccine-triggered immune response-protection relationship for hookworm infection

Longtime behavior of nonlocal Cahn-Hilliard equations

Here we consider the nonlocal Cahn-Hilliard equation with constant mobility in a bounded domain. We prove that the associated dynamical system has an exponential attractor, provided that the potential is regular. In order to do that a crucial step is showing the eventual boundedness of the order parameter uniformly with respect to the initial datum. This is obtained through an Alikakos-Moser type argument. We establish a similar result for the viscous nonlocal Cahn-Hilliard equation with singular (e.g., logarithmic) potential. In this case the validity of the so-called separation property is crucial. We also discuss the convergence of a solution to a single stationary state. The separation property in the nonviscous case is known to hold when the mobility degenerates at the pure phases in a proper way and the potential is of logarithmic type. Thus, the existence of an exponential attractor can be proven in this case as well

Theory of Thermodynamic Stresses in Colloidal Dispersions at the Glass Transition

We discuss the nonlinear rheology of dense colloidal dispersions at the glass transition. A first principles approach starting with interacting Brownian particles in given arbitrary homogeneous (incompressible) flow neglecting hydrodynamic interactions is sketched. It e.g. explains steady state flow curves for finite shear rates measured in dense suspensions of thermosensitive core-shell particles consisting of a polystyrene core and a crosslinked poly(N-isopropylacrylamide)(PNIPAM) shell. The exponents of simple and generalized Herschel Bulkley laws are computed for hard spheres.Comment: 3 pages, 1 figure; contribution to The XVth International Congress on Rheology, August 3-8, 2008, Monterey, California; submitted to J. Rheo

On the nonequilibrium entropy of large and small systems

Thermodynamics makes definite predictions about the thermal behavior of macroscopic systems in and out of equilibrium. Statistical mechanics aims to derive this behavior from the dynamics and statistics of the atoms and molecules making up these systems. A key element in this derivation is the large number of microscopic degrees of freedom of macroscopic systems. Therefore, the extension of thermodynamic concepts, such as entropy, to small (nano) systems raises many questions. Here we shall reexamine various definitions of entropy for nonequilibrium systems, large and small. These include thermodynamic (hydrodynamic), Boltzmann, and Gibbs-Shannon entropies. We shall argue that, despite its common use, the last is not an appropriate physical entropy for such systems, either isolated or in contact with thermal reservoirs: physical entropies should depend on the microstate of the system, not on a subjective probability distribution. To square this point of view with experimental results of Bechhoefer we shall argue that the Gibbs-Shannon entropy of a nano particle in a thermal fluid should be interpreted as the Boltzmann entropy of a dilute gas of Brownian particles in the fluid

Spinodal Decomposition in Binary Gases

We carried out three-dimensional simulations, with about 1.4 million particles, of phase segregation in a low density binary fluid mixture, described mesoscopically by energy and momentum conserving Boltzmann-Vlasov equations. Using a combination of Direct Simulation Monte Carlo(DSMC) for the short range collisions and a version of Particle-In-Cell(PIC) evolution for the smooth long range interaction, we found dynamical scaling after the ratio of the interface thickness(whose shape is described approximately by a hyperbolic tangent profile) to the domain size is less than ~0.1. The scaling length R(t) grows at late times like t^alpha, with alpha=1 for critical quenches and alpha=1/3 for off-critical ones. We also measured the variation of temperature, total particle density and hydrodynamic velocity during the segregation process.Comment: 11 pages, Revtex, 4 Postscript figures, submitted to PR

Descrição Metodológica do Mapeamento das Instituições de Longa-Permanência para Idosos no Brasil

Aim: describe the methodological approach adopted to build a Brazilian database of LCTFs in the country. Methods: This exploratory research was conducted between August 2020 and 2021 based on primarily publicly accessible data. First, the database of the Sistema Único de Assistência Social for 2019 was adopted as the primary source of information. In addition, public agencies and managers were consulted and invited to share their databases. Likewise, researchers and private entities also collaborated by making their spreadsheets available. The information collected was placed in individual spreadsheets for each Brazilian state. LTCFs not catering to older adults (aged 60 and over) were excluded. Duplicate data were excluded when overlaps were identified for each new aggregated source. Results &amp; Discussion: This brief communication describes the methodology adopted for mapping the current status of Brazilian LTCFs. Despite its caveats, this study represents an important advance in the identification, characterization, and monitoring of these services nationwide. A total of 5769 facilities were found in the 2019 SUAS census. After excluding facilities not caring for residents aged 60 or over, this total decreased to 2381 LTCFs. Consolidating and filtering the information from multiple data sources led to the identification of 7029 LTCFs for the country as a whole

A qualitative study of stakeholders' perspectives on the social network service environment

Over two billion people are using the Internet at present, assisted by the mediating activities of software agents which deal with the diversity and complexity of information. There are, however, ethical issues due to the monitoring-and-surveillance, data mining and autonomous nature of software agents. Considering the context, this study aims to comprehend stakeholders' perspectives on the social network service environment in order to identify the main considerations for the design of software agents in social network services in the near future. Twenty-one stakeholders, belonging to three key stakeholder groups, were recruited using a purposive sampling strategy for unstandardised semi-structured e-mail interviews. The interview data were analysed using a qualitative content analysis method. It was possible to identify three main considerations for the design of software agents in social network services, which were classified into the following categories: comprehensive understanding of users' perception of privacy, user type recognition algorithms for software agent development and existing software agents enhancement