Hamiltonian and self-adjoint control systems

This paper outlines results recently obtained in the problem of determining when an input-output map has a Hamiltonian realization. The results are obtained in terms of variations of the system trajectories, as in the solution of the Inverse Problem in Classical Mechanics. The variational and adjoint systems are introduced for any given nonlinear system, and self-adjointness defined. Under appropriate conditions self-adjointness characterizes Hamiltonian systems. A further characterization is given directly in terms of variations in the input and output trajectories, proving an earlier conjecture by the first author

Numerical simulations of multiple scattering of the f−f-mode by flux tubes

We use numerial simulations to study the absorption and phase shift of surface-gravity waves caused by groups of magnetic flux tubes. The dependence of the scattering coefficients with the distance between the tubes and their positions is analyzed for several cases with two or three flux tubes embedded in a quiet Sun atmosphere. The results are compared with those obtained neglecting completely or partially multiple scattering effects. We show that multiple scattering has a significant impact on the absorption measurements and tends to reduce the phase shift. We also consider more general cases of ensembles of randomly distributed flux tubes, and we have evaluated the effects on the scattering measurements of changing the number of tubes included in the bundle and the average distance between flux tubes. We find that for the longest wavelength incoming waves multiple scattering enhances the absorption, and its efficiency increases with the number of flux tubes and the reduction of the distance between them.Comment: Accepted for publication in The Astrophysical Journa

Evaluation of the capability of local helioseismology to discern between monolithic and spaghetti sunspot models

The helioseismic properties of the wave scattering generated by monolithic and spaghetti sunspots are analyzed by means of numerical simulations. In these computations, an incident f or p1 mode travels through the sunspot model, which produces absorption and phase shift of the waves. The scattering is studied by inspecting the wavefield, computing travel-time shifts, and performing Fourier-Hankel analysis. The comparison between the results obtained for both sunspot models reveals that the differences in the absorption coefficient can be detected above noise level. The spaghetti model produces an steep increase of the phase shift with the degree of the mode at short wavelengths, while mode-mixing is more efficient for the monolithic model. These results provide a clue for what to look for in solar observations to discern the constitution of sunspots between the proposed monolithic and spaghetti models.Comment: Accepted for publication in The Astrophysical Journa

Improved test methods for determining lightning-induced voltages in aircraft

A lumped parameter transmission line with a surge impedance matching that of the aircraft and its return lines was evaluated as a replacement for earlier current generators. Various test circuit parameters were evaluated using a 1/10 scale relative geometric model. Induced voltage response was evaluated by taking measurements on the NASA-Dryden Digital Fly by Wire F-8 aircraft. Return conductor arrangements as well as other circuit changes were also evaluated, with all induced voltage measurements being made on the same circuit for comparison purposes. The lumped parameter transmission line generates a concave front current wave with the peak di/dt near the peak of the current wave which is more representative of lightning. However, the induced voltage measurements when scaled by appropriate scale factors (peak current or di/dt) resulting from both techniques yield comparable results

Helioseismic holography of simulated sunspots: magnetic and thermal contributions to travel times

Wave propagation through sunspots involves conversion between waves of acoustic and magnetic character. In addition, the thermal structure of sunspots is very different than that of the quiet Sun. As a consequence, the interpretation of local helioseismic measurements of sunspots has long been a challenge. With the aim of understanding these measurements, we carry out numerical simulations of wave propagation through sunspots. Helioseismic holography measurements made from the resulting simulated wavefields show qualitative agreement with observations of real sunspots. We use additional numerical experiments to determine, separately, the influence of the thermal structure of the sunspot and the direct effect of the sunspot magnetic field. We use the ray approximation to show that the travel-time shifts in the thermal (non-magnetic) sunspot model are primarily produced by changes in the wave path due to the Wilson depression rather than variations in the wave speed. This shows that inversions for the subsurface structure of sunspots must account for local changes in the density. In some ranges of horizontal phase speed and frequency there is agreement (within the noise level in the simulations) between the travel times measured in the full magnetic sunspot model and the thermal model. If this conclusion proves to be robust for a wide range of models, it would suggest a path towards inversions for sunspot structure.Comment: Accepted for publication in The Astrophysical Journa

Reusable thermal cycling clamp

A reusable metal clamp for retaining a fused quartz ampoule during temperature cycling in the range of 20 deg C to 1000 deg C is described. A compressible graphite foil having a high radial coefficient of thermal expansion is interposed between the fused quartz ampoule and metal clamp to maintain a snug fit between these components at all temperature levels in the cycle

Physical Baryon Resonance Spectroscopy from Lattice QCD

We complement recent advances in the calculation of the masses of excited baryons in quenched lattice QCD with finite-range regulated chiral effective field theory enabling contact with the physical quark mass region. We examine the P-wave contributions to the low-lying nucleon and delta resonances.Comment: Contributed paper at FB17, the 17th International Conference on Few-Body Problems in Physics, Durham, NC, June 5-10, 2003. 3 pages, 6 figure

Validating Forward Modeling and Inversions of Helioseismic Holography Measurements

Here we use synthetic data to explore the performance of forward models and inverse methods for helioseismic holography. Specifically, this work presents the first comprehensive test of inverse modeling for flows using lateral-vantage (deep-focus) holography. We derive sensitivity functions in the Born approximation. We then use these sensitivity functions in a series of forward models and inversions of flows from a publicly available magnetohydrodynamic quiet-Sun simulation. The forward travel times computed using the kernels generally compare favorably with measurements obtained by applying holography, in a lateral-vantage configuration, on a 15-hour time series of artificial Dopplergrams extracted from the simulation. Inversions for the horizontal flow components are able to reproduce the flows in the upper 3Mm of the domain, but are compromised by noise at greater depths.Comment: accepted for publication by the Astrophysical

Shallow Composition and Structure of the San Gabriel Fault, California in Drill Core and Geophysical Logs: Implications for Fault Slip and Energetics

Earthquakes are the sudden and intensive release of energy due to slip along faults. This energy may be felt on the Earth’s surface and may cause displacement of the Earth’s crust (seismic slip). As an earthquake ruptures, rocks in and around the fault are damaged and altered. When a fault displaces without earthquakes, it is referred to as aseismic creep. Faults may experience both seismic slip and aseismic creep throughout their cycles. In order to better model earthquake hazards and understand the cause of seismic slip versus aseismic creep in the shallow crust, we need to characterize the properties of the altered and damaged fault-related rocks. The San Gabriel fault in California is an ancient strike-slip fault, similar to the modern San Andreas fault, that accommodated slip millions of years ago. In this project, we examine field samples and drill core drilled through the fault-related rocks that formed in the San Gabriel fault at depths of 2-2.5 km. We integrate various techniques to examine the altered and damaged fault-related rock at the mesoscopic (hand sample size) to the microscopic scale in order to characterize the properties of the fault-related rock. Synchrotron X-ray fluorescence (XRF) mapping, a new technique in the examination of shallow faults, allows us to scan surfaces of fault-related rocks and map element location and concentration in the samples. The results document hydrothermal-assisted processes that alter the fault-related rock. We identify deformation and alteration mechanisms that indicate that shallow SGF accommodates both seismic slip (earthquakes) and aseismic creep processes. We suggest that seismic slip versus aseismic creep behavior is influenced by fluid-assisted processes visible in the fault-related rocks at the mesoscopic and microscopic scales and the formation of and changes in clay minerals. This work can be used to better model earthquake hazards in active faults, such as the San Andreas fault in California