A note on the steady-state response of an elastic half-space

With reference to the influence of local geology on earthquake ground motions, a more complete analytical formulation is made of the well-known problem of a horizontally stratified, linearly-elastic half-space subjected to vertically traveling, sinusoidal, plane waves. A more general interpretation of a result of Kanai is given, and a recursion formula is derived for computing amplification spectra. Some special properties of the system are pointed out and numerical examples are given

Influence of local geology on earthquake ground motion

As a simplified approach for estimating theoretically the influence of local subsoils upon the ground motion during an earthquake, the problem of an idealized layered system subjected to vertically incident plane body waves was studied. Both the technique of steady-state analysis and the technique of transient analysis have been used to analyze the problem. In the steady-state analysis, a recursion formula has been derived for obtaining the response of a layered system to sinusoidally steady-state input. Several conclusions are drawn concerning the nature of the amplification spectrum of a nonviscous layered system having its layer stiffnesses increasing with depth. Numerical examples are given to demonstrate the effect of layer parameters on the amplification spectrum of a layered system. In the transient analysis, two modified shear beam models have been established for obtaining approximately the response of a layered system to earthquake -like excitation. The method of continuous modal analysis was adopted for approximate analysis of the models, with energy dissipation in the layers, if any, taken into account. Numerical examples are given to demonstrate the accuracy of the models and the effect of a layered system in modifying the input motion. Conditions are established, under which the theory is applicable to predict the influence of local subsoils on the ground motion during an earthquake. To demonstrate the applicability of the models to actual cases, three examples of actually recorded earthquake events are examined. It is concluded that significant modification of the incoming seismic waves, as predicted by the theory, is likely to occur in well defined soft subsoils during an earthquake, provided that certain conditions concerning the nature of the incoming seismic waves are satisfied

Calculation of surface motions of a layered half-space

A new method is presented for computing the transient response of a set of horizontally stratified, linearly elastic layers overlying a uniform half-space and excited by vertically incident, transient plane waves. In addition, a simple approximate method of satisfactory accuracy is developed that reduces the computing time required. Calculated responses are compared with motions recorded under Union Bay in Seattle to evaluate the agreement between recorded and calculated motions

Latanoprost with high precision, piezo-print microdose delivery for IOP lowering: clinical results of the PG21 study of 0.4 µg daily microdose.

Background:Topical high-precision piezo-print delivery of microdoses of latanoprost achieved significant IOP reduction consistent with the eyedropper effect but with a 75% reduced exposure to drugs and preservatives. Prostaglandin analogs are a mainstay glaucoma therapy. However, conventional eyedroppers deliver 30-50 µL drops that greatly exceed the physiologic 7-µL ocular tear film capacity. Eyedropper overdosing floods the eye with excess drug compounds and preservatives, resulting in ocular surface toxicity, periorbitopathy, and other well-characterized ocular side effects. Piezoelectric high-precision microdosing provides targeted delivery that can reduce exposure to both drug and preservatives compared to conventional eyedropper delivery, with the potential to deliver similar biologic effect. Methods:Both eyes (N=60) of 30 healthy volunteers received single 8-µL microdoses of 0.005% latanoprost (0.4 µg; µRx-latanoprost) on the morning of Days 1 and 2 using a high-precision, piezo-print horizontal delivery system. Diurnal IOP was measured before and 2 days after microdosing. Main efficacy outcomes were diurnal IOP change after µRx-latanoprost microdosing and accurate microdosing success rates, and the primary safety outcome was adverse event (AE) incidence. Results:µRx-latanoprost reduced baseline IOP by 26% and 30% at 1 and 2 days postadministration, respectively. Successful topical dosing was achieved in 100% of technician-assisted deliveries. All patients successfully self-administered microdoses after receiving training. Microdose administration was well tolerated and did not result in any AEs. Conclusion:Microdosing of 0.4 µg of µRx-latanoprost achieved significant IOP reduction. Lower ocular exposure with topical prostaglandin analog microdosing can enable new therapeutic opportunities for optimizing glaucoma treatment. Microdosing may also be beneficial in reducing ocular side effects associated with excessive drug product and preservatives often used to treat chronic ocular diseases such as glaucoma

Broken time-reversal symmetry in Josephson junction involving two-band superconductors

A novel time-reversal symmetry breaking state is found theoretically in the Josephson junction between the two-gap superconductor and the conventional s-wave superconductor. This occurs due to the frustration between the three order parameters analogous to the two antiferromagnetically coupled XY-spins put under a magnetic field. This leads to the interface states with the energies inside the superconducting gap. Possible experimental observations of this state with broken time-reversal symmetry are discussed.Comment: 9 pages, 1 figur

Rho primes in analyzing e+e- annihilation, MARK III, LASS and ARGUS data

The results of an analysis are presented of some recent data on the reactions $e^+e^-\to\pi^+\pi^-\pi^+\pi^-$, $e^+e^-\to\pi^+\pi^-\pi^0\pi^0$ with the subtracted $\omega\pi^0$ events, $e^+e^-\to\omega\pi^0$, $e^+e^-\to\eta \pi^+\pi^-$, $e^+e^-\to\pi^+\pi^-$, $K^-p\to\pi^+\pi^-\Lambda$, the decays $J/\psi\to\pi^+\pi^-\pi^0$, $tau^-\to\nu_tau\pi^+\pi^-\pi^-\pi^0$ $tau^-\to\nu_\tau\omega\pi^-$, upon taking into account both the strong energy dependence of the partial widths on energy and the previously neglected mixing of the $\rho$ type resonances. The above effects are shown to exert an essential influence on the specific values of masses and coupling constants of heavy resonances and hence are necessary to be accounted for in establishing their true nature.Comment: 20 pages, ReVTeX, 9 Postscript figures As compared to hep-ph/9607398, new material concerning the analysis of the ARGUS data on the tau decays into four pion hadronic states is adde

Families of Graphs With Chromatic Zeros Lying on Circles

We define an infinite set of families of graphs, which we call $p$-wheels and denote $(Wh)^{(p)}_n$, that generalize the wheel ($p=1$) and biwheel ($p=2$) graphs. The chromatic polynomial for $(Wh)^{(p)}_n$ is calculated, and remarkably simple properties of the chromatic zeros are found: (i) the real zeros occur at $q=0,1,...p+1$ for $n-p$ even and $q=0,1,...p+2$ for $n-p$ odd; and (ii) the complex zeros all lie, equally spaced, on the unit circle $|q-(p+1)|=1$ in the complex $q$ plane. In the $n \to \infty$ limit, the zeros on this circle merge to form a boundary curve separating two regions where the limiting function $W(\{(Wh)^{(p)}\},q)$ is analytic, viz., the exterior and interior of the above circle. Connections with statistical mechanics are noted.Comment: 8 pages, Late

Local density of states and scanning tunneling currents in graphene

We present exact analytical calculations of scanning tunneling currents in locally disordered graphene using a multimode description of the microscope tip. Analytical expressions for the local density of states (LDOS) are given for energies beyond the Dirac cone approximation. We show that the LDOS at the $A$ and $B$ sublattices of graphene are out of phase by $\pi$ implying that the averaged LDOS, as one moves away from the impurity, shows no trace of the $2q_F$ (with $q_F$ the Fermi momentum) Friedel modulation. This means that a STM experiment lacking atomic resolution at the sublattice level will not be able of detecting the presence of the Friedel oscillations [this seems to be the case in the experiments reported in Phys. Rev. Lett. {\bf 101}, 206802 (2008)]. The momentum maps of the LDOS for different types of impurities are given. In the case of the vacancy, $2q_F$ features are seen in these maps. In all momentum space maps, $K$ and $K+K^\prime$ features are seen. The $K+K^\prime$ features are different from what is seen around zero momentum. An interpretation for these features is given. The calculations reported here are valid for chemical substitution impurities, such as boron and nitrogen atoms, as well as for vacancies. It is shown that the density of states close to the impurity is very sensitive to type of disorder: diagonal, non-diagonal, or vacancies. In the case of weakly coupled (to the carbon atoms) impurities, the local density of states presents strong resonances at finite energies, which leads to steps in the scanning tunneling currents and to suppression of the Fano factor.Comment: 21 pages. Figures 6 and 7 are correctly displayed in this new versio