All Outputs (99)

Two-dimensional state sum models and spin structures (2014)
Journal Article

The state sum models in two dimensions introduced by Fukuma, Hosono and Kawai are generalised by allowing algebraic data from a non-symmetric Frobenius algebra. Without any further data, this leads to a state sum model on the sphere. When the data is... Read More about Two-dimensional state sum models and spin structures.

Optimal performance of endoreversible quantum refrigerators (2014)
Journal Article

The derivation of general performance benchmarks is important in the design of highly optimized heat engines and refrigerators. To obtain them, one may model phenomenologically the leading sources of irreversibility ending up with results that are mo... Read More about Optimal performance of endoreversible quantum refrigerators.

Nonassociative geometry in quasi-Hopf representation categories I: bimodules and their internal homomorphisms (2014)
Journal Article

We systematically study noncommutative and nonassociative algebras A and their bimodules as algebras and bimodules internal to the representation category of a quasitriangular quasi-Hopf algebra. We enlarge the morphisms of the monoidal category of A... Read More about Nonassociative geometry in quasi-Hopf representation categories I: bimodules and their internal homomorphisms.

Nonlinear compliance modulates dynamic bronchoconstriction in a multiscale airway model (2014)
Journal Article

Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds (2014)
Journal Article

We apply compensated convex transforms to define a multiscale Hausdorff stable method to extract intersections between smooth compact manifolds represented by their characteristic functions or as point clouds embedded in Rn. We prove extraction resul... Read More about Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds.

Laplace approximation of Lauricella functions F A and F D (2014)
Journal Article

The Lauricella functions, which are generalizations of the Gauss hypergeometric function 2 F 1, arise naturally in many areas of mathematics and statistics. So far as we are aware, there is little or nothing in the literature on how to calculate nume... Read More about Laplace approximation of Lauricella functions F A and F D.

Iterative regularization for ensemble data assimilation in reservoir models (2014)
Journal Article

Snakes and ladders in an inhomogeneous neural field model (2014)
Journal Article

Continuous neural field models with inhomogeneous synaptic connectivities are known to support traveling fronts as well as stable bumps of localized activity. We analyze stationary localized structures in a neural field model with periodic modulation... Read More about Snakes and ladders in an inhomogeneous neural field model.

A boundary integral formalism for stochastic ray tracing in billiards (2014)
Journal Article

Determining the flow of rays or non-interacting particles driven by a force or velocity field is fundamental to modelling many physical processes. These include particle flows arising in fluid mechanics and ray flows arising in the geometrical optics... Read More about A boundary integral formalism for stochastic ray tracing in billiards.

Duality-based two-level error estimation for time-dependent PDEs: application to linear and nonlinear parabolic equations (2014)
Journal Article

We introduce a duality-based two-level error estimator for linear and nonlinear time-dependent problems. The error measure can be a space-time norm, energy norm, final-time error or other error related functional. The general methodology is developed... Read More about Duality-based two-level error estimation for time-dependent PDEs: application to linear and nonlinear parabolic equations.

Quantum estimation of the Schwarzschild spacetime parameters of the Earth (2014)
Journal Article

We propose a quantum experiment to measure with high precision the Schwarzschild spacetime parameters of the Earth. The scheme can also be applied to measure distances by taking into account the curvature of the Earth’s spacetime. As a wave packet of... Read More about Quantum estimation of the Schwarzschild spacetime parameters of the Earth.

Separating invariants and local cohomology (2014)
Journal Article

The study of separating invariants is a recent trend in invariant theory. For a finite group acting linearly on a vector space, a separating set is a set of invariants whose elements separate the orbits of G. In some ways, separating sets often exhib... Read More about Separating invariants and local cohomology.

Equivalence classes and local asymptotic normality in system identification for quantum Markov chains (2014)
Journal Article

We consider the problem of identifying and estimating dynamical parameters of an ergodic quantum Markov chain, when only the stationary output is accessible for measurements. The starting point of the analysis is the fact that the knowledge of the ou... Read More about Equivalence classes and local asymptotic normality in system identification for quantum Markov chains.

Onset and decay of the 1 + 1 Hawking–Unruh effect: what the derivative-coupling detector saw (2014)
Journal Article

We study an Unruh–DeWitt particle detector that is coupled to the proper time derivative of a real scalar field in 1 + 1 spacetime dimensions. Working within first-order perturbation theory, we cast the transition probability into a regulator- free f... Read More about Onset and decay of the 1 + 1 Hawking–Unruh effect: what the derivative-coupling detector saw.

Nonlinear multigrid methods for second order differential operators with nonlinear diffusion coefficient (2014)
Journal Article

Nonlinear multigrid methods such as the Full Approximation Scheme (FAS) and Newton-multigrid (Newton-MG) are well established as fast solvers for nonlinear PDEs of elliptic and parabolic type. In this paper we consider Newton-MG and FAS iterations ap... Read More about Nonlinear multigrid methods for second order differential operators with nonlinear diffusion coefficient.

Compensated convexity and Hausdorff stable geometric singularity extractions (2014)
Journal Article

We develop and apply the theory of lower and upper compensated convex transforms introduced in [K. Zhang, Compensated convexity and its applications, Ann. Inst. H. Poincaré Anal. Non Linéaire 25 (2008) 743–771] to define multiscale, parametrized, geo... Read More about Compensated convexity and Hausdorff stable geometric singularity extractions.

Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in (2014)
Journal Article

We investigate the occurrence of coarse macroscopic states in an agent-based model of consumer lock-in. The system studied here is a modification of an existing model by Garlic and Chli [24] and it serves as a prototypical Ising-type sociological sys... Read More about Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in.

Superattracting fixed points of quasiregular mappings (2014)
Journal Article

We investigate the rate of convergence of the iterates of an n-dimensional quasiregular mapping within the basin of attraction of a fixed point of high local index. A key tool is a refinement of a result that gives bounds on the distortion of the ima... Read More about Superattracting fixed points of quasiregular mappings.

Application of stochastic phenomenological modelling to cell-to-cell and beat-to-beat electrophysiological variability in cardiac tissue (2014)
Journal Article

Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows (2014)
Journal Article

In this article we consider the application of goal-oriented mesh adaptation to problems posed on complicated domains which may contain a huge number of local geometrical features, or micro-structures. Here, we exploit the composite variant of the di... Read More about Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows.