Kraichnan–Leith–Batchelor similarity theory and two-dimensional inverse cascades

We study the scaling properties and Kraichnan–Leith–Batchelor (KLB) theory of forced inverse cascades in generalized two-dimensional (2D) fluids (α-turbulence models) simulated at resolution 8192x8192. We consider α=1 (surface quasigeostrophic flow), α=2 (2D Euler flow) and α=3. The forcing scale is well resolved, a direct cascade is present and there is no large-scale dissipation. Coherent vortices spanning a range of sizes, most larger than the forcing scale, are present for both α=1 and α=2. The active scalar field for α=3 contains comparatively few and small vortices. The energy spectral slopes in the inverse cascade are steeper than the KLB prediction −(7−α)/3 in all three systems. Since we stop the simulations well before the cascades have reached the domain scale, vortex formation and spectral steepening are not due to condensation effects; nor are they caused by large-scale dissipation, which is absent. One- and two-point p.d.f.s, hyperflatness factors and structure functions indicate that the inverse cascades are intermittent and non-Gaussian over much of the inertial range for α=1 and α=2, while the α=3 inverse cascade is much closer to Gaussian and non-intermittent. For α=3 the steep spectrum is close to that associated with enstrophy equipartition. Continuous wavelet analysis shows approximate KLB scaling ℰ(k)∝k−2 (α=1) and ℰ(k)∝k−5/3 (α=2) in the interstitial regions between the coherent vortices. Our results demonstrate that coherent vortex formation (α=1 and α=2) and non-realizability (α=3) cause 2D inverse cascades to deviate from the KLB predictions, but that the flow between the vortices exhibits KLB scaling and non-intermittent statistics for α=1 and α=2.

Rethinking disability theory and practice: challenging essentialism

This edited volume argues that even in recent Critical Disability Studies which have sought to critique essentialist assumptions in relation to Disability, nevertheless essentialisms remain which predetermine and predirect definitions and arguments in the field. This volume analyses such essentialisms in a wide range of areas such as childhood, gender, sexuality, reproduction, ADHD, autism, the animal, d/Deafness, hirsutism, the body, and vision. Particularly issues such as 'agency', 'voice' and 'body' are explored in terms of their political implications.

Fundamental insights into ontogenetic growth from theory and fish

The fundamental features of growth may be universal, because growth trajectories of most animals are very similar, but a unified mechanistic theory of growth remains elusive. Still needed is a synthetic explanation for how and why growth rates vary as body size changes, both within individuals over their ontogeny and between populations and species over their evolution. Here we use Bertalanffy growth equations to characterize growth of ray-finned fishes in terms of two parameters, the growth rate coefficient, K, and final body mass, m∞. We derive two alternative empirically testable hypotheses and test them by analyzing data from FishBase. Across 576 species, which vary in size at maturity by almost nine orders of magnitude, K scaled as m_∞^(-0.23). This supports our first hypothesis that growth rate scales as m_∞^(-0.25) as predicted by metabolic scaling theory; it implies that species which grow to larger mature sizes grow faster as juveniles. Within fish species, however, K scaled as m_∞^(-0.35). This supports our second hypothesis which predicts that growth rate scales as m_∞^(-0.33) when all juveniles grow at the same rate. The unexpected disparity between across- and within-species scaling challenges existing theoretical interpretations. We suggest that the similar ontogenetic programs of closely related populations constrain growth to m_∞^(-0.33) scaling, but as species diverge over evolutionary time they evolve the near-optimal m_∞^(-0.25) scaling predicted by metabolic scaling theory. Our findings have important practical implications because fish supply essential protein in human diets, and sustainable yields from wild harvests and aquaculture depend on growth rates.

Invariant theory and reversible-equivariant vector fields

In this paper we present results for the systematic study of reversible-equivariant vector fields - namely, in the simultaneous presence of symmetries and reversing symmetries - by employing algebraic techniques from invariant theory for compact Lie groups. The Hilbert-Poincare series and their associated Molien formulae are introduced,and we prove the character formulae for the computation of dimensions of spaces of homogeneous anti-invariant polynomial functions and reversible-equivariant polynomial mappings. A symbolic algorithm is obtained for the computation of generators for the module of reversible-equivariant polynomial mappings over the ring of invariant polynomials. We show that this computation can be obtained directly from a well-known situation, namely from the generators of the ring of invariants and the module of the equivariants. (C) 2008 Elsevier B.V, All rights reserved.

Finite temperature correction to the Thomas-Fermi approximation for a Bose-Einstein condensate: comparison between theory and experiment

We observe experimentally a deviation of the radius of a Bose-Einstein condensate from the standard Thomas-Fermi prediction, after free expansion, as a function of temperature. A modified Hartree-Fock model is used to explain the observations, mainly based on the influence of the thermal cloud on the condensate cloud.

On the Derived Categories and Quasitilted Algebras

In this paper, we present some results on the bounded derived category of Artin algebras, and in particular on the indecomposable objects in these categories, using homological properties. Given a complex X*, we consider the set J(X*) = {i is an element of Z vertical bar H(i)(X*) not equal 0} and we define the application l(X*) = maxJ(X*) - minJ(X*) + 1. We give relationships between some homological properties of an algebra and the respective application l. On the other hand, using homological properties again, we determine two subcategories of the bounded derived category of an algebra, which turn out to be the bounded derived categories of quasi-tilted algebras. As a consequence of these results we obtain new characterizations of quasi-tilted and quasi-tilted gentle algebras.

Nuclear elements of degree 6 in the free alternative algebra

We construct five new elements of degree 6 in the nucleus of the free alternative algebra. We use the representation theory of the symmetric group to locate the elements. We use the computer algebra system ALBERT and an extension of ALBERT to express the elements in compact form and to show that these new elements are not a consequence of the known clegree-5 elements in the nucleus. We prove that these five new elements and four known elements form a basis for the subspace of nuclear elements of degree 6. Our calculations are done using modular arithmetic to save memory and time. The calculations can be done in characteristic zero or any prime greater than 6, and similar results are expected. We generated the nuclear elements using prime 103. We check our answer using five other primes.

An algebraic theory for generalized Jordan chains and partial signatures in the Lagrangian Grassmannian

We discuss an algebraic theory for generalized Jordan chains and partial signatures, that are invariants associated to sequences of symmetric bilinear forms on a vector space. We introduce an intrinsic notion of partial signatures in the Lagrangian Grassmannian of a symplectic space that does not use local coordinates, and we give a formula for the Maslov index of arbitrary real analytic paths in terms of partial signatures.

A Character Formula for the Category (O)over-tilde of Modules for Affine sl(2)

One may construct, for any function on the integers, an irreducible module of level zero for affine sl(2) using the values of the function as structure constants. The modules constructed using exponential-polynomial functions realize the irreducible modules with finite-dimensional weight spaces in the category (O) over tilde of Chari. In this work, an expression for the formal character of such a module is derived using the highest weight theory of truncations of the loop algebra.

Equilibrium theory with asymmetric information and infinitely many states

Radner (1968) proved the existence of a competitive equilibrium for differential information economies with finitely many states. We extend this result to economies with infinitely many states of nature.

Essays on monetary and banking theory

Esta tese de Doutorado é dedicada ao estudo de instabilidade financeira e dinâmica em Teoria Monet ária. E demonstrado que corridas banc árias são eliminadas sem custos no modelo padrão de teoria banc ária quando a popula ção não é pequena. É proposta uma extensão em que incerteza agregada é mais severa e o custo da estabilidade financeira é relevante. Finalmente, estabelece-se otimalidade de transições na distribui ção de moeda em economias em que oportunidades de trocas são escassas e heterogêneas. Em particular, otimalidade da inflação depende dos incentivos dinâmicos proporcionados por tais transi ções. O capí tulo 1 estabelece o resultado de estabilidade sem custos para economias grandes ao estudar os efeitos do tamanho populacional na an álise de corridas banc árias de Peck & Shell. No capí tulo 2, otimalidade de dinâmica é estudada no modelo de monet ário de Kiyotaki & Wright quando a sociedade é capaz de implementar uma polí tica inflacion ária. Apesar de adotar a abordagem de desenho de mecanismos, este capí tulo faz um paralelo com a an álise de Sargent & Wallace (1981) ao destacar efeitos de incentivos dinâmicos sobre a interação entre as polí ticas monet ária e fiscal. O cap ítulo 3 retoma o tema de estabilidade fi nanceira ao quanti car os custos envolvidos no desenho ótimo de um setor bancário à prova de corridas e ao propor uma estrutura informacional alternativa que possibilita bancos insolventes. A primeira an álise mostra que o esquema de estabilidade ótima exibe altas taxas de juros de longo prazo e a segunda que monitoramento imperfeito pode levar a corridas bancárias com insolvência.