Effect of polymer surface activity on cavitation nuclei stability against dissolution

The persistence of acoustic cavitation in a pulsed wave ultrasound regime depends upon the ability of cavitation nuclei, i.e., bubbles, to survive the off time between pulses. Due to the dependence of bubble dissolution on surface tension, surface-active agents may affect the stability of bubbles against dissolution. In this study, measurements of bubble dissolution rates in solutions of the surface-active polymer poly(propyl acrylic acid) (PPAA) were conducted to test this premise. The surface activity of PPAA varies with solution pH and concentration of dissolved polymer molecules. The surface tension of PPAA solutions (55-72 dynes/cm) that associated with the polymer surface activity was measured using the Wilhelmy plate technique. Samples of these polymer solutions then were exposed to 1.1 MHz high intensity focused ultrasound, and the dissolution of bubbles created by inertial cavitation was monitored using an active cavitation detection scheme. Analysis of the pulse echo data demonstrated that bubble dissolution time was inversely proportional to the surface tension of the solution. Finally, comparison of the experimental results with dissolution times computed from the Epstein-Plesset equation suggests that the radii of residual bubbles from inertial cavitation increase as the surface tension decreases.     

Macrocycle-Derived Functional Xanthenes and Progress Towards Concurrent Detection of Glucose and Fructose

The detection of saccharides in biological media is of great current importance for the monitoring of disease states. We have previously reported that solutions of boronic acid-functionalized macrocycles form acyclic oligomeric materials in situ. The oligomers contain fluorescent xanthene moieties. Current efforts are aimed at modulating the spectroscopic responses of these materials for the analysis of specific sugars. We describe conditions whereby the xanthene boronic acids exhibit high colorimetric fructose selectivity. In contrast, at physiological levels selective glucose monitoring can be achieved via fluorescence. Additionally, we describe a method which exhibits promise for detecting both glucose and fructose at dual wavelengths in the UV-Vis region. Mechanistic rationale for each of these findings is presented.     

1+1 dimensional compactifications of string theory

We argue that stable, maximally symmetric compactifications of string theory to 1+1 dimensions are in conflict with holography. In particular, the finite horizon entropies of the Rindler wedge in 1+1 dimensional Minkowski and anti-de Sitter space, and of the de Sitter horizon in any dimension, are inconsistent with the symmetries of these spaces. The argument parallels one made recently by the same authors, in which we demonstrated the incompatibility of the finiteness of the entropy and the symmetries of de Sitter space in any dimension. If the horizon entropy is either infinite or zero, the conflict is resolved.     

Entropy-stabilized smectic C phase in a system of zigzag-shaped molecules

We report Monte Carlo simulations of a system of rigid zigzag-shaped molecules that demonstrate that simple excluded-volume interactions are sufficient to produce a fluid tilted lamellar [smectic C (SmC)] liquid crystal phase. The molecules are composed of three rigidly linked hard spherocylinders arranged in a zigzag fashion. By varying the zigzag angle we have mapped out the whole phase diagram as a function of pressure and zigzag angle Psi. For Psi between 35 degrees and 80 degrees our model simulation exhibits the SmC phase. This is the first conclusive evidence where steric interactions arising out of molecular shape alone induce the occurrence of the SmC phase for a wide range of zigzag angles. For smaller Psi, a transition from tilted crystal to crystal is observed.     

1/f Flux noise in Josephson phase qubits

We present a new method to measure 1/f noise in Josephson quantum bits (qubits) that yields low-frequency spectra below 1 Hz. A comparison of the noise taken at positive and negative bias of a phase qubit shows the dominant noise source to be flux noise and not junction critical-current noise, with a magnitude similar to that measured previously in other systems. Theoretical calculations show that the level of flux noise is not compatible with the standard model of noise from two-level state defects in the surface oxides of the films.     

Two-dimensional infrared spectroscopy detected by chirped pulse upconversion

A two-dimensional (2D) infrared spectrum of Mn2(CO)10 is measured by using chirped-pulse upconversion (CPU) of the nonlinear signal field plus a reference local oscillator. By converting the spectrum to the visible, a silicon CCD camera can be used. The method offers an attractive alternative to direct IR detection due to the technological maturity of silicon and its greater intrinsic detectivity over HgCdTe. Using CPU, we acquired a rephasing 2D IR spectrum in a few seconds.     

The effects of unequal diffusion coefficients on periodic travelling waves in oscillatory reaction-diffusion systems

Many oscillatory biological systems show periodic travelling waves. These are often modelled using coupled reaction-diffusion equations. However, the effects of different movement rates (diffusion coefficients) of the interacting components on the predictions of these equations are largely unknown. Here we investigate the ways in which varying the diffusion coefficients in such equations alters the wave speed, time period, wavelength, amplitude and stability of periodic wave solutions. We focus on two sets of kinetics that are commonly used in ecological applications: lambda-omega equations, which are the normal form of an oscillatory coupled reaction-diffusion system close to a supercritical Hopf bifurcation, and a standard predator-prey model. Our results show that changing the ratio of the diffusion coefficients can significantly alter the shape of the one-parameter family of periodic travelling wave solutions. The position of the boundary between stable and unstable waves also depends on the ratio of the diffusion coefficients: in all cases, stability changes through an Eckhaus (‘sideband’) instability. These effects are always symmetrical in the two diffusion coefficients for the lambda-omega equations, but are asymmetric in the predator-prey equations, especially when the limit cycle of the kinetics is of large amplitude. In particular, there are two separate regions of stable waves in the travelling wave family for some parameter values in the predator-prey scenario. Our results also show the existence of a one-parameter family of travelling waves, but not necessarily a Hopf bifurcation, for all values of the diffusion coefficients. Simulations of the full partial differential equations reveals that varying the ratio of the diffusion coefficients can significantly change the properties of periodic travelling waves that arise from particular wave generation mechanisms, and our analysis of the travelling wave families assists in the understanding of these effects.     

Geometric algebra techniques for general relativity

Geometric (Clifford) algebra provides an efficient mathematical language for describing physical problems. We formulate general relativity in this language. The resulting formalism combines the efficiency of differential forms with the straightforwardness of coordinate methods. We focus our attention on orthonormal frames and the associated connection bivector, using them to find the Schwarzschild and Kerr solutions, along with a detailed exposition of the Petrov types for the Weyl tensor.     

Social structure of Facebook networks

We study the social structure of Facebook “friendship” networks at one hundred American colleges and universities at a single point in time, and we examine the roles of user attributes–gender, class year, major, high school, and residence–at these institutions. We investigate the influence of common attributes at the dyad level in terms of assortativity coefficients and regression models. We then examine larger-scale groupings by detecting communities algorithmically and comparing them to network partitions based on user characteristics. We thereby examine the relative importance of different characteristics at different institutions, finding for example that common high school is more important to the social organization of large institutions and that the importance of common major varies significantly between institutions. Our calculations illustrate how microscopic and macroscopic perspectives give complementary insights on the social organization at universities and suggest future studies to investigate such phenomena further.