Single Inflection Research Articles

Evaluating the properties of impulse signals transmitted over circuits with distributed and lumped parameters

The dependability of the ABTC-MSh automatic block system entirely depends on the functional safety and operational stability of its component devices, most of which operate in pulse mode. One of the key components of pulse signal converters is various transformers and chokes, whose calculation and development is, in practice, often difficult due to insufficient consideration of stray parameters and operational specificity of such electromagnetic systems when the core is magnetized. The paper estimates the results of coordination of the transformer’s electrical characteristics with the load impedance and that of the pulse signal source suitable for analysing and constructing signal-shaping networks and delay lines based on lumped elements. Aim. The aim of the work is to substantiate an engineering technique for calculating the duration of the leading edge of a signal in the process of setting its level at the output of the forming circuit of a pulse transformer when matching with loads and estimating the delay time for switching on the actuator at a given response threshold, depending on the parameters of the second-order circuit, which is often used as a feedback element of pulse converters and auto-regulation systems. Methods. The time characteristics and pulse form are determined for a transformer whose equivalent circuit corresponds to the item’s operation in high frequencies and takes into account the stray parameters normalized to to the primary side. The output signal function is described in accordance with the linear electric circuit theory in operator form and, after a series of Laplace transformations, the generalized expression of the transmission factor is reduced to a standard form for a second-order circuit. The analytical solution was found by determining the values of the zeros and poles of the function on the plane of complex numbers as roots of quadratic equations expressed in terms of the coefficient of circuit damping. Graphs of the field dependences of the processes of establishing the pulse amplitude at the output of the forming circuit and the proportions of the amplitude outlier on the attenuation coefficient are given for various ratios of the coefficients of matching the transformer wave resistance with the load impedances and the pulse signal source. Point estimates of the pulse edge duration are made using the Mathcad programming function and taking into account the dimension of TRUE/FALSE matrices that reflect the transition from zero to one. This allows proposing linear approximations of the duration dependences within the given interval with a single inflection point that corresponds to the condition of complete matching of all resistances. Information is provided on the deviation of the approximation from the calculated data, the delay time of the actuator by the threshold. It is also discussed whether it is admissible to represent distributed parameters in the form of lumped elements while implementing artificial delay lines and higher-order circuits. Results. Conclusions. The specified problem is resolved by defining a unique calculated dependence that associates the signal edge duration to the transmission coefficient of the examined second-order circuit. The validity of the method for dependence deduction is based on describing the output signal of a pulse transformer in a general form, subsequent analysis of the expression and deduction of an accurate analytical solution, taking into account the primary stray parameters of the transformer and load values.

Effects of pressure on gas generation and pore evolution in thermally matured calcareous mudrock: Insights from gold-tube pyrolysis of the Eagle Ford Shale using miniature core plugs

Together with an increased interest in deep petroleum and shale gas exploration over the last decade, the effects of pressure on gas generation and pore evolution in organic-rich shales have received renewed attention. In this study, miniature core plugs drilled from a thermally matured Eagle Ford Shale sample were pyrolyzed in sealed gold tubes to investigate the effects of pressure on gas generation coupled with pore evolution in the presence of a relatively intact rock fabric. The gold-tube-capsuled samples were isothermally heated at a temperature of 425 °C for 36 h under different confining pressure conditions (10, 25, 35, 50, 68, 80, and 120 MPa), with maturation being induced from the original oil window to the gas window.Experimental results show that increasing the confining pressure from 10 to 120 MPa has initially retards and then promotes the generation of low molecular hydrocarbons (C1–C5 alkanes), whereas gas dryness (C1/C1–5, vol%) increases continuously from 51% to 63% in this pressure range. The inflection pressures that correspond to the maximum retardation of the generation of individual hydrocarbon compounds are shifted to higher values with increasing the molecule carbon number, e.g., 35 MPa for methane, 50 MPa for ethane to butane, and 68 MPa for pentane. Similar pressure effects have also been found for liquid hydrocarbons (C6–14 hydrocarbons and C14+ compounds), with a single inflection pressure of 68 MPa. These observations indicate that high pressure inhibits residual oil cracking but simultaneously favors generation of methane-rich gas. A mechanism for the interaction of retained hydrocarbons and porous matured kerogen (and/or pyrobitumen) is thus suggested to explain the enhanced methane generation. The extent of such interactions is highly dependent on petroleum expulsion efficiency from an intact rock fabric.BET specific surface area and pore volume measured by N2 adsorption decrease significantly for samples matured at 10–35 MPa and then increase at confining pressures above 50 MPa. The simultaneous variations in pore development and methane generation with increasing confining pressure indicate that the observed effect of confining pressure on the evolution of the pore structure of shales depends on both oil retention and gas generation. Our experimental results provide some new insights into gas generation and pore evolution in shale systems, and the retardation effect of pressure on hydrocarbon generation and expulsion as well as pore evolution may provide a mechanism for the Type II kerogen-dominated oil-prone shales to become potential shale gas reservoirs.

A Quantitative Evaluation Method for Obstacle Avoidance Performance of Unmanned Ship

In response to the urgent need for quantitative evaluation of the obstacle avoidance performance of an unmanned ship, a quantitative evaluation model is established to evaluate quantitatively the obstacle perception performance, static obstacle avoidance performance and dynamic obstacle avoidance performance of an unmanned ship. The base data for calculating are derived from the shore-based database; the evaluation factor layer is evaluated by the cost function method. Based on the established evaluation model, the quantitative evaluation score of the obstacle perception performance of the unmanned ship is obtained by data analysis for the 50 to 100 m buoy and 100 m island obstacle perception test. The quantitative evaluation score of the static obstacle avoidance performance obtained by testing the performance of a single obstacle, continuous obstacle and inflection obstacle is 68.8 points. For buoys as dynamic obstacles, the dynamic obstacle avoidance performance quantitative evaluation score of 64.13 points is obtained by testing the performance of obstacle avoidance in chasing, facing and crossing encounters. The analysis of the test data saved to the database verify the rationality of the quantitative evaluation model, which can provide reference for the quantitative evaluation and improvement of the unmanned ship’s obstacle avoidance performance.

Single- and double-kink solutions of a one-dimensional, viscoelastic generalization of Burgers’ equation

PurposeThe purpose of this paper is to determine both analytically and numerically the kink solutions to a new one-dimensional, viscoelastic generalization of Burgers’ equation, which includes a non-linear constitutive law, and the number of kinks as functions of the non-linearity and relaxation parameters.Design/methodology/approachAn analytical procedure and two explicit finite difference methods based on first-order accurate approximations to the first-order derivatives are used to determine the single- and double-kink solutions.FindingsIt is shown that only two parameters characterize the solution and that the existence of a shock wave requires that the (semi-positive) relaxation parameter be less than unity and the non-linearity parameter be less than two. It is also shown that negative values of the non-linearity parameter result in kinks with a single inflection point and strain and dissipation rates with a single relative minimum and a single, relative maximum, respectively. For non-linearity parameters between one and two, it is shown that the kink has three inflection points that merge into a single one as this parameter approaches one and that the strain and dissipation rates exhibit relative maxima and minima whose magnitudes decrease and increase as the relaxation and nonlinearity coefficients, respectively, are increased. It is also shown that the viscoelastic generalization of the Burgers equation presented here is related to an ϕ8−scalar field.Originality/valueA new, one-dimensional, viscoelastic generalization of Burgers’ equation, which includes a non-linear constitutive law and relaxation is proposed, and its kink solutions are determined both analytically and numerically. The equation and its solutions are connected with scalar field theories and may be used to both studies the effects of the non-linearity and relaxation and assess the accuracy of numerical methods for first-order, non-linear partial differential equations.

Investigation of the complexation behavior of polyethylene oxide with surfactant ternary mixture: Conductometry

AbstractIn binary system consisting only of the oppositely charged surfactants, a single type of aggregates (mostly probably vesicles) was identified. Upon polymer addition, a shift in aggregation concentration was observed; however, no additional clustering occurred and single inflection point was visible in all property versus concentration plots. The binding behavior in ternary mixtures comprising of poly (ethylene oxide), sodium dodecyl sulfate, and acetyl trimethyl ammonium bromide has been studied by using conductivity. The aggregation and binding phenomena were thermodynamically feasible, unraveled by the negative values of Gibbs free energy. An increased amount of adsorbed poly (ethylene oxide) caused an increase in these values, showing an alteration in interfacial free energy due to release of water molecules from vesicles' surface. The area per molecule calculated for ternary system indicted the existence of compact packing in mixed clusters.

Streamflow partitioning using the Budyko framework in a northern glaciated watershed under drought to deluge conditions

We use the Budyko framework to examine streamflow changes due to climate variation and human activities in the Mauvais Coulee Basin, a 1002 km2 sub-basin that contributes streamflow to Devils Lake, a terminal lake that has experienced catastrophic flooding over the past three decades. The basin lies within the northern glaciated prairies, contains innumerable wetland complexes that follow fill-spill hydrological principles, has undergone extensive land use change to support dryland farming, and has experienced a drought to deluge hydroclimatic transition over the last century. We implement the Budyko framework to partition the runoff increase to the lake between its climatic or human components. Initial results attribute 45% of the streamflow increase to climate factors, and 55% to human activities. Implementation of the Budyko framework to examine streamflow partitioning, however, rests upon a series of assumptions that are usually not directly verified. We then examine each Budyko framework assumption to determine its suitability for our study site and study period. None of the required assumptions are fully satisfied. Our study site and study period encompass two distinct hydroclimatic modes, contain no clear single inflection point separating baseline and altered periods, experience root zone soil moisture storage changes during the study period, and exhibit a non-stationary precipitation-streamflow relationship during the transitional period between the two hydroclimatic modes. Streamflow attribution produced by the standard application of the Budyko framework is not applicable to our study site or study period. We recommend that local-scale investigations of streamflow partitioning based upon the Budyko framework be more intentional in verifying model assumptions as a standard practice in implementing the method.

Changes in emergency department visits for zolpidem‐attributed adverse drug reactions after FDA Drug Safety Communications

To identify possible changes in U.S. emergency department (ED) visits from zolpidem-attributed adverse drug reactions (ADRs) after 2013 Food and Drug Administration (FDA) Drug Safety Communications (DSCs), which notified the public about FDA's new dosing recommendations for zolpidem. We estimated the occurrence of ED visits from zolpidem-attributed ADRs using nationally representative, public health surveillance of medication harms (National Electronic Injury Surveillance System-Cooperative Adverse Drug Event Surveillance project, 2010-2017). We estimated the number of zolpidem prescriptions using IQVIA National Prescription Audit, 2010-2017. We calculated rates of ED visits for zolpidem-attributed ADRs per 10 000 dispensed zolpidem prescriptions and identified time trends and potential inflection points using joinpoint regression. For comparison, we repeated these analyses for sedating antidepressants commonly used to treat disordered sleep (trazodone, doxepin, and mirtazapine). The best-fit regression model for rates of ED visits for zolpidem-attributed ADRs by 6-month intervals identified a single inflection point in the second half of 2014 (P = .024) with a 6.7% biannual decrease from 2010 to 2014 ([-13.1%, 0.3%], P = .059) and a 13.9% biannual increase from the second half of 2014 through 2017 ([-1.1%, 31.3%], P = .068). No change or inflection points were identified for rates of ED visits for sedating antidepressant-attributed ADRs. While there was a nominal decline in the rate of ED visits for ADRs in the time period before and for 18 months after FDA's 2013 zolpidem DSCs, the decrease was not sustained, and thus questions remain concerning the long-term impact of the zolpidem DSCs on ADRs.

Primordial black holes dark matter from inflection point models of inflation and the effects of reheating

We study the generation of primordial black holes (PBH) in a single field inflection point model of inflation wherein the effective potential is expanded up to the sextic order and the inversion symmetry is imposed such that only even powers are retained in the potential. Such a potential allows the existence of an inflection point which leads to a dynamical phase of ultra slow roll evolution, thereby causing an enhancement of the primordial perturbation spectrum at smaller scales. Working with a quasi-inflection point in the potential, we find that PBHs can be produced in our scenario in the asteroid-mass window with a nearly monochromatic mass fraction which can account for the total dark matter in the universe. For different choices of quasi-inflection points and other parameters of our model, we can also generate PBHs in higher mass windows but the primordial spectrum of curvature perturbations becomes strongly tilted at the CMB scales. Moreover, we study the effects of a reheating epoch after the end of inflation on the PBHs mass fraction and find that an epoch of a matter dominated reheating can shift the mass fraction to a larger mass window as well as increase their fractional contribution to the total dark matter even for the case of a monochromatic mass fraction.

Geometric interpolation by PH curves with quadratic or quartic rational normals

Pythagorean-hodograph (PH) curves have nice properties and have found important applications in geometric modeling and CNC machining. While the unit normals of PH curves of degree n are generally rational curves of degree n−1, this paper investigates PH curves of arbitrary degrees but with only quadratic rational unit normals when the curves are convex or with quartic rational unit normals when the curves have single inflection points. PH curves with quadratic or quartic rational normals have simple Gauss maps and hodographs of the curves are given by low degree tangent vector fields together with simple real scaling functions. Practical algorithms for interpolation of point-normal pairs or point-normal-curvature pairs together with unit normals at selected parameter coordinates or at inflection points by the investigated PH curves without or with the constraint of arc lengths have been given. The parameters for defining the interpolating PH curves are either obtained directly from the input data or by solving simple linear systems. This method of PH curve interpolation has unique solutions and the shapes of the interpolating PH curves are controlled well by the interpolated data. Even though the interpolating curves may have cusps, the regularity of the PH curves can be checked easily based on the signs of the real scaling functions within the hodographs.

Tidal interactions and principle of corresponding states: from micro to macro cosmos. A century after van der Waals' Nobel prize

The current attempt is aimed to honor the first centennial of Johannes Diderik van der Waals (VDW) awarding Nobel Prize in Physics. The VDW theory of ordinary fluids is reviewed in the first part of the paper, where special effort is devoted to the equation of state and the law of corresponding states. In addition, a few mathematical features involving properties of cubic equations are discussed, for appreciating the intrinsic beauty of the VDW theory. A theory of astrophysical fluids is shortly reviewed in the second part of the paper, grounding on the tensor virial theorem for two-component systems, and an equation of state is formulated with a convenient choice of reduced variables. Additional effort is devoted to particular choices of density profiles, namely a simple guidance case and two cases of astrophysical interest. The related macroisothermal curves are found to be qualitatively similar to VDW isothermal curves below the critical threshold and, for sufficiently steep density profiles, a critical macroisothermal curve exists, with a single horizontal inflexion point. Under the working hypothesis of a phase transition (assumed to be gas-stars) for astrophysical fluids, similar to the vapour-liquid phase transition in ordinary fluids, the location of gas clouds, stellar systems, galaxies, cluster of galaxies, on the plane scanned by reduced variables, is tentatively assigned. A brief discussion shows how van der Waals' two great discoveries, namely a gas equation of state where tidal interactions between molecules are taken into account, and the law of corresponding states, related to microcosmos, find a counterpart with regard to macrocosmos. In conclusion, after more than a century since the awarding of the Nobel Prize in Physics, van der Waals' ideas are still valid and helpful to day for a full understanding of the universe.

Study of high temperature phase stability and phase transformation kinetics of sigma and parent alpha phase in Fe55Cr45 (wt. %) alloy

This study presents an extensive experimental characterization of high temperature phase stability and phase transformation kinetics of intermetallic sigma and alpha phases of Fe55Cr45 alloy carried out by dynamic calorimetry. Sigma phase was synthesized from its parent alpha phase of Fe55Cr45 alloy by annealing at 973 K for 360 h in vacuum. A comparative thermal study of sigma and alpha phase alloy was performed from 373 to 1400 K by Differential Scanning Calorimeter. Single inflection of ferro to para magnetic transition (Tc) was observed in DSC upto melting at 831 K for alpha phase. For sigma phase, the sigma to alpha decomposition temperature was measured as 1122 K. It was observed that sigma phase decomposition temperature is nearly 30 K higher than the presently reported 1093 K. Kinetics study of sigma to alpha phase transformation has been carried out by employing various heating rates from 1 to 50 K min−1 in DSC. The non isothermal KJMA model has been adopted to model the fraction transformed to determine the order and kinetics parameters. The activation energy for sigma to alpha phase transformation was obtained 240–260 kJ mol−1 by employing KJMA model.

Pseudo-Rigid-Body Model for the Flexural Beam With an Inflection Point in Compliant Mechanisms

The pseudo-rigid-body model (PRBM) used to simulate compliant beams without inflection point had been well developed. In this paper, two types of PRBMs are proposed to simulate the large deflection of flexible beam with an inflection point in different configurations. These models are composed of five rigid links connected by three joints added with torsional springs and one hinge without spring representing the inflection point in the flexural beam. The characteristic radius factors of the PRBMs are determined by solving the objective function established according to the relative angular displacement of the two rigid links jointed by the hinge via genetic algorithm. The spring stiffness coefficients are obtained using a linear regression technique. The effective ranges of these two models are determined by the load index. The numerical result shows that both the tip locus and inflection point of the flexural beam with single inflection can be precisely simulated using the model proposed in this paper.

Low-temperature magnetic properties of monoclinic pyrrhotite with particular relevance to the Besnus transition

Monoclinic pyrrhotite (Fe7S8) owes its ferrimagnetism to an ordered array of Fe vacancies. Its magnetic properties change markedly around 30 K, in what is known as the Besnus transition. Plausible explanations for the Besnus transition are either due to changes in crystalline anisotropy from a transformation in crystal symmetry or from the establishment of a two-phase system with magnetic interaction between the two phases. To help resolve this discrepancy, we measured hysteresis loops every 5° and backfield curves every 10° in the basal plane of an oriented single crystal of monoclinic pyrrhotite at 300 K and every 2 K from 50 K through the Besnus transition until 20 K. Between 50 and 30 K, hysteresis loops possess double inflections between crystallographic a-axes and only a single inflection parallel to the a-axes. Magnetization energy calculations and relative differences of the loops show a sixfold symmetry in this temperature range. We propose that the inflections stem from magnetic axis switching, which is both field and temperature dependent, in a manner somewhat analogous to an isotropic point where magnetocrystalline constants change their sign. The Besnus transition is best characterized by changes in magnetic remanence and coercivity over a 6° temperature span (28–34 K) with a maximum rate of change at 30 K. A surprising yet puzzling finding is that the coercivity ratio becomes less than unity below the transition when fourfold symmetry arises. Because the changes in magnetic parameters are linked to the crystal structure, we conclude the Besnus transition owes its origin to a distortion of the crystallographic axes below 30 K rather than an apparition of a two-phase system. An isothermal magnetization of natural pyrrhotite cycled from room temperature to successively lower temperatures through the Besnus transition decreases 2–4 times less than equivalent grain sizes of magnetite, with less than a 10 per cent loss in remanence between 300 and 150 K in pseudo-single-domain (PSD) pyrrhotite. As PSD monoclinic pyrrhotite carries the magnetic remanence in some meteorites, it is likely that low-temperature cycling in space then warming to ambient conditions at the Earth's surface will have only a minor influence on palaeointensity values derived from those meteorites.

On the Attainable Set for a Scalar Nonconvex Conservation Law

We deal with a Cauchy problem for a scalar conservation law in one space dimension. The flux function is assumed to be nonconvex, in particular, to have a single inflection point. We consider a compactly supported initial datum and regard it as a control. The main result of the paper states sufficient conditions for a function $v$ to be attained at a fixed time $T$ by a trajectory of the conservation law.

Plane quartics with at least 8 hyperinflection points

A recent result shows that a general smooth plane quartic can be recovered from its 24 inflection lines and a single inflection point. Nevertheless, the question of whether or not a smooth plane curve of degree at least 4 is determined fromits inflection lines is still open. Over a field of characteristic 0,we showthat it is possible to reconstruct any smooth plane quartic with at least 8 hyperinflection points by its inflection lines. Our methods apply also in positive characteristic, where we show a similar result, with two exceptions in characteristic 13.

Design and Characterization of a Peristaltic Actuator Inspired by Esophageal Swallowing

The specification and design of a novel peristaltic actuator is communicated. The actuation manifests as a continuous, distributed, and compliant peristaltic actuation. The occlusive nature of force distribution on the transport conduit results in materials being transported in front of a wave which has features of geometry and wave tail seal pressure. The behavior of these aspects profoundly affects the transport process. The device, of silicone rubber construction, has no internal skeletal structure and is pneumatically actuated which allows for continuous and compliant transport. The device is characterized by the synergy of geometrical and occlusive pressure measurements in response to actuation. This is performed for the “dry swallow” case (with no bolus) for single peak, single inflection waves. Techniques typical of medical investigation were exploited. Wave geometry was captured by articulography, complemented by wave seal pressure investigation by manometry. This paper describes the inspiration, specification, and experimental techniques used to develop and characterize the behavior of the biologically inspired, peristaltic, robotic device for assertion pressures up to 71.5 kPa. It is found that the device is capable of producing wave amplitudes and seal pressures of a similar magnitude (complete occlusion with >15-kPa seal) to the human esophagus which confirms achievement of the fundamental peristaltic parameters.

Curve construction based on four [formula omitted]-Bernstein-like basis functions

Four new αβ-Bernstein-like basis functions with two exponential shape parameters, are constructed in this paper, which include the cubic Said–Ball basis functions and the cubic Bernstein basis functions. Within the general framework of Quasi Extended Chebyshev space, we prove that the proposed αβ-Bernstein-like basis is an optimal normalized totally positive basis. In order to compute the corresponding αβ-Bézier-like curves stably and efficiently, a new corner cutting algorithm is developed. Necessary and sufficient conditions are derived for the planar αβ-Bézier-like curve having single or double inflection points, a loop or a cusp, or be locally or globally convex in terms of the relative position of its control polygons’ side vectors. Based on the new proposed αβ-Bernstein-like basis, a class of αβ-B-spline-like basis functions with two local exponential shape parameters is constructed. Their totally positive property is also proved. The associated αβ-B-spline-like curves have C2 continuity at single knots and include the cubic non-uniform B-spline curves as a special case, and can be C2∩FCk+3 (k∈Z+) continuous for particular choice of shape parameters. The exponential shape parameters serve as tension shape parameters and play a predictable adjusting role on generating curves.

Exponential Growth Model: From Horizontal to Linear Asymptote

We present a smooth function that can be used as regression curve for modeling growth phenomena requiring an increasing curvilinear concave asymptote. This model is obtained as the product of a concave asymptotic curve and the exponential model. In addition to its increasing character with a curvilinear asymptote, including horizontal or linear increasing asymptote, the resulting model provides curves with a single inflection point. Numerical examples are presented.

Optimum Power Randomization for the Minimization of Outage Probability

The optimum power randomization problem is studied to minimize outage probability in flat block-fading Gaussian channels under an average transmit power constraint and in the presence of channel distribution information at the transmitter. When the probability density function of the channel power gain is continuously differentiable with a finite second moment, it is shown that the outage probability curve is a nonincreasing function of the normalized transmit power with at least one inflection point and the total number of inflection points is odd. Based on this result, it is proved that the optimum power transmission strategy involves randomization between at most two power levels. In the case of a single inflection point, the optimum strategy simplifies to on-off signaling for weak transmitters. Through analytical and numerical discussions, it is shown that the proposed framework can be adapted to a wide variety of scenarios including log-normal shadowing, diversity combining over Rayleigh fading channels, Nakagami-m fading, spectrum sharing, and jamming applications. We also show that power randomization does not necessarily improve the outage performance when the finite second moment assumption is violated by the power distribution of the fading.

GROWTH MODELS WITH OBLIQUE ASYMPTOTE

A class of smooth functions which can be used as regression models for modelling phenomena requiring an oblique asymptote is analyzed. These types of models were defined as a product of a linear function and some well known growth models. In addition to their increasing character with an oblique asymptote, the resulting models provide curves with a single inflection point.