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.