Extraction of the proton charge radius from experiments

Static properties of hadrons such as their radii and other moments of the electric and magnetic distributions can only be extracted using theoretical methods and not directly measured from experiments. As a result, discrepancies between the extracted values from different precision measurements can exist. The proton charge radius, $r_p$, which is either extracted from electron proton elastic scattering data or from hydrogen atom spectroscopy seems to be no exception. The value $r_p = 0.84087(39)$ fm extracted from muonic hydrogen spectroscopy is about 4% smaller than that obtained from electron proton scattering or standard hydrogen spectroscopy. The resolution of this so called proton radius puzzle has been attempted in many different ways over the past six years. The present article reviews these attempts with a focus on the methods of extracting the radius.Comment: Mini review, 14 pages, 1 figur

Sensitivity analysis for shape perturbation of cavity or internal crack using BIE and adjoint variable approach

This paper deals with the application of the adjoint variable approach to sensitivity analysis of objective functions used for defect detection from knowledge of supplementary boundary data, in connection with the use of BIE/BEM formulations for the relevant forward problem. The main objective is to establish expressions for crack shape sensitivity, based on the adjoint variable approach, that are suitable for BEM implementation. In order to do so, it is useful to consider first the case of a cavity defect, for which such boundary-only sensitivity expressions are obtained for general initial geometry and shape perturbations. The analysis made in the cavity defect case is then seen to break down in the limiting case of a crack. However, a closer analysis reveals that sensitivity formulas suitable for BEM implementation can still be established. First, particular sensitivity formulas are obtained for special shape transformations (translation, rotation or expansion of the crack) for either two- or three-dimensional geometries which, except for the case of crack expansion together with dynamical governing equations, are made only of surface integrals (three-dimensional geometries) or line integrals (two-dimensional geometries). Next, arbitrary shape transformations are accommodated by using an additive decomposition of the transformation velocity over a tubular neighbourhood of the crack front, which leads to sensitivity formulas. This leads to sensitivity formulas involving integrals on the crack, the tubular neighbourhood and its boundary. Finally, the limiting case of the latter results when the tubular neighbourhood shrinks around the crack front is shown to yield a sensitivity formula involving the stress intensity factors of both the forward and the adjoint solutions. Classical path-independent integrals are recovered as special cases. The main exposition is done in connection with the scalar transient wave equation. The results are then extended to the linear time-domain elastodynamics framework. Linear static governing equations are contained as obvious special cases. Numerical results for crack shape sensitivity computation are presented for two-dimensional time-domain elastodynamics

Relations de dispersion pour des chaînes linéaire comportant des interactions harmoniques auto-similaires

Many systems in nature have arborescent and bifurcated structures such as trees, fern, snails, lungs, the blood vessel system, etc. and look self-similar over a wide range of scales. Which are the mechanical and dynamic properties that evolution has optimized by choosing self-similarity? How can we describe the mechanics of self-similar structures in the static and dynamic framework? Physical systems with self-similarity as a symmetry property require the introduction of non-local particle-particle interactions and a (quasi-) continuous distribution of mass. We construct self-similar functions and linear operators such as a self-similar variant of the Laplacian and of the D'Alembertian wave operator. The obtained self-similar linear wave equation describes the dynamics of a quasi-continuous linear chain of infinite length with a spatially self-similar distribution of nonlocal inter-particle springs. The self-similarity of the nonlocal harmonic particle-particle interactions results in a dispersion relation of the form of a Weierstrass-Mandelbrot function which exhibits self-similar and fractal features. We deduce a continuum approximation that links the self-similar Laplacian to fractional integrals and which yields in the low-frequency regime a power law frequency dependence for the oscillator density. For details of the present model we refer to our recent paper (Michelitsch et al., Phys. Rev. E 80, 011135 (2009))

Random walks with long-range steps generated by functions of Laplacian matrices

In this paper, we explore different Markovian random walk strategies on networks with transition probabilities between nodes defined in terms of functions of the Laplacian matrix. We generalize random walk strategies with local information in the Laplacian matrix, that describes the connections of a network, to a dynamics determined by functions of this matrix. The resulting processes are non-local allowing transitions of the random walker from one node to nodes beyond its nearest neighbors. We find that only two types of Laplacian functions are admissible with distinct behaviors for long-range steps in the infinite network limit: type (i) functions generate Brownian motions, type (ii) functions L\'evy flights. For this asymptotic long-range step behavior only the lowest non-vanishing order of the Laplacian function is relevant, namely first order for type (i), and fractional order for type (ii) functions. In the first part, we discuss spectral properties of the Laplacian matrix and a series of relations that are maintained by a particular type of functions that allow to define random walks on any type of undirected connected networks. Once described general properties, we explore characteristics of random walk strategies that emerge from particular cases with functions defined in terms of exponentials, logarithms and powers of the Laplacian as well as relations of these dynamics with non-local strategies like L\'evy flights and fractional transport. Finally, we analyze the global capacity of these random walk strategies to explore networks like lattices and trees and different types of random and complex networks.Comment: 33 pages, 5 figure

Gravitational Equilibrium in the Presence of a Positive Cosmological Constant

We reconsider the virial theorem in the presence of a positive cosmological constant Lambda. Assuming steady state, we derive an inequality of the form rho >= A (Lambda / 4 pi GN) for the mean density rho of the astrophysical object. With a minimum at Asphere = 2, its value can increase by several orders of magnitude as the shape of the object deviates from a spherically symmetric one. This, among others, indicates that flattened matter distributions like e.g. clusters or superclusters, with low density, cannot be in gravitational equilibrium.Comment: 7 pages, no figure

Evidence of Pentaquark States from K+ N Scattering Data?

Motivated by the recent experimental evidence of the exotic B = S = +1 baryonic state Theta(1540), we examine the older existing data on K+ N elastic scattering through the time delay method. We find positive peaks in time delay around 1.545 and 1.6 GeV in the D03 and P01 partial waves of K+ N scattering respectively, in agreement with experiments. We also find an indication of the J=3/2 Theta* spin-orbit partner to the Theta, in the P03 partial wave at 1.6 GeV. We discuss the pros and contras of these findings in support of the interpretation of these peaks as possible exotics.Comment: 10 pages, 4 figure

A note on the Cops & Robber game on graphs embedded in non-orientable surfaces

The Cops and Robber game is played on undirected finite graphs. A number of cops and one robber are positioned on vertices and take turns in sliding along edges. The cops win if they can catch the robber. The minimum number of cops needed to win on a graph is called its cop number. It is known that the cop number of a graph embedded on a surface $X$ of genus $g$ is at most $3g/2 + 3$, if $X$ is orientable (Schroeder 2004), and at most $2g+1$, otherwise (Nowakowski & Schroeder 1997). We improve the bounds for non-orientable surfaces by reduction to the orientable case using covering spaces. As corollaries, using Schroeder's results, we obtain the following: the maximum cop number of graphs embeddable in the projective plane is 3; the cop number of graphs embeddable in the Klein Bottle is at most 4, and an upper bound is $3g/2 + 3/2$ for all other $g$.Comment: 5 pages, 1 figur

Exact Solution of the Discrete (1+1)-dimensional RSOS Model with Field and Surface Interactions

We present the solution of a linear Restricted Solid--on--Solid (RSOS) model in a field. Aside from the origins of this model in the context of describing the phase boundary in a magnet, interest also comes from more recent work on the steady state of non-equilibrium models of molecular motors. While similar to a previously solved (non-restricted) SOS model in its physical behaviour, mathematically the solution is more complex. Involving basic hypergeometric functions ${}_3\phi_2$, it introduces a new form of solution to the lexicon of directed lattice path generating functions.Comment: 10 pages, 2 figure

Sub-nanosecond signal propagation in anisotropy engineered nanomagnetic logic chains

Energy efficient nanomagnetic logic (NML) computing architectures propagate and process binary information by relying on dipolar field coupling to reorient closely-spaced nanoscale magnets. Signal propagation in nanomagnet chains of various sizes, shapes, and magnetic orientations has been previously characterized by static magnetic imaging experiments with low-speed adiabatic operation; however the mechanisms which determine the final state and their reproducibility over millions of cycles in high-speed operation (sub-ns time scale) have yet to be experimentally investigated. Monitoring NML operation at its ultimate intrinsic speed reveals features undetectable by conventional static imaging including individual nanomagnetic switching events and systematic error nucleation during signal propagation. Here, we present a new study of NML operation in a high speed regime at fast repetition rates. We perform direct imaging of digital signal propagation in permalloy nanomagnet chains with varying degrees of shape-engineered biaxial anisotropy using full-field magnetic soft x-ray transmission microscopy after applying single nanosecond magnetic field pulses. Further, we use time-resolved magnetic photo-emission electron microscopy to evaluate the sub-nanosecond dipolar coupling signal propagation dynamics in optimized chains with 100 ps time resolution as they are cycled with nanosecond field pulses at a rate of 3 MHz. An intrinsic switching time of 100 ps per magnet is observed. These experiments, and accompanying macro-spin and micromagnetic simulations, reveal the underlying physics of NML architectures repetitively operated on nanosecond timescales and identify relevant engineering parameters to optimize performance and reliability.Comment: Main article (22 pages, 4 figures), Supplementary info (11 pages, 5 sections