Rheology of gelling polymers in the Zimm model

In order to study rheological properties of gelling systems in dilute solution, we investigate the viscosity and the normal stresses in the Zimm model for randomly crosslinked monomers. The distribution of cluster topologies and sizes is assumed to be given either by Erd\H os-R\'enyi random graphs or three-dimensional bond percolation. Within this model the critical behaviour of the viscosity and of the first normal stress coefficient is determined by the power-law scaling of their averages over clusters of a given size $n$ with $n$. We investigate these Mark--Houwink like scaling relations numerically and conclude that the scaling exponents are independent of the hydrodynamic interaction strength. The numerically determined exponents agree well with experimental data for branched polymers. However, we show that this traditional model of polymer physics is not able to yield a critical divergence at the gel point of the viscosity for a polydisperse dilute solution of gelation clusters. A generally accepted scaling relation for the Zimm exponent of the viscosity is thereby disproved.Comment: 9 pages, 2 figure

Relating optical and microwave grain metrics of snow: the relevance of grain shape

Grain shape is commonly understood as a morphological characteristic of snow that is independent of the optical diameter (or specific surface area) influencing its physical properties. In this study we use tomography images to investigate two objectively defined metrics of grain shape that naturally extend the characterization of snow in terms of the optical diameter. One is the curvature length <i>λ</i>₂, related to the third-order term in the expansion of the two-point correlation function, and the other is the second moment <i>μ</i>₂ of the chord length distributions. We show that the exponential correlation length, widely used for microwave modeling, can be related to the optical diameter and <i>λ</i>₂. Likewise, we show that the absorption enhancement parameter <i>B</i> and the asymmetry factor <i>g</i>^G, required for optical modeling, can be related to the optical diameter and <i>μ</i>₂. We establish various statistical relations between all size metrics obtained from the two-point correlation function and the chord length distribution. Overall our results suggest that the characterization of grain shape via <i>λ</i>₂ or <i>μ</i>₂ is virtually equivalent since both capture similar aspects of size dispersity. Our results provide a common ground for the different grain metrics required for optical and microwave modeling of snow

Anomalous stress relaxation in random macromolecular networks

Within the framework of a simple Rouse-type model we present exact analytical results for dynamical critical behaviour on the sol side of the gelation transition. The stress-relaxation function is shown to exhibit a stretched-exponential long-time decay. The divergence of the static shear viscosity is governed by the critical exponent $k=\phi -\beta$, where $\phi$ is the (first) crossover exponent of random resistor networks, and $\beta$ is the critical exponent for the gel fraction. We also derive new results on the behaviour of normal stress coefficients.Comment: 13 pages, 6 figures; contribution to the proceedings of the Minerva International Workshop on Frontiers In The Physics Of Complex Systems (25-28 March 2001) - to appear in a special issue of Physica

Comparison of elastic moduli from seismic diving-wave and ice-core microstructure analysis in Antarctic polar firn

We compared elastic moduli in polar firn derived from diving wave refraction seismic velocity analysis, firn-core density measurements and microstructure modelling based on firn-core data. The seismic data were obtained with a small electrodynamic vibrator source near Kohnen Station, East Antarctica. The analysis of diving waves resulted in velocity–depth profiles for different wave types (P-, SH- and SV-waves). Dynamic elastic moduli of firn were derived by combining P- and S-wave velocities and densities obtained from firn-core measurements. The structural finite-element method (FEM) was used to calculate the components of the elastic tensor from firn microstructure derived from X-ray tomography of firn-core samples at depths of 10, 42, 71 and 99 m, providing static elastic moduli. Shear and bulk moduli range from 0.39 to 2.42 GPa and 0.68 to 2.42 GPa, respectively. The elastic moduli from seismic observations and the structural FEM agree within 8.5% for the deepest achieved values at a depth of 71 m, and are within the uncertainty range. Our observations demonstrate that the elastic moduli of the firn can be consistently obtained from two independent methods which are based on dynamic (seismic) and static (tomography and FEM) observations, respectively, for deeper layers in the firn below ∼10 m depth

Comparison of elastic moduli from seismic diving-wave and ice-core microstructure analysis in Antarctic polar firn

The densification of firn depends on the elastic properties of firn, processes which are still not fully explained by the usual models. Geophysical methods provide spatially distributed data, while the analysis of firn cores is restricted to finite locations, but with a different vertical resolution. In this study, we compared elastic moduli in polar firn derived from refraction seismic velocity analysis and vertical density profiles from the firn-core measurements to elastic properties derived from microstructure modelling based on firn-core data. The seismic data were obtained with a small electrodynamic vibrator source (ElViS) near Kohnen Station, East Antarctica. The analysis of divingwaves resulted in velocity–depth profiles for P-, SH- and SV-wave velocities. Elastic moduli of firn were derived by combining P- and S-wave velocities and densities obtained from firn-core measurements. P-wave velocities derived from diving-wave analysis range from 2060 m s−1at 10 m depth to 3400 m s−1at 70 m depth, S-wave velocities from 1250 m s−1 to 1700 m s−1, respectively. The structural finite-element method (FEM) was used to calculate the components of the elastic tensor from firn microstructure derivedfrom X-ray tomography of firn-core samples at depths of 10, 42, 71 and 99 m. Shear and bulk moduli range from 0.39 GPa to 2.42 GPa and 0.68 GPa to 2.42 GPa, respectively. The elastic moduli from seismic observations and the structural FEM agree within 8.5% for the values derived at a depth of 71 m, and are within the uncertainty range. Our study demonstrates that elastic moduli of firn can be consistently obtained from two independent methods, which are based on dynamic (seismic) and static (tomography and FEM) observations, respectively. The agreement of the results for both methods indicates that elastic properties in firn can be acquired as spatially distributed data with the seismic approach, supported by local density information. Thus, information about elastic properties can be derived over larger lateral distances than would be possible with the static method. This enables the analysis of the firn and conclusions of the densification models might be drawn from observations of spatial and temporal changes in elastic properties

Dynamics of gelling liquids: a short survey

The dynamics of randomly crosslinked liquids is addressed via a Rouse- and a Zimm-type model with crosslink statistics taken either from bond percolation or Erdoes-Renyi random graphs. While the Rouse-type model isolates the effects of the random connectivity on the dynamics of molecular clusters, the Zimm-type model also accounts for hydrodynamic interactions on a preaveraged level. The incoherent intermediate scattering function is computed in thermal equilibrium, its critical behaviour near the sol-gel transition is analysed and related to the scaling of cluster diffusion constants at the critical point. Second, non-equilibrium dynamics is studied by looking at stress relaxation in a simple shear flow. Anomalous stress relaxation and critical rheological properties are derived. Some of the results contradict long-standing scaling arguments, which are shown to be flawed by inconsistencies.Comment: 21 pages, 3 figures; Dedicated to Lothar Schaefer on the occasion of his 60th birthday; Changes: added comments on the gel phase and some reference

Multi-tracer study of gas trapping in an East Antarctic ice core

We study a firn and ice core drilled at the new "Lock-In" site in East Antarctica, located 136 km away from Concordia station towards Durmont d'Urville. High resolution chemical and physical measurements were performed on the core, with a particular focus on the trapping zone of the firn where air bubbles are formed. We measured the air content in the ice, closed and open porous volumes in the firn, firn density, firn liquid conductivity and major ion concentrations, as well as methane concentrations in the ice. The closed and open porosity volumes of firn samples were obtained by the two independent methods of pycnometry and tomography, that yield similar results. The measured increase of the closed porosity with density is used to estimate the air content trapped in the ice with the aid of a simple gas trapping model. Results show a discrepancy, with the model trapping too much air. Experimental errors have been considered but do not explain the discrepancy between the model and the observations. The model and data can be reconciled with the introduction of a reduced compression of the closed porosity compared to the open porosity. Yet, it is not clear if this limited compression of closed pores is the actual mechanism responsible for the low amount of air in the ice. High resolution density measurements reveal the presence of a strong layering, manifesting itself as centimeter scale variations. Despite this heterogeneous stratification, all layers, including the ones that are especially dense or less dense compared to their surroundings, display similar pore morphology and closed porosity as function of density. This implies that all layers close in a similar way, even though some close in advance or later compared to the bulk firn. Investigation of the chemistry data suggests that in the trapping zone, the observed stratification is partly related to the presence of chemical impurities

The ANTOP study: focal psychodynamic psychotherapy, cognitive-behavioural therapy, and treatment-as-usual in outpatients with anorexia nervosa - a randomized controlled trial

<p>Abstract</p> <p>Background</p> <p>Anorexia nervosa is a serious eating disorder leading to high morbidity and mortality as a result of both malnutrition and suicide. The seriousness of the disorder requires extensive knowledge of effective treatment options. However, evidence for treatment efficacy in this area is remarkably weak. A recent Cochrane review states that there is an urgent need for large, well-designed treatment studies for patients with anorexia nervosa. The aim of this particular multi-centre study is to evaluate the efficacy of two standardized outpatient treatments for patients with anorexia nervosa: focal psychodynamic (FPT) and cognitive behavioural therapy (CBT). Each therapeutic approach is compared to a "treatment-as-usual" control group.</p> <p>Methods/Design</p> <p>237 patients meeting eligibility criteria are randomly and evenly assigned to the three groups – two intervention groups (CBT and FPT) and one control group. The treatment period for each intervention group is 10 months, consisting of 40 sessions respectively. Body weight, eating disorder related symptoms, and variables of therapeutic alliance are measured during the course of treatment. Psychotherapy sessions are audiotaped for adherence monitoring. The treatment in the control group, both the dosage and type of therapy, is not regulated in the study protocol, but rather reflects the current practice of established outpatient care. The primary outcome measure is the body mass index (BMI) at the end of the treatment (10 months after randomization).</p> <p>Discussion</p> <p>The study design surmounts the disadvantages of previous studies in that it provides a randomized controlled design, a large sample size, adequate inclusion criteria, an adequate treatment protocol, and a clear separation of the treatment conditions in order to avoid contamination. Nevertheless, the study has to deal with difficulties specific to the psychopathology of anorexia nervosa. The treatment protocol allows for dealing with the typically occurring medical complications without dropping patients from the protocol. However, because patients are difficult to recruit and often ambivalent about treatment, a drop-out rate of 30% is assumed for sample size calculation. Due to the ethical problem of denying active treatment to patients with anorexia nervosa, the control group is defined as "treatment-as-usual".</p> <p>Trial registration</p> <p>Current Controlled Trials ISRCTN72809357</p