Vortices in excitable media underlie dangerous cardiac arrhythmias. One way to eliminate them is by stimulating the excitable medium with a period smaller than the period of the vortex. So far, this phenomenon has been studied mostly for two-dimensional vortices known as spiral waves. Here we present a first study of this phenomenon for three-dimensional vortices, or scroll waves, in a slab. We consider two main types of scroll waves dynamics with positive filament tension and with negative filament tension and show that such elimination is possible for some values of the period in all cases. However, in the case of negative filament tension for relatively long stimulation periods, three-dimensional instabilities occur and make elimination impossible. We derive equations of motion for the drift of paced filaments and identify a bifurcation parameter that determines whether the filaments orient themselves perpendicular to the impeding wave train or not.A class of explicit numerical schemes is developed to solve for the relativistic dynamics and spin of particles in electromagnetic fields, using the Lorentz-Bargmann-Michel-Telegdi equation formulated in the Clifford algebra representation of Baylis. It is demonstrated that these numerical methods, reminiscent of the leapfrog and Verlet methods, share a number of important properties they are energy conserving, volume conserving, and second-order convergent. These properties are analyzed empirically by benchmarking against known analytical solutions in constant uniform electrodynamic fields. It is demonstrated that the numerical error in a constant magnetic field remains bounded for long-time simulations in contrast to the Boris pusher, whose angular error increases linearly with time. Finally, the intricate spin dynamics of a particle is investigated in a plane-wave field configuration.Evaporation of streams of liquid droplets in environments at vacuum pressures below the vapor pressure has not been widely studied. Here, experiments and simulations are reported that quantify the change in droplet diameter when a steady stream of ≈100 μm diameter drops is injected into a chamber initially evacuated to less then 10^-8bar. In experiments, droplets fall through the center of a 0.8 m long liquid nitrogen cooled shroud, simulating infinity radiation and vapor mass flux boundary conditions. Experimentally measured changes in drop diameters vary from ≈0 to 6 μm when the initial vapor pressure is increased from 10^-6 to 10^-3 bar by heating the liquid. Measured diameter changes are predicted by a model based on the Hertz-Knudsen equation. One uncertainty in the calculation is the "sticking coefficient" β. Assuming a constant β for all conditions studied here, predicted diameter changes best match measurements with β≈0.3. This value falls within the range of β reported in the literature for organic liquids. Finally, at the higher vapor pressure conditions considered here, the drop stream disperses transverse to the main flow direction. This spread is attributed to forces imparted by an absolute pressure gradient produced by the evaporating stream.We study the statistics of the first hitting time between a one-dimensional run-and-tumble particle and a target site that switches intermittently between visible and invisible phases.  https://www.selleckchem.com/products/lificiguat-yc-1.html  The two-state dynamics of the target is independent of the motion of the particle, which can be absorbed by the target only in its visible phase. We obtain the mean first hitting time when the motion takes place in a finite domain with reflecting boundaries. Considering the turning rate of the particle as a tuning parameter, we find that ballistic motion represents the best strategy to minimize the mean first hitting time. However, the relative fluctuations of the first hitting time are large and exhibit nonmonotonous behaviors with respect to the turning rate or the target transition rates. Paradoxically, these fluctuations can be the largest for targets that are visible most of the time, and not for those that are mostly invisible or rapidly transiting between the two states. On the infinite line, the classical asymptotic behavior ∝t^-3/2 of the first hitting time distribution is typically preceded, due to target intermittency, by an intermediate scaling regime varying as t^-1/2. The extent of this transient regime becomes very long when the target is most of the time invisible, especially at low turning rates. In both finite and infinite geometries, we draw analogies with partial absorption problems.Power grid networks, as well as neuronal networks with synaptic plasticity, describe real-world systems of tremendous importance for our daily life. The investigation of these seemingly unrelated types of dynamical networks has attracted increasing attention over the past decade. In this paper, we provide insight into the fundamental relation between these two types of networks. For this, we consider well-established models based on phase oscillators and show their intimate relation. In particular, we prove that phase oscillator models with inertia can be viewed as a particular class of adaptive networks. This relation holds even for more general classes of power grid models that include voltage dynamics. As an immediate consequence of this relation, we discover a plethora of multicluster states for phase oscillators with inertia. Moreover, the phenomenon of cascading line failure in power grids is translated into an adaptive neuronal network.This Letter presents a numerical study across parameter space to calculate the aspect ratio (ratio of length to diameter) of a fair "three-sided coin" a cylinder that when tossed, has equal probabilities of landing heads, tails, or sideways. The results are cast in the context of previous analytical studies, and the various mechanisms that govern the dynamics of coin tossing are compared and contrasted. After more than 7×10^8 tosses of coins of various aspect ratios, this study finds the critical aspect ratio to be slightly less than (but not exactly equal to) sqrt[3]/2≈0.866.Percolation models shed a light on network integrity and functionality and have numerous applications in network theory. This paper studies a targeted percolation (α model) with incomplete knowledge where the highest degree node in a randomly selected set of n nodes is removed at each step, and the model features a tunable probability that the removed node is instead a random one. A "mirror image" process (β model) in which the target is the lowest degree node is also investigated. We analytically calculate the giant component size, the critical occupation probability, and the scaling law for the percolation threshold with respect to the knowledge level n under both models. We also derive self-consistency equations to analyze the k-core organization including the size of the k core and its corona in the context of attacks under tunable limited knowledge. These percolation models are characterized by some interesting critical phenomena and reveal profound quantitative structure discrepancies between Erdős-Rényi networks and power-law networks.