Wave impedance matrices for cylindrically anisotropic radially inhomogeneous elastic solids

Impedance matrices are obtained for radially inhomogeneous structures using the Stroh-like system of six first order differential equations for the time harmonic displacement-traction 6-vector. Particular attention is paid to the newly identified solid-cylinder impedance matrix ${\mathbf Z} (r)$ appropriate to cylinders with material at $r=0$, and its limiting value at that point, the solid-cylinder impedance matrix ${\mathbf Z}_0$. We show that ${\mathbf Z}_0$ is a fundamental material property depending only on the elastic moduli and the azimuthal order $n$, that ${\mathbf Z} (r)$ is Hermitian and ${\mathbf Z}_0$ is negative semi-definite. Explicit solutions for ${\mathbf Z}_0$ are presented for monoclinic and higher material symmetry, and the special cases of $n=0$ and 1 are treated in detail. Two methods are proposed for finding ${\mathbf Z} (r)$, one based on the Frobenius series solution and the other using a differential Riccati equation with ${\mathbf Z}_0$ as initial value. %in a consistent manner as the solution of an algebraic Riccati equation. The radiation impedance matrix is defined and shown to be non-Hermitian. These impedance matrices enable concise and efficient formulations of dispersion equations for wave guides, and solutions of scattering and related wave problems in cylinders.Comment: 39 pages, 2 figure

The effect of the oceans on the terrestrial crater size-frequency distribution: Insight from numerical modeling

From the proceedings of the Workshop on Impact Craters as Indicators for Planetary Environmental Evolution and Astrobiology held in June 2006 in Östersund, Sweden.On Earth, oceanic impacts are twice as likely to occur as continental impacts, yet the effect of the oceans has not been previously considered when estimating the terrestrial crater size-frequency distribution. Despite recent progress in understanding the qualitative and quantitative effect of a water layer on the impact process through novel laboratory experiments, detailed numerical modeling, and interpretation of geological and geophysical data, no definitive relationship between impactor properties, water depth, and final crater diameter exists. In this paper, we determine the relationship between final (and transient) crater diameter and the ratio of water depth to impactor diameter using the results of numerical impact models. This relationship applies for normal incidence impacts of stoney asteroids into water-covered, crystalline oceanic crust at a velocity of 15 km s-1. We use these relationships to construct the first estimates of terrestrial crater size-frequency distributions (over the last 100 million years) that take into account the depth-area distribution of oceans on Earth. We find that the oceans reduce the number of craters smaller than 1 km in diameter by about two-thirds, the number of craters ~30 km in diameter by about one-third, and that for craters larger than ~100 km in diameter, the oceans have little effect. Above a diameter of ~12 km, more craters occur on the ocean floor than on land; below this diameter more craters form on land than in the oceans. We also estimate that there have been in the region of 150 impact events in the last 100 million years that formed an impact-related resurge feature, or disturbance on the seafloor, instead of a crater.The Meteoritics & Planetary Science archives are made available by the Meteoritical Society and the University of Arizona Libraries. Contact [email protected] for further information.Migrated from OJS platform February 202

Nonlinear shear wave interaction at a frictional interface: Energy dissipation and generation of harmonics

Analytical and numerical modelling of the nonlinear interaction of shear wave with a frictional interface is presented. The system studied is composed of two homogeneous and isotropic elastic solids, brought into frictional contact by remote normal compression. A shear wave, either time harmonic or a narrow band pulse, is incident normal to the interface and propagates through the contact. Two friction laws are considered and their influence on interface behavior is investigated : Coulomb's law with a constant friction coefficient and a slip-weakening friction law which involves static and dynamic friction coefficients. The relationship between the nonlinear harmonics and the dissipated energy, and their dependence on the contact dynamics (friction law, sliding and tangential stress) and on the normal contact stress are examined in detail. The analytical and numerical results indicate universal type laws for the amplitude of the higher harmonics and for the dissipated energy, properly non-dimensionalized in terms of the pre-stress, the friction coefficient and the incident amplitude. The results suggest that measurements of higher harmonics can be used to quantify friction and dissipation effects of a sliding interface.Comment: 17 pages, 10 figure

Effective speed of sound in phononic crystals

A new formula for the effective quasistatic speed of sound $c$ in 2D and 3D periodic materials is reported. The approach uses a monodromy-matrix operator to enable direct integration in one of the coordinates and exponentially fast convergence in others. As a result, the solution for $c$ has a more closed form than previous formulas. It significantly improves the efficiency and accuracy of evaluating $c$ for high-contrast composites as demonstrated by a 2D example with extreme behavior.Comment: 4 pages, 1 figur

Coupling of nuclear wavepacket motion and charge separation in bacterial reaction centers

AbstractThe mechanism of the charge separation and stabilization of separated charges was studied using the femtosecond absorption spectroscopy. It was found that nuclear wavepacket motions on potential energy surface of the excited state of the primary electron donor P* leads to a coherent formation of the charge separated states P+BA−, P+HA− and P+HB− (where BA, HB and HA are the primary and secondary electron acceptors, respectively) in native, pheophytin-modified and mutant reaction centers (RCs) of Rhodobacter sphaeroides R-26 and in Chloroflexus aurantiacus RCs. The processes were studied by measurements of coherent oscillations in kinetics at 890 and 935 nm (the stimulated emission bands of P*), at 800 nm (the absorption band of BA) and at 1020 nm (the absorption band of BA−) as well as at 760 nm (the absorption band of HA) and at 750 nm (the absorption band of HB). It was found that wavepacket motion on the 130–150 cm−1 potential surface of P* is accompanied by approaches to the intercrossing region between P* and P+BA− surfaces at 120 and 380 fs delays emitting light at 935 nm (P*) and absorbing light at 1020 nm (P+BA−). In the presence of Tyr M210 (Rb. sphaeroides) or M195 (C. aurantiacus) the stabilization of P+BA− is observed within a few picosseconds in contrast to YM210W. At even earlier delay (∼40 fs) the emission at 895 nm and bleaching at 748 nm are observed in C. aurantiacus RCs showing the wavepacket approach to the intercrossing between the P* and P+HB− surfaces at that time. The 32 cm−1 rotation mode of HOH was found to modulate the electron transfer rate probably due to including of this molecule in polar chain connecting PB and BA and participating in the charge separation. The mechanism of the charge separation and stabilization of separated charges is discussed in terms of the role of nuclear motions, of polar groups connecting P and acceptors and of proton of OH group of TyrM210

Modified bacterial reaction centers

Pigments of borohydride-treated reaction centers of Rhodobacter sphaeroides R 26 and Rhodopseudomonas viridis were analyzed by HPLC with polychromatic detection. In both species, pigment composition and contents were unchanged. Reaction centers from Rhodobacter sphaeroides R26 were prepared in which bacteriochlorophylls (BA,B) and bacteriopheophytins (HA,B) were exchanged with their potential borohydride products reduced at C-31. [3-Hydroxyethyl]-BChl a exchanges selectively into the BA,B pockets, and 31-OH-BPh a to the HA,B pockets. Stable reaction centers are obtained in both cases. A comparison of the absorption and circular dichroism spectra of reaction centers after exchange with 31-OH pigments, and of borohydride-modified reaction centers, reveal distinct differences. It is concluded that during borohydride reduction none of the pigments is chemically modified or extracted from the reaction centers