Long-Range Response to Transmission Line Disturbances in DC Electricity Grids

We consider a DC electricity grid composed of transmission lines connecting power generators and consumers at its nodes. The DC grid is described by nonlinear equations derived from Kirchhoff's law. For an initial distribution of consumed and generated power, and given transmission line conductances, we determine the geographical distribution of voltages at the nodes. Adjusting the generated power for the Joule heating losses, we then calculate the electrical power flow through the transmission lines. Next, we study the response of the grid to an additional transmission line between two sites of the grid and calculate the resulting change in the power flow distribution. This change is found to decay slowly in space, with a power of the distance from the additional line. We find the geographical distribution of the power transmission, when a link is added. With a finite probability the maximal load in the grid becomes larger when a transmission line is added, a phenomenon that is known as Braess' paradox. We find that this phenomenon is more pronounced in a DC grid described by the nonlinear equations derived from Kirchhoff's law than in a linearised flow model studied previously in Ref. \cite{witthaut2013}. We observe furthermore that the increase in the load of the transmission lines due to an added line is of the same order of magnitude as Joule heating. Interestingly, for a fixed system size the load of the lines increases with the degree of disorder in the geographical distribution of consumers and producers.Comment: 10 pages, 13 figure

Coarse-Grained Modeling of Genetic Circuits as a Function of the Inherent Time Scales

From a coarse-grained perspective the motif of a self-activating species, activating a second species which acts as its own repressor, is widely found in biological systems, in particular in genetic systems with inherent oscillatory behavior. Here we consider a specific realization of this motif as a genetic circuit, in which genes are described as directly producing proteins, leaving out the intermediate step of mRNA production. We focus on the effect that inherent time scales on the underlying fine-grained scale can have on the bifurcation patterns on a coarser scale in time. Time scales are set by the binding and unbinding rates of the transcription factors to the promoter regions of the genes. Depending on the ratio of these rates to the decay times of the proteins, the appropriate averaging procedure for obtaining a coarse-grained description changes and leads to sets of deterministic equations, which differ in their bifurcation structure. In particular the desired intermediate range of regular limit cycles fades away when the binding rates of genes are of the same order or less than the decay time of at least one of the proteins. Our analysis illustrates that the common topology of the widely found motif alone does not necessarily imply universal features in the dynamics.Comment: 29 pages, 16 figure

On the arrest of synchronized oscillations

We study the mutual conversion of regimes of collective fixed-point behavior and collective synchronized oscillations in a system of coupled dynamical units, which individually can be in an excitable or oscillatory state. The conversion is triggered by the change of a single bifurcation parameter. Of particular interest is the arrest of oscillations. We identify the criterion that determines the seeds of arrest and the propagation of arrest fronts in terms of the vicinity to the future attractor. Due to a high degree of multistability we observe versatile patterns of phase locked motion in the oscillatory regime. Quenching the system into the regime, where oscillatory states are metastable, we observe qualitatively distinct approaches of the fixed-point attractor, depending on the initial seeds. If the seeds of arrest are isolated single sites of the lattice, the arrest propagates via bubble formation, visually similar to nucleation processes; if the seed is extended along a line of lowest amplitudes, the freezing follows the spatial patterns of phase-locked motion with long interfaces between arrested and oscillating units. For spiral patterns of oscillator phases these interfaces are arranged along the arms of the spirals

Theoretical study of the impact of adaptation on cell-fate heterogeneity and fractional killing

Abstract Fractional killing illustrates the cell propensity to display a heterogeneous fate response over a wide range of stimuli. The interplay between the nonlinear and stochastic dynamics of biochemical networks plays a fundamental role in shaping this probabilistic response and in reconciling requirements for heterogeneity and controllability of cell-fate decisions. The stress-induced fate choice between life and death depends on an early adaptation response which may contribute to fractional killing by amplifying small differences between cells. To test this hypothesis, we consider a stochastic modeling framework suited for comprehensive sensitivity analysis of dose response curve through the computation of a fractionality index. Combining bifurcation analysis and Langevin simulation, we show that adaptation dynamics enhances noise-induced cell-fate heterogeneity by shifting from a saddle-node to a saddle-collision transition scenario. The generality of this result is further assessed by a computational analysis of a detailed regulatory network model of apoptosis initiation and by a theoretical analysis of stochastic bifurcation mechanisms. Overall, the present study identifies a cooperative interplay between stochastic, adaptation and decision intracellular processes that could promote cell-fate heterogeneity in many contexts

Hydrodynamic flow and concentration gradients in the gut enhance neutral bacterial diversity

International audienceThe gut microbiota features important genetic diversity, and the specific spatial features of the gut may shape evolution within this environment. We investigate the fixation probability of neutral bacterial mutants within a minimal model of the gut that includes hydrodynamic flow and resulting gradients of food and bacterial concentrations. We find that this fixation probability is substantially increased compared to an equivalent well-mixed system, in the regime where the profiles of food and bacterial concentration are strongly spatially-dependent. Fixation probability then becomes independent of total population size. We show that our results can be rationalized by introducing an active population, which consists of those bacteria that are actively consuming food and dividing. The active population size yields an effective population size for neutral mutant fixation probability in the gut

Scaling laws of cell-fate responses to transient stress

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Breaking of time-translation invariance in Kuramoto dynamics with multiple time scales

We identify the breaking of time-translation invariance in a deterministic system of repulsively coupled Kuramoto oscillators, which are exposed to a distribution of natural frequencies. We analyze random and regular implementations of frequency distributions and consider grid sizes with different characteristics of the attractor space, which is by construction quite rich. This may cause long transients until the deterministic trajectories find their stationary orbits. The stationary orbits are limit cycles with periods that extend over orders of magnitude. It is the long transient times that cause the breaking of time-translation invariance in autocorrelation functions of oscillator phases. This feature disappears close to the transition to the monostable phase, where the phase trajectories are just irregular and no stationary behavior can be identified