Computationally efficient methods for modelling laser wakefield acceleration in the blowout regime

Electron self-injection and acceleration until dephasing in the blowout regime is studied for a set of initial conditions typical of recent experiments with 100 terawatt-class lasers. Two different approaches to computationally efficient, fully explicit, three-dimensional particle-in-cell modelling are examined. First, the Cartesian code VORPAL using a perfect-dispersion electromagnetic solver precisely describes the laser pulse and bubble dynamics, taking advantage of coarser resolution in the propagation direction, with a proportionally larger time step. Using third-order splines for macroparticles helps suppress the sampling noise while keeping the usage of computational resources modest. The second way to reduce the simulation load is using reduced-geometry codes. In our case, the quasi-cylindrical code CALDER-CIRC uses decomposition of fields and currents into a set of poloidal modes, while the macroparticles move in the Cartesian 3D space. Cylindrical symmetry of the interaction allows using just two modes, reducing the computational load to roughly that of a planar Cartesian simulation while preserving the 3D nature of the interaction. This significant economy of resources allows using fine resolution in the direction of propagation and a small time step, making numerical dispersion vanishingly small, together with a large number of particles per cell, enabling good particle statistics. Quantitative agreement of the two simulations indicates that they are free of numerical artefacts. Both approaches thus retrieve physically correct evolution of the plasma bubble, recovering the intrinsic connection of electron self-injection to the nonlinear optical evolution of the driver

Spectral Bandwidth Reduction of Thomson Scattered Light by Pulse Chirping

Based on single particle tracking in the framework of classical Thomson scattering with incoherent superposition, we developed a fully relativistic, three dimensional numerical code that calculates and quantifies the characteristics of emitted radiation when a relativistic electron beam collides head-on with a focused counter-propagating intense laser field. The developed code has been benchmarked against analytical expressions, based on the plane wave approximation to the laser field, derived in (1). For sufficiently long duration laser pulses, we find that the scattered radiation spectrum is broadened due to interferences arising from the pulsed nature of the laser. We show that by appropriately chirping the scattering laser pulse, the spectral broadening could be minimized.Comment: 11 pages, 3 figures, 25 reference

An Exactly Conservative Integrator for the n-Body Problem

The two-dimensional n-body problem of classical mechanics is a non-integrable Hamiltonian system for n > 2. Traditional numerical integration algorithms, which are polynomials in the time step, typically lead to systematic drifts in the computed value of the total energy and angular momentum. Even symplectic integration schemes exactly conserve only an approximate Hamiltonian. We present an algorithm that conserves the true Hamiltonian and the total angular momentum to machine precision. It is derived by applying conventional discretizations in a new space obtained by transformation of the dependent variables. We develop the method first for the restricted circular three-body problem, then for the general two-dimensional three-body problem, and finally for the planar n-body problem. Jacobi coordinates are used to reduce the two-dimensional n-body problem to an (n-1)-body problem that incorporates the constant linear momentum and center of mass constraints. For a four-body choreography, we find that a larger time step can be used with our conservative algorithm than with symplectic and conventional integrators.Comment: 17 pages, 3 figures; to appear in J. Phys. A.: Math. Ge

Effective Hamiltonian approach to adiabatic approximation in open systems

The adiabatic approximation in open systems is formulated through the effective Hamiltonian approach. By introducing an ancilla, we embed the open system dynamics into a non-Hermitian quantum dynamics of a composite system, the adiabatic evolution of the open system is then defined as the adiabatic dynamics of the composite system. Validity and invalidity conditions for this approximation are established and discussed. A High-order adiabatic approximation for open systems is introduced. As an example, the adiabatic condition for an open spin-$\frac 1 2$ particle in time-dependent magnetic fields is analyzed.Comment: 6 pages, 2 figure

The Robinson-Trautman Type III Prolongation Structure Contains K2_2

The minimal prolongation structure for the Robinson-Trautman equations of Petrov type III is shown to always include the infinite-dimensional, contragredient algebra, K$_2$, which is of infinite growth. Knowledge of faithful representations of this algebra would allow the determination of B\"acklund transformations to evolve new solutions.Comment: 20 pages, plain TeX, no figures, submitted to Commun. Math. Phy

Measles among migrants in the European Union and the European Economic Area

Aims: Progress towards meeting the goal of measles elimination in the EU and the European Economic Area (EEA) by 2015 is being obstructed, as some children are either not immunized on time or never immunized. One group thought to be at increased risk of measles is migrants; however, the extent to which this is the case is poorly understood, due to a lack of data. This paper addresses this evidence gap by providing an overview of the burden of measles in migrant populations in the EU/EEA. Methods: Data were collected through a comprehensive literature review, a country survey of EU/EEA member states and information from measles experts gathered at an infectious disease workshop. Results: Our results showed incomplete data on measles in migrant populations, as national surveillance systems do not systematically record migration-specific information; however, evidence from the literature review and country survey suggested that some measles outbreaks in the EU/EEA were due to sub-optimal vaccination coverage in migrant populations. Conclusions: We conclude that it is essential that routine surveillance of measles cases and measles, mumps and rubella (MMR) vaccination coverage become strengthened, to capture migrant-specific data. These data can help to inform the provision of preventive services, which may need to reach out to vulnerable migrant populations that currently face barriers in accessing routine immunization and health services

Nonlinear Elasticity in Biological Gels

Unlike most synthetic materials, biological materials often stiffen as they are deformed. This nonlinear elastic response, critical for the physiological function of some tissues, has been documented since at least the 19th century, but the molecular structure and the design principles responsible for it are unknown. Current models for this response require geometrically complex ordered structures unique to each material. In this Article we show that a much simpler molecular theory accounts for strain stiffening in a wide range of molecularly distinct biopolymer gels formed from purified cytoskeletal and extracellular proteins. This theory shows that systems of semi-flexible chains such as filamentous proteins arranged in an open crosslinked meshwork invariably stiffen at low strains without the need for a specific architecture or multiple elements with different intrinsic stiffnesses.Comment: 23 pages, 5 figures, submitted to Natur

The Isgur-Wise function in a relativistic model for qQˉq\bar Q system

We use the Dirac equation with a ``(asymptotically free) Coulomb + (Lorentz scalar) linear '' potential to estimate the light quark wavefunction for $q\bar Q$ mesons in the limit $m_Q\to \infty$. We use these wavefunctions to calculate the Isgur-Wise function $\xi (v.v^\prime )$ for orbital and radial ground states in the phenomenologically interesting range $1\leq v.v^ \prime \leq 4$. We find a simple expression for the zero-recoil slope, $\xi^ \prime (1) =-1/2- \epsilon^2 /3$, where $\epsilon$ is the energy eigenvalue of the light quark, which can be identified with the $\bar\Lambda$ parameter of the Heavy Quark Effective Theory. This result implies an upper bound of $-1/2$ for the slope $\xi^\prime (1)$. Also, because for a very light quark $q (q=u, d)$ the size $\sqrt {}$ of the meson is determined mainly by the ``confining'' term in the potential $(\gamma_\circ \sigma r)$, the shape of $\xi_{u,d}(v.v^\prime )$ is seen to be mostly sensitive to the dimensionless ratio $\bar \Lambda_{u,d}^2/\sigma$. We present results for the ranges of parameters $150 MeV <\bar \Lambda_{u,d} <600 MeV$ $(\bar\Lambda_s \approx \bar\Lambda_{u,d}+100 MeV)$, $0.14 {GeV}^2 \leq \sigma \leq 0.25 {GeV}^2$ and light quark masses $m_u, m_d \approx 0, m_s=175 MeV$ and compare to existing experimental data and other theoretical estimates. Fits to the data give: ${\bar\Lambda_{u,d}}^2/\sigma =4.8\pm 1.7$, $-\xi^\prime_{u,d}(1)=2.4\pm 0.7$ and $\vert V_{cb} \vert \sqrt {\frac {\tau_B}{1.48 ps}}=0.050\pm 0.008$ [ARGUS '93]; ${\bar\Lambda_{u,d}}^2/\sigma = 3.4\pm 1.8$, $-\xi^\prime_{u,d}(1)=1.8\pm 0.7$ and $\vert V_{cb} \vert \sqrt { \frac {\tau_B}{1.48 ps}}=0.043\pm 0.008$ [CLEO '93]; ${\bar\Lambda_{u,d}}^2/Comment: 22 pages, Latex, 4 figures (not included) available by fax or via email upon reques

A statistical gap-filling method to interpolate global monthly surface ocean carbon dioxide data

We have developed a statistical gap-filling method adapted to the specific coverage and prop-erties of observed fugacity of surface ocean CO2(fCO2). We have used this method to interpolate the Sur-face Ocean CO2Atlas (SOCAT) v2 database on a 2.5832.58 global grid (south of 708N) for 1985–2011 atmonthly resolution. The method combines a spatial interpolation based on a ‘‘radius of influence’’ to deter-mine nearby similar fCO2values with temporal harmonic and cubic spline curve-fitting, and also fits long-term trends and seasonal cycles. Interannual variability is established using deviations of observations fromthe fitted trends and seasonal cycles. An uncertainty is computed for all interpolated values based on thespatial and temporal range of the interpolation. Tests of the method using model data show that it performsas well as or better than previous regional interpolation methods, but in addition it provides a near-globaland interannual coverage