Network evolution and the spatiotemporal dynamics of knowledge sourcing

Knowledge accessing from external organisations is important to firms, especially entrepreneurial ones which often cannot generate internally all the knowledge necessary for innovation. There is, however, a lack of evidence concerning the association between the evolution of firms and the evolution of their networks. The aim of this paper is to begin to fill this gap by undertaking an exploratory analysis of the relationship between the vintage of firms and their knowledge sourcing networks. Drawing on an analysis of firms in the UK, the paper finds some evidence of a U-shaped relationship existing between firm age and the frequency of accessing knowledge from certain sources. Emerging entrepreneurial firms tend to be highly active with regard to accessing knowledge for a range of sources and geographic locations, with the rate of networking dropping somewhat during the period of peak firm growth. For instance, it is found that firms tend to less frequently access knowledge sources such as universities and research institutes in their own region during a stage of peak turnover growth. Overall, the results suggest a complex relationship between the lifecycle of the firm and its networking patterns. It is concluded that policymakers need to become more aware that network formation and utilisation by firms is likely to vary dependent upon their lifecycle position.

Langevin dynamics, large deviations and instantons for the quasi-geostrophic model and two-dimensional Euler equations

We investigate a class of simple models for Langevin dynamics of turbulent flows, including the one-layer quasi-geostrophic equation and the two-dimensional Euler equations. Starting from a path integral representation of the transition probability, we compute the most probable fluctuation paths from one attractor to any state within its basin of attraction. We prove that such fluctuation paths are the time reversed trajectories of the relaxation paths for a corresponding dual dynamics, which are also within the framework of quasi-geostrophic Langevin dynamics. Cases with or without detailed balance are studied. We discuss a specific example for which the stationary measure displays either a second order (continuous) or a first order (discontinuous) phase transition and a tricritical point. In situations where a first order phase transition is observed, the dynamics are bistable. Then, the transition paths between two coexisting attractors are instantons (fluctuation paths from an attractor to a saddle), which are related to the relaxation paths of the corresponding dual dynamics. For this example, we show how one can analytically determine the instantons and compute the transition probabilities for rare transitions between two attractors.

Dynamics of vector rogue waves in a fiber laser with a ring cavity

A pulse–pulse interaction that leads to rogue wave (RW) generation in lasers was previously attributed either to soliton–soliton or soliton–dispersive-wave interaction. The beating between polarization modes in the absence of a saturable absorber causes similar effects. Accounting for these polarization modes in a laser resonator is the purpose of the distributed vector model of laser resonators. Furthermore, high pump power, high amplitude, and short pulse duration are not necessary conditions to observe pulse attraction, repulsion, and collisions and the resonance exchange of energy between among them. The regimes of interest can be tuned just by changing the birefringence in the cavity with the pump power slightly higher than the laser threshold. This allows the observation of a wide range of RW patterns in the same experiment, as well as to classify them. The dynamics of the interaction between pulses leads us to the conclusion that all of these effects occur due to nonlinearity induced by the inverse population in the active fiber as well as an intrinsic nonlinearity in the passive part of the cavity. Most of the mechanisms of pulse–pulse interaction were found to be mutually exclusive. This means that all the observed RW patterns, namely, the “lonely,” “twins,” “three sisters,” and “cross,” are probably different cases of the same process.