Inverse Quadratic Function Research Articles

Модель "трубок-слоев" намагничиваемой цепочки шаров: магнитные свойства, оценка гиперусиления поля между шарами

A chain of granules is the magnetic flux conductive channel in the magnetized granular material. Experimental data on magnetic fluxes were obtained for eight conditional cores (different relative radii rc / R = 0.2--0.9) of the magnetized chain of spheres making it possible to establish the magnetic flux data for seven "pipe-layers" of the rp / R = 0.25--0.85 average radius. In the H magnetized field strength range from 10 to 50--55 kA/m, field dependences of this parameter and of the more universal parameter (independent of the radius of the spheres in the chain) of the magnetic flux density, i.e., magnetic induction in each "pipes", are close to the linear ones. Thus, the values of their magnetic permeability μp which are individual for different "pipes", turn out to be essentially constant in this range of H, which also carries important information about how many times the local field intensity h between the spheres exceeds the value of H. At rp / R ≤ 0.4, the h values are exceeding by an order of magnitude or more the H value, and at rp / R > > 0.4 and up to the periphery of the inter-sphere --- by several times. The μp = h / H decreasing dependence on rp / R, which is of interest in solving problems of the materials fine magnetic separation (using the magnetized matrix media), obeys the inverse quadratic function, and the field inhomogeneity level to the inverse cubic function

Near-perfect quantitatively tunable Q factors of quasi-bound states in the continuum via material-based thermal-optic perturbations.

We successfully achieved high-Q dual-band quasi-bound states in the continuum (BICs) by introducing geometrical perturbations and thermally induced material perturbations into silicon half-disk nanodimers. Importantly, it is found that the Q factor obtained from the thermally induced material perturbations fits better with the inverse quadratic function of the asymmetry relation than that of the geometrical-perturbations-based system. Notably, we demonstrated that changes occurring at the sub-K scale can enable the simultaneous realization of the full width at half maximum offset distance for quasi-BICs and a maximum contrast ratio exceeding 44 dB. Our research provides novel, to the best of our knowledge, insights for potential applications in nano-lasers, temperature sensors, and infrared imaging.

Error and stability estimates of a time-fractional option pricing model under fully spatial–temporal graded meshes

To price vanilla European and American options via the fractional Black–Scholes model, first a (2−α)-order discretization scheme for the Caputo fractional derivative based upon graded meshes along time is presented. This is fruitful for problems having nonsmooth data at the initial time. Second, a nonuniform discretization of space is also considered and the coefficient weights based upon meshless radial basis function generated finite difference (RBF-FD) methodology are contributed under the inverse quadratic function. The fully space–time nonuniform solution method is then constructed via the presented discretization formulas. Numerical tests are given to show effectiveness and accuracy of our numerical scheme.

Ultrasonic Thermometry Algorithm Based on Inverse Quadratic Function.

At present, there are two ways to obtain temperature information: contact type and nonintrusive type. As a nonintrusive temperature measurement method, ultrasonic thermometry can be used to acquire the temperature distribution of complex fields conveniently. By measuring the time-of-flight (TOF) between ultrasonic transmitters and receivers, and according to the relationship between temperature and ultrasonic velocity, the temperature distribution can be reconstructed. Among the existing algorithms, the least square method (LSM) will lose much information near the edges of the temperature field, and the algebra reconstruction technique (ART) is time-consuming with low reconstruction accuracy. In this article, an improved reconstruction algorithm based on an inverse quadratic function and singular value decomposition (IQ-SVD) is proposed, which can effectively increase the reconstruction accuracy. The simulations of the real temperature data are conducted in ideal and noisy environments, respectively. Moreover, the influence of region division and shape parameters on reconstruction accuracy is discussed. The simulation results indicate that, compared with conventional algorithms, the proposed algorithm can accurately reflect the temperature distribution, and the root mean square error in the central region and the edge region is reduced by 0.49% at least, and 1.28% at most.

The application of radial basis function interpolation in reactor core power distribution on-line monitoring

Reactor core power mapping can be regarded as an interpolation problem of scattered data which is common in many scientific and engineering fields, and the Radial Basis Function (RBF) method provides an excellent tool for interpolating multidimensional scattered data and thus an appropriate approach for power mapping. By using the dual form of the RBF interpolation expression, this study shows that the Ordinary Kriging (OK) method authors utilized before can be regarded as an instance of RBF framework. Moreover, Gaussian function, multiquadric function, inverse quadratic function and inverse multiquadric function have been implemented in RBF interpolation framework to carry out core power mapping. Measurements from DayaBay Unit 1 PWR are used to verify the accuracies of these four RBF functions, and comparisons are made among these four methods and the OK method. The reconstructed assembly power distribution results and the calculation speeds show that the RBF interpolation framework is suitable for on-line core power distribution monitoring.

Positive change following adversity and psychological adjustment over time in abused foster youth

Many foster youth experience maltreatment in their family-of-origin and additional maltreatment while in foster care. Not surprisingly, rates of depression are higher in foster youth than the general population, and peak during ages 17–19 during the stressful transition into adulthood. However, no known studies have reported on whether foster youth perceive positive changes following such adversity, and whether positive change facilitates psychological adjustment over time. The current study examined components of positive change (i.e., compassion for others and self-efficacy) with depression severity from age 17 to 18 as youth prepared to exit foster care. Participants were youth from the Mental Health Service Use of Youth Leaving Foster Care study who endorsed child maltreatment. Components of positive change and severity of abuse were measured initially. Depression was measured initially and every three months over the following year. Latent growth curve modeling was used to examine the course of depression as a function of initial levels of positive change and severity of abuse. Results revealed that decreases in depression followed an inverse quadratic function in which the steepest declines occurred in the first three months and leveled off after that. Severity of abuse was positively correlated with higher initial levels of depression and negatively correlated with decreases in depression. Greater self-efficacy was negatively associated with initial levels of depression and predicted decreases in depression over the year, whereas compassion for others was neither associated with initial depression nor changes in depression. Implications for intervention, theory, and research are discussed.

The strain rate effect on the buckling of single-layer MoS2.

The Euler buckling theory states that the buckling critical strain is an inverse quadratic function of the length for a thin plate in the static compression process. However, the suitability of this theory in the dynamical process is unclear, so we perform molecular dynamics simulations to examine the applicability of the Euler buckling theory for the fast compression of the single-layer MoS2. We find that the Euler buckling theory is not applicable in such dynamical process, as the buckling critical strain becomes a length-independent constant in the buckled system with many ripples. However, the Euler buckling theory can be resumed in the dynamical process after restricting the theory to an individual ripple in the buckled structure.

Transport critical current dependence on magnetic fields in ceramic high temperature superconducting samples

The expression for the Josephson current flowing through the rectangular junctions was averaged over the values determining its properties in the case when magnetic field is less then first critical magnetic field of superconducting grains. The averaging results permit to explain the earlier performed experimental investigations of the scaling properties of critical state in random 3-d Josephson net created by transport current. At low magnetic field the average Josephson current is a quadratic function of the magnetic field and at high field the average current is an inverse quadratic function.

How Reward and Emotional Stimuli Induce Different Reactions Across the Menstrual Cycle

Despite widespread belief that moods are affected by the menstrual cycle, researchers on emotion and reward have not paid much attention to the menstrual cycle until recently. However, recent research has revealed different reactions to emotional stimuli and to rewarding stimuli across the different phases of the menstrual cycle. The current paper reviews the emerging literature on how ovarian hormone fluctuation during the menstrual cycle modulates reactions to emotional stimuli and to reward. Behavioral and neuroimaging studies in humans suggest that estrogen and progesterone have opposing influences. That is, it appears that estrogen enhances reactions to reward, but progesterone counters the facilitative effects of estrogen and decreases reactions to rewards. In contrast, reactions to emotionally arousing stimuli (particularly negative stimuli) appear to be decreased by estrogen but enhanced by progesterone. Potential factors that can modulate the effects of the ovarian hormones (e.g., an inverse quadratic function of hormones' effects; the structural changes of the hippocampus across the menstrual cycle) are also discussed.

Estimation of economically optimum seed rates for winter wheat from series of trials

The results of recent trials for winter wheat (Triticum aestivum L.) have influenced farming practice in the UK by encouraging the use of lower seed rates. Spink et al. (2000) have demonstrated that, particularly if sown early, wheat can compensate for reduced plant populations by increased tiller production.Results from seed-rate trials are usually analysed separately for each environment or each combination of environment and variety, and not combined into a single model. They therefore address the question of what the best seed rate would have been for each combination, rather than answer the more relevant question of what rate to choose for a future site. The current paper presents a Bayesian method for combining data from seed-rate trials and choosing optimum seed rates: this method can incorporate information on seed and treatment costs, crop value and covariates. More importantly, for use as an advisory tool, it allows incorporation of expert knowledge of the crop and of the target site.The method is illustrated using two series of trials: the first, carried out at two sites in 1997–99, investigated the effects of sowing date and variety in addition to seed rate. The second was conducted at seven sites in 2001–03 and included latitude and certain management factors. Recommended seed rates based on these series vary substantially with sowing date and latitude.Two non-linear dose-response functions are fitted to the data, the widely used exponential-plus-linear function and the inverse-quadratic function (Nelder 1966). The inverse-quadratic function is found to provide a better fit to the data than the exponential-plus-linear and the latter function gives estimated optimum rates which are as much as 40% lower. The economic consequences of using one function rather than the other are not great in these circumstances.The method is found to be robust to changes in the prior distribution and to other changes in the model used for dependence of yield on sowing date, latitude, variety and management factors.

Variation in effective pollination rates in relation to the spatial and temporal distribution of pollen release in rejuvenated perennial ryegrass

Genebank accessions stored as seed populations require periodic rejuvenation in order to maintain sufficient numbers of viable seeds. During rejuvenation the genetic composition of accessions may be altered for a variety of reasons, of which variation in pollination rates between plants is the least understood. In the present study, a paternity exclusion analysis was performed on a rejuvenated accession of perennial ryegrass. In addition, flowering data of the 49 parental plants were collected during the flowering season. The aim of the study was to determine how accurate variation in pollination rates between plants can be predicted from data on the spatial and temporal distribution of pollen release. The parental population and a total of 551 offspring from 12 progeny arrays were genotyped by means of molecular analysis. Using 25 microsatellites, paternity was identified for 81.9% of the offspring, while remaining ambiguities were resolved by AFLP analysis, except in four cases. Within the total sample 9 cases of contamination were observed. Mating within the study population was clearly non-random, as 61.9% of the identified pollen donors were located within 1 m distance from the mother plant. Observed pollination rates were very well described by an inverse quadratic function of inter-plant distance between potential mating pairs. Incorporation of the recorded flowering data in the calculation of expected pollination rates improved the goodness of fit with observed values by only 0.77%. Suggestions to reduce the variance in paternal contributions were presented. However, contamination was considered more threatening to the genetic integrity of perennial ryegrass germplasm than variation in pollination rates between plants, and indicated the need for improved measures to avoid gene flow from other germplasm.

Assessment and parameterisation of Coulomb-enhanced Auger recombination coefficients in lowly injected crystalline silicon

In traditional band-to-band Auger recombination theory, the low-injection carrier lifetime is an inverse quadratic function of the doping density. However, for doping densities below about 3×1018 cm−3, the low-injection Auger lifetimes measured in the past on silicon were significantly smaller than predicted by this theory. Recently, a new theory has been developed [A. Hangleiter and R. Häcker, Phys. Rev. Lett. 65, 215 (1990)] that attributes these deviations to Coulombic interactions between mobile charge carriers. This theory has been supported experimentally to a high degree of accuracy in n-type silicon; however, no satisfactory support for it has been found in p-type silicon for doping densities below 3×1017 cm−3. In this work, we investigate the most recent lifetime measurements of crystalline silicon and support experimentally the Coulomb-enhanced Auger theory in p-type silicon in the doping range down to 1×1016 cm−3. Based on the experimental data, we present an empirical parameterisation of the low-injection Auger lifetime. This parameterisation is valid in n- and p-type silicon with arbitrary doping concentrations and for temperatures between 70 and 400 K. We implement this parameterisation into a numerical device simulator to demonstrate how the new Auger limit influences the open-circuit voltage capability of silicon solar cells. Further, we briefly discuss why the Auger recombination rates are less enhanced under high-injection conditions than under low-injection conditions.

Heats of transport of ideal gases and gas mixtures

Kinetic theory expressions for thermal transpiration interpreted within the framework of non-equilibrium thermodynamics provide a detailed description of the heat of transport in terms of gas properties. For a pure monatomic gas, the heat of transport decreases from a constant value in the Knudsen limit to zero in the continuum region, the variation being an inverse quadratic function of pressure. For this case, the heat of transport depends markedly on temperature. Inelastic collisions involving rotational degrees of freedom, as occur in polyatomic gases, result in small but measurable deviations from monatomic gas behaviour. With binary gas mixtures, interactions between the different species cause appreciable deviations from simple mixing rules.

Acoustic Ray Theory Calculations

An acoustic ray trace program has been developed at the Naval Research Laboratory based upon a smoothed fit of sound speed profile data to an inverse quadratic function of depth. The program computes closed-form solutions for ray trajectories, travel times, and propagation losses between discrete layer boundaries in the profile. There is provision for range-dependent changes in sound speed profile, and for representation of the sea bottom as either flat or linearly segmented. Receiver intensities can be calculated as random or phase-dependent ray series, or by a technique of statistical distribution of arrivals. Results are given for the application of the program to a bistatic reverberation problem. Separate ray traces from source and receiver were made and arrivals on the bottom were matched to yield the receiver arrival pulse structure.