LRA Community:
http://hdl.handle.net/2381/445
Wed, 23 Apr 2014 20:36:21 GMT2014-04-23T20:36:21ZLRA Community:http://https://lra.le.ac.uk:80/retrieve/2392/mathsequation.jpg
http://hdl.handle.net/2381/445
The input-output relationship approach to structural identifiability analysis
http://hdl.handle.net/2381/28585
Title: The input-output relationship approach to structural identifiability analysis
Authors: Bearup, Daniel J.; Evans, Neil D.; Chappell, Michael J.
Abstract: Analysis of the identifiability of a given model system is an essential prerequisite to the determination of model parameters from physical data. However, the tools available for the analysis of non-linear systems can be limited both in applicability and by computational intractability for any but the simplest of models. The input-output relation of a model summarises the input-output structure of the whole system and as such provides the potential for an alternative approach to this analysis. However for this approach to be valid it is necessary to determine whether the monomials of a differential polynomial are linearly independent. A simple test for this property is presented in this work. The derivation and analysis of this relation can be implemented symbolically within Maple. These techniques are applied to analyse classical models from biomedical systems modelling and those of enzyme catalysed reaction schemes.Wed, 12 Feb 2014 14:16:49 GMThttp://hdl.handle.net/2381/285852014-02-12T14:16:49ZAdaptive discontinuous Galerkin methods for nonstationary convection–diffusion problems
http://hdl.handle.net/2381/28539
Title: Adaptive discontinuous Galerkin methods for nonstationary convection–diffusion problems
Authors: Cangiani, Andrea; Georgoulis, Emmanuil H.; Metcalfe, Stephen
Abstract: This work is concerned with the derivation of a robust a posteriori error estimator for a discontinuous Galerkin (dG) method discretization of a linear nonstationary convection–diffusion initial/boundary value problem and with the implementation of a corresponding adaptive algorithm. More specifically, we derive a posteriori bounds for the error in the L[superscript 2](H[superscript 1]) + L∞(L[superscript 2])-type norm for an interior penalty dG discretization in space and a backward Euler discretization in time. Finally, an adaptive algorithm is proposed utilizing the error estimator. Optimal rate of convergence of the adaptive algorithm is observed in a number of test problems and for various Pèclet numbers.Thu, 23 Jan 2014 09:55:27 GMThttp://hdl.handle.net/2381/285392014-01-23T09:55:27ZOn the prescribed mean curvature problem on the standard n-dimensional ball
http://hdl.handle.net/2381/28493
Title: On the prescribed mean curvature problem on the standard n-dimensional ball
Authors: Sharaf, Khadijah Abdullah Mohammed
Abstract: In this thesis, we consider the problem of existence of conformal scalar flat metric with prescribed boundary mean curvature on the standard n-dimensional ball. Let B[superscript n] be the unit ball in R[superscript n], n ≥ 3, with Euclidean metric g[subscript 0]. Its boundary will be denoted by S[superscript n-1] and will be endowed with the standard metric still denoted by g[subscript 0]. Let H : S[superscript n-1] → R be a given function, we study the problem of finding a conformal metric g = u 4/n-2 g[subscript 0] such that R[subscript g] = 0 in B[superscript n] and h[subscript g] = H on S[superscript n-1]. Here R[subscript g] is the scalar curvature of the metric g in B[superscript n] and h[subscript g] is the mean curvature of g on S[superscript n-1]. This problem is equivalent to solving the following nonlinear boundary value equation: (see PDF for equation) where v is the outward unit vector with respect to the metric g[subscript 0]. In general there are several difficulties in facing this problem by means of variational methods. Indeed, in virtue of the non-compactness of the embedding H[superscript 1](B[superscript n]) → L 2(n-1)/n-2 (∂B[superscript n]), the Euler-Lagrange functional J associated to the problem, does not satisfy the Palais-Smale condition, and that leads to the failure of the standard critical point theory.
One part of this thesis deals with the case where H is a Morse function satisfying a non degeneracy condition. Using an algebraic topological method and the tools of the theory of the critical points at infinity, we provide a variety of classes of functions that can be realized as the mean curvature on the boundary of the the n-dimensional balls.
The other part deals with the case where the non degeneracy condition is not satisfied and replaced by the so called β-flatness condition. In this case, we give precise estimates on the losses of the compactness and we identify the critical points at infinity of the variational problem. Then, we establish under generic boundary condition a Morse inequalities at infinity, which give a lower bound on the number of solutions to the above problem.Fri, 06 Dec 2013 13:36:38 GMThttp://hdl.handle.net/2381/284932013-12-06T13:36:38ZOn the composition and neutrix composition of the delta function with the hyperbolic tangent and its inverse functions
http://hdl.handle.net/2381/28477
Title: On the composition and neutrix composition of the delta function with the hyperbolic tangent and its inverse functions
Authors: Fisher, Brian; Kılıcman, Adem
Abstract: Let F be a distribution in D[superscript 1] and let f be a locally summable function. The composition F(f(x)) of F and f is said to exist and be equal to the distribution h(x) if the limit of the sequence {F[subscript n](f(x))} is equal to h(x), where F[subscript n](x)= F(x) ∗ δ[subscript n](x) for n = 1, 2, . . . and {δ[subscript n](x)} is a certain regular sequence converging to the Dirac delta function. It is proved that the neutrix composition δ([superscript rs-1])((tanh x[subscript +])[superscript 1/r]) exists and δ([superscript rs-1])((tanh x[subscript +])[superscript 1/r]) = ∑[superscript s-1, subscript k=0] ∑[superscript K[subscript k], subscript i=0] ((-1)[superscript k]c[subscript s-2i-1,k] (rs)!/2sk!)δ([superscript k])(x) for r,s = 1, 2, . . ., where K[subscript k] is the integer part of (s-k-1)/2 and the constants c[subscript j,k] are defined by the expansion (tanh[superscript -1]x)superscript k = {∑[superscript ∞, subscript i=0] (x[superscript 2i+1]/(2i + 1))}[superscript k] = ∑[superscript ∞, subscript j=k] c[subscript j,k]x[superscript j], for k = 0,1,2,.... Further results also provided.Wed, 04 Dec 2013 15:41:51 GMThttp://hdl.handle.net/2381/284772013-12-04T15:41:51ZOn the Neutrix Composition of the Delta and Inverse Hyperbolic Sine Functions
http://hdl.handle.net/2381/28476
Title: On the Neutrix Composition of the Delta and Inverse Hyperbolic Sine Functions
Authors: Fisher, Brian; Kılıcman, Adem
Abstract: Let F be a distribution in D[superscript 1] and let f be a locally summable function. The composition F(f(x)) of F and f is said to exist and be equal to the distribution h(x) if the limit of the sequence {F[subscript n](f(x))} is equal to h(x), where F[subscript n](x)= F(x) ∗ δ[subscript n](x) for n = 1, 2, . . . and {δ[subscript n](x)} is a certain regular sequence converging to the Dirac delta function. In the ordinary sense, the composition δ([superscript s])[(sinh[superscript −1]x[subscript +])[superscript r] does not exists. In this study, it is proved that the neutrix composition δ([superscript s])[(sinh[superscript −1]x[subscript +])[superscript r] exists and is given by δ([superscript s])[(sinh[superscript −1]x[subscript +])[superscript r] = ∑[superscript sr+r-1, subscript k=0] ∑[superscript k, subscript i=0] ([superscript k, subscript i]) ((-1)[superscript k] rc[subscript s,k,i]/2[superscript k+1]k!)δ([superscript k])(x), for s = 0, 1, 2, . . . and r = 1, 2, . . ., where c[subscript s,k,i] = (−1)[superscript s]s![(k − 2i + 1)[superscript rs−1] + (k − 2i − 1)[superscript rs+r−1]/(2(rs + r − 1)!). Further results
are also proved.Wed, 04 Dec 2013 14:56:21 GMThttp://hdl.handle.net/2381/284762013-12-04T14:56:21ZFurther Results on the Dilogarithm Integral
http://hdl.handle.net/2381/28472
Title: Further Results on the Dilogarithm Integral
Authors: Jolevska-Tuneska, Biljana; Fisher, Brian
Abstract: The dilogarithm integral Li(x[superscript s]) and its associated functions Li[subscript +](x[superscript s]) and Li[subscript -](x[superscript s]) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of these functions and other functions are then found.Tue, 03 Dec 2013 16:35:00 GMThttp://hdl.handle.net/2381/284722013-12-03T16:35:00ZThe effects of axial flow and surface mass-flux on the stability of the rotating-sphere boundary layer
http://hdl.handle.net/2381/28456
Title: The effects of axial flow and surface mass-flux on the stability of the rotating-sphere boundary layer
Authors: Barrow, Alistair
Abstract: A theoretical investigation is carried out into the linear stability of the boundary-layer flow around a rotating sphere immersed in an incompressible viscous fluid. Two potentially stabilising mechanisms are considered: a forced uniform axial flow in the surrounding fluid, and the introduction of mass suction/injection through the surface of the sphere. The investigation is broadly split into a “local” analysis, where a parallel-flow assumption is made which limits the study to individual latitudinal positions; and a “global” analysis, where the entire streamwise extent of the flow is considered. In the local analysis, both stationary and travelling convective disturbances are considered. For a representative subset of the parameter space, critical Reynolds numbers are presented for the predicted onset of convective and absolute instabilities. Axial flow and surface suction are typically found to postpone the onset of all types of instability by raising the critical Reynolds number, whereas surface injection has the opposite effect. This is further demonstrated by a consideration of the convective and absolute growth rates at various parameter values.
The results of the global analysis suggest that the rotating sphere can support a self-sustained, linearly globally-unstable global mode for sufficiently large rotation rates. This is in contrast to the case of the rotating disk, where it is generally accepted that self-sustained linear global modes do not occur.Wed, 27 Nov 2013 09:39:53 GMThttp://hdl.handle.net/2381/284562013-11-27T09:39:53ZApproximation on the complex sphere
http://hdl.handle.net/2381/28368
Title: Approximation on the complex sphere
Authors: Alsaud, Huda Saleh
Abstract: The aim of this thesis is to study approximation of multivariate functions on the complex sphere by spherical harmonic polynomials. Spherical harmonics arise naturally in many theoretical and practical applications. We consider different aspects of the approximation by spherical harmonic which play an important role in a wide range of topics. We study approximation on the spheres by spherical polynomials from the geometric point of view. In particular, we study and develop a generating function of Jacobi polynomials and its special cases which are of geometric nature and give a new representation for the left hand side of a well-known formulae for generating functions for Jacobi polynomials (of integer indices) in terms of associated Legendre functions. This representation arises as a consequence of the interpretation of projective spaces as quotient spaces of complex spheres. In addition, we develop new elements of harmonic analysis on the complex sphere, and use these to establish Jackson's and Kolmogorov's inequalities. We apply these results to get order sharp estimates for m-term approximation. The results obtained are a synthesis of new results on classical orthogonal polynomials geometric properties of Euclidean spaces. As another aspect of approximation, we consider interpolation by radial basis functions. In particular, we study interpolation on the spheres and its error estimate. We show that the improved error of convergence in n dimensional real sphere, given in [7], remain true in the case of the complex sphere.Fri, 08 Nov 2013 12:38:44 GMThttp://hdl.handle.net/2381/283682013-11-08T12:38:44ZSolid-Liquid Interfacial Properties of Fe and Fe-C Alloys from Molecular Dynamics Simulations
http://hdl.handle.net/2381/28269
Title: Solid-Liquid Interfacial Properties of Fe and Fe-C Alloys from Molecular Dynamics Simulations
Authors: Melnykov, Mykhailo
Abstract: This project is devoted to the study of solid-liquid interfaces in pure Fe and Fe-C alloys using molecular simulation. It consists of three parts: first, we use the coexisting phases approach to calculate melting phase diagrams of several recent Fe-C interaction potentials, such as Embedded Atom Method (EAM) potential of Lau et al., EAM potential of Hepburn and Ackland, and Analytic Bond Order (ABOP) potential of Henriksson and Nordlund. Melting of both bcc (ferrite) and fcc (austenite) crystal structures is investigated with C concentrations up to 5 wt%. The results are compared with the experimental data and suggest that the potential of Hepburn and Ackland is the most accurate in reproducing the melting phase diagram of the ferrite but the austenite cannot be stabilised at any C concentration for this potential.
The potential of Lau et al. yields the best qualitative agreement with the real phase diagram in that the ferrite-liquid coexistence at low C concentrations is replaced by the austenite-liquid coexistence at higher C concentrations. However, the crossover C concentration is much larger and the ferrite melting temperature is much higher than in the real Fe-C alloy. The ABOP potential of Henriksson and Nordlund correctly predicts the relative stability of ferrite and austenite at melting, but significantly underestimates the solubility of C in the solid phases.
Second, we develop a new direct method for calculating the solid-liquid interfacial free energy using deformation of the solid-liquid coexistence system.
The deformation is designed to change the area of the interface, while preserving the volume of the system and crystal structure of the solid phase. The interfacial free energy is calculated as the deformation work divided by the change of the interfacial area. The method is applied to the bcc solid-liquid interface of pure Fe described by the Hepburn and Ackland potential. The obtained results are somewhat different from those calculated by the established methods so further development and analysis are required.
Third, we investigate the dependence on C concentration of the bcc solid-liquid interfacial free energy of Fe-C alloy described by the Hepburn and Ackland potential. We use the method proposed by Frolov and Mishin which is analogous to the Gibbs-Duhem integration along the solid-liquid coexistence line. The calculations are performed for three different crystal orientations (100), (110) and (111), allowing us to determine the anisotropy of the interfacial free energy and its dependence on C concentration along the coexistence line. Although the precision is somewhat limited by the high computational cost of such calculations.Tue, 08 Oct 2013 15:00:03 GMThttp://hdl.handle.net/2381/282692013-10-08T15:00:03ZA Classification of Toral and Planar Attractors and Substitution Tiling Spaces
http://hdl.handle.net/2381/28227
Title: A Classification of Toral and Planar Attractors and Substitution Tiling Spaces
Authors: McCann, Sheila Margaret
Abstract: We focus on dynamical systems which are one-dimensional expanding
attractors with a local product structure of an arc times a Cantor set. We
define a class of Denjoy continua and show that each one of the class is homeomorphic to an orientable DA attractor with four complementary domains which in turn is homeomorphic to a tiling space consisting of aperiodic substitution tilings. The planar attractors are non-orientable as is the Plykin attractor in the 2-sphere which we describe.
We classify these attractors and tiling spaces up to homeomorphism and the
symmetries of the underlying spaces up to isomorphism. The criterion for
homeomorphism is the irrational slope of the expanding eigenvector of the
defining matrix from whence the attractor was formed whilst the criterion for
isomorphism is the matrix itself. We find that the permutation groups arising
from the 4 'special points' which serve as the repelling set of an attractor are isomorphic to subgroups of S[subscript 4]. Restricted to these 4 special points, we show that the isotopy class group of the self-homeomorphisms of an attractor, and likewise those of a tiling space, is isomorphic to Z ⊕ Z[subscript 2].Thu, 26 Sep 2013 09:27:20 GMThttp://hdl.handle.net/2381/282272013-09-26T09:27:20ZThe Stability and Transition of the Compressible Boundary-Layer Flow over Broad Rotating Cones
http://hdl.handle.net/2381/28219
Title: The Stability and Transition of the Compressible Boundary-Layer Flow over Broad Rotating Cones
Authors: Towers, Paul David
Abstract: The subject of fluid flows over axisymmetric bodies has increased in recent
times, as they can be used to model flows over a swept wing, spinning projectiles and aeroengines amongst other things. A better mathematical understanding of the transition from laminar to turbulent flow within the boundary layer could lead to an improvement in the design of such applications.
We consider a compressible fluid flow over a rotating cone, defined by half-angle ψ. The mean flow boundary-layer equations are derived and we conduct a high Reynolds number asymptotic linear stability analysis. The flow is susceptible to instabilities caused by inviscid crossflow modes (type I ) and modes caused by a viscous-Coriolis balance force (type II ). Both are considered, along with the effects of changes in the cone half-angle, the magnitude of the local Mach number and the temperature at the cone wall. A surface suction along the cone wall is also analysed.Wed, 25 Sep 2013 15:03:47 GMThttp://hdl.handle.net/2381/282192013-09-25T15:03:47ZAdaptive Radial Basis Function Interpolation for Time-Dependent Partial Differential Equations
http://hdl.handle.net/2381/28184
Title: Adaptive Radial Basis Function Interpolation for Time-Dependent Partial Differential Equations
Authors: Naqvi, Syeda Laila
Abstract: In this thesis we have proposed the meshless adaptive method by radial basis functions (RBFs) for the solution of the time-dependent partial differential equations (PDEs) where the approximate solution is obtained by the multiquadrics (MQ) and the local scattered data reconstruction has been done by polyharmonic splines. We choose MQ because of its exponential convergence for sufficiently smooth functions. The solution of partial differential equations arising in science and engineering, frequently have large variations occurring over small portion of the physical domain, the challenge then is to resolve the solution behaviour there. For the sake of efficiency we require a finer grid in those parts of the physical domain whereas a much coarser grid can be used otherwise.
During our journey, we come up with different ideas and have found many interesting results but the main motivation for the one-dimensional case was the Korteweg-de Vries (KdV) equation rather than the common test problems. The KdV equation is a nonlinear hyperbolic equation with smooth solutions at all times. Furthermore the methods available in the literature for solving this problem are rather fully implicit or limited literature can be found using explicit and semi-explicit methods. Our approach is to adaptively select the nodes, using the radial basis function interpolation.
We aimed in, the extension of our method in solving two-dimensional partial differential equations, however to get an insight of the method we developed the algorithms for one-dimensional PDEs and two-dimensional interpolation problem. The experiments show that the method is able to track the developing features of the profile of the solution. Furthermore this work is based on computations and not on proofs.Fri, 13 Sep 2013 09:46:03 GMThttp://hdl.handle.net/2381/281842013-09-13T09:46:03ZDiscontinuous Galerkin Methods for Mass Transfer through Semi-Permeable Membranes
http://hdl.handle.net/2381/28090
Title: Discontinuous Galerkin Methods for Mass Transfer through Semi-Permeable Membranes
Authors: Cangiani, Andrea; Georgoulis, Emmanuil H.; Jensen, Max
Abstract: A discontinuous Galerkin (dG) method for the numerical solution of initial/boundary value multi-compartment partial differential equation (PDE) models, interconnected with interface conditions, is presented and analysed. The study of interface problems is motivated by models of mass transfer of solutes through semi-permeable membranes. More specifically, a model problem consisting of a system of semilinear parabolic advection-diffusion-reaction partial differential equations in each compartment, equipped with respective initial and boundary conditions, is considered. Nonlinear interface conditions modelling selective permeability, congestion and partial reflection are applied to the compartment interfaces. An interior penalty dG method is presented for this problem and it is analysed in the space-discrete setting. The a priori analysis shows that the method yields optimal a priori bounds, provided the exact solution is sufficiently smooth. Numerical experiments indicate agreement with the theoretical bounds and highlight the stability of the numerical method in the advection-dominated regime.Tue, 27 Aug 2013 15:28:56 GMThttp://hdl.handle.net/2381/280902013-08-27T15:28:56ZErratum: Collision dynamics of granular particles with adhesion (Physical Review E (2007) 76 (051302))
http://hdl.handle.net/2381/28089
Title: Erratum: Collision dynamics of granular particles with adhesion (Physical Review E (2007) 76 (051302))
Authors: Brilliantov, Nikolai V.; Albers, Nicole; Spahn, Frank; Pöschel, Thorsten
Abstract: An erratum to the article available at http://hdl.handle.net/2381/20218.Tue, 27 Aug 2013 14:59:00 GMThttp://hdl.handle.net/2381/280892013-08-27T14:59:00ZThe canonical ensemble via symplectic integrators using Nosé and Nosé–Poincaré chains
http://hdl.handle.net/2381/28031
Title: The canonical ensemble via symplectic integrators using Nosé and Nosé–Poincaré chains
Authors: Leimkuhler, Benedict J.; Sweet, Christopher R.
Abstract: Simulations that sample from the canonical ensemble can be generated by the addition of a single degree of freedom, provided that the system is ergodic, as described by Nosé with subsequent modifications by Hoover to allow sampling in real time. Nosé–Hoover dynamics is not ergodic for small or stiff systems and the addition of auxiliary thermostats is needed to overcome this deficiency. Nosé–Hoover dynamics, like its derivatives, does not have a Hamiltonian structure, precluding the use of symplectic integrators which are noted for their long term stability and structure preservation. As an alternative to Nosé–Hoover, the Hamiltonian Nosé–Poincaré method was proposed by Bond, Laird, and Leimkuhler [J. Comput. Phys. 151, 114 (1999)], but the straightforward addition of thermostatting chains does not sample from the canonical ensemble. In this paper a method is proposed whereby additional thermostats can be applied to a Hamiltonian system while retaining sampling from the canonical ensemble. This technique has been used to construct thermostatting chains for the Nosé and Nosé–Poincaré methods.Wed, 26 Jun 2013 15:14:48 GMThttp://hdl.handle.net/2381/280312013-06-26T15:14:48ZThe anisotropic hard-sphere crystal-melt interfacial free energy from fluctuations.
http://hdl.handle.net/2381/28028
Title: The anisotropic hard-sphere crystal-melt interfacial free energy from fluctuations.
Authors: Davidchack, Ruslan L.; Morris, James R.; Laird, Brian B.
Abstract: We have calculated the interfacial free energy for the hard-sphere system, as a function of crystal interface orientation, using a method that examines the fluctuations in the height of the interface during molecular dynamics simulations. The approach is particularly sensitive for the anisotropy of the interfacial free energy. We find an average interfacial free energy of gamma=0.56+/-0.02k(B)Tsigma(-2). This value is lower than earlier results based upon direct calculations of the free energy [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 85, 4751 (2000)]. However, both the average value and the anisotropy agree with the recent values obtained by extrapolation from direct calculations for a series of the inverse-power potentials [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 94, 086102 (2005)].Wed, 26 Jun 2013 14:36:42 GMThttp://hdl.handle.net/2381/280282013-06-26T14:36:42ZPricing Discretely Monitored Barrier Options and Credit Default Swaps under Lévy Processes
http://hdl.handle.net/2381/27912
Title: Pricing Discretely Monitored Barrier Options and Credit Default Swaps under Lévy Processes
Authors: de Innocentis, Marco
Abstract: We introduce a new, fast and accurate method to calculate prices and sensitivities of European vanilla and digital options under the Variance Gamma model. For near at-the-money options of short maturity, our method is much faster than those based on discretization and truncation of the inverse Fourier transform integral (iFT method).
We show that the results calculated with our method agree with those obtained with the iFT algorithm using very long and fine grids. Taking the results of our method as a benchmark, we show that the parabolic modification of the iFT method (Boyarchenko and Levendorskiĭ, 2012) is much more efficient than the standard (flat) version. Based on this conclusion, we consider an approach which uses a combination of backward induction and parabolic iFT to price discretely monitored barrier options, as well as credit default swaps, under wide classes of Lévy models. At each step of backward induction, we use piece-wise polynomial interpolation and parabolic iFT, which allows for efficient error control. We derive accurate recommendations for the choice of parameters of the numerical scheme, and produce numerical examples showing that oversimplified prescriptions in other methods can result in large errors.Thu, 30 May 2013 12:30:38 GMThttp://hdl.handle.net/2381/279122013-05-30T12:30:38ZRole of three-body interactions in formation of bulk viscosity in liquid argon
http://hdl.handle.net/2381/27877
Title: Role of three-body interactions in formation of bulk viscosity in liquid argon
Authors: Lishchuk, Sergey V.
Abstract: With the aim of locating the origin of discrepancy between experimental and computer simulation
results on bulk viscosity of liquid argon, a molecular dynamic simulation of argon interacting via
ab initio pair potential and triple-dipole three-body potential has been undertaken. Bulk viscosity,
obtained using Green-Kubo formula, is different from the values obtained from modeling argon
using Lennard-Jones potential, the former being closer to the experimental data. The conclusion is
made that many-body inter-atomic interaction plays a significant role in formation of bulk viscosity.Wed, 24 Apr 2013 14:51:14 GMThttp://hdl.handle.net/2381/278772013-04-24T14:51:14ZAdaptive Observers and Parameter Estimation for a Class of Systems Nonlinear in the Parameters
http://hdl.handle.net/2381/27849
Title: Adaptive Observers and Parameter Estimation for a Class of Systems Nonlinear in the Parameters
Authors: Tyukin, Ivan Y.; Steur, Erik; Nijmeijer, Henk; Leeuwen, Cees van
Abstract: We consider the problem of asymptotic reconstruction of the state and parameter values in systems of ordinary differential equations. A solution to this problem is proposed for a class of systems of which the unknowns are allowed to be nonlinearly parameterized functions of state and time. Going beyond the concept of asymptotic Lyapunov stability, we provide for this class a reconstruction technique based on the notions of weakly attracting sets and non-uniform convergence. Reconstruction of state and parameter values is subjected to persistency of excitation conditions. In absence of nonlinear parametrization the resulting observers reduce to standard estimation schemes. This allows to view the proposed method as a generalization of the conventional canonical adaptive observer design.Tue, 09 Apr 2013 14:30:08 GMThttp://hdl.handle.net/2381/278492013-04-09T14:30:08ZInner Ideals of Simple Locally Finite Lie Algebras
http://hdl.handle.net/2381/27828
Title: Inner Ideals of Simple Locally Finite Lie Algebras
Authors: Rowley, Jamie Robert Derek
Abstract: Inner ideals of simple locally finite dimensional Lie algebras over an algebraically closed field of characteristic 0 are described. In particular, it is shown that a simple locally finite dimensional Lie algebra has a non-zero proper inner ideal if and only if it is of diagonal type. Regular inner ideals of diagonal type Lie algebras are characterized in terms of left and right ideals of the enveloping algebra. Regular inner ideals of finitary simple Lie algebras are described. Inner ideals of some finite dimensional Lie algebras are studied. Maximal inner ideals of simple plain locally finite dimensional Lie algebras are classified.Wed, 27 Mar 2013 12:16:08 GMThttp://hdl.handle.net/2381/278282013-03-27T12:16:08ZLyapunov-like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems
http://hdl.handle.net/2381/27778
Title: Lyapunov-like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems
Authors: Gorban, Alexander N.; Tyukin, Ivan; Steur, Erik; Nijmeijer, Henk
Abstract: We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable subsystems with one-dimensional unstable dynamics or critically stable dynamics. Systems of this type arise in problems of nonlinear output regulation, parameter estimation and adaptive control. In addition to providing boundedness and convergence criteria the results allow to derive domains of initial conditions corresponding to solutions leaving a given neighborhood of the origin at least once. In contrast to other works addressing convergence issues in unstable systems, our results require neither input-output characterizations for the stable part nor estimates of convergence rates. The results are illustrated with examples, including the analysis of phase synchronization of neural oscillators with heterogenous coupling.
Description: Embargo length currently unknown. The article is still in press and full text will be made available once it has been published.Wed, 06 Mar 2013 16:08:28 GMThttp://hdl.handle.net/2381/277782013-03-06T16:08:28ZNonuniform small-gain theorems for systems with unstable invariant sets
http://hdl.handle.net/2381/27777
Title: Nonuniform small-gain theorems for systems with unstable invariant sets
Authors: Tyukin, Ivan; Steur, Erik; Nijmeijer, Henk; Van Leeuwen, Cees
Abstract: We consider the problem of asymptotic convergence to invariant sets in interconnected nonlinear dynamical systems. Standard approaches often require that the invariant sets be uniformly attracting, e. g., stable in the Lyapunov sense. This, however, is neither a necessary requirement nor is always useful. Systems may, for instance, be inherently unstable ( e. g., intermittent, itinerant, meta-stable) or the problem statement may include requirements that cannot be satisfied with stable solutions. This is often the case in general optimization problems and in nonlinear parameter identification or adaptation. Conventional techniques for these cases either rely on detailed knowledge of the system's vector-fields or require boundedness of its states. The presently proposed method relies only on estimates of the input-output maps and steady-state characteristics. The method requires the possibility of representing the system as an interconnection of a stable and contracting part with an unstable and exploratory part. We illustrate with examples how the method can be applied to problems of analyzing the asymptotic behavior of locally unstable systems as well as to problems of parameter identification and adaptation in the presence of nonlinear parametrizations. The relation of our results to conventional small-gain theorems is discussed.Wed, 06 Mar 2013 15:37:09 GMThttp://hdl.handle.net/2381/277772013-03-06T15:37:09ZKernel Approximation on Compact Homogeneous Spaces
http://hdl.handle.net/2381/27598
Title: Kernel Approximation on Compact Homogeneous Spaces
Authors: Odell, Carl Richard
Abstract: This thesis is concerned with approximation on compact homogeneous spaces.
The first part of the research involves a particular kind of compact homogeneous space, the hypersphere, S ͩˉ¹ embedded in R ͩ. It is a calculation of three integrals associated with approximation using radial basis functions, calculating the Fourier-Gegenbauer coefficients for two such functions. The latter part of the research is a calculation of an error bound for compact homogeneous spaces when interpolating with a G-invariant kernel, a generalisation of a result already known for spheres.Wed, 28 Nov 2012 10:06:45 GMThttp://hdl.handle.net/2381/275982012-11-28T10:06:45ZThe Convective Instability of the Boundary-Layer Flow over Families of Rotating Spheroids
http://hdl.handle.net/2381/27576
Title: The Convective Instability of the Boundary-Layer Flow over Families of Rotating Spheroids
Authors: Samad, Abdul
Abstract: The majority of this work is concerned with the local-linear convective instability analysis of the incompressible boundary-layer flows over prolate spheroids and oblate spheroids rotating in otherwise still fluid. The laminar boundary layer and the perturbation equations have been formulated by introducing two distinct orthogonal coordinate systems. A cross-sectional eccentricity parameter e is introduced to identify each spheroid within its family. Both systems of equations reduce exactly to those already established for the rotating sphere boundary layer. The effects of viscosity and streamline-curvature are included in each analysis.
We predict that for prolate spheroids at low to moderate latitudes, increasing eccentricity has a strong stabilizing effect. However, at high latitudes of ϴ ≥ 60, increasing eccentricity is seen to have a destabilizing effect. For oblate spheroids, increasing eccentricity has a stabilizing effect at all latitudes. Near the pole of both types of spheroids, the critical Reynolds numbers approach that for the rotating disk boundary layer. However, in prolate spheroid case near the pole for very large values of e, the critical Reynolds numbers exceed that for the rotating disk. We show that high curvature near the pole of prolate spheroids is responsible for the increase in critical Reynolds number with increasing eccentricity.
For both types of spheroids at moderate eccentricity, we predict that the most amplified modes travel at approximately 76% of the surface speed at all latitudes. This is consistent with the existing studies of boundary-layer flows over the related rotating-disk, -sphere and -cone geometries. However, for large values of eccentricity, the traveling speed of the most amplified modes increases up to approximately 90% of the surface speed of oblate spheroids and up to 100% in the prolate spheroid case.Wed, 07 Nov 2012 11:58:20 GMThttp://hdl.handle.net/2381/275762012-11-07T11:58:20ZTowards complete detection of unstable periodic orbits in chaotic systems
http://hdl.handle.net/2381/26993
Title: Towards complete detection of unstable periodic orbits in chaotic systems
Authors: Davidchack, RL; Lai, Y-C; Klebanoff, A; Bollt, EMWed, 24 Oct 2012 09:22:48 GMThttp://hdl.handle.net/2381/269932012-10-24T09:22:48ZTriple cohomology of Lie-Rinehart algebras and the canonical class of associative algebras
http://hdl.handle.net/2381/26994
Title: Triple cohomology of Lie-Rinehart algebras and the canonical class of associative algebras
Authors: Casas, JM; Ladra, M; Pirashvili, TWed, 24 Oct 2012 09:22:48 GMThttp://hdl.handle.net/2381/269942012-10-24T09:22:48ZVanishing line for the descent spectral sequence
http://hdl.handle.net/2381/26995
Title: Vanishing line for the descent spectral sequence
Authors: Pirashvili, TWed, 24 Oct 2012 09:22:48 GMThttp://hdl.handle.net/2381/269952012-10-24T09:22:48ZThird Mac Lane cohomology
http://hdl.handle.net/2381/26990
Title: Third Mac Lane cohomology
Authors: Baues, H-J; Jibladze, M; Pirashvili, TWed, 24 Oct 2012 09:22:48 GMThttp://hdl.handle.net/2381/269902012-10-24T09:22:48ZTowards a correct description of zooplankton feeding in models: Taking into account food-mediated unsynchronized vertical migration
http://hdl.handle.net/2381/26992
Title: Towards a correct description of zooplankton feeding in models: Taking into account food-mediated unsynchronized vertical migration
Authors: Morozov, AY; Morozov, AY; Arashkevich, EGWed, 24 Oct 2012 09:22:48 GMThttp://hdl.handle.net/2381/269922012-10-24T09:22:48ZWall-induced prefreezing in hard spheres: A thermodynamic perspective
http://hdl.handle.net/2381/26997
Title: Wall-induced prefreezing in hard spheres: A thermodynamic perspective
Authors: Laird, BB; Davidchack, RLWed, 24 Oct 2012 09:22:48 GMThttp://hdl.handle.net/2381/269972012-10-24T09:22:48ZVariations on the cohomology of loop spaces on generalized homogeneous spaces
http://hdl.handle.net/2381/26996
Title: Variations on the cohomology of loop spaces on generalized homogeneous spaces
Authors: Neumann, FWed, 24 Oct 2012 09:22:48 GMThttp://hdl.handle.net/2381/269962012-10-24T09:22:48ZThe hochschild cohomology ring of a class of special biserial algebras
http://hdl.handle.net/2381/26980
Title: The hochschild cohomology ring of a class of special biserial algebras
Authors: Snashall, N; Taillefer, R; Taillefer, RWed, 24 Oct 2012 09:22:47 GMThttp://hdl.handle.net/2381/269802012-10-24T09:22:47ZThe Hochschild cohomology ring of a selfinjective algebra of finite representation type
http://hdl.handle.net/2381/26983
Title: The Hochschild cohomology ring of a selfinjective algebra of finite representation type
Authors: Green, EL; Snashall, N; Solberg, ØWed, 24 Oct 2012 09:22:47 GMThttp://hdl.handle.net/2381/269832012-10-24T09:22:47ZThe K-theory of C -algebras with finite dimensional irreducible representations
http://hdl.handle.net/2381/26985
Title: The K-theory of C -algebras with finite dimensional irreducible representations
Authors: Hunton, J; Shchukin, MWed, 24 Oct 2012 09:22:47 GMThttp://hdl.handle.net/2381/269852012-10-24T09:22:47ZThe simplest random walks for the Dirichlet problem
http://hdl.handle.net/2381/26986
Title: The simplest random walks for the Dirichlet problem
Authors: Milstein, GN; Milstein, GN; Tretyakov, MV; Tretyakov, MVWed, 24 Oct 2012 09:22:47 GMThttp://hdl.handle.net/2381/269862012-10-24T09:22:47ZThe economics of motion perception and invariants of visual sensitivity.
http://hdl.handle.net/2381/26975
Title: The economics of motion perception and invariants of visual sensitivity.
Authors: Gepshtein, S; Tyukin, I; Kubovy, M
Abstract: Neural systems face the challenge of optimizing their performance with limited resources, just as economic systems do. Here, we use tools of neoclassical economic theory to explore how a frugal visual system should use a limited number of neurons to optimize perception of motion. The theory prescribes that vision should allocate its resources to different conditions of stimulation according to the degree of balance between measurement uncertainties and stimulus uncertainties. We find that human vision approximately follows the optimal prescription. The equilibrium theory explains why human visual sensitivity is distributed the way it is and why qualitatively different regimes of apparent motion are observed at different speeds. The theory offers a new normative framework for understanding the mechanisms of visual sensitivity at the threshold of visibility and above the threshold and predicts large-scale changes in visual sensitivity in response to changes in the statistics of stimulation and system goals.Wed, 24 Oct 2012 09:22:46 GMThttp://hdl.handle.net/2381/269752012-10-24T09:22:46ZSubalgebras of group cohomology defined by infinite loop spaces
http://hdl.handle.net/2381/26950
Title: Subalgebras of group cohomology defined by infinite loop spaces
Authors: Hunton, JR; Schuster, BWed, 24 Oct 2012 09:22:45 GMThttp://hdl.handle.net/2381/269502012-10-24T09:22:45ZSolving parabolic stochastic partial differential equations via averaging over characteristics
http://hdl.handle.net/2381/26937
Title: Solving parabolic stochastic partial differential equations via averaging over characteristics
Authors: Milstein, GN; Tretyakov, MVWed, 24 Oct 2012 09:22:44 GMThttp://hdl.handle.net/2381/269372012-10-24T09:22:44ZStrict polynomial functors and coherent functors
http://hdl.handle.net/2381/26945
Title: Strict polynomial functors and coherent functors
Authors: Franjou, V; Pirashvili, TWed, 24 Oct 2012 09:22:44 GMThttp://hdl.handle.net/2381/269452012-10-24T09:22:44ZStability and stabilization of the lattice Boltzmann method
http://hdl.handle.net/2381/26940
Title: Stability and stabilization of the lattice Boltzmann method
Authors: Brownlee, RA; Gorban, AN; Levesley, JWed, 24 Oct 2012 09:22:44 GMThttp://hdl.handle.net/2381/269402012-10-24T09:22:44ZSodium salts in E-ring ice grains from an ocean below the surface of Enceladus.
http://hdl.handle.net/2381/26932
Title: Sodium salts in E-ring ice grains from an ocean below the surface of Enceladus.
Authors: Postberg, F; Kempf, S; Schmidt, J; Brilliantov, N; Beinsen, A; Abel, B; Buck, U; Srama, R
Abstract: Saturn's moon Enceladus emits plumes of water vapour and ice particles from fractures near its south pole, suggesting the possibility of a subsurface ocean. These plume particles are the dominant source of Saturn's E ring. A previous in situ analysis of these particles concluded that the minor organic or siliceous components, identified in many ice grains, could be evidence for interaction between Enceladus' rocky core and liquid water. It was not clear, however, whether the liquid is still present today or whether it has frozen. Here we report the identification of a population of E-ring grains that are rich in sodium salts ( approximately 0.5-2% by mass), which can arise only if the plumes originate from liquid water. The abundance of various salt components in these particles, as well as the inferred basic pH, exhibit a compelling similarity to the predicted composition of a subsurface Enceladus ocean in contact with its rock core. The plume vapour is expected to be free of atomic sodium. Thus, the absence of sodium from optical spectra is in good agreement with our results. In the E ring the upper limit for spectroscopy is insufficiently sensitive to detect the concentrations we found.Wed, 24 Oct 2012 09:22:43 GMThttp://hdl.handle.net/2381/269322012-10-24T09:22:43ZSequences of Willmore surfaces
http://hdl.handle.net/2381/26927
Title: Sequences of Willmore surfaces
Authors: Leschke, K; Pedit, F; Pedit, FWed, 24 Oct 2012 09:22:43 GMThttp://hdl.handle.net/2381/269272012-10-24T09:22:43ZSemi-passivity and synchronization of diffusively coupled neuronal oscillators
http://hdl.handle.net/2381/26925
Title: Semi-passivity and synchronization of diffusively coupled neuronal oscillators
Authors: Steur, E; Nijmeijer, H; Tyukin, I; Tyukin, IWed, 24 Oct 2012 09:22:43 GMThttp://hdl.handle.net/2381/269252012-10-24T09:22:43ZQuasi-equilibrium closure hierarchies for the Boltzmann equation
http://hdl.handle.net/2381/26905
Title: Quasi-equilibrium closure hierarchies for the Boltzmann equation
Authors: Gorban, AN; Gorban, AN; Karlin, IV; Gorban, ANWed, 24 Oct 2012 09:22:42 GMThttp://hdl.handle.net/2381/269052012-10-24T09:22:42ZRadial basis interpolation on homogeneous manifolds: Convergence rates
http://hdl.handle.net/2381/26906
Title: Radial basis interpolation on homogeneous manifolds: Convergence rates
Authors: Levesley, J; Ragozin, DLWed, 24 Oct 2012 09:22:42 GMThttp://hdl.handle.net/2381/269062012-10-24T09:22:42ZReaction-diffusion waves in biology.
http://hdl.handle.net/2381/26909
Title: Reaction-diffusion waves in biology.
Authors: Volpert, V; Petrovskii, S
Abstract: The theory of reaction-diffusion waves begins in the 1930s with the works in population dynamics, combustion theory and chemical kinetics. At the present time, it is a well developed area of research which includes qualitative properties of travelling waves for the scalar reaction-diffusion equation and for system of equations, complex nonlinear dynamics, numerous applications in physics, chemistry, biology, medicine. This paper reviews biological applications of reaction-diffusion waves.Wed, 24 Oct 2012 09:22:42 GMThttp://hdl.handle.net/2381/269092012-10-24T09:22:42ZQuantization of orbit bundles in gl
(ℂ)
http://hdl.handle.net/2381/26904
Title: Quantization of orbit bundles in gl
(ℂ)
Authors: Mudrov, A; Mudrov, A; Ostapenko, VWed, 24 Oct 2012 09:22:42 GMThttp://hdl.handle.net/2381/269042012-10-24T09:22:42ZOn the Hochschild cohomology of tame Hecke algebras
http://hdl.handle.net/2381/26896
Title: On the Hochschild cohomology of tame Hecke algebras
Authors: Erdmann, K; Schroll, SWed, 24 Oct 2012 09:22:41 GMThttp://hdl.handle.net/2381/268962012-10-24T09:22:41ZOn the state space geometry of the Kuramoto-Sivashinsky flow in a periodic domain
http://hdl.handle.net/2381/26897
Title: On the state space geometry of the Kuramoto-Sivashinsky flow in a periodic domain
Authors: Cvitanović, P; Siminos, E; Davidchack, RLWed, 24 Oct 2012 09:22:41 GMThttp://hdl.handle.net/2381/268972012-10-24T09:22:41ZOn decomposition numbers and Alvis-Curtis duality
http://hdl.handle.net/2381/26894
Title: On decomposition numbers and Alvis-Curtis duality
Authors: Ackermann, B; Schroll, SWed, 24 Oct 2012 09:22:41 GMThttp://hdl.handle.net/2381/268942012-10-24T09:22:41Z