Monotonic Form Research Articles

A new scheme of nonlinear energy transfer among wind waves: RIAM method-algorithm and performance-

A numerical scheme for calculating the nonlinear energy transfer among wind waves (RIAM method) was developed on the basis of the rigorous method of Masuda. Then the performance of the RIAM method was examined by applying it to various forms of wind-wave spectra and different situations of wind-wave evolution, in comparison mainly with the WAM method. The computational time of the Masuda method was reduced by a factor of 300 by the RIAM method, which is still 2000 times slower than the WAM method simply because the RIAM method processes thousands of resonance configurations whereas the WAM method does only one. The RIAM method proves to give accurate results even for spectra of narrow band widths or bimodal spectra, whereas the WAM method often calculates an unrealistic magnitude and pattern of nonlinear energy transfer functions. In the duration-limited evolution of wind-wave spectra, the RIAM method yields a unimodal directional distribution on the low-frequency side of the spectral peak, whereas the WAM method produces a spurious bimodal one there. At higher frequencies, however, both methods give a bimodal directional distribution with two oblique maxima. The RIAM method enhances the growth of the total energy and peak period of wind waves in comparison with the WAM method. Nevertheless, Toba's constant of his 3/2-power law approaches almost the same standard value of 0.06 in both methods. For spectra of a narrow band width or for those perturbed by a small hump or depression, the RIAM method tends to recover the monotonic smoother form of spectrum whereas the WAM method often yields unrealistic humps or depressions.

Meniscus in a Narrow Slit

This note presents a closed-form analytical solution to the augmented Young–Laplace equation for the meniscus profile in a narrow slit. The solution is valid for any monotonic form of the disjoining pressure function.

Two-Dimensional Meniscus in a Wedge

This paper presents a closed-form analytical solution of the augmented Young-Laplace equation for the meniscus profile in a two-dimensional wedge-shaped capillary. The solution is valid for monotonic forms of disjoining pressure which are repulsive in nature. In the limit of negligible disjoining pressure, it is shown to reduce to the classical solution of constant curvature. The character of the solution is examined and examples of practical interest which demonstrate the application of the solution to the computation of the meniscus profile in a wedge-shaped capillary are discussed.

Wetting phenomena and the decay of correlations at fluid interfaces

The physics of wetting in three dimensional systems with planar symmetry is revisited in order to explore the extreme sensitivity to microscopic interactions that underlies even thick film adsorption phenomena in d=3. Beginning with short-ranged models of wetting by liquid at a wall-vapor interface, weighted density functional theory is used to obtain an accurate description of the mean-field interface potential along the entire saturated liquid branch. Well away from the bulk critical point, the long-range decay of this class of interface potentials is damped oscillatory rather than the generally assumed monotonic form. This result is best understood in the context of a recently published general theory of the asymptotic structure of liquids and their mixtures. The inescapable conclusion from mean-field theory is that over much of the saturated liquid curve, complete wetting is replaced by thick film pseudowetting associated with layering phenomena. However, oscillatory structure at microscopic wavelengths is strongly renormalized by the inclusion of capillary-wave fluctuations. To assess this aspect, the paper reviews the explicit linear renormalization group calculation of Chernov and Mikheev [Phys. Rev. Lett. 60, 2488 (1988)]. One must distinguish between two cases: (i) pure wetting, where capillary-wave fluctuations renormalize the decay length of the damped oscillatory structure, and (ii) wetting in the presence of external capillary-wave damping (such as Earth's gravity), where the renormalization can dramatically reduce an oscillatory amplitude but cannot formally prevent the suppression of complete wetting.The second main aim of the paper is an attempt at a general survey of the plethora of length scales potentially relevant to thick film wetting phenomena in d=3. A full description of short-ranged models of simple fluids is presented in terms of the behavior of monotonic and oscillatory decay lengths along the saturated liquid branch. Additional length scales of the same class arise from competition with exponentially decaying wall fields. Power-law interactions (dispersion forces) lead to a qualitatively different asymptotic regime. Notwithstanding the ultimate dominance of power-law structure at the longest range, moderately thick film wetting should still be influenced by short-ranged intermolecular forces, particularly in mean field. Finally, the equally crucial significance of asymptotic structure to wetting phenomena in liquid mixtures and in charged fluid systems is highlighted and attention drawn to recently published theories of the required asymptotic forms. In summary, the physics of wetting phenomena in three-dimensional systems is probably close to being fully understood, but the resulting picture for typical experimental systems is amazingly complex.

Signal-to-background in EPMA: Measurement and Monte Carlo calculation

By the method of Monte Carlo calculation, the dependence of the signal-to-background ratio of detected X-rays on the energy of electrons as well as on the thickness of the sample was calculated. The range of energy was 40 ÷ 120 keV, the range of thickness was approximately 8 ÷ 80 μg/cm2 (40 ÷ 400 nm at density ϱ = 2 g/cm3). The results were compared with measurements in electron microscope on thin resin standard for biological microanalysis. The measured dependence of signal-to-background ratio on the energy of electrons has the maximum at 80 keV, the calculated one changes at increased thickness from a monotonic form to one with a maximum at a particular thickness. The absolute values (Hall correction procedure was used for measured values) differs mainly at the highest energy used (120 keV); the difference is probably caused by unproper correction of measured value of background at this energy. Simultaneously, the source distribution of emitted X-ray photons is calculated. Its knowledge gives the possibility to estimate simply the interaction volume diameter and, by this way, to determine the spatial resolution of electron probe X-ray microanalysis.

Inequalities for Means

A monotone form of L′Hospital′s rule is obtained and applied to derive inequalities between the arithmetic-geometric mean of Gauss, the logarithmic mean, and Stolarsky′s identric mean. Some related inequalities are given for complete elliptic integrals.

A critically loaded multiclass Erlang loss system

We consider a generalization of the classical Erlang loss model to multiple classes of customers. Each of the J customer classes has an associated Poisson arrival process and an arbitrary holding time distribution. Classj customers requireMj servers simultaneously. We determine the asymptotic form of the blocking probabilities for all customer classes in the regime known as critical loading, where both the number of servers and offered load are large and almost equal. Asymptotically, the blocking probability of classj customers is proportional toMj. This asymptotic result provides an approximation for the blocking probabilities which is reasonably accurate. We also consider the behavior of the Erlang fixed point (reduced load approximation) for this model under critical loading. Although the blocking probability of classj customers given by the Erlang fixed point is again asymptotically proportional toMj, the Erlang fixed point typically gives the wrong limit. Next we show that under critical loading the throughputs have a pleasingly simple form of monotonicity with respect to arrival rates: the throughput of classi is increasing in the arrival rate of classi and decreasing in the arrival rate of classj forj≠i. Finally, we compare two simple control policies for this system under critical loading.

On the existence of equilibrium points in a class of asymmetric market entry games

Sufficient conditions for the existence of equilibria in pure strategies in Market Entry Games are provided. These conditions are (i) a form of payoff monotonicity and (ii) acyclicity of a particular “dominance” relation defined on the set of players; they do not exclude asymmetry of the players. The result is applicable to asymmetric oligopoly models with technological nonconvexities such as fixed costs.

On Shape-Preserving Interpolation and Semi-Lagrangian Transport

A large number of interpolation schemes are evaluated in terms of their relative accuracy. The large number of schemes arises by considering combinations of interpolating forms (piecewise cubic polynomials, piecewise rational quadratic and cubic polynomials, and piecewise quadratic Bernstein polynomials), derivative estimates (Akima, Hyman, arithmetic, geometric and harmonic means, and Fritsch–Butland), and modification of these estimates required to ensure monotonicity and/or convexity upon the interpolant. Shape-preserving methods maintain in the interpolant the monotonicity and/or convexity implied in the discrete data.The schemes are first compared by evaluating their ability to interpolate evenly spaced data drawn from three test shapes (Gaussian, cosine bell, and triangle) at two resolutions. Details of the cosine bell tests are presented in this paper. Details of the other tests are presented in a companion technical report. Of the monotonic interpolants, the following are the most accurate: (1) The Hermite cubic interpolant with the derivative estimate of Hyman modified to produce monotonicity as suggested by de Boor and Swartz. (2) The second version of the rational cubic spline suggested by Delbourgo and Gregory, with the derivative estimate of Hyman modified to produce monotonicity. (3) The piecewise quadratic Bernstein polynomials suggested by McAllistor and Roulier with the derivative estimate of Hyman again modified. Imposing strict monotonicity at discrete extrema introduces significant errors. More accurate interpolations result if this requirement is relaxed at extrema. The Hermite cubic interpolant is improved by relaxing the strict monotonicity constraint to one suggested by Hyman at extrema. In a like manner, the accuracy of the rational and piecewise quadratic Bernstein polynomial interpolants can be improved by requiring only that convexity/concavity be satisfied rather than monotonicity.Some of the more accurate interpolants are incorporated into the semi-Lagrangian transport method and tested by examining the accuracy of the solution to one-dimensional advection of test shapes in a uniform velocity field. The semi-Lagrangian method using monotonic interpolators provides monotonic solutions. The semi-Lagrangian method using interpolators that maintain convex/concave constraints give solutions that are essentially nonoscillatory. The monotonic forms damp the solution with time, more so for narrow than broad structures. The best monotonic forms are the Hermite cubic interpolant with the Akima or Hyman derivative estimates modified to produce monotonicity with $C^0 $ continuity. The corresponding $C^1 $ continuous forms have unacceptable phase errors with the Hermite interpolant. The rational cubic with the Hyman derivative estimate modified to produce monotonicity is comparable to the $C^0 $ Hermite form described above. The $C^1 $ rational form does not have the phase error seen in the $C^1 $ Hermite interpolant. The essentially nonoscillatory forms damp much less than the monotonic forms. The solutions that used rational cubic interpolants with a Hyman derivative estimate modified to satisfy a convexity/concavity constraint were the most satisfactory of the shape-preserving schemes.

Solution of an Ill-Conditioned Fast Decoupled Load Flow Problem Using Acceleration

Acceleration is used for monotonic form and oscillatory form of convergence of individual voltage magnitudes and angles of the fast decoupled Newton Raphson Load Flow Problem. This causes the otherwise slowly converging solutions to rapidly converge. The technique is illustrated by considering a particular ill-conditioned system configuration in an expansion study.

The orientational-correlation time intercept in liquids

We propose a theory for the zero viscosity (η) or infinite temperature (T) intercept (τ0) in the much used quasihydrodynamic expression τ2=τ0+(const)(η/T) for the second rank orientational correlation time (τ2). Whereas we associate the (η/T) term with the integral over the torque–torque correlation function, we attribute the origin of τ0 to the integral over the cross-correlation function between torques and kinetic or convective terms. We are unable to evaluate the time dependence of this cross-correlation function exactly, but if a Gaussian form is assumed, a negative value is obtained for τ0. Experimentally, τ0 is sometimes positive and sometimes negative, which suggests that a monotonic form for the time dependence of the cross-correlation function might be inadequate. Because we have not been able to evaluate this cross-correlation function our explanation must still be considered a conjecture.

Copolyesteramides—I. Anionic copolymers of ω-laurolactam with ϵ-caprolactone

Anionic copolymerisation of ω-laurolactam with ε-caprolactone yields copolyesteramides with NH(CH 2) 11CO and O(CH 2) 5CO unit contents similar to those in the feeds. Over the major part of the composition range, only the amide component crystallises, showing the γ-nylon 12 form. A transition of crystalline type to that of poly(ε-caprolactone) occurs at low ( ca. 20 mol%) amide-group content and with marked depression of the degree of crystallinity of the polyester component. I.R. spectroscopy indicates the co-existence of amide-ester with amide-amide hydrogen-bonding in the copolymers, and the monotonic form of the T m vs composition curve is explained in terms of this dual bonding. It is suggested that such interactions between the sub-species may be a general feature underlying the properties of linear aliphatic copolyesteramides.

Image Forces at the Metal Electrode‐Electrolyte Solution Interface: Account of Spatial Dispersion of the Solution Permittivity

AbstractThe effect of spatial dispersion of the permittivity of an electrolyte solution on the character of image forces W(a) near a metal electrode is investigated. The effect of penetration of an electric field into the metal is taken into account. The asymptotic expressions obtained for W(a) show that in highly dilute electrolyte solutions the charge in addition to usual attraction encounters an effective repulsion in two distance regions from the metal, so that the image of W(a) has an essentially non–monotonic form. For a more concentrated solution, the image of W(a) is modified and may take a form corresponding to a monotonic repulsion of the charge from the interface.

Collisionless electron shocks in electron-beam–plasma systems

One-dimensional Vlasov simulations show that when an electron beam is suddenly injected into a plasma, a fast-moving monotonic shock forms during the early stage of the transient plasma response. In the shock, the ions are nearly immobile. The shock appears to be an electrostatic electron-beam–plasma mode. The shock evolves from an initial positive potential perturbation, which is supported by an ion burst. The steepening of the perturbation into a shock is characterized by an electron-beam–plasma mode.

The effect of increased intracranical pressure on pulse wave (author's transl)

It is well known that the intracranial pulse wave amplitude increases with rising intracranial pressure (ICP). However, little is known about how the form of the pulse wave changes with variation in ICP. One or two peaks were observed in the descending slope of the pulse wave, synchronous with the heart beat in dogs. As ICP increased, the amplitude as well as the peak of the pulse wave became more prominent and the shape finally became monotonous. These changes can be used as a diagnostic tool to assess the intracranial volume-pressure relationships. In dogs where the vasotonicity was strengthened by a hypertensive drug (noradrenalin), alteration of the pulse wave occurred with ICP elevation. However, when the systemic blood pressure was elevated by inflation of an aortic balloon, ICP elevation resulted in the monotonous form of the pulse wave. On the contrary, when the vasotonicity was weakened by a hypotensive drug (regitine), the form of the pulse wave became monotonous. However, exsanguination did not change the form of the wave under ICP elevation. These results suggest that the cerebrovascular tone contributes to the form of the pulse wave under increased ICP.

Monotonicity properties of interpolation spaces II

For any interpolation pair (A 0 A 1), Peetre’sK-functional is defined by: $$K\left( {t,a;A_0 ,A_1 } \right) = \mathop {\inf }\limits_{a = a_0 + a_1 } \left( {\left\| {a_0 } \right\|_{A_0 } + t\left\| {a_1 } \right\|_{A_1 } } \right).$$ It is known that for several important interpolation pairs (A 0,A 1), all the interpolation spacesA of the pair can be characterised by the property ofK-monotonicity, that is, ifa∈A andK(t, b; A0, A1)≦K(t, a; A0, A1) for all positivet thenb∈A also. We give a necessary condition for an interpolation pair to have its interpolation spaces characterized byK-monotonicity. We describe a weaker form ofK-monotonicity which holds for all the interpolation spaces of any interpolation pair and show that in a certain sense it is the strongest form of monotonicity which holds in such generality. On the other hand there exist pairs whose interpolation spaces exhibit properties lying somewhere betweenK-monotonicity and weakK-monotonicity. Finally we give an alternative proof of a result of Gunnar Sparr, that all the interpolation spaces for (L v p , L w q ) areK-monotone.

Pattern discrimination using ellipsoidally symmetric multivariate density functions

A brief review of ellipsoidally symmetric density functions is done. For the case of monotonic functional forms and distributions with common covariance matrices, a lower bound on the probability of correct classification is calculated in terms of either an incomplete beta or gamma integral, for a class of common functional forms. The lower bound is a monotonically increasing function of the Mahalanobis distance for all monotonic ellipsoidally symmetric forms.

Monotonicity properties of interpolation spaces

For any interpolation pair (A0A1), Peetre’s K-functional is defined by: $K\left( {t,a;A_0 ,A_1 } \right) = \mathop {\inf }\limits_{a = a_0 + a_1 } \left( {\left\| {a_0 } \right\|_{A_0 } + t\left\| {a_1 } \right\|_{A_1 } } \right).$ It is known that for several important interpolation pairs (A0, A1), all the interpolation spaces A of the pair can be characterised by the property of K-monotonicity, that is, if a∈A and K(t, b; A0, A1)≦K(t, a; A0, A1) for all positive t then b∈A also. We give a necessary condition for an interpolation pair to have its interpolation spaces characterized by K-monotonicity. We describe a weaker form of K-monotonicity which holds for all the interpolation spaces of any interpolation pair and show that in a certain sense it is the strongest form of monotonicity which holds in such generality. On the other hand there exist pairs whose interpolation spaces exhibit properties lying somewhere between K-monotonicity and weak K-monotonicity. Finally we give an alternative proof of a result of Gunnar Sparr, that all the interpolation spaces for (L ${}_{v}^{p}$ , L ${}_{w}^{q}$ ) are K-monotone.

An attribute of matrices of monotonic form and uses of their properties

Matrices of monotonic form possess useful properties enabling estimates of the errors of some operator equation methods to be obtained in a convenient form [II, and also making it possible to reduce the amount of calculation in the use of known expressions for estimates of the irremovable error of the solution of systems of linear algebraic equations 121. In this paper we establish sufficient criteria for a matrix to belong to the class of matrices of monotonic form, describe a method of calculating the first norms of the inverse matrices of the latter, and also for matrices which become matrices of monotonic form on multiplication by -1.

Linking Form of Hypothesis to Type of Statistic: An Application of Goodman's Z

This paper suggests that types of statistics used in analyzing data should be linked to logical forms of hypotheses. It presents a proposal to include the weak conditional associations of (p -* q) and (q -> p), along with the straight biconditional monotonic form, in a basic paradigm of logical hypothesis forms. Finally, it suggests that Goodman's flexible Z be applied in testing the validity of basic logical hypothesis forms and examines the plausibility of so doing.