Minimum Zero Research Articles

Mean-Square Radius of Gyration of Oligo- and Poly(α-methylstyrene)s in Dilute Solution

The mean-square radius of gyration 〈S2〉 was determined from small-angle X-ray and light scattering measurements for 20 samples of atactic oligo- and poly(α-methylstyrene)s (a-PαMS), each with the fraction of racemic diads fr = 0.72, in the range of weight-average molecular weight from 6.48 × 102 (pentamer) to 3.22 × 106 in cyclohexane at 30.5 °C (ϑ). The ratio 〈S2〉/xw as a function of the weight-average degree of polymerization xw first increases steeply for xw ≲ 20, then passes through a flat hump at xw ≃ 40, and finally approaches its asymptotic value for xw ≳ 1 ×103. On the basis of the helical wormlike (HW) chain model the HW model parameters are λ-1κ0 = 3.0, λ-1τ0 = 0.9, λ-1 = 46.8 A, and ML = 39.8 A-1, where κ0 and τ0 are the differential-geometrical curvature and tortion, respectively, of the characteristic helix of the HW chain taken at the minimum zero of its elastic energy, λ-1 is the stiffness parameter, and ML is the shift factor defined as the molecular weight per unit contour length of the c...

Application of theE-? turbulence closure model to separated atmospheric surface-layer flows

Neutrally buoyant atmospheric surface-layer flow over a thin vertical wall has been studied using a turbulence closure scheme designed specifically to address flow problems containing high shears. The turbulent flow model consists of a general solution of the time averaged, steady state, twodimensional Navier-Stokes equations, where theE-e turbulence model has been used to close the system of equations. Model output compares favorably with measurements made in both a full-scale field study and in an atmospheric wind tunnel. In the simulation of flow over a solid wall, two recirculation eddies are produced. The smallest eddy is located windward of the wall with a separation point located atx/h=−0.8, and the largest is located in the lee of the wall atx/h=5.8. Immediately downwind of the wall top, the turbulent kinetic energy, the energy dissipation rate, and the momentum flux all reach a local maximum. These peak values generally maintain their height positionz/h=1.0, but decrease progressively downwind. The turbulent viscosity is strongly modified under the influence of the wall, with a local maximum forming in the lee of the wall top, and a local minimum forming at a heightz/h=2.0 above the lee recirculation eddy. The surface momentum flux reduction due to the presence of the wall begins atx/h=−10.0. Minimum zero fluxes occur at the surface separation points, and a local peak in momentum flux is produced at the centers of each recirculation eddy. Downwind of the wall, the modeled surface flux reaches an equilibrium at roughlyx/h=30.0.

Computing aspects of the entropic theory of one-dimensional dynamical systems

The method for computing the topological entropy of the dynamical systems generated by one-dimensional piecewise-continuous piecewise-monotonous maps of interval is proposed. The method is based on the kneading theory and allows one to reduce the computational process to that of seeking the minimum positive zero of some polynomial. A mathematical model of a clock has been studied, which confirmed the high efficiency of the method. The topological entropy is related to the Lyapunov characteristic exponent and to the structure of attractors. The problems involved in the numerical realization of the proposed algorithm are discussed.

Stability and attractor in a higher-dimensional cosmology. II

For pt.I see ibid., vol.3, p.233 (1986). In most higher-dimensional theories, the effective matter Lagrangian after compactification is described not only by the radius of the internal space but also by a set of scalar fields (e.g. a dilaton). The author presents stability conditions for (the four-dimensional Friedmann universe (F4))*(a constant internal space (K)) in the above class. The stability against non-linear (large) perturbations and the attractor property of the F4*K solution are also investigated in order to explain why our universe is the present one. If the local zero minimum of the effective four-dimensional potential U is isolated, the stable F4*K solution is always one of the attractors when the 3-space is expanding. In the case that U has a degenerate zero minimum, which appears in theories involving some scale invariance, sufficient conditions for the F4*K solution to be the attractor are presented. Both the S2 monopole compactification in the six-dimensional, N=2 supergravity theory and the Calabi-Yau compactification in the ten-dimensional, N=1 supergravity theory with or without the gluino condensation SUSY breaking potential are the cases in question. As an example of an isolated zero minimum, the model by Chapline and Gibbons (1984) (a coset compactification in the ten-dimensional, N=1 supergravity theory plus the SUSY breaking mass term) with a cosmological constant is also discussed.

Primordial two-component inflation

We present a class of inflationable no-scale GUT supergravity models with the following characteristic properties: (i) superheavy (∼ M P) or superlight (< 1 keV) gravitinos avoiding the cosmological gravitino problem; (ii) a natural Higgs triplet-doublet splitting; (iii) proton decay mainly into kaons at an observable level τ p ∼ 10 32±1 years; (iv) sufficient cosmological baryon asymmetry due to the decays of superheavy Higgs triplets ( M H 3 ⩾ 10 15 GeV); (v) acceptable inflationary picture, where the physics responsible for the slow roll-over and energy density perturbations is decoupled from the physics of reheating, which can be as high as O(10 16) GeV: (vi) rapid, second-order GUT phase transition to the SU(3) × SU(2) × U(1) minimum triggered by and happening during inflation, allowing thus for enough GUT magnetic monopole dilution. The inflaton field knocks the GUT-breaking Higgs (guton) field out of its zero minimum. The field responsible for reheating when then be a mixture of the inflaton and the guton.

Rating cultivars and trials in applied plant breeding

The number of means ‘m’, from which a particular cultivar differs significantly, is used to arrange cultivars in order of descending superiority. For n cultivars under study, the maximum ‘m’ value corresponding to the best cultivar is n-1, indicating that it exceeds significantly the n-1 other cultivars, and the minimum zero. Because ‘m’ represents an objective and reliable statistical measure of cultivar performance, it has been used to calculate two indexes: (1) performance index, P=100 m/(n-1), giving the percentage of means which a particular cultivar exceeds significantly, and (2) differentiation index, D=200 Σm/n (n-1), giving the percentage of paired comparisons between cultivars that show significant differences. Rating cultivars according to P across years (Py), sites (Ps), and years plus sites (Pys), gives an overall picture of the relative superiority of the entries. Rating trials according to D allows comparisons between trials and offers the possibility when the same sets of entries are compared each year across sites, to identify sites that give maximum differentiation.

Asymptotic properties of sequences of iterates of nonlinear transformations

By considering functions defined on the unit interval with a single zero minimum and a single unit maximum we are led to a version of the doubling or universal transformation. The fixed point functions of this doubling transformation have certain invariance properties under conjugacy. These invariance properties lead to a widening of the concept of universality to power law conjugacy classes in which the Feigenbaum divergence parameter δ is a function only of the product of the powers with which iterating functions approach unity at the maximum and zero at the minimum. We also construct an effective method for computing the divergence parameter from iterates, and derivatives of iterates, generated by the appropriate fixed point function.

Determination of bandwidth and frequency changes by Raman difference spectroscopy

The mathematical expressions necessary for analyzing the Raman difference spectra resulting from bandwidth and/or frequency differences between two samples have been derived for both Lorentzian and Gaussian band shapes. Intermediate bands may be analyzed using interpolation. The results show that the difference spectra have two maxima separated by a minimum near zero intensity whenever bandwidth changes are dominant. If the frequency shift is zero, these two maxima have the same intensity. Nonzero frequency shifts result in two unequal maxima and their intensity difference may be used to calculate the magnitude of the shift. Three examples of experimental spectra have been analyzed in order to demonstrate the applicability of the technique.

On the universality and computation of Feigenbaum's δ

Universal properties of maps on the unit interval with a single zero minimum and unit maximum are shown to depend on the product of the powers describing the behavior of the function at its minimum and at its maximum. A rapidly convergent algorithm for computing δ is presented.

Self-energy and self-force of dislocations

Abstract The self-energy of a planar dislocation loop is derived as a single plus a double line integral around the loop. The self-force felt by the loop is the variational derivative of the self-energy and involves local terms plus a line integral. The equilibrium shape (of minimum energy or zero force) is thus determined by the Euler equation of a variational problem. Solution of this integro-differential equation requires iterative methods.

Prediction of return with the minimum variance zero-beta portfolio

This paper tests prediction of returns on stocks using a direct estimate of the minimum variance zero beta portfolio z. The composition of this portfolio is implicit in Black's paper on capital market equilibrium in the absence of riskless borrowing or lending. Portfolios of stocks drawn from the same industries are used to estimate z. The predictions of Black's equilibrium return equation are compared with those of cross-sectional regressions of return on risk.

Scattering or toroidal orbits by standing even modes

The orbits of magnetically trapped and weakly circulating particles in axisymmetric toroidal confinement configurations are investigated in the presence of coherent electrostatic modes which are standing along the magnetic field lines. In particular, modes with electric potentials that are even around the point of minimum magnetic field and zero at the point of maximum magnetic field are considered as they are typical of an important class of trapped particle instabilities. 'Quasi-banana' orbits, that remain trapped, and 'quasi-circulating' orbits, that are alternately trapped and circulating, are found. Deeply trapped particles are not significantly affected by even modes and the radial excursions, of the weakly trapped or weakly circulating orbits that are effected by these modes, are much smaller than those resulting from odd modes of comparable amplitudes.

Experimental characterization of transfer Efficiency in charge-coupled devices

The most important characteristic of a charge-coupled device is its charge transfer efficiency (CTE). There are three basic types of loss which degrade CTE: fixed loss, proportional loss, and nonlinear loss. Examples are given of each type of loss and techniques for measurement of all three types of loss are described. A method of determining the minimum fat zero which eliminates fixed loss is shown and an experiment is presented which confirms that fixed loss due to surface states can be completely eliminated by the use of a fat zero. The effect of interelectrode gaps on CTE is discussed in detail. A nonlinear loss model is used to describe the dispersion due to barriers in the gaps and the very detrimental effect of wells in the gap region is shown. The techniques presented in the analysis of these losses are very general and can be used whenever a detailed description of the transfer loss mechanism is required.

Dynamic Temperature Measurements in Alternatic Current Arcs

Using spectroscopic and high speed data acquisition (less than 5 μs) techniques, instantaneous measurements of the radial distribution of temperature within atmospheric argon alternating current arcs have been obtained. Incorporation of electronic synchronization methods has permitted such distributions to be determined at any predetermined relative time within the current cycle. The methods described can be applied to phenomena occurring within circuit breaker and switchgear devices. Phase lag between minimum centerline temperature and current zero was observed. The timewise variation of arc radius within the currents cycle was determined.

Theory of Intercollisional Interference Effects. IV. Does a Zero Minimum in Induced Absorption Imply the Proportionality of the Induced Dipole Moment to the Force?

We show that, within the limits of the theory of intercollisional interference effects developed for collision-induced absorption by a Lorentz gas in paper I of this series, an intercollisional interference minimum which goes precisely to zero implies that the induced dipole moment is exactly proportional to the intermolecular force.

Transverse surface impedance of germanium when generation of nonequilibrium carriers is caused by alternating current

Measurements of the transverse surface impedance have been made on samples of intrinsic germanium in the frequency interval 0.64–60 MHz for surface potentials between −6.5 kT/ q to 15 kT/ q. At frequencies higher than 9 MHz the capacitance and the resistance of the semiconductor surface layer do not depend upon the surface potential, whereas at lower frequencies both have a minimum near zero surface potential. The results obtained are compared with the theory 11–13). The dependencies observed are explained by the generation of nonequilibrium electrons and holes in the near-surface region when high-frequency current flows through it, and also by redistribution of charge induced in a semiconductor at high frequencies. A part of the charge will be situated in a diffusion region, the thickness of which is much larger than the screening length.

Flow behavior of concentrated solutions of an SBS block copolymer

AbstractThe non‐Newtonian viscosity of concentrated solutions of a styrene‐butadiene‐styrene, SBS, block copolymer was measured with a novel capillary viscometer. Polymer concentrations ranged from 0.165 to 0.306 g/cc. Apparent shear rates ranged from 1 to 105 sec−1. Five different solvents were employed. All of the flow curves can be reduced to a single master curve with the same shape exhibited by monodisperse polystyrenes and the Graessley theory. The shift factor for the shear rate axis, τ0, approximately parallels the Rouse relaxation time, τR, but shows a residual concentration and solvent dependence not predicted by the Rouse form. For different solvents at the same concentration, better solvents show a minimum relative zero shear viscosity, η0/ηs, and a maximum ratio τR/τ0. It is concluded that all solvent effects are not adequately incorporated into the zero shear viscosity for the purposes of constructing master plots; however, the shape of the master plot is not affected by the solvent or the polymer block structure.

Fringes in Transmission with Zero Minimum Intensity Resulting from Phase Modulation of One Beam

Fringes in Transmission with Zero Minimum Intensity Resulting from Phase Modulation of One Beam

Zero Shift in Piezoelectric Transducers

“Zero Shift,” as applied to acceleration measurements, is a term that refers to spurious changes in the recorded zero value. The changes are the result of faulty instrumentation response to the measured acceleration. Zero shifts caused by insufficient RC time constant, amplifier saturation, and cable effects, are well known and are not considered in detail. Zero shifts caused by spurious transducer output signals resulting from large magnitude shock (order of 1000 g) are of principal concern. Consideration is given to (a) separation of zero shifts caused by the transducer from those resulting from other causes; (b) the effect this phenomenon has on the accuracy of the indicated shock motion; (c) the various possible sources of the zero shift (progress in this area will include the work of various manufacturers as well as Sandia); and (d) a review of the experimental results obtained at Sandia using transducers designed for minimum zero shift.