## Elliptical Discussions

Posted in Cute Problems, Education, Maynooth, The Universe and Stuff with tags , , on April 7, 2022 by telescoper

It’s the ninth week of Semester 2 and I’m coming to the end of lectures and laboratory sessions for my Computational Physics module; for the remaining three weeks (plus the Easter vacation) the students in this class will be mainly concentrating on the mini-projects that form part of the assessment.

This afternoon, though we had a session on how to transform higher-order differential equations into sets of coupled first-order ODEs suitable for vectorization and consequent solution using standard techniques. The problem we focussed on today was the simple problem of orbital motion of a test particle under the gravitational force in plane-polar coordinates, which can be prepared for physical solution thusly:

This sort of thing reminds me of my undergraduate theory project at Cambridge, where I did a similar thing to solve the equations governing the action of a four-level laser, though that was in Fortran rather than Python. In my own solution I used Python’s off-the-shelf solver `odeint`.

I like the orbital motion problem a lot because it’s a bit more than a coding exercise: students have to think about how to choose initial data, how to test the their code and interpret the results. Even before that there’s the issue of what units to use; SI units are a bit daft for astronomical problems. For solar system calculations it makes sense to use Astronomical Units for distances and years for time; in such a system it’s easy to work out that GM is just 4π2, which avoids having to deal with ridiculously large or ridiculously small numbers.

Anyway, the fun thing about this lab was that once everyone had got their code working they could try setting initial data to get a circular orbit as a special case, explore how the shape of elliptical orbits depends on the input data, how to make an unbound orbit, and so on. It’s important to understand the output of a numerical calculation in terms of basic physical principles. All that led to a discussion in class of solar system exploration, transfer orbits, what would happen if the mass of the Sun suddenly changed, or if G was a function of time, and lots of other things.

I find sessions like this that encourage students to explore problems themselves very rewarding and I think they add a valuable extra dimension to standard teaching formats. I hope the projects that they’ll be doing from now on – involving topics in areas ranging from atomic physics, cosmology, particle physics and climate science, and done in groups – will provoke even more discussion of this type.

## A Day of Computing

Posted in Biographical, Education, Maynooth, The Universe and Stuff with tags , , , , , , on February 3, 2022 by telescoper

Last Semester, Thursday was what I optimistically called a “Research Day” (on the basis that I had no teaching on it). This Semester it’s one of my busiest teaching days, with lecturing in the morning and a lab session in the afternoon, both for Computational Physics.

For most of the last two years I’ve been delivering the lectures and running the lab remotely, but now that we’re back teaching face-to-face I gave the lecture in person and was in the lab with the class for this afternoon’s session. I’ve got about twice as many students this year as last year swill be running two lab sessions (one next Tuesday repeating the material from the Thursday one, and so on throughout the term).

Running the lab remotely worked reasonably well because Python is available to download for free and works on a standard Windows-based PC. In the lab however we use a Linux (Ubuntu) system, which gives the students the chance to try a different operating system (and one which is for many purposes better than Windows).

It’s good to be back running the computing laboratory class in person but I was a bit nervous this morning because since I last did it that way the machines we have in our laboratory have all been upgraded to a new operating system and have a new (and very different) version of Python (3.9 versus the now obsolete 2.7). I’ve been around long enough to realize that things can go wrong in such situations, so I warned the class during this morning’s lecture that there might be teething troubles. Sure enough we had quite a few technical glitches but, to be honest, it it could have been a lot worse. Next Tuesday’s lab should be a bit less stressful as we’ve fixed a few of the things that went wrong.

So, by no means a disaster, but a busy and quite stressful day. Time to go home and relax.

## Ireland’s Covid-19 Models

Posted in Covid-19, mathematics, Maynooth with tags , , , , , on July 1, 2021 by telescoper

Yesterday the Chair of the National Public Health Emergency Team (NPHET), who also happens to be the President of Maynooth University, Professor Philip Nolan published a lengthy but interesting Twitter thread (which you can find unrolled here). In these tweets he explained the reason behind NPHET’s recommendation to pause the process of relaxing Covid-19 restrictions, postponing the next phase which was due to begin on 5th July with indoor dining.

The basic reason for this is obvious. When restrictions were lifted last summer the reproduction number increased to a value in the range 1.4 to 1.6 but the infection rate was then just a handful per day (on July 1st 2020 the number of new cases reported was 6). Now the figures are orders of magnitude higher (yesterday saw 452 new cases). A period of exponential growth starting from such a high base would be catastrophic. It was bad enough last year starting from much lower levels and the Delta variant currently in circulation is more transmissable. Vaccination obviously helps, but only about 40% of the Irish population is fully immunized.

Incidentally the target earlier this year was that 82% of the adult population should have received one jab. We are missing detailed numbers because of the recent ransomware attack on the HSE system, but it is clear that number has been missed by a considerable margin. The correct figure is more like 67%. Moreover, one dose does not provide adequate protection against the Delta variant so we’re really not in a good position this summer. In fact I think there’s a strong possibility that we’ll be starting the 2021/22 academic year in worse shape than we did last year.

In general think the Government’s decision was entirely reasonable, though it obviously didn’t go down well with the hospitality sector and others. What does not seem reasonable to me is the suggestion that restaurants should be open for indoor dining only for people who are fully vaccinated. This would not only be very difficult to police, but also ignores the fact that the vast majority of people serving food in such environments would not be vaccinated and are therefore at high risk.

As things stand, I think it highly unlikely that campuses will be open in September. Rapidly growing pockets of Delta variant have already been seeded in Ireland (and elsewhere in Europe). It seems much more likely to me that September will see us yet again in a hard lockdown with all teaching online.

But the main reason for writing this post is that the thread I mentioned above includes a link to a paper on the arXiv (by Gleeson et al.) that describes the model used to describe the pandemic here in Ireland. Here is the abstract:

We describe the population-based SEIR (susceptible, exposed, infected, removed) model developed by the Irish Epidemiological Modelling Advisory Group (IEMAG), which advises the Irish government on COVID-19 responses. The model assumes a time-varying effective contact rate (equivalently, a time-varying reproduction number) to model the effect of non-pharmaceutical interventions. A crucial technical challenge in applying such models is their accurate calibration to observed data, e.g., to the daily number of confirmed new cases, as the past history of the disease strongly affects predictions of future scenarios. We demonstrate an approach based on inversion of the SEIR equations in conjunction with statistical modelling and spline-fitting of the data, to produce a robust methodology for calibration of a wide class of models of this type.

This model is a more complicated variation of the standard compartment-based models described here. Here’s a schematic of the structure:

This model that makes a number of simplifying assumptions but it does capture the main features of the growth of the pandemic reasonably well.

Coincidentally I set a Computational Physics project this year that involved developing a Python code that does numerical solutions of this model. It’s not physics of course, but the network of equations is similar to what you mind find in physical systems – it’s basically just a set of coupled ODEs- and I thought it would be interesting because it was topical. The main point is that if you study Theoretical Physics you can apply the knowledge and skills you obtain in a huge range of fields and disciplines. Developing the model does of course require domain-specific epidemiological knowledge but the general task of modelling complex time-evolving systems is definitely something physicists should be adept at doing. Transferable skills is the name of the game!

P.S. It came as no surprise to learn that the first author of the modelling paper, Prof. James Gleeson of the University of Limerick, has an MSc in Mathematical Physics.

## Language Lessons

Posted in History, Irish Language, Maynooth with tags , , , , , , , , , , on February 4, 2021 by telescoper

Thursday is Computational Physics Day this term so this morning I delivered the first Panopto lecture of that module and in the afternoon we had our first laboratory session. The students are all at home of course so we had to run the lab with them using their own laptops rather than the dedicated Linux cluster we have in the Department and interacting via Microsoft Teams.  The first lab is very introductory so it was really just me presenting and them following on their machines without too much interaction. The ability to share a screen is actually very useful though and I imagine using it quite a lot to share Spyder. It went fairly well, I think, with all the students getting started out on the business of learning Python.

In between lecturing the morning and running the laboratory session this afternoon I had the chance to study another kind of language. Soon after I first arrived in Maynooth I got an email from Maynooth University about Irish language classes. Feeling a bit ashamed about not having learned Welsh in all my time in Cardiff, I thought I’d sign up for the Beginners class and fill in a Doodle Poll to help the organizers schedule it. Unfortunately, when the result was announced  it was at a time that I couldn’t make owing to teaching, so I couldn’t do it. That  happened a couple of times, in fact. This year however I’ve managed to register at a time I can make, though obviously the sessions are online.

I’m not sure how wise it is for me to try learning a new language during a term as busy as this, but I have to say I enjoyed the first session enormously. It was all very introductory, but I’ve learnt a few things about pronunciation – unsurprisingly the Irish word for pronunciation fuaimniú is unsurprisingly quite difficult to pronounce – and the difference between slender and broad vowels. I also learnt that to construct a verbal noun, instead of putting -ing on the end as you would in English, in Irish you use the word ag in front of the verb.

That’s not to say I had no problems. I’m still not sure I can say  Dia duit (hello) properly. The second “d” is hardly pronounced.

Irish isn’t much like Welsh, which I failed to learn previously.  Although Irish and Welsh are both Celtic languages they are from two distinct groups: the Goidelic group that comprises Irish, Manx and Scottish Gaelic; and the Brythonic group that comprises Welsh, Cornish and Breton. These are sometimes referred to as q-Celtic and p-Celtic, respectively, although not everyone agrees that is a useful categorization. Incidentally, Scottish Gaelic is not the language spoken by the Celtic people who lived in Scotland at the time of the Romans, the Picts, which is lost. Scottish Gaelic is actually descended from Middle Irish. Also incidentally, Breton was taken to Brittany by a mass migration of people from South-West Britain fleeing the Anglo-Saxons which peaked somewhere around 500 AD. I guess that was the first Brexodus.

Welsh and Irish don’t sound at all similar to me, which is not surprising really. It is thought that the Brythonic languages evolved from a language  brought to Britain by people from somewhere in Gaul (probably Northern France), whereas the people whose language led to the Goidelic tongues were probably from somewhere in the Iberia (modern-day Spain or Portugal). The modern versions of Irish and Welsh do contain words borrowed from Latin, French and English so there are similarities there too.

Only a diacritic mark appears in Irish, the síneadh fada (`long accent’), sometimes called the fada for short, which looks the same as the acute accent in, e.g., French. There’s actually one in síneadh if you look hard enough. It just means the vowel is pronounced long (i.e. the first syllable of síneadh is pronounced SHEEN). The word sean (meaning old) is pronounced like “shan” whereas Seán the name is pronounced “Shawn”.

One does find quite a few texts (especially online) where the fada is carelessly omitted, but it really is quite important. For example Cáca is the Irish word for `cake’, while the unaccented Caca means `excrement’…

I took the above text in Irish and English from the front cover of an old examination paper. You can see the accents as well as another feature of Irish which is slightly similar to Welsh, the mysterious lower-case h in front of Éireann. This is a consequence of an initial mutation, in which the initial character of word changes in various situations according to syntax or morphology (i.e. following certain words changing the case of a noun or following certain sounds). This specific case is an an example of h-prothesis (of an initial vowel).

In Welsh, mutations involve the substitution of one character for another. For example, `Wales’ is Cymru but if you cross the border into Wales you may see a sign saying Croeso i Gymru, the `C’ having mutated. The Irish language is a bit friendlier to the learner than Welsh, however, as the mutated character (h in the example above) is inserted in front of the unmutated character. Seeing both the mutated and unmutated character helps a person with limited vocabulary (such as myself) figure out what’s going on.

Mutations of consonants also occur in Irish. These can involve lenition (literally `weakening’, also known as aspiration) or eclipsis (nasalisation). In the case of eclipsis the unmutated consonant is preceded by another denoting the actual sound, e.g. b becomes m in terms of pronunciation, but what is written is mb. On the other hand, lenition is denoted by an following the unmutated consonant. In older forms of Irish the overdot (ponc séimhithe) -another diacritic – was used to denote lenition.

Anyway, I’ve seen Dia duit written Dia dhuit which might explain why the d sounds so weak. We live and learn. If I keep at it long enough I might eventually be able to understand the TG4 commentary on the hurling..

## The Start of Spring Semester

Posted in Biographical, Education, Maynooth with tags , , , , , , , on February 1, 2021 by telescoper

It’s February 1st 2021, which means that today is Imbolc, a Gaelic festival marking the point halfway between the winter solstice and vernal equinox, i.e. it’s a Cross-Quarter Day. To be pedantic, Imbolc is actually the period between this evening and tomorrow evening as in the Celtic calendar days were counted from sunset to sunset.

The first Day of February is also the Feast day of St Brigid of Kildare (c. 451-525), one of Ireland’s patron saints along with Saints Patrick and Colm Cille. One of her miraculous powers was the ability to change water into ale, which perhaps explains her enduring popularity among the Irish.

In Ireland this day is sometimes regarded as the first day of spring, as it is roughly the time when the first spring lambs are born. It corresponds to the Welsh Gŵyl Fair y Canhwyllau and is also known as the `Cross Quarter Day’ or (my favourite) `The Quickening of the Year’. According to legend it is also the day on which jackdaws mate. Given how many of them there are around Maynooth there should be a lot of action today.

Today is, appropriately enough in the light of all this, the start of the Spring Semester of teaching at Maynooth University, the fourth Spring Semester I will have experienced here although this is obviously not like the others in that we’ll be teaching online at least for the first half and probably for the entirety. I was planning to stay at home today but I realised I’d left some things I need in the office on campus so will have to go to collect them. That’s why I’m up early. That and the need to shake myself out of the lockdown torpor that has afflicted me since New Year. It’s time to get my act together, pull my finger out, put my best foot forward, etc.

This Semester I am teaching Engineering Mathematics II, Computational Physics I and Advanced Electromagnetism. The former, what you would probably call a `service course’, covers a mixture of things, mainly Linear Algebra but with some other bits thrown in for fun, such as Laplace transforms. Interestingly I find the Mathematical Physics students do not encounter Laplace Transforms in the first year, but perhaps engineers use them more often than physicists do? I think I’ve written only one paper that made use of a Laplace transform. Anyway, I have to start with this topic as the students need some knowledge of it for some other module they’re taking this semester. I reckon six lectures will be enough to give them what they need. That’s two weeks of lectures, there being three lectures a week for this module.

Once again my teaching timetable for this module is quite nice. I have lectures on Monday, Tuesday and Wednesday and then the students have a choice of tutorial (on either Thursday or Friday). That means I can get through a decent amount of material each week before each tutorial. I don’t do the tutorials, by the way: that’s left to one of our PhD students, who gets paid for doing that and correcting the weekly coursework. There are about 50 students on this module, divided into two courses: Electronic Engineering and Robotics and Intelligent Devices. We don’t have Civil or Mechanical or Chemical Engineering, etc, at Maynooth, in case you were wondering. Lectures will be done as webcasts using Panopto but also recorded for later viewing.

My first Computational Physics lecture, which I will do from home, is on Thursday, after which there is a lab session which we will do via Microsoft Teams. That’s the way we did it after lockdown last year and it worked OK. Students attend one two-hour lab session in addition to the lecture, on either Thursday or Tuesday. The first lecture being on Thursday the first lab session will be Thursday afternoon, with the same material being covered the following Tuesday. Fortunately, Python is free to download and easy to install so it’s quite straightforward to run the labs remotely. Teams has a screen sharing facility so it’s quite easy for myself or my demonstrator to see what is wrong in the same way we would do in a laboratory class.

The Advanced Electromagnetism module is a new one for me but I’m quite looking forward to it. Being a final-year module its content is less prescriptive than others and I’ll be adding a few things that I find interesting. Both lectures for that one are on Wednesdays and again will be given as webcasts with recordings available later.

Today is a particularly busy day because in addition to my first lecture (at 2pm) I have a meeting of Academic Council (3pm via Teams), a Euclid telecon (via Zoom) and a meeting with my PhD student via Teams. I have also been trying to sort out tutors and tutorials for the forthcoming Semester: these don’t start until next week so there’s time, but it has been quite a challenge to get everyone sorted. Fortunately I think that’s now done.

Oh, and another thing. I signed up for Irish language lessons (Beginners Level) and will be having classes once a week from now on.

It’s going to be a very busy term but I reckon being busy is probably going to be a good way to get through the next few months.

## Spring Semester Starts

Posted in Biographical, Education, Maynooth with tags , , , , , , on February 3, 2020 by telescoper

It’s February 3rd 2020, which means that today is two days after Imbolc, a Gaelic festival marking the point halfway between the winter solstice and vernal equinox. The 1st Day of February is also the Feast day of St Brigid of Kildare (c. 451-525), one of Ireland’s patron saints along with Saints Patrick and Colm Cille. One of her miraculous powers was the ability to change water into ale, which perhaps explains her enduring popularity among the Irish.

In Ireland this day is sometimes regarded as the first day of spring, as it is roughly the time when the first spring lambs are born. It corresponds to the Welsh Gŵyl Fair y Canhwyllau and is also known as the `Cross Quarter Day’ or (my favourite) `The Quickening of the Year’.

Today is, appropriately enough in the light of all this, the start of the Spring Semester of teaching at Maynooth University, the third Spring Semester I will have experienced here. The weather has even played along; it has definitely been spring-like. The Campus, whicgh has beenhas been very quiet for the last week or so since the examinations finished, is full of students again.

This Semester, as was the case last year, I am teaching Engineering Mathematics II and Computational Physics I. The former, what you would probably call a `service course’, covers a mixture of things, mainly Linear Algebra but with some other bits thrown in for fun, such as Laplace transforms. Interestingly I find the Mathematical Physics students do not encounter Laplace Transforms in the first year, but perhaps engineers use them more often than physicists do? I think I’ve written only one paper that made use of a Laplace transform. Anyway, I have to start with this topic as the students need some knowledge of it for some other module they’re taking this semester. I reckon six lectures will be enough to give them what they need. That’s two weeks of lectures, there being three lectures a week for this module.

Once again my teaching timetable for this module is quite nice. I have lectures on Monday, Tuesday and Wednesday and then the students have a choice of tutorial (on either Thursday or Friday). That means I can get through a decent amount of material each week before each tutorial. I don’t do the tutorials, by the way: that’s left to one of our PhD students, who gets paid for doing that and correcting the weekly coursework. There are about 50 students on this module, divided into two courses: Electronic Engineering and Robotics and Intelligent Devices. We don’t have Civil or Mechanical or Chemical Engineering, etc at Maynooth, in case you were wondering.

Anyway, my first lecture was this afternoon at 2pm and had a good turnout. It was so sunny outside that we had to close all the blinds. That’s quite an unusual event for a February lecture!

My first Computational Physics lecture is on Thursday, after which it will be back to the Department for some frantic behind-the-scenes activity ahead of the afternoon lab session, which is in a computer room near my office. Students attend one two-hour lab session in addition to the lecture, on either Thursday or Tuesday. The first lecture being on Thursday the first lab session will be Thursday afternoon, with the same material being covered the following Tuesday.

While my teaching duties are the same this year as they were in the corresponding semester last year, there is a significant difference this year in that I am now also Head of Department. Either side of my first lecture I had to attend a meeting of the Faculty Executive for Science & Engineering, a meeting on `Project LEGO’ (which, sadly, did not involve any actual Lego but was instead about the proposed redesign of the University’s website) and a meeting of Academic Council. I have also been trying to sort out tutors and tutorials for the forthcoming Semester: these don’t start until next week so there’s time, but it’s quite a challenge to get everyone sorted out. A few timetable clashes have also come to light. So, in summary, I’m a bit worn out after today and will shortly go home to vegetate.

At least I didn’t have to find time for the regular Monday afternoon Euclid telecon in which I usually participate. There wasn’t one today because the working group of which I am part is actually meeting in person for a few days… in Paris! I couldn’t go because of all the above!

## Marking the End of Term

Posted in Maynooth with tags , , , , , on May 11, 2019 by telescoper

So here we are, then. The term is finally over. Lectures officially finished yesterday, and there’s now another week or so before examinations start (next Friday, 17th May). The examinations for my two modules take place on Tuesday 21st and Wednesday 22nd May, and after that I’ll be busy with marking for a while. In fact, I’ll probably be getting much busier in general pretty soon, but more of that in due course…

Marking doesn’t just mean written examinations. I have been teaching a module on Computational Physics to 3rd Year students here in Maynooth, and 40% of the assessment for that is a mini-project (usually done in groups of two or three). Early on the term, I put up a list of a dozen or so projects and ask them to pick first second and third choices so I can form groups in such a way that most students get to work on a project they like the look of. This year I made up a new set of projects, but I feel a bit sorry for one of them (`Scattering in a Spherical Potential’), which didn’t appear anywhere \at all on any student’s list of preferences. That’s a shame as I thought it was a well-rounded project, with lots of potential. Hopefully it will prove more popular next year…

Anyway, the deadline for projects to be handed in came yesterday so I’ve got a stack of those to mark which, you will realise, why I am indulging in a displacement activity by writing this blog post. My plan is to mark these next week so that they’re done before the written examinations come in.

Before I get on with what I should be doing I’ll just mention another thing that happened yesterday: the President of Ireland (Uachtarán na hÉireann), Michael D. Higgins visited Maynooth University yesterday:

That’s him at the front, on the right, of course. The reason for his visit was to attend a memorial service.

Posted in Biographical, Education, mathematics, Maynooth, Music with tags , , , , on February 3, 2019 by telescoper

It’s 3rd February 2019, which means that today is two days after Imbolc, a Gaelic festival marking the point halfway between the winter solstice and vernal equinox. This either happens 1st or 2nd February, and this year it was former, i.e. last Friday In Ireland this day is sometimes regarded as the first day of spring, as it is roughly the time when the first spring lambs are born. It corresponds to the Welsh Gŵyl Fair y Canhwyllau and is also known as the `Cross Quarter Day’ or (my favourite) `The Quickening of the Year’.

I wrote a post about this time last year, on the day I gave my first ever lecture in Maynooth University, on Computational Physics, in a theatre called Physics Hall. That was on Thursday February 1st 2018. It’s hard to believe that was a full year ago. Time certainly has gone quickly this year.

Owing to the vagaries of the academic calendar we’re a week later getting back to teaching this year than last year so my first Computational Physics lecture won’t be until this Thursday (7th February) at 9am, but sadly it won’t be in Physics Hall, which I rather liked, but in Hall C – a much less atmospheric venue, but one rather closer to my office, which will be handy if I forget anything (which I am prone to do). There are about 25 students taking this module, a few down on last year, which means they should fit comfortably into our computer lab. I’m not surprised they moved the lecture, really. The capacity of Physics Hall is 90, and even last year I only had about 30 students. Still, it did have a piano (which Hall C does not):

Computational Physics doesn’t start until Thursday. Before that I have to start my other module: Engineering Mathematics II. This (what you would probably call a `service course’) covers a mixture of things, mainly Linear Algebra but with some other bits thrown in for fun, such as Laplace transforms. Interestingly I find the Mathematical Physics students do not encounter Laplace Transforms in the first year, but perhaps engineers use them more often than physicists do? I think I’ve written only one paper that made use of a Laplace transform. Anyway, I have to start with this topic as the students need some knowledge of it for some other module they’re taking this semester. I reckon six lectures will be enough to give them what they need. That’s two weeks of lectures, there being three lectures a week for this module.

By coincidence rather than good planning, the timetable for this module is quite nice. I have lectures on Monday, Tuesday and Wednesday and then the students have a choice of tutorial (on either Thursday or Friday). That means I can get through a decent amount of material each week before each tutorial. I don’t do the tutorials, by the way: that’s left to one of our PhD students, who gets paid for doing that and correcting the weekly coursework. There are about 50 students on this module, divided into two courses: Electronic Engineering and Robotics and Intelligent Devices. We don’t have Civil or Mechanical or Chemical Engineering, etc at Maynooth.

Campus has been very quiet for the last week or so. The exam period finished in late January but lectures don’t start until tomorrow morning (Monday 4th February) so there have been few students around. No doubt it will be a different story tomorrow. I’ve done my first week’s notes and compiled my first problem set so I’m more-or-less ready to go. First lecture at 2pm tomorrow in Hall H, which is one of the rooms I taught in last term so at least I know where it is!

## Fun with the Airy Equation

Posted in Education, mathematics with tags , , , , , , on April 12, 2018 by telescoper

Today being a Maynooth Thursday, it has, as usual, has been dominated by computational physics teaching. We’re currently doing methods for solving ordinary differential equations. At the last minute before this afternoon’s lab session I decided to include an exercise that involved solving the following harmless-looking equation: $y'' = xy.$

This is usually known as Airy’s equation and it comes up quite frequently in problems connected with optics. It was first investigated by a former Astronomer Royal George Airy, after whom the function is named; incidentally, he was born in Alnwick (Northumberland, i.e. not the Midlands).

Despite its apparent simplicity, the Airy equation describes some very interesting phenomena. Indeed it is the simplest ODE (that I know of) that has the property that there’s a point at which the behaviour of the solution turns from oscillatory to exponential. Here’s a result of a numerical integration of the equation: obtained using a simple Python script:

(I stopped the integration at $x=5$ as the magnitude of the solution grows very quickly beyond that value for the particular initial conditions chosen).

One of the reasons for including this example (apart from the fact that Airy was a Geordie) is that the students were so surprised by the behaviour of the solution and most of them assumed that there was some problem with the numerical stability of their results. Some integration methods do struggle with such simple equations as the simple harmonic oscillator, but just sometimes weird numerical results are not mere numerical artifacts!

Anyway, my point is not about this particular equation or even about computational physics, but a general pedagogical one: finding interesting results for yourself is much more likely to motivate you to think about what they mean than if they’re just described to you by someone else. I think that goes for numerical experiments in a computer lab just as much as it does for any other kind of practical experiment in a science laboratory.

## Spring comes to Maynooth

Posted in Biographical, Cardiff, Maynooth with tags , , on April 5, 2018 by telescoper

After a good night’s sleep last night I was up early this morning to give my usual Thursday 9am lecture on Computational Physics. It was a bright sunny morning, though there was overnight frost and a distinct chill in the air, as I made my way to Physics Hall. Once there, for the first time this year, I had to close the blinds because the Sun was shining too bright for the projector screen. It has hitherto always been too gloomy outside for this to happen. The picture above (of St Joseph’s Square, on the South Campus) was taken as I left St Patrick’s House after a very nice lunch of roast lamb in Pugin Hall. By this time of day it was pleasantly warm.

Here’s a nice picture of the Library circulated by the Maynooth social media folk earlier today.

Anyway, this mornings’s lecture was an introduction numerical solutions of ordinary differential equations, beginning with Euler’s method applied to initial value problems. Further studies of this topic – which is very important for bidding computational physics – will take up the rest of the lectures as we explore the delights of, e.g. Runge-Kutta codes and boundary value problems. This morning’s lecture was followed this afternoon by a two-hour lab session in which the students had to write their own ODE solver.

Among the advantages (for me) of teaching this module is that I’m actually becoming reasonably competent at Python. At any rate I’ve difficult improved my ability to spot bugs in codes written by other people. In fact, it is traditional for the exam in this module to include a question that involves finding 10 mistakes in a piece of Python code. That’s a fun challenge, the only real problem for me being to write a bit of code with only 10 mistakes in it in the first place…

Talking of exams, the timetables for my two current employers are now out. Computational Physics in Maynooth is on Friday 11th May while Physics of the Early Universe in Cardiff is almost a fortnight later, on Thursday 24th May. The Easter recess is shorter here in Maynooth than in Cardiff, where lectures do not resume until April 16th (assuming the UCU strike does not continue), which is why the exams in Maynooth are earlier. I’m grateful there isn’t a clash. I should have ample time to mark the Maynooth ones before the Cardiff ones are due. After the first week or so of May I won’t have to teach in both institutions, so my somewhat hectic schedule should become a little more relaxed from then onwards.

I mentioned the UCU strike above in passing. The UCU leadership has decided that there will be an online ballot on whether to accept the `offer’ recently made by the management organisation UUK. The ballot will be open until April 13th. If the vote goes against acceptance then Cardiff staff will be back on strike from 16th April, and there will be further industrial action over the examination period. I can’t predict what the result of the ballot will be. Although the UCU leadership is recommending acceptance I don’t know anyone personally who intends to vote for it, but there’s a probably a big selection effect there! There is a distinct possibility that examinations will be badly disrupted not only in Cardiff but all over the UK. It’s a very sad state of affairs but all those on strike (and the majority of students) consider the UUK side to be to blame…