Approximation of conformal mappings using conformally equivalent triangular lattices

Consider discrete conformal maps defined on the basis of two conformally equivalent triangle meshes, that is edge lengths are related by scale factors associated to the vertices. Given a smooth conformal map $f$, we show that it can be approximated by such discrete conformal maps $f^\epsilon$. In particular, let $T$ be an infinite regular triangulation of the plane with congruent triangles and only acute angles (i.e.\ $<\pi/2$). We scale this tiling by $\epsilon>0$ and approximate a compact subset of the domain of $f$ with a portion of it. For $\epsilon$ small enough we prove that there exists a conformally equivalent triangle mesh whose scale factors are given by $\log|f'|$ on the boundary. Furthermore we show that the corresponding discrete conformal maps $f^\epsilon$ converge to $f$ uniformly in $C^1$ with error of order $\epsilon$.Comment: 14 pages, 3 figures; v2 typos corrected, revised introduction, some proofs extende

An Information System Framework and Prototype for Collaborative and Standardized Chinese Liquor Production

20th Americas Conference on Information Systems, AMCIS 2014, Savannah, GA, 7-9 August 2014There is a pressing need for Chinese liquor producers to use information systems in managing production process and improving production efficiency for meeting fiercely increasing market competition. Unlike liquor production in other countries, Chinese liquor production replies on experience and manual operations greatly, which has very low-level automation and informatization. This paper takes a famous Chinese liquor producer as the target case company, introduces typical information systems used in Chinese liquor production, explores the motivations to implement information systems, and examines the benefits, the problems encountered as well as the key success factors in implementation and applications of information systems in Chinese liquor production industry.Department of Management and MarketingRefereed conference pape

Improved three-dimensional color-gradient lattice Boltzmann model for immiscible two-phase flows

In this paper, an improved three-dimensional color-gradient lattice Boltzmann (LB) model is proposed for simulating immiscible two-phase flows. Compared with the previous three-dimensional color-gradient LB models, which suffer from the lack of Galilean invariance and considerable numerical errors in many cases owing to the error terms in the recovered macroscopic equations, the present model eliminates the error terms and therefore improves the numerical accuracy and enhances the Galilean invariance. To validate the proposed model, numerical simulations are performed. First, the test of a moving droplet in a uniform flow field is employed to verify the Galilean invariance of the improved model. Subsequently, numerical simulations are carried out for the layered two-phase flow and three-dimensional Rayleigh-Taylor instability. It is shown that, using the improved model, the numerical accuracy can be significantly improved in comparison with the color-gradient LB model without the improvements. Finally, the capability of the improved color-gradient LB model for simulating dynamic two-phase flows at a relatively large density ratio is demonstrated via the simulation of droplet impact on a solid surface

Oldest known pantherine skull and evolution of the tiger

The tiger is one of the most iconic extant animals, and its origin and evolution have been intensely debated. Fossils attributable to extant pantherine species-lineages are less than 2 MYA and the earliest tiger fossils are from the Calabrian, Lower Pleistocene. Molecular studies predict a much younger age for the divergence of modern tiger subspecies at <100 KYA, although their cranial morphology is readily distinguishable, indicating that early Pleistocene tigers would likely have differed markedly anatomically from extant tigers. Such inferences are hampered by the fact that well-known fossil tiger material is middle to late Pleistocene in age. Here we describe a new species of pantherine cat from Longdan, Gansu Province, China, Panthera zdanskyi sp. nov. With an estimated age of 2.55–2.16 MYA it represents the oldest complete skull of a pantherine cat hitherto found. Although smaller, it appears morphologically to be surprisingly similar to modern tigers considering its age. Morphological, morphometric, and cladistic analyses are congruent in confirming its very close affinity to the tiger, and it may be regarded as the most primitive species of the tiger lineage, demonstrating the first unequivocal presence of a modern pantherine species-lineage in the basal stage of the Pleistocene (Gelasian; traditionally considered to be Late Pliocene). This find supports a north-central Chinese origin of the tiger lineage, and demonstrates that various parts of the cranium, mandible, and dentition evolved at different rates. An increase in size and a reduction in the relative size of parts of the dentition appear to have been prominent features of tiger evolution, whereas the distinctive cranial morphology of modern tigers was established very early in their evolutionary history. The evolutionary trend of increasing size in the tiger lineage is likely coupled to the evolution of its primary prey species

How large should whales be?

The evolution and distribution of species body sizes for terrestrial mammals is well-explained by a macroevolutionary tradeoff between short-term selective advantages and long-term extinction risks from increased species body size, unfolding above the 2g minimum size induced by thermoregulation in air. Here, we consider whether this same tradeoff, formalized as a constrained convection-reaction-diffusion system, can also explain the sizes of fully aquatic mammals, which have not previously been considered. By replacing the terrestrial minimum with a pelagic one, at roughly 7000g, the terrestrial mammal tradeoff model accurately predicts, with no tunable parameters, the observed body masses of all extant cetacean species, including the 175,000,000g Blue Whale. This strong agreement between theory and data suggests that a universal macroevolutionary tradeoff governs body size evolution for all mammals, regardless of their habitat. The dramatic sizes of cetaceans can thus be attributed mainly to the increased convective heat loss is water, which shifts the species size distribution upward and pushes its right tail into ranges inaccessible to terrestrial mammals. Under this macroevolutionary tradeoff, the largest expected species occurs where the rate at which smaller-bodied species move up into large-bodied niches approximately equals the rate at which extinction removes them.Comment: 7 pages, 3 figures, 2 data table

The Comparative Osteology of the Petrotympanic Complex (Ear Region) of Extant Baleen Whales (Cetacea: Mysticeti)

Anatomical comparisons of the ear region of baleen whales (Mysticeti) are provided through detailed osteological descriptions and high-resolution photographs of the petrotympanic complex (tympanic bulla and petrosal bone) of all extant species of mysticete cetaceans. Salient morphological features are illustrated and identified, including overall shape of the bulla, size of the conical process of the bulla, morphology of the promontorium, and the size and shape of the anterior process of the petrosal. We place our comparative osteological observations into a phylogenetic context in order to initiate an exploration into petrotympanic evolution within Mysticeti.The morphology of the petrotympanic complex is diagnostic for individual species of baleen whale (e.g., sigmoid and conical processes positioned at midline of bulla in Balaenoptera musculus; confluence of fenestra cochleae and perilymphatic foramen in Eschrichtius robustus), and several mysticete clades are united by derived characteristics. Balaenids and neobalaenids share derived features of the bulla, such as a rhomboid shape and a reduced anterior lobe (swelling) in ventral aspect, and eschrichtiids share derived morphologies of the petrosal with balaenopterids, including loss of a medial promontory groove and dorsomedial elongation of the promontorium. Monophyly of Balaenoidea (Balaenidae and Neobalaenidae) and Balaenopteroidea (Balaenopteridae and Eschrichtiidae) was recovered in phylogenetic analyses utilizing data exclusively from the petrotympanic complex.This study fills a major gap in our knowledge of the complex structures of the mysticete petrotympanic complex, which is an important anatomical region for the interpretation of the evolutionary history of mammals. In addition, we introduce a novel body of phylogenetically informative characters from the ear region of mysticetes. Our detailed anatomical descriptions, illustrations, and comparisons provide valuable data for current and future studies on the phylogenetic relationships, evolution, and auditory physiology of mysticetes and other cetaceans throughout Earth's history

The sudden change phenomenon of quantum discord

Even if the parameters determining a system's state are varied smoothly, the behavior of quantum correlations alike to quantum discord, and of its classical counterparts, can be very peculiar, with the appearance of non-analyticities in its rate of change. Here we review this sudden change phenomenon (SCP) discussing some important points related to it: Its uncovering, interpretations, and experimental verifications, its use in the context of the emergence of the pointer basis in a quantum measurement process, its appearance and universality under Markovian and non-Markovian dynamics, its theoretical and experimental investigation in some other physical scenarios, and the related phenomenon of double sudden change of trace distance discord. Several open questions are identified, and we envisage that in answering them we will gain significant further insight about the relation between the SCP and the symmetry-geometric aspects of the quantum state space.Comment: Lectures on General Quantum Correlations and their Applications, F. F. Fanchini, D. O. Soares Pinto, and G. Adesso (Eds.), Springer (2017), pp 309-33

Microstructure and properties of a deformation-processed Cu-Cr-Ag in situ composite by directional solidification

Cu-7Cr-0.07Ag alloys were prepared by casting and directional solidification, from which deformation-processed in situ composites were prepared by thermo-mechanical processing. The microstructure, mechanical properties, and electrical properties were investigated using optical microscopy, scanning electronic microscopy, tensile testing, and a micro-ohmmeter. The second-phase Cr grains of the directional solidification Cu-7Cr-0.07Ag in situ composite were parallel to the drawing direction and were finer, which led to a higher tensile strength and a better combination of properties

Overview on the phenomenon of two-qubit entanglement revivals in classical environments

The occurrence of revivals of quantum entanglement between separated open quantum systems has been shown not only for dissipative non-Markovian quantum environments but also for classical environments in absence of back-action. While the phenomenon is well understood in the first case, the possibility to retrieve entanglement when the composite quantum system is subject to local classical noise has generated a debate regarding its interpretation. This dynamical property of open quantum systems assumes an important role in quantum information theory from both fundamental and practical perspectives. Hybrid quantum-classical systems are in fact promising candidates to investigate the interplay among quantum and classical features and to look for possible control strategies of a quantum system by means of a classical device. Here we present an overview on this topic, reporting the most recent theoretical and experimental results about the revivals of entanglement between two qubits locally interacting with classical environments. We also review and discuss the interpretations provided so far to explain this phenomenon, suggesting that they can be cast under a unified viewpoint.Comment: 16 pages, 9 figures. Chapter written for the upcoming book "Lectures on general quantum correlations and their applications