Ratchet-induced variations in bulk states of an active ideal gas.

We study the distribution of active, noninteracting particles over two bulk states separated by a ratchet potential. By solving the steady-state Smoluchowski equations in a flux-free setting, we show that the ratchet potential affects the distribution of particles over the bulks and thus exerts an influence of infinitely long range. As we show, an external potential that is nonlinear is crucial for having such a long-range influence. We characterize how the difference in bulk densities depends on activity and on the ratchet potential, and we identify power law dependencies on system parameters in several limiting cases. While weakly active systems are often understood in terms of an effective temperature, we present an analytical solution that explicitly shows that this is not possible in the current setting. Instead, we rationalize our results by a simple transition state model that presumes particles to cross the potential barrier by Arrhenius rates modified for activity. While this model does not quantitatively describe the difference in bulk densities for feasible parameter values, it does reproduce-in its regime of applicability-the complete power law behavior correctly.

Non-equilibrium surface tension of the vapour-liquid interface of active Lennard-Jones particles.

We study a three-dimensional system of self-propelled Brownian particles interacting via the Lennard-Jones potential. Using Brownian dynamics simulations in an elongated simulation box, we investigate the steady states of vapour-liquid phase coexistence of active Lennard-Jones particles with planar interfaces. We measure the normal and tangential components of the pressure tensor along the direction perpendicular to the interface and verify mechanical equilibrium of the two coexisting phases. In addition, we determine the non-equilibrium interfacial tension by integrating the difference of the normal and tangential components of the pressure tensor and show that the surface tension as a function of strength of particle attractions is well fitted by simple power laws. Finally, we measure the interfacial stiffness using capillary wave theory and the equipartition theorem and find a simple linear relation between surface tension and interfacial stiffness with a proportionality constant characterized by an effective temperature.

Vapour-liquid coexistence of an active Lennard-Jones fluid.

We study a three-dimensional system of self-propelled Lennard-Jones particles using Brownian dynamics simulations. Using recent theoretical results for active matter, we calculate the pressure and report equations of state for the system. Additionally, we chart the vapour-liquid coexistence and show that the coexistence densities can be well described using simple power laws. Lastly, we demonstrate that our out-of-equilibrium system shows deviations from both the law of rectilinear diameters and the law of corresponding states.

Metastability in networks of nonlinear stochastic integrate-and-fire neurons.

Neurons in the brain continuously process the barrage of sensory inputs they receive from the environment. A wide array of experimental work has shown that the collective activity of neural populations encodes and processes this constant bombardment of information. How these collective patterns of activity depend on single neuron properties is often unclear. Single-neuron recordings have shown that individual neural responses to inputs are nonlinear, which prevents a straightforward extrapolation from single neuron features to emergent collective states. In this work, we use a field theoretic formulation of a stochastic leaky integrate-and-fire model to study the impact of nonlinear intensity functions on macroscopic network activity. We show that the interplay between nonlinear spike emission and membrane potential resets can i) give rise to metastable transitions between active firing rate states, and ii) can enhance or suppress mean firing rates and membrane potentials in opposite directions.

Tracking momentary fluctuations in human attention with a cognitive brain-machine interface.

Selective attention produces systematic effects on neural states. It is unclear whether, conversely, momentary fluctuations in neural states have behavioral significance for attention. We investigated this question in the human brain with a cognitive brain-machine interface (cBMI) for tracking electrophysiological steady-state visually evoked potentials (SSVEPs) in real-time. Discrimination accuracy (d') was significantly higher when target stimuli were triggered at high, versus low, SSVEP power states. Target and distractor SSVEP power was uncorrelated across the hemifields, and target d' was unaffected by distractor SSVEP power states. Next, we trained participants on an auditory neurofeedback paradigm to generate biased, cross-hemispheric competitive interactions between target and distractor SSVEPs. The strongest behavioral effects emerged when competitive SSVEP dynamics unfolded at a timescale corresponding to the deployment of endogenous attention. In sum, SSVEP power dynamics provide a reliable readout of attentional state, a result with critical implications for tracking and training human attention.