Autonomous Brownian gyrators: A study on gyrating characteristics.

We study the nonequilibrium steady-state (NESS) dynamics of two-dimensional Brownian gyrators under harmonic and nonharmonic potentials via computer simulations and analyses based on the Fokker-Planck equation, while our nonharmonic cases feature a double-well potential and an isotropic quartic potential. In particular, we report two simple methods that can help understand gyrating patterns. For harmonic potentials, we use the Fokker-Planck equation to survey the NESS dynamical characteristics; i.

Stable iridium(iv) complexes supported by tetradentate salen ligands. Synthesis, structures and reactivity.

A series of trans-dichloroiridium(iv)-salen complexes were synthesized and structurally characterized by spectroscopic means and X-ray crystal structures. These Ir(iv) complexes are able to catalyze intramolecular C-H amination of aryl azides. The catalytic amination was drastically accelerated under microwave-assisted conditions, and possibly involves Ir-imido intermediates as supported by high-resolution ESI-MS analysis.

Rubik's cube: an energy perspective.

What if we played the Rubik's cube game by simple intuition? We would rotate the cube, probably in the hope of getting a more organized pattern in each next step. Yet frustration occurs easily, and we soon find ourselves trapped as the game progresses no further. Played in this completely strategy-less style, the entire problem of the Rubik's cube game can be compared to that of complex chemical reactions such as protein folding, only with less guidance in the searching process.

A cell-model study on counterion fluctuations in macroionic systems: effect of non-extensiveness in entropy.

Rigorously speaking, entropy is slightly non-extensive, and this non-extensiveness, which characterizes the degree of fluctuations, can contribute to effective interactions between mesoscopic objects. In this paper, we consider a pair of macroions, each accompanied by 1000 counterions, and with a cell-model description we demonstrate that the slow variation of non-extensiveness in counterion entropy over macroionic distance leads to an effective long-range attraction between the macroions. With the aid of Monte Carlo simulation and a Bragg-Williams theory including counterion number fluctuations, we find the depth of attraction in free energy to be approximately 0.

Polarization of ions under geometric confinement in the strong-interacting regime: a two-ring model study.

We study the polarization and electrostatic interactions of an ionic system under geometric confinement in the strong-interacting regime. The geometric confinement is introduced via a simple two-ring model, where ions of each species are confined on a ring, respectively. The observed polarization curve exhibits staircase transitions in the low-temperature regime, due to the crossover between energy local minima.

Studies on electrostatic interactions of colloidal particles in two dimensions: a modeling approach.

We study the effective electrostatic interactions between a pair of charged colloidal particles without salt ions while the system is confined in two dimensions. In particular, we use a simplified model to elucidate the effects of rotational fluctuations in counterion distribution. The results exhibit effective colloidal attractions under appropriate conditions.

Phase behavior of polyelectrolyte solutions with salt.

We have computed the phase diagrams of solutions of flexible polyelectrolyte chains with added simple electrolytes. The calculations are based on our recent theory [M. Muthukumar, Macromolecules 35, 9142 (2002)], which accounts for conformational fluctuations of chains, charge density correlations arising from dissolved ions, hydrophobic interaction between polymer backbone and solvent, and translational entropy of all species in the system.

Diffusion dynamics, moments, and distribution of first-passage time on the protein-folding energy landscape, with applications to single molecules.

We study the dynamics of protein folding via statistical energy-landscape theory. In particular, we concentrate on the local-connectivity case with the folding progress described by the fraction of native conformations. We found that the first passage-time (FPT) distribution undergoes a dynamic transition at a temperature below which the FPT distribution develops a power-law tail, a signature of the intermittent nonexponential kinetic phenomena for the folding dynamics.