Electrostatic forces on charged surfaces of bilayer lipid membranes

Simulating protein-membrane interactions is an important and dynamic area of research. A proper definition of electrostatic forces on membrane surfaces is necessary for developing electromechanical models of protein-membrane interactions. Here we modeled the bilayer membrane as a continuum with general continuous distributions of lipids charges on membrane surfaces. A new electrostatic potential energy functional was then defined for this solvated protein-membrane system. We investigated the geometrical transformation properties of the membrane surfaces under a smooth velocity field. These properties allows us to apply the Hadamard-Zolesio structure theorem, and the electrostatic forces on membrane surfaces can be computed as the shape derivative of the electrostatic energy functional

Models of Financial Markets with Extensive Participation Incentives

We consider models of financial markets in which all parties involved find incentives to participate. Strategies are evaluated directly by their virtual wealths. By tuning the price sensitivity and market impact, a phase diagram with several attractor behaviors resembling those of real markets emerge, reflecting the roles played by the arbitrageurs and trendsetters, and including a phase with irregular price trends and positive sums. The positive-sumness of the players' wealths provides participation incentives for them. Evolution and the bid-ask spread provide mechanisms for the gain in wealth of both the players and market-makers. New players survive in the market if the evolutionary rate is sufficiently slow. We test the applicability of the model on real Hang Seng Index data over 20 years. Comparisons with other models show that our model has a superior average performance when applied to real financial data.Comment: 17 pages, 16 figure

Self-Organization of Balanced Nodes in Random Networks with Transportation Bandwidths

We apply statistical physics to study the task of resource allocation in random networks with limited bandwidths along the transportation links. The mean-field approach is applicable when the connectivity is sufficiently high. It allows us to derive the resource shortage of a node as a well-defined function of its capacity. For networks with uniformly high connectivity, an efficient profile of the allocated resources is obtained, which exhibits features similar to the Maxwell construction. These results have good agreements with simulations, where nodes self-organize to balance their shortages, forming extensive clusters of nodes interconnected by unsaturated links. The deviations from the mean-field analyses show that nodes are likely to be rich in the locality of gifted neighbors. In scale-free networks, hubs make sacrifice for enhanced balancing of nodes with low connectivity.Comment: 7 pages, 8 figure

Single-image measurements of monochromatic subdiffraction dimolecular separations

Measuring subdiffraction separations between single fluorescent particles is important for biological, nano-, and medical-technology studies. Major challenges include (i) measuring changing molecular separations with high temporal resolution while (ii) using identical fluorescent labels. Here we report a method that measures subdiffraction separations between two identical fluorophores by using a single image of milliseconds exposure time and a standard single-molecule fluorescent imaging setup. The fluorophores do not need to be bleached and the separations can be measured down to 40 nm with nanometer precision. The method is called single-molecule image deconvolution -- SMID, and in this article it measures the standard deviation (SD) of Gaussian-approximated combined fluorescent intensity profiles of the two subdiffraction-separated fluorophores. This study enables measurements of (i) subdiffraction dimolecular separations using a single image, lifting the temporal resolution of seconds to milliseconds, while (ii) using identical fluorophores. The single-image nature of this dimer separation study makes it a single-image molecular analysis (SIMA) study.Comment: 16 pages, 5 figure

SU(4) Theory for Spin Systems with Orbital Degeneracy

The isotropic limit of spin systems with orbital degeneracy is shown to have global SU(4) symmetry. On many 2D lattices, the ground state does not posses long range order, which may explain the observed spin liquid properties of $LiNiO_2$. In the SU(4) Neel ordered state, spin-spin correlations can be antiferromagneitc between two neighboring sites with parallel magnetic moments.Comment: 11 pages, 2 figures. submitted to PR