Generalized N-rotor problems, synchronized subsystems, and associated solitons.

We consider systems of N particles interacting on the unit circle through 2π-periodic potentials. An example is the N-rotor problem that arises as the classical limit of coupled Josephson junctions and for various energies is known to have a wide range of behaviors such as global chaos and ergodicity, together with families of periodic solutions and transitions from order to chaos. We focus here on selected initial values for generalized systems in which the second order Euler-Lagrange equations reduce to first order equations, which we show by example can describe an ensemble of oscillators with associated emergent phenomena such as synchronization.

Graphene Coating of Nafion Membranes for Enhanced Fuel Cell Performance.

Electrochemically exfoliated graphene (e-G) thin films on Nafion membranes exhibit a selective barrier effect against undesirable fuel crossover. This approach combines the high proton conductivity of state-of-the-art Nafion and the ability of e-G layers to effectively block the transport of methanol and hydrogen. Nafion membranes are coated with aqueous dispersions of e-G on the anode side, making use of a facile and scalable spray process.

Combined higher-order interactions of mixed symmetry on the sphere.

We consider systems of N particles interacting on the unit sphere in d-dimensional space with dynamics defined as the gradient flow of rotationally invariant potentials. The Kuramoto model on the sphere is a well-studied example of such a system but allows only pairwise interactions. Using the Kuramoto model as a guide, we construct n-body potentials from products and sums of rotation invariants, namely, bilinear inner products and multilinear determinants, which lead to a wide variety of higher-order systems with differing synchronization characteristics.

Scalable one-step production of electrochemically exfoliated graphene decorated with transition metal oxides for high-performance supercapacitors.

Graphene and related materials have been widely studied due to their superior properties in a wide range of applications. However, large-scale production remains a critical challenge to enable commercial acceptance. Here, we present a facile, scalable, one-step electrochemical method for producing hybrid transition metal oxide (V, Fe, Ti, or Mn)/graphene materials (TMO-EGs) as active materials for supercapacitors.

Solitons in complex systems of chiral fields with Kuramoto interactions.

We construct a complex system of N chiral fields, each regarded as a node or a constituent of a complex field-theoretic system, which interact by means of chirally invariant potentials across a network of connections. In the classical case, these interactions are identical or similar to Kuramoto interactions, leading to synchronization phenomena for the well-known Kuramoto model and its many extensions and generalizations to higher dimensions. We consider chiral systems of arbitrary size N, where each constituent carries a conserved charge of topological origin, which evolve according to a coupled system of second-order, Lorentz invariant, nonlinear partial differential equations.