Contraction operators and principal currents

We investigate the intersection geometry of currents associated with a maximal dissipative operator or the compression of a partial isometry to its initial space.The authors gratefully acknowledge the support of the National Science Foundation.     

Pair correlations in a ferromagnetic colloid

We discuss some properties of the equation of state and of the static correlations for spherical ferromagnetic grains, at thermal equilibrium, in a passive fluid. At high external fieldsH, low concentrations, and not too high temperatures, the grains tend to formchains along the directions ofH. In zero field (but otherwise identical conditions), some chains are still present but oriented at random and in competition with closed rings and clusters. Various experimental methods which could give information on these chain structures are listed.     

Response of an isolated magnetic grain suspended in a liquid to a rotating field

We have studied the response of an isolated uniaxial magnetic grain suspended in a liquid to an applied fieldh rotating with frequencyω. In the presence of an applied static field (H?h), at low frequencies (i.e. for fast relaxation), the easy axis followsh, while at high frequencies the behavior is similar to that of a bulk sample. In zero static field, the response of a ferromagnetic grain is more complicated; there exists a critical frequencyω _e below which a steady state is reached, with the easy axis followingh. Forω>ω _e the mechanical behavior depends crucially on the initial conditions. Finally, a superparamagnetic grain has a (different) critical frequencyω _e, below which it reacts similarly to the ferromagnetic particle, while forω>ω _e it does not follow steadily the rotating field, but can only oscillate about its initial position.     

Novel electrostatic attraction from plasmon fluctuations

In this Letter, we show that, at low temperatures, zero-point fluctuations of the plasmon modes of two mutually coupled 2D planar Wigner crystals give rise to a novel long-range attractive force. For the case where the distance d between two planar surfaces is large, this attractive force has an unusual power-law decay, which scales as d(-7/2), unlike other fluctuation-induced forces. Specifically, we note that its range is longer than the "standard" zero-temperature van der Waals interaction. This result may, in principle, be observed in bilayer electronic systems and provides insight into the nature of correlation effects for highly charged surfaces.     

Long-range interaction between heterogeneously charged membranes

Despite their neutrality, surfaces or membranes with equal amounts of positive and negative charge can exhibit long-range electrostatic interactions if the surface charge is heterogeneous; this can happen when the surface charges form finite-size domain structures. These domains can be formed in lipid membranes where the balance of the different ranges of strong but short-ranged hydrophobic interactions and longer-ranged electrostatic repulsion result in a finite, stable domain size. If the domain size is large enough, oppositely charged domains in two opposing surfaces or membranes can be strongly correlated by the electrostatic interactions; these correlations give rise to an attractive interaction of the two membranes or surfaces over separations on the order of the domain size. We use numerical simulations to demonstrate the existence of strong attractions at separations of tens of nanometers. Large line tensions result in larger domains but also increase the charge density within the domain. This promotes correlations and, as a result, increases the intermembrane attraction. On the other hand, increasing the salt concentration increases both the domain size and degree of domain anticorrelation, but the interactions are ultimately reduced due to increased screening. The result is a decrease in the net attraction as salt concentration is increased.     

Mesoscale computer modeling of lipid-DNA complexes for gene therapy

We report on a molecular simulation method, which captures the self-assembly of cationic lipid-DNA (CL-DNA) gene delivery complexes. Computational efficiency required for large length- and time-scale simulations is achieved through a coarse-grained representation of the intramolecular details and via intermolecular potentials, which effectively mimic the hydrophobic effect without an explicit solvent. The broad utility of the model is illustrated by demonstrating excellent agreement with x-ray diffraction experimental data for the dependence of the spacing between DNA chains on the concentration of CLs. At high concentrations, the large electrostatic pressure induces the formation of pores in the membranes through which the DNA molecules may escape the complex. We relate this observation to the origin of recently observed enhanced transfection efficiency of lamellar CL-DNA complexes at high charge densities.     

Dithienylethene-Based Single Molecular Photothermal Linear Actuator

By employing a mechanically controllable break junction technique, we have realized an ideal single molecular linear actuator based on dithienylethene (DTE) based molecular architecture, which undergoes reversible photothermal isomerization when subjected to UV irradiation under ambient conditions. As a result, open form (compressed, UV OFF) and closed form (elongated, UV ON) of dithienylethene-based molecular junctions are achieved. Interestingly, the mechanical actuation is achieved without changing the conductance of the molecular junction around the Fermi level over several cycles, which is an essential property required for an ideal single molecular actuator. Our study demonstrates a unique example of achieving a perfect balance between tunneling width and barrier height change upon photothermal isomerization, resulting in no change in conductance but a change in the molecular length, which results in mechanical actuation at the single molecular level.     

Bridging contributions to polyelectrolyte brush collapse in multivalent salt solutions

Polyelectrolyte brushes are essential in many aspects of surface functionality, particularly for colloidal stabilization and lubrication in biological and materials science applications. It has been shown experimentally that the brushes undergo an abrupt shrinkage in the presence of multivalent counter-ions. This transition is studied here using a phenomenological mean-field approach with a model that specifically includes bridging of the polyelectrolyte chains by the multiple charges on the multivalent counter-ions. Using an energy balance represented by the sum of electrostatic, polymeric and entropic mean-field terms, additional parameterized phenomenological terms are introduced for counter-ion condensation and for the attractive interaction between adjacent polyelectrolyte chains to account for the bridging effect. The free energy is minimized with respect to the counter-ion populations and the brush height. In agreement with experimental observations, increasing the concentration of multivalent ions leads to a sharp collapse of the polyelectrolyte brush height. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016, 54, 284–291