22,198 research outputs found
A C++11 implementation of arbitrary-rank tensors for high-performance computing
This article discusses an efficient implementation of tensors of arbitrary
rank by using some of the idioms introduced by the recently published C++ ISO
Standard (C++11). With the aims at providing a basic building block for
high-performance computing, a single Array class template is carefully crafted,
from which vectors, matrices, and even higher-order tensors can be created. An
expression template facility is also built around the array class template to
provide convenient mathematical syntax. As a result, by using templates, an
extra high-level layer is added to the C++ language when dealing with algebraic
objects and their operations, without compromising performance. The
implementation is tested running on both CPU and GPU.Comment: 21 pages, 6 figures, 1 tabl
An Elementary Treatment of the Reverse Sprinkler
We discuss the reverse sprinkler problem: How does a sprinkler turn when
submerged and made to suck in water? We propose a solution that requires only a
knowledge of mechanics and fluid dynamics at the introductory university level.
We argue that as the flow of water starts, the sprinkler briefly experiences a
torque that would make it turn toward the incoming water, while as the flow of
water ceases it briefly experiences a torque in the opposite direction. No
torque is expected when water is flowing steadily into it unless dissipative
effects, such as viscosity, are considered. Dissipative effects result in a
small torque that would cause the sprinkler arm to accelerate toward the
steadily incoming water. Our conclusions are discussed in light of an analysis
of forces, conservation of angular momentum, and the experimental results
reported by others. We review the conflicting published treatments of this
problem, some of which have been incorrect and many of which have introduced
complications that obscure the basic physics involved.Comment: 16 pages, 8 figures. The subject of this paper is often referred to
in the literature as the "Feynman sprinkler" or the "Feynman inverse
sprinkler." v2:references added, discussion of angular momentum conservation
clarified, section III expanded to include consideration of dissipative
phenomena such as viscosity. v3:minor corrections of style. To appear in the
American Journal of Physic
Haldane phase in one-dimensional topological Kondo insulators
We investigate the groundstate properties of a recently proposed model for a
topological Kondo insulator in one dimension (i.e., the -wave
Kondo-Heisenberg lattice model) by means of the Density Matrix Renormalization
Group method. The non-standard Kondo interaction in this model is different
from the usual (i.e., local) Kondo interaction in that the localized spins
couple to the "-wave" spin density of conduction electrons, inducing a
topologically non-trivial insulating groundstate. Based on the analysis of the
charge- and spin-excitation gaps, the string order parameter, and the spin
profile in the groundstate, we show that, at half-filling and low energies, the
system is in the Haldane phase and hosts topologically protected spin-1/2
end-states. Beyond its intrinsic interest as a useful "toy-model" to understand
the effects of strong correlations on topological insulators, we show that the
-wave Kondo-Heisenberg model can be implemented in band optical lattices
loaded with ultra-cold Fermi gases.Comment: 8 pages, 4 figures, 1 appendi
Learning Externalities and Economic Growth
It is a well known fact that not all countries develop at the same time. The industrial revolution began over 200 years ago in England and has been spreading over the world ever since. In their paper Barriers to Riches, Parente and Prescott notice that countries that enter the industrial stage later on grow faster than what the early starters did. I present a simple model with learning externalities that generates this kind of behavior. I follow Lucas (1998) and solve the optimization problem of the representative agent under the assumption that the external effect is given by the world leader's human capital.
Aztec obsidian industries
Obsidian was the primary lithic or stone material used for cutting activities in Aztec society, including domestic food production, craft production, hunting, warfare, and ritual. The demands of millions of consumers within and outside of the Aztec Empire shaped a diversity of industries and distribution networks that operated through merchants, markets, and state taxes in goods and labor. This chapter provides an overview of the primary obsidian sources, quarry activities, artifact types, use contexts, and innovations in lithic technology during the Aztec (Middle and Late Postclassic) period. A particular focus is the Sierra de Las Navajas (or Pachuca) mine and the detailed history of quarrying and manufacturing activities that have been documented there
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