Abstract: Weather and climate models comprise a so-called 'adiabatic dynamical core' and a collection of 'parametrizations' (often given the unfortunate name of 'physics'). The former is a more or less well understood numerical solution of dynamical equations based on the Euler equations. The latter attempt to represent a wide variety of physical processes. 

Abstract: TBA

Abstract: Control moment gyros (CMGs) are momentum exchange devices which are considered to be good actuators for spacecraft due to their fast slewing capabilities. They consist of  systems of gimballed momentum wheels. Singularities occur when, no matter how the gimbal angles are moved, the angular momentum cannot be increased in a given direction. We analyze the relationship between gimbal angles and the angular momentum for different CMG  geometries to understand the different types of singularities which occur in these systems.

Abstract: Our intention is to show the Gardner method for generation of conservation laws for partial difference equations. We apply it to all the ABS equations and to an asymmetric quad-graph equation. We also show that the Gardner method can be applied for symmetries. Namely, we use it to generate an infinite number of symmetries from known one.

Abstract: As formation flying missions are becoming a reality, relative motion modelling has received an enhanced interest through the past decade. 

Abstract: TBA

Abstract: A successive  averaging method is developed for explaining the regularization mechanism in the periodic Korteweg- deVries (KdV) equation in the homogeneous Sobolev spaces  H^s for s>0.  Specifically, a proof is given of global existence existence, uniqueness, and Lipschitz continuous dependence on the initial data of the solutions of the periodic KdV. For the case  where the initial data is in L_2 we also show the Lipschitz continuous dependence of these solutions with respect to the initial data as maps from H^s to H^s for -1 < s < 0.

Abstract: A big problem in malaria control is the rapidity with which mosquitoes can develop resistance to insecticides. The possibility of creating evolution-proof insecticides is therefore of considerable interest. Biologists have suggested that effective malaria control, with only weak selection for insecticide resistance, could be achieved if insecticides target only old mosquitoes that have already laid most of their eggs. The strategy aims to exploit the fact that most malarial mosquitoes do not live long enough to transmit the disease. 

Abstract: It is seen in some natural biological situations, that a living organism requiring a change in its location and orientation is able to do so by executing a sequence of internally controlled motions. These motions cause a resultant location change due to the conservation of momentum.

Abstract: Abstract:  Linkages in the plane are know to have geometrically interesting configuration spaces M.  
One can describe the dynamics of some simple idealized  linkages in terms of the geodesic flow on M, for an  appropriate Riemannian metric. We describe how to associate to the linkage the curvature of this metric, which has a direct bearing on the dynamics of geodesic  flow, and thus of the linkage.

Abstract: In this talk we will discuss a unifying approach to the smoothing estimates for dispersive equations based on the canonical transforms from the microlocal analysis, as well as on the comparison principles for evolution equations. The talk will be based on the joint work with Mitsuru Sugimoto (Nagoya).

Abstract: Insects have evolved diverse and delicate morphological structures in order to capture the inherently low energy of a propagating sound wave. In mosquitoes, the capture of acoustic energy, and its transduction into neuronal signals, is assisted by the active mechanical participation of the scolopidia.

Abstract: A new theory of viscous oscillatory flows has been developed. Our theory represents an adaptation of the Vishik-Lyusternik approach combined with the two-timing and averaging methods. We consider high Reynold's number viscous incompressible flows driven by a vibrating boundary for the simple geometry of a half-space.  From the physical viewpoint the required boundary conditions may be seen as the tangential vibrations of material points of a plane stretchable membrane. The main result is the construction of general, global, and uniformly valid asymptotic solutions of the Navier-Stokes equations. These solutions satisfy general oscillating boundary conditions and three different regimes of the scaling parameters (that correspond to the strong, moderate, and weak nonlinearities).

Abstract: Abstract: The vector nonlinear Schroedinger equation (VNLS) models the propagation of an ultra-short light pulse along an optical fibre. The equation is integrable, affords multi-soliton soliton solutions, and also finite-gap solutions where the underlying algebraic curve is trigonal. The vector nature of the complex-valued dependent variable contains information about the polarisation state of the electromagnetic field.

Abstract: We prove by an explicit construction that solutions to incompressible 3D Euler equations, defined in the periodic cube, can be mapped bijectively to a new system of equations whose solutions are globally regular.  We establish that the usual Beale-Kato-Majda criterion for finite-time singularity (or blowup) of a solution to the 3D Euler system is equivalent to a condition on the corresponding regular solution of the new system.

Abstract: We present recent results regarding escape rates and conditionally invariant measures for a periodic Lorentz gas with holes.  We then derive a variational principle connecting the escape rate to the pressure on the survivor set, the set of points which never enters the hole.  This relation generalizes to a broad class of systems with holes and requires only weak assumptions on the size and boundary of the hole.

Abstract: TBA

Abstract: Magnetic liquid or ferrofluids are complex fluids which interact with external magnetic field. Many effects can be observed.

Abstract: Several dispersive wave equations can be formulated as Hamiltonian PDEs.  Steady travelling waves can then be interpreted as critical points of the Hamiltonian functional.  Furthermore, their stability is linked to the spectrum of the Hessian of this functional.  In this talk, the Maslov index, an index defined on paths of Lagrangian spaces, is used to study this spectrum in the case of traveling waves arising in various higher-order Korteweg-de Vries-type equations.

Abstract: Air cushioning in droplet impacts will be investigated. A model will be presented, which couples an inviscid liquid droplet to a gas film satisfying a lubricating squeeze film equation. As the droplet approaches impact a high pressure is generated in the gas film, which causes the droplet free-surface to deform and ultimately trap a gas bubble. Predictions of the size of this trapped bubble will be made and compared to experimental data.

Abstract: TBA

Abstract: In the weakly nonlinear long wave regime, solitary waves are often modeled by the Korteweg-de Vries equation, which is well-known to support an exact solitary wave solution. However, when the effect of background rotation is taken into account, the resulting relevant nonlinear wave equation, the Ostrovsky equation, does not support an exact solitary wave solution. Instead an initial solitary like disturbance decays into radiating oscillatory waves. In this talk, we will demonstrate through a combination of theoretical analyses, numerical simulations and laboratory experiments that the long time outcome of this radiation is a nonlinear wave packet, whose carrier wavenumber is determined by an extremum in the group velocity.

Abstract: TBA

Abstract: Plants defend themselves using chemical toxins the concentration of which often varies with the age of twig segments. In boreal forests, woody internodes of the youngest segments of the twigs of the deciduous angiosperm species that herbivores such as hares prefer to eat are more defended by toxins than the woody internodes of the older segments that subtend and support the younger segments. Thus, the per capita daily intake of the biomass of the older segments of twigs by herbivores is much higher than their intake of the biomass of the younger segments of twigs. 

Abstract: In this talk I shall present the "reflection Hopf algebra" formalism. This formalism may be used in boundary scattering theory and is a natural extension of the usual Hopf algebra for the analysis of the reflection processes. I shall give several examples where this formalism proved to be very useful. They include the (generalized) twisted Yangians in AdS/CFT correspondence and the coideal quantum affine algebra of the Deformed Hubbard Chain. The talk will be based on arXiv: 1010.3761, 1101.6062 and 1110.4596.

Abstract: TBA

(N.B. Seminar at 2 pm in LTB)

Abstract: We illustrate the role of non-Abelian T-duality in string theory  with emphasis on backgrounds with non-vanishing Ramond flux fields. We discuss generic features such as the fate  of geometric isometries and of supersymmetry. We present important examples in the gauge/gravity correspondence,  that is AdS_3 X S^3 X T^4 and AdS_5 X S^5$. In conjunction, we comment on possible integrable structures in the  T-dual theory.

Abstract: TBA

Abstract: The non-linear wave equation (sometimes called the non-linear Klien-Gordon equation) is a much studied equation with applications in Josephson transmission lines, dislocations in crystals, DNA processes and much more.  It possess many types of solutions which may include stationary front solutions.  In this talk we shall consider what effect adding a step-like inhomogeneity has on the stability of such fronts and present some of the results we have derived over the last three years.

Abstract: Any triangle ABC has a pedal triangle (whose vertices are the feet of the perpendiculars from each vertex to the opposite side).  We study how the shape changes as we repeatedly take the pedal triangle.  Does the sequence of triangles converge?  (Background material on Euclidean Geometry will be included for those too young to have studied this.)

The AdS/CFT correspondence has produced remarkable connections between different areas of physics and mathematics. In this talk I will start by reviewing the relation between the Wilson loop observable in gauge theories and the problem of finding minimal area surfaces in hyperbolic (or AdS) space. Until recently only very few explicit solutions were known to such problem but I will show how, using Riemann theta functions an infinite parameter family of new solutions can be found. Moreover a one parameter family of deformations is identified such that the area is preserved. The solution to this problem uses methods from the theory of solitons and non-linear differential equations and sheds a new interesting light on the connection between the Wilson loop observable in gauge theories and integrable systems.

Abstract: TBA

Abstract: Here we give a pedagogical introduction to Euler-Poincar\'e flows on the (extended) Virasoro orbit, divided into three parts. In the first part, we introduce some basic notions of Euler-Poincar\'e flows, Virasoro orbit etc. The second part describes an Euler-Poincar\'e formulation of a new class of peakon equations with cubic nonlinearity found by Z. Qiao and V. Novikov. We show that the Hamiltonian structures obtained by Qiao and Hone and Wang can be obtained by our method. The last part introduces integrable ODEs associated to stabilizer set of Virasoro orbit.

Abstract: TBA

Abstract: Biochemical pathways involve the interaction of large number of species, a property which can make their simulations computationally expensive and their analysis prohibitively complicated. To reduce this complexity, it is common practice to group a bunch of elementary reactions together as a single complex reaction and to do the analysis / simulation with this simplified model. But is this justified? Are the statistics at least qualitatively correct if one does such a procedure? In this talk I'll address these questions, illustrate the problems of such approaches and a new method which we developed to obtain a statistically correct coarse-grained description of the chemical master equation.

Abstract: TBA

Abstract: The recently developed method of control based continuation allows the continuation of periodic solutions directly in physical experiments. The key ideas of this approach are (1) to introduce a control scheme that locally stabilizes periodic solutions without perturbing them, and (2) to use continuation to guide the experiment around folds and through bifurcation points. The experiment runs asynchronously from the actual continuation method, which communicates with the experiment by setting a control target and by taking measurements. In this talk we will present results obtained in a lab experiment of an impact oscillator that exhibits a large hysteresis loop. We will indicate current challenges with this method and how we intend to tackle them.

Abstract: TBA

Abstract: Isostatic mounts are used in applications like telescopes and robotics to move and hold part of a structure in a desired pose relative to the rest, by driving some controls rather than driving the subsystem directly. To achieve this successfully requires an understanding of the coupled space of configurations and controls, and of the singularities of the mapping from the coupled space to the space of controls. It is crucial to avoid such singularities because generically they lead to large constraint forces and internal stresses which can cause distortion. In this paper we outline design principles for isostatic mount systems for dynamic structures, with particular emphasis on robots.

Abstract: The economist Paul Krugman was awarded the Nobel prize for his work in economic geography. In his book "The Self-Organizing Economy" he promotes a Santa Fe-style approach to modelling complex economic systems. Krugman's arguments are illustrated with some simple mathematical models. In this talk, I explain how one such model has exact solutions with very similar properties to the peaked solitons ("peakons") that appearing in an integrable partial differential derived by Camassa and Holm in shallow water theory. The exact solutions in Krugman's integro-differential model turn out explain the numerical behaviour he observed. This is joint work with J. Kelsey and F. Medda.

Abstract: TBA

Abstract: Molecular monolayers, especially water monolayers, are playing a crucial role in modern science and technology. In order to derive simplified models of monolayer dynamics, we consider the set of rolling self-interacting particles on a plane with an off-set center of mass and a non-isotropic inertia tensor.  To connect with water monolayer dynamics, we assume the properties of the particles like mass, inertia tensor and dipole moment to be the same as water molecules. The perfect rolling constraint is considered as a simplified model of a very strong, but rapidly decaying bond with the surface. Since the rolling constraint is non-holonomic, it prevents the application of the standard tools of statistical mechanics: for example the system exhibits  two temperatures -- translational and rotational-- for some degrees of freedom, and no temperature can be defined for other degrees of freedom.

Abstract: The famous Laguerre polynomials are orthogonal over [0,\infty) with respect to a negative exponential weight function. They are thus natural  candidates for the efficient numerical approximation of such decaying exponential behaviour. We shall give a number of examples, including stable manifolds and fluid mechanics problems related to dynamical systems.

Abstract: TBA

Abstract: We demonstrate existence of discrete solitons in Discrete Nonlinear Schrodinger equation (dlns) with saturable nonlinearity. We consider two types of solutions to (dlns) periodic and vanishing at infinity. In the second part of our talk, we prove the existence of periodic and solitary traveling waves in Fermi-Pasta-Ulam lattices with saturable nonlinearities. Calculus of variations and Nehari manifolds are employed to establish the existence of these solutions. We present some extensions of our results, combining the Nehari manifold approach and the Mountain Pass argument.

Abstract: Superstring theory on AdS_5 x S^5 is classically equivalent, via the Pohlmeyer reduction, to a fermionic generalization of an extended sine-Gordon model. The Pohlmeyer-reduced and light-cone gauge string S-matrices turn out to be different limits of a larger interpolating S-matrix, based on the q-deformed R-matrix of Beisert and Koroteev, 2008. In this talk I will briefly review the reduction before discussing recent progress in constructing the quantum S-matrix of the reduced and interpolating theories. It is suggested that the interpolating S-matrix may provide a new way to regularize computations in the string theory.

Abstract: TBA

Abstract: TBA

Abstract: TBA

Abstract: In this talk, I will discuss how a new kind of quantized geometry, the quantum Nambu geometry, arises in string theory. I will also describe its mathematical properties and demonstrate that the quantum Nambu geometry is intrinsically different from the ordinary Lie algebra type noncommutative geometry. I will also discuss a proposal for a matrix model description of M5-brane in a constant C-field.

Abstract: TBA

Abstract: TBA

Abstract: Liquid crystals are fluids carrying an orientational degree of freedom. Their rotational symmetries can be used to reduce their Lagrangian description. This talk shows how Euler-Poincaré reduction produces a unifying framework for liquid crystal dynamics. As a result, two major liquid crystal theories turn out to be equivalent. Moreover, these theories can be extended to deal with orientational defects, aka disclinations.

Abstract: Growing plant cells undergo rapid axial elongation with negligible radial expansion: high internal turgor pressure causes viscous stretching of the cell wall. 

Abstract: An informal overview of quantum mechanics, from first principles to path integrals and quantum integrable systems

Abstract: 

Models describing waves in anisotropic media or media with imperfections
usually have inhomogeneous terms. Examples of such models can be found
in many applications, for example in nonlinear optical waveguides, water
waves moving over a bottom with topology, currents in nonuniform
Josephson junctions, DNA-RNAP interactions etc. This talk considers the
effects of (non-local) inhomogeneities on the existence and stability of
fronts in nonlinear wave equations.

This seminar is part of the virtual AG (Access Grid) Dynamics Seminar
series, a series of occasional seminars intended for those interested in
Nonlinear Dynamics and Dynamical Systems who have Access Grid facilities
(as used in the MAGIC network). More information can be found at
http://www1.maths.leeds.ac.uk/~alastair/ag_dynamics_seminar/

People in Surrey can attend the talk in real-time and life in the
Computing AGN room 39BB02. It would be nice if some people could go
along so that the seminar room is not too sparse.

Abstract: TBA

Abstract: An informal overview of quantum mechanics, from first principles to path integrals and quantum integrable systems

Abstract: TBA

Abstract: It has recently been argued that the seek for "consensus" and some form of "incompatibility" are basic mechanisms to explain the dynamics of cultural change and diversity [1]. Here, we will consider a basic, but mathematically amenable, three-state bounded compromise voter model (a constrained generalization of the classic two-state voter model [2]) that includes these ingredients. In this opinion dynamics model, a population of size N is composed of "leftists" and "rightists" that interact with "centrists" on a complete graph: a leftist and centrist can both become leftists with rate (1+q)/2 or centrists with rate (1-q)/2 (and similarly for rightists and centrists), where q denotes a selective bias towards extremism (q>0) or centrism (q<0). This system admits three absorbing fixed points and a "polarization" line along which a frozen mixture of leftists and rightists coexist. In the realm of the Fokker-Planck equation, and using a mapping onto a population genetics model, we compute the fixation probability of ending in every absorbing state and the mean times for these events. We therefore show, especially in the limit of weak bias and large population size (|q|~1/N, N>>1), how fluctuations alter the mean field predictions: polarization is likely when q>0, but there is always a finite probability to reach a consensus; the opposite happens when q<0. The findings are illustrated and corroborated by stochastic simulations. This presentation is based on the recent Ref.[3]"

Abstract: An informal overview of quantum mechanics, from first principles to path integrals and quantum integrable systems

Abstract: TBA

Abstract: There is a growing realization among evolutionary biologists that heritable phenotypic variation is not always encoded in the DNA.

Abstract: An informal overview of quantum mechanics, from first principles to path integrals and quantum integrable systems

Abstract: An informal overview of quantum mechanics, from first principles to path integrals and quantum integrable systems

Abstract: Motivated by electrodynamic space tethers we consider the statics problem of a conducting rod in a uniform magnetic field. This problem has close analogies with that of a spinning top in rigid-body dynamics. We show that some cases are integrable while others are nonintegrable. For the latter we use a (Hamiltonian) Melnikov approach that highlights problems with similar Melnikov applications in rigid-body dynamics in the literature as well as ways around these problems.

Abstract: A molecular motor is a nano-scale protein which converts chemical energy into mechanical work. For example, myosin-V is a double headed processive molecular motor that transports a variety of cargos within biological cells. It achieves this by walking head-over-head along an actin track, passing through a sequence of coordinated biochemical reactions and mechanical motions, taking several successive steps before detaching.

There is much debate as to the exact nature of the stepping mechanism of myosin-V due to the noise to which nano-scale measurements are subject. Mechanochemical aspects have been experimentally investigated and averaged quantities, such as velocities and run lengths, have been measured. This work focuses on theoretical methods to extract more information - such as a more precise stepping mechanism - from these experimental results aiming to improve the quality of molecular motor modelling.

Abstract: We consider the Lorentz process in the plane with periodic configuration of convex obstacles and with finite horizon. We define T(r) as the first return time of the flow to the r-neighbourhood of the initial position. We are interested in the behaviour of T(r) as r goes to zero. This is a joint work with Benoit Saussol.

Abstract: In this talk I will review my previous work on stability and mixing in two-dimensional vortices. This will include a threshold calculation for the existence of nonlinear cat's eye structures and an investigation into nonlinear vorticity staircase structures in a Gaussian vortex.

Abstract: We develop and test a mechanistic model of how diversity varies with body mass in marine ecosystems. The model predicts the form of the ``diversity spectrum,'' which quantifies the distribution of species' asymptotic body masses and is a species analogue of the classic size spectrum of individuals. 

Abstract: An informal overview of quantum mechanics, from first principles to path integrals and quantum integrable systems

Abstract: TBA

Abstract: The fact that piecewise contractions are asymptotically periodic was proved in 2008. This general result raises further questions about the periodic dynamics displayed by piecewise contractions, and the seminar takes a close look at a family of periodic solutions to a particular mapping, the two-halfplane map, and constructs the sets of parameters where the family exists, in the limit of strong contraction. As the family chosen is only one among many, the talk concentrates on techniques for constructing the parameter sets in the hope that these can be employed in further studies of the problem.

Abstract: In this talk I will be presenting some of my work, in collaboration with many others, on the growth and regulation of bacterial biofilms; these are slimy colonies of non-motile bacteria on solid-fluid surfaces that have a number of implications in medicine and industry. The models to be discussed consist of nonlinear systems of PDEs and were analysed using asymptotic and computational methods. The main results and insights drawn from the work will be summarised.

Abstract: An informal overview of quantum mechanics, from first principles to path integrals and quantum integrable systems

Abstract: Subject of this talk is the twistor geometry discussion of a five-dimensional generalisation of the instanton equation known as the contact instanton equation. This equation was recently introduced in the context of (twisted) supersymmetric Yang-Mills theory on the five-dimensional sphere. If time permits, certain extensions to higher dimensions and supersymmetric generalisations will also be presented.

Abstract: Food webs are the networks of who-eats-who in ecology. Despite being large and complex, the food webs observed in nature show relatively stable, stationary dynamics. Understanding this stability of food webs is a central challenge in ecology and could also inspire the design of more robust technical and organizational networks. Exploring food web stability is challenging because the food webs constitute high-dimensional and strongly nonlinear systems with dynamics on many different time scales. 

Abstract: An informal overview of quantum mechanics, from first principles to path integrals and quantum integrable systems

Abstract: We will discuss special quantum group symmetries of the integrable system associated to the AdS/CFT correspondence and its quantum deformations.

Abstract: Baker posed a question in the 1960's about when a rational map of degree d can be lacking periodic points of (minimum) period k. He gave the short list of pairs (d,k) that can occur.  In this talk we discuss the complete solution to this problem proved by Hawkins' Ph.D. student Rika Hagihara. 

Abstract: The propagation of long wavelength disturbances on the surface of a fluid layer of finite depth is considered. An arbitrary stress is applied at the surface with both tangential and normal components. 

Abstract: The asymptotic behaviour of the random (Markovian) walk on the integers in a randomly generated environment of transition probabilities was first characterised by Solomon in the setting where jumps  are restricted to {+1,-1}. Subsequent work by Key extended this characterisation to the setting where jumps are uniformly bounded, while Balthausen and Goldsheid achieved similar results in the more general setting of the strip k x Z (k \in N). We consider a deterministic version of this problem in which the Markov assumption is relaxed, and establish a zero-one law for the deterministic walk in a deterministic environment (DWDE).

Abstract: We consider (attracting) free semigroup actions (with two generators) on an interval. It is known that, if those two maps are sufficiently C2-close to the identity, then the (forward) minimal set. Namely, it must be an interval. (This statement is not accurate. I will give the precise statement in my talk.)

Abstract: TBA