DSpace Community:
http://hdl.handle.net/2381/445
Fri, 27 May 2016 14:11:20 GMT
20160527T14:11:20Z
DSpace Community:
http://lra.le.ac.uk:80/retrieve/2392/mathsequation.jpg
http://hdl.handle.net/2381/445

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.
Wed, 18 May 2016 12:05:18 GMT
http://hdl.handle.net/2381/37594
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.
Wed, 18 May 2016 11:50:36 GMT
http://hdl.handle.net/2381/37591
20160518T11:50:36Z

Towards roughnessbased drag reduction in crossflow dominated flows
http://hdl.handle.net/2381/37570
Title: Towards roughnessbased drag reduction in crossflow dominated flows
Authors: Garrett, Sephen J.; Cooper, A. J.; Ozkan, M.; Thomas, P. J.
Abstract: Recent theoretical results are presented from our ongoing study investigating the distinct convective instability properties of the boundarylayer flow over rough rotating disks. In this study, radial anisotropic surface roughness (concentric grooves) is modelled using the partialslip approach of Miklavčič & Wang (2004) and the surfacegeometry approach of Yoon et. Al (2007). An energy analysis reveals that for both instability modes, the main contributors to the energy balance are the energy production by the Reynolds stresses and conventional viscous dissipation. For the Type I mode, energy dissipation increases and the Reynoldsstress energy production decreases with roughness under both models. This suggests a clear stabilising effect of the anisotropic roughness on the Type I mode. For the Type II mode, the Reynoldsstress energy production increases with roughness under both models. However, the energy dissipation of the Type II mode decreases with the roughness under the surfacegeometry model and increases under the partialslip model. This sensitivity to the precise form of the anisotropic roughness suggests that maximising dissipation by an appropriately designed roughness can theoretically lead to an overall beneficial stabilisation of both the Type I and Type II modes. This is a potential route to overall boundarylayertransition delay and drag reduction in crossflow dominated flows.
Description: This paper is under embargo as it has been submitted for publication to European Journal of Mechanics  B/Fluids. If accepted the file associated with this record is embargoed until 24 months after the date of publication.
Tue, 17 May 2016 09:01:51 GMT
http://hdl.handle.net/2381/37570
20160517T09:01:51Z

An energy analysis of convective instabilities of the Bödewadt and Ekman boundary layers over rough surfaces
http://hdl.handle.net/2381/37569
Title: An energy analysis of convective instabilities of the Bödewadt and Ekman boundary layers over rough surfaces
Authors: Alveroglu, B.; Segalini, A.; Garrett, Stephen J.
Abstract: An energy balance equation for the threedimensional Bödewadt and Ekman layers of the so called “BEK family" of rotating boundarylayer flows is derived. A Chebyshev discretisation method is used to solve the equations and investigate the effect of surface roughness on the physical mechanisms of transition. All roughness types lead to a stabilization of the Type I (crossflow) instability mode for both flows, with the exception of azimuthallyanisotropic roughness (radial grooves) within the Bödewadt layer which is destabilising. In the case of the viscous Type II instability mode, the results predict a destabilisation effect of radiallyanisotropic roughness (concentric grooves) on both flows, whereas both azimuthallyanisotropic roughness and isotropic roughness have a stabilisation effect. The results presented here confirm the results of our prior linear stability analyses.
Description: This paper is under embargo as it has been submitted for publication to European Journal of Mechanics  B/Fluids. If accepted the file associated with this record is embargoed until 24 months after the date of publication.
Tue, 17 May 2016 08:48:49 GMT
http://hdl.handle.net/2381/37569
20160517T08:48:49Z

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.
Fri, 13 May 2016 14:33:57 GMT
http://hdl.handle.net/2381/37550
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.
Fri, 13 May 2016 14:30:09 GMT
http://hdl.handle.net/2381/37549
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.
Fri, 13 May 2016 14:25:52 GMT
http://hdl.handle.net/2381/37548
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.
Fri, 13 May 2016 14:22:20 GMT
http://hdl.handle.net/2381/37547
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.
Fri, 13 May 2016 14:18:00 GMT
http://hdl.handle.net/2381/37546
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.
Fri, 13 May 2016 14:12:57 GMT
http://hdl.handle.net/2381/37544
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.
Fri, 13 May 2016 14:06:58 GMT
http://hdl.handle.net/2381/37543
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.
Fri, 13 May 2016 13:19:06 GMT
http://hdl.handle.net/2381/37541
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.
Fri, 13 May 2016 11:32:13 GMT
http://hdl.handle.net/2381/37538
20160513T11:32:13Z

Stability modes in vortex structure formation: Canonical examples for rotating components
http://hdl.handle.net/2381/37476
Title: Stability modes in vortex structure formation: Canonical examples for rotating components
Authors: Gostelow, J. Paul; Garrett, Stephen J.; Rona, Aldo; Adebayo, David S.
Abstract: Three rather different physical cases have been studied. All represent very practical geometries for which the modal behavior of vortex structures is not completely understood. The work on these problems is ongoing with the objective of obtaining physical confirmation, enhanced understanding and predictive capability for the vortex structures encountered in rotating machines.
Wed, 04 May 2016 14:50:44 GMT
http://hdl.handle.net/2381/37476
20160504T14:50:44Z

Cohomology of tiling spaces: beyond primitive substitutions
http://hdl.handle.net/2381/37469
Title: Cohomology of tiling spaces: beyond primitive substitutions
Authors: Rust, Daniel George
Abstract: This thesis explores the combinatorial and topological properties of tiling spaces
associated to 1dimensional symbolic systems of aperiodic type and their associated
algebraic invariants. We develop a framework for studying systems which are more
general than primitive substitutions, naturally partitioned into two instances: in the
first instance we allow systems associated to sequences of substitutions of primitive
type from a finite family of substitutions (called mixed substitutions); in the second
instance we concentrate on systems associated to a single substitution, but where
we entirely remove the condition of primitivity.
We generalise the notion of a BargeDiamond complex, in the onedimensional case,
to any mixed system of symbolic substitutions. This gives a way of describing
the associated tiling space as an inverse limit of complexes. We give an effective
method for calculating the Cech cohomology of the tiling space via an exact sequence
relating the associated sequence of substitution matrices and certain subcomplexes
appearing in the approximants. As an application, we show that there exists a
system of substitutions on two letters which exhibit an uncountable collection of
minimal tiling spaces with distinct isomorphism classes of Cech cohomology.
In considering nonprimitive substitutions, we naturally divide this set of substitutions
into two cases: the minimal substitutions and the nonminimal substitutions.
We provide a detailed method for replacing any nonprimitive but minimal substitution
with a topologically conjugate primitive substitution, and a more simple
method for replacing the substitution with a primitive substitution whose tiling
space is orbit equivalent. We show that an AndersonPutnam complex with a collaring
of some appropriately large radius suffices to provide a model of the tiling
space as an inverse limit with a single map. We apply these methods to effectively
calculate the Cech cohomology of any substitution which does not admit a periodic
point in its subshift. Using its set of closed invariant subspaces, we provide a pair
of invariants which are each strictly finer than the usual Cech cohomology for a
substitution tiling space.
Fri, 29 Apr 2016 13:40:19 GMT
http://hdl.handle.net/2381/37469
20160429T13:40:19Z

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.
Mon, 18 Apr 2016 11:58:33 GMT
http://hdl.handle.net/2381/37346
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.
Tue, 12 Apr 2016 11:41:18 GMT
http://hdl.handle.net/2381/37265
20160412T11:41:18Z

A classification of the point spectrum of constant length substitution tiling spaces and general fixed point theorems for tilings
http://hdl.handle.net/2381/37027
Title: A classification of the point spectrum of constant length substitution tiling spaces and general fixed point theorems for tilings
Authors: Abuzaid, Dina Asaad
Abstract: We examine the point spectrum of the various tiling spaces that result from
different choices of tile lengths for substitution of constant length on a two or a three letter
alphabet. In some cases we establish insensitivity to changes in length. In a wide range
of cases, we establish that the typical choice of length leads to trivial point spectrum.
We also consider a problem related to tilings of the integers and their connection to fixed
point theorems. Using this connection, we prove a generalization of the Banach Contraction
Principle.
Fri, 11 Mar 2016 16:11:58 GMT
http://hdl.handle.net/2381/37027
20160311T16:11:58Z

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.
Mon, 07 Mar 2016 11:36:56 GMT
http://hdl.handle.net/2381/36986
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.
Mon, 07 Mar 2016 11:32:29 GMT
http://hdl.handle.net/2381/36985
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.
Thu, 03 Mar 2016 11:51:44 GMT
http://hdl.handle.net/2381/36963
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.
Thu, 25 Feb 2016 13:44:07 GMT
http://hdl.handle.net/2381/36889
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.
Thu, 25 Feb 2016 13:41:12 GMT
http://hdl.handle.net/2381/36888
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.
Thu, 25 Feb 2016 13:34:13 GMT
http://hdl.handle.net/2381/36887
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.
Thu, 25 Feb 2016 13:28:22 GMT
http://hdl.handle.net/2381/36886
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.
Thu, 25 Feb 2016 13:21:15 GMT
http://hdl.handle.net/2381/36885
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.
Thu, 25 Feb 2016 13:07:28 GMT
http://hdl.handle.net/2381/36884
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.
Thu, 18 Feb 2016 12:27:41 GMT
http://hdl.handle.net/2381/36790
20160218T12:27:41Z

Multiscale principal component analysis
http://hdl.handle.net/2381/36616
Title: Multiscale principal component analysis
Authors: Akinduko, Ayodeji Akinwumi
Abstract: The problem of approximating multidimensional data with objects of lower dimension is a classical problem in complexity reduction. It is important that data approximation capture the structure(s) and dynamics of the data, however distortion to data by many methods during approximation implies that some geometric structure(s) of the data may not be preserved during data approximation. For methods that model the manifold of the data, the quality of approximation depends crucially on the initialization of the method. The first part of this thesis investigates the effect of initialization on manifold modelling methods. Using Self Organising Maps (SOM) as a case study, we compared the quality of learning of manifold methods for two popular initialization methods; random initialization and principal component initialization. To further understand the dynamics of manifold learning, datasets were further classified into linear, quasilinear and nonlinear.
The second part of this thesis focuses on revealing geometric structure(s) in high dimension data using an extension of Principal Component Analysis (PCA). Feature extraction using (PCA) favours direction with large variance which could obfuscate other interesting geometric structure(s) that could be present in the data. To reveal these intrinsic structures, we analysed the local PCA structures of the dataset. An equivalent definition of PCA is that it seeks subspaces that maximize the sum of pairwise distances of data projection; extending this definition we define localization in term of scale as maximizing the sum of weighted squared pairwise distances between data projections for various distributions of weights (scales). Since for complex data various regions of the dataspace could have different PCA structures, we also define localization with regards to dataspace. The resulting local PCA structures were represented by the projection matrix corresponding to the subspaces and analysed to reveal some structures in the data at various localizations.
Tue, 09 Feb 2016 10:10:00 GMT
http://hdl.handle.net/2381/36616
20160209T10:10:00Z

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.
Mon, 01 Feb 2016 09:58:41 GMT
http://hdl.handle.net/2381/36471
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.
Wed, 27 Jan 2016 10:37:50 GMT
http://hdl.handle.net/2381/36413
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.
Fri, 15 Jan 2016 15:52:52 GMT
http://hdl.handle.net/2381/36295
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.
Tue, 12 Jan 2016 12:48:18 GMT
http://hdl.handle.net/2381/36266
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.
Mon, 11 Jan 2016 11:41:27 GMT
http://hdl.handle.net/2381/36247
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].
Mon, 11 Jan 2016 10:48:23 GMT
http://hdl.handle.net/2381/36243
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.
Wed, 06 Jan 2016 12:56:39 GMT
http://hdl.handle.net/2381/36189
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.
Tue, 05 Jan 2016 10:28:25 GMT
http://hdl.handle.net/2381/36151
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
Mon, 04 Jan 2016 15:10:01 GMT
http://hdl.handle.net/2381/36144
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.
Mon, 04 Jan 2016 14:57:48 GMT
http://hdl.handle.net/2381/36143
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.
Wed, 23 Dec 2015 13:36:29 GMT
http://hdl.handle.net/2381/36136
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.
Tue, 22 Dec 2015 16:43:17 GMT
http://hdl.handle.net/2381/36130
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
Tue, 22 Dec 2015 14:47:21 GMT
http://hdl.handle.net/2381/36118
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.
Fri, 18 Dec 2015 12:05:34 GMT
http://hdl.handle.net/2381/36102
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.
Fri, 11 Dec 2015 16:00:50 GMT
http://hdl.handle.net/2381/36058
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.
Thu, 10 Dec 2015 09:45:42 GMT
http://hdl.handle.net/2381/36037
20151210T09:45:42Z

Using partially specified models to detect and quantify structural sensitivity in biological systems
http://hdl.handle.net/2381/35950
Title: Using partially specified models to detect and quantify structural sensitivity in biological systems
Authors: Adamson, Matthew William
Abstract: Mathematical models in ecology and evolution are highly simplified representations of a complex underlying reality. For this reason, there is always a high degree of uncertainty with regards to the model specification—not just in terms of parameters, but also in the form taken by the model equations themselves. This uncertainty becomes critical for models in which the use of two different functions fitting the same dataset can yield substantially different model predictions—a property known as structural sensitivity. In this case, even if the model is purely deterministic, the uncertainty in the model functions carries through into uncertainty in the model predictions, and new frameworks are required to tackle this fundamental problem. Here, we construct a framework that uses partially specified models: ODE models in which unknown functions are represented not by a specific functional form, but by an entire data range and constraints of biological realism. Partially specified models can be used to rigorously detect when models are structurally sensitive in their predictions concerning the character of an equilibrium point by projecting the data range into a generalised bifurcation space formed of equilibrium values and derivatives of any unspecified functions. The key question of how to carry out this projection is a serious mathematical challenge and an obstacle to the use of partially specified models. We address this challenge by developing several powerful techniques to perform such a projection.
Wed, 25 Nov 2015 15:53:12 GMT
http://hdl.handle.net/2381/35950
20151125T15:53:12Z

Optimum shape problems in distributed parameter control theory.
http://hdl.handle.net/2381/34581
Title: Optimum shape problems in distributed parameter control theory.
Authors: Girgis, Siham Boctor.
Abstract: The work is concerned with optimum shape problems in the distributed parameter area and it consists of four parts. In Part I we consider first the basic variational theory due to Gelfand and Fomin emphasising the importance of the transversality condition in optimum shape situations; also in Part I we discuss an application of the basic theory in a particular problem where the state equations (the constraints) are hyperbolic in character. In Part II we consider a heat transfer problem between two streams of different temperatures, moving parallel to one another and with constant speeds, the aim being to choose the inlet conditions of one stream in order to achieve desired outlet conditions for the other stream. Two different aspects of the heat transfer problem are considered. In Part III we consider a hydrodynamic problem using shallow water theory in which we seek the optimum shape of a harbour boundary in order to redistribute the liquid energy in some desired way. Here onedimensional and twodimensional aspects of the problem are discussed, in the former fairly precise results are achieved, and in the latter the solution of the problem is shown to depend on the solution of coupled integral equations. In Part IV we consider the problem of optimum shape of an axially symmetric elastic body (subject to the classical equations of elasticity) in order to minimise the axial moment of inertia or the weight of the body. An approximate method for finding the optimum shape is presented though considerable work remains to be done in this problem.
Thu, 19 Nov 2015 08:55:48 GMT
http://hdl.handle.net/2381/34581
20151119T08:55:48Z

Distributed parameter theory in optimal control.
http://hdl.handle.net/2381/34582
Title: Distributed parameter theory in optimal control.
Authors: Gregson, M. J.
Abstract: The main result of this work is the solution of open loop optimal control problems for counterflow diffusion processes, which occur very widely in chemical and mechanical engineering. In these processes two fluids pass each other moving in opposite directions separated by a membrane which is permeable to heat or a chemical solute. The membrane may also take the form of a liquidgas interface. Subject to certain simplifying assumptions, the equations describing such processes are 01 (x,t), 02 (x,t) are the temperatures, or concentrations of solute, of the two fluids and u(t), v(t) are time dependent flow rates. k is a transfer coefficient which is assumed constant, and C1, C2 are thermal or solute capacities of the fluids per unit length of tube. h is an equilibrium constant; h = 1 for heat transfer. Possible controls are the inlet temperature or concentration of one stream and the flow rates, while possible objectives are the regulation of the outlet temperature or concentration of the other stream, or the maximisation of heat or solute transfer. Subsidiary results are the optimal control of simpler but related hyperbolic systems. One of these is the restricted counterflow problem in which the controlling stream is assumed to be so massive that it is unaffected by giving up heat or solute to the controlled stream, i.e. the system is described by the equations ; Another is the furnace equation in which u and w are possible controls. Different classes of problem arise according to whether the multiplicative controls u and v are subject to rigid constraints (frequently leading to "bangbang" controls), or whether they are constants, functions of x and t, or functions of t only. Variational methods based on the maximum principle of A.I. Egorov are employed. Analytic solutions and numerical solutions using finite differences are obtained to the various problems. The simplifying assumptions made are probably too severe for many of the results to be directly applicable to industry. However the qualitative features of the optimal control of these processes are explained, and it is not too difficult to build more complex models.
Thu, 19 Nov 2015 08:55:48 GMT
http://hdl.handle.net/2381/34582
20151119T08:55:48Z

Applications of variational theory in certain optimum shape problems in hydrodynamics.
http://hdl.handle.net/2381/34580
Title: Applications of variational theory in certain optimum shape problems in hydrodynamics.
Authors: Essawy, Abdelrahman Hussein.
Abstract: PART I In a recent paper Wu, T.Y. & Whitney, A.K., the authors studied optimum shape problems in hydrodynamics. These problems are stated in the form of a singular integral equation depending on the unknown shape and an unknown singularity distribution; the shape is then to be determined so that some given performance criterion has to be {lcub}maximized/minimized{rcub} In the optimum problem to be studied in this part we continue to assume that the state equation is a linear integral equation but we generalize the Wu & Whitney theory in two different ways. This method is applied to functional of quadratic form and a necessary condition for the extremum to be a minimum is derived. PART II The purpose of this part is to evaluate the optimum shape of a twodimensional hydrofoil of given length and prescribed mean curvature which produces {lcub}maximum lift/minimum drag{rcub} The problem is discussed in three cases when there is a {lcub}full/partial/zero{rcub} cavity flow past the hydrofoil. The liquid flow is assumed to be twodimensional steady, irrotational and incompressible and a linearized theory is assumed. Twodimensional vortex and source distributions are used to simulate the two dimensional {lcub}full/partial/zero{rcub} cavity flow past a thin hydrofoil. This method leads to a system of integral equations and these are solved exactly using the CarlemanMuskhelishvili technique. This method is similar to that used by Davies, T.V. We use variational calculus techniques to obtain the optimum shape of the hydrofoil in order to {lcub}maximized/minimized{rcub} the {lcub}lift/drag{rcub} coefficient subject to constraints on curvature and given length. The mathematical problem is that of extremizing a functional depending on {lcub}? vortex strength/ ? source strength{rcub} these three functions are related by singular integral equations. The analytical solution for the unknown shape z and the unknown singularity distribution y has branchtype singularities at the two ends of the hydrofoil. Analytical solution by singular integral equations is discussed and the approximate solution by the RayleighRitz method is derived. A sufficient condition for the extremum to be a minimum is derived from consideration of the second variation. PART III The purpose of this work is to evaluate the optimum shape of a twodimensional hydrofoil of given length and prescribed mean curvature which produces minimum drag. A thin hydrofoil of arbitrary shape is in steady, rectilinear, horizontal motion at a depth h beneath the free surface of a liquid. The usual assumptions in problems of this kind are taken as a basis, namely, the liquid is nonviscous and moving twodimensionally, steadily and without vorticity, the only force acting on it is gravity. With these assumptions together with a linearization assumption we determine the forces, due to the hydrofoil beneath a free surface of the liquid. We use variational calculus techniques similar to those used in Part II to obtain the optimum shape so that the drag is minimized. A sufficient condition for the extremum to be a minimum is derived from consideration of the second variation. In this part some general expressions are established concerning the forces acting on a submerged vortex and source element beneath a free surface using Blasius theorem.
Thu, 19 Nov 2015 08:55:47 GMT
http://hdl.handle.net/2381/34580
20151119T08:55:47Z

Optimum shape problems for distributed parameter systems.
http://hdl.handle.net/2381/34579
Title: Optimum shape problems for distributed parameter systems.
Authors: Edwards, Janet M
Abstract: In this thesis the variation of a functional defined on a variable domain has been studied and applied to the problem of finding the optimum shape of the domain in which some performance criterion has an extreme. The method most frequently used is one due to Gelf and Fomin. It is applied to problems governed by first and second order partial differential equations, unsteady one dimensional gas movements and the problem of minimum drag on a body with axial symmetry in Stokes flow.
Thu, 19 Nov 2015 08:55:47 GMT
http://hdl.handle.net/2381/34579
20151119T08:55:47Z