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Recent documents in Articlesen-usThu, 26 Jun 2014 01:54:32 PDT3600Free Energies for Materials with Memory in Terms of State Functionals
http://arrow.dit.ie/scschmatart/172
http://arrow.dit.ie/scschmatart/172Tue, 24 Jun 2014 06:45:35 PDT
Abstract The aim of thiswork is to determinewhat free energy functionals are expressible as quadratic forms of the state functional It which is discussed in earlier papers. The single integral form is shown to include the functional wF proposed a few years ago, and also a further category of functionals which are easily described but more complicated to construct. These latter examples exist only for certain types of materials. The double integral case is examined in detail, against the background of a newsystematic approach developed recently for double integral quadratic forms in terms of strain history, which was used to uncover new free energy functionals. However, while, in principle, the same method should apply to free energieswhich can be given by quadratic forms in terms of It , it emerges that this requirement is very restrictive; indeed, only the minimum free energy can be expressed in such a manner
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Murrough GoldenMatrix G-strands
http://arrow.dit.ie/scschmatart/171
http://arrow.dit.ie/scschmatart/171Fri, 13 Jun 2014 02:03:05 PDT
We discuss three examples in which one may extend integrable Euler–Poincare ordinary differential equations to integrable Euler–Poincare partial differential equations in the matrix G-Strand context. After describing matrix G-Strand examples for SO(3) and SO(4) we turn our attention to SE(3) where the matrix G-Strand equations recover the exact rod theory in the convective representation. We then find a zero curvature representation of these equations and establish the conditions under which they are completely integrable. Thus, the G-Strand equations turn out to be a rich source of integrable systems. The treatment is meant to be expository and most concepts are explained in examples in the language of vectors in R^{3}.
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Darryl Holm et al.On Mikhailov's Reduction Group
http://arrow.dit.ie/scschmatart/170
http://arrow.dit.ie/scschmatart/170Tue, 03 Jun 2014 07:08:17 PDT
We present a generalization of the notion of reduction group which allows one to study in a uniform way certain classes of nonlocal $S$-integrable equations like Ablowitz-Musslimani's nonlocal Schr\"odinger equation. Another aspect of the proposed generalization is the possibility to derive in a systematic way solutions to S-integrable equations with prescribed symmetries.
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Tihomir I. ValchevNumerical Simulations of Steady and Pulsed Non-Adiabatic Magnetised Jets From Young Stars
http://arrow.dit.ie/scschmatart/169
http://arrow.dit.ie/scschmatart/169Thu, 22 May 2014 05:02:15 PDTStephen O'Sullivan et al.An Explicit Scheme for Multifluid Magnetohydrodynamics
http://arrow.dit.ie/scschmatart/168
http://arrow.dit.ie/scschmatart/168Thu, 22 May 2014 04:52:25 PDTStephen O'Sullivan et al.A Three‐Dimensional Numerical Method for Modelling Weakly Ionized Plasmas
http://arrow.dit.ie/scschmatart/167
http://arrow.dit.ie/scschmatart/167Thu, 22 May 2014 04:47:11 PDTStephen O'Sullivan et al.Interacting Jets From Binary Protostars
http://arrow.dit.ie/scschmatart/166
http://arrow.dit.ie/scschmatart/166Thu, 22 May 2014 04:42:53 PDT
Aims. We investigate potential models that could explain why multiple proto-stellar systems predominantly show single jets. During their formation, stars most frequently produce energetic outﬂows and jets. However, binary jets have only been observed in a very small number of systems. Methods. We model numerically 3D binary jets for various outﬂow parameters. We also model the propagation of jets from a speciﬁc source, namely L1551 IRS 5, known to have two jets, using recent observations as constraints for simulations with a new MHD code. We examine their morphology and dynamics, and produce synthetic emission maps. Results. We ﬁnd that the two jets interfere up to the stage where one of them is almost destroyed or engulfed into the second one. We are able to reproduce some of the observational features of L1551 such as the bending of the secondary jet. Conclusions. While the eﬀects of orbital motion are negligible over the jets dynamical timeline, their interaction has signiﬁcant impact on their morphology. If the jets are not strictly parallel, as in most observed cases, we show that the magnetic ﬁeld can help the collimation and refocusing of both of the two jets.
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Gareth Murphy et al.A cosmic ray current-driven instability in partially ionised media
http://arrow.dit.ie/scschmatart/165
http://arrow.dit.ie/scschmatart/165Wed, 21 May 2014 07:27:36 PDTBrian Reville et al.The transport of Cosmic Rays in Self‐Excited Magnetic Turbulence
http://arrow.dit.ie/scschmatart/164
http://arrow.dit.ie/scschmatart/164Wed, 21 May 2014 07:22:19 PDTBrian Reville et al.Environmental limits on the nonresonant cosmic-ray current-driven instability
http://arrow.dit.ie/scschmatart/163
http://arrow.dit.ie/scschmatart/163Wed, 21 May 2014 07:12:21 PDTBrian Reville et al.Nonideal Magnetohydrodynamic Turbulent Decay in Molecular Clouds
http://arrow.dit.ie/scschmatart/162
http://arrow.dit.ie/scschmatart/162Wed, 21 May 2014 07:02:51 PDTTurlough Downes et al.Stochastic particle acceleration in the lobes of giant radio galaxies
http://arrow.dit.ie/scschmatart/161
http://arrow.dit.ie/scschmatart/161Wed, 21 May 2014 04:37:07 PDT
We investigate the acceleration of particles by Alfv ́en waves via the second-order Fermi process in the lobes of giant radio galaxies. Such sites are candidates for the accelerators of ultra-high-energy cosmic rays (UHECR). We focus on the nearby Fanaroff–Riley type I radio galaxy Centaurus A. This is motivated by the coincidence of its position with the arrival direction of several of the highest energy Auger events. The conditions necessary for consistency with the acceleration time-scales predicted by quasi-linear theory are reviewed. Test particle calculations are performed in fields which guarantee electric fields with no component parallel to the local magnetic field. The results of quasi-linear theory are, to an order of magnitude, found to be accurate at low turbulence levels for non-relativistic Alfven waves and at both low and high turbulence levels in the mildly relativistic case. We conclude that for pure stochastic acceleration via Alfv ́en waves to be plausible as the generator of UHECR in Cen A, the baryon number density would need to be several orders of magnitude below currently held upper limits.
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Stephen O'Sullivan et al.A Model for Predicting Extragalactic Jet Lifetimes
http://arrow.dit.ie/scschmatart/160
http://arrow.dit.ie/scschmatart/160Wed, 21 May 2014 04:17:51 PDT
Abstract. In this letter, we propose a model to explain the disintegration of ex- tragalactic jets and to predict the associated timescale. The model assumes that a jet is current and charge neutral as well as collimated at its source; however, the forward electron current gradually decays producing a magnetic field transverse to the direction of jet propagation. This growing transverse magnetic field eventually causes the jet to disintegrate.
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Daniel S. Spicer et al.A Stability Study of a New Explicit Numerical Scheme for a System of Differential Equations with a Large Skew-Symmetric Component
http://arrow.dit.ie/scschmatart/159
http://arrow.dit.ie/scschmatart/159Tue, 20 May 2014 07:17:25 PDT
Abstract. Explicit numerical methods for the solution of a system of stiff differential equations suffer from a time step size that approaches zero in order to satisfy stability conditions. Implicit schemes allow a larger time-step, but require more computations. When the differential equations are dominated by a skew-symmetric component, the problem is not stiffness in the sense that the size of the eigenvalues are unequal, rather the that the real eigenvalues are dominated by imaginary eigenvalues. We present and compare analytical results for stable time step limits for several explicit methods including the super-time-stepping method of Alexiades, Amiez, and Gremaud which is a explicit Runge-Kutta method for parabolic partial differential equations and a new method modeled on a predictor-corrector scheme with multiplicative operator splitting. This new explicit method, presented in regular and super-time-stepping form, increases stability without forcing the step size to zero.
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Katharine Gurski et al.On the Acceleration of Explicit Finite Difference Methods for Option Pricing
http://arrow.dit.ie/scschmatart/158
http://arrow.dit.ie/scschmatart/158Tue, 20 May 2014 07:02:32 PDT
Implicit finite difference methods are conventionally preferred over their explicit counterparts for the numerical valuation of options. In large part the reason for this is a severe stability constraint known as the Courant–Friedrichs–Lewy (CFL) condition which limits the latter class’s efficiency. Implicit methods, however, are difficult to implement for all but the most simple of pricing models, whereas explicit techniques are easily adapted to complex problems. For the first time in a financial context, we present an acceleration technique, applicable to explicit finite difference schemes describing diffusive processes with symmetric evolution operators, called Super-Time-Stepping. We show that this method can be implemented as part of a more general approach for non-symmetric operators. Formal stability is thereby deduced for the exemplar cases of European and American put options priced under the Black–Scholes equation. Furthermore, we introduce a novel approach to describing the efficiencies of finite difference schemes as semi-empirical power laws relating the minimal real time required to carry out the numerical integration to a solution with a specified accuracy. Tests are described in which the method is shown to significantly ameliorate the severity of the CFL constraint whilst retaining the simplicity of the underlying explicit method. Degrees of acceleration are achieved yielding comparable, or superior, efficiencies to a set of benchmark implicit schemes. We infer that the described method is a powerful tool, the explicit nature of which makes it ideally suited to the treatment of symmetric and non-symmetric diffusion operators describing complex financial instruments including multi-dimensional systems requiring representation on decomposed and/or adaptive meshes.
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Stephen O'Sullivan et al.Pricing European And American Options In The Heston Model With Accelerated Explicit Finite Differencing Methods
http://arrow.dit.ie/scschmatart/157
http://arrow.dit.ie/scschmatart/157Tue, 20 May 2014 06:57:38 PDTConall O'Sullivan et al.Multifluid Magnetohydrodynamic Turbulent Decay
http://arrow.dit.ie/scschmatart/156
http://arrow.dit.ie/scschmatart/156Tue, 20 May 2014 02:27:29 PDT
It is generally believed that turbulence has a significant impact on the dynamics and evolution of molecular clouds and the star formation that occurs within them. Non-ideal magnetohydrodynamic (MHD) effects are known to influence the nature of this turbulence. We present the results of a suite of 5123 resolution simulations of the decay of initially super-Alfv enic and supersonic fully multifluid MHD turbulence. We find that ambipolar diffusion increases the rate of decay of the turbulence while the Hall effect has virtually no impact. The decay of the kinetic energy can be fitted as a power law in time and the exponent is found to be−134 for fully multifluid MHD turbulence. The power spectra of density, velocity, and magnetic field are all steepened significantly by the inclusion of non-ideal terms. The dominant reason for this steepening is ambipolar diffusion with the Hall effectagain playing a minimal role except at short length scales where it creates extra structure in the magnetic field.Interestingly we find that, at least at these resolutions, the majority of the physics of multifluid turbulence can be captured by simply introducing fixed (in time and space) resistive terms into the induction equation without the need for a full multifluid MHD treatment. The velocity dispersion is also examined and, in common with previously published results, it is found not to be power law in nature
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Turlough Downes et al.Rational Generalised Moonshine from Orbifolds
http://arrow.dit.ie/scschmatart/155
http://arrow.dit.ie/scschmatart/155Mon, 19 May 2014 08:48:04 PDT
Frenkel, Lepowsky and Meurman constructed the Moonshine Module (MM) as a Z_{2} orbifold of the Leech Lattice Meromorphic Conformal field theory. The group of automorphisms of this theory is the 'Monster Group' M - the largest finite sporadic simple group (with order ~ 8. 10^{53 }). 'Monstrous Moonshine' is the famous observation that the Thompson series, corresponding to each class of M, is a hauptmodule for some genus zero fixing group. Norton considered Generalised Moonshine Functions (GMF), depending on two commuting Monster elements, and suggested that they are also hauptmodules. Using meromorphid Abelian orbifoldings of MM we identify the singularity structure of the GMF in some nontrivial cases so that the genus zero property is demonstrated and the corresponding genus zero fixing group is identified.
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Rossen Ivanov et al.From Permutahedron to Aassociahedron
http://arrow.dit.ie/scschmatart/154
http://arrow.dit.ie/scschmatart/154Mon, 19 May 2014 08:48:02 PDT
For each finite real reflection group $W$, we identify a copy of the type-$W$ simplicial generalised associahedron inside the corresponding simplicial permutahedron. This defines a bijection between the facets of the generalised associahedron and the elements of the type $W$ non-crossing partition lattice which is more tractable than previous such bijections. We show that the simplicial fan determined by this associahedron coincides with the Cambrian fan for $W$.
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Colum Watt et al.Climbing Eements in Finite Coxeter Groups
http://arrow.dit.ie/scschmatart/153
http://arrow.dit.ie/scschmatart/153Mon, 19 May 2014 08:48:00 PDT
We define the notion of a climbing element in a finite real reflection group relative to a total order on the reflection set and we characterise these elements in the case where the total order arises from a bipartite Coxeter element.
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Colum Watt et al.