The role of flexibility in the light of the COVID-19 pandemic and beyond:Contributing to a sustainable and resilient energy future in Europe

The energy sector provides fuel for much of everyday life, particularly economically and socially. Fighting against the COVID-19 pandemic, a well-functioning and resilient energy sector is vital for maintaining the operation of critical infrastructures, including, most importantly, the health sector, and timely economic recovery. Notwithstanding its importance in everyday life and crises, the energy sector itself is currently in a complex and far-reaching transformation to combat climate change whilst supporting the transition to a low-carbon economy and society, mainly through the development of variable renewable energy sources (RES) such as wind and solar photovoltaics. This paper highlights the need for energy resilience as countries face the triple challenge of the COVID-19 health crisis, the consequent economic crisis, and the climate crisis. Focusing on Europe, it is advanced here that with the ability to balance fluctuating electricity generation and demand, flexibility allows the energy sector to utilise low-carbon RES reliably, ensuring a more resilient and sustainable energy future. This paper derives five urgent policy recommendations for Europe that address possible impacts of COVID-19 on the economic and societal prerequisites for flexibility in energy systems

Sources and sinks separating domains of left- and right-traveling waves: Experiment versus amplitude equations

In many pattern forming systems that exhibit traveling waves, sources and sinks occur which separate patches of oppositely traveling waves. We show that simple qualitative features of their dynamics can be compared to predictions from coupled amplitude equations. In heated wire convection experiments, we find a discrepancy between the observed multiplicity of sources and theoretical predictions. The expression for the observed motion of sinks is incompatible with any amplitude equation description.Comment: 4 pages, RevTeX, 3 figur

Thermally Induced Fluctuations Below the Onset of Rayleigh-B\'enard Convection

We report quantitative experimental results for the intensity of noise-induced fluctuations below the critical temperature difference $\Delta T_c$ for Rayleigh-B\'enard convection. The structure factor of the fluctuating convection rolls is consistent with the expected rotational invariance of the system. In agreement with predictions based on stochastic hydrodynamic equations, the fluctuation intensity is found to be proportional to $1/\sqrt{-\epsilon}$ where $\epsilon \equiv \Delta T / \Delta T_c -1$. The noise power necessary to explain the measurements agrees with the prediction for thermal noise. (WAC95-1)Comment: 13 pages of text and 4 Figures in a tar-compressed and uuencoded file (using uufiles package). Detailed instructions of unpacking are include

Attractive Interaction Between Pulses in a Model for Binary-Mixture Convection

Recent experiments on convection in binary mixtures have shown that the interaction between localized waves (pulses) can be repulsive as well as {\it attractive} and depends strongly on the relative {\it orientation} of the pulses. It is demonstrated that the concentration mode, which is characteristic of the extended Ginzburg-Landau equations introduced recently, allows a natural understanding of that result. Within the standard complex Ginzburg-Landau equation this would not be possible.Comment: 7 pages revtex with 3 postscript figures (uuencoded

Modeling oscillatory Microtubule--Polymerization

Polymerization of microtubules is ubiquitous in biological cells and under certain conditions it becomes oscillatory in time. Here simple reaction models are analyzed that capture such oscillations as well as the length distribution of microtubules. We assume reaction conditions that are stationary over many oscillation periods, and it is a Hopf bifurcation that leads to a persistent oscillatory microtubule polymerization in these models. Analytical expressions are derived for the threshold of the bifurcation and the oscillation frequency in terms of reaction rates as well as typical trends of their parameter dependence are presented. Both, a catastrophe rate that depends on the density of {\it guanosine triphosphate} (GTP) liganded tubulin dimers and a delay reaction, such as the depolymerization of shrinking microtubules or the decay of oligomers, support oscillations. For a tubulin dimer concentration below the threshold oscillatory microtubule polymerization occurs transiently on the route to a stationary state, as shown by numerical solutions of the model equations. Close to threshold a so--called amplitude equation is derived and it is shown that the bifurcation to microtubule oscillations is supercritical.Comment: 21 pages and 12 figure

Influence of the Soret effect on convection of binary fluids

Convection in horizontal layers of binary fluids heated from below and in particular the influence of the Soret effect on the bifurcation properties of extended stationary and traveling patterns that occur for negative Soret coupling is investigated theoretically. The fixed points corresponding to these two convection structures are determined for realistic boundary conditions with a many mode Galerkin scheme for temperature and concentration and an accurate one mode truncation of the velocity field. This solution procedure yields the stable and unstable solutions for all stationary and traveling patterns so that complete phase diagrams for the different convection types in typical binary liquid mixtures can easily be computed. Also the transition from weakly to strongly nonlinear states can be analyzed in detail. An investigation of the concentration current and of the relevance of its constituents shows the way for a simplification of the mode representation of temperature and concentration field as well as for an analytically manageable few mode description.Comment: 30 pages, 12 figure

Influence of through-flow on linear pattern formation properties in binary mixture convection

We investigate how a horizontal plane Poiseuille shear flow changes linear convection properties in binary fluid layers heated from below. The full linear field equations are solved with a shooting method for realistic top and bottom boundary conditions. Through-flow induced changes of the bifurcation thresholds (stability boundaries) for different types of convective solutions are deter- mined in the control parameter space spanned by Rayleigh number, Soret coupling (positive as well as negative), and through-flow Reynolds number. We elucidate the through-flow induced lifting of the Hopf symmetry degeneracy of left and right traveling waves in mixtures with negative Soret coupling. Finally we determine with a saddle point analysis of the complex dispersion relation of the field equations over the complex wave number plane the borders between absolute and convective instabilities for different types of perturbations in comparison with the appropriate Ginzburg-Landau amplitude equation approximation. PACS:47.20.-k,47.20.Bp, 47.15.-x,47.54.+rComment: 19 pages, 15 Postscript figure

Presynaptic α2δ subunits are key organizers of glutamatergic synapses

In nerve cells the genes encoding for α2δ subunits of voltage-gated calcium channels have been linked to synaptic functions and neurological disease. Here we show that α2δ subunits are essential for the formation and organization of glutamatergic synapses. Using a cellular α2δ subunit triple-knockout/knockdown model, we demonstrate a failure in presynaptic differentiation evidenced by defective presynaptic calcium channel clustering and calcium influx, smaller presynaptic active zones, and a strongly reduced accumulation of presynaptic vesicle-associated proteins (synapsin and vGLUT). The presynaptic defect is associated with the downscaling of postsynaptic AMPA receptors and the postsynaptic density. The role of α2δ isoforms as synaptic organizers is highly redundant, as each individual α2δ isoform can rescue presynaptic calcium channel trafficking and expression of synaptic proteins. Moreover, α2δ-2 and α2δ-3 with mutated metal ion-dependent adhesion sites can fully rescue presynaptic synapsin expression but only partially calcium channel trafficking, suggesting that the regulatory role of α2δ subunits is independent from its role as a calcium channel subunit. Our findings influence the current view on excitatory synapse formation. First, our study suggests that postsynaptic differentiation is secondary to presynaptic differentiation. Second, the dependence of presynaptic differentiation on α2δ implicates α2δ subunits as potential nucleation points for the organization of synapses. Finally, our results suggest that α2δ subunits act as transsynaptic organizers of glutamatergic synapses, thereby aligning the synaptic active zone with the postsynaptic density

Finite size effects near the onset of the oscillatory instability

A system of two complex Ginzburg - Landau equations is considered that applies at the onset of the oscillatory instability in spatial domains whose size is large (but finite) in one direction; the dependent variables are the slowly modulated complex amplitudes of two counterpropagating wavetrains. In order to obtain a well posed problem, four boundary conditions must be imposed at the boundaries. Two of them were already known, and the other two are first derived in this paper. In the generic case when the group velocity is of order unity, the resulting problem has terms that are not of the same order of magnitude. This fact allows us to consider two distinguished limits and to derive two associated (simpler) sub-models, that are briefly discussed. Our results predict quite a rich variety of complex dynamics that is due to both the modulational instability and finite size effects