Classical plume theory: 1937-2010 and beyond

Developing a theoretical description of turbulent plumes, the likes of which may be seen rising above industrial chimneys, is a daunting thought. Plumes are ubiquitous on a wide range of scales in both the natural and the man-made environments. Examples that immediately come to mind are the vapour plumes above industrial smoke stacks or the ash plumes forming particle-laden clouds above an erupting volcano. However, plumes also occur where they are less visually apparent, such as the rising stream of warmair above a domestic radiator, of oil from a subsea blowout or, at a larger scale, of air above the so-called urban heat island. In many instances, not only the plume itself is of interest but also its influence on the environment as a whole through the process of entrainment. Zeldovich (1937, The asymptotic laws of freely-ascending convective flows. Zh. Eksp. Teor. Fiz., 7, 1463-1465 (in Russian)), Batchelor (1954, Heat convection and buoyancy effects in fluids. Q. J. R. Meteor. Soc., 80, 339-358) and Morton et al. (1956, Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A, 234, 1-23) laid the foundations for classical plume theory, a theoretical description that is elegant in its simplicity and yet encapsulates the complex turbulent engulfment of ambient fluid into the plume. Testament to the insight and approach developed in these early models of plumes is that the essential theory remains unchanged and is widely applied today. We describe the foundations of plume theory and link the theoretical developments with the measurements made in experiments necessary to close these models before discussing some recent developments in plume theory, including an approach which generalizes results obtained separately for the Boussinesq and the non-Boussinesq plume cases. The theory presented - despite its simplicity - has been very successful at describing and explaining the behaviour of plumes across the wide range of scales they are observed. We present solutions to the coupled set of ordinary differential equations (the plume conservation equations) that Morton et al. (1956) derived from the Navier-Stokes equations which govern fluid motion. In order to describe and contrast the bulk behaviour of rising plumes from general area sources, we present closed-form solutions to the plume conservation equations that were achieved by solving for the variation with height of Morton's non-dimensional flux parameter Γ - this single flux parameter gives a unique representation of the behaviour of steady plumes and enables a characterization of the different types of plume. We discuss advantages of solutions in this form before describing extensions to plume theory and suggesting directions for new research. © 2010 The Author. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

What is the weakest topology in which feedback stability is robust?

Mathematical theorems in control theory are only of interest in so far as their assumptions relate to practical situations. The space of systems with transfer functions in ℋ∞, for example, has many advantages mathematically, but includes large classes of non-physical systems, and one must be careful in drawing inferences from results in that setting. Similarly, the graph topology has long been known to be the weakest, or coarsest, topology in which (1) feedback stability is a robust property (i.e. preserved in small neighbourhoods) and (2) the map from open-to-closed-loop transfer functions is continuous. However, it is not known whether continuity is a necessary part of this statement, or only required for the existing proofs. It is entirely possible that the answer depends on the underlying classes of systems used. The class of systems we concern ourselves with here is the set of systems that can be approximated, in the graph topology, by real rational transfer function matrices. That is, lumped parameter models, or those distributed systems for which it makes sense to use finite element methods. This is precisely the set of systems that have continuous frequency responses in the extended complex plane. For this class, we show that there is indeed a weaker topology; in which feedback stability is robust but for which the maps from open-to-closed-loop transfer functions are not necessarily continuous. © 2013 Copyright Taylor and Francis Group, LLC.

Reduced dynamics with renormalization in solid-state charge qubit measurement

Quantum measurement will inevitably cause backaction on the measured system, resulting in the well-known dephasing and relaxation. In this paper, in the context of solid-state qubit measurement by a mesoscopic detector, we show that an alternative backaction known as renormalization is important under some circumstances. This effect is largely overlooked in the theory of quantum measurement.

Information geometry theory of high-dimension space and application for speaker independent continuous digit speech recognition

In the light of descriptive geometry and notions in set theory, this paper re-defines the basic elements in space such as curve and surface and so on, presents some fundamental notions with respect to the point cover based on the High-dimension space (HDS) point covering theory, finally takes points from mapping part of speech signals to HDS, so as to analyze distribution information of these speech points in HDS, and various geometric covering objects for speech points and their relationship. Besides, this paper also proposes a new algorithm for speaker independent continuous digit speech recognition based on the HDS point dynamic searching theory without end-points detection and segmentation. First from the different digit syllables in real continuous digit speech, we establish the covering area in feature space for continuous speech. During recognition, we make use of the point covering dynamic searching theory in HDS to do recognition, and then get the satisfying recognized results. At last, compared to HMM (Hidden Markov models)-based method, from the development trend of the comparing results, as sample amount increasing, the difference of recognition rate between two methods will decrease slowly, while sample amount approaching to be very large, two recognition rates all close to 100% little by little. As seen from the results, the recognition rate of HDS point covering method is higher than that of in HMM (Hidden Markov models) based method, because, the point covering describes the morphological distribution for speech in HDS, whereas HMM-based method is only a probability distribution, whose accuracy is certainly inferior to point covering.

Set invariance in control

The properties of positively invariant sets are involved in many different problems in control theory, such as constrained control, robustness analysis, synthesis and optimization. In this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems.

Microscopic examination of NpNn dominance in the evolution of nuclear structure

The proton-neutron interaction in determining the evolution of nuclear structure has been studied by using the Brillouin-Wigner perturbation expansion. The particle-hole and particle-particle p-n interactions are unifiedly described in the theory. The obtained formulas of level energies and excitation energies scaled in the small- and large-NpNn limits can well explain the linearity of the extracted proton-neutron interaction energies and the attenuation of the 2(1)(+) excitation energies against the valence nucleon product NpNn for five mass regions from A = 100-200.

Getting Constitutional Theory into Proportion: A Matter of Interpretation?

Gibbs, N., Getting Constitutional Theory into Proportion: A Matter of Interpretation?, Oxford Journal of Legal Studies, 27 (1), 175-191. RAE2008

The Synthesis of Arbitrary Stable Dynamics in Non-linear Neural Networks II: Feedback and Universality

We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.

Participation by place-based community organisations in local development: case studies from East Cork

The past two decades have witnessed concerted efforts by theorists and policy-makers to place civil society at the centre of social, economic and environmental development processes. To this end, policies grounded in a Third Way approach have sought to forge stronger linkages between the state and voluntary community-based organisations. Concepts such as active citizenship, social capital, partnership and sustainability have underpinned this political philosophy, which reflects a movement in development theory and political science away from notions of state-led development and unfettered neo-liberalism. In the Irish context, a series of initiatives have given expression to this new policy agenda, the foremost amongst them the publication of a White Paper in 2000. New local governance structures and development schemes have multiplied since the early 1990s, while the physical planning system has also been modified. All this has taken place against the backdrop of unprecedented economic development and social change precipitated by the ‘Celtic Tiger’.This thesis examines the interaction between community organisations, state institutions and other actors in development processes in East Cork. It focuses upon place-based community organisations, who seek to represent the interests of their particular localities. A case study approach is employed to explore the realpolitik of local development and to gauge the extent to which grassroots community organisations wield influence in determining the development of their communities. The study concludes that the transfer of decision-making power to community organisations has been more illusory than real and that, in practical terms, such groups remain marginal in the circuits of power. However, the situation of community organisations operating in different geographical locales cannot be reduced to an overarching theoretical logic. The case studies show that the modus operandi of community groups varies considerably and can be influenced by specific local geographies, events and personalities.

Literature and the shaman: Jung, trauma stories and new origin stories in The Lion, the witch and the wardrobe by C.S. Lewis

The paper first considers the role of Jungian ideas in relation to academic disciplines and to literary studies in particular. Jung is a significant resource in negotiating developments in literary theory because of his characteristic treatment of the ‘other’. The paper then looks at The Lion, the Witch and the Wardrobe (1950) by C.S. Lewis whose own construction of archetypes is very close to Jung’s. By drawing upon new post-Jungian work from Jerome Bernstein’s Living in the Borderland (2005), the novel is revealed to be intimately concerned with narratives of trauma and of origin. Indeed, a Jungian and post-Jungian approach is able to situate the text both within nature and in the historical traumas of war as well as the personal traumas of subjectivity. Where Bernstein connects his work to the postcolonial ethos of the modern Navajo shaman, this new weaving of literary and cultural theory points to the residue of shamanism within the arts of the West. [From the Publisher]

The Masculine Habitus as 'Distributed Cognition': A Case Study of 5- to 6-Year-Old Boys in an English Inner-City, Multi-Ethnic Primary School

This article provides a case study demonstrating the active role that 5- to 6-year-old boys in an English inner-city, multi-ethnic primary school play in the appropriation and reproduction of their masculine identities. It is argued that the emphasis on physicality, violence and racism found among the boys cannot be understood without reference to the immediate contexts of the local community and the school within which they are located. In making this argument the article draws upon and applies the concept of the habitus and develops this with the notion of 'distributed cognition' as proposed in sociocultural theory. Some of the implications of this analysis for working with boys in early years settings are discussed in the conclusion.

On Being Too Nice: Message Interaction in an Asynchronous Learning Network

The interact system model (ISM) is used to examine the interactions between messages submitted during online discussions related to a graduate education course in curriculum theory. Interactions are analyzed using complexity science and conclusions are drawn concerning structures that could enhance discussion and support the construction of collective understandings.

Analogies between linguistics and information theory

An analogy is established between the syntagm and paradigm from Saussurean linguistics and the message and messages for selection from the information theory initiated by Claude Shannon. The analogy is pursued both as an end itself and for its analytic value in understanding patterns of retrieval from full text systems. The multivalency of individual words when isolated from their syntagm is contrasted with the relative stability of meaning of multi-word sequences, when searching ordinary written discourse. The syntagm is understood as the linear sequence of oral and written language. Saussureâ??s understanding of the word, as a unit which compels recognition by the mind, is endorsed, although not regarded as final. The lesser multivalency of multi-word sequences is understood as the greater determination of signification by the extended syntagm. The paradigm is primarily understood as the network of associations a word acquires when considered apart from the syntagm. The restriction of information theory to expression or signals, and its focus on the combinatorial aspects of the message, is sustained. The message in the model of communication in information theory can include sequences of written language. Shannonâ??s understanding of the written word, as a cohesive group of letters, with strong internal statistical influences, is added to the Saussurean conception. Sequences of more than one word are regarded as weakly correlated concatenations of cohesive units.

Reduced K-theory for Azumaya algebras

Abstract In the theory of central simple algebras, often we are dealing with abelian groups which arise from the kernel or co-kernel of functors which respect transfer maps (for example K-functors). Since a central simple algebra splits and the functors above are “trivial” in the split case, one can prove certain calculus on these functors. The common examples are kernel or co-kernel of the maps Ki(F)?Ki(D), where Ki are Quillen K-groups, D is a division algebra and F its center, or the homotopy fiber arising from the long exact sequence of above map, or the reduced Whitehead group SK1. In this note we introduce an abstract functor over the category of Azumaya algebras which covers all the functors mentioned above and prove the usual calculus for it. This, for example, immediately shows that K-theory of an Azumaya algebra over a local ring is “almost” the same as K-theory of the base ring. The main result is to prove that reduced K-theory of an Azumaya algebra over a Henselian ring coincides with reduced K-theory of its residue central simple algebra. The note ends with some calculation trying to determine the homotopy fibers mentioned above.

Welfare Effort and Poverty from the Monetary and Capabilities Approach: A Cross-Country Analysis in Latin American and the Caribbean (1990-2010)

There is abundant empirical evidence on the negative relationship between welfare effort and poverty. However, poverty indicators traditionally used have been representative of the monetary approach, excluding its multidimensional reality from the analysis. Using three regression techniques for the period 1990-2010 and controlling for demographic and cyclical factors, this paper examines the relationship between social spending per capita —as the indicator of welfare effort— and poverty in up to 21 countries of the region. The proportion of the population with an income below its national basic basket of goods and services (PM1) and the proportion of population with an income below 50% of the median income per capita (PM2) were the two poverty indicators considered from the monetarist approach to measure poverty. From the capability approach the proportion of the population with food inadequacy (PC1) and the proportion of the population without access to improved water sources or sanitation facilities (PC2) were used. The fi ndings confi rm that social spending is actually useful to explain changes in poverty (PM1, PC1 and PC2), as there is a high negative and signifi cant correlation between the variables before and after controlling for demographic and cyclical factors. In two regression techniques, social spending per capita did not show a negative relationship with the PM2. Countries with greater welfare effort for the period 1990-2010 were not necessarily those with the lowest level of poverty. Ultimately social spending per capita was more useful to explain changes in poverty from the capability approach.