Accessing the Microscopic World

The Exploratorium in San Francisco offers museum visitors the opportunity to use and manipulate state-of-the-art microscopes to visualize an array of living specimen

Improving the smoothed complexity of FLIP for max cut problems

Finding locally optimal solutions for max-cut and max-$k$-cut are well-known PLS-complete problems. An instinctive approach to finding such a locally optimum solution is the FLIP method. Even though FLIP requires exponential time in worst-case instances, it tends to terminate quickly in practical instances. To explain this discrepancy, the run-time of FLIP has been studied in the smoothed complexity framework. Etscheid and R\"{o}glin showed that the smoothed complexity of FLIP for max-cut in arbitrary graphs is quasi-polynomial. Angel, Bubeck, Peres, and Wei showed that the smoothed complexity of FLIP for max-cut in complete graphs is $O(\phi^5n^{15.1})$, where $\phi$ is an upper bound on the random edge-weight density and $n$ is the number of vertices in the input graph. While Angel et al.'s result showed the first polynomial smoothed complexity, they also conjectured that their run-time bound is far from optimal. In this work, we make substantial progress towards improving the run-time bound. We prove that the smoothed complexity of FLIP in complete graphs is $O(\phi n^{7.83})$. Our results are based on a carefully chosen matrix whose rank captures the run-time of the method along with improved rank bounds for this matrix and an improved union bound based on this matrix. In addition, our techniques provide a general framework for analyzing FLIP in the smoothed framework. We illustrate this general framework by showing that the smoothed complexity of FLIP for max-$3$-cut in complete graphs is polynomial and for max-$k$-cut in arbitrary graphs is quasi-polynomial. We believe that our techniques should also be of interest towards addressing the smoothed complexity of FLIP for max-$k$-cut in complete graphs for larger constants $k$.Comment: 36 page

A Computer Model of the Tidal Phenomena in Cook Inlet, Alaska

The work upon which this report is based was supported by funds (Project A-028-ALAS) provided by the United States Department of the Interior, Office of Water Resources Research, as authorized under the Water Resources Act of 1964, as amended

Water Balance of a Small Lake in a Permafrost Region

The work upon which this report is based was supported in part by funds (Project A-031-ALAS) provided by the United States Department of the Interior, Office of Water Resources Research, as authorized under the Water Resources Act of 1964, as amended

1955 The Analysis

https://jdc.jefferson.edu/analysis/1013/thumbnail.jp

Upgrading of NASA-Ames high-energy hypersonic facilities: A Study

This study reviews facility capabilities of NASA, Ames Research Center to simulate hypersonic flight with particular emphasis on arc heaters. Scaling laws are developed and compared with ARCFLO II calculations and with existing data. The calculations indicate that a 300 MW, 100 atmosphere arc heater is feasible. Recommendations for the arc heater, which will operate at voltages up to 50 kilovolts, and the associated elements needed for a test facility are included

Submarine Groundwater Discharge in the Southern Chesapeake Bay: Constraints From Numerical Models

Terrestrial and oceanic forces drive fluid flow within the coastal zone to produce submarine groundwater discharge (SGD). Groundwater flowing from the seabed serves as a significant pathway for contaminants and nutrients, producing an active biogeochemical reaction zone. In order to quantify the importance of SGD in geochemical and hydrologic budgets for the lower Chesapeake Bay, three coastal Virginia transects (southern Eastern Shore, Lafayette River, and Ocean View beach) with different topographic gradients were modeled using similar boundary conditions and consistent treatment of hydrogeologic layers. A sensitivity study was performed on the variables of recharge rate, seawater density, and hydraulic permeability. Each two-dimensional transect is approximately 5 km in the shore-perpendicular direction with vertical elevations ranging from 10 m above sea level to 50 m below sea level. A pre-processing suite of code displays NOAA topography and bathymetry data, allows the user to identify a desired transect, and outputs a cross-sectional numerical domain for a series of steady-state calculations solved by a USGS program called SUTRA. SUTRA’s hybrid finite element and finite difference method computes buoyancy-driven flow of variable-density groundwater, solves the coupled solute transport equation, and predicts areas of discharge and recharge across the nearshore coastal zone. Model results suggested SGD in all transects, with common flow pattern characteristics including freshwater discharging below the elevation of sea level, seawater recirculating in steep bathymetry, and intervening zones of relatively low flow. Although fluid velocity at the low tide mark was significantly dependent upon the slope of the transect, response to recharge rate was small over the range of modeled values. Permeability had the greatest effect on SGD; varying hydraulic conductivity by over an order of magnitude produced similar magnitude changes in discharge. Overall, this series of models provides a framework for identifying zones of high groundwater flow, reveals the variability of SGD rates between locations, and suggests which field measurements would be most valuable to better constrain the geochemical groundwater contribution to the coastal zone

Grain Sorghum Canopy Temperature as a Function of Meteorological Conditions

About 70% of the water that falls on the Continental United States is utilized, not as most of us would expect, by drainage into our vast rivers and lakes, but by direct evaporation from our soil surface or by transpiration from plants. It is estimated that three thousand billion gallons of water per day are returned to the atmosphere from the soil and plants in the United States. As weather modification and water management become more practical in the Great Plains Region, it is going to be more and more important and necessary for us to be able to predict rapidly and\u27 accurately the water, nutritional, and thermal properties of soil and plants. Presently the only feasible methods for determining the physical conditions of soils and plants require ground truth observations. Determining the conditions over a large area is difficult if not impossible without large numbers of people and equipment utilizing much time and expense. With recent developments and improvements in aircraft and satellite capabilities, it is now possible to view remote sensing imagery taken from many different spectral passbands, representing large land areas. In order for imagery to be of practical importance, adequate information for analyzing and interpreting the imagery is necessary. During the growing season radiation in the infrared spectrum does not penetrate deeply into a crop canopy, therefore, imagery in this spectral/passband is imagery of the crop canopy. To properly interpret: canopy imagery, knowledge of the interaction between the crop and its environment must be known. I assert that the status of crop transpiration rate and viability, which are closely associated with soil water, nutrition, and meteorological conditions, can be determined as a function of the deviation of the crop canopy temperature from the ambient air temperature. In order to determine the manner in which the crop canopy temperature responds to meteorological conditions, a study was initiated with the following objectives: 1. Evaluate the departure of surface temperature from ambient temperature for various soil, plant, and weather conditions. 2. Test the applications of surface temperature-evapotranspiration equations against other well-known evapotranspiration equations. 3. Develop a reliable evapotranspiration equation based on the temperature of the evaporating surface