6,676 research outputs found
A polyphonic acoustic vortex and its complementary chords
Using an annular phased array of eight loudspeakers, we generate sound beams that simultaneously contain phase singularities at a number of different frequencies. These frequencies correspond to different musical notes and the singularities can be set to overlap along the beam axis, creating a polyphonic acoustic vortex. Perturbing the drive amplitudes of the speakers means that the singularities no longer overlap, each note being nulled at a slightly different lateral position, where the volume of the other notes is now nonzero. The remaining notes form a tri-note chord. We contrast this acoustic phenomenon to the optical case where the perturbation of a white light vortex leads to a spectral spatial distribution
Lie Symmetry Analysis of the Black-Scholes-Merton Model for European Options with Stochastic Volatility
We perform a classification of the Lie point symmetries for the
Black--Scholes--Merton Model for European options with stochastic volatility,
, in which the last is defined by a stochastic differential equation
with an Orstein--Uhlenbeck term. In this model, the value of the option is
given by a linear (1 + 2) evolution partial differential equation in which the
price of the option depends upon two independent variables, the value of the
underlying asset, , and a new variable, . We find that for arbitrary
functional form of the volatility, , the (1 + 2) evolution equation
always admits two Lie point symmetries in addition to the automatic linear
symmetry and the infinite number of solution symmetries. However, when
and as the price of the option depends upon the second
Brownian motion in which the volatility is defined, the (1 + 2) evolution is
not reduced to the Black--Scholes--Merton Equation, the model admits five Lie
point symmetries in addition to the linear symmetry and the infinite number of
solution symmetries. We apply the zeroth-order invariants of the Lie symmetries
and we reduce the (1 + 2) evolution equation to a linear second-order ordinary
differential equation. Finally, we study two models of special interest, the
Heston model and the Stein--Stein model.Comment: Published version, 14pages, 4 figure
Ermakov's Superintegrable Toy and Nonlocal Symmetries
We investigate the symmetry properties of a pair of Ermakov equations. The
system is superintegrable and yet possesses only three Lie point symmetries
with the algebra sl(2,R). The number of point symmetries is insufficient and
the algebra unsuitable for the complete specification of the system. We use the
method of reduction of order to reduce the nonlinear fourth-order system to a
third-order system comprising a linear second-order equation and a conservation
law. We obtain the representation of the complete symmetry group from this
system. Four of the required symmetries are nonlocal and the algebra is the
direct sum of a one-dimensional Abelian algebra with the semidirect sum of a
two-dimensional solvable algebra with a two-dimensional Abelian algebra. The
problem illustrates the difficulties which can arise in very elementary
systems. Our treatment demonstrates the existence of possible routes to
overcome these problems in a systematic fashion.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
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Gaining assurance in a voter-verifiable voting system
The literature on e-voting systems has many examples of discussion of the correctness of the computer and communication algorithms of such systems, as well as discussions of their vulnerabilities. However, a gap in the literature concerns the practical need (before adoption of a specific e-voting system) for a complete case demonstrating that the system as a whole has sufficiently high probability of exhibiting the desired properties when in use in an actual election. This paper discusses the problem of producing such a case, with reference to a specific system: a version of the PrĂȘt Ă Voter scheme for voter-verifiable e-voting. We show a possible organisation of a case in terms of four main requirements â accuracy, privacy, termination and âtrustednessââ and show some of the detailed organisation that such a case should have, the diverse kinds of evidence that needs to be gathered and some of the interesting difficulties that arise
Characterization of solar-grade silicon produced by the SiF4-Na process
A process was developed for producing low cost solar grade silicon by the reaction between SiF4 gas and sodium metal. The results of the characterization of the silicon are presented. These results include impurity levels, electronic properties of the silicon after crystal growth, and the performance of solar photovoltaic cells fabricated from wafers of the single crystals. The efficiency of the solar cells fabricated from semiconductor silicon and SiF4-Na silicon was the same
Analytic Behaviour of Competition among Three Species
We analyse the classical model of competition between three species studied
by May and Leonard ({\it SIAM J Appl Math} \textbf{29} (1975) 243-256) with the
approaches of singularity analysis and symmetry analysis to identify values of
the parameters for which the system is integrable. We observe some striking
relations between critical values arising from the approach of dynamical
systems and the singularity and symmetry analyses.Comment: 14 pages, to appear in Journal of Nonlinear Mathematical Physic
Intelligent sampling for the measurement of structured surfaces
Uniform sampling in metrology has known drawbacks such as coherent spectral aliasing and a lack of efficiency in terms of measuring time and data storage. The requirement for intelligent sampling strategies has been outlined over recent years, particularly where the measurement of structured surfaces is concerned. Most of the present research on intelligent sampling has focused on dimensional metrology using coordinate-measuring machines with little reported on the area of surface metrology. In the research reported here, potential intelligent sampling strategies for surface topography measurement of structured surfaces are investigated by using numerical simulation and experimental verification. The methods include the jittered uniform method, low-discrepancy pattern sampling and several adaptive methods which originate from computer graphics, coordinate metrology and previous research by the authors. By combining the use of advanced reconstruction methods and feature-based characterization techniques, the measurement performance of the sampling methods is studied using case studies. The advantages, stability and feasibility of these techniques for practical measurements are discussed
Gender violence in schools: taking the âgirls-as-victimsâ discourse forward
This paper draws attention to the gendered nature of violence in schools. Recent recognition that schools can be violent places has tended to ignore the fact that many such acts originate in unequal and antagonistic gender relations, which are tolerated and ânormalisedâ by everyday school structures and processes. After examining some key concepts and definitions, we provide a brief overview of the scope and various manifestations of gender violence in schools, noting that most research to date has focused on girls as victims of gender violence within a heterosexual context and ignores other forms such as homophobic and girl violence. We then move on to look at a few interventions designed to address gender violence in schools in the developing world and end by highlighting the need for more research and improved understanding of the problem and how it can be addressed
A nonlocal connection between certain linear and nonlinear ordinary differential equations/oscillators
We explore a nonlocal connection between certain linear and nonlinear
ordinary differential equations (ODEs), representing physically important
oscillator systems, and identify a class of integrable nonlinear ODEs of any
order. We also devise a method to derive explicit general solutions of the
nonlinear ODEs. Interestingly, many well known integrable models can be
accommodated into our scheme and our procedure thereby provides further
understanding of these models.Comment: 12 pages. J. Phys. A: Math. Gen. 39 (2006) in pres
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