On the zeroth law of turbulence for the stochastically forced Navier-Stokes equations

<p style='text-indent:20px;'>We consider the three-dimensional stochastically forced Navier–Stokes equations subjected to white-in-time (colored-in-space) forcing in the absence of boundaries. Upper bounds of the mean value of the time-averaged energy dissipation rate are derived directly from the equations for weak (martingale) solutions. This estimate is consistent with the Kolmogorov dissipation law. Moreover, an additional hypothesis of energy balance implies the zeroth law of turbulence in the absence of a deterministic force.</p>

Core-Periphery Relations in the Eurozone

We argue that the case for the existence of some deterministic force that condemns countries in the periphery to stay in the periphery indefinitely, is weak. Countries that are in the periphery today can become part of the core and vice versa. We also argue that the long run success of the Eurozone depends on a continuing process of political unification. Political unification is needed because the Eurozone has dramatically weakened the power and legitimacy of nation states without creating a nation at the European level. This is particularly true in the field of stabilization. The political willingness to go in this direction, however, is non-existent today. There is no willingness to provide a common insurance mechanism that would put taxpayers in one country at risk of having to transfer money to other countries. Under those conditions the sovereign bond markets in the Eurozone will continue to be prone to instability.

Environmental Disturbances Decrease the Variability of Microbial Populations within Periphyton

ABSTRACT There are many reasons why microbial community composition is difficult to model. For example, the high diversity and high rate of change of these communities make it challenging to identify causes of community turnover. Furthermore, the processes that shape community composition can be either deterministic, which cause communities to converge upon similar compositions, or stochastic, which increase variability in community composition. However, modeling microbial community composition is possible only if microbes show repeatable responses to extrinsic forcing. In this study, we hypothesized that environmental stress acts as a deterministic force that shapes microbial community composition. Other studies have investigated if disturbances can alter microbial community composition, but relatively few studies ask about the repeatability of the effects of disturbances. Mechanistic models implicitly assume that communities show consistent responses to stressors; here, we define and quantify microbial variability to test this assumption. A central pursuit of microbial ecology is to accurately model changes in microbial community composition in response to environmental factors. This goal requires a thorough understanding of the drivers of variability in microbial populations. However, most microbial ecology studies focus on the effects of environmental factors on mean population abundances, rather than on population variability. Here, we imposed several experimental disturbances upon periphyton communities and analyzed the variability of populations within disturbed communities compared with those in undisturbed communities. We analyzed both the bacterial and the diatom communities in the periphyton under nine different disturbance regimes, including regimes that contained multiple disturbances. We found several similarities in the responses of the two communities to disturbance; all significant treatment effects showed that populations became less variable as the result of environmental disturbances. Furthermore, multiple disturbances to these communities were often interactive, meaning that the effects of two disturbances could not have been predicted from studying single disturbances in isolation. These results suggest that environmental factors had repeatable effects on populations within microbial communities, thereby creating communities that were more similar as a result of disturbances. These experiments add to the predictive framework of microbial ecology by quantifying variability in microbial populations and by demonstrating that disturbances can place consistent constraints on the abundance of microbial populations. Although models will never be fully predictive due to stochastic forces, these results indicate that environmental stressors may increase the ability of models to capture microbial community dynamics because of their consistent effects on microbial populations. IMPORTANCE There are many reasons why microbial community composition is difficult to model. For example, the high diversity and high rate of change of these communities make it challenging to identify causes of community turnover. Furthermore, the processes that shape community composition can be either deterministic, which cause communities to converge upon similar compositions, or stochastic, which increase variability in community composition. However, modeling microbial community composition is possible only if microbes show repeatable responses to extrinsic forcing. In this study, we hypothesized that environmental stress acts as a deterministic force that shapes microbial community composition. Other studies have investigated if disturbances can alter microbial community composition, but relatively few studies ask about the repeatability of the effects of disturbances. Mechanistic models implicitly assume that communities show consistent responses to stressors; here, we define and quantify microbial variability to test this assumption. Author Video: An author video summary of this article is available.

WEAK DISORDER IN PERIODIC POTENTIALS: ANOMALOUS TRANSPORT AND DIFFUSION

Particles driven through a periodic potential by an external constant force are known to exhibit a pronounced peak of the diffusion around the critical deterministic force that defines the transition between locked and running states. It has recently been shown both experimentally and numerically that this peak is greatly enhanced if some amount of spatial disorder is superimposed on the periodic potential. Here, we show that this enhancement is a fingerprint of a broad phenomenology that goes well beyond a simple augmentation. For some values of the model parameters, including the characteristic distances associated with the periodic and random components of the potential, the magnitude of the external force, and the temperature, the system can exhibit a rich variety of regimes from normal diffusion to superdiffusion, subdiffusion and even subtransport.