Similarity Analysis Method Research Articles

Aircraft Trajectory Optimization in the Horizontal Plane

Abstract The problem of minimum time trajectory optimization for aircraft in the presence of winds is considered. The solutions are obtained by employing a parametrization technique based on the famous theorem of Caratheodory in order to reduce the problem into a finite dimensional optimization problem, without using the minimum principle or similar analysis methods. Numerical solutions are presented for cases with and without the presence of winds in order to demonstrate the effect of winds on the trajectory planning.

Titan Haze: Structure and Properties of Cyanoacetylene and Cyanoacetylene–Acetylene Photopolymers

The structure and morphological properties of polymers produced photochemically from the UV irradiation of cyanoacetylene and cyanoacetylene mixtures have been examined to evaluate their possible contribution to the haze layers found on Titan. A structural analysis of these polymers may contribute to our understanding of the data returned from the Huygens probe of the Cassini mission that will pass through the atmosphere of Titan in the year 2004. Infrared analysis, elemental analysis, and thermal methods (thermogravimetric analysis, thermolysis, pyrolysis) were used to examine structures of polycyanoacetylenes produced by irradiation of the gas phase HC 3N at 185 and 254 nm. The resulting brown to black polymer, which exists as small particles, is believed to be a branched chain of conjugated carbon–carbon double bonds, which, on exposure to heat, cyclizes to form a graphitic structure. Similar methods of analysis were used to show that when HC 3N is photolyzed in the presence of Titan's other atmospheric constituents (CH 4, C 2H 6, C 2H 2, and CO), a copolymer is formed in which the added gases are incorporated as substituents on the polymer chain. Of special significance is the copolymer of HC 3N and acetylene (C 2H 2). Even in experiments where C 2H 2was absorbing nearly all of the incident photons, the ratio of C 2H 2to HC 3N found in the resulting polymer was only 2:1. Scanning electron microscopy was used to visually examine the polymer particles. While pure polyacetylene particles are amorphous spheres roughly 1 μm in diameter, polycyanoacetylenes appear to be strands of rough, solid particles slightly smaller in size. The copolymer of HC 3N and C 2H 2exhibits characteristics of both pure polymers. This is particularly important as pure polyacetylenes do not match the optical constants measured for Titan's atmospheric hazes. The copolymers produced by the incorporation of other minor atmospheric constituents, like HC 3N, into the polyacetylenes are expected to have optical constants more comparable to those of the Titan haze.

Aircraft Trajectory Optimization in the Horizontal Plane

The problem of minimum time trajectory optimization for aircraft in the presence of winds is considered. The solutions are obtained by employing a parametrization technique based on the famous theorem of Caratheodory in order to reduce the problem into a finite dimensional optimization problem, without using the minimum principle or similar analysis methods. Numerical solutions are presented for cases with and without the presence of winds in order to demonstrate the effect of winds on the trajectory planning.

Reassessment of the reported correlations between gravitational waves and neutrinos associated with SN 1987A.

Correlations of considerable apparent significance have been reported between data taken by two bar-type gravitational wave detectors and particle events recorded in the Mt. Blanc, Kamiokande, and IMB particle detectors during a 2-h period near the explosion of Supernova 1987A. In particular, the correlations among the gravitational wave detectors and the Mt. Blanc neutrinos were claimed to have a chance probability of less than ${10}^{\mathrm{\ensuremath{-}}6}$. If this low probability implies that the correlations are a real physical effect, then new physics will be required to explain them. However, one of the statistical tests used to establish these correlations is seriously flawed, and most others were devised a posteriori and contain considerable freedom to make choices that affect the probability of finding correlations. By a careful consideration of these free parameters, and by applying similar analysis methods to simulated pseudorandom data sets, we show that the actual frequency with which correlations similar to those in the Mt. Blanc data would occur in random data streams is between 0.1% and 10%. Moreover, if the Mt. Blanc correlations were real, then one would expect them in the other particle detectors. After inspecting the evidence, we also conclude that there are no physically significant correlations of the Mt. Blanc--type between the gravitational wave detectors and the Kamiokande and/or IMB particles. This makes it very likely that the Mt. Blanc correlations are due, not to any physical effect, but simply to chance.

Reconnaissance geochemistry and its environmental relevance

Abstract In Canada, geochemical reconnaissance using lake and stream sediments and waters has been a cooperative program between federal and provincial geological survey organizations since the 1970's. Similar methods of sampling, analysis and quality control were established to ensure comparable data across the country. As of 1992, 2.5 million km2, or approximately one quarter of Canada's landmass has been covered. The original purpose of this National Geochemical Reconnaissance (NGR) was to assist mineral exploration. However, with time, the relevance of the data to environmental issues has become increasingly apparent. The concentrations of metals in the natural environment vary widely and in some areas unaffected by human activity may reach levels that elsewhere have been considered to have an effect on the ecosystem. Environmental agencies need to incorporate the natural distribution of metals into assessments of ecosystem health and anthropogenic pollution. Sediment quality guidelines, standards or clean-up criteria, are required for the assessment and remediation of contaminated areas under a variety of programs in Canada. These standards need to take into account the natural background of metals in the affected areas. For instance, under the Canadian Environmental Protection Act, a sediment Cd concentration of 0.6 ppm is used to screen ocean dumping permits and yet 20% of the lake and stream sediment samples collected by the NGR exceed this level naturally. We present Canada-wide maps illustrating the regional variability of As, Cd, Cu, Hg, Ni, Pb, Zn and U in sediments, together with more detailed maps for selected areas. Cumulative frequency distribution plots for these elements plus Cr have been constructed based on up to 250,000 samples. At the scale that the maps are presented, anomalies a few km2 or tens of km2 in extent, which may be associated with individual mineral deposits, are not visible. What may be observed are large, regional anomalies hundreds or thousands of km2 in extent. In some cases these may mark important mineral districts, such as U around the Athabasca and Elliot Lake uranium districts and the suite of metals that are enriched in stream sediments from the Selwyn Basin, Yukon that contains a variety of Sedex, Mississippi Valley and intrusion-related mineral deposits.

Similarity Solutions of the Force-free Magnetic Field Equations

Abstract Force-free magnetic fields are described as solutions of special nonlinear partial differential equations which are replaced frequently through linear equations. To record the diversity of the structures of these fields, a discussion of the nonlinear equations is necessary. For this purpose the method of similarity analysis is used. The Lie symmetry groups admitted by the nonlinear equations for force-free magnetic fields are presented. To record and classify the different types of group-invariant solutions, one-and two-dimensional optimal systems of subalgebras are listed. The reduced equations of the two-dimensional optimal system are systems of ordinary differential equations, and their solutions define similarity solutions which are force-free magnetic fields. Only in one case is it necessary to calculate similarity solutions numerically. The corresponding reduced equations are a nonautonomous dynamical system with the similarity variable in the place of time.

Non-Lorentzian Rayleigh spectra of bulk homopolymers far above the glass transition.

Non-Lorentzian depolarized Rayleigh-scattering spectra have been clearly observed by Fabry-Perot interferometry in bulk homopolymers, polyisoprene and 1,4-polybutadiene, far above the glass-transition temperature. We have developed two alternative phenomenological methods for analyzing this kind of spectra. First of all we have used a scattering model function based on the Havriliak-Negami relaxation function which, in fact, is compatible with a Kohlrausch-Williams-Watts relaxation function in the time domain. In the case of polyisoprene, the results obtained by this method are in good agreement with the obtained ones through other different relaxation techniques when a similar method of analysis is applied. Besides, we have extended to the frequency domain the contin algorithm which calculates an apparent distribution function of relaxation times from nonexponential time domain relaxation functions. The results obtained as well as the applicability of both methods are discussed.

Determination of Fracture Toughness for Wood

Determination of fracture toughness values in modes I and II for wood are considered. The testing methods are based on the American Society for Testing and Materials standard “plane strain fracture toughness of metallic materials,” which considers mode I only. For the \IK\N\dI test, a modification of the standard is proposed. It is proposed that crack initiation be done with a very thin blade saw, and a larger nonlinearity of the load-displacement curve is suggested. For the \IK\N\dI\dI test, a similar testing and analysis method is applied to a beam specimen with an end crack. Fracture toughness values are presented, and their dependence on the material and experimental parameters is studied. For mode I, the orientation of the specimen is of great importance. For mode II, the most important variable is the density of the wood material. The fracture toughness value for modes I and II was not affected by the moisture content of the specimens in the range of 10–20%.

Studies on protein-DNA interactions using the resonant recognition model. Application to repressors and transforming proteins.

The structural features of protein-DNA interactions have been evaluated using a new information theory algorithm for the analysis of protein structure/function dependence: the so-called resonant recognition model. The physicochemical basis of this analysis was firstly validated with the trp-repressor-operator interaction as a well-defined example. The amino acid and structural features predicted by these procedures to be crucial for repressor-operator interaction were found to be clustered around the known three-dimensional structure of the active site of the trp repressor. Similar methods of analysis have been extended to the less-well-defined example of the Ha-ras p21 protein family. The results of this analysis have indicated two distinct interactive regions in p21, one associated with the guanine-nucleotide-binding site, whilst the second is proposed to be associated with a binding site for an activator protein. These studies indicate that the p21 protein, besides the ability to function as a plasma-membrane-associated guanine-nucleotide-binding regulatory protein and bind free guanine nucleotides in the cytoplasm, has the structural ability to bind guanine incorporated in DNA. Thus, p21-related proteins may have the potential to function as an DNA-binding and regulating protein with the mode of upstream DNA binding closely related to their oncogenic function.

Meningococcal Meningitis in Sub-Saharan Africa: A Model for the Epidemic Process

Epidemic group A meningococcal meningitis follows a unique and distinctive pattern in sub-Saharan Africa. Advances in molecular and field epidemiology have begun to elucidate the mechanisms of meningococcal meningitis epidemics. Epidemics result from a complex combination of host, organism, and environmental risk factors. Recent studies suggest that "antigenic shifts" in group A meningococcal clones may trigger an outbreak of disease by suddenly decreasing herd immunity within a population. Although the introduction of new group A meningococcal strains into a susceptible population contributes to the likelihood of an epidemic, the presence of additional environmental factors, such as low humidity and coincident respiratory tract infections, are also necessary for an epidemic to occur. Despite the unique behavior of group A meningococcal disease in sub-Saharan Africa, the application of similar methods of epidemiological analysis may be useful for determining epidemic processes for other diseases.

Lithofacies Analysis of Colluvial Sediments--An Aid in Interpreting the Recent History of Quaternary Normal Faults in the Basin and Range Province, Western United States

Inferring the frequency and magnitude of past earthquakes from the stratigraphy in exposures of normal-faulted sediments is difficult because colluvial lithofacies assemblages adjacent to faults are complex. Similarities in facies assemblages adjacent to young fault scarps in arid to semiarid areas, such as the Basin and Range province, allow lithofacies to be grouped into two genetic architectural elements: debris and wash elements. Upper and lower facies associations can commonly be recognized within each element. A lithofacies code scheme, similar to those used in the analysis of fluvial and glacial lithofacies sequences, provides a concise way of illustrating lithofacies relations in fault exposures. The source lithology of colluvial lithofacies is shown in the code, and soil-horizon symbols can be included. The architecture of lithofacies assemblages near fault scarps in semiarid areas is explained by a model of colluvial sedimentation in response to a single surface faulting event. Analysis of lithofacies assemblages exposed in three trenches across normal faults in the eastern Basin and Range shows how the model can be used to interpret fault histories. Similar facies analysis methods may be useful in interpreting colluvial sequences formed by non-tectonic processes.

Partially Invariant Solutions for Two-dimensional Ideal MHD Equations

Abstract A generalization of the usual method of similarity analysis of differential equations, the method of partially invariant solutions, was introduced by Ovsiannikov. The degree of non-invariance of these solutions is characterized by the defect of invariance d. We develop an algorithm leading to partially invariant solutions of quasilinear systems of first-order partial differential equations. We apply the algorithm to the non-linear equations of the two-dimensional non-stationary ideal MHD with a magnetic field perpendicular to the plane of motion.

Methods of similarity analysis in the study of nonlinear dynamics of a gas mixture

Abstract On the basis of a Lie group analysis similarity variables are first derived, and, then, some exact invariant solutions are constructed for a semi-linear hyperbolic system governing the evolution of the number densities of a mixture of N = 2 gases of interacting particles.

An Isoeffect Approach to the Study of Combined Effects of Mixed Radiations: The Nonparametric Analysis of in Vivo Data

The combined effects of mixed radiations can be examined using a system of simple isoeffect relations which are derived from a recent analysis of in vitro results obtained for a variety of radiation mixtures. Similar isoeffect analysis methods have been used for over two decades in studies of the combined action of toxic agents such as drugs and antibiotics. Because of the isoeffect approach, the method is particularly useful for the analysis of ordinal data for which conventional models that are based on parametric dose-effect relations may not be suitable. This is illustrated by applying the method to the analysis of a set of recently published in vivo data using the mouse foot skin reaction system for mixtures of neutrons and X rays. The good agreement between this method and the ordinal data also helps to provide further experimental support for the existence of a class of radiobiological data for which the simple isoeffect relations are valid.

Tin(II) chloride in the analytical chemistry of the platinum metals: From the “purple of cassius” to polyurethane foams

Tin(II) chloride has played a central role in the non-instrumental analytical chemistry of the platinum group metals, the characteristic reaction between tin(II) chloride and platinum(II/IV) chloride having been documented for more than 180 years. The intense colour of hydrochloric acid solutions containing small amounts of Pt(II/IV) and tin(II) chloride constituted one of the first trace colorimetric methods for the determination of Pt in the sub parts per million range. Similar spectrophotometric methods of trace analysis for Rh have been known for more than half a century. Remarkably the detailed nature of the interaction of tin(II) chloride with the platinum group metals has only been elucidated relatively recently, and there is evidence of recent renewed interest in platinum group metal complexes involving the SnCl 3 − moiety as ligand. We wish here to give a brief history of the use of tin(II) chloride in the analytical chemistry of the platinum group metals, highlighted by some of our recent work involving the selective immobilization of chloro(trichlorostannato)platinum/rhodium complex anions by polyurethane foams as a means of separation and pre-concentration of small amounts of Rh and Pt.

An investigation of arterial insufficiency in the rat hindlimb. Correlation of skeletal muscle bloodflow and glucose utilization in vivo.

Muscle bloodflow and the rate of glucose uptake and phosphorylation were measured in vivo in rats 7 days after unilateral femoral artery ligation and section. Bloodflow was determined by using radiolabelled microspheres. At rest, bloodflow to the gastrocnemius, plantaris and soleus muscles of the ligated limb was similar to their respective mean contralateral control values; however, bilateral sciatic nerve stimulation at 1 Hz caused a less pronounced hyperaemic response in the muscles of the ligated limb, being 59, 63 and 49% of their mean control values in the gastrocnemius, plantaris and soleus muscles respectively. The rate of glucose utilization was determined by using the 2-deoxy[3H]glucose method [Ferré, Leturque, Burnol, Penicaud & Girard (1985) Biochem. J. 228, 103-110]. At rest, the rate of glucose uptake and phosphorylation was statistically significantly increased in the gastrocnemius and soleus muscles of the ligated limb, being 126 and 140% of the mean control values respectively. Bilateral sciatic nerve stimulation at 1 Hz caused a 3-5-fold increase in the rate of glucose utilization by the ligated and contralateral control limbs; furthermore, the rate of glucose utilization was significantly increased in the muscles of the ligated limb, being 140, 129 and 207% of their mean control values respectively. For the range of bloodflow to normally perfused skeletal muscle at rest or during isometric contraction determined in the present study, a linear correlation between the rate of glucose utilization and bloodflow can be demonstrated. Applying similar methods of regression analysis to glucose utilization and bloodflow to muscles of the ligated limb reveals a similar linear correlation. However, the rate of glucose utilization at a given bloodflow is increased in muscles of the ligated limb, indicating an adaptation of skeletal muscle to hypoperfusion.

Une certaine methode de calcul des echangeurs de chaleur

A heat transfer analysis of a type of heat exchanger is presented in this paper. The conservation laws are limited to the energy balance equations expressed by the first order partial differential equations system (1) or (2). Similar problems have been considered in the past but the exact solution has not been presented. The analytical solution of the equation system is given in the form (3). The heat exchanger equations are the particular case of this equation system. A similar analysis method can be applied in the theory of recuperators and regenerators. Obtaining the general solution for the extension of the heat exchanger problem increases the number of the physical phenomenons which can be analyzed with the aid of the method presented here. Numerous conservation laws can be described by the differential equations systems discussed in this paper, while the method used allows the analysis of various problems described by this type of equation to be simplified.

The Scarcity Syndrome: Comment

American Journal of Agricultural EconomicsVolume 65, Issue 1 p. 158-159 Note The Scarcity Syndrome: Comment Michael V. Martin, Michael V. Martin associate professor Department of Agricultural and Resource Economics, Oregon State UniversitySearch for more papers by this authorRay F. Brokken, Ray F. Brokken agricultural economist with National Economic Division and adjunct professor Department of Agricultural and Resource Economics Economic Research Service, U.S. Department of Agriculture, Oregon State UniversitySearch for more papers by this author Michael V. Martin, Michael V. Martin associate professor Department of Agricultural and Resource Economics, Oregon State UniversitySearch for more papers by this authorRay F. Brokken, Ray F. Brokken agricultural economist with National Economic Division and adjunct professor Department of Agricultural and Resource Economics Economic Research Service, U.S. Department of Agriculture, Oregon State UniversitySearch for more papers by this author First published: 01 February 1983 https://doi.org/10.2307/1240353AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article. Volume65, Issue1February 1983Pages 158-159 RelatedInformation

Unified Analysis of Drawdown and Buildup Data for Physical Model Reservoir Flow With Producing Well at Center of Vertical Fracture

Abstract A physical model of a gas reservoir having a vertical fracture with fracture half-length xf = 0.0635 m was developed. The model is a right circular cylinder of latex concrete with the radius xe = 0.305 m so that the xe/xf ratio is 4.8. The producing well is located at the center of the fracture. Experimental drawdown and buildup data taken from this reservoir were analyzed using available theoretical developments from the literature. The effect of pressure on permeability (the Klinkenberg effect) was included in the analysis. Simplex optimization was used in conjunction with unified (drawdown plus buildup) super-positioning to give fracture half-lengths of 0.0631 and 0.0635 m from two sets of experimental data. Corresponding values for permeability for these two sets of data were 0.0605 × 10−18 and 0.0624 × 10−18 m2, respectively, at a Klinkenberg coefficient of 5900 kPa. The fracture half-length and permeability are shown to be highly correlated. Thus, the results have more uncertainty than would be found in determining parameters by similar methods of analysis for an unfractured system. Bearing this in mind, the agreement between the known fracture half-length and values determined from the analysis of experimental data is excellent. Thus, we have demonstrated the utility of unified analysis as well as the ability to create an artificial fracture. Since the location of the model fracture relative to producing and observation wells is at the discretion of the designer, our model presents a unique opportunity to study various configurations which might be difficult to handle by mathematical modeling alone.

Mathematical theory of reduction of physical parameters and similarity analysis

The method of similarity analysis in the study of differential equations is extended to study the variability of parameters in a physical system. The analysis provides an insight into the meaning of “physical” similarity, which usually means the possibility of a reduction in the number of physical parameters characterizing the system. Theorems relating similarities to groups of invariant transformations are proved and employed to show how the number of parameters can be reduced.