Applied and Computational Mathematics Seminars 2017/18

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Time: 10:00 -- 11:00

Title: CMM Center for Mathematical Modeling

Speaker: Prof. Alejandro Jofré (Director, CMM, U. de Chile)

Venue: JK Lab (room 125 Science Centre North)

In this talk I describe CMM's activities on fundamental research and applications to four main topics: Mining, optimal allocation of natural resources, BioMathematics, Bigdata in Astronomy, Marketing and mining.



Time: 14:00 -- 15:00

Title: Optimization and Energy

Speaker: Prof. Alejandro Jofré (Director, CMM, U. de Chile)

Venue: ALE 232 (room EP232 Science Centre North)


In this talk we introduce an optimization/game-theory model to describe an energy-producer market working on a network (transmission). We characterize a Nash equilibrium and pricing rules in this stochastic setting, as well as some stability properties.

Title:    Vortex and mass dynamics over surfaces, Maxwell laws & the axioms of mechanics

Speaker:         Stefanella Boatto
Universidade Federal do Rio de Janeiro (Brazil)
& INRIA-CetraleSupélec (France)

Date:        Wednesday, 11th October 2017

Time:        3pm

Location:     Room 1.25, O'Brien Centre for Science (North)

In the basic courses of mechanics a first approach to the central forces and, in particular, to the gravitational force, is made through Newton's laws and the expression of the Newtonian gravitational force

F=G m1 m2 / r^2.
It is well to remember that the 1 / r^2 dependence on the expression of force is a due contribution to Hooke's experiences in (see, among others, Arnold's book "Huygens and Barrow, Newton and Hooke"). In this approach the gravitational potential U(r) (F(x)=-\nabla_x U) is derived from the knowledge of the force.

How to find the expression of gravitational force when studying the mass dynamics in other geometries? For example on surfaces?

We have the problem of not being able to perform two-dimensional experiments to measure the force between two bodies and therefore we must find the answer to the following:

How to define a central force in an arbitrary geometry?
Given the distribution of matter on a given surface what is the fundamental equation for deducing the corresponding gravitational potential?
We propose a formulation of the dynamics directly in the intrinsic geometry of the surface and that uses fundamental solutions of the equation of the gravitational field. We show how the equations of gravitational dynamics are closely linked to those of electric charges and to the dynamics of point vortices.

Furthermore, we shall show how known laws, such as Kepler's laws and some mechanics axioms (Newton's Laws), may depend on the geometry of the space, i.e. they are not universal properties.

In collaboration with David Dritschel (Univ. of St-Andrews, Scotland), Rodrigo Schaefer (IM, UFRJ/UPC, Barcelone, Catalunya, Spain).


Title: Assimilating Four Decades of Observations

Speaker:   Eoin Whelan (Met Éireann)

Date:  Thursday 19th October 2017

Time:  12pm

Location:  Room 1.25, O'Brien Centre for Science (North)


Reanalysis is a technique used to reconstruct past climate using a state of the art Numerical Weather Prediction system.

Met Éireann has recently completed a high-resolution reanalysis of Ireland's climate, called MÉRA. This reanalysis assimilated in-situ observations over the period 1981-2015 using three-dimensional variational data assimilation  (3D-Var).

An overview of 3D-Var and validation results from MÉRA are presented.

Title:        Modeling Natural Hazards – Requirements and Selected Approaches

Speaker:     Jörn Behrens (Universität Hamburg)

Date:        Wednesday, 25th October 2017

Time:        3pm

Location:     Room 1.25, O'Brien Centre for Science (North)

Several extreme natural disasters in recent years - to mention the 2004 Sumatra-Andaman and 2011 Tohoku Tsunami events, 2005 Hurricane Katrina, 2013 Taifun Haiyan, 2010 Eyjafjallajökull Volcano eruption - reminded the world of the vulnerability of modern societies and highly populated areas. In order to save life and property, early warning and preparedness is essential, which in turn requires fast and accurate simulation results for forecasting and scenario simulations. This presentation discusses requirements in such operations from a mathematical and computational point of view. One major concern is the multi-scale character of many such problem settings. Solution approaches to the requirements of multi-scale representation, accuracy, efficiency and visualization are presented. We try to extract overarching computational strategies for disaster mitigation.

Title:    Overview of the Marine Institute's Ocean Modelling Activities

Speaker:         Tomasz Dabrowski (Marine Institute)

Date:        Wednesday, 1st November 2017

Time:        3pm

Location:     Room 1.25, O'Brien Centre for Science (North)

Operational hydrodynamic models are run daily in an operational automated system at the Marine Institute to produce both hindcasts and forecasts to build up a database of modelled data to support marine research. The operational modelling suite at the MI is based on the open-source community driven Regional Ocean Modelling System (ROMS) for ocean physics and Simulating WAves Nearshore (SWAN) and use operationally available atmospheric and open ocean boundary forcing data. The Marine Institute are also responsible for the biogeochemical modelling service within the framework of the Copernicus Marine Environment Monitoring Service. The biogeochemical model used is PISCES. Downstream modelling services include the areas of aquaculture, fisheries, oil spill modelling, search and rescue, storm surges and climate studies. The presentation will outline the set-up of the models and an will provide an overview of the downstream services.

Title:    Models of large boulder generation and transport by waves.

Speaker:     James Herterich (UCD)

Date:    Wednesday, 15th November 2017

Time:        3pm

Location:        Room 1.25, O'Brien Centre for Science (North)

Coastal boulder deposits consist of megagravel, with 100+ tonne blocks close to sea level, as well as boulders of many 10s of tonnes mass emplaced at elevations 10s of metres above high water and up to 250m inland. The largest boulders can be moved by several metres during storm events. Understanding the mechanisms of boulder generation and transport gives a unique insight to the powerful events that occur along high-energy coastlines.

We present a model of boulder generation via a hydraulic press-like action on exposed beams on platforms. The stress generated in the rock can propagate cracks to full fracture. Hydrodynamics, mechanics, and fracture models are discussed in relation to the problem, alongside field evidence.

The subsequent transport of large boulders by overtopping waves and surges has been actively modelled for the last 20+ years. We discuss some fundamentals in the models, and show improvements in determining the forces involved in a number of situations. We use complex variable techniques, treating the boulder as an obstacle in the flow.

Title:        Scattering of two spinning black holes in post-Minkowskian gravity.

Speaker:     Justin Vines ,Max-Planck Institute for Gravitational Physics.

Date:        Wednesday, 22nd November 2017

Time:        3pm

Location:     Room 1.25, O'Brien Centre for Science (North)

The advent of gravitational-wave astronomy motivates detailed study of the classical gravitational dynamics of spinning black holes in binary systems.  Analytical calculations to those ends (for arbitrary mass ratios) have traditionally focused on post-Newtonian perturbation theory (expansion in 1/c), naturally paired with an expansion in small spins.  I will discuss a complimentary approach using post-Minkowskian perturbation theory (expansion in G), paired with a nonperturbative treatment of the spins.  New results for two-spinning-black-hole scattering at first post-Minkowskian order (linear order in G), given in simple closed forms to all orders in spin, reveal remarkable relationships between arbitrary-mass-ratio two-body dynamics and test-body dynamics in a fixed background, and between the dynamics of spinning and nonspinning black holes.

Title:    Some recent developments in tsunami observations and theory

Speaker:         Emile Okal (Northwestern University)

Date:        Monday, 4th December 2017

Time:        2pm

Location:     Room 1.25, O'Brien Centre for Science (North)

We present three recent observational and theoretical developments in tsunami science

1.    While it has long been known that tsunamis can be focused and defocused by bathymetric heterogeneities, we consider the case of the sharp refraction expected at a continental shelf, where velocities can vary by as much as a factor of 4 to 5. We confirm that Snell's law is indeed upheld, using both real and simulated time series. This implies that in the presence of a wide continental shelf, distant tsunamis can be considered as impacting the coast at normal incidence.

2.    Motivated by our experience during the 2011 Tohoku tsunami in Tahiti, we explore the conditions under which the leading wave may or may not be that with maximum amplitude. Based on available analytical solutions for simple source models, we find that this "sequencing" of tsunami waves is due to the initiation of dispersion outside the Shallow-Water-Approximation, and as such controlled by a simple combination of distance, effective source size and water depth.

3.    Following the detection of a millimetric tsunami by DART buoys during the 2013 deep Okhotsk earthquake, we explore theoretically the excitation of tsunamis by deep earthquakes. While known events have not produced tsunamis with damaging potential, our lack of knowledge of the maximum size of deep earthquakes leaves open this possibility.

Title:    A regime-based perspective on variability of the Southern Hemisphere mid-latitude jet

Speaker:         Nick Byrne (Reading University)

Date:            Wednesday, 13th December 2017

Time:            3pm

Location:         Room 1.25, O'Brien Centre for Science (North)

Variability of the large-scale mid-latitude Southern Hemisphere circulation is dominated by apparently random wanderings of the mid-latitude jet. These wanderings of the jet have an important influence on a variety of components of the Southern Hemisphere climate system, including the location of synoptic storms and Antarctic sea-ice extent. For example, the unprecedented retreat of Antarctic sea-ice that occurred during the spring of 2016 has been linked to unusual behaviour of the jet and increased synoptic storm activity.
In this talk several lines of evidence will be presented to argue that variations of the Southern Hemisphere mid-latitude jet are more systematic than previously thought. In particular, it will be argued that jet variability during austral spring and summer is closely coupled to the seasonal cycle of the polar vortex in the stratosphere. Based on this connection with the seasonal cycle of the stratospheric circulation, an alternative perspective of tropospheric jet variability will be proposed. This alternative perspective will subsequently be used to re-interpret several previous results in the literature, and also to motivate a partial explanation for the unprecedented Antarctic sea-ice behaviour during spring 2016.


Title: Acoustic-gravity waves, theory & applications

Speaker: Usama Kadri (Cardiff University)

Date: Wednesday, 24 January, 2018

Time: 3pm

Location: SCN 1.25, O'Brien Centre for Science (North)


Acoustic–gravity waves (AGWs) are compression-type waves generated as a response to a sudden change in the water pressure, e.g. due to nonlinear interaction of surface waves, submarine earthquakes, landslides, falling meteorites and objects impacting the sea surface.

AGWs can travel at near the speed of sound in water (ca. 1500 m/s), but can also penetrate through the sea-floor surface amplifying their speed, which turns them into excellent precursors. “Acoustic–gravity waves” is an emerging field that is rapidly gaining popularity among the scientific community, as it finds broad utility in physical oceanography, marine biology, geophysics, water engineering, and quantum analogues.

This talk is an overview on AGWs, with emphasis on recent developments, current challenges, and future directions.

 Title:    From the wave spectrum to power output: statistical aspects and efficient computational tools

Speaker:      Alexis Merigaud (Maynooth)

Date:        Wednesday, 31st January 2018

Time:         3pm

Location:        Room 1.25 O’Brien Centre for Science North


This presentation will consist of two short parts:

1)    Most of the time in the power production regime of wave energy converters (WECs), the wave elevation can be described as a stationary, homogeneous Gaussian random field, if the temporal and spatial areas considered are "small enough" (~30 min, 1-2 km). In the light of the theory of discrete-time stochastic processes, we briefly discuss possible statistical representations of the wave elevation, when sampled at regular time intervals through a measurement system. We find that auto-regressive processes or the (more general) class of regular processes are two appropriate and useful descriptions. We then show how those two characterisations lead to short-term wave elevation prediction techniques.

2)    Computationally-efficient simulation methods are useful for WEC optimisation or power assessment. Relying on a projection of the system variables and equations onto a Fourier basis, the harmonic balance (HB) method can be used to compute the steady-state response of a non-linear system subject to a periodic input signal. Applications of the technique to non-linear WEC simulation in irregular waves are shown.

Three short (~12 min.) presentations by the PhD students in the Weather, Climate and Energy research group.

Date:          Wednesday 14th February 2018

Time:           3pm

Location:        Room 1.25, Science Centre North

Talk 1

Title: Shortwave Radiation in Reanalyses: Skill Scores and Spatial Patterns.

by: Eadaoin Doddy

I will present work done to assess the accuracy of different reanalyses for daily shortwave radiation (SW) values across Ireland. The high-resolution regional reanalysis, MÉRA and two low-resolution global reanalyses; ERA-Interim and MERRA2 are compared to observations for up to 30 years. Post-processing methods are explored with a view to providing an improved dataset for the renewable energy community in Ireland. The spatial pattern of SW is also assessed for the three reanalysis datasets. Daily SW varies in an east-west direction which is highlighted by the land-sea contrast. MÉRA does well in capturing this spatial pattern. ERA-Interim also captures this pattern, however it is less pronounced in MERRA2. Satellite data will be used to explore reasons for this SW spatial pattern. I will end with a discussion of future work involving adaptive spatial multivariate post-processing for the renewable energy sector in Ireland.

Talk 2

Title: Wind-Solar Correlations in Reanalysis Datasets

by: Seánie Griffin

Combining wind and solar power production has the potential to reduce the overall variability of renewable energy generation. Skill scores for 10m wind speed are assessed for MÉRA, the high-resolution reanalysis produced by Met Éireann, and also two coarse resolution global reanalyses: ERA-Interim and MERRA2. Wind-solar correlations are compared to those calculated using observed data from stations around Ireland, across different timescales. Reanalysis datasets are found to frequently overestimate the strength of the negative correlation between wind speed and shortwave radiation. Correlations are also seen to vary with wind direction. Finally an overview will be given of future work to improve the skill of Numerical Weather Prediction models for renewable energy forecasting.

Talk 3

Title: Large scale atmospheric pressure patterns and wind and solar season to season variability – a case study for Ireland and the UK

by: Joao Monteiro Correia

In Ireland and the UK, long-term atmospheric variability has been linked previously with large-scale atmospheric patterns such as the North Atlantic Oscillation (NAO), the East Atlantic (EA) and Scandinavian (SCAND) patterns. These patterns, identified from pressure anomalies, influence other meteorological variables relevant to renewable power generation. Further assessments of these influences are required for successful integration of renewable energy technologies in the energy grid. Using various datasets, this work explores the links between the atmospheric patterns referred to above and both wind speed and solar radiation in the region of interest. The main result of my research so far is that winter solar radiation variability is linked strongly to the NAO and SCAND patterns, and that that relationship expresses itself in zonal gradients, across both Ireland and the UK.

Title:    Towards improved phenomenological waveform models
Speaker:         Marta Colleoni (University of the Balearic Islands)

Date:        Wednesday, 28th February 2018

Time:        3pm

Location:     Room 1.25, Science Centre North

In preparation for the new Advanced LIGO Observation Run (O3), the waveform models employed by gravitational wave searches are being refined in order to achieve a better recovery of the parameters of the sources. The so-called Phenom(enological) templates represent a flexible and cost-effective tool to study the signals emitted during compact binary coalescences. I will describe how Phenom models are currently being extended to improve their coverage of the parameter space and increase detection efficiency.

Title:    A Brief History of Gravitational Wave Emission

Speaker:     Daniel Kennefick (University of Arkansas)

Date:    Wednesday, 7th March 2018

Time:    3pm

Location:     Room 1.25, O’Brien Centre for Science (North)

Over a billion years ago gravitational waves from two colliding black holes started on their journey towards Earth.  A century ago Albert Einstein predicted their existence.  Then he changed his mind.  Then he changed his mind again.  Others joined the argument.  Finally, forty years ago evidence that they were real came when a binary neutron star was discovered in our galaxy which was decaying in our orbit in just the fashion Einstein predicted, having emitted gravitational waves 21,000 years ago. Subsequently large detectors were constructed on the Earth, such as LIGO, GEO600 and VIRGO to try to detect gravitational waves.  But so difficult was theoretically modelling what they would look like that twenty years ago recent Nobel laureate Kip Thorne made a wager that theorists would still not have predicted their form before the detectors saw them.  In 2005 a breakthrough was made in supercomputer simulations of binary black holes so that templates were available just in time when the gravitational waves arrived on Earth two years ago after their billion year journey.

Title:    Southern Hemisphere summertime Rossby waves and weather in the Australian region

Speaker:         Laura Cooke (UCD)

Date:            Wednesday, 28th March 2018

Time:            3pm

Location:     Room 1.25, O’Brien Centre for Science (North)

Motivated by recent studies on significant weather patterns in Australia, in this talk I will investigate the life cycle of summertime transient Rossby wave packets in the Southern Hemisphere.

A variable, I, representing the strength of the interaction between wave packets and the jet stream is used as the basis for composites in 5 regions of the Southern Hemisphere. In each case, cyclogenesis precedes a very clear transient Rossby wave packet. While in most cases, waves propagate far downstream, in some they also refract strongly equatorward and are associated with enhanced tropical convection. I will discuss the characteristics of the different wave behaviours and their associated weather patterns.

In addition, I will summarise my new role at UCD and proposed research that I will undertake with Conor Sweeney's group through the Energy Systems Integration partnership Programme (ESIPP).
 Figure caption: DJF seasonal average of I: Advection of potential vorticity by the divergent part of the wind (PVU s−1 ) at 350 K (shaded) with boxed regions (pink) and the 350 K jet isotachs [20, 25, 30, 35] ms−1 (green contours)