8,224 research outputs found
Cheng Equation: A Revisit Through Symmetry Analysis
The symmetry analysis of the Cheng Equation is performed. The Cheng Equation
is reduced to a first-order equation of either Abel's Equations, the analytic
solution of which is given in terms of special functions. Moreover, for a
particular symmetry the system is reduced to the Riccati Equation or to the
linear nonhomogeneous equation of Euler type. Henceforth, the general solution
of the Cheng Equation with the use of the Lie theory is discussed, as also the
application of Lie symmetries in a generalized Cheng equation.Comment: 10 pages. Accepted for publication in Quaestiones Mathematicae
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Lie symmetries of (1+2) nonautonomous evolution equations in Financial Mathematics
We analyse two classes of evolution equations which are of special
interest in Financial Mathematics, namely the Two-dimensional Black-Scholes
Equation and the equation for the Two-factor Commodities Problem. Our approach
is that of Lie Symmetry Analysis. We study these equations for the case in
which they are autonomous and for the case in which the parameters of the
equations are unspecified functions of time. For the autonomous Black-Scholes
Equation we find that the symmetry is maximal and so the equation is reducible
to the Classical Heat Equation. This is not the case for the
nonautonomous equation for which the number of symmetries is submaximal. In the
case of the two-factor equation the number of symmetries is submaximal in both
autonomous and nonautonomous cases. When the solution symmetries are used to
reduce each equation to a equation, the resulting equation is of
maximal symmetry and so equivalent to the Classical Heat Equation.Comment: 15 pages, 1 figure, to be published in Mathematics in the Special
issue "Mathematical Finance
The WMAP normalization of inflationary cosmologies
We use the three-year WMAP observations to determine the normalization of the
matter power spectrum in inflationary cosmologies. In this context, the
quantity of interest is not the normalization marginalized over all parameters,
but rather the normalization as a function of the inflationary parameters n and
r with marginalization over the remaining cosmological parameters. We compute
this normalization and provide an accurate fitting function. The statistical
uncertainty in the normalization is 3 percent, roughly half that achieved by
COBE. We use the k-l relation for the standard cosmological model to identify
the pivot scale for the WMAP normalization. We also quote the inflationary
energy scale corresponding to the WMAP normalization.Comment: 4 pages RevTex4 with two figure
Coarse-grained Interaction Potentials for Anisotropic Molecules
We have proposed an efficient parameterization method for a recent variant of
the Gay-Berne potential for dissimilar and biaxial particles and demonstrated
it for a set of small organic molecules. Compared to the previously proposed
coarse-grained models, the new potential exhibits a superior performance in
close contact and large distant interactions. The repercussions of thermal
vibrations and elasticity has been studied through a statistical method. The
study justifies that the potential of mean force is representable with the same
functional form, extending the application of this coarse-grained description
to a broader range of molecules. Moreover, the advantage of employing
coarse-grained models over truncated atomistic summations with large distance
cutoffs has been briefly studied.Comment: 8 pages, 4 tables and 6 figures. To appear in J. Chem. Phy
Contextual Teaching with Computer-Assisted Instruction
Computer technology has made substantial contributions to education and educators are now confronted with determining how to best incorporate it as a teaching tool. Educators have also long struggled with how to make what is learned in school more useful in other contexts. This review of recent literature was undertaken in an attempt to determine if computer-assisted instruction is compatible with contextual teaching and learning approaches. The four computer-assisted assets of flexibility, format, interactivity and navigational methods were examined because they yield the most interpretive evidence of compatibility with contextual teaching and learning approaches and their characteristics. It was concluded that all four of the assets identified were compatible and should be included within contextual approaches
Computing the Effective Hamiltonian of Low-Energy Vacuum Gauge Fields
A standard approach to investigate the non-perturbative QCD dynamics is
through vacuum models which emphasize the role played by specific gauge field
fluctuations, such as instantons, monopoles or vortexes. The effective
Hamiltonian describing the dynamics of the low-energy degrees of freedom in
such approaches is usually postulated phenomenologically, or obtained through
uncontrolled approximations. In a recent paper, we have shown how lattice field
theory simulations can be used to rigorously compute the effective Hamiltonian
of arbitrary vacuum models by stochastically performing the path integral over
all the vacuum field fluctuations which are not explicitly taken into account.
In this work, we present the first illustrative application of such an approach
to a gauge theory and we use it to compute the instanton size distribution in
SU(2) gluon-dynamics in a fully model independent and parameter-free way.Comment: 10 pages, 4 figure
Modelling the Galactic Magnetic Field on the Plane in 2D
We present a method for parametric modelling of the physical components of
the Galaxy's magnetised interstellar medium, simulating the observables, and
mapping out the likelihood space using a Markov Chain Monte-Carlo analysis. We
then demonstrate it using total and polarised synchrotron emission data as well
as rotation measures of extragalactic sources. With these three datasets, we
define and study three components of the magnetic field: the large-scale
coherent field, the small-scale isotropic random field, and the ordered field.
In this first paper, we use only data along the Galactic plane and test a
simple 2D logarithmic spiral model for the magnetic field that includes a
compression and a shearing of the random component giving rise to an ordered
component. We demonstrate with simulations that the method can indeed constrain
multiple parameters yielding measures of, for example, the ratios of the
magnetic field components. Though subject to uncertainties in thermal and
cosmic ray electron densities and depending on our particular model
parametrisation, our preliminary analysis shows that the coherent component is
a small fraction of the total magnetic field and that an ordered component
comparable in strength to the isotropic random component is required to explain
the polarisation fraction of synchrotron emission. We outline further work to
extend this type of analysis to study the magnetic spiral arm structure, the
details of the turbulence as well as the 3D structure of the magnetic field.Comment: 18 pages, 11 figures, updated to published MNRAS versio
Calculating potentials of mean force and diffusion coefficients from nonequilibirum processes without Jarzynski's equality
In general, the direct application of the Jarzynski equality (JE) to
reconstruct potentials of mean force (PMFs) from a small number of
nonequilibrium unidirectional steered molecular dynamics (SMD) paths is
hindered by the lack of sampling of extremely rare paths with negative
dissipative work. Such trajectories, that transiently violate the second law,
are crucial for the validity of JE. As a solution to this daunting problem, we
propose a simple and efficient method, referred to as the FR method, for
calculating simultaneously both the PMF U(z) and the corresponding diffusion
coefficient D(z) along a reaction coordinate z for a classical many particle
system by employing a small number of fast SMD pullings in both forward (F) and
time reverse (R) directions, without invoking JE. By employing Crook's
transient fluctuation theorem (that is more general than JE) and the stiff
spring approximation, we show that: (i) the mean dissipative work W_d in the F
and R pullings are equal, (ii) both U(z) and W_d can be expressed in terms of
the easily calculable mean work of the F and R processes, and (iii) D(z) can be
expressed in terms of the slope of W_d. To test its viability, the FR method is
applied to determine U(z) and D(z) of single-file water molecules in
single-walled carbon nanotubes (SWNTs). The obtained U(z) is found to be in
very good agreement with the results from other PMF calculation methods, e.g.,
umbrella sampling. Finally, U(z) and D(z) are used as input in a stochastic
model, based on the Fokker-Planck equation, for describing water transport
through SWNTs on a mesoscopic time scale that in general is inaccessible to MD
simulations.Comment: ReVTeX4, 13 pages, 6 EPS figures, Submitted to Journal of Chemical
Physic
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
Development of probabilistic models for quantitative pathway analysis of plant pest introduction for the EU territory
This report demonstrates a probabilistic quantitative pathway analysis model that can be used in risk assessment for plant pest introduction into EU territory on a range of edible commodities (apples, oranges, stone fruits and wheat). Two types of model were developed: a general commodity model that simulates distribution of an imported infested/infected commodity to and within the EU from source countries by month; and a consignment model that simulates the movement and distribution of individual consignments from source countries to destinations in the EU. The general pathway model has two modules. Module 1 is a trade pathway model, with a Eurostat database of five years of monthly trade volumes for each specific commodity into the EU28 from all source countries and territories. Infestation levels based on interception records, commercial quality standards or other information determine volume of infested commodity entering and transhipped within the EU. Module 2 allocates commodity volumes to processing, retail use and waste streams and overlays the distribution onto EU NUTS2 regions based on population densities and processing unit locations. Transfer potential to domestic host crops is a function of distribution of imported infested product and area of domestic production in NUTS2 regions, pest dispersal potential, and phenology of susceptibility in domestic crops. The consignment model covers the several routes on supply chains for processing and retail use. The output of the general pathway model is a distribution of estimated volumes of infested produce by NUTS2 region across the EU28, by month or annually; this is then related to the accessible susceptible domestic crop. Risk is expressed as a potential volume of infested fruit in potential contact with an area of susceptible domestic host crop. The output of the consignment model is a volume of infested produce retained at each stage along the specific consignment trade chain
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