Showing papers by "Stevens Institute of Technology published in 1971"

Economically optimal determination of the parameters of np-control charts

Abstract: This paper seeks a theoretical basis for determining the optimal parameters of the X-chart under the specified conditions. These parameters are the sample size, the factor determining the spread of the control limits, and the intersample interval. The paper shows how to determine these parameters under sound practical assumptions so that the relevant cost function is minimized. Illustrative examples show how the formulated model can be applied.

Constitutive equations for polymer solutions derived from the bead/spring model of Rouse and Zimm

Abstract: The theory of dilute polymer solutions based on the bead/spring model in the form given by Zimm is reformulated for arbitrary homogeneous flow histories. It is shown that the center of resistance of a polymer molecule moves with the solvent. By a preliminary transformation [3.4], the equations for the center-of- resistance motion are separated from those for the motion of the N spring vectors. The spring-vector equations involve a symmetric non-singular matrix B [3.14] whose characteristic values equal the non-zero characteristic values of Zimms singular matrix HA. A further transformation [4.2] which diagonalizes B yields separate differential eq. [5.4] for pq*, the polymer contribution to the stress tensor associated with the q normal mode. Transformation to an embedded basis enables one to integrate these equations so as to obtain pq* in terms of the flow history ([5.6], [5.9]), and summation over q then gives the required constitutive eq. [5.17] for the polymer solution. These are of the same form as the “rubber-like liquid” constitutive equations (with addition of a solvent-contribution term) derived from the network theory of Lodge, but the memory function is determined to within three constants (e. g. N, h*, τ1). Peterlina solution for the normal-coordinate distribution function in steady shear flow is generalized for an arbitrary homogeneous (time-dependent or steady) flow and expressed in terms of pq* which can be evaluated when the flow history is given.

Flame spread over fuel beds: solid-phase energy considerations

Abstract: This paper reports on an analytical and experimental investigation of flame spread over the surface of a solid-fuel bed in an oxygen-inert environment. It is postulated that the processes controlling the flame-spreading phenomenon occur in a very small “ignition region” at the leading edge of the spreading flame adjacent to the surface, and attention is focused on this small region. The solid-phase energy equation is uncoupled from the gas-phase conservation equations and solved separately, retaining as a boundary condition the heat flux into the surface from the adjacent gas phase. The resulting solutions, in the form of simple algebraic equations, show clearly the different relationships between the physically important parameters associated with flame propagation over: (1) a “thick” fuel bed (thermal wave penetration into the solid beneath the ignition region much less than the fuel-bed depth), and (2) a “thin” fuel bed (subsurface temperature gradients negligible). The “critical thickness” criterion for separating the regions of thin and thick fuel-bed flame-spreading characteristics evolves as a naturally occurring parameter of the problem. The main dependence of heat flux on environmental parameters is obtained from consideration of the gas-phase conservation equations in a quiescent environment. By combining the results from the gas-phase and solid-phase analyses, simple algebraic relationships are obtained between flame-spreading velocity and parameters of theoretical and practical interest. Experimentally, using the techniques described in Ref. 1, the dependence of flame-spreading velocity on pressure level, oxidant mole fraction, diluent gas, initial temperature and fuel-bed depth is determined for polymeric and cellulosic materials. In addition, the influence of forced convective motion of the environment on flame spreading velocity is investigated experimentally. The analytical results provide excellent correlation for all data obtained in a quiescent environment, with the exception of the influence of initial temperature. Data obtained by other investigators are shown to be correlated as well. It is concluded that the role played by the solid phase in the over-all flame-spreading mechanism is generally understood, but the gas-phase processes require further definition.

Structural and behavioral equivalences of tessellation automata

Abstract: The concepts of structural and behavioral isomorphism on tessellation automata are investigated. Certain equivalence relations preserving one or both forms of isomorphism lead to standardizations of neighborhood structure. The concepts of blocking and the blocked structure play a central role. A weaker form of behavioral isomorphism is also introduced leading to further simplifications of standard neighborhood structure. Finally, a concept of simulation is investigated.

Crystallization studies on deformed polybutene-1 melts.

Abstract: : An apparatus was designed and built which allowed an investigation concerning the morphology and kinetics of crystallization of a deformed polybutene-1 melt. The polymer was quenched from a temperature above its melting point to one of two crystallization temperatures. The supercooled melt was then sheared and allowed to crystallize isothermally while the internal stress in the melt was continuously recorded. A polarizing microscope was employed for the simultaneous study of the resulting morphological changes. By properly accounting for thermal contractions within the apparatus caused by the quenching operation, as well as the imposed shear strain, a strain history of the polymer during crystallization was developed. From this strain history and the assumption that the volume contraction resulting from crystallization was isotropic, approximate kinetics of crystallization in a deformed polymer melt were determined. (Author)

The relationship between information processing and driving accident and violation record

Abstract: Seventeen subjects matched for driving experience were divided into four groups according to their accident and traffic violation records. They were tested for their ability to process information. Subjects who had a high accident record processed information at a significantly (p < .01) lower rate than nonaccident subjects. Subjects who had many violations, but no accidents, were the best information processors. There was a significant (p <.01) interaction between accident and violation record. These results and their implications are discussed.

Covariance, invariance, and equivalence: a viewpoint.

Abstract: We have given what, we hope, are precise statements of the main principles that underly general relativity. It is not our intention to argue that these statements correspond to the original statements of these principles. We have used the original terms, principle of equivalence, etc., to designate the formulations given here primarily for convenience and because we feel that our formulations are, at least, in the spirit of the general accepted meaning of these appellations. Our formulation of these principles rests primarily on the observation that there are two types of objects that appear in the descriptions of physical systems, which we have termed absolute and dynamical. A covariance group consists of those transformations which transform one observable set of values of these objects into another observable set and correspond to the passive transformations that one can carry out on the system. An invariance group is the subgroup of a covariance group that leaves invariant the absolute objects. If there are no absolute objects, the two groups coincide. The principle of general covariance asserts that the Einstein group, that is, ‘the group of arbitrary local coordinate transformations’, is a covariance group of all physical systems that can be described by space-time theories. The requirement that the Einstein group is also an invariance group of all physical systems constitutes the principle of general invariance. Support for this latter principle comes first from a Machian type of argument that there should be no absolute objects in nature. A weak form of the principle of equivalence that asserts the equivalence of inertial effects to gravitational effects (but not necessarily conversely) allows one to conclude the impossibility of distinguishing between arbitrary active and passive coordinate transformations. Since the latter transformations constitute the Einstein group, we conclude that the former also constitute this group. Since the active transformations constitute an invariance group, we are again led to the conclusion that the Einstein group is the invariance group, of all spacetime systems.

Recycle gel permeation chromatography. III. Design modifications and some results with polycarbonate

Abstract: : In previous communications a new recycle device for Gel Permeation Chromatography (GPC) was described and its advantages demonstrated with an analysis of epoxy resins. This device uses a principle which was termed alternate pumping (AP). In the present communication, a modified design for AP recycle is described and some results with a polycarbonate resin are analyzed. This new design differs from the previous one in two major features. It utilizes only one 6-port switching valve and it excludes the refractometer cell from the recycle loop. These features simplify the recycle system and eliminate the problems that were caused by subjecting the refractometer cell to high pressures. (Author)

Semantics for the sentential calculus with identity

Abstract: 1. The SCI (Sentential Calculus with Identity) is obtained from the classical sentential calculus by the addition of (1) a new binary connective, the identity con? nective (denoted by"=") and (2) axioms which 'say5 that "p == q" means ccp is identical to q" (also: "the situation p is the same as the situation q"). The new axioms are the weakest possible; no presuppositious about the meaning of "is identical to35 are in? cluded (other than "p = p"). We do not attempt to say what the range of the sentential variables p,q,r, ... is. (In the classical propositional calculus, they are intended to range over a two element set.) In this paper, a number of results about the semantics of the SCI are given without proof. The proofs of these and other results are contained in the much longer "In? vestigations into the Sentential Calculus with Identity53 [1].

Synthesis and thermal degradation of some ferrocene‐containing polyazines and poly‐schiff bases

Abstract: : A series of ferrocene-containing polymeric azines and polymeric Schiff bases were synthesized by means of acid-catalyzed solutions poly-condensations. The molecular structures of the polymers synthesized have been determined and information concerning their thermal behavior has been obtained. Comparative thermal stabilities of the products of polymerization of aliphatic and aromatic diamines with 1,1'-diformylferrocene and 1,1'-diacetylferrocene were investigated by thermogravimetric analysis both in air and in an inert atmosphere. In the inert atmosphere, initial weight loss due to thermal stress did not occur below 300C in all cases and in many cases 50-70% residue of polymer sample remained at 700C. The use of a fluorinated diamine led to the synthesis of a polymer which did not exhibit any significant enhancement of thermal properties. Investigation of the polymer products by direct inlet mass spectroscopy led to the observation that several of the systems contained significant amounts of cyclic dimers, although linear polymers were the major products in most cases. Extraction of the cyclic dimers followed by molecular weight determinations by vapor phase osmometry confirmed their molecular structures. (Author)

Effect of oxidation‐reduction potential on the metal salt‐catalyzed autoxidation of atactic polypropylene

Abstract: : The purpose of the paper was to establish an order of metal catalyst activity during the autoxidation of atactic polypropylene films by measuring carbonyl formation, and to correlate such activity with oxidation-reduction potential. (Author)

The three-dimensional starting solution for a melting slab

Abstract: A short-time closed-form solution is developed for the melting or solidification of a half-space under a general surface heat input, such that change of phase starts at a point of the surface, and then spreads simultaneously both towards the interior of the body and along its surface. The solution is obtained by the embedding technique, and show that the shape of the phase intersurface is, when suitably normalized, a universal function, i.e. it is independent of the distribution and rate of the applied heat input and of the material properties. Initial melt propagation in directions normal to and along the surface are respectively proportional to $(t-t\_{\text{m}}$)$^{\frac{3}{2}}$ and $(t-t\_{\text{m}})$$^{\frac{1}{2}}$, where $t_{\text{m}}$ is the time of start of melting.

An application of the extended Kantorovich method to MHD duct flow

Abstract: The extended Kantorovich method developed byA. D. Kerr and recently applied to the solution of a clamped plate byA. D. Kerr andH. Alexander, is used in the present paper to analyze the steady flow of a viscous, electrically conducting fluid through a perfectly insulated rectangular duct under a uniform, arbitrarily oriented, externally applied magnetic field. It is shown that the generated solution is independent of the choice of initial function, and that the convergence of the iterative procedure is very rapid. The obtained solution exhibits good correlation with the exact solution for small values of the Hartmann number. The inaccuracy at high Hartmann numbers is shown to be a result of a shortcoming in the method as it is presently applied.

Kinetics of thermal oxidation of polyolefins—A review

Abstract: The kinetics of uncatalyzed autoxidations for polyolefin films, such as atactic and isotactic polypropylene and poly-(butene-1) are reviewed in light of recent work. Reaction temperatures generally varied from 100 to 150°C and oxygen concentrations from 5 to 100% by volume. A general reaction scheme is suggested and kinetic expressions subsequently derived therefrom have been satisfactorily applied to account for experimental results. Linear relationships between a maximum rate and concentration of oxygen for both low and high concentrations were obtained. In the case of the catalyzed autoxidations [Co(III) acetylacetonate] the general reaction scheme was modified to take into account the presence of the catalyst. From this modified scheme, various kinetic expressions relating maximum rate and concentrations of oxygen, polymer and the catalyst were derived. First-order reaction with respect to the concentration of the catalyst was found at low concentrations of the catalyst, and near zero-order at relatively high catalyst concentrations. A correlation between catalytic activities of metal acetylacetonates [Co(III), Mn(III), Cr(III), Fe(III) and Cu(II)] and the oxidation-reduction potentials has been established. Experimental dependencies of maximum carbonyl formation rates as a function of polymer concentration were found to agree well with the theoretical both for catalyzed and uncatalyzed oxidations.

A statistically based mathematical water quality model for a non-estuarine river system

Abstract: A mathematical model has been formulated, solely through the use of the mathematical statistics, for the purpose of predicting river water quality without reference to the causal chemical, biological and physical relationships. In a sense, this is a “black box” approach wherein with a known input, one may reliably predict the output. The use of a main force statistical method for predicting river-water quality can provide accurate predictive information with a minimum of time and money expended if a sufficiently large data base is available for the river system in question. What has been lacking in the past is a model which is not only statistically significant but contains only those water quality parameters which contribute significantly to the estimation of the dependent variable. The model which is herein described discusses the formulation procedure, data collection requirements, model hypothesis testing and significance procedures, and finally validation methods employed in verifying the final model equations. A description of how the simulated results are employed in the forecasting procedure is also developed.