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

Moderate deviations for random field Curie-Weiss models

The random field Curie-Weiss model is derived from the classical Curie-Weiss model by replacing the deterministic global magnetic field by random local magnetic fields. This opens up a new and interestingly rich phase structure. In this setting, we derive moderate deviations principles for the random total magnetization $S_n$, which is the partial sum of (dependent) spins. A typical result is that under appropriate assumptions on the distribution of the local external fields there exist a real number $m$, a positive real number $\lambda$, and a positive integer $k$ such that $(S_n-nm)/n^{\alpha}$ satisfies a moderate deviations principle with speed $n^{1-2k(1-\alpha)}$ and rate function $\lambda x^{2k}/(2k)!$, where $1-1/(2(2k-1)) < \alpha < 1$.Comment: 21 page

The educator’s role in Higher Education: position papers from a project of the Special Interest Group Higher Education of the Worshipful Company of Educators

The Company of Educators was set up in the year 2017 and currently has over thirty members who are Freemen and Liverymen of the company interested in Higher Education, Higher Education policy, research, and research training. Topics of interest include educational methods and concepts for universities, training of doctoral students, training of skills relevant for higher education; mentoring and career development of junior academics. The group is chaired by Benedikt Löwe. So far, the SIGHE had two meetings, one at Christ's College, Cambridge, on 3 November 2017 and one at New College, Oxford, on 20 January 2018. During these meetings, SIGHE decided on a number of projects that would define and inform the discussion of the members of the group. The first project, entitled The educator’s role in Higher Education: What distinguishes it from other educational sectors?, is coordinated by James Crabbe and Max Weaver. The two coordinators have produced two position papers that constitute this document. The position papers are to be seen as personal statements of their respective authors rather than a description of the position of the SIGHE, let alone the company. They are supposed to provoke useful reflection and discussion. The authors of the papers encourage readers to contact them directly and discuss the content of the papers

Functional somatic disorders: discussion paper for a new common classification for research and clinical use

Background Functional somatic symptoms and disorders are common and complex phenomena involving both bodily and brain processes. They pose major challenges across medical specialties. These disorders are common and have significant impacts on patients’ quality of life and healthcare costs. Main body We outline five problems pointing to the need for a new classification: (1) developments in understanding aetiological mechanisms; (2) the current division of disorders according to the treating specialist; (3) failure of current classifications to cover the variety of disorders and their severity (for example, patients with symptoms from multiple organs systems); (4) the need to find acceptable categories and labels for patients that promote therapeutic partnership; and (5) the need to develop clinical services and research for people with severe disorders. We propose ‘functional somatic disorders’ (FSD) as an umbrella term for various conditions characterised by persistent and troublesome physical symptoms. FSDs are diagnosed clinically, on the basis of characteristic symptom patterns. As with all diagnoses, a diagnosis of FSD should be made after considering other possible somatic and mental differential diagnoses. We propose that FSD should occupy a neutral space within disease classifications, favouring neither somatic disease aetiology, nor mental disorder. FSD should be subclassified as (a) multisystem, (b) single system, or (c) single symptom. While additional specifiers may be added to take account of psychological features or co-occurring diseases, neither of these is sufficient or necessary to make the diagnosis. We recommend that FSD criteria are written so as to harmonise with existing syndrome diagnoses. Where currently defined syndromes fall within the FSD spectrum – and also within organ system-specific chapters of a classification – they should be afforded dual parentage (for example, irritable bowel syndrome can belong to both gastrointestinal disorders and FSD). Conclusion We propose a new classification, ‘functional somatic disorder’, which is neither purely somatic nor purely mental, but occupies a neutral space between these two historical poles. This classification reflects both emerging aetiological evidence of the complex interactions between brain and body and the need to resolve the historical split between somatic and mental disorders

Variational bounds for the shear viscosity of gelling melts

We study shear stress relaxation for a gelling melt of randomly crosslinked, interacting monomers. We derive a lower bound for the static shear viscosity $\eta$, which implies that it diverges algebraically with a critical exponent $k\ge 2\nu-\beta$. Here, $\nu$ and $\beta$ are the critical exponents of percolation theory for the correlation length and the gel fraction. In particular, the divergence is stronger than in the Rouse model, proving the relevance of excluded-volume interactions for the dynamic critical behaviour at the gel transition. Precisely at the critical point, our exact results imply a Mark-Houwink relation for the shear viscosity of isolated clusters of fixed size.Comment: 5 pages; CHANGES: typos corrected, some references added; version as publishe

Компресорні установки

Зміст видання відповідає освітньо-професійній програмі підготовки кадрів з вищою освітою напряму „Електротехніка та електротехнології“, зокрема – програмі дисципліни „Енергетичні установки“. Розглянуто основні положення теорії компресорних машин, будову, експлуатаційні особливості та методи регулювання режиму роботи поршневих, ротаційних, гвинтових, водокільцевих і відцентрових компресорів. Посібник адресовано студентам спеціальності „Енергетичний менеджмент“, які вивчають дисципліну „Енергетичні установки“. Він може бути корисним також студентам напрямів „Гірництво“, „Інженерна механіка“ та „Електромеханіка“ при вивченні стаціонарних установок гірничих підприємств

Unfolding-based Diagnosis of Systems with an Evolving Topology

We propose a framework for model-based diagnosis of systems with mobility and variable topologies, modelled as graph transformation systems. Generally speaking, model-based diagnosis is aimed at constructing explanations of observed faulty behaviours on the basis of a given model of the system. Since the number of possible explanations may be huge, we exploit the unfolding as a compact data structure to store them, along the lines of previous work dealing with Petri net models. Given a model of a system and an observation, the explanations can be constructed by unfolding the model constrained by the observation, and then removing incomplete explanations in a pruning phase. The theory is formalised in a general categorical setting: constraining the system by the observation corresponds to taking a product in the chosen category of graph grammars, so that the correctness of the procedure can be proved by using the fact that the unfolding is a right adjoint and thus it preserves products. The theory should hence be easily applicable to a wide class of system models, including graph grammars and Petri nets