Professor Ruslan Davidchack

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

Molecular simulation: 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: Analog representation of a measurement process;

Implementation of nonlinear filters for continuous measurement processes.

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

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