Error Of Closure Research Articles

Performance of Kobryn-Gusarov-Kovalenko closure from a thermodynamic viewpoint for one-component Lennard-Jones fluids

The performance of Kobryn-Gusarov-Kovalenko (KGK) closure was examined in terms of the thermodynamics for one-component Lennard-Jones fluids. The result was compared to molecular dynamics simulation as well as to hypernetted chain, Kovalenko-Hirata (KH), Percus-Yevick and Verlet-modified closures. As the density increases, the error of KGK closure shows a turnover, regarding the excess internal energy, pressure and isothermal compressibility. On the other hand, it was numerically confirmed that the energy and the virial equations are consistent under both KH and KGK closures. The accuracies of density-derivative and temperature-derivative of the radial distribution function are also discussed.

Educating Students with Land Surveying

This descriptive research focuses on the role of land surveying in the development of an architectural plan starting at the initial architectural sketch through the detailed engineering planning which will leads smoothly to the construction phase. It comprises a leveling network that has been established and all points have been described completely. Parameters such as horizontal distance, horizontal angles and elevation differences between all points were measured through many closed leveling loops using theodolite (Leica Builder 300), tape measure & wheels (steel tape) and stave (leveling rod). The observations were used in a mathematical model and processed by traverse adjustment techniques. It is essential to check the error of closure for interior angles and for both latitude and departure before applying the double meridian distance (DMD) method to obtain the required area of the land. The adjusted unknowns and observations were computed precisely to about a few millimeters accuracy. Technical descriptions of the land such as distance, bearing, boundaries and area are necessary to visualize the shape & exact location of the land.

Analysis of Double Meridian Distance for a Closed Traverse Area towards Developing a Contour Map and Land Title

This research aimed to analyze double meridian distance for a closed traverse area in developing a land title for a propose gymnasium in Qassim University. Theodolite, leveling rod and steel tape plays an important role in measuring elevations, bearings and distances of the boundaries of a lot. Contour map is necessary to determine the traces of level surfaces of successive elevation. This will enable to identify the type of contour map and type of contour lines necessary for this project. Corel draw software is used to draw contour map and guide to interpret the significance of the variables. It is essential to check the error of closure for interior angles and for both latitude and departure before applying the Double Meridian Distance (DMD) method to obtain the total area of the lot. Technical descriptions of the land such as distance, bearing, boundaries and area are necessary to visualize the shape & exact location of the land. Developing a land title will be obtained using the technical descriptions of the lot in preparation for the type of gymnasium necessary for Qassim University.

Discrete Models of Fluids: Spatial Averaging, Closure, and Model Reduction

We consider semidiscrete ODE models of single-phase fluids and two-fluid mixtures. In the presence of multiple fine-scale heterogeneities, the size of these ODE systems can be very large. Spatial averaging is then a useful tool for reducing computational complexity of the problem. The averages satisfy exact balance equations of mass, momentum, and energy. These equations do not form a satisfactory continuum model because evaluation of stress and heat flux requires solving the underlying ODEs. To produce continuum equations that can be simulated without resolving microscale dynamics, we recently proposed a closure method based on the use of regularized deconvolution. Here we continue the investigation of deconvolution closure with the long term objective of developing consistent computational upscaling for multiphase particle methods. The structure of the fine-scale particle solvers is reminiscent of molecular dynamics. For this reason we use nonlinear averaging introduced for atomistic systems by Noll, Hardy, and Murdoch-Bedeaux. We also consider a simpler linear averaging originally developed in large eddy simulation of turbulence. We present several simple but representative examples of spatially averaged ODEs, where the closure error can be analyzed. Based on this analysis we suggest a general strategy for reducing the relative error of approximate closure. For problems with periodic highly oscillatory material parameters we propose a spectral boosting technique that augments the standard deconvolution and helps to correctly account for dispersion effects. We also conduct several numerical experiments, one of which is a complete mesoscale simulation of a stratified two-fluid flow in a channel. In this simulation, the operation count per coarse time step scales sublinearly with the number of particles.

지상 레이저 스캐닝과 TS 측량을 이용한 멀티빔 시스템의 검·보정

수로측량에서 멀티빔 시스템에 의해 측량된 자료는 여러 가지 요인들에 의해 다양한 오차들을 포함한다. 이들은 패치 테스트라는 검정 단계를 통해 보정되며, 기존의 방법을 이용한 경우 정확한 시스템 검정을 위해 약 8회 내외의 테스트가 수행되어야한다. 본 연구에서 보다 신속하고 정확한 멀티빔 시스템 검 보정을 위해, 지상 레이저 스캐닝기술과 TS 측량을 이용하여 선박의 정확한 오프셋이 결정되었고, 이러한 자료를 초기 입력값으로 한 패치 테스트가 수행되었다. 그 결과, TS 측량에서 폐합오차가 0.001 m, 스캐닝에서의 후시 관측 오차가 0.005 m 이내였다. 동일한 지역 좌표계로 획득된 모든 측량자료는 선박 기준 좌표계로 변환되었고, 이 과정에서 모든 회전각에 대한 결정계수는 0.99 이상, 표준편차는 0.008 m 이하로 나타났다. 끝으로, 계산된 탑재 센서 오프셋과 모션 센서 오프셋을 이용한 패치 테스트에서 멀티빔 송수파기 오프셋은 단 1회의 보정만으로 수로측량 업무규정을 만족하였다. 이러한 결과에 비춰볼 때, 멀티빔 시스템의 검 보정에서 지상 레이저 스캐닝 및 TS 측량의 활용 가능성이 충분히 있다고 판단된다. In hydrographic survey, data surveyed with multibeam system includes various errors due to multiple factors. These are corrected by a calibration called patch test, and if existing method is used, the test needs to be conducted for about 8 times for precise system calibration. For more prompt and precise multibeam system calibration, the exact offset of a ship was determined using terrestrial laser scanning and TS surveying, which was used as the initial input for the patch test. In the result, the error of closure was 0.001 m or less for TS surveying and backsight error was 0.005 m or less for scanning. All the surveying data based on the same local coordinate was converted into vessel reference coordinate during which R-square for all rotation angles was 0.99 or higher and standard deviation was 0.008 m or less. Finally, in a patch test using calculated offset of sensors and motion sensor offset, the offset of MBES transducer satisfied manual on hydrography only with 1-time calibration. With these results, it is thought that terrestrial laser scanning and TS surveying can fully be utilized for multibeam system calibration.

Estimating Net Interracial Mobility in the U.S. A Residual Methods Approach.

This paper presents a residual methods approach to identifying social mobility across race/ethnic categories. In traditional demographic accounting models, population growth is limited to changes in natural increase and migration. Other sources of growth are absorbed by the model residual and can only be estimated indirectly. While these residual estimates have been used to illuminate a number of elusive demographic processes, there has been little effort to incorporate shifts in racial identification into formal accounts of population change. In light of growing evidence that a number of Americans view race/ethnic identities as a personal choice, and not a fixed characteristic, mobility across racial categories may play important roles in the growth of race/ethnic sub-populations and changes to the composition of the U.S. To examine this potential, we derive a reduced-form population balancing equation that treats fertility and international migration as given and estimates survival from period life table data. After subtracting out national increase and migration and adjusting the balance of observed growth for changes in racial measurement and census coverage, we argue that the remaining error of closure provides a reasonable estimate of net interracial mobility among the native born. Using recent Census and ACS microdata, we illustrate the impact that identity shifts may have had on the growth of race/ethnic sub-populations in the past quarter century. Findings suggest a small drift from the non-Hispanic white population into race/ethnic minority groups, though the pattern varies by age and between time periods.

Hydrodynamic model of wind field in a moving typhoon

An algorithm is developed for solving the hydrodynamic equations describing wind field structure in a typhoon. The specific feature of the algorithm consists in solving an overdetermined set of equations: given radial profiles of pressure and vertical velocity component, horizontal wind components are found. Projection of angular momentum on tangential direction plays a role of “error of closure.” The calculated wind fields in resting and moving typhoons are presented. As an example, the whole lifecycle of Typhoon Ivan (September 2–17, 2004) is described in detail.

Creating a sense of ‘CLOSURE’: Providing confidence intervals on some recent estimates of indigenous populations

The error of closure is the population growth that cannot be accounted for by either natural increase or quantifiable non-demographic factors, and is an issue that is particularly pronounced for indigenous peoples. This paper estimates Australia’s indigenous population using the dual system estimation method, and compares these to those produced using the standard undercount method. The main conclusion is that dual system estimates of the indigenous population appear to be reasonably accurate at the national level, which provide an appreciation of the reliability of existing estimates. Notwithstanding, policy makers need to take into account that population statistics are merely estimates.

Evaluation of projections of populations for the aboriginal identity groups in Canada, 1996-2001

The population projections for the Aboriginal identity groups (North American Indians, Métis and Inuit) by age and sex from 1996 to 2001 were developed at the Canada level, using the cohort-component method. The purpose of this paper is to compare and analyze the error of closure between the projected 2001 and adjusted 2001 population counts due to net census undercounts. It is observed that the error of closure for the 2001 projected Aboriginal population based on the 1996 adjusted census population seems to be lower by 7% over the 2001 Census adjusted Aboriginal population. In contrast, the projected populations for North American Indians and Inuit are lower by -0.20% and -2.73%. However, for the Métis the error of closure is extremely high, at -24.84%. Reasons for the higher error of closure for the Métis such as the effects of intra-generational ethnic mobility will be discussed in the paper.

Impact of intercensal population projections and error of closure on breast cancer surveillance: examples from 10 California counties

IntroductionIn 2001, data from the California Cancer Registry suggested that breast cancer incidence rates among non-Hispanic white (nHW) women in Marin County, California, had increased almost 60% between 1991 and 1999. This analysis examines the extent to which these and other breast cancer incidence trends could have been impacted by bias in intercensal population projections.MethodWe obtained population projections for the year 2000 projected from the 1990 census from the California Department of Finance (DOF) and population counts from the 2000 US Census for nHW women living in 10 California counties and quantified age-specific differences in counts. We also computed age-adjusted incidence rates of invasive breast cancer in order to examine and quantify the impact of differences between the population data sources.ResultsDifferences between year 2000 DOF projections and year 2000 census counts varied by county and age and ranged from underestimates of 60% to overestimates of 64%. For Marin County, the DOF underestimated the number of nHW women aged 45 to 64 years by 32% compared to the 2000 US census. This difference produced a significant 22% discrepancy between breast cancer incidence rates calculated using the two population data sources. In Los Angeles and Santa Clara counties, DOF-based incidence rates were significantly lower than rates based on census data. Rates did not differ significantly by population data source in the remaining seven counties examined.ConclusionAlthough year 2000 population estimates from the DOF did not differ markedly from census counts at the state or county levels, greater discrepancies were observed for race-stratified, age-specific groups within counties. Because breast cancer incidence rates must be calculated with age-specific data, differences between population data sources at the age-race level may lead to mis-estimation of breast cancer incidence rates in county populations affected by these differences, as was observed in Marin County. Although intercensal rates based on population projections are important for timely breast cancer surveillance, these rates are prone to bias due to the error of closure between population projections and decennial census population counts. Intercensal rates should be interpreted with this potential bias in mind.

Population Estimation Error and Its Impact on 1991–1999 Cancer Rates*

The error of closure in the 2000 census, or the difference between estimated and enumerated populations, poses special problems for public agencies that rely on census data. Nationally and at the state level, populations were only slightly underestimated, but underestimations were high in rapidly growing counties in the South and intermontaine West, as well as in New York City. Race-specific estimates proved far less reliable, with severe overestimates and underestimates of all racial groups in various counties nationwide. We offer explanations for the estimation error and discuss its impact on cancer rates and trends and its implications for cancer surveillance research.

Thermochronology of the Grenville Orogeny in west Texas

Abstract The Carrizo Mountain Group (CMG) comprises the westernmost exposures of the metamorphic core of the Grenville Orogen in Texas. Unlike the correlative Llano uplift, 500 km to the east, the CMG underwent one phase of medium P/T metamorphism; peak T was attained during D2 in all CMG exposures. The peak metamorphic paleotemperatures decrease to the northwest, in the overall direction of tectonic transport, from staurolite to biotite grade. Garnet in the southeast Carrizo Mountains grew isothermally and probably during decompression (i.e. part of a clockwise P–T loop) at ca. 520 °C, in between biotite-grade D1 and D3 events. Hornblende in this region cooled below closure T, during D2, at 1057±6 Ma, within error of muscovite closure in the northwest Carrizo Mountains at 1059±2 Ma. Hornblende in higher grade exposures to the southeast cooled through closure T as late as 1002±7 Ma. Muscovite in the garnet-grade and higher exposures closed to Ar diffusion at 992±4 Ma to 981±3 Ma. Biotite and (partially recrystallized) hornblende from the northwest Carrizo Mountains cooled through closure in this same time period. We interpret these data as signifying: (1) Ar loss due to peak metamorphism in hornblende (southeast Carrizo Mountains) and muscovite (northwest Carrizo Mountains) at ca. 1059 Ma; 2) post-Tmax cooling through 500 °C in the higher grade outcrops until ca. 1000 Ma; and (3) cooling of all CMG exposures through 300 °C, due to uplift along the Streeruwitz thrust and erosion, from 1000 to 980 Ma. These ages significantly post-date known tectonism in the Llano uplift and extend the duration of Grenville orogenesis in Texas by ca. 115 million years. The 1000–980 Ma time period is a time of thrusting in frontal regions of the Grenville Province of Canada and the northeastern US, and shearing in the Natal Province, South Africa, suggesting ultimate closure of the Grenville Orogen and supporting recent Rodinia reconstructions.

Derivation by statistical methods of phase information from multiple-wavelength anomalous diffraction data. Basic questions, 'best' electron-density map, implementation and tests.

A probability distribution of the structure factor is established from the analysis of the effects of errors involved in the multiple-wavelength anomalous diffraction (MAD) method. This probability distribution, derived from those of the intensities, is two-dimensional for acentric reflections and uni-dimensional for centric reflections. It permits, using the centroid of the distribution, the calculation of the modulus and the phase of the 'best' structure factor. The procedure for extracting the phase and its figure of merit is presented. Tests performed on simulated data show the contribution of this method with respect to other methods which use a distribution of only the phase as a function of the error of closure.

A flexible portable system for measurement of air temperature and humidity

The Department of Physical Geography, Lund, has, in cooperation with Chemical Dynamic Sweden AB (CDS) in Skara, Sweden, developed a flexible portable system which can be used for temperature and humidity measurements both from a car or while carried on foot. The major system is composed of two minor systems, the field system and the stationary system. The field system is built around a micrologger from Campbell Scientific Inc. (CSI, Model 21X) and consists of six different sensors (five which measure air temperature and one which measures humidity), a cassette memory, a switch closure and a box with buttons for adding extra information to the memory (location, etc.). The sensors are attached to a mast at different levels (0.2, 1.0, 2.0 and 3.0 m) and are easy to move. The stationary equipment consists of an IBM AT computer, a cassette interface (CSI, Model C20) and a flex-hammer printer. Tests have shown that the accuracy of the temperature measurements is ∼ ± 0.3°C. The accuracy of the humidity measurements is ± 1% RH. The error of the switch closure, which measures the way the car runs, has been measured at 0.03%. It takes the logger 80.5 ms to measure the six sensors and put the values in the memory. This means that it is possible to measure each fifth meter at a speed of 50 km h −1. Tests have shown that 50 km h −1 is the highest speed recommended for car measurements. In our case, we have chosen to make measurements at every 10 m from a car at a speed of 40 km h −1. The system has been used since 1986 in a project concerning nocturnal air temperature in an orchard district and was found to be very convenient and reliable.

The effect of intercepted rainfall on the water balance of a hardwood forest

Evaporation from a large hardwood forest is estimated from measurements of the required meteorological variables and from measured stomatal resistances. A correction factor is derived to overcome the incorrect assumption that evaporative demand remains the same during wet and dry periods. The factor is based on the ratio of the isothermal resistances during the wet and subsequent dry periods. The stomatal measurements were converted to canopy resistances by dividing by the leaf area index and were used to obtain the water balance for the entire season. The results are analyzed to show that evaporation from a wet canopy is often 2–3 times greater than transpiration from the same surface. Rates of interceptional loss, calculated from the wet and dry evaporation rates, were verified by direct measurements of throughfall and stemflow. Net interceptional loss, equal to the excess evaporation from a wet canopy over a dry one, depended on rainfall duration and character and was on the average about 60–80% of total interception, In the overall summer water balance of 442 mm of precipitation and 52‐mm depletion of soil storage, transpiration via the trees accounted for 261 mm; evaporation from the wetted leaves and branches for 111 mm, and runoff for 131 mm, giving an error of closure in the water balance of only 9 mm. If transpiration only had been used instead of interception when the canopy was wet, the error in the water balance would have been 100 mm.

Accuracy of Determination of Relative Gravity by Torsion Balance

Determination of relative gravity by the Eotvos torsion balance has been shown by Oltay and others to be as accurate as the determination by the invariable pendulum. In the present paper, the probable error of the torsion balance determination of relative gravity is calculated from the error of closure of 45 traverses comprising 2,800 stations, most of them in the Gulf Coast region. The probable error of each individual observation in those surveys is calculated to have been ±2.2 Eotvos units for the traverses taken together, or from ±1.9 E for the traverses with the larger station interval to ±5 E for the traverses for the small station interval. But the greater error of the individual observations in the traverses which have the shorter station interval h s been compensated, intentionally, by that shorter interval, and the probable error of the determination of relative gravity by those 45 traverses is approximately 0.4 milledyne per 10 kilometers of traverse without regard to the magnitude of the probable error of the individual observations or of the station interval. The probable error of the determination of relative gravity between key points in good torsion balance surveys presumably is approximately ±2.5 to ±3.5 E per 10 kilometers airline distance between the two places. If pendulum determinations of relative gravity are used to supplement and to increase the accuracy of torsion balance surveys, there is a minimum interval at which the pendulum stations should be placed, for at lesser intervals the determination of relat ve gravity by the torsion balance is more accurate than that by the pendulum. That minimum interval ranges from 100 to 200 kilometers for the pendulum observations of the first quarter of the century to 8 to 50 kilometers for first class modern pendulum observations.

Excessive cases of lateral refraction

Lateral, or horizontal, refraction is quite frequently encountered in the angular measurements of triangulation systems, but its occurrence is usually spasmodic and may usually be attributed to air currents or pockets on lines in proximity to buildings, mountain masses, etc. Two cases of consistent lateral refraction have occurred in Canada which permit the underlying causes in these cases to be investigated and, perhaps, explained.An extended and persistent example of lateral refraction was met on the triangulation net of the St. Lawrence River and Gulf, the field work of which covered some 325 miles and extended over four seasons. In this net the lines along the river bank were so consistently “bent” towards the river that a practice had to be adopted of ending observations on these lines only when the results on at least two nights showed a satisfactory agreement. Lateral refraction affecting the observations by from 5 seconds to 15 seconds of are was not at all uncommon, and it has been estimated that almost three times the amount of clear weather ordinarily necessary to secure the required program of observations was used to secure the required accuracy. Even with the precautions which were taken, the evidence shows a regular bending towards the river of the lines parallel to the river. This is evidenced by the error of closure of triangles, the sum of the three observed angles being less than the theoretical sum in the majority of cases.