Search Results (12 total)

We have carried out numerical simulations of strongly gravitating systems based on the Einstein equations coupled to the relativistic hydrodynamic equations using adaptive mesh refinement (AMR) techniques. We show AMR simulations of NS binary inspiral and coalescence carried out on a workstation having an accuracy equivalent to that of a 1025³ regular unigrid simulation, which is, to the best of our knowledge, larger than all previous simulations of similar NS systems on supercomputers. We believe the capability opens new possibilities in general relativistic simulations.

It has been conjectured that in head-on collisions of neutron stars (NSs), the merged object would not collapse promptly even if the total mass is higher than the maximum stable mass of a cold NS. In this paper, we show that the reverse is true: even if the total mass is less than the maximum stable mass, the merged object can collapse promptly. We demonstrate this for the case of NSs with a realistic equation of state (EOS) (the Lattimer-Swesty EOS) in head-on and near head-on collisions. We propose a “prompt collapse conjecture” for a generic NS EOS for head-on and near head-on collisions.

Sensitive micropipet methods have been used to measure the elastic stretch modulus and bending rigidity of biomembranes studded with water-soluble polymers. The fully extended lengths of the chemically grafted chains ranged from 10–50× the length of the embedding membrane lipid. Concentrations of the polymer were varied from 1–10× the surface density needed for isolated chains to touch, nominally satisfying the scaling theory requirement for semidilute brushes. Over this range, the membrane stretch modulus was unchanged by the polymer layers, but the bending rigidity increased by as much as 10k_BT. Surprisingly, the increase in rigidity deviated significantly from scaling theory predictions, revealing a large marginal brush regime between dilute mushrooms and a semidilute brush.

We introduce a new method to measure the energetics and range of weak biochemical bonds using functionalized vesicles. Large bilayer regions are held in molecular proximity by osmotic depletion forces to enable rapid specific bonding. By fixing an electrical charge to the tethering site of the functional group on one surface, persistent adhesion of the vesicles after removal of the depletion stress is titrated against the clamped electrostatic potential of the opposite surface. We demonstrate the method with DNA bases and obtain new information on the range of their specific interactions.

Phase-contrast microscopy is used to monitor the shapes of micron-scale fluid-phase phospholipid-bilayer vesicles in an aqueous solution. At fixed temperature, each vesicle undergoes thermal shape fluctuations. We are able, experimentally, to characterize the thermal shape ensemble by digitizing the vesicle outline in real time and storing the time sequence of images. Analysis of this ensemble using the area-difference-elasticity (ADE) model of vesicle shapes allows us to associate (map) each time sequence to a point in the zero-temperature (shape) phase diagram. Changing the laboratory temperature modifies the control parameters (area, volume, etc.) of each vesicle, so it sweeps out a trajectory across the theoretical phase diagram. It is a nontrivial test of the ADE model to check that these trajectories remain confined to regions of the phase diagram where the corresponding shapes are locally stable. In particular, we study the thermal trajectories of three prolate vesicles which, upon heating, experienced a mechanical instability leading to budding. We verify that the position of the observed instability and the geometry of the budded shape are in reasonable accord with the theoretical predictions. The inability of previous experiments to detect the ``hidden'' control parameters (relaxed area difference and spontaneous curvature) make this the first direct quantitative confrontation between vesicle-shape theory and experiment.

We report the first systematic observations of precursor effects in shape transitions of phospholipid-bilayer vesicles in aqueous solution. Vesicles change abruptly, as temperature T is raised, from a prolate ellipsoidal shape to a “budded” shape consisting of two unequal spheres connected by a narrow neck. On the low- T side of this transition, we see large thermal shape fluctuations (quasicritical fluctuations) and long relaxation times (quasicritical slowing down), which may be interpreted, in the context of a φ⁶ Landau theory, as the fluctuations of a metastable state near its spinodal instability.

Sensitive micropipet methods have been used to measure the relation between tension and the projected surface area in fluid membranes of vesicles over a 4-order-of-magnitude range in tension (10^-3–10 dyn/cm). In the low-tension regime (<0.5 dyn/cm), the data confirm the prediction of equilibrium theory that the projected area should increase logarithmically with tension as shape fluctuations become progressively restricted. The slope of log(tension) versus area dilation yields and the elastic bending modulus of the membrane. In the high-tension regime, the projected area crosses over to vary linearly with tension due to direct expansion of area per molecule.

We discuss the interaction of a slow electron with the surface of a semi-infinite dielectric with dielectric constant that differs from unity by virtue of the presence of an infrared-active TO phonon. We obtain an expression for the effective interaction energy between the electron and the surface which reduces to the expression obtained from image-potential theory when the electron is far from the surface, either inside or outside the crystal. When the electron is near the surface, the effective potential differs from the image potential and becomes nonlocal. The form of the image potential is obtained by adapting to the present problem a method used by Lee, Low, and Pines in bulk polaron theory. We have applied the theory to the study of the binding of electrons to the crystal surface produced by the coupling of the electron to surface optical phonons and bulk LO phonons. We consider both the case where the electron is outside the crystal and trapped on the surface (the exterior-surface polaron) and the case where it is on the inside (the interior-surface polaron).

We describe a quantum-mechanical theory of the inelastic scattering of low-energy electrons by multiphonon processes, from the surface of a semi-infinite crystal. A model introduced in an earlier paper is also employed in this work. The model describes the interaction of an incident low-energy electron with surface optical phonons by means of the macroscopic electric field set up outside the crystal by the ion motion. The model may be used to describe scattering either from ionic crystals, such as ZnO, or from nonionic crystals. In this paper, we find an explicit expression for the wave function of the outgoing electron, and we obtain an expression for the probability that n phonons are created or absorbed in the scattering process. Two cases are considered. First we examine the cross section for scattering off thermal phonons, and second from a coherent surface wave excited by external means. For the first case, our result agrees with the earlier semiclassical theory of Lucas and Sunjic. However, the model here is more general than theirs, since it is fully quantum mechanical. We show explicitly that the energy-loss cross section is proportional to the intensity of the specular beam, for scattering off both ionic and covalent crystals. For the second case (scattering from surface optical phonons generated coherently by an external source), we obtain a closed expression for the cross section. The physical origin of differences between the expressions is discussed.

The purpose of this paper is to present a quantum-mechanical theory of the inelastic scattering of slow electrons by long-wavelength surface optical phonons for simple models of an ionic crystal and for a nonionic crystal such as silicon. It is argued that a quantum-mechanical approach is necessary for this problem. However, the expression we obtain for the one-phonon cross section is found to be identical to the one that follows from the earlier classical theory of Lucas and co-workers, provided one replaces their parameter P₀ by the quantum-mechanical reflection coefficient for specular reflection. The angular distribution of the scattered electrons and the energy dependence of the one-phonon cross section are discussed for the case of ZnO and silicon, where the surface optical modes have a very different character. For the surface mode in silicon, we define a dipole-moment effective charge, which is nonzero by virtue of the absence of inversion symmetry in the surface region. A quantitative estimate of the magnitude of this parameter is extracted from the data of Ibach.

Studies performed on the conduction and switching phenomena in films of certain amorphous chalcogenide semiconductors indicate that the electrical switching may be associated with a field-influenced dielectric phase transition. The normalized conduction found at voltages below switching displays an Ohmic and an exponential region, both associated with the same conduction process. This conduction is independent of frequency from dc to 100 kHz.