results for au:MacKay_R in:physics

- The transition states and dividing surfaces used to find rate constants for bimolecular reactions are shown to undergo qualitative changes, known as Morse bifurcations, and to exist for a large range of energies, not just immediately above the critical energy for first connection between reactants and products. Specifically, we consider capture between two molecules and the associated transition states for the case of non-zero angular momentum and general attitudes. The capture between an atom and a diatom, and then a general molecule are presented, providing concrete examples of Morse bifurcations of transition states and dividing surfaces. The reduction of the $n$-body systems representing the reactions is discussed and reviewed with comments on the difficulties associated with choosing appropriate charts and the global geometry of the reduced spaces.
- We make the case for mathematicians and statisticians to stake their claim in the fast-moving and high-impact research field that is becoming known as Future Cities. After assessing the Future Cities arena, we provide some illustrative challenges where mathematical scientists can make an impact.
- This work reviews the present position of and surveys future perspectives in the physics of chaotic advection: the field that emerged three decades ago at the intersection of fluid mechanics and nonlinear dynamics, which encompasses a range of applications with length scales ranging from micrometers to hundreds of kilometers, including systems as diverse as mixing and thermal processing of viscous fluids, microfluidics, biological flows, and oceanographic and atmospheric flows.
- Oct 02 2013 physics.acc-ph physics.med-ph arXiv:1310.0237v1Recent developments for the delivery of proton and ion beam therapy have been significant, and a number of technological solutions now exist for the creation and utilisation of these particles for the treatment of cancer. In this paper we review the historical development of particle accelerators used for external beam radiotherapy and discuss the more recent progress towards more capable and cost-effective sources of particles.
- A transition state for a Hamiltonian system is a closed, invariant, oriented, codimension-2 submanifold of an energy-level that can be spanned by two compact codimension-1 surfaces of unidirectional flux whose union, called a dividing surface, locally separates the energy-level into two components and has no local recrossings. For this to happen robustly to all smooth perturbations, the transition state must be normally hyperbolic. The dividing surface then has locally minimal geometric flux through it, giving an upper bound on the rate of transport in either direction. Transition states diffeomorphic to $\mathbb S^{2m-3}$ are known to exist for energies just above any index-1 critical point of a Hamiltonian of $m$ degrees of freedom, with dividing surfaces $\mathbb S^{2m-2}$. The question addressed here is what qualitative changes in the transition state, and consequently the dividing surface, may occur as the energy or other parameters are varied? We find that there is a class of systems for which the transition state becomes singular and then regains normal hyperbolicity with a change in diffeomorphism class. These are Morse bifurcations. Various examples are considered. Firstly, some simple examples in which transition states connect or disconnect, and the dividing surface may become a torus or other. Then, we show how sequences of Morse bifurcations producing various interesting forms of transition state and dividing surface are present in reacting systems, by considering a hypothetical class of bimolecular reactions in gas phase.
- Apr 02 2013 physics.ed-ph physics.soc-ph arXiv:1304.0412v1Education is a major force for economic and social wellbeing. Despite high aspirations, education at all levels can be expensive and ineffective. Three Grand Challenges are identified: (1) enable people to learn orders of magnitude more effectively, (2) enable people to learn at orders of magnitude less cost, and (3) demonstrate success by exemplary interdisciplinary education in complex systems science. A ten year `man-on-the-moon' project is proposed in which FuturICT's unique combination of Complexity, Social and Computing Sciences could provide an urgently needed transdisciplinary language for making sense of educational systems. In close dialogue with educational theory and practice, and grounded in the emerging data science and learning analytics paradigms, this will translate into practical tools (both analytical and computational) for researchers, practitioners and leaders; generative principles for resilient educational ecosystems; and innovation for radically scalable, yet personalised, learner engagement and assessment. The proposed \em Education Accelerator will serve as a `wind tunnel' for testing these ideas in the context of real educational programmes, with an international virtual campus delivering complex systems education exploiting the new understanding of complex, social, computationally enhanced organisational structure developed within FuturICT.
- FuturICT foundations are social science, complex systems science, and ICT. The main concerns and challenges in the science of complex systems in the context of FuturICT are laid out in this paper with special emphasis on the Complex Systems route to Social Sciences. This include complex systems having: many heterogeneous interacting parts; multiple scales; complicated transition laws; unexpected or unpredicted emergence; sensitive dependence on initial conditions; path-dependent dynamics; networked hierarchical connectivities; interaction of autonomous agents; self-organisation; non-equilibrium dynamics; combinatorial explosion; adaptivity to changing environments; co-evolving subsystems; ill-defined boundaries; and multilevel dynamics. In this context, science is seen as the process of abstracting the dynamics of systems from data. This presents many challenges including: data gathering by large-scale experiment, participatory sensing and social computation, managing huge distributed dynamic and heterogeneous databases; moving from data to dynamical models, going beyond correlations to cause-effect relationships, understanding the relationship between simple and comprehensive models with appropriate choices of variables, ensemble modeling and data assimilation, modeling systems of systems of systems with many levels between micro and macro; and formulating new approaches to prediction, forecasting, and risk, especially in systems that can reflect on and change their behaviour in response to predictions, and systems whose apparently predictable behaviour is disrupted by apparently unpredictable rare or extreme events. These challenges are part of the FuturICT agenda.
- The equilibrium states of the discrete Peyrard-Bishop Hamiltonian with one end fixed are computed exactly from the two-dimensional nonlinear Morse map. These exact nonlinear structures are interpreted as domain walls (DW), interpolating between bound and unbound segments of the chain. The free energy of the DWs is calculated to leading order beyond the Gaussian approximation. Thermodynamic instabilities (e.g. DNA unzipping and/or thermal denaturation) can be understood in terms of DW formation.