Professor Ruslan Davidchack

As an undergraduate, I studied theoretical physics at the Ivan Franko National University of Lviv, Ukraine. I completed my PhD in Computational Statistical Mechanics in 1998 at the University of Kansas, USA. I joined the University of Leicester in September 2000 as a Lecturer and became Professor of Computational Modelling and Simulation in 2013.  In 2013-2016 I was Head of Mathematics Department and currently I am the Deputy Head in the School of Computing and Mathematical Sciences.

My research interests are in developing computational methods and tools for applications in molecular simulations, nonlinear dynamics, and signal processing:

Molecular simulations: Structural and dynamic properties of solid-liquid interfaces; calculating free energy of solid-liquid interfaces; estimating thermodynamic errors of numerical integrators for molecular dynamics.

Nonlinear dynamics: Methods for locating unstable periodic orbits in chaotic dynamical systems; symbolic dynamics generating partitions and homoclinic tangencies in non-hyperbolic chaotic systems; transition to chaos with multiple positive Lyapunov exponents (sometimes called "hyper-chaos"); chaotic transitions in semiconductor lasers subject to delayed optical feedback.

Measurements and data processing: Analogue representation of a measurement process; Implementation of nonlinear filters for continuous measurement processes; physical-layer wireless communications.

Selected Publications

1. N Di Pasquale, RL Davidchack, Shuttleworth equation: A molecular simulations perspective, Journal of Chemical Physics 153 (15), 154705 (2020).
2. RL Davidchack, BB Laird, Surface free energy of a hard-sphere fluid at curved walls: Deviations from morphometric thermodynamics, Journal of Chemical Physics 149 (17), 174706 (2018).
3. NB Budanur, P Cvitanović, RL Davidchack, E Siminos, Reduction of SO(2) symmetry for spatially extended dynamical systems, Physical Review Letters 114 (8), 084102 (2015).
4. P Cvitanovic, RL Davidchack, E Siminos, On the state space geometry of the Kuramoto-Sivashinsky flow in a periodic domain, SIAM Journal on Applied Dynamical Systems 9 (1), 1-33. (2010).
5. RL Davidchack, R Handel, MV Tretyakov, Langevin thermostat for rigid body dynamics, Journal of Chemical Physics 130 (23), 234101 (2009).
6. L Ding, RL Davidchack, J Pan, A molecular dynamics study of sintering between nanoparticles, Computational Materials Science 45 (2), 247-256 (2009).
7. RL Davidchack, BB Laird, Crystal structure and interaction dependence of the crystal-melt interfacial free energy, Physical Review Letters 94 (8), 086102 (2005).
8. AV Nikitin, RL Davidchack, Signal analysis through analog representation, Proceedings of the Royal Society of London. Series A 459 (2033), 1171-1192 (2003).
9. RL Davidchack, BB Laird, Direct calculation of the hard-sphere crystal/melt interfacial free energy, Physical Review Letters 85 (22), 4751 (2000).
10. RL Davidchack, YC Lai, Efficient algorithm for detecting unstable periodic orbits in chaotic systems, Physical Review E 60 (5), 6172. (1999).

I'm happy to supervise PhD students on a wide range of topics within my areas of expertise.

Current teaching:

MA2252 Introduction to Computing

MA3012 Scientific Computing

Past teaching:

MA1011 Methods of Applied Mathematics

MA1251 Chaos and Fractals

MA2081 Vector Calculus and Fluid Dynamics

MA3511 Communicating Mathematics

MA4041 Methods of Molecular Simulation

Computational modelling; molecular simulations; dynamical systems

Associate Editor for Communications in Nonlinear Science and Numerical Simulation, Elsevier.

On Maths and Music

Mathematics… It’s not just about numbers, it’s not just about intellectual challenge, it’s not just about usefulness.  It is so much more!  It is beauty, it is passion, it is raw emotions expressed in the clearest of forms, it is the highest form of intellectual art known to mankind!

All mathematicians feel this, know this, they are driven by this.  Unfortunately, we are not very good at communicating this to the rest of the world.  We try to tell the rest of the world what the rest of the world can understand.  The world understands economics - we explain Mathematics in terms of how useful it is for the economy.  The world understands and appreciates technology - we try to come up with mathematical techniques which are useful for solving technological problems.

But all these explanations give extremely limited, narrow, truncated (dare I say ‘castrated’?) view of Mathematics. This view is devoid of passion, of fire burning in the hearts and minds of mathematicians.  We need to find another language to communicate this to the rest of the world…

So, here’s an attempt, based on my belief that the rest of the world has an appreciation for the beauty and passion of music.

Mathematics is like a piano.  Pure Maths: white keys, Applied Maths: black. Each key is a specific area of Mathematics (algebra, geometry, …) .   If we understand this, we will understand that, first and foremost, there is no division in Mathematics into Pure an Applied.  If you only play white, or only black notes, you will get deficient music.  All notes are needed, both pure and applied, to create beautiful music!  If anyone tries to ‘specialise’ Mathematics, by only retaining ‘useful’ bits, they are putting a straightjacket on it. It will not be able to function as intended and, ultimately, it will not be able to deliver even the ‘useful’ things.

Mathematicians are like composers.  Most of us, mortal mathematicians, only know how to make music using a few notes.  Some are better at playing white notes, some black. Only the top mathematical geniuses are able to use all the notes.  Gauss, Euler, Poincare… Were they pure or applied mathematicians?...

Every theorem is like a musical piece.  Mathematicians can also play the piano. We can play music created by other composers – we can understand and appreciate their score.

But Mathematics is not just an ordinary piano.  It is a magical piano!  The best of the mathematicians don’t just compose music from the known notes.  They create new notes!  New fields of Mathematics – white notes.  New applications of existing fields – black notes.  The piano becomes bigger and bigger, it allows us to play more and more sophisticated tunes.

Also, unlike composers, mathematicians can create music together!  Individually, we (mortal mathematicians) might not be skilful and creative enough to use all the notes, but together we can create musical pieces which draw on many notes and are very beautiful!  If we are separated, ‘specialised’, we cannot create beautiful pieces of music and, ultimately, cannot be ‘useful’ to the rest of the world!

In June we had Jacob Lurie visiting Leicester and giving a talk as part of his LMS Hardy’s tour.  Wow!!!  That was a virtuoso performance!  What a plethora of notes!  What exquisite sound!  It was like listening to Chopin, Liszt, Rachmaninoff!   Mathematicians in the audience could ‘hear’ it.  Their eyes were aglow, maybe even tearful.  It was raw passion!

How can we communicate our passion for Maths to the rest of the world?  Well, I’ve given it a try…

Ruslan Davidchack                                                                                                                                   29/09/2016