Showing papers by "Stevens Institute of Technology published in 1985"

Perturbation Methods in Applied Mathematics

Abstract: 1 Introduction.- 2 Limit Process Expansions Applied to Ordinary Differential Equations.- 3 Multiple-Variable Expansion Procedures.- 4 Applications to Partial Differential Equations.- 5 Examples from Fluid Mechanics.- Author Index.

Ab initio relativistic effective potentials with spin–orbit operators. IV. Cs through Rn

Abstract: A refined version of the ‘‘shape consistent’’ effective potential procedure of Christiansen, Lee, and Pitzer was used to compute averaged relativistic effective potentials (AREP) and spin‐orbit operators for the atoms Li through Ar. These are tabulated in analytic form. Small optimized Gaussian basis sets with expansion coefficients for the lowest energy state for each atom are given and the reliability of the potentials relative to all electric calculations is discussed. Finally a procedure for computing molecular moments and Breit corrections is suggested.

Improved measures of stability robustness for linear state space models

Abstract: In this paper, the aspect of "stability robustness" of linear systems is analyzed in the time domain. A bound on the structured perturbation of an asymptotically stable linear system is obtained to maintain stability using a Lyapunov matrix equation solution. The resulting bound is shown to be an improved bound over the ones recently reported in the literature. Also, special cases of the nominal system matrix are considered, for which the bound is given in terms of the nominal matrix, thereby, avoiding the solution of the Lyapunov matrix equation. Examples given include comparison of the proposed approach with the recently reported results.

A three-dimensional simulation of the Hudson-Raritan Estuary. Part I: description of the model and model simulations.

Abstract: A time-dependent, three-dimensional, finite difference simulation of the Hudson‐Raritan estuary is presented. The calculation covers July–September 1980. The model estuary is forced by time-dependent observed winds, tidal elevation at open boundaries, and river and sewage discharges. Turbulence mixing coefficients in the estuary are calculated according to a second-moment, turbulence-closure submodel. Horizontal diffusivities are zero in the simulation and small-scale eddies produced by the interaction of unsteady, three-dimensional velocity and salinity fields with coastline and bottom bathymetry were resolved by the model. These eddies are important physical elements in shear dispersion processes in an estuary. Model results show unstably stratified water columns produced by advection of waters of different densities. These instabilities produce intense mixing with vertical eddy diffusivities reaching 2–3 times their neutral values. They occur most frequently at slack currents, during initial s...

Quantum-limited laser frequency-modulation spectroscopy

Abstract: Frequency-modulation (FM) spectroscopy permits high-resolution, high-sensitivity, easily calibrated absorption measurements of atomic and molecular species and narrow spectral features in solids. This paper reviews some important developments in laser FM spectroscopy, from its inception as a spectroscopic tool to the demonstration of quantum-limited absorption measurements, emphasizing the sensitivity limitations caused by residual amplitude modulation (RAM). Moreover, a detailed account is presented of a new double-beam, single-detector technique that efficiently suppresses the RAM and permits quantum-limited performance to be achieved in laser FM spectroscopy. We also include some recent results of the first reported FM spectroscopic investigations of the NO2 molecule.

Reliable circulant networks with minimum transmission delay

Abstract: It is well known that maximum connectivity graphs play an important role in the design of reliable networks. The class of symmetric graphs called circulants is known to contain such maximum connectivity graphs. Although not all circulants have this maximum connectivity property, those that do have a great variation in their diameters. Since diameter is a measure of transmission delay, the minimum diameter, maximum connectivity circulant problem is considered here. Several results are given for the general case and a simple solution is derived for the connectivity four case.

Polyatomic, anharmonic, vibrational–rotational analysis. Application to accurate ab initio results for formaldehyde

Abstract: A computer program SURVIB is described for calculating vibrational anharmonicity constants for polyatomic molecules. The program requires as input a grid of calculated energies in the vicinity of a stationary point. This grid is fit, in a least squares sense, to a polynomial function of the internal coordinates. This analytic representation of the energy surface is employed in a normal mode analysis, and the energy is reexpanded as a polynominal function of the normal mode coordinates (expressed as vectors in the mass-weighted atomic Cartesian coordinate space). The resulting coefficients are used in a second-order perturbation theory analysis to obtain the vibrational anharmonicity constants. Also reported is an application of this program to formaldehyde employing ab initio, RHF, MP2, MP3, and RHF-CI calculations. The spectroscopic constants obtained for H2CO are in good agreement with experimentally derived values recently reported by Reisner.

Selective-permeation gas-separation process and apparatus

Abstract: A permeant gas is selectively transferred from a feed-gas mixture which comprises the permeant gas and at least one other component to an output fluid by the process of the invention. The process involves introducing a selective-permeation liquid into a permeation-transfer chamber. A gas-depletion channel and a gas-enrichment channel pass through the permeation chamber and are separated from the chamber respectively by porous walls. The selective-permeation liquid contacts the porous walls but does not flow into the gas-depletion or gas-enrichment channels. The feed-gas mixture is introduced into the gas-depletion channel so that permeant gas in the mixture can pass through the pores of the walls of the channel into the selective-permeation liquid and from the selective-permeation liquid through the pores of the walls of the gas-enrichment channel into the gas-enrichment channel. Permeant gas is withdrawn from the gas-enrichment channel and a stream of gas depleted in the permeant gas is withdrawn from the gas-depletion channel. A gas-transfer unit permits the process of the invention to be carried out effectively.

A Three-Dimensional Simulation of the Hudson–Raritan Estuary. Part II: Comparison with Observation

Abstract: Results from a time-dependent, three-dimensional numerical simulation of the Hudson–Raritan estuary are compared with observations. The comparison includes: 1) instantaneous salinity contours across a transect in the estuary; 2) amplitudes and phase of tidal constituents at four tide gauge and five current meter stations, 3) mean currents at nine meter locations, and mean salinity in the Hudson River, 4) kinetic energy spectra; and 5) response to wind forcing of subtidal current at an observational station near the mouth of the estuary. Observations confirm the model's prediction of existence of density advection instabilities induced by differential advection of the three-dimensional density field. These instabilities produce intense vertical mixing and should significantly modify dispersion processes in the estuary. Effects of neap–spring tides on vertical stratifications are also simulated by the model. Simulated M2 phase at three tide gauge stations show improvement over the M2 phases obtaine...

Cosmological heavy-neutrino problem

Abstract: A new method of deriving the Lee-Weinberg equation is presented. This method makes the approximations clear and suggest how they can be improved. A nearly exact formula for the number of heavy neutrinos left over after the annihilation process is given.

Combinatorial optimization problems in the analysis and design of probabilistic networks

Abstract: This paper presents some results regarding the design of reliable networks. The problem under consideration involves networks which are undirected graphs having equal and independent edge failure probabilities. The index of reliability is the probability that the network fails (becomes disconnected). For “small” edge failure probabilities and given p and q there exists a class of p vertex, q edge graphs with the property that any graph in the class has a smaller probability of disconnection than any graph outside of the class. We solve the problem of synthesizing graphs in this class.

Time-domain stability robustness measures for linear regulators

Abstract: The stability robustness aspect of linear systems is analyzed in the time domain. A bound on the perturbation of an asymptotically stable linear system is obtained to maintain stability using Liapunov matrix equation solution. The resulting bound is shown to be an improved upper bound over the ones recently reported in the literature. The proposed methodology is then extended to Linear Quadratic (LQ) and Linear Quadratic Gaussian (LQG) regulators. Examples given include comparison with an aircraft control problem previously analyzed.

A Three-Dimensional Simulation of the Hudson–Raritan Estuary. Part III: Salt Flux Analyses

Abstract: Salt fluxes and volume transports in an estuary vary considerably over subtidal time scales of a few days to weeks in response to wind and neap–spring tidal forcings. Results from a numerical simulation of the Hudson–Raritan estuary are used to study subtidal variations of salt fluxes and the physical mechanisms for salt balance in the estuary. Simulated salt fluxes are compared with available observations. Observations support the model's finding that analysis of volume and salt fluxes based on short-length data records (<30 days) can lead to misleading conclusions. “Tidal trapping” effects due to coastline irregularities contribute most to the salt balance at the Sandy Hook–Rockaway Point transect and at the Narrows. A two-week observational record is analyzed to support this finding. Simulated subtidal variation of the tidal trapping term at the Sandy Hook–Rockaway Point transect compares well with that observed. In Raritan Bay, where tidal currents are weak and effects of winds are significan...

An Intelligent System for Formulating Linear Programs

Abstract: The research and system development work described in this paper is aimed at overcoming some of the problems associated with the development of large, complex linear programming problems. The most overwhelming problem is that of size. It is not uncommon for large planning and policy analysis problems to have tens of thousands of constraints and activities. Matrix generator systems have been designed to help in this process. However, the amount of manual labor involved is still very great and the formulation process is subject to errors which are difficult to detect. We provide an overview of a system which uses artificial intelligence and database techniques to help a knowledgeable user formulate large linear programs. The system automates many of the tedious processes associated with large-scale modeling and provides a top-down development environment with a number of different forms of problem representation.

Modeling the pressure gradient-velocity correlation of turbulence

Abstract: The modeling of the pressure gradient–velocity correlation of turbulence is considered. Two distinctly different approaches have been proposed in the turbulence literature: one in which the pressure gradient–velocity correlation is decomposed into a pressure‐strain correlation and a pressure‐diffusion correlation, and another in which the pressure gradient–velocity correlation is split into its deviatoric and isotropic parts. By examining the limit of two‐dimensional turbulence, it is demonstrated that the models obtained from the former approach are inconsistent with the Navier–Stokes equations in a fundamental way, whereas the models obtained from the latter approach are not. Consequently, it appears that the direct modeling of the pressure gradient–velocity correlation in its deviatoric and isotropic parts should be favored. The implications that this result has on turbulence modeling are discussed briefly.

Solid-state source of ions and atoms

Abstract: A source (100, 101, 200, 300, 400) of a beam of positive ions or atoms comprises an ion-emission pellet (1, 401) consisting essentially of a solid electrolyte. Preferred solid electrolytes for the pellet (10, 49) are alkali or alkali-earth mordenites. A pellet heater is capable of heating the pellet (1, 401) to an ion-emission temperature at which ions are emitted from the pellet. A beam-forming electrode (2, 4, 31, 60) contacts an ion-emission surface (22) of the pellet (1, 401). The beat-forming electrode (2, 4,31, 60) has at least one passageway extending through it into which ions from the ion-emission surface (22) can pass. Ions emitted into the passageway are discharged from the source as unneutralized ions or neutralized atoms. The ion-emission surface (22) of the pellet (1) may optionally be coated with a layer (2, 31) of porous tungsten or other refractory, high-work-function material to establish an essentially equal potential across the surface (22) and to neutralize ions emitted from the surface (22) when the source (101, 300) is operated as an atom source.

Tidal modeling of the Hudson-Raritan estuary

Abstract: Tidal flow characteristics in the Hudson-Raritan Estuary are studied with a two-dimensional, depth-averaged finite difference model. Rivers are modeled as one-dimensional channels with variable width and depth and are calculated as part of the two-dimensional calculations at no extra computational cost. An extensive comparison of numerical, tidal calculations with observational data than has previously appeared in the literature is presented. Computed velocity and tidal elevation fields compare well with observations. Comparison with observations at the Sandy Hook-Rockaway Point transect indicates that the barotropic tidal residual current contributes significantly to the overall steady circulation in the harbor. The residual current is mainly induced by the coastal geometry and bottom topography through the nonlinear inertia effects.

Investigation of ion binding in ionic polysaccharide solutions using Tb(III) as a luminescent probe

Abstract: The luminescence properties of a series of lanthanide-substituted ionic polysaccharides have been examined in an attempt to learn about the nature of interactions between the metalions and the polymers. Emission and excitation spectra were obtained for Tb(III) complexes with carboxymethyl cellulose, Sclerox S-1.0, alginate, polygalacturonic acid, amylose sulfate, dextran sulfate, and i-carrageenan. Studies of the chirality associated with the metal-ion binding sites were performed through the use of circularly polarized luminescence spectroscopy. It was learned that the lanthanide ions could form complexes with polysaccharides in the electrostatic manner of polyelectrolytes, and that specific ligating groups could further influence the metal-ion binding characteristics.

Subgrid scale stress models for the large-eddy simulation of rotating turbulent flows

Abstract: The modeling of the subgrid scale stresses is considered from a theoretical standpoint with a view toward developing models that are more suitable for the large-eddy simulation of rotating turbulent flows. It is proven, as a rigorous consequence of the Navier-Stokes equations, that such models must be generally invariant under the extended Galilean group and must be frame-indifferent in the limit of two-dimensional turbulence which can be approached in a rapidly rotating framework. Furthermore, it is shown that a significant increase in the rotation rate must be accompanied by a substantial reduction in the energy dissipation rate of the turbulence. Vorticity subgrid scale stress models as well as several other commonly used models are shown to be in serious violation of one or more of these constraints and, hence, are not generally suitable for the description of rotating flows. Alternative models with the correct physical properties are discussed and compared.

On discrete scattering Hurwitz polynomials

Abstract: Discrete scattering Hurwitz polynomials play for discrete systems a similar role as scattering Hurwitz polynomials do for classical systems. A number of properties of discrete scattering Hurwitz polynomials are presented. These properties are obtained by deriving them from the corresponding properties of scattering Hurwitz polynomials. This is achieved by considering polynomials associated in a proper way to given polynomials and by examining the nature of the corresponding transformations.

Convective stability of a variable-viscosity fluid in a vertical slot

Abstract: Stability of convective motion generated by a lateral temperature difference in a variable-viscosity fluid contained in a vertical slot was studied experimentally. The experiments were carried out in a narrow tank 30 cm high × 11.5 cm deep × 2 cm wide with glycerin–water solutions of 70, 80 and 90% glycerine. The onset of instabilities was detected by means of shadowgraphs. As the critical temperature difference was exceeded, a regular array of convection cells appeared. The critical Rayleigh number showed a slight decreasing trend as the Prandtl number of the fluid was increased, with a concomitant increase in the viscosity variation. The critical wavenumber remained practically constant for the three solutions used. At large Rayleigh numbers, approximately seven times the critical value, boundary layers along the walls became unstable and the cellular convection pattern became disrupted.