Local vs. global redundancy – trade-offs between resilience against cascading failures and frequency stability

When designing or extending electricity grids, both frequency stability and resilience against cascading failures have to be considered amongst other aspects of energy security and economics such as construction costs due to total line length. Here, we compare an improved simulation model for cascading failures with state-of-the-art simulation models for short-term grid dynamics. Random ensembles of realistic power grid topologies are generated using a recent model that allows for a tuning of global vs local redundancy. The former can be measured by the algebraic connectivity of the network, whereas the latter can be measured by the networks transitivity. We show that, while frequency stability of an electricity grid benefits from a global form of redundancy, resilience against cascading failures rather requires a more local form of redundancy and further analyse the corresponding trade-off.     

The impact of model detail on power grid resilience measures

Extreme events are a challenge to natural as well as man-made systems. For critical infrastructure like power grids, we need to understand their resilience against large disturbances. Recently, new measures of the resilience of dynamical systems have been developed in the complex system literature. Basin stability and survivability respectively assess the asymptotic and transient behavior of a system when subjected to arbitrary, localized but large perturbations in frequency and phase. To employ these methods that assess power grid resilience, we need to choose a certain model detail of the power grid. For the grid topology we considered the Scandinavian grid and an ensemble of power grids generated with a random growth model. So far the most popular model that has been studied is the classical swing equation model for the frequency response of generators and motors. In this paper we study a more sophisticated model of synchronous machines that also takes voltage dynamics into account, and compare it to the previously studied model. This model has been found to give an accurate picture of the long term evolution of synchronous machines in the engineering literature for post fault studies. We find evidence that some stable fix points of the swing equation become unstable when we add voltage dynamics. If this occurs the asymptotic behavior of the system can be dramatically altered, and basin stability estimates obtained with the swing equation can be dramatically wrong. We also find that the survivability does not change significantly when taking the voltage dynamics into account. Further, the limit cycle type asymptotic behaviour is strongly correlated with transient voltages that violate typical operational voltage bounds. Thus, transient voltage bounds are dominated by transient frequency bounds and play no large role for realistic parameters.     

An Antibody with a Variable‐Region Coiled‐Coil “Knob” Domain

The X‐ray crystal structure of a bovine antibody (BLV1H12) revealed a unique structure in its ultralong heavy chain complementarity determining region 3 (CDR3H) that folds into a solvent‐exposed β‐strand “stalk” fused to a disulfide crosslinked “knob” domain. We have substituted an antiparallel heterodimeric coiled‐coil motif for the β‐strand stalk in this antibody. The resulting antibody (Ab‐coil) expresses in mammalian cells and has a stability similar to that of the parent bovine antibody. MS analysis of H–D exchange supports the coiled‐coil structure of the substituted peptides. Substitution of the knob‐domain of Ab‐coil with bovine granulocyte colony‐stimulating factor (bGCSF) results in a stably expressed chimeric antibody, which proliferates mouse NFS‐60 cells with a potency comparable to that of bGCSF. This work demonstrates the utility of this novel coiled‐coil CDR3 motif as a means for generating stable, potent antibody fusion proteins with useful pharmacological properties.     

A Rapidly Reversible Chemical Dimerizer System to Study Lipid Signaling in Living Cells

Chemical dimerizers are powerful tools for non‐invasive manipulation of enzyme activities in intact cells. Here we introduce the first rapidly reversible small‐molecule‐based dimerization system and demonstrate a sufficiently fast switch‐off to determine kinetics of lipid metabolizing enzymes in living cells. We applied this new method to induce and stop phosphatidylinositol 3‐kinase (PI3K) activity, allowing us to quantitatively measure the turnover of phosphatidylinositol 3,4,5‐trisphosphate (PIP₃) and its downstream effectors by confocal fluorescence microscopy as well as standard biochemical methods.     

Solidification of semicrystalline polymers using a variable interface temperature model

Solidification of semicrystalline materials often occurs in significantly undercooled melts. The crystal growth process in such melts is convoluted due to the fact that the interface between the solid and liquid domains of the microscopic crystals is at an unknown temperature. However, it is possible to let the temperature of this interface be unspecified and solve the problem with a semianalytical method if the growth velocity is prescribed. Solutions for the temperature profiles in both solid and liquid phases are presented in this work, along with the interface temperature, for phase change processes controlled by the kinetics of crystallization rather than diffusion processes, which is typical for polymers. The method is used for one-dimensional problems in cartesian, cylindrical, and spherical geometries that correspond to commonly found microstructures. It is found that the temperature of the interface is significantly below the equilibrium melting point and a quasi steady-state regime is reached rapidly. Comparison with the classical Neumann's solution shows that the temperature profiles are similar but the position of the interface differs considerably. © 1996 John Wiley & Sons, Inc.     

Third-order Nonlinear Optical Properties of Octa-substituted Metal-free Phthalocyanine Thin Films

Third-order nonlinear optical susceptibility, χ⁽³⁾ of symmetrically octa-substituted metal-free phthalocyanine thin films measured by the third-harmonic generation technique are reported. The metal-free phthalocyanine has been found to show a χ⁽³⁾ (−3ω; ω,ω, ω) value as large as 7.73×10⁻¹² esu at 1.80 μm. The figure of merit, χ⁽³⁾/α, was estimated to be 4.17×10¹⁷ esu cm at 1.05 μm and 6.97×10¹⁶ esu cm at 1.65 μm. Both linear and third-order optical properties of liquid-crystalline metal-free phthalocyanines are discussed     

Global and local performance metric with inertia effects

Nonlinear Dynamics - A complex system’s structural–dynamical interplay plays a profound role in determining its collective behavior. Irregular behavior in the form of macroscopic chaos,...     

Scaling of the temperature-dependent resistivity in SrFe2−xNixAs2

We show that the zero-field normal-state resistivity of temperature-dependent resistivity ρ(T) of SrFe_2?xNi_xAs₂ can be reproduced by the expression ρ(T) = ρ₀ + c T exp(?2Δ/T). ρ(T) can be scaled using both this expression where the energy scale Δ, c and the residual resistivity ρ₀ are scaling parameters and a recently proposed model-independent scaling method (H.G. Luo, Y.H. Su, T. Xiang, Phys. Rev. B 77 (2008) 014529). The scaling parameters have been calculated and the compositional variation of 2Δ(x) has been determined. This dependence show almost a linear decreasing in the underdoped regime similar to that reported for cuprates. The existence of a universal metallic ρ(T) curve in a wide temperature range which, however, is restricted for the underdoped compounds to temperatures above a structural and anitiferromagnetic transition is interpreted as an indication of a single mechanism which dominates the scattering of the charge carriers in SrFe_2?xNi_xAs₂ (x = 0–0.3).     

Level 17 Ramanujan–Sato series

The Ramanujan Journal - Two level 17 modular functions $$\begin{aligned} r = q^2 \prod _{n=1}^{\infty } (1-q^{n})^{\left( \frac{n}{17} \right) },\qquad s = q^{2} \prod _{n=1}^{\infty } \frac{(1 -...