Applied and Computational Mathematics Seminars 2018/2019

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Title: Energy flux enhancement, intermittency and turbulence via Fourier triad phase dynamics in 1D Burgers equation

Speakers: Dr. Miguel Bustamante (UCD)

Date: Monday 17th September 2018

Time: 1pm

Location: Room 1.25, Science Centre North

Abstract:
We present a theoretical and numerical study of Fourier space triad phase dynamics in one-dimensional stochastically forced Burgers equation at Reynolds number Re ≈ 2.7×10^4. We demonstrate that Fourier triad phases over the inertial range display a collective behaviour characterised by intermittent periods of synchronisation and alignment, reminiscent of Kuramoto model (Kuramoto 1984) and directly related to collisions of shocks in physical space. These periods of synchronisation favour efficient energy fluxes across the inertial range towards small scales, resulting in strong bursts of dissipation and enhanced coherence of Fourier energy spectrum. The fast time scale of the onset of synchronisation relegates energy dynamics to a passive role: this is further examined using a reduced system with the Fourier amplitudes fixed in time -- a phase-only model. We show that intermittent triad phase dynamics persists without amplitude evolution and we broadly recover many of the characteristics of the full Burgers system. In addition, for both full Burgers and phase-only systems the physical space velocity statistics reveals that triad phase alignment is directly related to the non-Gaussian statistics typically associated with structure-function intermittency in turbulent systems.
This work was done in collaboration with Dr. Brendan P. Murray. It is published in Journal of Fluid Mechanics 850, 624-645 (2018). You can find an arXiv preprint here: https://arxiv.org/abs/1705.08960.

Title: Stochastic Backlund transformations

Speakers: Prof. Neil O’Connell (UCD)

Date: Monday 24th September 2018

Time: 1pm

Location: Room 1.25, Science Centre North


Abstract:
How does one introduce randomness into a classical Hamiltonian system in order to produce something which is related to the ‘corresponding’ quantum system? I will discuss this question from a probabilistic point of view, in the context of a one-dimensional example with exponential potential. I will also give some background and motivation.

Coffee and tea will be available in the School Common Room from 12.40pm

 


Title:        Gluing methods for Vortex dynamics in Euler flows

Speakers:    Manuel del Pino,(University of Bath and University of Chile)

Date:        Monday 3rd December 2018

Time:     1pm

Location:    Room 1.25, Science Centre North


Abstract:    
We consider the two-dimensional Euler flow for an incompressible fluid confined to a smooth domain. We construct smooth solutions with concentrated vorticities around k points which evolve according to the Hamiltonian system for the Kirchhoff-Routh energy, using an outer-inner solution gluing approach.

The asymptotically singular profile around each point resembles a scaled finite mass solution of Liouville's equation. We also discuss the vortex filament conjecture for the three-dimensional case.

This is joint work with Juan Dávila, Monica Musso and Juncheng Wei.


Coffee and tea will be available in the School Common Room from 12.40pm.





 


Title:        Storm surge forecasting and other operational ocean modelling at the Met Office

Speakers:    Clare O’Neill (Met. Office, UK)

Date:        Monday 26th November 2018

Time:     1pm

Location:    Room 1.25, Science Centre North


Abstract:    


The Met Office runs a wide variety of operational marine models, from waves to storm surge to ecosystems. These generate products for a variety of customers and partners including other national meteorological services, environment agencies, the UK navy, and the Copernicus Marine Environment Monitoring Service. This presentation will give an overview of the activities and outputs of the Met Office's Ocean Forecasting Research and Development group. It will then focus on the storm surge forecast system in particular, describing the current system as well as research activities aimed at improving forecasts in the future.


Coffee and tea will be available in the School Common Room from 12.40pm.





Title:        Revisiting black-hole perturbation theory: the hyperboloidal slice approach

Speakers:    Rodrigo Macedo (Queen Mary, University of London)

Date:        Monday 19th November 2018

Time:     1pm

Location:    Room 1.25, Science Centre North

Abstract:  

 
After reviewing the well-stablished notion of black-hole perturbation theory and the concept of quasinormal modes, we present a spectral representation of solutions to relativistic wave equations based on a geometrical approach in which the constant-time surfaces extend until future null infinity. Here, we restrict ourselves to an asymptotically flat, spherical symmetric spacetime (with focus on the Reisnner-Nordstrom solution). With the help of a Laplace transformation on the wave equation in question, we provide a geometrical interpretation to known algorithms (i.e. Leaver’s approach) apart from deriving an algorithm for obtaining all ingredients of the desired spectral decomposition, including quasi-normal modes, quasi-normal mode amplitudes as well as the jump of the Laplace-transform along the branch cut. The work explains extensively this procedure and includes detailed discussions of relevant aspects the contribution of infinity frequencies modes to the early time response of the black hole and its relation to the QNM-amplitudes grows rate.

Coffee and tea will be available in the School Common Room afterwards


Title:        Buckling and wrinkling of thin viscous and elastic sheets

Speakers:    Doireann O'Keily (University of Oxford)

Date:        Monday 22nd October 2018

Time:     1pm

Location:    Room 1.25, Science Centre North


Abstract:
Thin structures typically buckle out of plane when compressed, giving rise to a myriad of shapes. These range from classic Euler buckling to honey coiling to microscale wrinkling patterns, and in some cases correspond to failure, but in others may be exploited for applications such as flexible electronics. In this talk I will present two examples of compression-driven out-of-plane deformation in thin sheets. The first is a failure mode in the manufacture of glass sheets, and the second concerns the dynamic wrinkling of thin elastic sheets under confinement. This talk will involve a combination of experimental results and mathematical modelling.


Coffee and tea will be available in the School Common Room afterwards


Title:        Gravitational self-interactions of cosmic string loops

Speakers:    Jeremy Wachter (University of the Basque Country)

Date:        Monday 5th November 2018

Time:     1pm

Location:    Room 1.25, Science Centre North

Abstract:
Gravitational wave signals from cosmic strings are strongly influenced by the presence and character of generic features on string loops known as kinks and cusps. We find analytically the leading-order effect of gravitational self-interactions on strings near kinks and cusps, and discuss how these effects might influence loop evolution. We show the results of numerically evolving particular kinds of loops undergoing self-interactions, and comment on how the gravitational wave spectrum from loops might be affected.

Coffee and tea will be available in the School Common Room afterwards

Title:        Layers, instabilities and relaminarisation in horizontally shearing stratified flows

Speakers:    Dan Lucas (Keele University)

Date:        Monday 1st October 2018

Time:     1pm

Location:    Room 1.25, Science Centre North

Abstract:
In this talk we survey several new results for turbulent flows driven by a shear which is perpendicular to a stable stratification. First we show how in a body forced system layer formation can be associated to a stratified linear instability via nonlinear unstable steady solutions. We also show how mixing processes can be encapsulated by unstable periodic orbits embedded in the turbulence. Next we explore the differences when we instead drive the flow by moving boundaries in a plane Couette flow configuration. Here we find layers confined near the walls which are seemingly disconnected from any linear mechanism. However the layer scale provides insight into the way turbulence is shut-off when stratification becomes very large. Finally we investigate the effect of linear instabilities on the transition to turbulence in this system at very large Reynolds numbers and stratifications.

Coffee and tea will be available in the School Common Room from 12.40pm

 

Title:        Travelling-wave spatially periodic forcing of asymmetric binary mixtures

Speakers:    Lennon O'Naraigh (UCD)

Date:        Monday 8th October 2018

Time:     1pm

Location:    Room 1.25, Science Centre North

Abstract:
We study travelling-wave spatially periodic solutions of a forced Cahn-Hilliard equation. This is a model for phase separation of a binary mixture, subject to external forcing. We look at arbitrary values of the mean mixture concentration, corresponding to asymmetric mixtures (previous studies have only considered the symmetric case). We characterize in depth one particular solution which consists of an oscillation around the mean concentration level, using a range of techniques, both numerical and analytical. We determine the stability of this solution to small-amplitude perturbations. Next, we use methods developed elsewhere in the context of shallow-water waves to uncover a (possibly infinite) family of multiple-spike solutions for the concentration profile, which linear stability analysis demonstrates to be unstable. Throughout the work, we perform thorough parametric studies to outline for which parameter values the different solution types occur.

Coffee and tea will be available in the School Common Room afterwards


Title:        Time Domain Method for the Green Function in Schwarzschild Spacetime

Speakers:        Conor O’Toole (UCD)

Date:        Monday 15th October 2018

Time:     1pm

Location:    Room 1.25, Science Centre North

Abstract:


We discuss a method for modelling stellar-mass bodies inspiralling into massive (10^6 solar masses and up) black holes. This problem has significance for the European Space Agency's LISA mission, the first space-based gravitational wave observatory, planned for launch in 2034. The approach taken is to calculate the Green Function, in particular for an object moving around a Schwarzschild (non-rotating) black hole. This can then be used to calculate the so-called "self-force", orbital evolution and resulting gravitational radiation. By rewriting the wave equation in this background spacetime, we show how this problem can be posed as an initial value problem in effectively flat, 2D spacetime, allowing for a relatively straightforward numerical calculation of the Green's Function. We will outline this algorithm, the necessary initial conditions, and present results of this approach.


Title:        On the convergence of the normal form transformation in discrete wave turbulence theory for the Charney-Hasegawa-Mima (CHM) equation

Speakers:        Shane Walsh (UCD)

Abstract:

A crucial problem in discrete wave turbulence theory concerns extending the validity of the normal form
transformation beyond the weakly nonlinear limit. The main difficulty is that even if the transformation converges in a given domain around the origin, there is no assurance that all orbits starting in the domain will remain there at all times. Therefore a situation could arise whereby the original system exhibits behavior that is not captured by the normal form system evolution, regardless of the order of the transformation.

We demonstrate this for the CHM equation, Galerkin-truncated to 4 Fourier modes. By calculating the
transformation to 7th order (keeping all resonances up to 8-wave), we perform numerical simulations of both the original and mapped equations to find that the problems occur precisely when the initial conditions lead to precession resonance, a finite-amplitude phenomenon characterized by strong energy transfers across Fourier modes [1].

We use the dynamical systems approach to extend this result to complex wave-turbulent regimes in the CHM equation, leading to a working definition of convergence radius for normal transformations in terms of invariant manifolds.


Coffee and tea will be available in the School Common Room afterwards



Title:    An optimization-game theory approach for energy markets and massive entry of renewal energy.        A trade-off between cost and intermittency.

Speaker:    Alejandro Jofré (Universidad de Chile)

Date:        Thursday 13th December 2018

Time:     2pm

Location:    Room 1.25, Science Centre North


Second Talk:

Title:    Optimal reconstruction of constitutive relations in complex multiphysics phenomena.

Speakers:    Bartosz Protas (McMaster University)

Date:        Thursday 13th December 2018

Time:     3pm

Location:    Room 1.25, Science Centre North


Note: There will be coffee/tea and biscuits before each talk.

Title:        Layers, instabilities and relaminarisation in horizontally shearing stratified flows

Speakers:    Dan Lucas (Keele University)

Date:        Monday 1st October 2018

Time:     1pm

Location:    Room 1.25, Science Centre North

Abstract:
In this talk we survey several new results for turbulent flows driven by a shear which is perpendicular to a stable stratification. First we show how in a body forced system layer formation can be associated to a stratified linear instability via nonlinear unstable steady solutions. We also show how mixing processes can be encapsulated by unstable periodic orbits embedded in the turbulence. Next we explore the differences when we instead drive the flow by moving boundaries in a plane Couette flow configuration. Here we find layers confined near the walls which are seemingly disconnected from any linear mechanism. However the layer scale provides insight into the way turbulence is shut-off when stratification becomes very large. Finally we investigate the effect of linear instabilities on the transition to turbulence in this system at very large Reynolds numbers and stratifications.

Coffee and tea will be available in the School Common Room from 12.40pm

Title:        Megagravel transport by storm waves


Speakers:    Ronadh Cox (UCD)


Date:        Monday 28th January 2019

Time:     1pm

Location:    Room 1.25, Science Centre North

Abstract:    
Coastal boulder deposits accumulate above high tide, emplaced by high-energy wave events. They include megagravel weighing >600 t close to sea level, 100 t up to about 12 m above high water, and 3 t boulders up to 51 m. How these clasts are transported, and how they are deposited to form imbricated, stacked boulder ridges, remain open questions. Field observations of the process are difficult because transport events are rare and unpredictable (plus they occur during dangerous storms). To complement numerical approaches being implemented by the Dias group here at UCD, we carried out scaled, force-balanced experiments at Queen's University Belfast, where we built a 1:100 model in a laboratory wave tank. The majority of boulder displacements were caused by a small subset of incident waves. Interestingly, the largest waves are not necessarily the most effective: instead, wave-front steepness just before cliff impact seems to determine whether a strong cross-platform flow will develop. The most powerful bores were generated by waves that approached the cliff unbroken, and had a front slope angle in the range 15°-25°. These waves moved very large boulders, with masses in excess of those predicted by existing hydrodynamic equations. This demonstrates that equations often used to analyze coastal boulder deposits in fact do not accurately hind-cast the wave conditions required for megagravel transport.

Coffee and tea will be available in the School Common Room from 12.40pm.

 

Title:        Koopman wavefunctions in classical mechanics and hybrid classical-quantum systems

Speakers:    Cesare Tronci (University of Surrey)

Date:        Wednesday 6th February 2019
            (note different day)

Time:     1pm

Location:    Room 1.25, Science Centre North

Abstract:    
Upon revisiting the Hamiltonian structure of classical wavefunctions in Koopman-von Neumann theory, this talk addresses the long-standing problem of formulating a dynamical theory of classical-quantum coupling. The proposed model not only describes the influence of a classical system onto a quantum one, but also the reverse effect – the quantum backreaction. These interactions are described by a new Hamiltonian wave equation overcoming shortcomings of currently employed models. It is shown that the density matrix of the quantum subsystem is always positive, while no such general conclusion is yet available for the Liouville density of the classical subsystem. The proposed hybrid description is illustrated on the exactly solvable example of a degenerate two-level quantum system coupled to a classical harmonic oscillator.

Coffee and tea will be available in the School Common Room from 12.40pm.

 


Title:        How will climate change affect aircraft flight routes and turbulence?

Speakers:    Paul D. Williams (University of Reading)

Date:        Monday 18th February 2019

Time:     1pm

Location:    Room 1.25, Science Centre North


Abstract:    
The calculation of aircraft flight routes and turbulence is an important area of applied and computational mathematics. Flight-routing through a given wind field is a minimisation problem, and turbulence forecasting relies on methods for diagnosing subgrid-scale turbulence from the large-scale flow. This seminar will discuss how climate change is modifying the results of these calculations. By inducing secular changes in the wind field at aircraft cruising altitudes, climate change is projected to modify flight routes and generate up to three times as much severe turbulence in the coming decades. Come along to find out how climate change will affect your future flights.

Coffee and tea will be available in the School Common Room from 12.40pm.

 
Title:        Air-sea interactions observed with wave-wave scattering processes: are the big waves getting bigger?

Speakers:    Fabrice Ardhuin (IFREMER)

Date:        Tuesday 19th February 2019

Time:     2pm

Location:    Room 1.25, Science Centre North



Coffee and tea will be available in the School Common Room from 1.40pm.

Title:         Dynamics of Quantised Vortices and Electron Bubbles in the Gross-Pitaevskii Model of a Superfluid
Speakers: Alberto Villois (University of Alberto Villois)
Date:         Monday 25th February 2019
Time:         1pm
Location:  Room 1.25, Science Centre North

Abstract:    
In this talk I will focus on the dynamics of quantised vortices in superfluid liquid helium-4 and their interaction with particle impurities, such as electron bubbles. The bubble dynamics are studied in the adiabatic approximation using the Gross-Pitaevskii equation to model the superfluid wavefunction and a Schrödinger equation to model the electron wavefunction. This model allows me to recover the key dynamics of the ion-vortex interactions that arise and the subsequent ion-vortex complexes that can form. The vortex-nucleation limited mobility of the ion is determined and proven to be in reasonable agreement with measured data. Moreover, considering the scenario of an ion trapped in the core of a vortex line, I will investigate how small and large amplitude Kelvin waves and solitary waves affect the drift velocity of the ion. In particular, I will show how Hasimoto soliton-bubble complexes propagating along the vortex can arise.

 

(2nd of two talks)

Title:        Linear potential flow simulation of wave energy converters

Speakers:    Matthieu Ancellin (UCD)

Date:        Monday 4th March 2019

Time:     2pm  -  (note different time)

Location:    Room 1.25, Science Centre North

Title:        Geometric theory of flexible and expandable tubes conveying fluid

Speakers:    Vakhtang Putkaradze (University of Alberta)

Date:        Monday 11th March 2019

Time:     1pm

Location:    Room 1.25, Science Centre North

Abstract:    
We present a theory for the three-dimensional evolution of tubes with expandable walls conveying fluid. Our theory can accommodate arbitrary deformations of the tube, arbitrary elasticity of the walls, and both compressible and incompressible flows inside the tube. We also present the theory of propagation of shock waves in such tubes and derive the conservation laws and Rankine-Hugoniot conditions in arbitrary spatial configuration of the tubes, and compute several examples of particular solutions. The theory is derived from a variational treatment of Cosserat rod theory extended to incorporate expandable walls and moving flow inside the tube. Time permitting, we shall also show how the geometric approach to the problem allows writing the Poisson bracket for the system. The results presented here are useful for biological flows and industrial applications involving high-speed motion of gas in flexible tubes.

Joint work with Francois Gay-Balmaz (ENS/CNRS). Research partially supported by NSERC and the University of Alberta. This talk has also been made possible by the awarding of a James M Flaherty Visiting Professorship from the Ireland Canada University Foundation, with the assistance of the Government of Canada/avec l’appui du gouvernement du Canada.


Coffee and tea will be available in the School Common Room from 12.40pm.



Title:        Characterisation and predictability of weather-dependent power system variables

Speakers:    Hannah Bloomfield and Daniel Drew
            (University of Reading)

Date:        Monday 25th March 2019

Time:     1pm

Location:    Room 1.25, Science Centre North

Abstract:    
We investigate the implications of increasing weather sensitivity on European power systems, in particular the UK. Multi-decadal hourly time series of meteorological re-analysis are used to construct synthetic demand, wind power and solar power data for 28 European countries. Multiple power system scenarios are analysed, informed by National Grid’s Future Energy Scenarios. These models are used to explore a range of events which may cause stress to the power system and the associated meteorological conditions. For example: annual peak demand, wind power ramps, periods of high renewables low demand (i.e., low inertia), and inter-annual variability of demand. Furthermore, the predictability of the meteorological events which are of most concern has been investigated for a range of lead times using various Numerical Weather Prediction (NWP) models.

Coffee and tea will be available in the School Common Room from 12.40pm.

Title:          Wave-Vortex interactions in the ocean

Speakers: Jim Thomas (Woods Hole Oceanographic Institute)

Date         Tuesday 26th March 2019

Time:         2pm

Location:   Room 1.25, Science Centre North

Abstract: Fluid flow in the ocean is strongly influenced by rotation of the planet and density stratification. Consequently, the flow consists of an intertwined mixture of fast propagating waves and slow evolving vortices or eddies. State-of-the-art numerical models are still far from resolving the wide range of spatio-temporal scales that constitute the flow. This calls for the derivation and implementation of simple, reduced mathematical models that can capture important dynamic features of the flow at various scales, while being numerically inexpensive and efficient. In this talk I will present a set of reduced models that capture important features of oceanic waves, vortices, and the nonlinear dynamics resulting from their interactions.


Title:            Some investigations on equatorial ocean dynamics

Speakers:    Biswajit Basu             (Woods Hole Oceanographic Institute)

Date:           Monday 1st April 2019

Time:            1pm

Location:      Room 1.25, Science Centre North


Abstract:  

 
This talk focuses on some investigations into a recently developed non-linear, three dimensional equatorial model for ocean dynamics. The development of the model had been motivated by observations and the model is able to capture some essential properties of the flow in the equatorial region, specifically in the Pacific. Analysis of velocity field and flow paths indicate that several known and unknown features (which are essentially non-linear and three dimensional such as upwelling/downwelling, cellular flow structures, divergence of flow from the equator and extra-equatorial flows, subsurface ocean 'bridge' in the equatorial direction and sharp change in gradient of the flow path) exist and can be simulated by the model.

Coffee and tea will be available in the School Common Room from 12.40pm.


Speaker: Alejandro Orfila (Spanish National Research Council and the University of the Balearic Islands)

Time: Thursday, 4th April 2019 at 2pm

Location: H2.32, UCD O'Brien Centre for Science (Hub)

Title: Effect of small scale transport processes on phytoplankton distribution in coastal seas

Abstract:

Coastal ocean ecosystems are major contributors to the global biogeochemical cycles and biological productivity. Physical factors induced by the turbulent flow play a crucial role in regulating marine ecosystems. However, while large-scale open-ocean dynamics is well described by geostrophy, the role of multiscale transport processes in coastal regions is still poorly understood due to the lack of continuous high-resolution observations. Here, the influence of small-scale dynamics (O(3.5–25) km, i.e. spanning upper submesoscale and mesoscale processes) on surface phytoplankton derived from satellite chlorophyll-a (Chl-a) is studied using Lagrangian metrics computed from High-Frequency Radar currents. The combination of complementary Lagrangian diagnostics, including the Lagrangian divergence along fluid trajectories, provides an improved description of the 3D flow geometry which facilitates the interpretation of two non-exclusive physical mechanisms affecting phytoplankton dynamics and patchiness.

Seminar 2

 

Title: Extreme waves and climatic patterns of variability in North Atlantic Ocean and Mediterranean Sea

Abstract:

The spatial and temporal variability of extreme wave climate in the North Atlantic Ocean and the Mediterranean Sea is assessed using 3-hour output of wave model during a period of 31 years (1979-2009). The seasonality accounts for a 50% of the extreme wave height in the North Atlantic Ocean and for a 85\% in the Mediterranean Sea. Once removed the seasonality, the North Atlantic Oscillation and the Scandinavian Index mainly control the interannual variability of extreme waves during winters. To a lesser extent, the East Atlantic Oscillation also modulates extreme waves in some areas. In the Mediterranean Sea, the dominant modes regarding extreme waves, correspond to the East Atlantic and East Atlantic/Western Russia modes both in their negative phases.


Title:            Does geometric optics depend on geometry?

Speakers:    Abraham Harte (DCU)

Date:           Monday 8th April 2019

Time:           1pm

Location:       Room 1.25, Science Centre North


Abstract:    
An immediate answer to the question in the title might be that of course geometric optics depends on geometry; it's right there in the name! However, the point of this talk will be to explain that while geometric optics does depend on geometry, it does so only slightly. This can be important because certain astronomical observations attempt to infer the geometry of spacetime (and its matter content) using the properties of electromagnetic or gravitational waves which pass through it. Doing so naturally leads to the question of whether or not such inferences are unique: If a particular field is known to be compatible with a particular background metric, is it compatible with other metrics as well? I will explain that in fact, the number of possibilities is enormous. This is particularly true in the geometric optics approximation, where, for many observables, the class of allowed metrics involves seven free functions. Some of these functions may be identified with conformal and Kerr-Schild transformations, but there is much more besides. Going beyond geometric optics can provide a somewhat more discerning picture of the underlying geometry, but some observables remain invariant with respect to large classes of metric transformations.

Coffee and tea will be available in the School Common Room from 12.40pm.