DSpace Collection:
http://hdl.handle.net/2381/3823
20161024T07:02:39Z

Longterm transients and complex dynamics of a stagestructured population with time delay and the Allee effect
http://hdl.handle.net/2381/38197
Title: Longterm transients and complex dynamics of a stagestructured 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 longterm transients have been recognized as playing a crucial role in the dynamics of ecosystems. In particular, longterm 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 longterm 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 multiperiodic and chaotic attractors. We then show the existence of longterm 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.
20161012T10:23:36Z

hpVersion discontinuous Galerkin methods for advectiondiffusionreaction problems on polytopic meshes
http://hdl.handle.net/2381/38016
Title: hpVersion discontinuous Galerkin methods for advectiondiffusionreaction problems on polytopic meshes
Authors: Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H.; Houston, Paul
Abstract: We consider the hpversion interior penalty discontinuous Galerkin finite element method (DGFEM) for the numerical approximation of the advectiondiffusionreaction equation on general computational meshes consisting of polygonal/polyhedral (polytopic) elements. In particular, new hpversion a priori error bounds are derived based on a specific choice of the interior penalty parameter which allows for edge/facedegeneration. The proposed method employs elemental polynomial bases of total degree p (𝒫pbasis) 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 pversion DGFEM employing a 𝒫pbasis on both polytopic and tensorproduct elements with a (standard) DGFEM employing a (mapped) 𝒬pbasis. Moreover, a computational example is also presented which demonstrates the performance of the proposed hpversion DGFEM on general agglomerated meshes.
20160830T15:11:03Z

Kriging metamodel assisted calibration of computational fluid dynamics models
http://hdl.handle.net/2381/37745
Title: Kriging metamodel assisted calibration of computational fluid dynamics models
Authors: Kajero, Olumayowa T.; Thorpe, Rex B.; Chen, Tao; Wang, Bo; Yao, Yuan
Abstract: Computational fluid dynamics (CFD) is a simulation technique widely used in chemical and process engineering applications. However, computation has become a bottleneck when calibration of CFD models with experimental data (also known as model parameter estimation) is needed. In this research, the kriging metamodelling approach (also termed Gaussian process) was coupled with expected improvement (EI) to address this challenge. A new EI measure was developed for the sum of squared errors (SSE) which conforms to a generalised chisquare distribution and hence existing normal distributionbased EI measures are not applicable. The new EI measure is to suggest the CFD model parameter to simulate with, hence minimising SSE and improving match between simulation and experiments. The usefulness of the developed method was demonstrated through a case study of a singlephase flow in both a straighttype and a convergentdivergenttype annular jet pump, where a single model parameter was calibrated with experimental data.
Description: The file associated with this record is under a 12month embargo from publication in accordance with the publisher's selfarchiving policy. The full text may be available through the publisher links provided above.
20160614T11:09:22Z

Delay driven spatiotemporal chaos in single species population dynamics models
http://hdl.handle.net/2381/37594
Title: Delay driven spatiotemporal chaos in single species population dynamics models
Authors: Petrovskiy, Sergei; Jankovic, Masha; Banerjee, Malay
Abstract: Questions surrounding the prevalence of complex population dynamics form one of the central themes in ecology. Limit cycles and spatiotemporal chaos are examples that have been widely recognised theoretically, although their importance and applicability to natural populations remains debatable. The ecological processes underlying such dynamics are thought to be numerous, though there seems to be consent as to delayed density dependence being one of the main driving forces. Indeed, time delay is a common feature of many ecological systems and can significantly influence population dynamics. In general, time delays may arise from inter and intraspecific trophic interactions or population structure, however in the context of single species populations they are linked to more intrinsic biological phenomena such as gestation or resource regeneration. In this paper, we consider theoretically the spatiotemporal dynamics of a single species population using two different mathematical formulations. Firstly, we revisit the diffusive logistic equation in which the per capita growth is a function of some specified delayed argument. We then modify the model by incorporating a spatial convolution which results in a biologically more viable integrodifferential model. Using the combination of analytical and numerical techniques, we investigate the effect of time delay on pattern formation. In particular, we show that for sufficiently large values of time delay the system’s dynamics are indicative to spatiotemporal chaos. The chaotic dynamics arising in the wake of a travelling population front can be preceded by either a plateau corresponding to dynamical stabilisation of the unstable equilibrium or by periodic oscillations.
20160518T12:05:18Z

How animals move along? Exactly solvable model of superdiffusive spread resulting from animal's decision making
http://hdl.handle.net/2381/37591
Title: How animals move along? Exactly solvable model of superdiffusive spread resulting from animal's decision making
Authors: Petrovskiy, Sergei V.; Tilles, Paulo F. C.
Abstract: Patterns of individual animal movement have been a focus of considerable attention recently. Of particular interest is a question how different macroscopic properties of animal dispersal result from the stochastic processes occurring on the microscale of the individual behavior. In this paper, we perform a comprehensive analytical study of a model where the animal changes the movement velocity as a result of its behavioral response to environmental stochasticity. The stochasticity is assumed to manifest itself through certain signals, and the animal modifies its velocity as a response to the signals. We consider two different cases, i.e. where the change in the velocity is or is not correlated to its current value. We show that in both cases the early, transient stage of the animal movement is superdiffusive, i.e. ballistic. The largetime asymptotic behavior appears to be diffusive in the uncorrelated case but superballistic in the correlated case. We also calculate analytically the dispersal kernel of the movement and show that, whilst it converge to a normal distribution in the largetime limit, it possesses a fatter tail during the transient stage, i.e. at early and intermediate time. Since the transients are known to be highly relevant in ecology, our findings may indicate that the fat tails and superdiffusive spread that are sometimes observed in the movement data may be a feature of the transitional dynamics rather than an inherent property of the animal movement.
Description: Copyright © the authors, 2015. After embargo this version will be an openaccess article distributed under the terms of the Creative Commons AttributionNon CommercialNo Derivatives License (http://creativecommons.org/licenses/byncnd/4.0/ ), which permits use and distribution in any medium, provided the original work is properly cited, the use is noncommercial and no modifications or adaptations are made.
20160518T11:50:36Z

On a fixed point theorem of Greguš
http://hdl.handle.net/2381/37550
Title: On a fixed point theorem of Greguš
Authors: Fisher, Brian; Sessa, S.
Abstract: We consider two selfmaps T and I of a closed convex subset C of a Banach space X which are weakly commuting in X, i.e.
‖TIx−ITx‖≤‖Ix−Tx‖ for any x in X,
and satisfy the inequality
‖Tx−Ty‖≤a‖Ix−Iy‖+(1−a)max{‖Tx−Ix‖,‖Ty−Iy‖}
for all x, y in C, where 0<a<1. It is proved that if I is linear and nonexpansive in C and such that IC contains TC, then T and I have a unique common fixed point in C.
20160513T14:33:57Z

On common fixed points of weakly commuting mappings and setvalued mappings
http://hdl.handle.net/2381/37549
Title: On common fixed points of weakly commuting mappings and setvalued mappings
Authors: Sessa, S.; Fisher, B.
Abstract: Our main theorem establishes the uniqueness of the common fixed point of two setvalued mappings and of two singlevalued mappings defined on a complete metric space, under a contractive condition and a weak commutativity concept. This improves a theorem of the second author.
20160513T14:30:09Z

On a fixed point theorem of Pathak
http://hdl.handle.net/2381/37548
Title: On a fixed point theorem of Pathak
Authors: Fisher, Brian
Abstract: It is shown that the continuity of the mapping in Pathak's fixed point theorem for normed spaces is not necessary.
20160513T14:25:52Z

Common fixed point theorems for compatible mappings
http://hdl.handle.net/2381/37547
Title: Common fixed point theorems for compatible mappings
Authors: Taş, K.; Telci, M.; Fisher, Brian
Abstract: By using a compatibility condition due to Jungck we establish some common fixed point theorems for four mappings on complete and compact metric spaces These results also generalize a theorem of Sharma and Sahu.
20160513T14:22:20Z

Coincidence theorems for nonlinear hybrid contractions
http://hdl.handle.net/2381/37546
Title: Coincidence theorems for nonlinear hybrid contractions
Authors: Cho, Y. J.; Fisher, B.; Genga, G. S.
Abstract: In this paper, we give some common fixed point theorems for singlevalued mappings and multivalued mappings satisfying a rational inequality. Our theorems generalize some results of B. Fisher, M. L. Diviccaro et al. and V. Popa.
20160513T14:18:00Z

Related fixed point theorems on two complete and compact metric spaces
http://hdl.handle.net/2381/37544
Title: Related fixed point theorems on two complete and compact metric spaces
Authors: Namdeo, R. K.; Tiwari, N. K.; Fisher, B.; Taş, K.
Abstract: A new related fixed point theorem on two complete metric spaces is obtained. A generalization is given for two compact metric spaces.
20160513T14:12:57Z

A note on commutativity of nonassociative rings
http://hdl.handle.net/2381/37543
Title: A note on commutativity of nonassociative rings
Authors: Khan, M. S. S.
Abstract: A theorem on commutativity of nonassociate ring is given.
20160513T14:06:58Z

A Generalization of Prešić Type Mappings in MetricLike Spaces
http://hdl.handle.net/2381/37541
Title: A Generalization of Prešić Type Mappings in MetricLike Spaces
Authors: Shukla, S.; Fisher, Brian
Abstract: We generalize the result of Prešić in metriclike spaces by proving some common fixed point theorems for Prešić type mappings in metriclike spaces. An example is given which shows that the generalization is proper.
20160513T13:19:06Z

Phacoemulsification Surgery in Eyes with Neovascular AgeRelated Macular Degeneration
http://hdl.handle.net/2381/37538
Title: Phacoemulsification Surgery in Eyes with Neovascular AgeRelated Macular Degeneration
Authors: Grixti, A.; Papavasileiou, E.; Cortis, Dominic; Kumar, B. V.; Prasad, S.
Abstract: Purpose. To evaluate the visual outcomes and effect of phacoemulsification surgery on the progression of neovascular agerelated macular degeneration (AMD). Methods. Retrospective, noncomparative, and interventional case series. Thirty eyes from 29 subjects with neovascular AMD treated with intravitreal antivascular endothelial growth factor (VEGF) injections who underwent phacoemulsification and had a postsurgery followup of 6 months were included. LogMAR best corrected visual acuity (BCVA) was assessed preoperatively; 1 month, 3 months, and 6 months postoperatively; and finally at the last visit. The frequency of antiVEGF therapy, calculated as the number of intravitreal injections per month, and central macular thickness (CMT) before and after cataract surgery were determined. Results. Median (range) logMAR BCVA was 0.69 (0.16 to 1.32) preoperatively; 0.55 (−0.04 to 1.32) at 1 month, 0.52 (−0.1 to 1.32) at 3 months, and 0.50 (0.0 to 1.32) at 6 months postoperatively; and 0.6 (0.0 to 1.4) at final visit (P=0.0011). There was no difference in the frequency of antiVEGF injections between the immediate 6 months before and after phacoemulsification, which was equal to 0.1667 injections per month (P=0.6377). Median CMT measured 203 μm preoperatively, which temporarily increased to 238 μm at 1 month after surgery (P=0.0093) and then spontaneously returned to baseline, measuring 212.5 μm at 3 months postoperatively (P=0.3811). Conclusion. Phacoemulsification surgery significantly improved vision in patients with neovascular AMD, with no increased need for antiVEGF injections to keep the macula dry postoperatively.
20160513T11:32:13Z

Tiling spaces, codimension one attractors and shape
http://hdl.handle.net/2381/37346
Title: Tiling spaces, codimension one attractors and shape
Authors: Clark, Alexander; Hunton, J.
Abstract: We establish a close relationship between, on the one hand, expanding, codimension one attractors of diffeomorphisms on closed manifolds (examples of socalled strange attractors), and, on the other, spaces which arise in the study of aperiodic tilings. We show that every such orientable attractor is homeomorphic to a tiling space of either a substitution or a projection tiling, depending on its dimension. We also demonstrate that such an attractor is shape equivalent to a (d+1)dimensional torus with a finite number of points removed, or, in the nonorientable case, to a space with a twotoone covering by such a toruslesspoints. This puts considerable constraints on the topology of codimension one attractors, and constraints on which manifolds tiling spaces may be embedded in. In the process we develop a new invariant for aperiodic tilings, which, for 1dimensional tilings is in many cases finer than the cohomological or Ktheoretic invariants studied to date.
20160418T11:58:33Z

From Ambiguity Aversion to a Generalized Expected Utility. Modeling Preferences in a Quantum Probabilistic Framework
http://hdl.handle.net/2381/37265
Title: From Ambiguity Aversion to a Generalized Expected Utility. Modeling Preferences in a Quantum Probabilistic Framework
Authors: Aerts, D.; Sozzo, Sandro
Abstract: Ambiguity and ambiguity aversion have been widely studied in decision theory and economics both at a theoretical and an experimental level. After Ellsberg's seminal studies challenging subjective expected utility theory (SEUT), several (mainly normative) approaches have been put forward to reproduce ambiguity aversion and Ellsbergtype preferences. However, Machina and other authors have pointed out some fundamental difficulties of these generalizations of SEUT to cope with some variants of Ellsberg's thought experiments, which has recently been experimentally confirmed. Starting from our quantum modeling approach to human cognition, we develop here a general probabilistic framework to model human decisions under uncertainty. We show that our quantum theoretical model faithfully represents different sets of data collected on both the Ellsberg and the Machina paradox situations, and is flexible enough to describe different subjective attitudes with respect to ambiguity. Our approach opens the way toward a quantumbased generalization of expected utility theory (QEUT), where subjective probabilities depend on the state of the conceptual entity at play and its interaction with the decisionmaker, while preferences between acts are determined by the maximization of this 'statedependent expected utility'.
Description: The file associated with this record is under a 24month embargo from publication in accordance with the publisher's selfarchiving policy. The full text may be available through the publisher links provided above.
20160412T11:41:18Z

The centrifugal instability of the boundarylayer flow over a slender rotating cone in an enforced axial free stream
http://hdl.handle.net/2381/36986
Title: The centrifugal instability of the boundarylayer flow over a slender rotating cone in an enforced axial free stream
Authors: Hussain, Z.; Garrett, Stephen J.; Stephen, S. O.; Griffiths, Paul Travis
Abstract: In this study, a new centrifugal instability mode, which dominates within the boundarylayer flow over a slender rotating cone in still fluid, is used for the first time to model the problem within an enforced oncoming axial flow. The resulting problem necessitates an updated similarity solution to represent the basic flow more accurately than previous studies in the literature. The new mean flow field is subsequently perturbed, leading to disturbance equations that are solved via numerical and shortwavelength asymptotic approaches, yielding favourable comparisons with existing experiments. Essentially, the boundarylayer flow undergoes competition between the streamwise flow component, due to the oncoming flow, and the rotational flow component, due to effect of the spinning cone surface, which can be described mathematically in terms of a control parameter, namely the ratio of streamwise to axial flow. For a slender cone rotating in a sufficiently strong axial flow, the instability mode breaks down into Görtlertype counterrotating spiral vortices, governed by an underlying centrifugal mechanism, which is consistent with experimental and theoretical studies for a slender rotating cone in otherwise still fluid.
Description: The file associated with this record is under a 6month embargo from publication in accordance with the publisher's selfarchiving policy. The full text may be available through the publisher links provided above.
20160307T11:36:56Z

The neutral curve for stationary disturbances in rotating disk flow for powerlaw fluids
http://hdl.handle.net/2381/36985
Title: The neutral curve for stationary disturbances in rotating disk flow for powerlaw fluids
Authors: Griffiths, P. T.; Garrett, Stephen John; Stephen, S. O.
Abstract: This paper is concerned with the convective instabilities associated with the boundarylayer flow due to a rotating disk. Shearthinning fluids that adhere to the powerlaw relationship are considered. The neutral curves are computed using a sixthorder system of linear stability equations which include the effects of streamline curvature, Coriolis force and the nonNewtonian viscosity model. Akin to previous Newtonian studies it is found that the neutral curves have two critical values, these are associated with the type I upperbranch (crossflow) and type II lowerbranch (streamline curvature) modes. Our results indicate that an increase in shearthinning has a stabilising effect on both the type I and II modes, in terms of the critical Reynolds number and growth rate. Favourable agreement is obtained between existing asymptotic predictions and the numerical results presented here.
Description: The file associated with this record is under a 24month embargo from publication in accordance with the publisher's selfarchiving policy. The full text may be available through the publisher links provided above.
20160307T11:32:29Z

Stability of the boundary layer on a rotating disk for powerlaw fluids
http://hdl.handle.net/2381/36963
Title: Stability of the boundary layer on a rotating disk for powerlaw fluids
Authors: Griffiths, P. T.; Stephen, S. O.; Bassom, A. P.; Garrett, Stephen John
Abstract: The stability of the flow due to a rotating disk is considered for nonNewtonian fluids, specifically shearthinning fluids that satisfy the powerlaw (Ostwaldde Waele) relationship. In this case the basic flow is not an exact solution of the Navier–Stokes equations, however, in the limit of large Reynolds number the flow inside the threedimensional boundary layer can be determined via a similarity solution. An asymptotic analysis is presented in the limit of large Reynolds number. It is shown that the stationary spiral instabilities observed experimentally in the Newtonian case can be described for shearthinning fluids by a linear stability analysis. Predictions for the wavenumber and wave angle of the disturbances suggest that shearthinning fluids may have a stabilising effect on the flow.
20160303T11:51:44Z

Global linear stability of the boundarylayer flow over a rotating sphere
http://hdl.handle.net/2381/36889
Title: Global linear stability of the boundarylayer flow over a rotating sphere
Authors: Barrow, A.; Garrett, Stephen J.; Peake, N.
Abstract: We consider the linear global stability of the boundarylayer flow over a rotating sphere. Our results suggest that a selfexcited linear global mode can exist when the sphere rotates sufficiently fast, with properties fixed by the flow at latitudes between approximately 55°–65° from the pole (depending on the rotation rate). A neutral curve for global linear instabilities is presented with critical Reynolds number consistent with existing experimentally measured values for the appearance of turbulence. The existence of an unstable linear global mode is in contrast to the literature on the rotating disk, where it is expected that nonlinearity is required to prompt the transition to turbulence. Despite both being susceptible to local absolute instabilities, we conclude that the transition mechanism for the rotatingsphere flow may be different to that for the rotating disk.
20160225T13:44:07Z

The centrifugal instability of the boundarylayer flow over a slender rotating cone in an enforced axial freestream
http://hdl.handle.net/2381/36888
Title: The centrifugal instability of the boundarylayer flow over a slender rotating cone in an enforced axial freestream
Authors: Hussain, Z.; Garrett, Stephen J.; Stephen, S. O.; Griffiths, Paul T.
Abstract: In this study, a new centrifugal instability mode, which dominates within the boundarylayer flow over a slender rotating cone in still fluid, is used for the first time to model the problem within an enforced oncoming axial flow. The resulting problem necessitates an updated similarity solution to represent the basic flow more accurately than previous studies in the literature. The new mean flow field is subsequently perturbed, leading to disturbance equations that are solved via numerical and shortwavelength asymptotic approaches, yielding favourable comparisons with existing experiments. Essentially, the boundarylayer flow undergoes competition between the streamwise flow component, due to the oncoming flow, and the rotational flow component, due to effect of the spinning cone surface, which can be described mathematically in terms of a control parameter, namely the ratio of streamwise to axial flow. For a slender cone rotating in a sufficiently strong axial flow, the instability mode breaks down into Görtlertype counterrotating spiral vortices, governed by an underlying centrifugal mechanism, which is consistent with experimental and theoretical studies for a slender rotating cone in otherwise still fluid.
Description: The file associated with this record is under a 6month embargo from publication in accordance with the publisher's selfarchiving policy. The full text may be available through the publisher links provided above.
20160225T13:41:12Z

The effect of surface roughness on the convective instability of the BEK family of boundarylayer flows
http://hdl.handle.net/2381/36887
Title: The effect of surface roughness on the convective instability of the BEK family of boundarylayer flows
Authors: Alveroglu, Burhan; Segalini, A.; Garrett, Stephen J.
Abstract: A Chebyshev polynomial discretisation method is used to investigate the effect of both anisotropic (radially and azimuthally) and isotropic surface roughnesses on the convective instability of the BEK family of rotating boundarylayer flows. The meanflow profiles for the velocity components are obtained by modelling surface roughness with a partialslip approach. A linear stability analysis is then performed to investigate the effect of roughness on the convective instability characteristics of the inviscid Type I (crossflow) instability and the viscous Type II instability. It is revealed that all roughness types lead to a stabilisation of the Type I mode in all flows within the BEK family, with the exception of azimuthallyanisotropic roughness (radial grooves) within the Bödewadt layer which causes a mildly destabilising effect. In the case of the Type II mode, the results reveal the destabilising effect of radiallyanisotropic roughness (concentric grooves) on all the boundary layers, whereas both azimuthallyanisotropic and isotropic roughnesses have a stabilising effect on the mode for Ekman and von Kármán layers. Complementary results are also presented by considering the effects of roughness on the growth rates of each instability mode within the Ekman layer.
Description: The file associated with this record is under a 24month embargo from publication in accordance with the publisher's selfarchiving policy. The full text may be available through the publisher links provided above.
20160225T13:34:13Z

The effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layer
http://hdl.handle.net/2381/36886
Title: The effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layer
Authors: Cooper, A. J.; Harris, J. H.; Garrett, Stephen John; Oezkan, M.; Thomas, P. J.
Abstract: A theoretical study investigating the effects of both anisotropic and isotropic surface roughness on the convective stability of the boundarylayer flow over a rotating disk is described. Surface roughness is modelled using a partialslip approach, which yields steadyflow profiles for the relevant velocity components of the boundarylayer flow which are a departure from the classic von Kármán solution for a smooth disk. These are then subjected to a linear stability analysis to reveal how roughness affects the stability characteristics of the inviscid Type I (or crossflow) instability and the viscous Type II instability that arise in the rotating disk boundary layer. Stationary modes are studied and both anisotropic (concentric grooves and radial grooves) and isotropic (general) roughness are shown to have a stabilizing effect on the Type I instability. For the viscous Type II instability, it was found that a disk with concentric grooves has a strongly destabilizing effect, whereas a disk with radial grooves or general isotropic roughness has a stabilizing effect on this mode. In order to extract possible underlying physical mechanisms behind the effects of roughness, and in order to reconfirm the results of the linear stability analysis, an integral energy equation for threedimensional disturbances to the undisturbed threedimensional boundarylayer flow is used. For anisotropic roughness, the stabilizing effect on the Type I mode is brought about by reductions in energy production in the boundary layer, whilst the destabilizing effect of concentric grooves on the Type II mode results from a reduction in energy dissipation. For isotropic roughness, both modes are stabilized by combinations of reduced energy production and increased dissipation.
20160225T13:28:22Z

On the stability of von Kármán rotatingdisk boundary layers with radial anisotropic surface roughness
http://hdl.handle.net/2381/36885
Title: On the stability of von Kármán rotatingdisk boundary layers with radial anisotropic surface roughness
Authors: Garrett, Stephen J.; Cooper, A. J.; Harris, J. H.; Ozkan, M.; Segalini, A.; Thomas, P. J.
Abstract: We summarise results of a theoretical study investigating the distinct convective instability properties of steady boundarylayer flow over rough rotating disks. A generic roughness pattern of concentric circles with sinusoidal surface undulations in the radial direction is considered. The goal is to compare predictions obtained by means of two alternative, and fundamentally different, modelling approaches for surface roughness for the first time. The motivating rationale is to identify commonalities and isolate results that might potentially represent artefacts associated with the particular methodologies underlying one of the two modelling approaches. The most significant result of practical relevance obtained is that both approaches predict overall stabilising effects on type I instability mode of rotating disk flow. This mode leads to transition of the rotatingdisk boundary layer and, more generally, the transition of boundarylayers with a crossflow profile. Stabilisation of the type 1 mode means that it may be possible to exploit surface roughness for laminarflow control in boundary layers with a crossflow component. However, we also find differences between the two sets of model predictions, some subtle and some substantial. These will represent criteria for establishing which of the two alternative approaches is more suitable to correctly describe experimental data when these become available.
20160225T13:21:15Z

Global linear stability of the boundarylayer flow over a rotating sphere
http://hdl.handle.net/2381/36884
Title: Global linear stability of the boundarylayer flow over a rotating sphere
Authors: Barrow, A.; Garrett, Stephen John; Peake, N.
Abstract: We consider the linear global stability of the boundarylayer flow over a rotating sphere. Our results suggest that a selfexcited linear global mode can exist when the sphere rotates sufficiently fast, with properties fixed by the flow at latitudes between approximately 55°65° from the pole (depending on the rotation rate). A neutral curve for global linear instabilities is presented with critical Reynolds number consistent with existing experimentally measured values for the appearance of turbulence. The existence of an unstable linear global mode is in contrast to the literature on the rotating disk, where it is expected that nonlinearity is required to prompt the transition to turbulence. Despite both being susceptible to local absolute instabilities, we conclude that the transition mechanism for the rotatingsphere flow may be different to that for the rotating disk.
20160225T13:07:28Z

On Streamwise Vortices in Large Eddy Simulations of Initially Laminar Plane Mixing Layers
http://hdl.handle.net/2381/36790
Title: On Streamwise Vortices in Large Eddy Simulations of Initially Laminar Plane Mixing Layers
Authors: McMullan, William Andrew; Garrett, Stephen J.
Abstract: x
Description: The file associated with this record is under a 24month embargo from publication in accordance with the publisher's selfarchiving policy. The full text may be available through the publisher links provided above.
20160218T12:27:41Z

Outofband and adjacentchannel interference reduction by analog nonlinear filters
http://hdl.handle.net/2381/36471
Title: Outofband and adjacentchannel interference reduction by analog nonlinear filters
Authors: Nikitin, A. V.; Davidchack, Ruslan L.; Smith, J. E.
Abstract: In a perfect world, we would have ‘brick wall’ filters, nodistortion amplifiers and mixers, and wellcoordinated spectrum operations. The real world, however, is prone to various types of unintentional and intentional interference of technogenic (manmade) origin that can disrupt critical communication systems. In this paper, we introduce a methodology for mitigating technogenic interference in communication channels by analog nonlinear filters, with an emphasis on the mitigation of outofband and adjacentchannel interference.
Interference induced in a communications receiver by external transmitters can be viewed as wideband nonGaussian noise affecting a narrowerband signal of interest. This noise may contain a strong component within the receiver passband, which may dominate over the thermal noise. While the total wideband interference seen by the receiver may or may not be impulsive, we demonstrate that the interfering component due to power emitted by the transmitter into the receiver channel is likely to appear impulsive under a wide range of conditions. We give an example of mechanisms of impulsive interference in digital communication systems resulting from the nonsmooth nature of any physically realizable modulation scheme for transmission of a digital (discontinuous) message.
We show that impulsive interference can be effectively mitigated by nonlinear differential limiters (NDLs). An NDL can be configured to behave linearly when the input signal does not contain outliers. When outliers are encountered, the nonlinear response of the NDL limits the magnitude of the respective outliers in the output signal. The signal quality is improved in excess of that achievable by the respective linear filter, increasing the capacity of a communications channel. The behavior of an NDL, and its degree of nonlinearity, is controlled by a single parameter in a manner that enables significantly better overall suppression of the noisecontaining impulsive components compared to the respective linear filter. Adaptive configurations of NDLs are similarly controlled by a single parameter and are suitable for improving quality of nonstationary signals under timevarying noise conditions. NDLs are designed to be fully compatible with existing linear devices and systems and to be used as an enhancement, or as a lowcost alternative, to the stateofart interference mitigation methods.
20160201T09:58:41Z

Asymptotic variance of stationary reversible and normal Markov processes
http://hdl.handle.net/2381/36413
Title: Asymptotic variance of stationary reversible and normal Markov processes
Authors: Deligiannidis, G.; Peligrad, M.; Utev, Sergey
Abstract: We obtain necessary and sufficient conditions for the regular variation of the variance of partial sums of functionals of discrete and continuoustime stationary Markov processes with normal transition operators. We also construct a class of MetropolisHastings algorithms which satisfy a central limit theorem and invariance principle when the variance is not linear in n.
20160127T10:37:50Z

The HELP inequality for Hamiltonian systems
http://hdl.handle.net/2381/36295
Title: The HELP inequality for Hamiltonian systems
Authors: Brown, B. M.; Evans, W. D.; Marletta, M.
Abstract: We extend the Hardy–Everitt–Littlewood–Polya inequality, hitherto established for 2nth order formally selfadjoint ordinary differential equations, to a wide class of linear Hamiltonian systems. The method follows Dias (Ph.D. thesis, Cardiff: University of Wales, 1994) but without the Hilbert space setting which he uses.
20160115T15:52:52Z

Regularized semiclassical limits: linear flows with infinite Lyapunov exponents
http://hdl.handle.net/2381/36266
Title: Regularized semiclassical limits: linear flows with infinite Lyapunov exponents
Authors: Athanassoulis, Agisilaos; Kyza, I.; Katsaounis, T.
Abstract: Semiclassical asymptotics for Schrodinger equations with nonsmooth potentials give rise to illposed formal semiclassical limits. These problems have attracted a lot of attention in the last few years, as a proxy for the treatment of eigenvalue crossings, i.e. general systems. It has recently been shown that the semiclassical limit for conical singularities is in fact wellposed, as long as the Wigner measure (WM) stays away from singular saddle points. In this work we develop a family of refined semiclassical estimates, and use them to derive regularized transport equations for saddle points with infinite Lyapunov exponents, extending the aforementioned recent results. In the process we answer a related question posed by P. L. Lions and T. Paul in 1993. If we consider more singular potentials, our rigorous estimates break down. To investigate whether conical saddle points, such as x, admit a regularized transport asymptotic approximation, we employ a numerical solver based on posterior error controal. Thus rigorous uppen bounds for the asymptotic error on concrete problems are generated. In particular, specific phenomena which render invalid any regularized transport for x are identified and quantified. In that sense our rigorous results are sharp. Finally, we use our findings to formulate a precise conjecture for the condition under which conical saddle points admit a regularized transport solution for the WM.
Description: The file associated with this record is under a permanent embargo while publication is In Press in accordance with the publisher's selfarchiving policy. The full text may be available through the publisher links provided above.
20160112T12:48:18Z

On the XFEL Schrödinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging
http://hdl.handle.net/2381/36247
Title: On the XFEL Schrödinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging
Authors: Athanassoulis, Agisilaos; Antonelli, P.; Markowich, P. A.; Hajaiej, H.
Abstract: We analyse a nonlinear Schrödinger equation for the timeevolution of the wave function of an electron beam, interacting selfconsistently through a Hartree–Fock nonlinearity and through the repulsive Coulomb interaction of an atomic nucleus. The electrons are supposed to move under the action of a time dependent, rapidly periodically oscillating electromagnetic potential. This can be considered a simplified effective single particle model for an Xray free electron laser. We prove the existence and uniqueness for the Cauchy problem and the convergence of wavefunctions to corresponding solutions of a Schrödinger equation with a timeaveraged Coulomb potential in the high frequency limit for the oscillations of the electromagnetic potential.
20160111T11:41:27Z

Numerical Simulations of XRay Free Electron Lasers (XFEL)
http://hdl.handle.net/2381/36243
Title: Numerical Simulations of XRay Free Electron Lasers (XFEL)
Authors: Athanassoulis, Agisilaos; Markowich, P. A.; Antonelli, P.; Huang, Z.
Abstract: We study a nonlinear Schrödinger equation which arises as an effective single particle model in Xray free electron lasers (XFEL). This equation appears as a first principles model for the beammatter interactions that would take place in an XFEL molecular imaging experiment in [A. Fratalocchi and G. Ruocco, Phys. Rev. Lett., 106 (2011), 105504]. Since XFEL are more powerful by several orders of magnitude than more conventional lasers, the systematic investigation of many of the standard assumptions and approximations has attracted increased attention. In this model the electrons move under a rapidly oscillating electromagnetic field, and the convergence of the problem to an effective timeaveraged one is examined. We use an operator splitting pseudospectral method to investigate numerically the behavior of the model versus that of its timeaveraged version in complex situations, namely the energy subcritical/mass supercritical case and in the presence of a periodic lattice. We find the timeaveraged model to be an effective approximation, even close to blowup, for fast enough oscillations of the external field. This work extends previous analytical results for simpler cases [P. Antonelli, A. Athanassoulis, H. Hajaiej, and P. Markowich, Arch. Ration. Mech. Anal., 211 (2014), pp. 711732].
20160111T10:48:23Z

Synergy effect of cooperative investment
http://hdl.handle.net/2381/36189
Title: Synergy effect of cooperative investment
Authors: Grechuk, Bogdan; Zabarankin, M.
Abstract: Cooperative investment consists of two problems: finding an optimal cooperative investment strategy and fairly dividing investment outcome among participating agents. In general, the two problems cannot be solved separately. It is known that when agents’ preferences are represented by meandeviation functionals, sharing of optimal portfolio creates instruments that, on the one hand, satisfy individual risk preferences but, on the other hand, are not replicable on an incomplete market, so that each agent is strictly better off in participating in cooperative investment than investing alone. This synergy effect is shown to hold when agents’ acceptance sets are represented by cashinvariant utility functions in the case of multiperiod investment with an arbitrary feasible investment set. In this case, a set of all Paretooptimal allocations is characterized, and an equilibriumbased method for selecting a “fair” Paretooptimal allocation is suggested. It is also shown that if exists, the “fair” allocation belongs to the core of the corresponding cooperative game. The equilibriumbased method is then extended to the case of arbitrary utility functions. The obtained results are demonstrated in a multiperiod cooperative investment problem with investors imposing drawdown constraints on investment strategies.
Description: The file associated with this record is under a 12month embargo from publication in accordance with the publisher's selfarchiving policy, available at http://www.springer.com/gp/openaccess/authorsrights/selfarchivingpolicy/2124. The full text may be available through the publisher links provided above.
20160106T12:56:39Z

Related fixed points for setvalued mappings on two uniform spaces
http://hdl.handle.net/2381/36151
Title: Related fixed points for setvalued mappings on two uniform spaces
Authors: Türkoğlu, D.; Fisher, Brian
Abstract: Some related fixed point theorems for setvalued mappings on two complete and compact uniform spaces are proved.
Description: 2000 Mathematics Subject Classification: 54H25, 47H10.
20160105T10:28:25Z

On the Fresnel integrals and the convolution
http://hdl.handle.net/2381/36144
Title: On the Fresnel integrals and the convolution
Authors: Kiliçman, A.; Fisher, Brian
Abstract: The Fresnel cosine integral C(x), the Fresnel sine integral S(x), and the associated functions C+(x), C−(x), S+(x), and S−(x) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the Fresnel cosine integral and its associated functions with x+r and xr are evaluated.
Description: 2000 Mathematics Subject Classification: 33B10, 46F10
20160104T15:10:01Z

On the sine integral and the convolution
http://hdl.handle.net/2381/36143
Title: On the sine integral and the convolution
Authors: Fisher, Brian; AlSirehy, F.
Abstract: The sine integral Si(λx) and the cosine integral Ci(λx) and their associated functions Si+(λx), Si−(λx), Ci+(λx), Ci−(λx) are defined as locally summable functions on the real line. Some convolutions of these functions and sin(μx), sin+(μx), and sin−(μx) are found.
Description: 2000 Mathematics Subject Classification: 33B10, 46F10.
20160104T14:57:48Z

Inverse portfolio problem with coherent risk measures
http://hdl.handle.net/2381/36136
Title: Inverse portfolio problem with coherent risk measures
Authors: Grechuk, Bogdan; Zabarankin, M.
Abstract: In general, a portfolio problem minimizes risk (or negative utility) of a portfolio of financial assets with respect to portfolio weights subject to a budget constraint. The inverse portfolio problem then arises when an investor assumes that his/her risk preferences have a numerical representation in the form of a certain class of functionals, e.g. in the form of expected utility, coherent risk measure or meandeviation functional, and aims to identify such a functional, whose minimization results in a portfolio, e.g. a market index, that he/she is most satisfied with. In this work, the portfolio risk is determined by a coherent risk measure, and the rate of return of investor’s preferred portfolio is assumed to be known. The inverse portfolio problem then recovers investor’s coherent risk measure either through finding a convex set of feasible probability measures (risk envelope) or in the form of either mixed CVaR or negative Yaari’s dual utility. It is solved in singleperiod and multiperiod formulations and is demonstrated in a case study with the FTSE 100 index.
20151223T13:36:29Z

Implementing Automotive Telematics for Insurance Covers of Fleets
http://hdl.handle.net/2381/36130
Title: Implementing Automotive Telematics for Insurance Covers of Fleets
Authors: Azzopardi, M.; Cortis, Dominic
Abstract: The advantages of UsageBased Insurance for automotive covers over conventional rating methods have been discussed in literature for over four decades. Notwithstanding their adoption in insurance markets has been slow. This paper seeks to establish the viability of introducing fleet TelematicsBased Insurance by investigating the perceptions of insurance operators, tracking service providers and corporate fleet owners. At its core, the study involves a SWOTanalysis to appraise TelematicsBased Insurance against conventional premium rating systems. Twenty five key stakeholders in Malta, a country with an insurance industry that represents others in microcosm, were interviewed to develop our analysis. We assert that local insurers have interests in such insurance schemes as enhanced fleet management and monitoring translate into an improved insurance risk. The findings presented here have implications for all stakeholders as we argue that telematics enhance fleet management, TBI improves risk management for insurers and adoption of this technology is dependent on telematics providers increasing the perceived control by insurers over managing this technology.
20151222T16:43:17Z

Phacoemulsification Surgery in Eyes with Neovascular AgeRelated Macular Degeneration
http://hdl.handle.net/2381/36118
Title: Phacoemulsification Surgery in Eyes with Neovascular AgeRelated Macular Degeneration
Authors: Grixti, A.; Papavasileiou, E.; Cortis, Dominic; Kumar, B. V.; Prasad, S.
Abstract: Purpose. To evaluate the visual outcomes and effect of phacoemulsification surgery on the progression of neovascular agerelated
macular degeneration (AMD). Methods. Retrospective, noncomparative, and interventional case series. Thirty eyes from 29
subjects with neovascular AMD treated with intravitreal antivascular endothelial growth factor (VEGF) injections who underwent
phacoemulsification and had a postsurgery followup of 6 months were included. LogMAR best corrected visual acuity (BCVA)
was assessed preoperatively; 1 month, 3 months, and 6 months postoperatively; and finally at the last visit. The frequency of antiVEGF
therapy, calculated as the number of intravitreal injections per month, and central macular thickness (CMT) before and
after cataract surgery were determined. Results. Median (range) logMAR BCVA was 0.69 (0.16 to 1.32) preoperatively; 0.55 (−0.04
to 1.32) at 1 month, 0.52 (−0.1 to 1.32) at 3 months, and 0.50 (0.0 to 1.32) at 6 months postoperatively; and 0.6 (0.0 to 1.4) at final
visit (𝑃 = 0.0011). There was no difference in the frequency of antiVEGF injections between the immediate 6 months before
and after phacoemulsification, which was equal to 0.1667 injections per month (𝑃 = 0.6377). Median CMT measured 203 𝜇m
preoperatively, which temporarily increased to 238 𝜇m at 1 month after surgery (𝑃 = 0.0093) and then spontaneously returned
to baseline, measuring 212.5 𝜇m at 3 months postoperatively (𝑃 = 0.3811). Conclusion. Phacoemulsification surgery significantly
improved vision in patients with neovascular AMD, with no increased need for antiVEGF injections to keep the macula dry
postoperatively
20151222T14:47:21Z

Atiyah sequences, connections and characteristic forms for principal bundles over groupoids and stacks
http://hdl.handle.net/2381/36102
Title: Atiyah sequences, connections and characteristic forms for principal bundles over groupoids and stacks
Authors: Biswas, Indranil; Neumann, Frank
Abstract: We construct connections and characteristic forms for principal bundles over groupoids and stacks in the differentiable, holomorphic and algebraic category using Atiyah exact sequences associated with transversal tangential distributions.; Nous construisons les connexions et formes caractéristiques pour les fibrés principaux sur
les groupoïdes et les champs dans la catégorie différentiable, holomorphe et algébrique à
l’aide des suites d’Atiyah associées aux distributions transversales tangentielles.
20151218T12:05:34Z

Mathematical Modelling of PlanktonOxygen Dynamics Under the Climate Change
http://hdl.handle.net/2381/36058
Title: Mathematical Modelling of PlanktonOxygen Dynamics Under the Climate Change
Authors: Sekerci, Yadigar; Petrovskii, Sergei
Abstract: Ocean dynamics is known to have a strong effect on the global climate change and on the composition of the atmosphere. In particular, it is estimated that about 70 % of the atmospheric oxygen is produced in the oceans due to the photosynthetic activity of phytoplankton. However, the rate of oxygen production depends on water temperature and hence can be affected by the global warming. In this paper, we address this issue theoretically by considering a model of a coupled planktonoxygen dynamics where the rate of oxygen production slowly changes with time to account for the ocean warming. We show that a sustainable oxygen production is only possible in an intermediate range of the production rate. If, in the course of time, the oxygen production rate becomes too low or too high, the system's dynamics changes abruptly, resulting in the oxygen depletion and plankton extinction. Our results indicate that the depletion of atmospheric oxygen on global scale (which, if happens, obviously can kill most of life on Earth) is another possible catastrophic consequence of the global warming, a global ecological disaster that has been overlooked.
20151211T16:00:50Z

The centrifugal instability of the boundarylayer flow over slender rotating cones
http://hdl.handle.net/2381/36037
Title: The centrifugal instability of the boundarylayer flow over slender rotating cones
Authors: Hussain, Z.; Garrett, Stephen J.; Stephen, S. O.
Abstract: Existing experimental and theoretical studies are discussed which lead to the clear hypothesis of a hitherto unidentified convective instability mode that dominates within the boundarylayer flow over slender rotating cones. The mode manifests as Görtlertype counterrotating spiral vortices, indicative of a centrifugal mechanism. Although a formulation consistent with the classic rotatingdisk problem has been successful in predicting the stability characteristics over broad cones, it is unable to identify such a centrifugal mode as the halfangle is reduced. An alternative formulation is developed and the governing equations solved using both shortwavelength asymptotic and numerical approaches to independently identify the centrifugal mode.
20151210T09:45:42Z

Hard Spheres at a Planar Hard Wall: Simulations and DFT
http://hdl.handle.net/2381/33560
Title: Hard Spheres at a Planar Hard Wall: Simulations and DFT
Authors: Davidchack, Ruslan L.; Laird, Brian B.; Roth, Roland
Abstract: Hard spheres are a central and important model reference system for both homogeneous and
inhomogeneous fluid systems. In this paper we present new highprecision molecular dynamics computer
simulations for a hard sphere fluid at a planar hard wall. For this system we present
benchmark data for the density profile ρ(z ) at various bulk densities, the wall surface free
energy γ, the excess adsorption Γ, and the excess volume [superscript v]ex , which is closely related to Γ. We
compare all benchmark quantities with predictions from stateoftheart classical density
functional theory calculations within the framework of fundamental measure theory. While we find
overall good agreement between computer simulations and theory, significant deviations appear at
sufficiently high bulk densities.
Description: Supplementary data for this work can be found at http://hdl.handle.net/2381/33537
20151116T10:35:08Z

NonFickian diffusion and the accumulation of methane bubbles in deepwater sediments
http://hdl.handle.net/2381/33352
Title: NonFickian diffusion and the accumulation of methane bubbles in deepwater sediments
Authors: Goldobin, Dennis S.; Brilliantov, N. V.; Levesley, J.; Lovell, M. A.; Rochelle, C. A.; Jackson, P. D.; Haywood, A. M.; Hunter, S. J.; Rees, J. G.
Abstract: In the absence of fractures, methane bubbles in deepwater sediments can be immovably trapped within a porous matrix by surface tension. The dominant mechanism of transfer of gas mass therefore becomes the diffusion of gas molecules through porewater. The accurate description of this process requires nonFickian diffusion to be accounted for, including both thermal diffusion and gravitational action. We evaluate the diffusive flux of aqueous methane considering nonFickian diffusion and predict the existence of extensive bubble mass accumulation zones within deepwater sediments. The limitation on the hydrate deposit capacity is revealed; too weak deposits cannot reach the base of the hydrate stability zone and form any bubbly horizon.
20151022T11:42:58Z

Patchy Invasion of StageStructured Alien Species with ShortDistance and LongDistance Dispersal.
http://hdl.handle.net/2381/33307
Title: Patchy Invasion of StageStructured Alien Species with ShortDistance and LongDistance Dispersal.
Authors: Rodrigues, L. A.; Mistro, D. C.; Cara, E. R.; Petrovskaya, N.; Petrovskii, Sergei
Abstract: Understanding of spatiotemporal patterns arising in invasive species spread is necessary for successful management and control of harmful species, and mathematical modeling is widely recognized as a powerful research tool to achieve this goal. The conventional view of the typical invasion pattern as a continuous population traveling front has been recently challenged by both empirical and theoretical results revealing more complicated, alternative scenarios. In particular, the socalled patchy invasion has been a focus of considerable interest; however, its theoretical study was restricted to the case where the invasive species spreads by predominantly shortdistance dispersal. Meanwhile, there is considerable evidence that the longdistance dispersal is not an exotic phenomenon but a strategy that is used by many species. In this paper, we consider how the patchy invasion can be modified by the effect of the longdistance dispersal and the effect of the fat tails of the dispersal kernels.
Description: The file associated with this record is under a 12month embargo from publication in accordance with the publisher's selfarchiving policy, available at http://www.springer.com/gp/openaccess/authorsrights/selfarchivingpolicy/2124. The full text may be available in the publisher links provided above.
20151019T11:08:06Z

Approximation with Random Bases: Pro et Contra
http://hdl.handle.net/2381/33147
Title: Approximation with Random Bases: Pro et Contra
Authors: Gorban, Alexander N.; Tyukin, Ivan Yu.; Prokhorov, D. V.; Sofeikov, Konstantin I.
Abstract: In this work we discuss the problem of selecting suitable approximators from families of parameterized elementary functions that are known to be dense in a Hilbert space of functions. We consider and analyze published procedures, both randomized and deterministic, for selecting elements from these families that have been shown to ensure the rate of convergence in L2 norm of order O(1/N), where N is the number of elements. We show that both randomized and deterministic procedures are successful if additional information about the
families of functions to be approximated is provided. In the absence of such additional information one may observe exponential growth of the number of terms needed to approximate the function and/or extreme sensitivity of the
outcome of the approximation to parameters. Implications of our analysis for
applications of neural networks in modeling and control are illustrated with
examples.
Description: arXiv admin note: text overlap with arXiv:0905.0677 http://www.sherpa.ac.uk/romeo/issn/00200255/
20151001T11:29:45Z

On the diagonal subalgebra of an Ext algebra
http://hdl.handle.net/2381/33085
Title: On the diagonal subalgebra of an Ext algebra
Authors: Green, Edward L.; Snashall, Nicole; Solberg, Ø.; Zacharia, D.
Abstract: Let R be a Koszul algebra over a field k and M be a linear Rmodule. We study a graded subalgebra Δ[subscript: M] of the Extalgebra $\operatorname{Ext}_R^*(M,M)$ 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 Δ[subscript: M] is isomorphic to the graded center of the Koszul dual of R. [abstract with TEX support available at http://arxiv.org/abs/1412.4953]
20150922T11:20:56Z

Trivial extensions of gentle algebras and Brauer graph algebras
http://hdl.handle.net/2381/33046
Title: Trivial extensions of gentle algebras and Brauer graph algebras
Authors: Schroll, Sibylle
Abstract: We show that two wellstudied classes of tame algebras coincide: namely, the class of symmetric special biserial algebras coincides with the class of Brauer graph algebras. We then explore the connection between gentle algebras and symmetric special biserial algebras by explicitly determining the trivial extension of a gentle algebra by its minimal injective cogenerator. This is a symmetric special biserial algebra and hence a Brauer graph algebra of which we explicitly give the Brauer graph. We further show that a Brauer graph algebra gives rise, via admissible cuts, to many gentle algebras and that the trivial extension of a gentle algebra obtained via an admissible cut is the original Brauer graph algebra.As a consequence we prove that the trivial extension of a Jacobian algebra of an ideal triangulation of a Riemann surface with marked points in the boundary is isomorphic to the Brauer graph algebra with Brauer graph given by the arcs of the triangulation.
20150915T09:03:50Z

Time Dependent Diffusion as a Mean Field Counterpart of Levy Type Random Walk
http://hdl.handle.net/2381/32806
Title: Time Dependent Diffusion as a Mean Field Counterpart of Levy Type Random Walk
Authors: Ahmed, D. A.; Petrovskii, S.
Abstract: Insect trapping is commonly used in various pest insect monitoring programs as well as in many ecological field studies. An individual is said to be trapped if it falls within a well defined capturing zone, which it cannot escape. The accumulation of trapped individuals over time forms trap counts or alternatively, the flux of the population density into the trap. In this paper, we study the movement of insects whose dynamics are governed by time dependent diffusion and Lévy walks. We demonstrate that the diffusion model provides an alternative framework for the Cauchy type random walk (Lévy walk with Cauchy distributed steps). Furthermore, by calculating the trap counts using these two conceptually different movement models, we propose that trap counts for pests whose dynamics may be Lévy by nature can effectively be predicted by diffusive flux curves with timedependent diffusivity.
Description: Mathematics Subject Classification: 82B41 / 60K35 / 35Q92
20150722T16:11:10Z

Mathematical Modelling of Spatiotemporal Dynamics of Oxygen in a Plankton System
http://hdl.handle.net/2381/32804
Title: Mathematical Modelling of Spatiotemporal Dynamics of Oxygen in a Plankton System
Authors: Sekerci, Y.; Petrovskii, S.
Abstract: Oxygen production due to phytoplankton photosynthesis is a crucial phenomenon underlying the dynamics of marine ecosystems. However, most of the existing literature focus on other aspects of the plankton community functioning, thus leaving the issue of the coupled oxygenplankton dynamics understudied. In this paper, we consider a generic model of the oxygenphytoplanktonzooplankton dynamics to make an insight into the basic properties of the planktonoxygen interactions. The model is analyzed both analytically and numerically. We first consider the nonspatial model and show that it predicts possible oxygen depletion under certain environmental conditions. We then consider the spatially explicit model and show that it exhibits a rich variety of spatiotemporal patterns including travelling fronts of oxygen depletion, dynamical stabilization of unstable equilibrium and spatiotemporal chaos.
Description: Mathematics Subject Classification: 92D40 / 35B36 / 35Q92 / 37N25
20150722T15:49:51Z