Nonlinear phononic crystals based on chains of disks alternating with toroidal structures

We study experimentally the acoustic response of a load-bearing, phononic crystal composed of alternating steel disks, and polytetrafluoroethylene o-rings under precompression. The crystal allows for axial, rocking, and shear-polarized wavemodes when excited by a broad-band signal applied off-axis. Finite element analysis is employed to determine the system’s wave modes. The nonlinear interaction between disks and o-rings supports a dynamic response that is tunable with variations in static precompression, leading to controllable frequency shifts in a large band gap. A modal analysis reveals that four of the six principal wave modes are susceptible to external precompression while two modes are not

A Groenewold-Van Hove Theorem for S^2

We prove that there does not exist a nontrivial quantization of the Poisson algebra of the symplectic manifold S^2 which is irreducible on the subalgebra generated by the components {S_1,S_2,S_3} of the spin vector. We also show that there does not exist such a quantization of the Poisson subalgebra P consisting of polynomials in {S_1,S_2,S_3}. Furthermore, we show that the maximal Poisson subalgebra of P containing {1,S_1,S_2,S_3} that can be so quantized is just that generated by {1,S_1,S_2,S_3}.Comment: 20 pages, AMSLaTe

Constrained Dynamics for Quantum Mechanics I. Restricting a Particle to a Surface

We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of constraining and dynamics adjustment which produces the right Hamiltonian on the submanifold when tested on known examples. This method we hope will become the germ of a full Dirac algorithm for quantum constraints. We take a first step in generalising it to the situation where the constraint is a general selfadjoint operator with some additional structures.Comment: 49 pages, TEX, input files amssym.def, amssym.te

Glueball Spin

The spin of a glueball is usually taken as coming from the spin (and possibly the orbital angular momentum) of its constituent gluons. In light of the difficulties in accounting for the spin of the proton from its constituent quarks, the spin of glueballs is reexamined. The starting point is the fundamental QCD field angular momentum operator written in terms of the chromoelectric and chromomagnetic fields. First, we look at the restrictions placed on the structure of glueballs from the requirement that the QCD field angular momentum operator should satisfy the standard commutation relationships. This can be compared to the electromagnetic charge/monopole system, where the quantization of the field angular momentum places restrictions (i.e. the Dirac condition) on the system. Second, we look at the expectation value of this operator under some simplifying assumptions.Comment: 11 pages, 0 figures; added references and some discussio

Investigating children\u27s multiplicative thinking: implications for teaching

Multiplicative thinking is a \u27big idea\u27 of mathematics that underpins much of the mathematics learned beyond the early primary school years. This article reports on a recent study that utilised an interview tool and a written quiz to gather data about children\u27s multiplicative thinking. Our research has so far revealed that many primary aged children have a procedural view of multiplicative thinking which we believe inhibits their progress. There are two aspects to this article. First, we present some aspects of the interview tool and written quiz, along with some of findings, and we consider the implications of those findings. Second, we present a key teaching idea and an associated task that has been developed from our research. The main purpose of the article is to promote the development of conceptual understanding of the multiplicative situation as opposed to the teaching of procedures. In doing so, we encourage the explicit teaching of the many connections within the multiplicative situation and between it and other \u27big ideas\u27 such as proportional reasoning and algebraic thinking

The 6-vertex model of hydrogen-bonded crystals with bond defects

It is shown that the percolation model of hydrogen-bonded crystals, which is a 6-vertex model with bond defects, is completely equivalent with an 8-vertex model in an external electric field. Using this equivalence we solve exactly a particular 6-vertex model with bond defects. The general solution for the Bethe-like lattice is also analyzed.Comment: 13 pages, 6 figures; added references for section

Where lean construction and value management meet

The lean construction (LC) community’s key vision and goal is to provide value, yet they are increasingly challenged with understanding and dealing with the concept of value, with reports that value is one of the weakest points. Regardless of the previous studies and contributions already made on the concept of value in LC, the absence of a consistent understanding of value has resulted in misperceptions and indistinct boundaries with other construction value-related disciplines. Without a consistent understanding of value, the full potential of applying value-established concepts will not occur. Thus, the study of different concepts in construction will open new opportunities to deliver value in the future. Literature reviewed only revealed a small number of interdisciplinary comparisons of Lean manufacturing and LC with value management (VM)/value engineering (VE) on value. Secondary data was used to present an in-depth comparison of the principal points of the current practice and theories of LC and VM, which are seen as ways to improve the delivery of value to clients and building users. The study revealed a range of similarities at a high level, which could easily point to an early conclusion that LC and VM are interchangeable, leading to the same goal of value delivery and shared misapplication of cost reduction techniques. However, a more detailed examination indicates significant differences in the philosophy and scope in different areas, including project timing, practitioner duties, and areas of practice which could complement each other. Also the study identified that LC is a broader philosophy which covers more aspects than VM, it is evident that LC has advanced over the years towards discussions on the concept of value. The current work in LC on value relies less on other construction value-related disciplines such as VM, VE and partnering. Furthermore, LC literature still views value as a confusing concept associated with different interpretations, forming the basisof its understanding. The study established that value plays a central role in both LC and VM. Their combination could offer great synergy regarding the concept of value

Stochastic models which separate fractal dimension and Hurst effect

Fractal behavior and long-range dependence have been observed in an astonishing number of physical systems. Either phenomenon has been modeled by self-similar random functions, thereby implying a linear relationship between fractal dimension, a measure of roughness, and Hurst coefficient, a measure of long-memory dependence. This letter introduces simple stochastic models which allow for any combination of fractal dimension and Hurst exponent. We synthesize images from these models, with arbitrary fractal properties and power-law correlations, and propose a test for self-similarity.Comment: 8 pages, 2 figure

Guest Editorial Special Issue on: Big Data Analytics in Intelligent Systems

The amount of information that is being created, every day, is quickly growing. As such, it is now more common than ever to deal with extremely large datasets. As systems develop and become more intelligent and adaptive, analysing their behaviour is a challenge. The heterogeneity, volume and speed of data generation are increasing rapidly. This is further exacerbated by the use of wireless networks, sensors, smartphones and the Internet. Such systems are capable of generating a phenomenal amount of information and the need to analyse their behaviour, to detect security anomalies or predict future demands for example, is becoming harder. Furthermore, securing such systems is a challenge. As threats evolve, so should security measures develop and adopt increasingly intelligent security techniques. Adaptive systems must be employed and existing methods built upon to provide well-structured defence in depth. Despite the clear need to develop effective protection methods, the task is a difficult one, as there are significant weaknesses in the existing security currently in place. Consequently, this special issue of the Journal of Computer Sciences and Applications discusses big data analytics in intelligent systems. The specific topics of discussion include the Internet of Things, Web Services, Cloud Computing, Security and Interconnected Systems