Photon Emission in a Cascade from Relativistic Protons Initiated by Residual Thermal Photons in Gamma-Ray Bursts

Gamma-ray bursts are generally considered to be the result of internal shocks generated in an inhomogeneous relativistic outflow that arises from a fireball. In such shocks, the Fermi acceleration of protons is naturally expected to be at least as efficient as that of electrons. We investigate the consequences of proton acceleration in the residual thermal photon field of a fireball, especially those on the emission spectra of photons. In contrast to most other studies, we do not invoke a direct electron acceleration in shock waves. We show that the residual radiation field of the fireball can ignite the photopion production and subsequent cascade, and that the photons emitted in this process further enhance the photon-initiated cascade. We find that Fermi accelerated protons with $\gtrsim 10^{13}$ eV efficiently bring their energy into pion production and subsequent photon emission. The particles cascading from the pions emit photons over a wide energy range. The photons emitted from electron--positron pairs distribute continuously from the GeV range down to the X-ray range, while muons can emit gamma-rays by synchrotron radiation with a break at around 1--10 MeV. We also discuss several radiation processes which may possibly produce a break feature in the MeV range, as observed in addition to muon synchrotron radiation.Comment: 25 pages, 9 fugures. to appear in Publications of the Astronomical Society of Japan 5

Computer simulations of cosmic-ray diffusion near supernova remnant shock waves

A plasma simulation model was used to study the resonant interactions between streaming cosmic-ray ions and a self-consistent spectrum of Alfven waves, such as might exist in the interstellar medium upstream of a supernova remnant shock wave. The computational model is a hybrid one, in which the background interstellar medium is an MHD fluid and the cosmic-rays are discrete kinetic particles. The particle sources for the electromagnetic fields are obtained by averaging over the fast cyclotron motions. When the perturbed magnetic field is larger than 10 percent of the background field, the macro- and microphysics are no longer correctly predicted by quasi-linear theory. The particles are trapped by the waves and show sharp jumps in their pitch-angles relative to the background magnetic field, and the effective ninety-degree scattering time for diffusion parallel to the background magnetic field is reduced to between 5 and 30 cyclotron periods. Simulation results suggest that Type 1 supernova remnants may be the principal sites of cosmic ray acceleration

Comparative dynamics in perfect-foresight models

Forecasting Techniques;Dynamic Models

Metastable Features of Economic Networks and Responses to Exogenous Shocks

It has been proved that network structure plays an important role in addressing a collective behaviour. In this paper we consider a network of firms and corporations and study its metastable features in an Ising based model. In our model, we observe that if in a recession the government imposes a demand shock to stimulate the network, metastable features shape its response. Actually we find that there is a minimum bound where demand shocks with a size below it are unable to trigger the market out from recession. We then investigate the impact of network characteristics on this minimum bound. We surprisingly observe that in a Watts-Strogatz network though the minimum bound depends on the average of the degrees, when translated into the economics language, such a bound is independent of the average degrees. This bound is about $0.44 \Delta$GDP, where $\Delta$GDP is the gap of GDP between recession and expansion. We examine our suggestions for the cases of the United States and the European Union in the recent recession, and compare them with the imposed stimulations. While stimulation in the US has been above our threshold, in the EU it has been far below our threshold. Beside providing a minimum bound for a successful stimulation, our study on the metastable features suggests that in the time of crisis there is a "golden time passage" in which the minimum bound for successful stimulation can be much lower. So, our study strongly suggests stimulations to be started within this time passage.Comment: 13 pages, 10 figures, accepted for publication in PloS On

The Outburst of the Blazar AO 0235+164 in 2006 December: Shock-in-Jet Interpretation

We present the results of polarimetric ($R$ band) and multicolor photometric ($BVRIJHK$) observations of the blazar AO 0235+16 during an outburst in 2006 December. The data reveal a short timescale of variability (several hours), which increases from optical to near-IR wavelengths; even shorter variations are detected in polarization. The flux density correlates with the degree of polarization, and at maximum degree of polarization the electric vector tends to align with the parsec-scale jet direction. We find that a variable component with a steady power-law spectral energy distribution and very high optical polarization (30-50%) is responsible for the variability. We interpret these properties of the blazar withina model of a transverse shock propagating down the jet. In this case a small change in the viewing angle of the jet, by $\lesssim 1^o$, and a decrease in the shocked plasma compression by a factor of $\sim$1.5 are sufficient to account for the variability.Comment: 22 pages, 8 figures, accepted for Ap

The rigidity of choice: lifetime savings under information-processing constraints

This paper studies the implications of information-processing limits on the consumption and savings behavior of households through time. It presents a dynamic model in which consumers rationally choose the size and scope of the information they want to process about their fi�nancial possibilities, constrained by a Shannon channel. The model predicts that people with higher degrees of risk aversion rationally choose higher information. This happens for precautionary reasons since, with fi�nite processing rate, risk averse consumers prefer to be well informed about their fi�nancial possibilities before implementing consumption plan. Moreover, numerical results show that consumers with processing capacity constraints have asymmetric responses to shocks, with negative shocks producing more persistent effects than positive ones. This asymmetry results into more savings. I show that the predictions of the model can be effectively used to study the impact of tax reforms on consumers spending. The results are qualitatively consistent with the evidence on tax rebates (2001, 2008).Consumption, Rational Inattention, Dynamic programming

Optimal Control Theory for Undergraduates

Dynamic optimization is widely used in financial economics, macroeconomics and resource economics. This is accounting for some tension between the undergraduate and graduate teaching of economics because most undergraduate programs still concentrate on static economic analysis. This paper shows how, with the help of the Microsoft Excel Solver tool, the principles of dynamic economics can be taught to students with minimal knowledge of calculus. As it is assumed that the reader has no prior knowledge of optimal control theory, some attention is paid to the main concepts of dynamic optimization.Optimal Control Theory, Economic Education, Microsoft Excel

The impact of medical and nursing home expenses and social insurance

We consider a life-cycle model with idiosyncratic risk in labor earnings, out-of-pocket medical and nursing home expenses, and survival. Partial insurance is available through welfare, Medicaid, and social security. Calibrating the model to the United States, we find that 12 percent of aggregate savings is accumulated to finance and self-insure against old-age health expenses given the absence of complete public health care for the elderly and that nursing home expenses play an important role in the savings of the wealthy and on aggregate. Moreover, we find that the aggregate and distributional effects of public health care provision are highly dependent on the availability of other programs making up the social insurance system.

The Impact of Medical and Nursing Home Expenses and Social Insurance Policies on Savings and Inequality

We consider a life-cycle model with idiosyncratic risk in labor earnings, out-of-pocket medical and nursing home expenses, and survival. Partial insurance is available through welfare, Medicaid, and social security. Calibrating the model to the U.S., we find that nursing home expenses play an important role in the savings of the wealthy. In our policy analysis, we find that elimination of out-of-pocket expenses through public health care would reduce the capital stock by 12 percent, Medicaid and old-age welfare programs crowd out 44 percent of savings and greatly increase wealth inequality, and social security effects are influenced by out-of-pocket health expenses.social insurance; medical expenses, nursing home expenses; wealth inequality; savings