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In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems.
Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle. When difference equations are employed, the theory is called discrete dynamical systems. When the time variable runs over a set that is discrete over some intervals and continuous over other intervals or is any arbitrary time-set such as a Cantor set, one gets dynamic equations on time scales. Some situations may also be modeled by mixed operators, such as differential-difference equations.
Coveney is a Professor of Physical Chemistry, Honorary Professor of Computer Science, and the Director of the Centre for Computational Science (CCS) at University College London (UCL). He is also a Professor of Applied High Performance Computing at University of Amsterdam (UvA), Professor Adjunct in the Medical School at Yale University and Member of Academia Europaea.
The Doctor of Engineering, or Engineering Doctorate, is a degree awarded on the basis of advanced study and a practical project in the engineering and applied science for solving problems in the industry. In the United States, it is a terminal professional doctorate. A DEng/EngD is equivalent to a PhD in engineering, but different in that it has a solid industrial base and an additional taught element. The degree is usually aimed toward working professionals.
Professor John Richard Ockendon FRS is an applied mathematician noted especially for his contribution to fluid dynamics and novel applications of mathematics to real world problems. He is a professor at the University of Oxford and an Emeritus Fellow at St Catherine's College, Oxford, the first director of the Oxford Centre for Collaborative Applied Mathematics (OCCAM) and a former director of the Smith Institute for Industrial Mathematics and System Engineering.
Stephen Ray Wiggins is a Cherokee-American applied mathematician also of British heritage best known for his contributions in nonlinear dynamics, chaos theory and nonlinear phenomena, with applications to Lagrangian aspects of fluid transport and mixing and phase space aspects of theoretical chemistry.
Andrew Joseph Majda was an American mathematician and the Morse Professor of Arts and Sciences at the Courant Institute of Mathematical Sciences of New York University. He was known for his theoretical contributions to partial differential equations as well as his applied contributions to diverse areas including shock waves, combustion, incompressible flow, vortex dynamics, and atmospheric sciences. Majda was listed as an ISI highly cited researcher in mathematics.
Peter Grindrod is a British mathematician.
Sir Martin Hairer is an Austrian-British mathematician working in the field of stochastic analysis, in particular stochastic partial differential equations. He is Professor of Mathematics at EPFL and at Imperial College London. He previously held appointments at the University of Warwick and the Courant Institute of New York University. In 2014 he was awarded the Fields Medal, one of the highest honours a mathematician can achieve. In 2020 he won the 2021 Breakthrough Prize in Mathematics.
Blaine Alexander Price is a Professor of Computing at The Open University in the United Kingdom.
Luke Jerram is a British installation artist. He creates sculptures, large installations, and live arts projects.
The UK Large-Scale Complex IT Systems (LSCITS) Initiative is a research and graduate education programme focusing on the problems of developing large-scale, complex IT systems. The initiative is funded by the EPSRC, with more than ten million pounds of funding awarded between 2006 and 2013.
Gui-Qiang George Chen is a Chinese-born American-British mathematician. Currently, he is Statutory Professor in the Analysis of Partial Differential Equations, Director of the Oxford Centre for Nonlinear Partial Differential Equations, and Director of the EPSRC Centre for Doctoral Training in Partial Differential Equations at the Mathematical Institute, and Professorial Fellow at Keble College, located at the University of Oxford, as well as Life Member of Clare Hall, University of Cambridge.
Timothy Noel Palmer CBE FRS is a mathematical physicist by training. He has spent most of his career working on the dynamics and predictability of weather and climate. Among various research achievements, he pioneered the development of probabilistic ensemble forecasting techniques for weather and climate prediction. These techniques are now standard in operational weather and climate prediction around the world, and are central for reliable decision making for many commercial and humanitarian applications.
David S. Broomhead was a British mathematician specialising in dynamical systems and was professor of applied mathematics at the School of Mathematics, University of Manchester.
Panayotis G. Kevrekidis is a professor in the Department of Mathematics and Statistics at the University of Massachusetts Amherst. Kevrekidis earned his B.Sc. in physics in 1996 from the University of Athens. He obtained his M.S. in 1998 and Ph.D. in 2000 from Rutgers University, the latter under the joint supervision of Joel Lebowitz and Panos G. Georgopoulos. His thesis was entitled “Lattice Dynamics of Solitary Wave Excitations”. He then assumed a post-doctoral position split between the Program in Applied and Computational Mathematics of Princeton University (10/2000–02/2001) and the Theoretical Division and the Center for Nonlinear Studies of Los Alamos National Laboratory (03/2001–08/2001). From 09/2001, he joined the Department of Mathematics and Statistics of the University of Massachusetts Amherst as an assistant professor. He was awarded tenure and promotion to associate professor in 06/2005. As of 09/2010, he is a full professor at the same institution. He is presently the Stanislaw M. Ulam Scholar at the Center for Nonlinear Studies at Los Alamos National Laboratory.
Jonathan Peter Keating is a British mathematician. As of September 2019, he is the Sedleian Professor of Natural Philosophy at the University of Oxford, and from 2012 to 2019 was the Henry Overton Wills Professor of Mathematics at the University of Bristol, where he served as Dean of the Faculty of Science (2009–2013). He has made contributions to applied mathematics and mathematical physics, in particular to quantum chaos, random matrix theory and number theory.
Muthusamy Lakshmanan is an Indian theoretical physicist currently working as Professor of Eminence at the Department of Nonlinear Dynamics of Bharathidasan University. Presently he is the DST-SERB National Science Chair awarded by Science and Engineering Research Board, Department of Science and Technology. He has held several research fellowships which included Raja Rammanna fellowship of Department of Atomic Energy, Alexander von Humboldt fellowship, Japan Society for the Promotion of Science fellowship, Royal Society Nuffield Foundation fellowship, and NASI-Senior Scientist Platinum Jubilee Fellowship. In the year 2021, on August 15, he was conferred with Dr. A. P. J Abdul Kalam Award by the Government of Tamil Nadu.
Darryl Holm is an American applied mathematician, and Professor of Applied Mathematics and Mathematical Physics in the Department of Mathematics at Imperial College London. He studied Physics at the University of Minnesota (1963-1967), and Physics and Mathematics at the University of Michigan (1967-1971). He joined the Theoretical Design Division of Los Alamos National Laboratory (LANL) in 1972 where he worked on the physics of strong shock waves and high-temperature hydrodynamic phenomena. At LANL Darryl also wrote his PhD dissertation entitled "Symmetry breaking in fluid dynamics: Lie group reducible motions for real fluids", receiving his PhD in 1976, supervised by Roy Axford. A result discovered in this work was later used to substantiate the accuracy of the Los Alamos on-site yield verification method (CORRTEX) for the US-USSR Threshold Test Ban Treaty (TTBT). In 1980, Darryl moved to the Theoretical Division, where he helped found the Center for Nonlinear Studies and served as one of its acting directors.
Apala Majumdar is a British applied mathematician specialising in the mathematics of liquid crystals. She is a Professor of Applied Mathematics at the University of Strathclyde.
