Form Of Power Function Research Articles

Basis set convergence of potential energy surfaces: Ground electronic state of H2 and H

AbstractThe convergence behavior of the total energy with the increase of the basis set is analyzed in two‐electron systems, H2 and H , where the source of error is the basis set truncation. Extrapolation of total energy to the complete basis set limit is carried out with the exponential and inverse cubic power (or higher order) functional forms, as a function of the cardinal number X that describes the correlation consistent basis sets, used in this work. The ability of the different extrapolation schemes to generate accurate potential energy curves or surfaces, over a wide range of geometries, is examined, following the criteria outlined by Halkier et al. (Chem Phys Lett, 1999, 310, 385). Comparison with the most accurate potential energy curve and surface for the ground electronic state of H2 (X1Σ) and H (1A′), respectively, shows that a simple two point extrapolation with the quintuple and sextuple zeta correlation‐consistent basis sets results yields to practically “spectroscopic accuracy.” To assess the precision of the extrapolated potential energy surfaces, several properties are compared with the most accurate ones. As an example, the vibrational energies obtained with the extrapolated energies have an error of only a few tenths of a cm−1. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Cross‐biome transplants of plant litter show decomposition models extend to a broader climatic range but lose predictability at the decadal time scale

AbstractWe analyzed results from 10‐year long field incubations of foliar and fine root litter from the Long‐term Intersite Decomposition Experiment Team (LIDET) study. We tested whether a variety of climate and litter quality variables could be used to develop regression models of decomposition parameters across wide ranges in litter quality and climate and whether these models changed over short to long time periods. Six genera of foliar and three genera of root litters were studied with a 10‐fold range in the ratio of acid unhydrolyzable fraction (AUF, or ‘lignin’) to N. Litter was incubated at 27 field sites across numerous terrestrial biomes including arctic and alpine tundra, temperate and tropical forests, grasslands and warm deserts. We used three separate mathematical models of first‐order (exponential) decomposition, emphasizing either the first year or the entire decade. One model included the proportion of relatively stable material as an asymptote. For short‐term (first‐year) decomposition, nonlinear regressions of exponential or power function form were obtained with r2 values of 0.82 and 0.64 for foliar and fine‐root litter, respectively, across all biomes included. AUF and AUF : N ratio were the most explanative litter quality variables, while the combined temperature‐moisture terms AET (actual evapotranspiration) and CDI (climatic decomposition index) were best for climatic effects. Regressions contained some systematic bias for grasslands and arctic and boreal sites, but not for humid tropical forests or temperate deciduous and coniferous forests. The ability of the regression approach to fit climate‐driven decomposition models of the 10‐year field results was dramatically reduced from the ability to capture drivers of short‐term decomposition. Future work will require conceptual and methodological improvements to investigate processes controlling decadal‐scale litter decomposition, including the formation of a relatively stable fraction and its subsequent decomposition.

3要素固体モデルによる粘弾性特性の評価における軟質セル構造体の変形挙動の近似法の影響

Soft cellular solids like sponge and muscle have the nonlinear viscoelasticity due to the internal gas or liquid in cells and the behavior of the matrix of the solids. Their stress-time curves are different by the variation of their internal structures, and it causes difficulties in the evaluation of the mechanical characteristics of the solids. In this study, we adopted the multiplication form of power and exponent functions that is able to approximate the nonlinear and fluctuated behavior of soft cellular solids. Then, we examine the adequacy of this method by its application to the experimental results of tensile testings of SBR sponge and biological soft tissue. The results of the examination show that the adopted form of the functions have good ability to fit the complex results of the stress-time curves and it can realize good evaluation of viscoelasticity of soft cellular solid by using three-element solid model.

21505 軟質セル構造体の粘弾性特性の評価法(一般講演 機械材料・材料科学(2))

Soft cellular solids like sponge and muscle have the nonlinear viscoelasticity due to the internal gas or liquid in cells and the behavior of the matrix of the solids. Their stress-time curves are different by the variation of their internal structures, and it causes difficulties in the evaluation of the mechanical characteristic of the solids. In this study, we adopted the multiplication form of power and exponent function that is able to approximate the nonlinear behavior of soft cellular solids. Then, we examine the adequacy of this method by its application to the experimental result of tensile testing of SBR sponge and chicken muscular tissue.

Characteristics of soil water retention curve at macro-scale

Scale adaptable hydrological models have attracted more and more attentions in the hydrological modeling research community, and the constitutive relationship at the macro-scale is one of the most important issues, upon which there are not enough research activities yet. Taking the constitutive relationships of soil water movement—soil water retention curve (SWRC) as an example, this study extends the definition of SWRC at the micro-scale to that at the macro-scale, and aided by Monte Carlo method we demonstrate that soil property and the spatial distribution of soil moisture will affect the features of SWRC greatly. Furthermore, we assume that the spatial distribution of soil moisture is the result of self-organization of climate, soil, ground water and soil water movement under the specific boundary conditions, and we also carry out numerical experiments of soil water movement at the vertical direction in order to explore the relationship between SWRC at the macro-scale and the combinations of climate, soil, and groundwater. The results show that SWRCs at the macro-scale and micro-scale presents totally different features, e.g., the essential hysteresis phenomenon which is exaggerated with increasing aridity index and rising groundwater table. Soil property plays an important role in the shape of SWRC which will even lead to a rectangular shape under drier conditions, and power function form of SWRC widely adopted in hydrological model might be revised for most situations at the macro-scale.

Analytic solutions of an iterative differential equation under Brjuno condition

In this paper, the differential equation involving iterates of the unknown function, $$ x'(z) = [a^2 - x^2 (z)]x^{[m]} (z) $$ with a complex parameter a, is investigated in the complex field ℂ for the existence of analytic solutions. First of all, we discuss the existence and the continuous dependence on the parameter a of analytic solution for the above equation, by making use of Banach fixed point theorem. Then, as well as in many previous works, we reduce the equation with the Schroder transformation x(z) = y(αy−1(z)) to the following another functional differential equation without iteration of the unknown function $$ \alpha y'(\alpha z) = [a^2 - y^2 (\alpha z)]y'(z)y(\alpha ^m z), $$ which is called an auxiliary equation. By constructing local invertible analytic solutions of the auxiliary equation, analytic solutions of the form y(αy−1(z)) for the original iterative differential equation are obtained. We discuss not only these α given in Schroder transformation in the hyperbolic case 0 < |α| < 1 and resonance, i.e., at a root of the unity, but also those α near resonance (i.e., near a root of the unity) under Brjuno condition. Finally, we introduce explicit analytic solutions for the original iterative differential equation by means of a recurrent formula, and give some particular solutions in the form of power functions when a = 0.

Experimental investigation on TBAB clathrate hydrate slurry flows in a horizontal tube: Forced convective heat transfer behaviors

Tetra-n-butyl-ammonium bromide (TBAB) clathrate hydrate slurry (CHS) is one kind of secondary refrigerants, which is promising to be applied into air-conditioning or latent-heat transportation systems as a thermal storage or cold carrying medium for energy saving. It is a solid–liquid two phase mixture which is easy to produce and has high latent heat and good fluidity. In this paper, the heat transfer characteristics of TBAB slurry were investigated in a horizontal stainless steel tube under different solid mass fractions and flow velocities with constant heat flux. One velocity region of weakened heat transfer was found. Moreover, TBAB CHS was treated as a kind of Bingham fluids, and the influences of the solid particles, flow velocity and types of flow on the forced convective heat transfer coefficients of TBAB CHS were investigated. At last, criterial correlations of Nusselt number for laminar and turbulent flows in the form of power function were summarized, and the error with experimental results was within ±20%.

The Moving Crack Problem of Orthotropic Functionally Graded Materials under Antiplane Loading

Dynamic problems of Yoffe mode crack are studied under antiplane shear impact in infinite orthotropic functionally graded materials. The shear modules in two directions are assumed to vary in terms with power function form of dual parameters of arbitrary time power. By using integral transform-dual integral equations method, the stress field and dynamic stress intensity factor near crack tip are obtained. And the influences of material in homogenous coefficient and graded parameters and crack moving speed to dynamic stress intensity factor are analyzed in virtue of Matlab software. Results show that the dimensionless dynamic stress intensity factor will decrease with the increase of moving speed of crack, which is opposite to the result of the dynamic problem of infinite strip in FGM. And the dimensionless dynamic stress intensity factor will decrease with the increase of graded parameters and rise with the increase of material in homogenous coefficient.

Permanent Deformation Behavior of Naturally Occurring Bituminous Sands

Oil sand, or tar sand, is a generic name given to bituminous sand deposits that are rich in bitumen or asphalt content to the extent that oil can be extracted from these deposits. The typical 8% to 15% presence of bitumen in the soil composition makes these naturally occurring sands low load-bearing materials. In this study, repeated load triaxial tests were conducted on three types of oil sand materials with natural bitumen contents of 8.5%, 13.3%, and 14.5% by weight. The oil sand specimens were compacted close to field densities and then tested for permanent deformation at two temperatures using a newly proposed test procedure. The procedure applied stress states and ratios determined from field-loading characteristics of haul trucks and mining equipment at two different load pulse durations or loading frequencies (related to field-trafficking speeds). Both the test data and axial permanent strain models developed in the form of power functions of the number of repeated load applications indicated a strong dependency of oil sand permanent strain development on the applied vertical to horizontal (or major to minor principal) stress ratio. Using the test data, permanent strain and deformation models were developed with high correlation coefficients to account for the applied stress states and ratios, test temperature, and bitumen content. These models generalized for oil sand deformation behavior may be used as practical predictive equations to estimate the amount of rutting in oil sand materials and to alleviate potential sinkage problems faced by off-road haul trucks, shovels, and other mining equipment in the field.

Proposed power-functionN-body potential for the fcc structured metals Ag, Au, Cu, Ni, Pd, and Pt

We propose, for the fcc structured Ag, Au, Cu, Ni, Pd, and Pt metals, an $N$-body potential with a simple power-function form, which significantly simplifies the fitting procedure and computation. The proposed potentials are able to correctly reproduce the lattice constants, cohesion energies, elastic constants, relative stabilities of different structures, formation energies of vacancy, and surface energies. In addition, the thermal properties, such as melting points and heat capacities, etc., are also satisfactorily determined from the proposed potentials. Moreover, the proposed potential is applied to calculate the trigonal and tetragonal paths between the fcc and bcc structures, and the calculated paths match well with those obtained from the first principles calculations.

Local invertible analytic solutions for an iterative differential equation related to a discrete derivatives sequence

In this paper, we are concerned with the existence of analytic solutions of a class of iterative differential equation f ′ ( z ) = 1 K ( f 1 ( z ) ) a 1 ( f 2 ( z ) ) a 2 ⋯ ( f n ( z ) ) a n , in the complex field C , where K ∈ C ∖ { 0 } , a i ∈ R , f i ( z ) denotes ith iterate of f ( z ) , i = 1 , 2 , … , n . The above equation is closely related to a discrete derivatives sequence F ′ ( m ) (see [Y.-F.S. Pétermann, Jean-Luc Rémy, Ilan Vardi, Discrete derivative of sequences, Adv. in Appl. Math. 27 (2001) 562–584]). We first give the existence of analytic solutions of the form of power functions for such an equation. Then by constructing a convergent power series solution y ( z ) of an auxiliary equation of the form x ′ ( z ) = K α x ′ ( α z ) ( x ( α z ) ) a 1 ( x ( α 2 z ) ) a 2 ⋯ ( x ( α n z ) ) a n , invertible analytic solutions of the form f ( z ) = x ( α x −1 ( z ) ) for the original equation are obtained. We discuss not only the constant α at resonance, i.e. at a root of the unity, but also those α near resonance (near a root of the unity) under the Brjuno condition.

Allometry, Antilog Transformations, and the Perils of Prediction on the Original Scale

Biologists often use allometric equations that take the form of power functions (e.g., Y = aM(b), where M stands for mass and a and b are empirically fitted constants). Typically, these allometric equations are fitted by taking the antilog of log-log regressions. Predictions from these allometric equations are biased, and the bias my be appreciable. Methods for making predictions that correct for the bias are available, but they have rarely, if ever, been used by ecological and evolutionary physiologists. Just as physiologists would not use an instrument that was not properly calibrated, they should not use allometric equations to make predictions unless they account for the bias of those predictions. We analyzed 20 interspecific and 10 intraspecific data sets. We compared predictions from standard allometric equations with those from several alternative methods. Our analyses suggest that the bias of predictions from interspecific data sets may be substantial. For the intraspecific data sets we analyzed, the bias was likely to be small. Biologists, including ecological and evolutionary physiologists, should exercise care when using allometric equations to make predictions, particularly given that methods to adjust for bias are easily implemented.

Material Design of Functionally Graded Plates with Function of Electromagnetic Noise Suppression (Quantitative Evaluation on Suppression Effect of Electromagnetic Noise)

The purpose of this paper is to present a method of material design of functionally graded material (FGM) plates with a function of electromagnetic noise suppression under an incidence of electromagnetic plane wave. The FGM plates are considered as multilayered plates while electromagnetic properties are homogeneous inside the same layer. The approximate analytical solutions of electromagnetic field in the multilayered plates are therefore derived for electromagnetic plane waves. The expressions for reflection and transmission coefficients are then obtained based on the above analytical solutions. In this paper epoxy resin/titanium oxide FGM plates for numerical calculations were used with a graded composition expressed in the form of power function. The effects of the graded composition and thickness on the reflection and transmission coefficients were then quantitatively evaluated, and the suppression effect of electromagnetic noise was discussed.

Analytic solutions of a second-order nonautonomous iterative functional differential equation

In this paper a second-order nonautonomous iterative functional differential equation is considered. By reducing the equation with the Schröder transformation to another functional differential equation without iteration of the unknown function, we give existence of its local analytic solutions. We first discuss the case that the constant α given in the Schröder transformation does not lie on the unit circle in C and the case that the constant lies on the circle but fulfills the Diophantine condition. Then we further study the case that the constant is a unit root in C but the Diophantine condition is offended. Finally, we investigate analytic solutions of the form of power functions.

1414 電気的特性の温度依存性を考慮した電磁波吸収機能を有するFGM平板の材料設計(S18-3 材料設計・傾斜機能材料,S18 不規則性,不均一性構造・材料の数理モデルとその応用)

The purpose of this study is to present a method of material design of functionally graded material (FGM) plate developing the function of electromagnetic noise suppression of incident plane wave under thermal environment. The FGM plate is divided into n homogeneous layers, which have distinct, constant thermal and electromagnetic properties, and then the approximate analytical solutions are derived for transient temperature field and electromagnetic field. The numerical calculations are carried out for transient temperature distribution and electromagnetic noise suppression effect in the FGM plate with the graded compositional distribution expressed in the form of power function, and then the effect of the graded composition on the electromagnetic noise suppression is quantitatively evaluated.

Models for recession flows in the upper Blue Nile River

AbstractStream‐flow recessions are commonly characterized by the exponential equation or in the alternative power form equation of a single linear reservoir. The most common measure of recession is the recession constant K, which relates to the power function form of the recession equation for a linear reservoir. However, in reality it can be seen that the groundwater dynamics of even the simplest of aquifers may behave in a non‐linear fashion. In this study three different storage–outflow algorithms; single linear, non‐linear and multiple linear reservoir were considered to model the stream‐flow recession of the upper Blue Nile. The recession parameters for the linear and non‐linear models were derived by the use of least‐squares regression procedures. Whereas, for the multiple linear reservoir model, a second‐order autoregressive AR (2) model was applied first in order to determine the parameters by the least‐squares method. The modelling of the upper Blue Nile recession flow performed shortly after the wet season, when interflow and bank storage may be contributing considerably to the river flow, showed that the non‐linear reservoir model simulates well with the observed counterparts. The variation related to preceding flow on a recession parameter of the non‐linear reservoir remains significant, which was obtained by stratification of the recession curves. Although a similar stratification did not show any systematic variation on the recession parameters for the linear and multiple linear reservoir models. Copyright © 2004 John Wiley &amp; Sons, Ltd.

Anti-scourability of purple soil on hillslopes with different land uses

A large-scale flume (40 cm x 10 cm x 10 cm) was used to determine soil anti-scourability of 4 different land uses of purple soil in hilly areas of Sichuan, China under artificial removal of vegetation to examine the effects of land uses on sediment production by runoff. The results showed that soil anti-scourability declined with the increase of slope gradients in the form of power function, but there was a significant difference in the effects of slope gradients on anti-scourability between different land uses. The ratio of the mean values of soil anti-scourability was 1:2.2:2.5:3.6 for forest land, new waste pasture, old waste pasture, crop land respectively, indicating that forest and grass use can significantly improve soil anti-scourability. Compared with the observations from the runoff plots located at the same sites in this region, an inconsistent result was found between anti-scourability and anti-erodibility in hilly areas of Sichuan. Essential causes of the differences in soil anti-scourability were further discussed based on analyzing the influence of inherent soil characteristics induced by different land uses on soil anti-scourability.

Physical Properties of Granular Organic-based Fertilisers, Part 2:: Dynamic Properties Related to Water

Organic-based fertilisers are granular fertilisers that make use of the synergy between the mineral and organic components. The physical properties of organic-based fertilisers are relatively unknown. The main objective of this research was to compare the physical properties of bulk-blended organic-based (BOF) and compound organic-based fertilisers (COF) with those of mineral fertilisers (MF). New and modified methods were used to measure their atmospheric moisture sorption, capillary rise, slaking and dissolution in water over time. Air moisture sorption by fertilisers increased quadratically with time and with relative humidity. At 82% relative humidity, major changes in fertiliser behaviour occurred. The processes varied among fertilisers. Water sorption from the atmosphere was affected by bulk density as well as by the organic matter (OM), initial moisture, and P contents. The water sorption rate over time during capillary rise took the form of an inverse power function and increased as OM content increased. Some fertilisers were highly affected by tensions while others were only slightly affected, indicating differential rates of release under field conditions. During submersion in water, COF granules dissolved, swelled and slaked to different extents and their diameter decreased quadratically over time. The loss of mass during submersion was affected by OM and nitrogen contents as well as by the initial granule size. Differences between fertilisers were mostly related to the organic matter type and content. Examples of uses and applications of dynamic properties are given for different situations: fast or slow release; dry to wet conditions; and application at the soil surface or incorporation in the soil.

Lysogeny and virus‐induced mortality of bacterioplankton in surface, deep, and anoxic marine waters

Lysogeny (bacteria containing inducible prophages) and lytic viral infection (bacteria in a lytic stage of infection) were investigated at the community level in contrasting marine environments such as estuarine versus offshore waters, surface versus deep waters, and oxic versus anoxic waters in the Mediterranean and Baltic Seas. The frequency of lysogenic cells (FLC) in bacterioplankton communities ranged from not detectable to 84% as estimated by prophage induction due to mitomycin C, and highest values were typically found in deep waters (800–2,000 m). Transmission electron microscopy based estimates of virus‐induced mortality of bacterioplankton (VMB) ranged from a few percent to 71%, and highest values were found in anoxic waters of the Baltic Sea. FLC and the frequency of infected cells (FIC) were related in form of a negative power function indicating that environments exist where one of the two viral life strategies prevails. Across all investigated environments, FLC was negatively related to bacterial abundance and production, whereas FIC showed a positive relationship with viral and bacterial parameters. FIC was higher and FLC was lower in moderately productive estuarine and offshore surface waters than in less productive mesopelagic and deep waters. Thus, lysogeny seems to be a survival strategy at low host abundance and activity, whereas high host abundance and activity seems to favor the lytic life cycle. The key process for the prevalence of lytic infection compared to prophage replication at high host abundance could be competition due to outnumbering. Between 11% and 88% (average, 35%) of the bacteria contained a functional (lytic or lysogenic) viral genome.

Estimation of information value on the Internet: application of hedonic price model

This paper estimates the value of Internet information by using the hedonic price model (HPM). We specify a hedonic price function, and measure the consumer’s willingness to pay for attributes to the Internet connection charge. We also identify a functional form for the HPM by using the Box–Cox transformation of the variables in our analysis. Our results indicate that the variation in the Internet connection charge is dependent upon the amount of information searching and e-shopping. We also find that the power functional form provides the best fit in describing the relationship between the Internet connection charge and the service characteristics. Based on the results of this paper, we expect that the economic value on Internet information will become larger than at present since Internet information usage is increasing. Thus, ISP or content providers seeking price discrimination can charge for information service instead of offering it for free if the firms segment their customers by the differential willingness to pay for each information.