Homogeneous catalysts usually show higher catalytic activities than heterogeneous catalysts because of their high dispersion of catalytically active sites. We demonstrate here that heterogeneous catalysts of ionic liquids functionalized on superhydrophobic mesoporous polymers exhibit much higher activities in transesterification to form biodiesel than homogeneous catalysts of the ionic liquids ...

It is proved herein that certain smooth, global solutions of a class of quasi-linear, dissipative, dispersive wave equations have precisely the same leading order, long-time, asymptotic behavior as the solutions (with the same initial data) of the corresponding linearized equations. The solutions of the nonlinear equations are shown to be asymptotically self-similar with explicitly determined p...

The acquisition and dispersion of information, a critical aspect of economic decisions, can occur through a network of agents (Jackson, 2009). Empirical and theoretical findings suggest that an efficient information dispersion network takes the form of a star: small numbers of agents gather information and distribute it to a large group. Despite these findings, controlled tests of this theory f...

The turbulence field obtained using a large-eddy simulation model is used to simulate particle dispersion in the convective boundary layer with both forwardin-time and backward-in-time modes. A Lagrangian stochastic model is used to treat subgrid-scale turbulence. Results of forward dispersion match both laboratory experiments and previous numerical studies for different release heights in the ...

A quantum theory of dispersion for an inhomogeneous solid is obtained, from a starting point of multipolar coupled atoms interacting with an electromagnetic field. The dispersion relations obtained are equivalent to the standard classical Sellmeir equations obtained from the Drude-Lorentz model. In the homogeneous ~planewave! case, we obtain the detailed quantum mode structure of the coupled po...

The dispersion relation is fundamental to a physical phenomenon that develops in both space and time. This equation connects the spatial and temporal frequencies involved in the dynamic process through the material constants. Electromagnetic plane waves propagating in homogeneous media are bound by simple dispersion relation, which sets the magnitude of the spatial frequency, k, as being propor...

The prolongation of intraatrial and interatrial conduction time and the non-homogeneous propagation of sinus impulses are well known electrophysiologic characteristics in patients with atrial arrhythmias and especially paroxysmal atrial fibrillation (AF). Previous studies have demonstrated that individuals with clinical history of paroxysmal AF show a significantly increased P wave duration in ...

Metamaterials are effectively homogeneous materials that display extraordinary dispersion. Negative index metamaterials, zero index metamaterials and extremely anisotropic metamaterials are just a few examples. Instead of using locally resonating elements that may cause undesirable absorption, there are huge efforts to seek alternative routes to obtain these unusual properties. Here, we demonst...

We make use of continuum elasticity theory to investigate the collective modes that propagate along the edge of a two-dimensional electron liquid or crystal in a magnetic field. An exact solution of the equations of motion is obtained with the following simplifying assumptions: (i) The system is macroscopically homogeneous and isotropic in the half-plane delimited by the edge (ii) The electron-...

In this paper we present a model for modeling the diffusion and relative dispersion of particles in homogeneous isotropic turbulence. We use a Heisenberg-like Hamiltonian to incorporate spatial correlations between fluid particles, which are modeled by stochastic processes correlated in time. We are able to reproduce the ballistic regime in the mean square displacement of single particles and t...