The high power ferromagnetic resonance (FMR) response, as well as butterfly curves of the spin wave instability threshold microwave field amplitude hcrit versus in-plane static field H profiles, have been measured for Permalloy films with thicknesses of 104, 128, and 270nm at a nominal pumping frequency of 9.37GHz. The hcrit values range from about 1 to 7Oe. Both the resonance saturation response at the FMR field and the subsidiary absorption (SA) response for static fields below the FMR field are similar in appearance to those for bulk ferrites. Butterfly curves over the SA response region, while similar to those for ferrites, exhibit a film thickness dependent band edge cutoff effect not found in bulk ferrites. The SA butterfly curve data were analyzed on the basis of a spin wave instability theory adapted to thin films. The observed shift in the SA band edge cutoff with thickness agrees with calculations based on the thin film dispersion response and the assumption of first order instability processes with critical modes at one half the pumping frequency. The fitted SA spin wave linewidths give values consistent with metallic relaxation processes, but indicate critical modes with wave vectors that always make relatively small 0°–20° angles with the static field, very different from the critical modes for bulk ferrites. Three key conclusions from this work are (1) the nonlinear microwave FMR response in Permalloy films is a threshold effect related to well established spin wave instability processes, (2) the details of the SA response are controlled largely by the thin film spin wave dispersion, and (3) these nonlinear processes occur for very small precession angles.

The spatial evolution of multi-peaked microwave magnetic envelope solitons in a thin yttrium iron garnet (YIG) film has been measured and analyzed. The experiments were done on a long and narrow 5-m-thick single-crystal YIG film strip. Double-peaked and triple-peaked magnetostatic backward volume wave soliton pulses were excited at a nominal carrier frequency of 7.0 GHz. The measurements utilized a movable inductive magnetodynamic probe detection system. The formation of these multi-peaked soliton (MPS) pulses is a two step process. First, an initial single large amplitude pulse gradually separates into two or more nonsolitonic peaks. After a certain propagation time, these nonsolitonic peaks evolve, in sequence, into solitonic peaks with constant phase (CP) and an overall stair-like profile. Typically, the larger amplitude peaks lead in time and become solitonic first. As the MPS signals propagate and decay, the peaks lose their CP character in reverse sequence. The region of existence for the "fully formed" MPS pulses for which all the individual peaks have CP character is extremely narrow, typically on the order of a few tenths of a millimeter. The velocities of the individual peaks scale linearly with the peak powers. A nonlinear response analysis of the peak velocity based on the method of envelopes gives a reasonable match to the data.

Fast-Neutron imaging with PCII V. Dangendorf A new imaging method that combines high-efficiency fast-neutron detection with sub-ns time resolution is presented. This is achieved by exploiting the high neutron detection efficiency of a thick scintillator and the fast timing capability and flexibility of light-pulse detection with a dedicated image intensifier. The neutron converter is a plastic scintillator slab or, alternatively, a scintillating fibre screen. The scintillator is optically coupled to a pulse counting image intensifier which measures the 2-dimensional position coordinates and the Time-Of-Flight (TOF) of each detected neutron with an intrinsic time resolution of less than 1 ns. Large-area imaging devices with high count rate capability can be obtained by lateral segmentation of the optical readout channels.

The age dynamics of a natural forest is modeled by the von-Foerster partial differential equation for the age density, while the seedling density is obtained as a solution of an integro-differential equation. This seedling density equation contains a small parameter, the ratio of seedling re-establishment time and the life span of an average tree in the forest. Several models are introduced that take into account various mortality curves and growth functions of trees, the dependence of seedlings carrying capacity on forest size, and different types of seedlings re-establishment. Asymptotic, analytic and numerical methods are used to solve typical example problems.

Abstract.Certain models describing the age dynamics of a natural forest give rise to nonlinear integro-differential equations for the seedlings density as a function of time. The special feature of the problem is that corresponding solutions have non-smooth second derivatives. Since the biological model contains a small parameter, a perturbation method can be used to find an asymptotic solution. Banach's fixed point theorem is used to prove existence and uniqueness of the solution, the convergence of a numerical scheme, and the validity of the asymptotic approximation.In an example numerical and asymptotic approximations are compared for various choices of time steps.