Shifting our electricity generation from fossil fuel to renewable energy sources introduces large fluctuations to the power system. Here, we demonstrate how increased fluctuations, reduced damping, and reduced intertia may undermine the dynamical robustness of power grid networks. Focusing on fundamental noise models, we derive analytic insights into which factors limit the dynamic robustness a...

The partition function of the random energy model at inverse temperature β is defined by ZN (β) = ∑N k=1 exp(β √ nXk), where X1, X2, . . . are independent real standard normal random variables, and n = logN . We identify the asymptotic structure of complex zeros of ZN , as N → ∞, confirming predictions made in the theoretical physics literature. Also, we describe the limiting complex fluctuatio...

We introduce a class of stochastic weakly coupled map lattices, as models for studying heat conduction in solids. Each particle on the lattice evolves according to an internal dynamics that depends on its energy, and exchanges energy with its neighbors at a rate that depends on its internal state. We study energy fluctuations at equilibrium in a diffusive scaling. In some cases, we derive the h...

We analyze the energy density fluctuations contributed by scalar fields Φ with vanishing expectation values, 〈Φ〉 = 0, which are present in addition to the inflaton field. For simplicity we take Φ to be non–interacting and minimally coupled to gravity. We use normal ordering to define the renormalized energy density operator ρ, and we show that any normal ordering gives the same result for corre...

We report that the power driving gravity and capillary wave turbulence in a statistically stationary regime displays fluctuations much stronger than its mean value. We show that its probability density function (PDF) has a most probable value close to zero and involves two asymmetric roughly exponential tails. We understand the qualitative features of the PDF using a simple Langevin-type model.

Stochastic nature due to distance and energy fluctuations of single protein molecules involved in electron-transfer (ET) reactions is studied. Distance fluctuations have been assumed previously for causing the slow fluctuations in the ET rates between a donor-acceptor pair constrained to a native protein. Although the observed t(-1/2) power law can be derived using Langevin dynamics with a simp...