Champs Roaming Workshop. 1st + 2nd October 2022

Professor Stephen Wiggins organised the Champs Roaming Workshop. This was a long awaited workshop, which was originally planned to take place in early 2020 but had to be cancelled due to Covid. The rescheduled event took place at Michigan State University (MSU), a hybrid event with some in person and some attending online making it very accessible and also meaning several speakers were still able to participate despite not being able to travel. Professor Wiggins reported it was a really great meeting, lots of good discussions and that the topic of Roaming is currently incredibly popular. Whilst it was a small workshop, it was worth taking place and was some excellent outcomes and really positive for all involved after the disappointment of being cancelled in 2020.


Workshop on “Exact factorization, Geometric Phase and Bohmian mechanics“ 19th + 20th September 2022

Exact factorization, Geometric Phase and Bohmian mechanics

Dmitry Shalashilin Champs Co-Investigator based at Leeds University led the Champs workshop held at Engineers House. The event was a great success, bringing together lots of exciting speakers and was well attended. It took place on 19th + 20th September 2022, a two day workshop with workshop dinner held after the 1st night.

Roman Shubert, Bristol based Champs Co-Investigator reported there was lots of interesting ideas discussed and that it was a worthwhile event commenting that there was a good ratio of Students, Post Docs and Speakers who attended.

Mini symposium at BMC-BAMC 2021 – Vladimir Krajnak, Shibabrat Naik.

BMC-BAMC Glasgow 2021

We organized a mini-symposium on the theme of “Integrating dynamical systems with data driven methods” (MS09). The invited speakers presented theory and applications of data driven methods in fluid mechanics and chemical reactions. The mini-symposium had the following four talks. The program for Day 1 along with the scheduled talks is available here


Peter Ashwin (Exeter)

Plant ER networks and the dynamics of anchored 2D foams subject to viscous flow

The Endoplasmic Reticulum in plant cells can form a variety of rapidly changing structures including networks of filaments that are anchored to the cell membrane at various points. We discuss progress in biophysical modelling of the interaction of these geometric networks with other processes in play within the cell, in particular actin-driven cross-connections and viscous flow associated with cytoplasmic streaming. We show these processes can maintain an anchored 2D foam of filaments and, maybe more surprisingly the foam retains memory of past streaming speed and direction. (Joint work with Congping Lin, Wuhan).

Stefan Klus (Surrey)

Kernel methods for detecting coherent structures

Over the last years, numerical methods for the analysis of large data sets have gained a lot of attention. Recently, different purely data-driven methods have been proposed which enable the user to extract relevant information about the global behavior of the underlying dynamical system, to identify low-order dynamics, and to compute finite-dimensional approximations of transfer operators associated with the system. However, due to the curse of dimensionality, analyzing high-dimensional systems is often infeasible using conventional methods since the amount of memory required to compute and store the results grows exponentially with the size of the system. We extend transfer operator theory to reproducing kernel Hilbert spaces and show that these operators are related to Hilbert space representations of conditional distributions, known as conditional mean embeddings in the machine learning community. One main benefit of the presented kernel-based approaches is that these methods can be applied to any domain where a similarity measure given by a kernel is available. We illustrate the results with the aid of guiding examples and highlight potential applications in molecular dynamics, fluid dynamics, and quantum mechanics.

Kamyar Azizzadenesheli (Purdue)

A Crash Course on Neural Operators

Neural Operators are a new advancement in machine learning, applied mathematics, and science, that allows for efficiently learning operators from infinite-dimensional spaces, e.g. function spaces. In this talk, we cover the basics of Neural Operators, their properties, architectures, computation powers, limitations, and the theory behind them. We concluded the talk with a few empirical study partial differential equations (PDEs) to elaborate on the broad applicability of these methods.

Cecilia Clementi (Freie Universität Berlin)

Designing molecular models by machine learning and experimental data

The last years have seen an immense increase in high-throughput and high-resolution technologies for experimental observation as well as high-performance techniques to simulate molecular systems at a microscopic level, resulting in vast and ever-increasing amounts of high-dimensional data. However, experiments provide only a partial view of macromolecular processes and are limited in their temporal and spatial resolution. On the other hand, atomistic simulations are still not able to sample the conformation space of large complexes, thus leaving significant gaps in our ability to study molecular processes at a biologically relevant scale. We present our efforts to bridge these gaps, by exploiting the available data and using state-of-the-art machine-learning methods to design optimal coarse models for complex macromolecular systems. We show that it is possible to define simplified molecular models to reproduce the essential information contained both in microscopic simulation and experimental measurements.

Congratulations to new Champs PDRA Dr Grace Chuang – 2021 Chemistry National Meeting in Taiwan prize winner.

Congratulations to new Champs PDRA Dr Grace Chuang on being a prize winner at the 2021 Chemistry National Meeting in Taiwan. Grace was part of the physical chemistry group and passed the first and second evaluations to get the certification and a prize of £250.

2021化學年會重要時程 研究論文獎(研究生學位論文,大專生專題論文獎)稿截止日:2021 年 01 月 04 日當晚12點前為上傳最後期限Important Dates Online application dea 2021化學年會 2021化學年會 化學年會 2021中國化學年會 2021年化學年會 中央大學化學系 中國化學年會 化學 年會 化學年會地點 化學年會報名 化學年會投稿 …

Nonadiabatic Excited-State Molecular Dynamics Methodologies: Comparison and Convergence – A perspective article published by JPC Letters

A perspective article has been published by JPC Letters which reports implementation of the AIMC method in the Los Alamos NEXMD software used for simulation of energy transfer in organic molecules excited by light. The work was done by an international group of scientists from US, Argentina and UK but the method was originally developed by Dmitry Makhov and Dmitry Shalashilin at the University of Leeds, and was supported largely by the CHAMPS project.  The method is based on the idea of using phase space in quantum mechanics  and the role  of CHAMPS  was invaluable.

The paper also made it onto the journal cover:

Champs Project – Summer Students 2020

The Champs team have had a very successful summer with a number of students working closely with the Champs PI and several PDRAs on projects.

Below is a list of names of those who worked on the project over the summer and the titles of their project, a few of which have written papers.

Prof. Stephen Wiggins

Student name – Cate Mandell

Title of Project  – “The Role of Time Dependent Phase Space Structures on Reaction Dynamics and the No-Recrossing Property of Dividing Surfaces”

She wrote a paper on her research that has been accepted in the “International Journal of Bifurcation and Chaos”.

Student name – Zara Graham-Jones and Michael Turner, they worked together on the following project

Title of Project  – “Lagrangian Descriptors and Bohmian Mechanics” they have written a paper on their project

Dr Shibabrat Naik + Prof. Stephen Wiggins co-advised the following students and their respective topics:

Computation and visualization of phase space structures relevant for chemical reaction dynamics

Student name: Sam Spedding

Title: Two Degree of Freedom Hamiltonian Systems in Chemical Reaction Dynamics – A Phase Space Analysis

Student name: Bing En Gan

Title: Computation and visualization of phase space structures in Reaction Dynamics

Student name: Piero Sarti (LMS summer research award)

Title: Visualizing the 2-Well and 3-Well Deleon-Berne Hamiltonian

Student name: Annie Hu

Title: Poincaré sections, gap times, and directional flux in De Leon-Berne Hamiltonian 

Student name: Wenyang Lyu

Title: Classical-quantum correspondence in the saddle-node Hamiltonian

Published paper based on work over winter and spring term:

There are manuscripts in preparation based on the individual summer project reports.

Dr. Vladimir Krajnak

Student name – Mark Pearson

Title of Project – Phase space structures in the ‘Helium atom’

Dr Francisco Gonzalez Montoya

Student name –  Charlotte Quant

Title of Project  –  The Quantum Inverted Oscillator

Name – Edward Sharp

Title of Project  –  The Tunnel Effect and the Anderson Localization

Dr Makrina Agaoglou + Dr Matthaios Katsanikas

Student name – Yibin Geng.

Title of Project  –  “The dynamical matching as a bifurcation effect in caldera potential energy surfaces”

Student name – Rebecca Crossley

Title of Project  –  “From Poincare Maps to Lagrangian Descriptors: The case of the VRI potential”

Student name – Douglas Haigh

Title of Project  –  “The time evolution of the selectivity in a symmetric potential energy surface with a post-transition-state bifurcation”

The plan is to submit their drafts in scientific journals in the near future. Some of the titles might change for the submission.

3D printed Ozone PES – Role of 3D printing technology in dynamical systems applications

Role of 3D printing technology in dynamical systems applications

Shibabrat Naik, Stephen Wiggins

Understanding chemical reactions using dynamical systems theory is based on using the geometric view of the structures underlying the solutions of the equations of motion. The equations are derived from the potential energy due to the molecular configurations involved in the reaction. In both of these aspects, that is the geometry of the potential energy surfaces and the phase space structures, visualization in the real space of the physical world using 3D printing facility is increasing the educational and hands-on learning experience. In our research project supported by CHAMPS (EPSRC Grant No. EP/P021123/1) we used the 3D-printing facility in the School of Mathematics for prototyping a potential energy surface in the dissociation of ozone available in the literature ( This potential energy function at constant total energy is an 3D volume specified by a function obtained from fitting electronic energies and can be used in dynamical systems analysis of the dissociation.

The image on the left shows the generated prototype using the 3D printer and on the right is the image in the virtual space generated using the Sketchfab Labs ( The hands-on experience of a 3D prototype makes the geometric methods used in phase space perspective of chemical reaction dynamics accessible to a wider audience. In addition, we are planning to use the 3D printing facility to build some of the many mathematical objects called phase space structures that come out of dynamical systems analysis of chemical reactions. This will be useful for educational and conference presentation purposes.

CHAMPS – Jupyter Book, “Lagrangian Descriptors: Discovery and Quantification of Phase Space Structure and Transport”

The CHAMPS (Chemistry and Mathematics in Phase Space) research group is pleased to announce the availability of our latest Jupyter Book, “Lagrangian Descriptors: Discovery and Quantification of Phase Space Structure and Transport” available at This book is a companion to our recent Jupyter Book, Chemical Reactions: A Journey into Phase Space, available at
Our new Jupyter book contains substantial “computable content” in the form of Jupyter notebooks for computing the Lagrangian descriptors for a variety of dynamical systems.
We view both of our Jupyter books as community resources and we invite all those interested to participate in their further development through GitHub.

LD book sprint group photo
CHAMPS Project maths cohort L-R: Makrina Agaoglou, Francisco González-Montoya, Broncio Aguilar-Sanjuan, Vladimír Krajňák, Shibabrat Naik, Víctor José García Garrido, Matthaios Katsanikas, Stephen Wiggins.