A theory of rational spatial agglomerations

We model the behavior of rational forward-looking agents in a spatial economy. The economic geography structure is built on Fujita et al. (1999)'s racetrack economy. Workers choose optimally what to consume at each period, as well as which spatial itinerary to follow in the geographical space. The spatial extent of the resulting agglomerations increases with the taste for variety and the expenditure share on manufactured goods, and decreases with transport costs. Because forward-looking agents anticipate the future formation of agglomerations, they are more responsive to spatial utility differentials than myopic agents. As a consequence, the emerging agglomerations are larger under perfect foresight spatial adjustments than under myopic ones.

The growth rate and dimension theory of beta-expansions

In a recent paper of Feng and Sidorov they show that for β∈(1,(1+5√)/2) the set of β-expansions grows exponentially for every x∈(0,1/(β−1)). In this paper we study this growth rate further. We also consider the set of β-expansions from a dimension theory perspective.

Shear banding in molecular dynamics of polymer melts

In order to establish constitutive equations for a viscoelastic fluid uniform shear flow is usually required. However, in the last 10 years S. Q. Wang and co-workers have demonstrated that some entangled polymers do not flow with the uniform shear rate as usually assumed, but instead choose to separate into fast and slow flowing regions. This phenomenon, known as shear banding, causes flow instabilities and in principle invalidates all rheological measurements when it occurs. In this Letter we report the first observation of shear banding in molecular dynamics simulations of entangled polymer melts. We show that our observations are in a very good agreement with the phenomenology developed by Fielding and Olmsted. Our findings provide a simple way of validating the empirical macroscopic phenomenology of shear banding. © 2012 American Physical Society

Modelling the rheology of anisotropic particles adsorbed on a two-dimensional fluid interface

We present a general approach based on nonequilibrium thermodynamics for bridging the gap between a well-defined microscopic model and the macroscopic rheology of particle-stabilised interfaces. Our approach is illustrated by starting with a microscopic model of hard ellipsoids confined to a planar surface, which is intended to simply represent a particle-stabilised fluid–fluid interface. More complex microscopic models can be readily handled using the methods outlined in this paper. From the aforementioned microscopic starting point, we obtain the macroscopic, constitutive equations using a combination of systematic coarse-graining, computer experiments and Hamiltonian dynamics. Exemplary numerical solutions of the constitutive equations are given for a variety of experimentally relevant flow situations to explore the rheological behaviour of our model. In particular, we calculate the shear and dilatational moduli of the interface over a wide range of surface coverages, ranging from the dilute isotropic regime, to the concentrated nematic regime.

Long-run restrictions and survey forecasts of output, consumption and investment

We consider the extent to which long-horizon survey forecasts of consumption, investment and output growth are consistent with theory-based steady-state values, and whether imposing these restrictions on long-horizon forecasts will enhance their accuracy. The restrictions we impose are consistent with a two-sector model in which the variables grow at different rates in steady state. The restrictions are imposed by exponential-tilting of simple auxiliary forecast densities. We show that imposing the consumption-output restriction yields modest improvements in the long-horizon output growth forecasts, and larger improvements in the forecasts of the cointegrating combination of consumption and output: the transformation of the data on which accuracy is assessed plays an important role.

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.

On two rational difference equations

In this paper, we study the oscillating property of positive solutions and the global asymptotic stability of the unique equilibrium of the two rational difference equations [GRAPHICS] and [GRAPHICS] where a is a nonnegative constant. (c) 2005 Elsevier Inc. All rights reserved.

On the system of rational difference equations x(n) = A+(1)over-bar y(n-p), y(n) = A+(gamma(n-1))over-bar x(n-r)y(n-5)

In this paper, we study the behavior of the positive solutions of the system of two difference equations [GRAPHICS] where p >= 1, r >= 1, s >= 1, A >= 0, and x(1-r), x(2-r),..., x(0), y(1-max) {p.s},..., y(0) are positive real numbers. (c) 2005 Elsevier Inc. All rights reserved.

A generalized collectively compact operator theory with an application to integral equations on unbounded domains

In this paper a generalization of collectively compact operator theory in Banach spaces is developed. A feature of the new theory is that the operators involved are no longer required to be compact in the norm topology. Instead it is required that the image of a bounded set under the operator family is sequentially compact in a weaker topology. As an application, the theory developed is used to establish solvability results for a class of systems of second kind integral equations on unbounded domains, this class including in particular systems of Wiener-Hopf integral equations with L1 convolutions kernels

Theory and observations of ice particle evolution in cirrus using Doppler radar: evidence for aggregation

Vertically pointing Doppler radar has been used to study the evolution of ice particles as they sediment through a cirrus cloud. The measured Doppler fall speeds, together with radar-derived estimates for the altitude of cloud top, are used to estimate a characteristic fall time tc for the `average' ice particle. The change in radar reflectivity Z is studied as a function of tc, and is found to increase exponentially with fall time. We use the idea of dynamically scaling particle size distributions to show that this behaviour implies exponential growth of the average particle size, and argue that this exponential growth is a signature of ice crystal aggregation.

Boundary integral equations on unbounded rough surfaces: Fredholmness and the finite section method

We consider a class of boundary integral equations that arise in the study of strongly elliptic BVPs in unbounded domains of the form $D = \{(x, z)\in \mathbb{R}^{n+1} : x\in \mathbb{R}^n, z > f(x)\}$ where $f : \mathbb{R}^n \to\mathbb{R}$ is a sufficiently smooth bounded and continuous function. A number of specific problems of this type, for example acoustic scattering problems, problems involving elastic waves, and problems in potential theory, have been reformulated as second kind integral equations $u+Ku = v$ in the space $BC$ of bounded, continuous functions. Having recourse to the so-called limit operator method, we address two questions for the operator $A = I + K$ under consideration, with an emphasis on the function space setting $BC$. Firstly, under which conditions is $A$ a Fredholm operator, and, secondly, when is the finite section method applicable to $A$?

Intake, growth and meat quality of steers given diets based on varying proportions of maize silage and grass silage

Simmental × Holstein-Friesian steers were offered four forage diets. These comprised grass silage (G); proportionately 0·67 grass silage, proportionately 0·33 maize silage (GGM); 0·33 grass silage, 0·67 maize silage ( MMG); maize silage ( M) from 424 (s.d. = 11·5) kg to slaughter at a minimum weight of 560 kg. Forages were mixed and offered ad libitum. Steers were offered 2 kg of a concentrate daily, the concentrate being formulated such that all steers had similar crude protein intakes across dietary treatments. A sample of steers was slaughtered at the beginning of the experimental period to allow the calculation of the rate of gain of the carcass and its components. Carcass dissection of a sample of steers allowed the development of a prediction equation of carcass composition based on thoracic limb dissection of all carcasses. Forage dry matter intake and live-weight gain increased linearly as maize silage replaced grass silage in the forage mixture, resulting in improvements in food conversion ratio (all P = 0·001). Killing-out proportion increased with maize silage inclusion ( P < 0·001) but fat and conformation scores did not differ significantly between diets. However, increasing maize inclusion in the diet resulted in a greater weight ( P = 0·05) and proportion ( P = 0·008) of fat in the carcass, and significant increases in internal fat deposition. The inclusion of maize led to a progressive increase in the daily gains of carcass ( P < 0·001), and significant increases in the daily gains of both fat ( P < 0·001) and lean tissue ( P < 0·001). Fat colour was more yellow in cattle given diets G and GGM than diets MMG and M ( P < 0·001) and colour intensity was lower on diet M than the other three diets ( P < 0·001). There were no significant differences in any aspects of eating quality between diets. Therefore, maize silage has the potential to reduce the time taken for finishing beef animals to achieve slaughter weight with no apparent detrimental effects on subsequent meat quality.

Digestion, rumen fermentation and circulating concentrations of insulin, growth hormone and IGF-1 in steers fed diets based on different proportions of maize silage and grass silage

Replacing grass silage with maize silage results in a fundamental change in the ratio of structural to non-structural carbohydrates with commensurate changes in rumen fermentation patterns and nutrient utilisation. This study investigated the effects of feeding four forage mixtures, namely grass silage (G); 67 g/100 g grass silage133 g/100 g maize silage (GGM); 67 g/100 g maize silage133/100 g grass silage (MMG); maize silage (M) to four ruminally and duodenally canulated Holstein Friesian steers. All diets were formulated to be isonitrogenous (22.4 g N/kg DM) using a concentrate mixture. Dietary dry matter (DM) and organic matter (OM) digestibility increased with ascending maize silage inclusion (P,0.1) whereas starch and neutral detergent fibre digestibility declined (P,0.05). Ratio of non-glucogenic to glucogenic precursors in the rumen fluid increased with maize silage inclusion (P,0.01) with a commensurate reduction in rumen pH (P,0.05). Mean circulating concentrations of insulin were greatest and similar in diets MMG and GGM, lower in diet M and lowest in diet G (P,0.01). There were no effects of diet on the mean circulating concentration of growth hormone (GH), or the frequency, amplitude and duration of GH pulses, or the mean circulating concentrations of IGF-1. Increasing levels of DM, OM and starch intakes with the substitution of grass silage with maize silage affected overall digestion, nutrient partitioning and subsequent circulating concentrations of insulin.