Constrained Reductions of 2D dispersionless Toda Hierarchy, Hamiltonian Structure and Interface Dynamics

Finite-dimensional reductions of the 2D dispersionless Toda hierarchy, constrained by the ``string equation'' are studied. These include solutions determined by polynomial, rational or logarithmic functions, which are of interest in relation to the ``Laplacian growth'' problem governing interface dynamics. The consistency of such reductions is proved, and the Hamiltonian structure of the reduced dynamics is derived. The Poisson structure of the rationally reduced dispersionless Toda hierarchies is also derivedComment: 18 pages LaTex, accepted to J.Math.Phys, Significantly updated version of the previous submissio

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The anomalous behavior of coefficient of normal restitution in the oblique impact

The coefficient of normal restitution in an oblique impact is theoretically studied. Using a two-dimensional lattice models for an elastic disk and an elastic wall, we demonstrate that the coefficient of normal restitution can exceed one and has a peak against the incident angle in our simulation. Finally, we explain these phenomena based upon the phenomenological theory of elasticity.Comment: 4 pages, 4 figures, to be appeared in PR

Cost-effectiveness of extended-release niacin/laropiprant added to a stable simvastatin dose in secondary prevention patients not at cholesterol goal in Germany

Coronary heart disease (CHD) remains the leading cause of death in Germany despite statin use to reduce low-density lipoprotein cholesterol (LDL-C) levels; improving lipids beyond LDL-C may further reduce cardiovascular risk. A fixed-dose combination of extended-release niacin (ERN) with laropiprant (LRPT) provides comprehensive lipid management. We adapted a decision-analytic model to evaluate the economic value (incremental cost-effectiveness ratio [ICER] in terms of costs per life-years gained [LYG]) of ERN/LRPT 2 g over a lifetime in secondary prevention patients in a German setting. Two scenarios were modelled: (1) ERN/LRPT 2 g added to simvastatin 40 mg in patients not at LDL-C goal with simvastatin 40 mg; (2) adding ERN/LRPT 2 g compared with titration to simvastatin 40 mg in patients not at LDL-C goal with simvastatin 20 mg. In both scenarios, adding ERN/LRPT was cost-effective relative to simvastatin monotherapy at a commonly accepted threshold of €30,000 per LYG; ICERs for ERN/LRPT were €13,331 per LYG in scenario 1 and €17,684 per LYG in scenario 2. Subgroup analyses showed that ERN/LRPT was cost-effective in patients with or without diabetes, patients aged ≤65 or >65 years and patients with low baseline high-density lipoprotein cholesterol levels; ICERs ranged from €10,342 to €15,579 in scenario 1, and from €14,081 to €20,462 in scenario 2. In conclusion, comprehensive lipid management with ERN/LRPT 2 g is cost-effective in secondary prevention patients in Germany who have not achieved LDL-C goal with simvastatin monotherapy

Gravitational Lensing by Rotating Naked Singularities

We model massive compact objects in galactic nuclei as stationary, axially-symmetric naked singularities in the Einstein-massless scalar field theory and study the resulting gravitational lensing. In the weak deflection limit we study analytically the position of the two weak field images, the corresponding signed and absolute magnifications as well as the centroid up to post-Newtonian order. We show that there are a static post-Newtonian corrections to the signed magnification and their sum as well as to the critical curves, which are function of the scalar charge. The shift of the critical curves as a function of the lens angular momentum is found, and it is shown that they decrease slightingly for the weakly naked and vastly for the strongly naked singularities with the increase of the scalar charge. The point-like caustics drift away from the optical axis and do not depend on the scalar charge. In the strong deflection limit approximation we compute numerically the position of the relativistic images and their separability for weakly naked singularities. All of the lensing quantities are compared to particular cases as Schwarzschild and Kerr black holes as well as Janis--Newman--Winicour naked singularities.Comment: 35 pages, 30 figure

Oligocene-Miocene drainage evolution of NW Borneo: Stratigraphy, sedimentology and provenance of Tatau-Nyalau province sediments

Clastic sediments of Oligocene to Lower Miocene age form a major thick and widespread sequence in the Tatau-Nyalau province of the north Sarawak Miri Zone. New light and heavy mineral data, U-Pb detrital zircon geochronology and biostratigraphy are used to identify the age, depositional environment, and potential provenance of sediments to reconstruct the drainage evolution of NW Borneo. Based on the biostratigraphic ages, depositional environments and provenance characteristics we modify previous stratigraphy and divide the Oligocene to Lower Miocene sequences into the Nyalau Formation (Biban Sandstone Member and Upper Nyalau Member), Kakus Unit, and Merit-Pila Formation. Two dominant source provinces were identified: the Malay-Thai Tin Belt which supplied sediments dominated by Permian-Triassic zircons, and the Schwaner Mountains of central Borneo which are identified by abundant Cretaceous zircons. Sediments either came directly, or were recycled from older sedimentary rocks, from these sources. The Sunda River deposited the Nyalau Formation during the Oligocene to Early Miocene with a dominant Malay-Thai Tin Belt source. The Merit-Pila Formation of the Sibu Zone was deposited contemporaneously by a proto-Rajang River that drained Central Borneo (recycling the Rajang Group and Schwaner granitoids). Between c. 17 Ma the Sunda River system terminated and sedimentation was dominated by the northward prograding proto-Rajang River delta, depositing the Kakus Unit in the Miri Zone. This drainage system was active until the Late Miocene, before further uplift of Borneo terminated most sedimentation in the onshore part of present-day Borneo

Diffusion-Limited Aggregation on Curved Surfaces

We develop a general theory of transport-limited aggregation phenomena occurring on curved surfaces, based on stochastic iterated conformal maps and conformal projections to the complex plane. To illustrate the theory, we use stereographic projections to simulate diffusion-limited-aggregation (DLA) on surfaces of constant Gaussian curvature, including the sphere ($K>0$) and pseudo-sphere ($K<0$), which approximate "bumps" and "saddles" in smooth surfaces, respectively. Although curvature affects the global morphology of the aggregates, the fractal dimension (in the curved metric) is remarkably insensitive to curvature, as long as the particle size is much smaller than the radius of curvature. We conjecture that all aggregates grown by conformally invariant transport on curved surfaces have the same fractal dimension as DLA in the plane. Our simulations suggest, however, that the multifractal dimensions increase from hyperbolic ($K0$) geometry, which we attribute to curvature-dependent screening of tip branching.Comment: 4 pages, 3 fig

Kerr-Sen dilaton-axion black hole lensing in the strong deflection limit

In the present work we study numerically quasi-equatorial lensing by the charged, stationary, axially-symmetric Kerr-Sen dilaton-axion black hole in the strong deflection limit. In this approximation we compute the magnification and the positions of the relativistic images. The most outstanding effect is that the Kerr-Sen black hole caustics drift away from the optical axis and shift in clockwise direction with respect to the Kerr caustics. The intersections of the critical curves on the equatorial plane as a function of the black hole angular momentum are found, and it is shown that they decrease with the increase of the parameter $Q^{2}/M$. All of the lensing quantities are compared to particular cases as Schwarzschild, Kerr and Gibbons-Maeda black holes.Comment: 31 pages, 17 figures; V2 references added, some typos corrected, V3 references added, language corrections, V4 table added, minor technical correction