An alternative to the Allen-Cahn phase field model for interfaces in solids - numerical efficiency

The derivation of the Allen-Cahn and Cahn-Hilliard equations is based on the Clausius-Duhem inequality. This is not a derivation in the strict sense of the word, since other phase field equations can be fomulated satisfying this inequality. Motivated by the form of sharp interface problems, we formulate such an alternative equation and compare the properties of the models for the evolution of phase interfaces in solids, which consist of the elasticity equations and the Allen-Cahn equation or the alternative equation. We find that numerical simulations of phase interfaces with small interface energy based on the alternative model are more effective then simulations based on the Allen-Cahn model.Comment: arXiv admin note: text overlap with arXiv:1505.0544

On the origin of probability in quantum mechanics

I give a brief introduction to many worlds or "no wavefunction collapse" quantum mechanics, suitable for non-specialists. I then discuss the origin of probability in such formulations, distinguishing between objective and subjective notions of probability.Comment: 7 pages, 2 figures. This version to appear as a Brief Review in Modern Physics Letter

Permutation Classes of Polynomial Growth

A pattern class is a set of permutations closed under the formation of subpermutations. Such classes can be characterised as those permutations not involving a particular set of forbidden permutations. A simple collection of necessary and sufficient conditions on sets of forbidden permutations which ensure that the associated pattern class is of polynomial growth is determined. A catalogue of all such sets of forbidden permutations having three or fewer elements is provided together with bounds on the degrees of the associated enumerating polynomials.Comment: 17 pages, 4 figure

Recognition of viral glycoproteins by influenza A-specific cross- reactive cytolytic T lymphocytes

Two populations of cytolytic T lymphocytes (CTL) generated after influenza A virus infection can be distinguished into one with specificity for the sensitizing hemagglutinin type and a second with cross-reactivity for antigens induced by other type-A influenza viruses. The molecules carrying the antigenic determinants recognized by the cross-reactive CTL were studied. In L-929 cells abortively infected with fowl plague virus, matrix (M) protein synthesis is specifically inhibited, whereas the envelope glycoproteins, hemagglutinin and neuraminidase, are synthesized and incorporated into the plasma membrane. These target cells were lysed by cross-reactive CTL. The envelope proteins of type A/Victoria virus were separated from the other virion components and reconstituted into lipid vesicles that lacked M protein that subsequently were used to prepare artificial target cells. Target-cell formation with vesicles was achieved by addition of fusion-active Sendai virus. These artificial target cells were also susceptible to lysis by cross-reactive CTL. In contrast to previous observations that suggested that the M protein of influenza viruses is recognized by these effector cells, we present evidence that the antigencic determinants induced by the viral glycoproteins are recognized

N=2 Supermultiplet of Currents and Anomalous Transformations in Supersymmetric Gauge Theory

We examine some properties of supermultiplet consisting of the U(1)_{J} current, extended supercurrents, energy-momentum tensor and the central charge in N=2 supersymmetric Yang-Mills theory. The superconformal improvement requires adding another supermultiplet beginning with the U(1)_{R} current. We determine the anomalous (quantum mechanical) supersymmetry transformation associated with the central charge and the energy-momentum tensor to one-loop order.Comment: 8 pages, LaTe

Statistical mechanics of non-hamiltonian systems: Traffic flow

Statistical mechanics of a small system of cars on a single-lane road is developed. The system is not characterized by a Hamiltonian but by a conditional probability of a velocity of a car for the given velocity and distance of the car ahead. Distribution of car velocities for various densities of a group of cars are derived as well as probabilities of density fluctuations of the group for different velocities. For high braking abilities of cars free-flow and congested phases are found. Platoons of cars are formed for system of cars with inefficient brakes. A first order phase transition between free-flow and congested phase is suggested.Comment: 12 pages, 6 figures, presented at TGF, Paris, 200

Proton magnetic resonance imaging with a nitrogen-vacancy spin sensor

Nuclear magnetic resonance (NMR) imaging with nanometer resolution requires new detection techniques with sensitivity well beyond the capability of conventional inductive detection. Here, we demonstrate two dimensional imaging of $^1$H NMR from an organic test sample using a single nitrogen-vacancy center in diamond as the sensor. The NV center detects the oscillating magnetic field from precessing protons in the sample as the sample is scanned past the NV center. A spatial resolution of 12 nm is shown, limited primarily by the scan accuracy. With further development, NV-detected magnetic resonance imaging could lead to a new tool for three-dimensional imaging of complex nanostructures, including biomolecules.Comment: Main text: 19 pages including 5 figures Supplementary Information: 9 pages including 3 figure

The enumeration of permutations avoiding 2143 and 4231

We enumerate the pattern class Av(2143, 4231) and completely describe its permutations. The main tools are simple permutations and monotone grid classes

Turbulence damping as a measure of the flow dimensionality

The dimensionality of turbulence in fluid layers determines their properties. We study electromagnetically driven flows in finite depth fluid layers and show that eddy viscosity, which appears as a result of three-dimensional motions, leads to increased bottom damping. The anomaly coefficient, which characterizes the deviation of damping from the one derived using a quasi-two-dimensional model, can be used as a measure of the flow dimensionality. Experiments in turbulent layers show that when the anomaly coefficient becomes high, the turbulent inverse energy cascade is suppressed. In the opposite limit turbulence can self-organize into a coherent flow.Comment: 4 pages, 4 figure