Momentum-space Monte Carlo

Using the quenched, reduced form of large-N field theories, we show that it is possible to directly measure momentum-space Green functions, via Monte Carlo, without going through the intermediate step of measurement in position space plus Fourier transformation. This promises to be useful tool for investigating the infrared structure of planar field theories. As an application (and test) of the method, we compute mass-gaps in the quenched U(N) × U(N) lattice chiral model, in D = 1 and 2 dimensions.     

Resonances in bounded media: Nonlinear and boundary effects

We study the response of nonlinear wave systems in bounded domains at or near resonance. There are typically two qualitatively distinct types of response which may be observed relating to whether or not higher harmonics are themselves resonant. We introduce a variety of nonlinear model problems at or near resonance and study the subsequent response. We explain how the features of this problem such as the form of nonlinearity, boundary conditions, and the nature of spectrum play a fundamental role in the qualitative nature of the response. Numerical simulations are carried out to provide further explanation and comparison with analytic approximations. The results of this study provide a better understanding of the impact and interplay between nonlinear and boundary effects and thus in turn will contribute to providing new insights into various physically motivated problems in acoustics and other settings.     

Human reaction to vibrations from blasting activity – Norwegian exposure–effect relationships

Rock blasting may cause disturbances, fear, and annoyance in residential and community areas affected by such activities. These community reactions can be quite strong, even when the blasting activities and the resulting vibrations are unlikely to cause physical damage to building foundations or buildings. A socio-vibrational survey was undertaken to assess residential reactions to blasting activities. Vibration velocities were obtained for 520 respondent dwellings located in seven study areas, and compared to the residents’ assessments of environment quality. Even at low vibration values, many people report annoyance. Exposure–effect relationships with acceptable statistical error bands were obtained. The level of annoyance from long-term blasting activities (quarry blasting) was not higher than from finite periods of more intense blasting activities (road and rail tunnels). Providing information in advance of the blasting activities, can reduce community reactions. Self-reported sensitivity to vibrations was associated with significantly increased annoyance. Sensitivity to vibrations was uncorrelated with exposure to vibrations. Sensitivity to noise and sensitivity to vibration were moderately correlated.     

Resonances in Dispersive Wave Systems

Weakly nonlinear wave interactions under the assumption of a continuous, as opposed to discrete, spectrum of modes is studied. In particular, a general class of one-dimensional (1-D) dispersive systems containing weak quadratic nonlinearity is investigated. It is known that such systems can possess three-wave resonances, provided certain conditions on the wavenumber and frequency of the constituent modes are met. In the case of a continuous spectrum, it has been shown that an additional condition on the group velocities is required for a resonance to occur. Nonetheless, such so-called double resonances occur in a variety of physical regimes. A direct multiple scale analysis of a general model system is conducted. This leads to a system of three-wave equations analogous to those for the discrete case. Key distinctions include an asymmetry between the temporal evolution of the modes and a longer time scale of as opposed to O (ε t ). Extensions to additional dimensions and higher-order nonlinearities are then made. Numerical simulations are conducted for a variety of dispersions and nonlinearities providing qualitative and quantitative agreement.     

Superfluidity of neutron matter: (II). Triplet pairing

The possibility of neutron triplet pairing and superfluidity in neutron star matter is investigated, and the energy gap and corresponding critical temperature is calculated or estimated as a function of Fermi momentum or density. The calculations are performed for a “one-pion-exchange gaussian” potential, and compared with the results for neutron and proton singlet pairing and superfluidity calculated earlier.The results indicate that neutron superfluidity, corresponding specifically to ³P₂ state pairing, may exist in a high-density shell in the nuclear-matter region of a neutron star, i.e. for 1.6 × 10¹⁴g/cm³ < ρ < 1.4 × 10¹⁵g/cm³, and the maximum self-consistent energy gap is Δ⁰₁k_F ≈ 0.6 MeV and Δ⁰₃(k_F) ≈ 0.1 MeV for an effective mass $\text{m}{}^1\text{≈ 0.75}\text{and}\text{k}{}_{\mathrm{<mtext>F</mtext>}}\text{≈ 2.1}\text{fm}{}^{\mathrm{?1}}$, i.e. for a mas ? ≈ 5.2 × 10¹⁴g/cm³. For $\text{m}{}^1\text{= 1.0}$ we get correspondingly Δ⁰₁(k_F) ≈ 3.3 MeV and Δ⁰₃(k_F) ≈ 0.6 MeV for k_F ≈ 2.2 fm^?1.     

Stability analysis for a fully discrete spectral scheme for Boussinesq systems

In this paper we perform a stability analysis of a fully discrete numerical method for the solution of a family of Boussinesq systems, consisting of a Fourier collocation spectral method for the spatial discretization and a explicit fourth order Runge–Kutta (RK4) scheme for time integration. Our goal is to determine the influence of the parameters, associated to this family of systems, on the efficiency and accuracy of the numerical method. This analysis allows us to identify which regions in the parameter space are most appropriate for obtaining an efficient and accurate numerical solution. We show several numerical examples in order to validate the accuracy, stability and applicability of our MATLAB implementation of the numerical method.     

Evolution of Nonlinear Sloshing in a Tank Near Half the Fundamental Resonance

This article describes the evolution of shallow water waves in a tank that is closed at one end and is periodically forced at half the fundamental frequency at the other end. The nonlinear response occurs at the same order as the linear response and is governed by a forced Korteweg–de Vries ( K dV ) equation. Unlike the corresponding problem for a gas (or the hydraulic limit), there may be nonperiodic (beating) solutions and multiple steady solutions for the same frequency. The addition of a component at the fundamental frequency to the piston input can be used to cancel the nonlinear effects and leave only the linear response in the steady state.     

A note on the projectile charge dependence of inner shell ionisation of atoms by heavy charged particles

The formula for the binding of the electron to the impinging projectile in inner shell ionization of atoms by heavy charged particles in the static approximation, are generalized to arbitrary electron wavefunctions. The effect is calculated for K-shell electrons using relativistic wavefunctions. A qualitative difference in the impact parameter dependency of the effect between light and heavy target are found.