Sum-factorization techniques in Isogeometric Analysis

The fast assembling of stiffness and mass matrices is a key issue in isogeometric analysis, particularly if the spline degree is increased. We present two algorithms based on the idea of sum factorization, one for matrix assembling and one for matrix-free methods, and study the behavior of their computational complexity in terms of the spline order $p$. Opposed to the standard approach, these algorithms do not apply the idea element-wise, but globally or on macro-elements. If this approach is applied to Gauss quadrature, the computational complexity grows as $p^{d+2}$ instead of $p^{2d+1}$ as previously achieved.Comment: 34 pages, 8 figure

Studying the Perturbed Wess-Zumino-Novikov-Witten SU(2)k Theory Using the Truncated Conformal Spectrum Approach

We study the $SU(2)_k$ Wess-Zumino-Novikov-Witten (WZNW) theory perturbed by the trace of the primary field in the adjoint representation, a theory governing the low-energy behaviour of a class of strongly correlated electronic systems. While the model is non-integrable, its dynamics can be investigated using the numerical technique of the truncated conformal spectrum approach combined with numerical and analytical renormalization groups (TCSA+RG). The numerical results so obtained provide support for a semiclassical analysis valid at $k\gg 1$. Namely, we find that the low energy behavior is sensitive to the sign of the coupling constant, $\lambda$. Moreover for $\lambda>0$ this behavior depends on whether $k$ is even or odd. With $k$ even, we find definitive evidence that the model at low energies is equivalent to the massive $O(3)$ sigma model. For $k$ odd, the numerical evidence is more equivocal, but we find indications that the low energy effective theory is critical.Comment: 30 pages, 19 eps figures, LaTeX2e file. Version 2: manuscript accepted for publication; small changes in text and in one of the figure

Exact Maximal Height Distribution of Fluctuating Interfaces

We present an exact solution for the distribution P(h_m,L) of the maximal height h_m (measured with respect to the average spatial height) in the steady state of a fluctuating Edwards-Wilkinson interface in a one dimensional system of size L with both periodic and free boundary conditions. For the periodic case, we show that P(h_m,L)=L^{-1/2}f(h_m L^{-1/2}) for all L where the function f(x) is the Airy distribution function that describes the probability density of the area under a Brownian excursion over a unit interval. For the free boundary case, the same scaling holds but the scaling function is different from that of the periodic case. Numerical simulations are in excellent agreement with our analytical results. Our results provide an exactly solvable case for the distribution of extremum of a set of strongly correlated random variables.Comment: 4 pages revtex (two-column), 1 .eps figure include

Hello, Frisco! : I Called You Up To Say Hello!

https://digitalcommons.library.umaine.edu/mmb-vp/3149/thumbnail.jp

Comparison of environmental impacts of individual meals - Does it really make a difference to choose plant-based meals instead of meat-based ones?

More than one third of global greenhouse gas emissions (GHG) can be attributed to our food system. Limiting global warming to 1.5° or 2 °C will not be possible without reducing GHG emissions from the food system. Dietary change at the meal level is of great importance as day-to-day consumption patterns drive the global food production system. The aim of this paper was to assess the life cycle environmental impact of a sample of meals from different cuisines (chilli, lasagne, curry and teriyaki meals) and their meat-based, vegetarian, vegan, and whole-food vegan recipe variations. The environmental impacts (global warming, freshwater eutrophication, terrestrial acidification and water depletion potential) of 13 meals, made with 33 different ingredients, were estimated from cradle to plate using Life Cycle Assessment (LCA). Results showed that irrespective of the type of cuisine, the plant-based version of meals (vegan and whole-food vegan) had substantially lower environmental impacts across all impact categories than their vegetarian and meat-based versions. On average, meat-based meals had 14 times higher environmental impact, while vegetarian meals had 3 times higher environmental impact than vegan meals. Substantial reductions in the environmental impacts of meals can be achieved when animal-based ingredients (e.g., beef, cheese, pork, chicken) are replaced with whole or minimally processed plant-based ingredients (i.e., vegetables, legumes) in recipes. Swapping animal-based meals for plant-based versions, and preferably transitioning to plant-based diets, present important opportunities for mitigating climate change and safeguarding environmental sustainability