A Three-Term Conjugate Gradient Method with Sufficient Descent Property for Unconstrained Optimization

Conjugate gradient methods are widely used for solving large-scale unconstrained optimization problems, because they do not need the storage of matrices. In this paper, we propose a general form of three-term conjugate gradient methods which always generate a sufficient descent direction. We give a sufficient condition for the global convergence of the proposed general method. Moreover, we present a specific three-term conjugate gradient method based on the multi-step quasi-Newton method. Finally, some numerical results of the proposed method are given

Earth rotation and core topography

The NASA Geodynamics program has as one of its missions highly accurate monitoring of polar motion, including changes in length of day (LOD). These observations place fundamental constraints on processes occurring in the atmosphere, in the mantle, and in the core of the planet. Short-timescale (t less than or approx 1 yr) variations in LOD are mainly the result of interaction between the atmosphere and the solid earth, while variations in LOD on decade timescales result from the exchange of angular momentum between the mantle and the fluid core. One mechanism for this exchange of angular momentum is through topographic coupling between pressure variations associated with flow in the core interacting with topography at the core-mantel boundary (CMB). Work done under another NASA grant addressing the origin of long-wavelength geoid anomalies as well as evidence from seismology, resulted in several models of CMB topography. The purpose of work supported by NAG5-819 was to study further the problem of CMB topography, using geodesy, fluid mechanics, geomagnetics, and seismology. This is a final report

Landslide generated impulse waves

Landslide generated impulse waves were investigated in a two-dimensional physical laboratory model based on the generalized Froude similarity. Digital particle image velocimetry (PIV) was applied to the landslide impact and wave generation. Areas of interest up to 0.8m by 0.8m were investigated. The challenges posed to the measurement system in an extremely unsteady three-phase flow consisting of granular matter, air, and water were considered. The complex flow phenomena in the first stage of impulse wave initiation are: high-speed granular slide impact, slide deformation and penetration into the fluid, flow separation, hydrodynamic impact crater formation, and wave generation. During this first stage the three phases are separated along sharp interfaces changing significantly within time and space. Digital masking techniques are applied to distinguish between phases thereafter allowing phase separated image processing. PIV provided instantaneous velocity vector fields in a large area of interest and gave insight into the kinematics of the wave generation process. Differential estimates such as vorticity, divergence, elongational, and shear strain were extracted from the velocity vector fields. The fundamental assumption of irrotational flow in the Laplace equation was confirmed experimentally for these non-linear waves. Applicability of PIV at large scale as well as to flows with large velocity gradients is highlighte

Landslide generated impulse waves. 2. Hydrodynamic impact craters

Landslide generated impulse waves were investigated in a two-dimensional physical laboratory model based on the generalized Froude similarity. Digital particle image velocimetry (PIV) was applied to the landslide impact and wave generation. Areas of interest up to 0.8m by 0.8m were investigated. PIV provided instantaneous velocity vector fields in a large area of interest and gave insight into the kinematics of the wave generation process. Differential estimates such as vorticity, divergence, and elongational and shear strain were extracted from the velocity vector fields. At high impact velocities flow separation occurred on the slide shoulder resulting in a hydrodynamic impact crater, whereas at low impact velocities no flow detachment was observed. The hydrodynamic impact craters may be distinguished into outward and backward collapsing impact craters. The maximum crater volume, which corresponds to the water displacement volume, exceeded the landslide volume by up to an order of magnitude. The water displacement caused by the landslide generated the first wave crest and the collapse of the air cavity followed by a run-up along the slide ramp issued the second wave crest. The extracted water displacement curves may replace the complex wave generation process in numerical models. The water displacement and displacement rate were described by multiple regressions of the following three dimensionless quantities: the slide Froude number, the relative slide volume, and the relative slide thickness. The slide Froude number was identified as the dominant paramete

Relaxation of Surface Profiles by Evaporation Dynamics

We present simulations of the relaxation towards equilibrium of one dimensional steps and sinusoidal grooves imprinted on a surface below its roughening transition. We use a generalization of the hypercube stacking model of Forrest and Tang, that allows for temperature dependent next-nearest-neighbor interactions. For the step geometry the results at T=0 agree well with the t^(1/4) prediction of continuum theory for the spreading of the step. In the case of periodic profiles we modify the mobility for the tips of the profile and find the approximate solution of the resulting free boundary problem to be in reasonable agreement with the T=0 simulations.Comment: 6 pages, Revtex, 5 Postscript figures, to appear in PRB 15, October 199

A dynamic model of Venus's gravity field

Unlike Earth, long wavelength gravity anomalies and topography correlate well on Venus. Venus's admittance curve from spherical harmonic degree 2 to 18 is inconsistent with either Airy or Pratt isostasy, but is consistent with dynamic support from mantle convection. A model using whole mantle flow and a high viscosity near surface layer overlying a constant viscosity mantle reproduces this admittance curve. On Earth, the effective viscosity deduced from geoid modeling increases by a factor of 300 from the asthenosphere to the lower mantle. These viscosity estimates may be biased by the neglect of lateral variations in mantle viscosity associated with hot plumes and cold subducted slabs. The different effective viscosity profiles for Earth and Venus may reflect their convective styles, with tectonism and mantle heat transport dominated by hot plumes on Venus and by subducted slabs on Earth. Convection at degree 2 appears much stronger on Earth than on Venus. A degree 2 convective structure may be unstable on Venus, but may have been stabilized on Earth by the insulating effects of the Pangean supercontinental assemblage

Guidelines for the Diagnosis, Treatment and Prevention of Postoperative Infections

Bacterial contamination of the operative site is a common occurrence in obstetrics and gynecology. The widespread use of antibiotic prophylaxis has reduced but not eliminated serious postoperative infections. For most operations, a single dose of a limited-spectrum drug has been as effective as a multidose regimen. In the differential diagnosis it is important to consider cellulitis, abscess, necrotizing fasciitis and septic pelvic thrombophlebitis. Abscess and necrotizing fasciitis are expected to require invasive therapy in addition to antibiotics, while cellulitis and septic pelvic thrombophlebitis should respond to medical management alone. Although a postoperative fever is a warning sign of possible infection, it may also be caused by the antibiotics that are given for treatment. The use of prolonged courses of antibiotics once the patient is clinically well is discouraged. While clinical guidelines are provided for use in the diagnosis and management of postoperative infections, these recommendations are intended for general direction and not as an exclusive management plan

GPS survey of the western Tien Shan

There were two major developments in 1994 in our collaborative GPS experiment in the Tien Shan of the Former Soviet Union (FSU). Both were motivated by our expectation that we will ultimately obtain better science at lower cost if we involve our colleagues in the FSU more deeply in (1) the collection and (2) the analysis of data. As an experimental test of the concept of having our local collaborators carry out the field work semi-autonomously, we sent 6 MIT receivers to the Tien Shan for a period of 3 months. To enable our collaborators to have the capability for data analysis, we provided computers for two data analysis centers and organized a two-week training session. This report emphasizes the rationale for deeper involvement of FSU scientists, describes the training sessions, discusses the data collection, and presents the results. We also discuss future plans. More detailed discussion of background, general scientific objectives, discussions with collaborators, and results for the campaigns in 1992 and 1993 have been given in previous reports

Quantum lattice dynamical effects on the single-particle excitations in 1D Mott and Peierls insulators

As a generic model describing quasi-one-dimensional Mott and Peierls insulators, we investigate the Holstein-Hubbard model for half-filled bands using numerical techniques. Combining Lanczos diagonalization with Chebyshev moment expansion we calculate exactly the photoemission and inverse photoemission spectra and use these to establish the phase diagram of the model. While polaronic features emerge only at strong electron-phonon couplings, pronounced phonon signatures, such as multi-quanta band states, can be found in the Mott insulating regime as well. In order to corroborate the Mott to Peierls transition scenario, we determine the spin and charge excitation gaps by a finite-size scaling analysis based on density-matrix renormalization group calculations.Comment: 5 pages, 5 figure

Application of Global Positioning Measurements to Continental Collision in the Pamir-Tien Shan Region, Central Asia and GPS Survey of the Western Tien Shan

In this report, we summarize what we have accomplished with five years of funding from NASA under its DOSE program, and with a comparable level of funding from NSF. We describe the development of a GPS network in the Tien Shan of Kyrgyzstan and Kazakhstan of the former Soviet Union, the analysis of data, and the main results. This discussion presents the state of the current network, which has grown significantly since the termination of our DOSE grants, with continued support both from NSF through its continental dynamics program and from NASA's SENH program. Although grants from NASA's DOSE program did not support this growth not directly, it did so indirectly by building the infrastructure that has enabled further expansion in an area where otherwise there would be only a small GPS presence. We note how the network has grown over time, but the emphasis of this discussion is on the quantity and quality of measurements that we have made