DSpace Collection:http://hdl.handle.net/2381/38232017-03-23T22:03:22Z2017-03-23T22:03:22ZA dissipative force between colliding viscoelastic bodies: Rigorous approachBrilliantov, Nikolay V.Pimenova, Anastasiya V.Goldobin, Denis S.http://hdl.handle.net/2381/395442017-03-23T03:21:13Z2017-03-22T13:48:38ZTitle: A dissipative force between colliding viscoelastic bodies: Rigorous approach
Authors: Brilliantov, Nikolay V.; Pimenova, Anastasiya V.; Goldobin, Denis S.
Abstract: A collision of viscoelastic bodies is analysed within a mathematically rigorous approach. We develop a perturbation scheme to solve continuum mechanics equation, which deals simultaneously with strain and strain rate in the bulk of the bodies' material. We derive dissipative force that acts between particles and express it in terms of particles' deformation, deformation rate and material parameters. It differs noticeably from the currently used dissipative force, found within the quasi-static approximation and does not suffer from inconsistencies of this approximation. The proposed approach may be used for other continuum mechanics problems where the bulk dissipation is addressed.2017-03-22T13:48:38ZA Generalist Predator Regulating Spread of a Wildlife Disease: Exploring Two Infection Transmission ScenariosSen, M.Banerjee, M.Morozov, A.http://hdl.handle.net/2381/395432017-03-23T03:21:13Z2017-03-22T13:39:47ZTitle: A Generalist Predator Regulating Spread of a Wildlife Disease: Exploring Two Infection Transmission Scenarios
Authors: Sen, M.; Banerjee, M.; Morozov, A.
Abstract: Ecoepidemiology is a well-developed branch of theoretical ecology, which explores interplay between the trophic interactions and the disease spread. In most ecoepidemiological models, however, the authors assume the predator to be a specialist, which consumes only a single prey species. In few existing papers, in which the predator was suggested to be a generalist, the alternative food supply was always considered to be constant. This is obviously a simplification of reality, since predators can often choose between a number of different prey. Consumption of these alternative prey can dramatically change their densities and strongly influence the model predictions. In this paper, we try to bridge the gap and explore a generic eco-epidemiological system with a generalist predator, where the densities of all prey are dynamical variables. The model consists of two prey species, one of which is subject to an infectious disease, and a predator, which consumes both prey species. We investigate two main scenarios of infection transmission mode: (i) the disease transmission rate is predator independent and (ii) the transmission rate is a function of predator density. For both scenarios we fulfil an extensive bifurcation analysis. We show that including a second dynamical prey in the system can drastically change the dynamics of the single prey case. In particular, the presence of a second prey impedes disease spread by decreasing the basic reproduction number and can result in a substantial drop of the disease prevalence. We demonstrate that with efficient consumption of the second prey species by the predator, the predator-dependent disease transmission can not destabilize interactions, as in the case with a specialist predator. Interestingly, even if the population of the second prey eventually vanishes and only one prey species finally remains, the system with two prey species may exhibit different properties to those of the single prey system.2017-03-22T13:39:47ZModelling in Ecology, Epidemiology and Ecoepidemiology: Introduction to the Special IssueMorozov, A.http://hdl.handle.net/2381/395422017-03-23T03:21:13Z2017-03-22T10:03:33ZTitle: Modelling in Ecology, Epidemiology and Ecoepidemiology: Introduction to the Special Issue
Authors: Morozov, A.2017-03-22T10:03:33ZNoise-Produced Patterns in Images Constructed from Magnetic Flux Leakage DataGoldobin, D. S.Pimenova, A. V.Levesley, J.Elkington, P.Bacciarelli, M.http://hdl.handle.net/2381/395412017-03-23T03:21:12Z2017-03-22T09:58:52ZTitle: Noise-Produced Patterns in Images Constructed from Magnetic Flux Leakage Data
Authors: Goldobin, D. S.; Pimenova, A. V.; Levesley, J.; Elkington, P.; Bacciarelli, M.
Abstract: Magnetic flux leakage measurements help identify the position, size and shape of corrosion-related defects in steel casings used to protect boreholes drilled into oil and gas reservoirs. Images constructed from magnetic flux leakage data contain patterns related to noise inherent in the method. We investigate the patterns and their scaling properties for the case of delta-correlated input noise, and consider the implications for the method’s ability to resolve defects. The analytical evaluation of the noise-produced patterns is made possible by model reduction facilitated by large-scale approximation. With appropriate modification, the approach can be employed to analyze noise-produced patterns in other situations where the data of interest are not measured directly, but are related to the measured data by a complex linear transform involving integrations with respect to spatial coordinates.
Description: Mathematics Subject Classification: 78A30 / 78M34 / 60G602017-03-22T09:58:52ZMagnetic Flux Leakage Method: Large-Scale ApproximationPimenova, A. V.Goldobin, D. S.Levesley, J.Ivantsov, A. O.Elkington, P.Bacciarelli, M.http://hdl.handle.net/2381/395402017-03-23T03:21:12Z2017-03-22T09:55:42ZTitle: Magnetic Flux Leakage Method: Large-Scale Approximation
Authors: Pimenova, A. V.; Goldobin, D. S.; Levesley, J.; Ivantsov, A. O.; Elkington, P.; Bacciarelli, M.
Abstract: We consider the application of the magnetic flux leakage (MFL) method to the detection of defects in ferromagnetic (steel) tubulars. The problem setup corresponds to the cases where the distance from the casing and the point where the magnetic field is measured is small compared to the curvature radius of the undamaged casing and the scale of inhomogeneity of the magnetic field in the defect-free case. Mathematically this corresponds to the planar ferromagnetic layer in a uniform magnetic field oriented along this layer. Defects in the layer surface result in a strong deformation of the magnetic field, which provides opportunities for the reconstruction of the surface profile from measurements of the magnetic field. We deal with large-scale defects whose depth is small compared to their longitudinal sizes—these being typical of corrosive damage. Within the framework of large-scale approximation, analytical relations between the casing thickness profile and the measured magnetic field can be derived.
Description: Mathematics Subject Classification: 78A30 / 78M34 / 78A552017-03-22T09:55:42ZThree Waves of Chemical DynamicsGorban, A. N.Yablonsky, G. S.http://hdl.handle.net/2381/395392017-03-23T03:21:10Z2017-03-22T09:46:50ZTitle: Three Waves of Chemical Dynamics
Authors: Gorban, A. N.; Yablonsky, G. S.
Abstract: Three epochs in development of chemical dynamics are presented. We try to understand the modern research programs in the light of classical works.2017-03-22T09:46:50ZGeneration of mechanical force by grafted polyelectrolytes in an electric fieldBrilliantov, N. V.Budkov, Yu. A.Seidel, C.http://hdl.handle.net/2381/395302017-03-22T03:22:09Z2017-03-21T10:25:12ZTitle: Generation of mechanical force by grafted polyelectrolytes in an electric field
Authors: Brilliantov, N. V.; Budkov, Yu. A.; Seidel, C.
Abstract: We study theoretically and by means of molecular dynamics (MD) simulations the generation of mechanical force by grafted polyelectrolytes in an external electric field, which favors its adsorption on the grafting plane. The force arises in deformable bodies linked to the free end of the chain. Varying the field, one controls the length of the nonadsorbed part of the chain and hence the deformation of the target body, i.e., the arising force too. We consider target bodies with a linear force-deformation relation and with a Hertzian one. While the first relation models a coiled Gaussian chain, the second one describes the force response of a squeezed colloidal particle. The theoretical dependences of generated force and compression of the target body on an applied field agree very well with the results of MD simulations. The analyzed phenomenon may play an important role in future nanomachinery, e.g., it may be used to design nanovices to fix nanosized objects.2017-03-21T10:25:12ZForward-Invariant Peeling in Chemical Dynamics: a Simple Case StudyGorban, A. N.http://hdl.handle.net/2381/395282017-03-22T03:22:08Z2017-03-21T10:12:37ZTitle: Forward-Invariant Peeling in Chemical Dynamics: a Simple Case Study
Authors: Gorban, A. N.
Abstract: Forward-invariant peeling aims to produce forward-invariant subset from a given set in phase space. The structure of chemical kinetic equations allows us to describe the general operations of the forward-invariant peeling. For example, we study a simple reaction network with three components A1,A2,A3 and reactions A1 → A2 → A3 → A1, 2A1 ⇌ 3A2 (without any stoichiometric conservation law). We assume that kinetics obey the classical mass action law and reaction rate constants are positive intervals 0 <ki min ≤ ki ≤ ki max< ∞. Kinetics of this system is described by a system of differential inclusions. We produce forward-invariant sets for these kinetic inclusions from the sets { c | ci ≥ 0, ∑ ci ≥ ε } by the forward-invariant peeling (for sufficiently small ε> 0). In particular, this construction proves persistence of this kinetic system (a positive solution cannot approach the origin even asymptotically, as t → ∞).
Description: Mathematics Subject Classification: 37C10, 34D20, 93D052017-03-21T10:12:37ZGeneralized Mass Action Law and Thermodynamics of Nonlinear Markov ProcessesGorban, A. N.Kolokoltsov, V. N.http://hdl.handle.net/2381/395272017-03-22T03:22:08Z2017-03-21T09:59:51ZTitle: Generalized Mass Action Law and Thermodynamics of Nonlinear Markov Processes
Authors: Gorban, A. N.; Kolokoltsov, V. N.
Abstract: The nonlinear Markov processes are measure-valued dynamical systems which preserve positivity. They can be represented as the law of large numbers limits of general Markov models of interacting particles. In physics, the kinetic equations allow Lyapunov functionals (entropy, free energy, etc.). This may be considered as a sort of inheritance of the Lyapunov functionals from the microscopic master equations. We study nonlinear Markov processes that inherit thermodynamic properties from the microscopic linear Markov processes. We develop the thermodynamics of nonlinear Markov processes and analyze the asymptotic assumption, which are sufficient for this inheritance.
Description: Mathematics Subject Classification: 80A30 / 60J25 / 60J60 / 60J75 / 82B402017-03-21T09:59:51ZThe Impact of Fragmented Habitat's Size and Shape on Populations with Allee EffectAlharbi, W. G.Petrovskii, S. V.http://hdl.handle.net/2381/395242017-03-22T03:22:05Z2017-03-21T09:34:56ZTitle: The Impact of Fragmented Habitat's Size and Shape on Populations with Allee Effect
Authors: Alharbi, W. G.; Petrovskii, S. V.
Abstract: This study aims to explore the ways in which population dynamics are affected by the shape and size of fragmented habitats. Habitat fragmentation has become a key concern in ecology over the past 20 years as it is thought to increase the threat of extinction for a number of plant and animal species; particularly those close to the fragment edge. In this study, we consider this issue using mathematical modelling and computer simulations in several domains of various shape and with different strength of the Allee effect. A two-dimensional reaction-diffusion equation (taking the Allee effect into account) is used as a model. Extensive simulations are performed in order to determine how the boundaries impact the population persistence. Our results indicate the following: (i) for domains of simple shape (e.g. rectangle), the effect of the critical patch size (amplified by the Allee effect) is similar to what is observed in 1D space, in particular, the likelihood of population survival is determined by the interplay between the domain size and thee strength of the Allee effect; (ii) in domains of complicated shape, for the population to survive, the domain area needs to be larger than the area of the corresponding rectangle. Hence, it can be concluded that domain size and shape both have crucial effect on population survival.
Description: Mathematics Subject Classification: 92D40 / 35B36 / 35Q92 / 37N252017-03-21T09:34:56ZModelling in Ecology, Epidemiology and Ecoepidemiology: Introduction to the Special IssueMorozov, A.Petrovskii, S.http://hdl.handle.net/2381/395232017-03-21T03:21:58Z2017-03-20T17:05:07ZTitle: Modelling in Ecology, Epidemiology and Ecoepidemiology: Introduction to the Special Issue
Authors: Morozov, A.; Petrovskii, S.2017-03-20T17:05:07ZFast Sampling of Evolving Systems with Periodic TrajectoriesTyukin, I. Yu.Gorban, A. N.Tyukina, T. A.Al-Ameri, J. M.Korablev, Yu. A.http://hdl.handle.net/2381/395222017-03-21T03:21:57Z2017-03-20T16:55:54ZTitle: Fast Sampling of Evolving Systems with Periodic Trajectories
Authors: Tyukin, I. Yu.; Gorban, A. N.; Tyukina, T. A.; Al-Ameri, J. M.; Korablev, Yu. A.
Abstract: We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are supposed to be of a special class, albeit admitting nonlinear parametrization and nonlinearities. The method enables to represent a given periodic solution as sums of computable integrals and functions that are explicitly dependent on parameters of interest and initial conditions. This allows invoking parallel computational streams in order to increase speed of calculations. Performance and practical implications of the method are illustrated with examples including classical predator-prey system and models of neuronal cells.
Description: Mathematics Subject Classification: 93B30 / 34A05 / 92B99 / 93B152017-03-20T16:55:54ZTri-trophic Plankton Models Revised: Importance of Space, Food Web Structure and Functional Response ParametrisationEgilmez, H. I.Morozov, A. Yu.http://hdl.handle.net/2381/395192017-03-21T03:21:56Z2017-03-20T16:19:32ZTitle: Tri-trophic Plankton Models Revised: Importance of Space, Food Web Structure and Functional Response Parametrisation
Authors: Egilmez, H. I.; Morozov, A. Yu.
Abstract: Revealing mechanisms of efficient top-down control in eutrophic ecosystems remains a long term challenge in theoretical ecology. In this paper, we revisit the role of environmental heterogeneity, food web structure and shape of the predator functional response in persistence and stabilization of a planktonic system with high nutrient supply. We consider a 1D vertically resolved tri-trophic planktonic food web composed of a primary producer, an intermediate predator and a highly mobile top predator, such as a system of phytoplankton, microzooplankton and copepods. We explore the realistic scenario in which the top predator is omnivorous, i.e. when copepods can feed both on phytoplankton and microzooplankton. We show that the interplay between heterogeneity of the environment due to for instance, a light gradient in the water column, and trophic interaction between species can result in an efficient top-down control which would otherwise be impossible in the corresponding well-mixed system. We also find that allowing the top predator to feed on the primary producer may dramatically impede the coexistence of the three trophic levels, with only two levels generally surviving. The coexistence of all three trophic levels within a wide range of parameters becomes possible only when the top predator exhibits active food source switching behaviour. We also show the phenomenon of bistability in the considered tri-trophic food web: a small initial amount of the top predator should lead to its extinction whereas introduction of a supercritical initial amount will eventually result in establishment of the population. The demonstrated mechanism of top-down control seems to be rather generic and might be a good candidate to explain stability in some other non-planktonic tri-trophic ecosystems.
Description: Mathematics Subject Classification: 47A75 / 45K05 / 92D402017-03-20T16:19:32ZPreface. Bifurcations and Pattern Formation in Biological ApplicationsMorozov, A.Ptashnyk, M.Volpert, V.http://hdl.handle.net/2381/395172017-03-21T03:21:55Z2017-03-20T16:05:40ZTitle: Preface. Bifurcations and Pattern Formation in Biological Applications
Authors: Morozov, A.; Ptashnyk, M.; Volpert, V.
Abstract: In the preface we present a short overview of articles included in the issue "Bifurcations and pattern formation in biological applications" of the journal Mathematical Modelling of Natural Phenomena.2017-03-20T16:05:40ZA random walk description of individual animal movement accounting for periods of restTilles, Paulo F. C.Petrovskii, Sergei V.Natti, Paulo L.http://hdl.handle.net/2381/395162017-03-21T03:21:54Z2017-03-20T14:54:02ZTitle: A random walk description of individual animal movement accounting for periods of rest
Authors: Tilles, Paulo F. C.; Petrovskii, Sergei V.; Natti, Paulo L.
Abstract: Animals do not move all the time but alternate the period of actual movement (foraging) with periods of rest (e.g. eating or sleeping). Although the existence of rest times is widely acknowledged in the literature and has even become a focus of increased attention recently, the theoretical approaches to describe animal movement by calculating the dispersal kernel and/or the mean squared displacement (MSD) rarely take rests into account. In this study, we aim to bridge this gap. We consider a composite stochastic process where the periods of active dispersal or ‘bouts’ (described by a certain baseline probability density function (pdf) of animal dispersal) alternate with periods of immobility. For this process, we derive a general equation that determines the pdf of this composite movement. The equation is analysed in detail in two special but important cases such as the standard Brownian motion described by a Gaussian kernel and the Levy flight described by a Cauchy distribution. For the Brownian motion, we show that in the large-time asymptotics the effect of rests results in a rescaling of the diffusion coefficient. The movement occurs as a subdiffusive transition between the two diffusive asymptotics. Interestingly, the Levy flight case shows similar properties, which indicates a certain universality of our findings.2017-03-20T14:54:02ZCatching ghosts with a coarse net: use and abuse of spatial sampling data in detecting synchronization.Petrovskaya, NataliaPetrovskii, Sergeihttp://hdl.handle.net/2381/395152017-03-21T03:21:54Z2017-03-20T14:47:07ZTitle: Catching ghosts with a coarse net: use and abuse of spatial sampling data in detecting synchronization.
Authors: Petrovskaya, Natalia; Petrovskii, Sergei
Abstract: Synchronization of population dynamics in different habitats is a frequently observed phenomenon. A common mathematical tool to reveal synchronization is the (cross)correlation coefficient between time courses of values of the population size of a given species where the population size is evaluated from spatial sampling data. The corresponding sampling net or grid is often coarse, i.e. it does not resolve all details of the spatial configuration, and the evaluation error-i.e. the difference between the true value of the population size and its estimated value-can be considerable. We show that this estimation error can make the value of the correlation coefficient very inaccurate or even irrelevant. We consider several population models to show that the value of the correlation coefficient calculated on a coarse sampling grid rarely exceeds 0.5, even if the true value is close to 1, so that the synchronization is effectively lost. We also observe 'ghost synchronization' when the correlation coefficient calculated on a coarse sampling grid is close to 1 but in reality the dynamics are not correlated. Finally, we suggest a simple test to check the sampling grid coarseness and hence to distinguish between the true and artifactual values of the correlation coefficient.
Description: The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2017-03-20T14:47:07Z$hp$-Version space-time discontinuous Galerkin methods for parabolic problems on prismatic meshesCangiani, AndreaDong, ZhaonanGeorgoulis, Emmanuil H.http://hdl.handle.net/2381/394732017-03-16T03:21:58Z2017-03-15T16:01:58ZTitle: $hp$-Version space-time discontinuous Galerkin methods for parabolic problems on prismatic meshes
Authors: Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H.
Abstract: We present a new $hp$-version space-time discontinuous Galerkin (dG) finite element method for the numerical approximation of parabolic evolution equations on general spatial meshes consisting of polygonal/polyhedral (polytopic) elements, giving rise to prismatic space-time elements. A key feature of the proposed method is the use of space-time elemental polynomial bases of \emph{total} degree, say $p$, defined in the physical coordinate system, as opposed to standard dG-time-stepping methods whereby spatial elemental bases are tensorized with temporal basis functions. This approach leads to a fully discrete $hp$-dG scheme using less degrees of freedom for each time step, compared to standard dG time-stepping schemes employing tensorized space-time, with acceptable deterioration of the approximation properties. A second key feature of the new space-time dG method is the incorporation of very general spatial meshes consisting of possibly polygonal/polyhedral elements with \emph{arbitrary} number of faces. A priori error bounds are shown for the proposed method in various norms. An extensive comparison among the new space-time dG method, the (standard) tensorized space-time dG methods, the classical dG-time-stepping, and conforming finite element method in space, is presented in a series of numerical experiments.
Description: AMS subject classifications. 65N30, 65M60, 65J102017-03-15T16:01:58ZThe non-conforming virtual element method for the Stokes equationsCangiani, AndreaGyrya, VitaliyManzini, Gianmarcohttp://hdl.handle.net/2381/394722017-03-16T03:21:58Z2017-03-15T15:51:49ZTitle: The non-conforming virtual element method for the Stokes equations
Authors: Cangiani, Andrea; Gyrya, Vitaliy; Manzini, Gianmarco
Abstract: We present the non-conforming Virtual Element Method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component of the velocity is approximated using the nonconforming virtual element space. On each mesh element the local virtual space contains the space of polynomials of up to a given degree, plus suitable non-polynomial functions. The virtual element functions are implicitly defined as the solution of local Poisson problems with polynomial Neumann boundary conditions. As typical in VEM approaches, the explicit evaluation of the non-polynomial functions is not required. This approach makes it possible to construct nonconforming (virtual) spaces for any polynomial degree regardless of the parity, for two-and three-dimensional problems, and for meshes with very general polygonal and polyhedral elements. We show that the non-conforming VEM is inf-sup stable and establish optimal a priori error estimates for the velocity and pressure approximations. Numerical examples confirm the convergence analysis and the effectiveness of the method in providing high-order accurate approximations.
Description: AMS subject classifications. 65N30, 65N12, 65G99, 76R992017-03-15T15:51:49ZMapping cones in the bounded derived category of a gentle algebraCanakci, IlkePauksztello, DavidSchroll, Sibyllehttp://hdl.handle.net/2381/394632017-03-15T03:21:29Z2017-03-14T16:07:26ZTitle: Mapping cones in the bounded derived category of a gentle algebra
Authors: Canakci, Ilke; Pauksztello, David; Schroll, Sibylle
Abstract: Gentle algebras are a class of algebras that are derived tame. They therefore provide a concrete setting to study the structure of the (bounded) derived category in detail. In this article we explicitly describe the triangulated structure of the bounded derived category of a gentle algebra by describing its triangles. In particular, we develop a graphical calculus which gives the indecomposable summands of the mapping cones of morphisms in a canonical basis of the Hom-space between any two indecomposable complexes.
Description: 34 pages, many figures2017-03-14T16:07:26ZRepresentation theory of the Drinfeld doubles of a family of Hopf algebras II: corrections and new resultsErdmann, KarinGreen, Edward L.Snashall, NicoleTaillefer, Rachelhttp://hdl.handle.net/2381/393702017-02-25T04:03:47Z2017-02-24T14:45:11ZTitle: Representation theory of the Drinfeld doubles of a family of Hopf algebras II: corrections and new results
Authors: Erdmann, Karin; Green, Edward L.; Snashall, Nicole; Taillefer, Rachel
Abstract: We return to the fusion rules for the Drinfeld double of the duals of the generalised Taft algebras that we studied in [Erdmann et al., J. Pure Appl. Algebra 2006]. We first correct some proofs and statements in [Erdmann et al., J. Pure Appl. Algebra 2006] that were incorrect, using stable homomorphisms. We then complete this with new results on fusion rules for the modules we had not studied in [Erdmann et al., J. Pure Appl. Algebra 2006] and a classification of endotrivial and algebraic modules.2017-02-24T14:45:11ZGaussian process regression with functional covariates and multivariate responseWang, BoChen, TaoXu, Aipinghttp://hdl.handle.net/2381/393242017-03-06T16:41:08Z2017-02-03T15:36:06ZTitle: Gaussian process regression with functional covariates and multivariate response
Authors: Wang, Bo; Chen, Tao; Xu, Aiping
Abstract: Gaussian process regression (GPR) has been shown to be a powerful and effective nonparametric method for regression, classification and interpolation, due to many of its desirable properties. However, most GPR models consider univariate or multivariate covariates only. In this paper we extend the GPR models to cases where the covariates include both functional and multivariate variables and the response is multidimensional. The model naturally incorporates two different types of covariates: multivariate and functional, and the principal component analysis is used to de-correlate the multivariate response which avoids the widely recognised difficulty in the multi-output GPR models of formulating covariance functions which have to describe the correlations not only between data points but also between responses. The usefulness of the proposed method is demonstrated through a simulated example and two real data sets in chemometrics.
Description: The file associated with this record is embargoed until 12 months after the date of publication. The final published version may be available through the links above. Following the embargo period the above license applies.2017-02-03T15:36:06ZOn the effects of changing mortality patterns on investment, labour and consumption under uncertaintyEwald, C-O.Zhang, Aihuahttp://hdl.handle.net/2381/393202017-02-03T03:21:13Z2017-02-02T09:56:40ZTitle: On the effects of changing mortality patterns on investment, labour and consumption under uncertainty
Authors: Ewald, C-O.; Zhang, Aihua
Abstract: In this paper we extend the consumption-investment life cycle model for an
uncertain-lived agent, proposed by Richard (1974), to allow for
flexible labor supply. We further study the consumption, labor supply and portfolio
decisions of an agent facing age-dependent mortality risk, as presented by
UK actuarial life tables spanning the time period from 1951-2060 (including
mortality forecasts). We find that historical changes in mortality produces
significant changes in portfolio investment (more risk taking), labour (de- crease of hours) and consumption level (shift to higher level) contributing
up to 5% to GDP growth during the period from 1980 until 2010.
Description: JEL Subject Classi cation: G11; J11; J22; C61; 18 months embargo from publication2017-02-02T09:56:40ZDetailed balance in micro- and macrokinetics and micro-distinguishability of macro-processesGorban, A. N.http://hdl.handle.net/2381/392172017-01-19T03:16:37Z2017-01-18T16:43:31ZTitle: Detailed balance in micro- and macrokinetics and micro-distinguishability of macro-processes
Authors: Gorban, A. N.
Abstract: We develop a general framework for the discussion of detailed balance and analyse its microscopic background. We find that there should be two additions to the well-known T- or PT-invariance of the microscopic laws of motion:
1. Equilibrium should not spontaneously break the relevant T- or PT-symmetry.
2. The macroscopic processes should be microscopically distinguishable to guarantee persistence of detailed balance in the model reduction from micro- to macrokinetics.
We briefly discuss examples of the violation of these rules and the corresponding violation of detailed balance.2017-01-18T16:43:31ZEfficient Option Pricing under Levy Processes, with CVA and FVAShek, C. K.Law, J.Levendorskiĭ, Sergeihttp://hdl.handle.net/2381/391102017-01-11T03:20:36Z2017-01-10T10:09:37ZTitle: Efficient Option Pricing under Levy Processes, with CVA and FVA
Authors: Shek, C. K.; Law, J.; Levendorskiĭ, Sergei
Abstract: We generalize the Piterbarg [1] model to include (1) bilateral default risk as in Burgard and Kjaer [2], and (2) jumps in the dynamics of the underlying asset using general classes of Lévy processes of exponential type. We develop an efficient explicit-implicit scheme for European options and barrier options taking CVA-FVA into account. We highlight the importance of this work in the context of trading, pricing and management a derivative portfolio given the trajectory of regulations.2017-01-10T10:09:37ZQuantifying non-Newtonian effects in rotating boundary-layer flowsGriffiths, P. T.Garrett, S. J.Stephen, S. O.Hussain, Z.http://hdl.handle.net/2381/390892017-01-10T03:20:43Z2017-01-09T14:39:47ZTitle: Quantifying non-Newtonian effects in rotating boundary-layer flows
Authors: Griffiths, P. T.; Garrett, S. J.; Stephen, S. O.; Hussain, Z.
Abstract: The stability of the boundary-layer on a rotating disk is considered for fluids that adhere to a non-Newtonian governing viscosity relationship. For fluids with shear-rate dependent viscosity the base flow is no longer an exact solution of the Navier–Stokes equations, however, in the limit of large Reynolds number the flow inside the three-dimensional boundary-layer can be determined via a similarity solution. The convective instabilities associated with flows of this nature are described both asymptotically and numerically via separate linear stability analyses. Akin to previous Newtonian studies it is found that there exists two primary modes of instability; the upper-branch type I modes, and the lower-branch type II modes. Results show that both these modes can be stabilised or destabilised depending on the choice of non-Newtonian viscosity model. A number of comments are made regarding the suitability of some of the more well-known non-Newtonian constitutive relationships within the context of the rotating disk model. Such a study is presented with a view to suggesting potential control mechanisms for flows that are practically relevant to the turbo-machinery industry.
Description: 12 month embargo2017-01-09T14:39:47ZComparison of the effects of surface roughness and confinement on rotor–stator cavity flowÖzkan, M.Thomas, P. J.Cooper, A. J.Garrett, Stephen Johnhttp://hdl.handle.net/2381/390232016-12-21T03:31:56Z2016-12-20T16:51:40ZTitle: Comparison of the effects of surface roughness and confinement on rotor–stator cavity flow
Authors: Özkan, M.; Thomas, P. J.; Cooper, A. J.; Garrett, Stephen John
Abstract: Results of a computational study are discussed which investigate roughness-induced and geometry-induced (confinement) effects on the steady-state velocity components in 3-D boundary-layer flow over the rotor disc in a rotor–stator flow configuration. It is found that, for the rotor–stator flow investigated, the roughness-induced effects are very similar to geometry-induced effects, both in nature and magnitude. The overall aim was to compare these two types of effects with corresponding roughness-induced effects in the von Kármán boundary-layer flow over a disc spinning freely in an unrestricted fluid environment. The research was conducted in the context of a programme investigating surface roughness as a means of laminar flow control for the development of new passive drag-reduction techniques. The goal was to establish whether it was possible unequivocally to distinguish between roughness-induced and geometry-induced effects on the boundary-layer flow above the rotor disc. The results obtained suggest that, for the type of system discussed here, it must be expected to be difficult to distinguish between these effects in experiments. The similarities regarding the nature and magnitude of results obtained from comparing predictions for three different computational modelling approaches indicate the required sensitivity of measurement technologies aiming to resolve the investigated effects in experimental studies.2016-12-20T16:51:40ZOn the diagonal subalgebra of an Ext algebraGreen, E. L.Snashall, Nicole JaneSolberg, O.Zacharia, D.http://hdl.handle.net/2381/389662016-12-16T03:19:18Z2016-12-15T15:05:06ZTitle: On the diagonal subalgebra of an Ext algebra
Authors: Green, E. L.; Snashall, Nicole Jane; Solberg, O.; Zacharia, D.
Abstract: Let R be a Koszul algebra over a field k and M be a linear R-module. We study a graded subalgebra ΔM of the Ext-algebra ExtR⁎(M,M) called the diagonal subalgebra and its properties. Applications to the Hochschild cohomology ring of R and to periodicity of linear modules are given. Viewing R as a linear module over its enveloping algebra, we also show that ΔR is isomorphic to the graded center of the Koszul dual of R. When R is selfinjective and not necessarily graded, we study connections between periodic modules M, complexity of M and existence of non-nilpotent elements of positive degree in the Ext-algebra of M. Characterizations of periodic algebras are given.2016-12-15T15:05:06ZSpecial multiserial algebras are quotients of symmetric special multiserial algebrasGreen, E. L.Schroll, Sibyllehttp://hdl.handle.net/2381/388942016-12-13T03:20:03Z2016-12-12T14:48:22ZTitle: Special multiserial algebras are quotients of symmetric special multiserial algebras
Authors: Green, E. L.; Schroll, Sibylle
Abstract: In this paper we give a new definition of symmetric special multiserial algebras in terms of defining cycles. As a consequence, we show that every special multiserial algebra is a quotient of a symmetric special multiserial algebra.
Description: MSC 16G202016-12-12T14:48:22ZHourglass stabilization and the virtual element methodCangiani, A.Manzini, G.Russo, A.Sukumar, N.http://hdl.handle.net/2381/388482016-12-07T03:23:09Z2016-12-06T15:38:40ZTitle: Hourglass stabilization and the virtual element method
Authors: Cangiani, A.; Manzini, G.; Russo, A.; Sukumar, N.
Abstract: In this paper, we establish the connections between the virtual element method (VEM) and the hourglass control techniques that have been developed since the early 1980s to stabilize underintegrated C0 Lagrange finite element methods. In the VEM, the bilinear form is decomposed into two parts: a consistent term that reproduces a given polynomial space and a correction term that provides stability. The essential ingredients of inline image-continuous VEMs on polygonal and polyhedral meshes are described, which reveals that the variational approach adopted in the VEM affords a generalized and robust means to stabilize underintegrated finite elements. We focus on the heat conduction (Poisson) equation and present a virtual element approach for the isoparametric four-node quadrilateral and eight-node hexahedral elements. In addition, we show quantitative comparisons of the consistency and stabilization matrices in the VEM with those in the hourglass control method of Belytschko and coworkers. Numerical examples in two and three dimensions are presented for different stabilization parameters, which reveals that the method satisfies the patch test and delivers optimal rates of convergence in the L2 norm and the H1 seminorm for Poisson problems on quadrilateral, hexahedral, and arbitrary polygonal meshes.2016-12-06T15:38:40ZOn the stability of continuous-discontinuous Galerkin methods for advection-diffusion-reaction problemsCangiani, AndreaChapman, J.Georgoulis, EmmanuilJensen, M.http://hdl.handle.net/2381/388472016-12-07T03:23:06Z2016-12-06T15:29:49ZTitle: On the stability of continuous-discontinuous Galerkin methods for advection-diffusion-reaction problems
Authors: Cangiani, Andrea; Chapman, J.; Georgoulis, Emmanuil; Jensen, M.
Abstract: We consider a finite element method which couples the continuous Galerkin method away from internal and boundary layers with a discontinuous Galerkin method in the vicinity of layers. We prove that this consistent method is stable in the streamline diffusion norm if the convection field flows non-characteristically from the region of the continuous Galerkin to the region of the discontinuous Galerkin method. The stability properties of the coupled method are illustrated with a numerical experiment.2016-12-06T15:29:49ZÉtale homotopy types of moduli stacks of polarised abelian schemesFrediani, P.Neumann, Frankhttp://hdl.handle.net/2381/388282016-12-06T03:22:15Z2016-12-05T16:29:23ZTitle: Étale homotopy types of moduli stacks of polarised abelian schemes
Authors: Frediani, P.; Neumann, Frank
Abstract: We determine the Artin–Mazur étale homotopy types of moduli stacks of polarised abelian schemes using transcendental methods and derive some arithmetic properties of the étale fundamental groups of these moduli stacks. Finally we analyse the Torelli morphism between the moduli stacks of algebraic curves and principally polarised abelian schemes from an étale homotopy point of view.
Description: Mathematics Subject Classification
14F35 14K10 14H10 14C342016-12-05T16:29:23ZGeometry of moduli stacks of (k, l)-stable vector bundles over algebraic curvesMata-Gutiérrez, O.Neumann, Frankhttp://hdl.handle.net/2381/388272016-12-06T03:22:07Z2016-12-05T16:22:03ZTitle: Geometry of moduli stacks of (k, l)-stable vector bundles over algebraic curves
Authors: Mata-Gutiérrez, O.; Neumann, Frank
Abstract: We study the geometry of the moduli stack of vector bundles of fixed rank and degree over an algebraic curve by introducing a filtration made of open substacks build from (k,l)-stable vector bundles. The concept of (k,l)-stability was introduced by Narasimhan and Ramanan to study the geometry of the coarse moduli space of stable bundles. We will exhibit the stacky picture and analyse the geometric and cohomological properties of the moduli stacks of (k,l)-stable vector bundles. For particular pairs (k,l) of integers we also show that these moduli stacks admit coarse moduli spaces and we discuss their interplay.
Description: MSC
primary, 14H60, 14D23; secondary, 14D202016-12-05T16:22:03ZA New Bayesian Test to test for the Intractability-Countering HypothesisChakrabarty, Daliahttp://hdl.handle.net/2381/388042016-12-03T03:57:02Z2016-12-02T12:24:33ZTitle: A New Bayesian Test to test for the Intractability-Countering Hypothesis
Authors: Chakrabarty, Dalia
Abstract: We present a new test of hypothesis in which we seek the probability of the null conditioned on the data, where the null is a simplification undertaken to counter the intractability of the more complex model, that the simpler null model is nested within. With the more complex model rendered intractable, the null model uses a simplifying assumption that capacitates the learning of an unknown parameter vector given the data. Bayes factors are shown to be known only up to a ratio of unknown data-dependent constants–a problem that cannot be cured using prescriptions similar to those suggested to solve the problem caused to Bayes factor computation, by non-informative priors. Thus, a new test is needed in which we can circumvent Bayes factor computation. In this test, we undertake generation of data from the model in which the null hypothesis is true and can achieve support in the measured data for the null by comparing the marginalised posterior of the model parameter given the measured data, to that given such generated data. However, such a ratio of marginalised posteriors can confound interpretation of comparison of support in one measured data for a null, with that in another data set for a different null. Given an application in which such comparison is undertaken, we alternatively define support in a measured data set for a null by identifying the model parameters that are less consistent with the measured data than is minimally possible given the generated data, and realising that the higher the number of such parameter values, less is the support in the measured data for the null. Then, the probability of the null conditional on the data is given within an MCMC-based scheme, by marginalising the posterior given the measured data, over parameter values that are as, or more consistent with the measured data, than with the generated data. In the aforementioned application, we test the hypothesis that a galactic state space bears an isotropic geometry, where the (missing) data comprising measurements of some components of the state space vector of a sample of observed galactic particles, is implemented to Bayesianly learn the gravitational mass density of all matter in the galaxy. In lieu of an assumption about the state space being isotropic, the likelihood of the sought gravitational mass density given the data, is intractable. For a real example galaxy, we find unequal values of the probability of the null–that the host state space is isotropic–given two different data sets, implying that in this galaxy, the system state space constitutes at least two disjoint sub-volumes that the two data sets respectively live in. Implementation on simulated galactic data is also undertaken, as is an empirical illustration on the well-known O-ring data, to test for the form of the thermal variation of the failure probability of the O-rings.
Description: Details of the Bayesian learning of the gravitational mass density and state spacepd fof the galaxyare provided in SectionS-1of the attached supplementary material. SectionS-2discusses detailsof the Fully Bayesian Significance Test.2016-12-02T12:24:33ZPattern, process, scale, and model's sensitivity: Comment on "Phase separation driven by density-dependent movement: A novel mechanism for ecological patterns" by Quan-Xing Liu et al.Petrovskii, Sergeihttp://hdl.handle.net/2381/387642016-11-30T03:21:06Z2016-11-29T16:09:05ZTitle: Pattern, process, scale, and model's sensitivity: Comment on "Phase separation driven by density-dependent movement: A novel mechanism for ecological patterns" by Quan-Xing Liu et al.
Authors: Petrovskii, Sergei
Abstract: Spatial distribution of ecological populations is rarely homogeneous. Typically, the population density exhibits considerable variability of space, in an extreme yet not uncommon case creating a “patchy” pattern where areas of high population density alternate with areas where the population density is much lower or close to zero [1]. This phenomenon, often generically referred to as ecological patterning or ecological pattern formation, has long been a focus of interest in ecology and a number of theories and models have been developed aiming to explain it under different ecological and/or environmental conditions and on different spatial and temporal scales; see Table 1. A straightforward explanation of the heterogeneous distribution of population density relates it to the heterogeneity of the environment (e.g. to nonuniform distribution of resources) and this is indeed often the case [2]. However, a closer look reveals that this is not enough and in many cases the heterogeneity of population density is only weakly correlated to the heterogeneity of the environment [3] and [19]. Understanding that biological interactions play, on the relevant spatial and temporal scales [20], as important role in shaping the ecological patterns as the physical/chemical forcing resulted in a number of theories. The earliest one that used the idea of Turing's instability [4] was followed by several others [5], [6] and [21] including theories where pattern formation was due to a non-Turing mechanism [8] and [9] and theories where the movement behavior and/or density dependence was an essential factor [12] and [14].2016-11-29T16:09:05ZQuantifying uncertainty in partially specified biological models: How can optimal control theory help us?Adamson, M. W.Morozov, A. Y.Kuzenkov, O. A.http://hdl.handle.net/2381/387192016-11-26T04:12:09Z2016-11-25T09:58:35ZTitle: Quantifying uncertainty in partially specified biological models: How can optimal control theory help us?
Authors: Adamson, M. W.; Morozov, A. Y.; Kuzenkov, O. A.
Abstract: Mathematical models in biology are highly simplified representations of a complex underlying reality and there is always a high degree of uncertainty with regards to model function specification. This uncertainty becomes critical for models in which the use of different functions fitting the same dataset can yield substantially different predictions-a property known as structural sensitivity. Thus, even if the model is purely deterministic, then the uncertainty in the model functions carries through into uncertainty in model predictions, and new frameworks are required to tackle this fundamental problem. Here, we consider a framework that uses partially specified models in which some functions are not represented by a specific form. The main idea is to project infinite dimensional function space into a low-dimensional space taking into account biological constraints. The key question of how to carry out this projection has so far remained a serious mathematical challenge and hindered the use of partially specified models. Here, we propose and demonstrate a potentially powerful technique to perform such a projection by using optimal control theory to construct functions with the specified global properties. This approach opens up the prospect of a flexible and easy to use method to fulfil uncertainty analysis of biological models.2016-11-25T09:58:35ZPiece-wise quadratic approximations of arbitrary error functions for fast and robust machine learningGorban, A. N.Mirkes, E. M.Zinovyev, A.http://hdl.handle.net/2381/387112016-11-24T03:21:35Z2016-11-23T17:34:11ZTitle: Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning
Authors: Gorban, A. N.; Mirkes, E. M.; Zinovyev, A.
Abstract: Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-quadratic error functionals based on L1 norm or even sub-linear potentials corresponding to quasinorms Lp (0<p<1). The back side of these approaches is increase in computational cost for optimization. Till so far, no approaches have been suggested to deal with arbitrary error functionals, in a flexible and computationally efficient framework. In this paper, we develop a theory and basic universal data approximation algorithms (k-means, principal components, principal manifolds and graphs, regularized and sparse regression), based on piece-wise quadratic error potentials of subquadratic growth (PQSQ potentials). We develop a new and universal framework to minimize arbitrary sub-quadratic error potentials using an algorithm with guaranteed fast convergence to the local or global error minimum. The theory of PQSQ potentials is based on the notion of the cone of minorant functions, and represents a natural approximation formalism based on the application of min-plus algebra. The approach can be applied in most of existing machine learning methods, including methods of data approximation and regularized and sparse regression, leading to the improvement in the computational cost/accuracy trade-off. We demonstrate that on synthetic and real-life datasets PQSQ-based machine learning methods achieve orders of magnitude faster computational performance than the corresponding state-of-the-art methods, having similar or better approximation accuracy.2016-11-23T17:34:11ZR-matrix and inverse Shapovalov formMudrov, Andreyhttp://hdl.handle.net/2381/387102016-11-24T03:21:33Z2016-11-23T17:26:21ZTitle: R-matrix and inverse Shapovalov form
Authors: Mudrov, Andrey
Abstract: We construct the inverse Shapovalov form of a simple complex quantum group from its universal R-matrix based on a generalized Nagel-Moshinsky approach to lowering operators. We establish a connection between this algorithm and the ABRR equation for dynamical twist.2016-11-23T17:26:21ZEvolution of adaptation mechanisms: Adaptation energy, stress, and oscillating deathGorban, Alexander N.Tyukina, Tatiana A.Smirnova, E. V.Pokidysheva, L. I.http://hdl.handle.net/2381/386522017-01-19T02:45:07Z2016-11-21T14:29:22ZTitle: Evolution of adaptation mechanisms: Adaptation energy, stress, and oscillating death
Authors: Gorban, Alexander N.; Tyukina, Tatiana A.; Smirnova, E. V.; Pokidysheva, L. I.
Abstract: In 1938, Selye proposed the notion of adaptation energy and published ‘Experimental evidence supporting the conception of adaptation energy.’ Adaptation of an animal to different factors appears as the spending of one resource. Adaptation energy is a hypothetical extensive quantity spent for adaptation. This term causes much debate when one takes it literally, as a physical quantity, i.e. a sort of energy. The controversial points of view impede the systematic use of the notion of adaptation energy despite experimental evidence. Nevertheless, the response to many harmful factors often has general non-specific form and we suggest that the mechanisms of physiological adaptation admit a very general and nonspecific description.
We aim to demonstrate that Selye׳s adaptation energy is the cornerstone of the top-down approach to modelling of non-specific adaptation processes. We analyze Selye׳s axioms of adaptation energy together with Goldstone׳s modifications and propose a series of models for interpretation of these axioms. Adaptation energy is considered as an internal coordinate on the ‘dominant path’ in the model of adaptation. The phenomena of ‘oscillating death’ and ‘oscillating remission’ are predicted on the base of the dynamical models of adaptation. Natural selection plays a key role in the evolution of mechanisms of physiological adaptation. We use the fitness optimization approach to study of the distribution of resources for neutralization of harmful factors, during adaptation to a multifactor environment, and analyze the optimal strategies for different systems of factors.2016-11-21T14:29:22ZThe Ext algebra and a new generalisation of D-Koszul algebrasLeader, JoanneSnashall, Nicolehttp://hdl.handle.net/2381/385902017-03-14T02:45:07Z2016-11-16T15:48:30ZTitle: The Ext algebra and a new generalisation of D-Koszul algebras
Authors: Leader, Joanne; Snashall, Nicole
Abstract: We generalise Koszul and D-Koszul algebras by introducing a class of graded
algebras called (D, A)-stacked algebras. We give a characterisation of (D, A)-stacked
algebras and show that their Ext algebra is finitely generated as an algebra in degrees
0, 1, 2 and 3. In the monomial case, we give an explicit description of the Ext algebra
by quiver and relations, and show that the ideal of relations has a quadratic Gr¨obner
basis; this enables us to give a regrading of the Ext algebra under which the regraded
Ext algebra is a Koszul algebra.
Description: 2010 Mathematics Subject Classification. 16G20, 16S37, 16E30; The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2016-11-16T15:48:30ZMechanism of chain collapse of strongly charged polyelectrolytesTom, A. M.Vemparala, S.Rajesh, R.Brilliantov, Nikolai V.http://hdl.handle.net/2381/385802016-11-17T03:21:31Z2016-11-16T10:28:02ZTitle: Mechanism of chain collapse of strongly charged polyelectrolytes
Authors: Tom, A. M.; Vemparala, S.; Rajesh, R.; Brilliantov, Nikolai V.
Abstract: We perform extensive molecular dynamics simulations of a charged polymer in a good solvent in the regime where the chain is collapsed. We analyze the dependence of the gyration radius Rg on the reduced Bjerrum length ℓB and find two different regimes. In the first one, called a weak electrostatic regime, Rg∼ℓ−1/2B, which is consistent only with the predictions of the counterion-fluctuation theory. In the second one, called a strong electrostatic regime, we find Rg∼ℓ−1/5B. To explain the novel regime we modify the counterion-fluctuation theory.
Description: The simulations were carried out on the supercomputing
machines Annapurna, Nandadevi, and Satpura at The
Institute of Mathematical Sciences.2016-11-16T10:28:02ZOn the stability of the BEK family of rotating boundary-layer flows for power-law fluidsAbdulameer, M. A.Griffiths, P. T.Alveroğlu, B.Garrett, Stephen J.http://hdl.handle.net/2381/385472016-11-16T03:20:24Z2016-11-15T10:42:43ZTitle: On the stability of the BEK family of rotating boundary-layer flows for power-law fluids
Authors: Abdulameer, M. A.; Griffiths, P. T.; Alveroğlu, B.; Garrett, Stephen J.
Abstract: We consider the convective instability of the BEK family of rotating boundary-layer flows for shear-thinning power-law fluids. The Bödewadt, Ekman and von Kármán flows are particular cases within this family. A linear stability analysis is conducted using a Chebyshev polynomial method in order to investigate the effect of shear-thinning fluids on the convective type I (inviscid crossflow) and type II (viscous streamline curvature) modes of instability. The results reveal that an increase in shear-thinning has a universal stabilising effect across the entire BEK family. Our results are presented in terms of neutral curves, growth rates and an analysis of the energy balance. The newly-derived governing equations for both the steady mean flow and unsteady perturbation equations are given in full.
Description: The file associated with this record is under a 24 month embargo from publication in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2016-11-15T10:42:43ZViscous modes within the compressible boundary-layer flow due to a broad rotating coneTowers, P. D.Hussain, Z.Griffiths, P. T.Garrett, S. J.http://hdl.handle.net/2381/385142016-11-15T03:21:48Z2016-11-14T14:26:08ZTitle: Viscous modes within the compressible boundary-layer flow due to a broad rotating cone
Authors: Towers, P. D.; Hussain, Z.; Griffiths, P. T.; Garrett, S. J.
Abstract: We investigate the effects of compressibility and wall cooling on the stationary, viscous (Type II) instability mode within the 3D boundary layer over rotating cones with half-angle greater than 40°. The stationary mode is characterised by zero shear stress at the wall and a triple-deck solution is presented in the isothermal case. Asymptotic solutions are obtained which describe the structure of the wavenumber and the orientation of this mode as a function of local Mach number. It is found that a stationary mode is possible only over a finite range of local Mach number. Our conclusions are entirely consistent with the results of Seddougui 1990, A nonlinear investigation of the stability models of instability of the trhee-dimensional Compresible boundary layer due to a rotating disc Q. J. Mech. Appl. Math., 43, pt. 4. It is suggested that wall cooling has a significant stabilising effect, while reducing the half-angle is marginally destabilising. Solutions are presented for air.
Description: Author confirmed manuscript is post-print.2016-11-14T14:26:08ZDiscontinuous Galerkin methods for fast reactive mass transfer through semi-permeable membranesCangiani, AndreaGeorgoulis, Emmanuil H.Jensen, M.http://hdl.handle.net/2381/384672016-11-12T04:11:35Z2016-11-11T15:23:03ZTitle: Discontinuous Galerkin methods for fast reactive mass transfer through semi-permeable membranes
Authors: Cangiani, Andrea; Georgoulis, Emmanuil H.; Jensen, M.
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 analysed. The study of interface problems is motivated by models of mass transfer of solutes through semi-permeable membranes. The case of fast reactions is also included. More specifically, a model problem consisting of a system of semilinear parabolic advection–diffusion–reaction partial differential equations in each compartment with only local Lipschitz conditions on the nonlinear reaction terms, equipped with respective initial and boundary conditions, is considered. General nonlinear interface conditions modelling selective permeability, congestion and partial reflection are applied to the compartment interfaces. The interior penalty dG method for this problem, presented recently, is analysed both in the space-discrete and in fully discrete settings for the case of, possibly, fast reactions. 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.2016-11-11T15:23:03ZConforming and nonconforming virtual element methods for elliptic problemsCangiani, AndreaManzini, G.Sutton, Oliver J.http://hdl.handle.net/2381/384602016-11-12T04:11:33Z2016-11-11T14:31:40ZTitle: Conforming and nonconforming virtual element methods for elliptic problems
Authors: Cangiani, Andrea; Manzini, G.; Sutton, Oliver J.
Abstract: We present in a unified framework new conforming and nonconforming Virtual Element Methods (VEM) for general second order elliptic problems in two and three dimensions. The differential operator is split into its symmetric and non-symmetric parts and conditions for stability and accuracy on their discrete counterparts are established. These conditions are shown to lead to optimal $H^1$- and $L^2$-error estimates, confirmed by numerical experiments on a set of polygonal meshes. The accuracy of the numerical approximation provided by the two methods is shown to be comparable.2016-11-11T14:31:40ZOptimal Bounds for the Variance of Self-Intersection Local TimesDeligiannidis, G.Utev, Sergeyhttp://hdl.handle.net/2381/384062016-11-10T03:23:35Z2016-11-09T10:30:23ZTitle: Optimal Bounds for the Variance of Self-Intersection Local Times
Authors: Deligiannidis, G.; Utev, Sergey
Abstract: For a Zd-valued random walk (Sn)n N0, let l(n,x) be its local time at the site x Zd. For α N, define the α-fold self-intersection local time as Ln(α) xl(n,x)α. Also let LnSRW(α) be the corresponding quantities for the simple random walk in Zd. Without imposing any moment conditions, we show that the variance of the self-intersection local time of any genuinely d-dimensional random walk is bounded above by the corresponding quantity for the simple symmetric random walk; that is, var(Ln(α))=O(var (LnSRW(α))). In particular, for any genuinely d-dimensional random walk, with d≥4, we have var (Ln(α))=O(n). On the other hand, in dimensions d≤3 we show that if the behaviour resembles that of simple random walk, in the sense that lim infn→∞var Lnα/var(LnSRW(α))>0, then the increments of the random walk must have zero mean and finite second moment.2016-11-09T10:30:23ZMultiserial and special multiserial algebras and their representationsGreen, E. L.Schroll, Sibyllehttp://hdl.handle.net/2381/383912016-11-09T03:20:36Z2016-11-08T12:14:39ZTitle: Multiserial and special multiserial algebras and their representations
Authors: Green, E. L.; Schroll, Sibylle
Abstract: In this paper we study multiserial and special multiserial algebras. These algebras are a natural generalization of biserial and special biserial algebras to algebras of wild representation type. We define a module to be multiserial if its radical is the sum of uniserial modules whose pairwise intersection is either 0 or a simple module. We show that all finitely generated modules over a special multiserial algebra are multiserial. In particular, this implies that, in analogy to special biserial algebras being biserial, special multiserial algebras are multiserial. We then show that the class of symmetric special multiserial algebras coincides with the class of Brauer configuration algebras, where the latter are a generalization of Brauer graph algebras. We end by showing that any symmetric algebra with radical cube zero is special multiserial and so, in particular, it is a Brauer configuration algebra.
Description: MSC 16G20; 16G20; 16D10; 16D502016-11-08T12:14:39ZRevisiting Brownian motion as a description of animal movement: a comparison to experimental movement dataBearup, DanielBenefer, Carly M.Petrovskii, Sergei V.Blackshaw, Rod P.http://hdl.handle.net/2381/383762016-11-09T03:20:38Z2016-11-08T09:51:19ZTitle: Revisiting Brownian motion as a description of animal movement: a comparison to experimental movement data
Authors: Bearup, Daniel; Benefer, Carly M.; Petrovskii, Sergei V.; Blackshaw, Rod P.
Abstract: Summary:
1. Characterization of patterns of animal movement is a major challenge in ecology with applications to conservation, biological invasions and pest monitoring. Brownian random walks, and diffusive flux as their mean field counterpart, provide one framework in which to consider this problem. However, it remains subject to debate and controversy. This study presents a test of the diffusion framework using movement data obtained from controlled experiments.
2. Walking beetles (Tenebrio molitor) were released in an open circular arena with a central hole and the number of individuals falling from the arena edges was monitored over time. These boundary counts were compared, using curve fitting, to the predictions of a diffusion model. The diffusion model is solved precisely, without using numerical simulations.
3. We find that the shape of the curves derived from the diffusion model is a close match to those found experimentally. Furthermore, in general, estimates of the total population obtained from the relevant solution of the diffusion equation are in excellent agreement with the experimental population. Estimates of the dispersal rate of individuals depend on how accurately the initial release distribution is incorporated into the model.
4. We therefore show that diffusive flux is a very good approximation to the movement of a population of Tenebrio molitor beetles. As such, we suggest that it is an adequate theoretical/modelling framework for ecological studies that account for insect movement, although it can be context specific. An immediate practical application of this can be found in the interpretation of trap counts, in particular for the purpose of pest monitoring.
Description: The file associated with this record is under a 12 month embargo from publication in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2016-11-08T09:51:19ZTwisted Hochschild homology and MacLane homologyPirashvili, Teimurazhttp://hdl.handle.net/2381/383052016-11-01T03:19:15Z2016-10-31T15:53:14ZTitle: Twisted Hochschild homology and MacLane homology
Authors: Pirashvili, Teimuraz
Abstract: We prove that Hi.A; ˆ.A// D 0, i > 0. Here A is a commutative algebra over the
prime field Fp of characteristic p > 0 and ˆ.A/ is A considered as a bimodule,
where the left multiplication is the usual one, while the right multiplication is given
via Frobenius endomorphism and H denotes the Hochschild homology over Fp . This
result has implications in Mac Lane homology theory. Among other results, we prove
that HML .A; T / D 0, provided A is an algebra over a field K of characteristic p >0
and T is a strict homogeneous polynomial functor of degree d with 1<d <Card.K/.2016-10-31T15:53:14ZLong-term transients and complex dynamics of a stage-structured population with time delay and the Allee effectMorozov, A. Y.Banerjee, M.Petrovskii, Sergei V.http://hdl.handle.net/2381/381972017-02-26T02:45:08Z2016-10-12T10:23:36ZTitle: Long-term transients and complex dynamics of a stage-structured population with time delay and the Allee effect
Authors: Morozov, A. Y.; Banerjee, M.; Petrovskii, Sergei V.
Abstract: Traditionally, mathematical modeling in population ecology is mainly focused on asymptotic behavior of the model, i.e. as given by the system attractors. Recently, however, transient regimes and especially long-term transients have been recognized as playing a crucial role in the dynamics of ecosystems. In particular, long-term transients are a potential explanation of ecological regime shifts, when an apparently healthy population suddenly collapses and goes extinct. In this paper, we show that the interplay between delay in maturation and a strong Allee effect can result in long-term transients in a single species system. We first derive a simple ‘conceptual’ model of the population dynamics that incorporates both a strong Allee effect and maturation delay. Unlike much of the previous work, our approach is not empirical since our model is derived from basic principles. We show that the model exhibits a high complexity in its asymptotic dynamics including multi-periodic and chaotic attractors. We then show the existence of long-term transient dynamics in the system, when the population size oscillates for a long time between locally stable stationary states before it eventually settles either at the persistence equilibrium or goes extinct. The parametric space of the model is found to have a complex structure with the basins of attraction corresponding to the persistence and extinction states being of a complicated shape. This impedes the prediction of the eventual fate of the population, as a small variation in the maturation delay or the initial population size can either bring the population to extinction or ensure its persistence.
Description: Following the embargo period the above license applies.2016-10-12T10:23:36Zhp-Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshesCangiani, AndreaDong, ZhaonanGeorgoulis, Emmanuil H.Houston, Paulhttp://hdl.handle.net/2381/380162016-08-31T02:18:46Z2016-08-30T15:11:03ZTitle: hp-Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes
Authors: Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H.; Houston, Paul
Abstract: We consider the hp-version interior penalty discontinuous Galerkin finite element method (DGFEM) for the numerical approximation of the advection-diffusion-reaction equation on general computational meshes consisting of polygonal/polyhedral (polytopic) elements. In particular, new hp-version a priori error bounds are derived based on a specific choice of the interior penalty parameter which allows for edge/face-degeneration. The proposed method employs elemental polynomial bases of total degree p (𝒫p-basis) defined in the physical coordinate system, without requiring the mapping from a given reference or canonical frame. Numerical experiments highlighting the performance of the proposed DGFEM are presented. In particular, we study the competitiveness of the p-version DGFEM employing a 𝒫p-basis on both polytopic and tensor-product elements with a (standard) DGFEM employing a (mapped) 𝒬p-basis. Moreover, a computational example is also presented which demonstrates the performance of the proposed hp-version DGFEM on general agglomerated meshes.2016-08-30T15:11:03Z