Complex temporal patterns in molecular dynamics:a direct measure of the phase-space exploration by the trajectory at macroscopic time scales

Computer simulated trajectories of bulk water molecules form complex spatiotemporal structures at the picosecond time scale. This intrinsic complexity, which underlies the formation of molecular structures at longer time scales, has been quantified using a measure of statistical complexity. The method estimates the information contained in the molecular trajectory by detecting and quantifying temporal patterns present in the simulated data (velocity time series). Two types of temporal patterns are found. The first, defined by the short-time correlations corresponding to the velocity autocorrelation decay times (â‰0.1â€ps), remains asymptotically stable for time intervals longer than several tens of nanoseconds. The second is caused by previously unknown longer-time correlations (found at longer than the nanoseconds time scales) leading to a value of statistical complexity that slowly increases with time. A direct measure based on the notion of statistical complexity that describes how the trajectory explores the phase space and independent from the particular molecular signal used as the observed time series is introduced. © 2008 The American Physical Society.

Molecular phase space transport in water:non-stationary random walk model

Molecular transport in phase space is crucial for chemical reactions because it defines how pre-reactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a non-random character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of non-stationarity in the transition probabilities of the segments of molecular trajectories can account for the observed non-uniform filling of the phase space. Surprisingly, the characteristic periods in the model non-stationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds).

Participation Space Studies: a socio-technical exploration of activist and community groups’ use of online and offline spaces to support their work

Participation Space Studies explore eParticipation in the day-to-day activities of local, citizen-led groups, working to improve their communities. The focus is the relationship between activities and contexts. The concept of a participation space is introduced in order to reify online and offline contexts where people participate in democracy. Participation spaces include websites, blogs, email, social media presences, paper media, and physical spaces. They are understood as sociotechnical systems: assemblages of heterogeneous elements, with relevant histories and trajectories of development and use. This approach enables the parallel study of diverse spaces, on and offline. Participation spaces are investigated within three case studies, centred on interviews and participant observation. Each case concerns a community or activist group, in Scotland. The participation spaces are then modelled using a Socio-Technical Interaction Network (STIN) framework (Kling, McKim and King, 2003). The participation space concept effectively supports the parallel investigation of the diverse social and technical contexts of grassroots democracy and the relationship between the case-study groups and the technologies they use to support their work. Participants’ democratic participation is supported by online technologies, especially email, and they create online communities and networks around their goals. The studies illustrate the mutual shaping relationship between technology and democracy. Participants’ choice of technologies can be understood in spatial terms: boundaries, inhabitants, access, ownership, and cost. Participation spaces and infrastructures are used together and shared with other groups. Non-public online spaces, such as Facebook groups, are vital contexts for eParticipation; further, the majority of participants’ work is non-public, on and offline. It is informational, potentially invisible, work that supports public outputs. The groups involve people and influence events through emotional and symbolic impact, as well as rational argument. Images are powerful vehicles for this and digital images become an increasingly evident and important feature of participation spaces throughout the consecutively conducted case studies. Collaboration of diverse people via social media indicates that these spaces could be understood as boundary objects (Star and Griesemer, 1989). The Participation Space Studies draw from and contribute to eParticipation, social informatics, mediation, social shaping studies, and ethnographic studies of Internet use.

Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

In this paper, a space fractional di®usion equation (SFDE) with non- homogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally e±cient and accurate method for solving SFDE.