Neumann Method Research Articles

Analytical solutions to the one‐dimensional nonlinear diffusion equation for flow through porous media

The one‐dimensional nonlinear diffusion equation is solved approximately by an extension of the Neumann method for a step input to a semi‐infinite medium. The method of solution requires that the region under consideration be divided into an arbitrary number of zones, each zone having known constant diffusivities. The boundaries between zones move at rates that are initially unknown. Two problems are considered: (1) horizontal flow in an aquifer in which the transmissivity and storage coefficients are functions of hydraulic head and (2) horizontal absorption in an unsaturated soil for which the diffusivity is a function of moisture content. Computational results compare well with finite difference and other numerical solutions to the same problems. The technique has application to other nonlinear problems of the same type.

On the screening, diagnosis and investigation of hereditary aminoacidopathies

There are over 60 inborn errors of amino acid metabolism now recognizable to the clinician and biochemist. Some are associated with disease, others are not. Technology has played a large role in permitting the discovery of “new” aminoacidopathies, and in identifying subjects with acquired or inherited disorders of amino acid metabolism. Moreover simplified and efficient methods can permit mass screening of populations to find the rare person, with incipient disease due to perturbed amino acid metabolism, who may escape detection by the conventional methods of medical diagnosis. This article describes the range of methods available for specific investigation of aminoacidopathies in man, and discusses their relative advantages and disadvantages. The principles and practices of mass screening are also discussed, and a survey of simple laboratory tests, of use in the initial investigation of the patient, is included. Pitfalls in the interpretation of analytic data are considered, and classifications of the disorders of amino acid metabolism are given, with emphasis on the diagnostic approach to probands and heterozygotes and the various body fluids and cell types accessible to pre- and post-natal examination of amino acid metabolism. 1. The paper outlines the efforts made to improve the quality of the determination of amylase in serum by means of amylopectin combined with the “Reactone Red 2B” dye. 2. The enzyme kinetics were studied, after checking the maximum absorption of the hydrolysis products in solution, which are responsible for the amylase activity, and plotting a reference curve. 3. After assessing the precision of the aforesaid technique, the Neumann method (6) was used to determine the normal values for 186 persons. 4. When the activity in serum is high, the original serum must be diluted with albumin. 5. All the reagents required for the amylase determination and used in the study are commercially available from Warner Chillcott Laboratories, Morris Plains, N.J. 07950, under the trade name “Dy Amyl”.

An existence theorem for Robin's equation

AbstractAn existence theorem is proved for Robin's integral equation for the density of electric charge on a closed surface, under the assumptions that the surface is convex, smooth and twice continuously differentiable. The technique is essentially Neumann's method of the arithmetic mean, used by Robin himself to show that the solution, assumed to exist, can be successively approximated by a sequence. In order to facilitate the main argument of the proof, it is assumed initially that the Gaussian curvature is everywhere positive, but this restriction is subsequently removed.

Von Neumann's Comparison Method for Random Sampling from the Normal and Other Distributions

Von Neumann's Comparison Method for Random Sampling from the Normal and Other Distributions

Modification of the alternating direction implicit method and connections with von Neumann's method

Modification of the alternating direction implicit method and connections with von Neumann's method

GENERALIZATION OF A THEOREM BY JOHN VON NEUMANN ON THE TRACE OF CERTAIN MATRIX PRODUCTS1

ABSTRACTIn 1937, John von Neumann gave a theorem on the maximum of the real part of the trace of a matrix product Z1A1Z2A2 where A1,A2 are fixed complex matrices and Z1,Z2 run independently over all unitary matrices. The theorem is extended to admit analogously tr Z1A1 … ZnAn, n > 2. The Proof is not related to von Neumann's method. Four seemingly different, but in fact equivalent, versions of the result are given. These differences stem from initially requiring Aj to be real diagonal as well as from considering separately the maxima of the absolute value, the real part and the imaginary part of tr Z1A1 … ZnAn. An application is given by way of illustration.

Interaction of Supernova Remnants with the Interstellar Medium.

view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Interaction of Supernova Remnants with the Interstellar Medium. Goldreich, Peter ; Sargent, Wallace L. W. Abstract We investigate the way in which the shock-wave produced in the interstellar medium by a supernova explosion slows. The shock path and the motion of the gas behind the shock are computed numerically using von Neumann and Richtmyer's method of artificial viscosity. We take into account the effects of radiative cooling behind the shock front. The cooling has an important effect on the motion for old remnants and leads to thermal instabilities in obj ects as old as the Cygnus Loop. We conclude that the visible filaments in the Loop are regions of thermal instability where the density rises and the temperature falls by large factors from their values immediately behind the shock front in a distance of the order of 0.01 PC. A shell of cool gas having a density about 102 times that in the undisturbed interstellar medium must lie behind the filaments in the Cygnus Loop. The mass in this shell should be greater than 100 M0 and is perhaps as great as 1000 M0. We also investigate the motion taking into account the interstellar magnetic field. In this case, as has been shown by van der Laan, the compression of the magnetic field limits the density rise in the thermal instability behind the shod~. Publication: The Astronomical Journal Pub Date: February 1966 DOI: 10.1086/110009 Bibcode: 1966AJ.....71Q.162G full text sources ADS |

Current Distribution in a Thin-Film Superconducting Strip Transmission Line

In the long-wavelength limit, the current distribution in a thin-film superconducting strip transmission line can be described by an inhomogeneous Fredholm equation of the second kind. By considering a fluxoid conservation derivation of this equation, physical insight into the structure of the kernel follows naturally. An approximate analytic solution to the integral equation is derived for a specified range of geometrical parameters commonly encountered in practice. The solution is obtained by making use of the Liouville—Neumann method of successive iterations and approximating the resulting series by a series involving powers of a defined coupling factor. It is shown that the critical current of the thin-film superconducting strip transmission line, based on the calculations in the paper and a critical-current-density hypothesis, is underestimated by less than 10%.

An a priori determination of serial correlation in computer generated random numbers

1. Background. Ever since John Von Neumann introduced the method some ten years ago [11], users of pseudo-random numbers on modern digital computers have been generating their numbers as they were required in application, rather than drawing them from a table formed beforehand or obtaining them from a special-purpose device built expressly for this service. The advantages of Von Neumann's method were its speed, minimal storage requirements, and ability to be restarted from any desired point. For some years now the mid-square method has been replaced by other recursive methods which have increased further the advantages of this general technique of generation. The most popular of these has been the multiplicative method proposed by Lehmer in 1951 [2]. An interesting variation of this method, which we may call the method, recently has received the attention of several authors [1, 9, 10]. We adopt the notation of Coveyou, one of these authors. The mixed congruential method then may be written

New Look at von Neumann's Operator Method in Quantum Statistics. I

This paper attempts to explain both the basic concepts and the mathematical formalism of von Neumann's operator method in quantum statistics, in terms that should be understandable by anyone who has mastered first courses in quantum mechanics and statistical mechanics. A simple model is used throughout the paper to illustrate the various theorems and techniques. The discussion begins with the statistical interpretation of the Heisenberg uncertainty principle, the definition of mixed ensembles, and the meaning of measurement in quantum mechanics. The von Neumann projection operator is explained, and is used to set up the ensemble density matrix and the von Neumann entropy operator. In the second part of the paper, to be published later, the quantum-mechanical equation of change with time is applied to the von Neumann operators.

ON THE JOINT DISTRIBUTION OF THE CIRCULAR SERIAL CORRELATION COEFFICIENTS

Quenouille (1949) applied Koopmans's method (1942) to the problem of finding the exact joint distribution of the serial correlation coefficients in the null case. Madow's (1945) device was used to derive the non-null joint density function. For odd sample sizes, lie gave an explicit formula for the exact density function. Since the direct smoothing of this function is very difficult, Quenouille conjectured a smooth approximation to the exact density and supported his conjecture by various arguments about the expected form of the result. Jenkins (1954), following Dixon's (1944) method, has found a smoothed density for the first two serial correlation coefficients which, unlike Quenouille's density, has the correct moments up to order n. These smoothed densities were derived for the csase of no mean corrections.$ In ? 2 of the present paper, von Neumann's (1941) method is generalized to give integral equations for the joint density of the serial correlations. From these the relationship of the null and non-null densities is easily derived. In ? 3 the exact density of the circular serial correlations is obtained for arbitrary sample sizes, and a fuller discussion is given of the interesting summation rule involved. In ? 4 an attempt is made to derive an approximate null density when mean corrections are made by a new smoothing method. The form found differs only slightly from Quenouille's and is subject to the same weaknesses.

Application of second quantization methods to the classical statistical mechanics

The classical mechanics of indistinguishable particles discussed in I is further developed. The mechanical foundations of thermodynamics are discussed with the classical wave theory and the “quantized” fields in phase space. It is shown that the formalism eliminates automatically the Gibbs paradox. The classical statistics is treated with the Gibbs-von Neumann method and also by a generalized form of the Boltzmann method which allows to take into account the interactions. The introduction of finite cells in phase space leads to formulas similar to those of the quantal statistics for free particles, but no, more so for interacting particles. The statistical treatment of the «quantized» field in phase space leads immediately to the canonical grand ensemble. It is shown that the theory of the «quantized» fields in phase space can be derived from the theory of a «non-quantized» field in phase space, in which there are only continuous distributions of matter, by a procedure of «quantization» altogether similar to that of the quantum theory of fields, but not involving the Planck constant, or any other universal constant. The «non-quantized» field in phase space corresponds to a theory less accurate than the classical mechanics and gives an approximation of the same kind as the molecular chaos hypothesis of the kinetic gas theory, it contains both the dynamics and the heat theory of a continuous medium. A new derivation of the Boltzmann equation involving a special kind of time average is given and a similar equation is established for the two particle distribution function.

On the recorded motion of the S phase at Florissant*

Abstract The initial motions of the P and S phases have been tabulated from the original seismograms of sixty earthquakes which recorded at the Florissant station in the years 1927–1938. The epicenters of these earthquakes were within limited areas of the following regions: the Aleutian Islands, the west-central coast of South America, and Central America. The study indicates that the Florissant seismograms show a preferential direction of motion for both P and S waves in the recordings of certain earthquakes from selected regions. The data compiled on the S phase indicated that a majority of the Aleutian and South American earthquakes recorded a sharp impulsive initial northeast motion at Florissant. The Central American earthquakes studied recorded S phases of somewhat indefinite onset which did not exhibit a preferential motion as they were read. The results of the application of Neumann's method of S-wave analysis to the Saint Louis seismograms of two selected Aleutian Island earthquakes are presented and a brief discussion of some possible structural implications of the various data is given.

A Quantum Mechanics Treatment of the Water Molecule

The perturbation method of Heitler and London has been applied to study the interaction of the atoms in the water molecule. For a preliminary calculation an arbitrary internuclear distance has been assumed, and no ionic wave function has been considered. The calculated binding energy, 3.5 volts, is too small, as was to be expected. An analysis of the sources of this energy in various types of resonance or electron interchange is developed, and the results compared with Slater's simplified model. Methods for the evaluation of electron reactions involving three centers are described, including a possible alternative for the customary Neumann method, applicable to two-center problems. Formulas for products of bi-axial surface harmonics and their integrals are given.

On the factor to be used for the calculation of the phosphoric acid in Neumann's method. The factor as influenced by the water used for washing the yellow precipitate

On the factor to be used for the calculation of the phosphoric acid in Neumann's method. The factor as influenced by the water used for washing the yellow precipitate

The estimation of "acid-soluble" (inorganic?) and lipoid phosphorus in small quantities of serum

Phospholipins are quantitatively precipitated with the proteins when blood or serum is added to nine parts of a solution containing one per cent. each of acetic and picric acids. The precipitate does not absorb phosphates. This procedure has been combined with the Neumann method of oxidation and the method of Pouget and Chouchak for the estimation of phosphoric acid for the purpose of estimating the “acid-soluble” and the lipoid phosphorus in small quantities of serum (one cubic centimeter or less). The results agree with those previously obtained by other methods upon large amounts of serum. In nephritis, the “acid-soluble” phosphorus may be increased to as much as five times the normal amount. It may also be slightly increased after the ingestion of meat.

On the accuracy of Neumann's method for the estimation of phosphorus

On the accuracy of Neumann's method for the estimation of phosphorus

Local Anæsthesia for Aural Operations, with Special Reference to Dr. Neumann's Method

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Local Anæsthesia for Aural Operations, with Special Reference to Dr. Neumann's Method

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Laboratory Physics

THIS manual by the professor of physics in the Case School of Applied Science, Boston, is the result of twelve years of teaching experience, and most of the descriptions have been employed in type-written form for the past six years. It is not intended as a preparatory course; at the same time the majority of the experiments are of a fairly simple type. Constant references to existing text-books of practical physics (both English and American) show that the author has made free use of all sources of information, which is duly acknowledged. Many of the experiments are not usually met with in text-books, or at any rate are not met with in so full a form. Thus the complete calibration of a scale by Neumann and Thiesen's method is fully described (though without the theory, for which reference is made to Guillaume, “Thermo-métrie”), and there is an account of the use of Michel-son's interferometer.