Computation of rare transitions in the barotropic quasi-geostrophic equations

We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier–Stokes equations in regimes where bistability between two coexisting large-scale attractors exist. By means of large deviations and instanton theory with the use of an Onsager–Machlup path integral formalism for the transition probability, we show how one can directly compute the most probable transition path between two coexisting attractors analytically in an equilibrium (Langevin) framework and numerically otherWe adapt a class of numerical optimization algorithms known as minimum action methods to simple geophysical turbulent models. We show that by numerically minimizing an appropriate action functional in a large deviation limit, one can predict the most likely transition path for a rare transition between two states. By considering examples where theoretical predictions can be made, we show that the minimum action method successfully predicts the most likely transition path. Finally, we discuss the application and extension of such numerical optimization schemes to the computation of rare transitions observed in direct numerical simulations and experiments and to other, more complex, turbulent systems.

One-dimensional optical wave turbulence:experiment and theory

We present a review of the latest developments in one-dimensional (1D) optical wave turbulence (OWT). Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context. The experimental system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. The long-wave limit corresponds to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit, when wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional (2D) turbulence, which can be described by wave turbulence (WT) theory, and conclude that the cascades are induced by a six-wave resonant interaction process. WT theory predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schrödinger equation (NLSE) (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave numbers becomes strong. Subsequently, due to the focusing nature of the nonlinearity, this leads to modulational instability (MI) of the condensate and the formation of solitons. Finally, with the aid of the probability density function (PDF) description of WT theory, we explain the coexistence and mutual interactions between solitons and the weakly nonlinear random wave background in the form of a wave turbulence life cycle (WTLC).

Mixing theory for culture and harvest in bioreactors of human mesenchymal stem cells on microcarriers

The use of human mesenchymal stem cells (hMSCs) in regenerative medicine is a potential major advance for the treatment of many medical conditions, especially with the use of allogeneic therapies where the cells from a single donor can be used to treat ailments in many patients. Such cells must be grown attached to surfaces and for large scale production, it is shown that stirred bioreactors containing ~200 μm particles (microcarriers) can provide such a surface. It is also shown that the just suspended condition, agitator speed NJS, provides a satisfactory condition for cell growth by minimizing the specific energy dissipation rate, εT, in the bioreactor whilst still meeting the oxygen demand of the cells. For the cells to be used for therapeutic purposes, they must be detached from the microcarriers before being cryopreserved. A strategy based on a short period (~7 min) of very high εT, based on theories of secondary nucleation, is effective at removing >99% cells. Once removed, the cells are smaller than the Kolmogorov scale of turbulence and hence not damaged. This approach is shown to be successful for culture and detachment in 4 types of stirred bioreactors from 15 mL to 5 L.

Prospect theory and the effects of bankruptcy laws on entrepreneurial aspirations

We apply prospect theory to explain how personal and corporate bankruptcy laws affect risk perceptions of entrepreneurs at time of entry and therefore their growth ambitions. Previous theories have reached ambiguous conclusions as to whether countries with more debtor-friendly bankruptcy laws (i.e. laws that are more forgiving towards debtors in bankruptcy proceedings) are likely to have more entrepreneurs, or whether, creditorfriendly regimes have positive effects on new ventures via enhanced incentives for the supply of credit to entrepreneurs. Responding to this ambiguity, we apply prospect theory to propose that entrepreneurs do not attach the same significance to different elements of bankruptcy codes—and to explain which aspects of debtor-friendly bankruptcy laws matter more to entrepreneurs. Based on this, we derive and confirm hypotheses about the impact of aspects of bankruptcy codes on entrepreneurial activity using the Global Entrepreneurship Monitor combined with data on both personal and corporate bankruptcyregulations for 15 developed OECD countries. We use multilevel random coefficient logistic regressions to take account of the hierarchical nature of the data (country and individual levels). Because entrepreneurs and creditors are sensitive to different elements of the codes, there is scope for optimisation of the legal design of bankruptcy law to achieve both an adequate supply of credit and to encourage high-ambition entrepreneurship.