RADIATIVE SIGNATURES OF RELATIVISTIC SHOCKS

Particle-in-cell simulations of relativistic, weakly magnetized collisionless shocks show that particles can gain energy by repeatedly crossing the shock front. This requires scattering off self-generated small length-scale magnetic fluctuations. The radiative signature of this first-order Fermi acceleration mechanism is important for models of both the prompt and afterglow emission in gamma-ray bursts and depends on the strength parameter a = lambda e/delta B/mc(2) of the fluctuations (lambda is the length scale and vertical bar delta B vertical bar is the magnitude of the fluctuations). For electrons (and positrons), acceleration saturates when the radiative losses produced by the scattering cannot be compensated by the energy gained on crossing the shock. We show that this sets an upper limit on both the electron Lorentz factor gamma <10(6) (n/1 cm(-3))(-1/6)(-1/6) and on the energy of the photons radiated during the scattering process h omega(max) <40Max(a, 1)(n/1 cm(-3))(1/6)(-1/6) eV, where n is the number density of the plasma and (gamma) over bar is the thermal Lorentz factor of the downstream plasma, provided a <a(crit) similar to 10(6). This rules out "jitter" radiation on self-excited fluctuations with a <I as a source of gamma rays, although high-energy photons might still be produced when the jitter photons are upscattered in an analog of the synchrotron self-Compton process. In fluctuations with a > 1, radiation is generated by the standard synchrotron mechanism, and the maximum photon energy rises linearly with a, until saturating at 70 MeV, when a = a(crit).

On the maximum energy of shock-accelerated cosmic rays at ultra-relativistic shocks

The maximum energy to which cosmic rays can be accelerated at weakly magnetised ultra-relativistic shocks is investigated. We demonstrate that for such shocks, in which the scattering of energetic particles is mediated exclusively by ion skin-depth scale structures, as might be expected for a Weibel-mediated shock, there is an intrinsic limit on the maximum energy to which particles can be accelerated. This maximum energy is determined from the requirement that particles must be isotropized in the downstream plasma frame before the mean field transports them far downstream, and falls considerably short of what is required to produce ultra-high-energy cosmic rays. To circumvent this limit, a highly disorganized field is required on larger scales. The growth of cosmic ray-induced instabilities on wavelengths much longer than the ion-plasma skin depth, both upstream and downstream of the shock, is considered. While these instabilities may play an important role in magnetic field amplification at relativistic shocks, on scales comparable to the gyroradius of the most energetic particles, the calculated growth rates have insufficient time to modify the scattering. Since strong modification is a necessary condition for particles in the downstream region to re-cross the shock, in the absence of an alternative scattering mechanism, these results imply that acceleration to higher energies is ruled out. If weakly magnetized ultra-relativistic shocks are disfavoured as high-energy particle accelerators in general, the search for potential sources of ultra-high-energy cosmic rays can be narrowed.

Econometric analysis of stuctural systems with permanent and transitory shocks

This paper considers the implications of the permanent/transitory decomposition of shocks for identification of structural models in the general case where the model might contain more than one permanent structural shock. It provides a simple and intuitive generalization of the influential work of Blanchard and Quah [1989. The dynamic effects of aggregate demand and supply disturbances. The American Economic Review 79, 655–673], and shows that structural equations with known permanent shocks cannot contain error correction terms, thereby freeing up the latter to be used as instruments in estimating their parameters. The approach is illustrated by a re-examination of the identification schemes used by Wickens and Motto [2001. Estimating shocks and impulse response functions. Journal of Applied Econometrics 16, 371–387], Shapiro and Watson [1988. Sources of business cycle fluctuations. NBER Macroeconomics Annual 3, 111–148], King et al. [1991. Stochastic trends and economic fluctuations. American Economic Review 81, 819–840], Gali [1992. How well does the ISLM model fit postwar US data? Quarterly Journal of Economics 107, 709–735; 1999. Technology, employment, and the business cycle: Do technology shocks explain aggregate fluctuations? American Economic Review 89, 249–271] and Fisher [2006. The dynamic effects of neutral and investment-specific technology shocks. Journal of Political Economy 114, 413–451].

Identifying aggregate demand and supply shocks in a small open economy

The standard Blanchard-Quah (BQ) decomposition forces aggregate demand and supply shocks to be orthogonal. However, this assumption is problematic for a nation with an inflation target. The very notion of inflation targeting means that monetary policy reacts to changes in aggregate supply. This paper employs a modification of the BQ procedure that allows for correlated shifts in aggregate supply and demand. It is found that shocks to Australian aggregate demand and supply are highly correlated. The estimated shifts in the aggregate demand and supply curves are then used to measure the effects of inflation targeting on the Australian inflation rate and level of GDP.

Mesh-free approximations via the error reproducing kernel method and applications to nonlinear systems developing shocks

Error estimates for the error reproducing kernel method (ERKM) are provided. The ERKM is a mesh-free functional approximation scheme [A. Shaw, D. Roy, A NURBS-based error reproducing kernel method with applications in solid mechanics, Computational Mechanics (2006), to appear (available online)], wherein a targeted function and its derivatives are first approximated via non-uniform rational B-splines (NURBS) basis function. Errors in the NURBS approximation are then reproduced via a family of non-NURBS basis functions, constructed using a polynomial reproduction condition, and added to the NURBS approximation of the function obtained in the first step. In addition to the derivation of error estimates, convergence studies are undertaken for a couple of test boundary value problems with known exact solutions. The ERKM is next applied to a one-dimensional Burgers equation where, time evolution leads to a breakdown of the continuous solution and the appearance of a shock. Many available mesh-free schemes appear to be unable to capture this shock without numerical instability. However, given that any desired order of continuity is achievable through NURBS approximations, the ERKM can even accurately approximate functions with discontinuous derivatives. Moreover, due to the variation diminishing property of NURBS, it has advantages in representing sharp changes in gradients. This paper is focused on demonstrating this ability of ERKM via some numerical examples. Comparisons of some of the results with those via the standard form of the reproducing kernel particle method (RKPM) demonstrate the relative numerical advantages and accuracy of the ERKM.

Pressure shocks in relativistic viscous heat-conducting fluids

In this paper we have studied the propagation of pressure shocks in viscous, heat-conducting, relativistic fluids. Velocities of wave fronts and growth equations for the strength of the waves are obtained in the case of low and high temperatures with variable transport coefficients. On the basis of numerical integrations the growth equation results have been discussed. In the case of constant transport coefficients and for all admissible values of ratio of specific heats of the fluid, an analytical solution for the velocity of the wave as a function of distance along the normal trajectory to the wave front, has been obtained.

Some Exact-Solutions Describing Unsteady Plane Gas-Flows With Shocks

A new class of exact solutions of plane gasdynamic equations is found which describes piston-driven shocks into non-uniform media. The governing equations of these flows are taken in the coordinate system used earlier by Ustinov, and their similarity form is determined by the method of infinitesimal transformations. The solutions give shocks with velocities which either decay or grown in a finite or infinite time depending on the density distribution in the ambient medium, although their strength remains constant. The results of the present study are related to earlier investigations describing the propagation of shocks of constant strength into non-uniform media.

Studies on the international effects of real shocks

This doctoral thesis addresses the macroeconomic effects of real shocks in open economies in flexible exchange rate regimes. The first study of this thesis analyses the welfare effects of fiscal policy in a small open economy, where private and government consumption are substitutes in terms of private utility. The main findings are as follows: fiscal policy raises output, bringing it closer to its efficient level, but is not welfare-improving even though government spending directly affects private utility. The main reason for this is that the introduction of useful government spending implies a larger crowding-out effect on private consumption, when compared with the `pure waste' case. Utility decreases since one unit of government consumption yields less utility than one unit of private consumption. The second study of this thesis analyses the question of how the macroeconomic effects of fiscal policy in a small open economy depend on optimal intertemporal behaviour. The key result is that the effects of fiscal policy depend on the size of the elasticity of substitution between traded and nontraded goods. In particular, the sign of the current account response to fiscal policy depends on the interplay between the intertemporal elasticity of aggregate consumption and the elasticity of substitution between traded and nontraded goods. The third study analyses the consequences of productive government spending on the international transmission of fiscal policy. A standard result in the New Open Economy Macroeconomics literature is that a fiscal shock depreciates the exchange rate. I demonstrate that the response of the exchange rate depends on the productivity of government spending. If productivity is sufficiently high, a fiscal shock appreciates the exchange rate. It is also shown that the introduction of productive government spending increases both domestic and foreign welfare, when compared with the case where government spending is wasted. The fourth study analyses the question of how the international transmission of technology shocks depends on the specification of nominal rigidities. A growing body of empirical evidence suggests that a positive technology shock leads to a temporary decline in employment. In this study, I demonstrate that the open economy dimension can enhance the ability of sticky price models to account for the evidence. The reasoning is as follows. An improvement in technology appreciates the nominal exchange rate. Under producer-currency pricing, the exchange rate appreciation shifts global demand toward foreign goods away from domestic goods. This causes a temporary decline in domestic employment.

Transonic flutter, shocks, and parameter effects

There is a drop in the flutter boundary of an aeroelastic system placed in a transonic flow due to compressibility effects and is known as the transonic dip. Viscous effects can shift the lo-cation of the shock and depending on the shock strength the boundary layer may separate leading to changes in the flutter speed. An unsteady Euler flow solver coupled with the structural dynamic equations is used to understand the effect of shock on the transonic dip. The effect of various system parameters such as mass ratio, location of the center of mass, position of the elastic axis, ratio of uncoupled natural frequencies in heave and pitch are also studied. Steady turbulent flow results are presented to demonstrate the effect of viscosity on the location and strength of the shock.

Riemann shock tube: 1D normal shocks in air, simulations and experiments

This paper presents numerical simulation of the evolution of one-dimensional normal shocks, their propagation, reflection and interaction in air using a single diaphragm Riemann shock tube and validate them using experimental results. Mathematical model is derived for one-dimensional compressible flow of viscous and conducting medium. Dimensionless form of the mathematical model is used to construct space-time finite element processes based on minimization of the space-time residual functional. The space-time local approximation functions for space-time p-version hierarchical finite elements are considered in higher order GRAPHICS] spaces that permit desired order of global differentiability of local approximations in space and time. The resulting algebraic systems from this approach yield unconditionally positive-definite coefficient matrices, hence ensure unique numerical solution. The evolution is computed for a space-time strip corresponding to a time increment Delta t and then time march to obtain the evolution up to any desired value of time. Numerical studies are designed using recently invented hand-driven shock tube (Reddy tube) parameters, high/low side density and pressure values, high- and low-pressure side shock tube lengths, so that numerically computed results can be compared with actual experimental measurements.

A stabilization approach for mesh-free simulations of systems developing shocks or extreme strain localizations

A new stabilization scheme, based on a stochastic representation of the discretized field variables, is proposed with a view to reduce or even eliminate unphysical oscillations in the mesh-free numerical simulations of systems developing shocks or exhibiting localized bands of extreme deformation in the response. The origin of the stabilization scheme may be traced to nonlinear stochastic filtering and, consistent with a class of such filters, gain-based additive correction terms are applied to the simulated solution of the system, herein achieved through the element-free Galerkin method, in order to impose a set of constraints that help arresting the spurious oscillations. The method is numerically illustrated through its Applications to inviscid Burgers' equations, wherein shocks may develop as a result of intersections of the characteristics, and to a gradient plasticity model whose response is often characterized by a developing shear band as the external load is gradually increased. The potential of the method in stabilized yet accurate numerical simulations of such systems involving extreme gradient variations in the response is thus brought forth. (C) 2014 Elsevier Ltd. All rights reserved.