(Leon O. Chua, Celso Grebogi, Eward Ott)
Leon O. Chua is known for his invention of the memristor, the Chua circuit, and the father of non-linear circuit theory. He was conferred 17 honorary doctorates. He is a member of the Academia Europaea and the Hungarian Academy of Sciences. He received the first Kirchhoff Award, the IEEE Neural Networks Pioneer Award, the Guggenheim Fellow, the EDS Celebrated Member Prize, and the Julius Springer Prize in applied physics.
Celso Grebogi is the Sixth Century Chair at King’s College, University of Aberdeen, UK. He is the Founder and Director of the Institute for Complex Systems and Mathematical Biology, whose work in systems biology and complex systems became a leading in UK. He was also the co-founder of the Aberdeen-Lanzhou-Tempe Joint Research Centre in 2012, whose research work concentrates in the new interdisciplinary field there developed: Relativistic Quantum Chaos. He is an External Scientific Member (Mitglied - Director's level) of the Max-Planck-Society since 1998. He got his PhD in Theoretical Physics from the University of Maryland, postdoc in Physics and Applied Mathematics at UC Berkeley. He was previously with the University of Sao Paulo as Professor of Physics, and, before that, with the University of Maryland as Professor of Mathematics. He is a leading expert in chaotic and complex dynamics, including fractal geometry. His research involves bridging the gap between abstract concepts from mathematics and applications in the scientific disciplines, engineering, medicine and social fields. His research in systems biology integrates mathematical developments with biological experiments. He has made an enormous international impact with his seminal work in the area of chaos control; he was awarded the Thomson-Reuters Citation Laureate for this work – leading to a Motion supported by the Scottish Parliament, and it was also selected by the American Physical Society as a milestone in the last 50 years. His scientific accomplishments include over 500 publications and the delivery of over 500 invited talks at international conferences and academic institutions for which he received numerous distinctions including multiple Doctor Honoris Causa, the Senior Humboldt Prize, Fulbright Fellowship, Toshiba Chair as a World-renown Scholar, and half a dozen Honorary Professorships in China. He is a Fellow in various scientific societies, including the Royal Society of Edinburgh, The World Academy of Sciences, Academia Europaea, Brazilian Academy of Sciences, UK Institute of Physics, and American Physical Society. He has 27,000 citations and h-index = 80 in the Web of Science (45,000 citations and h-index = 94 in Google Scholar).
Edward Ott earned his bachelor's degree from Cooper Union in the field of electrical engineering. He received his master's and doctoral degrees in electrophysics from the Polytechnic Institute of Brooklyn. After a postdoctoral year at Cambridge University, he became a professor of electrical engineering at Cornell University. He joined the University of Maryland in 1979 and is a Distinguished University Professor in the Department of Electrical and Computer Engineering and the Department of Physics. Professor Ott's current research is on the basic theory and applications of nonlinear dynamics. Some of his current research projects are in wave chaos, dynamics on large interconnected networks, chaotic dynamics of fluids, and weather prediction. Professor Ott is a fellow of the American Physical Society, the Institute of Electrical and Electronics Engineers, and the Society for Industrial and Applied Mathematics (SIAM). He is the recipient of the APS Julius Edgar Lilienfield Prize for 2014.
(Victor Shrira, Vakhtang Putkaradze)
Victor Shrira has got his MSc degree from Nizhny Novgorod (Gorky) University (Russia), in 1975. He has got his PhD at P.P.Shirshov Institute for Oceanology, Moscow (1981), under the supervision of Prof. V.E.Zakharov. He continued to work at P.P.Shirshov Institute as a scientist, leading scientist and the Head of the Wave-Current Interaction group till 1997. In 1997 he was appointed as The Benson Ford Professor of Applied Mathematics at University College Cork (Ireland). From 2000 till present, VIS has been a Professor of Applied Mathematics at Keele University (UK). Since 1993 he had a string of Visiting Professorships, most frequently at the universities of Aix-Marseille and Toulon. Since 1994 he has been an editor of Nonlinear Processes in Geophysics. He has supervised a substantial number of PhD and MSc students and PostDocs, who remained at academia as active researchers. He published more than 100 papers on various aspects of nonlinear dynamics in the context of environmental flows. The main research accomplishments include:
· A weakly nonlinear theory of self-interaction of internal gravity waves in the ocean, which, inter alia, predicts a possibility of collapses of 3D wave packets.
· A novel asymptotic approach for describing nonlinear dynamics of finite amplitude long-wave perturbations in shear flows which enables a rigorous derivation of a wide class of novel (1+1)D and (2+1)D nonlinear evolution equations with nonlocal dispersion, the (2+1)D equations describe collapses, the self-focussing of the perturbations results in formation of point singularities in finite time.
· Major contributions into theory of wind waves on shear flows, in particular, found a novel class of surface solitary waves existing due to vertical shear, developed (with A.Slunyyaev) a paradigm changing approach towards nonlinear dynamics of waves on jet currents, which led to the discovery of robust strongly nonlinear long-lived envelope solitary waves. These waves might explain the observed prevalence of rogue waves on jet currents.
· A very efficient novel numerical approach for phase resolving simulations of 3-D water wave dynamics based on the reduced Zakharov integro-differential equation (jointly with S. Annenkov) which enabled us to tackle hitherto unthinkable simulations of deterministic and random wave field dynamics, in particular:
(i) to find the limits of predictability of deterministic description of water waves dynamics;
(ii) to verify the kinetic theory for water waves, to find the range of its applicability and identify the mechanism responsible for the discrepancy between the kinetic theory predictions and fieald observations.
· Theoretically predicted and then found in oceanic observations a novel type of waves occurring due to the `non-traditional' component of the Earth's rotation.
· Made significant contribution to statistical theory of nonlinear water waves. In particular, jointly with S.Annenkov,
(i) revealed the fundamental role of near-resonant interactions in evolution of nonlinear random wave fields;
(ii) derived the `Generalised Kinetic Equation' (GKE) and implemented it in various contexts
(iii) described long-term evolution of skewness and kurtosis which enables to find probability of rogue waves from first princciples;
(iv) have shown that it is small but finite non-Gaussianty that at large times results in the order one discrepancy in shape of the wave spectra between the observations and predictions based on the kinetic equation.
Vakhtang Putkaradze received his PhD from the University of Copenhagen, Denmark, and held faculty positions in New Mexico, Colorado State University, and, most recently, at the University of Alberta, where he was a Centennial Professor between 2012-2019. From 2019 to 2022, he led the science and tech part of the Transformation Team at ATCO Ltd, first as a Senior Director and then Vice-President. He has developed new mathematical tools for variational methods coupled with ideas from symmetry and geometry to various practical problems significant for applications. The techniques are particularly beneficial for problems with several interacting counterparts where deriving dynamics from first principles is challenging, such as fluid-structure interactions, dynamics of porous media, molecular dynamics of polymers involving electrostatic and elastic interactions, and applications of the theory of optimal control to problems such as rolling robots. He has received numerous prizes and awards for research and teaching, including Humboldt Fellowship, Senior JSPS fellowship, Flaherty Visiting Professorship, and CAIMS-Fields industrial math prize.
C.S. Hsu award
(Tassilo Kuepper , Dumitru Baleanu)
Tassilo Kuepper Born in 1947, scientific education at the University of Cologne (1966-1971) in Mathematics and Physics, doctoral degree in 1974 in Numerical Analysis with a thesis on „Range – Domain Implications for non-inverse-positive Boundary Value Problems“, Habilitation in 1979 on „Singular Bifurcation Problems“ and award as Heisenberg Fellow providing research stays at the Mathematical Research Center (Madison), University of Arizona (Tucson), California Institute of Technology (Pasadena) and Stanford University (1981-1982). Professor for Numerical Analysis in Dortmund (1982-1986), Professor for Applied Analysis in Hannover (1986-1990), Professor for Applied Mathematics in Cologne (1990-2012). Visiting Professorships at various Universities in Germany and abroad. Positions in Academic administration at the University of Cologne: Dean of Mathematics and Science Faculty (1995-1997), Prorektor (1997-2001), Rector (2001-2005). Awards as Heisenberg Fellow (1981), Honorary Professor at Jilin University Changchun in 1988, Beijing Normal University 2002 and Moscow Paedagogical State University 2006. Honorary Ph.D. Anadolu University Eskesehir 2004 and Volgograd State University 2010. University Medal University of Cologne 2014 ackknowledging activities to promote mathematical education locally and through international cooperation.
Dumitru Baleanu Dumitru Baleanu is a Professor at the Institute of Space Sciences, Magurele-Bucharest, Romania and a visiting staff member at the Department of Mathematics,Cankaya University, Ankara, Turkey. Dumitru Baleanu got his PhD from the Institute of Atomic Physics in 1996. His fields of interest include the fractional dynamics and its applications, fractional differential equations and their applications, discrete mathematics, image processing, bio-informatics, mathematical biology, mathematical physics, soliton theory, Lie symmetry, dynamic systems on time scales, computational complexity, the wavelet method and its applications, quantization of systems with constraints, the Hamilton-Jacobi formalism, geometries admitting generic and non-generic symmetries. Dumitru is a pioneer of the fractional variational principles and their applications in control theory. He is one of the co-authors of the seminal paper entitled “Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation”, published in Journal of Magnetic Resonance (2008),which plays now a fundamental role within diffusion weighted MRI. Dumitru had an important role in developing the non-singular operators with Mittag-Leffler kernels and their applications in real world phenomena.
V. Afraimovich Award
(Edson Denis Leonel)
Edson Denis Leonel I present some of my main contributions to understanding phase transitions in nonlinear dynamical systems. It is known in the literature that at a second-order phase transition, also called a continuous phase transition, the dynamical variable identifying the order parameter approaches zero continuously. In contrast, the susceptibility of the order parameter diverges. Near a phase transition, the observables characterizing the dynamics are described by power laws leading the dynamics to be scaling invariant. Examples include Lyapunov exponents, diffusion coefficient, quadratic mean velocity, periodic structures in the parameter plane producing objects called shrimps, distance from the attractor, chaotic transient, and the attractor itself, either regular or chaotic, among many others. When such measurable quantities are also scaling invariant, generally made via a control parameter or change in the initial condition, one can find a set of critical exponents that describe the dynamics of the observable by using scaling transformations. The central phenomenology to describe this property uses a set of scaling hypotheses and a generalized homogeneous function. From them, we find an analytic relation for the exponents leading to a scaling law. Indeed, scaling laws are helpful in the characterization and definition of universality classes and can be proved using numerical simulations or analytic descriptions. All of the above have been applied in numerous problems in nonlinear dynamics by myself.
My original contribution's breakthrough characterized a continuous phase transition in some chaotic systems. We focused on answering a set of four main questions:
1. Identify the broken symmetry.
2. Define the order parameter.
3. Discuss the elementary excitation.
4. Discuss the topological defects that impact the transport of particles.
Two main classes of problems were investigated: (i) conservative dynamics, whose time evolution is described by two-dimensional, nonlinear, and area-preserving mappings for the action and angle variable. The intensity of the nonlinearity given by a periodic function is made by a control parameter controlling a transition from integrability to non-integrability; (ii) dissipative systems whose transitions involve suppression of unlimited diffusion of the action variable that also includes a class of more complicated systems such as time-dependent dissipative billiards. In case (i), the own control parameter defines the elementary excitation. The topological defects are linked to periodic structures in the phase space leading the dynamics to experience stickiness. In case (ii), the topological defects are linked to attracting periodic orbits, which depend on the own control parameters. The elementary excitation also relies on the strength of the nonlinearity. The order parameter in both cases is related to the diffusion limit of the dynamical observable, which is closely related to the control parameters and approaches zero at the transition. At the same time, its susceptibility diverges at the same limit. Moreover, there is an algebraic break of symmetry in the two transitions.