Quadratic Distribution Research Articles

Research on Workpiece Surface Temperature and Surface Quality in High-Speed Cylindrical Grinding and its Inspiration

The temperature in cylindrical grinding contact zone is difficult for measurement. Relative to the fixed workpiece in surface grinding, the workpiece rotation in cylindrical grinding brings challenges to the temperature measurement. In grinding titanium alloy, more heat will be generated, and due to the poor thermal conductivity of this material, it is easy to make the high temperature rise in the grinding zone. The high surface temperature and its distribution along the depth of the workpiece have great impacts on the grinding burn, metamorphic layer and residual stress. In order to improve the surface quality of machined parts, based on the undeformed chip thickness, this paper proposed a quadratic curve heat flux distribution model to predict the surface temperature distribution in the grinding of titanium alloy (TC4). Experimental results showed that the quadratic curve model under the condition of the measured grinding power, can predict the temperature distribution in the cylindrical grinding zone. Meanwhile, it specifically discussed the impact of the wheel speed on the TC4 surface roughness and the stress distribution, and found the "high-speed" definition in high-speed grinding should be distinguished from the traditional way only judged by the wheel speed, different workpiece materials should be with different "speed" ranges for acquisition of better machining quality.

Several modeling methods for representation of AC magnetic properties of electrical steel sheets taking account of skin effect

AbstractSeveral homogenized models are compared for accurate representation of the AC magnetic properties of silicon steel sheets. Two of them are the generalized Pry and Bean models, which have a parameter for the frequency dependence of eddy‐current loss. The third model assumes a quadratic distribution of the magnetic flux density along the thickness direction. The other model is an extension of the linear magnetization model. Numerical simulations show that the third model yields inaccurate BH loops whereas the other models accurately represent BH loops. © 2011 Wiley Periodicals, Inc. Electr Eng Jpn, 177(3): 9–16, 2011; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/eej.21180

Shape of growth-rate distribution determines the type of Non-Gibrat’s Property

In this study, the authors examine exhaustive business data on Japanese firms, which cover nearly all companies in the mid- and large-scale ranges in terms of firm size, to reach several key findings on profits/sales distribution and business growth trends. Here, profits denote net profits. First, detailed balance is observed not only in profits data but also in sales data. Furthermore, the growth-rate distribution of sales has wider tails than the linear growth-rate distribution of profits in log–log scale. On the one hand, in the mid-scale range of profits, the probability of positive growth decreases and the probability of negative growth increases symmetrically as the initial value increases. This is called Non-Gibrat’s First Property. On the other hand, in the mid-scale range of sales, the probability of positive growth decreases as the initial value increases, while the probability of negative growth hardly changes. This is called Non-Gibrat’s Second Property. Under detailed balance, Non-Gibrat’s First and Second Properties are analytically derived from the linear and quadratic growth-rate distributions in log–log scale, respectively. In both cases, the log-normal distribution is inferred from Non-Gibrat’s Properties and detailed balance. These analytic results are verified by empirical data. Consequently, this clarifies the notion that the difference in shapes between growth-rate distributions of sales and profits is closely related to the difference between the two Non-Gibrat’s Properties in the mid-scale range.

ON THE ESTIMATION OF DISTANCE DISTRIBUTION FUNCTIONS FOR POINT PROCESSES AND RANDOM SETS

This paper discusses various estimators for the nearest neighbour distance distribution function D of a stationary point process and for the quadratic contact distribution function Hq of a stationary random closed set. It recommends the use of Hanisch's estimator of D, which is of Horvitz-Thompson type, and the minussampling estimator of Hq. This recommendation is based on simulations for Poisson processes and Boolean models.

Baryonic loop in theρ-meson self-energy

A relativistic formula is derived for the self-energy of $\ensuremath{\rho}$ meson in nuclear matter from a baryonic loop graph containing nucleon and $\ensuremath{\Delta}(1232)$. After identifying the Lindhard function, we find another term in it that contributes appreciably to the real part of the self-energy. We also note small errors that may appear in the numerical calculation owing to the use of incorrect $\ensuremath{\Delta}$ coupling with other fields and presence of quadratic distribution functions in the self-energy formula.

Free vibration analysis of piezoelectric coupled annular plates with variable thickness

This paper presents the free vibration analysis of piezoelectric coupled annular plates with variable thickness on the basis of the Mindlin plate theory. No work has yet been done on piezoelectric laminated plates while the thickness is variable. Two piezoelectric layers are embedded on the upper and lower surfaces of the host plate. The host plate thickness is linearly increased in the radial direction while the piezoelectric layers thicknesses remain constant along the radial direction. Different combinations of three types of boundary conditions i.e. clamped, simply supported, and free end conditions are considered at the inner and outer edges of plate. The Maxwell static electricity equation in piezoelectric layers is satisfied using a quadratic distribution of electric potential along the thickness. The natural frequencies are obtained utilizing a Rayleigh–Ritz energy approach and are validated by comparing with those obtained by finite element analysis. A good compliance is observed between numerical solution and finite element analysis. Convergence study is performed in order to verify the numerical stability of the present method. The effects of different geometrical parameters such as the thickness of piezoelectric layers and the angle of host plate on the natural frequencies of the assembly are investigated.

Typical Virtual Appliances: An optimized mechanism for virtual appliances provisioning and management

A computing infrastructure requirement in the cloud computing environment can be specified and composed using virtual appliances, which forms the infrastructure-as-a-service (IaaS). Due to the diversity of user requirements, a large number of virtual appliances may be needed. We propose a mechanism called Typical Virtual Appliances (TVAs), an efficient method for providing virtual appliances. In this paper, we present the concept of TVAs and formulate it as an optimization problem with given constraints. With analysis of the software download logs of real web sites, we discover that the number of user requirements follows a quadratic polynomial distribution, and the user requirements are clustered in nature. According to this finding, we develop a clustering-based TVAs generation algorithm, and we show that this algorithm can achieve the optimal result. The clustering algorithm can generate TVAs, which can be transformed to other virtual appliances easily and efficiently. We further design a TVA Management System (TVAMS) to support this mechanism. The simulation results show that our method can meet most of the user requirements efficiently with low storage overhead.

Quadratic curve heat flux distribution model in the grinding zone

In order to estimate temperature distribution and the influence of grinding parameters on grinding temperature in the grinding zone, a theoretical model used for calculating and simulating the grinding process must be established. Many simplified heat source models developed previously have some errors compared with the actual heat flux to the workpiece. Therefore, based on the triangular heat flux distribution model and temperature distributions measured, an inverse method for the heat transfer mechanism in the grinding zone was investigated and a quadratic curve heat flux distribution model was developed to determine the heat flux distribution and predict the surface temperature of the workpiece. From the theoretical expression of heat flux to the workpiece, it has been found that the quadratic curve heat flux is the superposition of square law heat flux, triangular heat flux, and uniform heat flux in the grinding zone. By comparison of theoretical analysis with the experimental results, it has been demonstrated that the solution using a quadratic curve heat flux can improve the grinding model by decreasing the error, although the uniform and triangular heat fluxes can explain the condition of the heat flux to the workpiece along the grinding zone.

On shear correction factors in the non-linear theory of elastic shells

Theoretical values of two correction factors α s = 5/6 and α t = 7/10 are established for the respective transverse shear stress resultants and stress couples within the general, dynamically and kinematically exact, six-field theory of elastic shells. These values do not depend on the shell material symmetry, geometry of the base surface, the shell thickness, or any kind of kinematic and/or dynamic constraints. The analysis is based on the complementary energy density following from the transverse shear stresses acting only on the shell cross section. The appropriate quadratic and cubic distributions of the stresses across the thickness allow one to derive the consistent constitutive equations for the transverse shear stress resultants and stress couples with α s and α t as the respective correction factors. Four numerical examples of highly non-linear shell structures illustrate the influence of different values of α s and α t on the results. In particular, some influence of α t is noticed on the placement of bifurcation points. In dynamic problem of flight of three intersecting plates analysed with Newmark-type temporal algorithm, the value of α t influences the moment at which the relative error of total energy of the system begins to grow indefinitely leading to the solution failure.

Equidistribution of Heegner points and ternary quadratic forms

We prove new equidistribution results for Galois orbits of Heegner points with respect to single reduction maps at inert primes. The arguments are based on two different techniques: primitive representations of integers by quadratic forms and distribution relations for Heegner points. Our results generalize an equidistribution result with respect to a single reduction map established by Cornut and Vatsal in the sense that we allow both the fundamental discriminant and the conductor to grow. Moreover, for fixed fundamental discriminant and variable conductor, we deduce an effective surjectivity theorem for the reduction map from Heegner points to supersingular points at a fixed inert prime. Our results are applicable to the setting considered by Kolyvagin in the construction of the Heegner points Euler system.

Selection of Dynamic Features Based on Time–Frequency Representations for Heart Murmur Detection from Phonocardiographic Signals

This work discusses a method for the selection of dynamic features, based on the calculation of the spectral power through time applied to the detection of systolic murmurs from phonocardiographic recordings. To investigate the dynamic properties of the spectral power during murmurs, several quadratic energy distributions have been studied, namely Wigner-Ville, Choi-Williams, smoothed pseudo Wigner-Ville, exponential, and hyperbolic T-distribution. The classification performance has been compared with that using a Short Time Fourier Transform and Continuous Wavelet Transform representations. Furthermore, this work discusses a variety of nonparametric techniques to estimate the spectral power contours as dynamic features that characterize the heart sounds (HS): instantaneous energy, eigenvectors, instantaneous frequency, equivalent bandwidth, subband spectral centroids, and Mel cepstral coefficients. In this way, the aforementioned time-frequency representations and their dynamic features were evaluated by means of their ability to detect the presence of murmurs using a simple k-Nearest Neighbors classifier. Moreover, the relevancies of the proposed dynamic features have been evaluated using a time-varying principal component analysis. The work presented is carried out using a database containing 22 phonocardiographic recordings (16 normal and 6 records with murmurs), segmented to extract 402 representative individual beats (201 per class). The results suggest that the smoothing given by the quadratic energy distribution significantly improves the classification performance for the detection of murmurs in HS. Moreover, it is shown that the power dynamic features which give the best overall classification performance are the MFCC contours. As a result, the proposed method can be implemented as a simple diagnostic tool for primary health-care purposes with high accuracy (up to 98%) discriminating between normal and pathologic beats.

The propagation of the shock wave from a strong explosion in a plane-parallel stratified medium: the Kompaneets approximation

Context. Using certain simplifications, Kompaneets derived a partial differential equation that states the local geometrical and kinematical conditions that each surface element of a shock wave, created by a point blast in a stratified gaseous medium, must satisfy. Kompaneets could solve his equation analytically for the case of a wave propagating in an exponentially stratified medium, obtaining the form of the shock front at progressive evolutionary stages. Complete analytical solutions of the Kompaneets equation for shock wave motion in further plane-parallel stratified media were not found, except for radially stratified media. Aims. We aim to analytically solve the Kompaneets equation for the motion of a shock wave in different plane-parallel stratified media that can reflect a wide variety of astrophysical contexts. We were particularly interested in solving the Kompaneets equation for a strong explosion in the interstellar medium of the Galactic disk, in which, due to intense winds and explosions of stars, gigantic gaseous structures known as superbubbles and supershells are formed. Methods. Using the Kompaneets approximation, we derived a pair of equations that we call adapted Kompaneets equations, that govern the propagation of a shock wave in a stratified medium and that permit us to obtain solutions in parametric form. The solutions provided by the system of adapted Kompaneets equations are equivalent to those of the Kompaneets equation. We solved the adapted Kompaneets equations for shock wave propagation in a generic stratified medium by means of a power-series method. Results. Using the series solution for a shock wave in a generic medium, we obtained the series solutions for four specific media whose respective density distributions in the direction perpendicular to the stratification plane are of an exponential, power-law type (one with exponent $k=-1$ and the other with $ k =-2$) and a quadratic hyperbolic-secant. From these series solutions, we deduced exact solutions for the four media in terms of elemental functions. The exact solution for shock wave propagation in a medium of quadratic hyperbolic-secant density distribution is very appropriate to describe the growth of superbubbles in the Galactic disk.

Empirical relationship between intra-purine and intra-pyrimidine differences in conserved gene sequences.

DNA sequences seen in the normal character-based representation appear to have a formidable mixing of the four nucleotides without any apparent order. Nucleotide frequencies and distributions in the sequences have been studied extensively, since the simple rule given by Chargaff almost a century ago that equates the total number of purines to the pyrimidines in a duplex DNA sequence. While it is difficult to trace any relationship between the bases from studies in the character representation of a DNA sequence, graphical representations may provide a clue. These novel representations of DNA sequences have been useful in providing an overview of base distribution and composition of the sequences and providing insights into many hidden structures. We report here our observation based on a graphical representation that the intra-purine and intra-pyrimidine differences in sequences of conserved genes generally follow a quadratic distribution relationship and show that this may have arisen from mutations in the sequences over evolutionary time scales. From this hitherto undescribed relationship for the gene sequences considered in this report we hypothesize that such relationships may be characteristic of these sequences and therefore could become a barrier to large scale sequence alterations that override such characteristics, perhaps through some monitoring process inbuilt in the DNA sequences. Such relationship also raises the possibility of intron sequences playing an important role in maintaining the characteristics and could be indicative of possible intron-late phenomena.

Variation of ion cloud dimensions in an RF field with potential quadratic distribution in the presence of a buffer gas

Expressions are derived in terms of the theory of charged particle motion in a variable electric field for the rate of change of the ion cloud dimensions in the presence of a buffer gas in both stability and instability regions. Analytical calculations are validated by computer simulations.

Modeling creep in a rotating disc with linear and quadratic composition gradients

PurposeThe purpose of this paper is to investigate the effect of imposing linear and quadratic composition gradients on the steady state creep behavior of a rotating functionally graded Al‐SiCP disc operating under a radial thermal gradient.Design/methodology/approachMathematical model to describe steady state creep behavior in rotating discs made of isotropic aluminum composite containing linear and quadratic distributions of Silicon Carbide (SiCP) in the radial direction has been formulated. The discs are assumed to operate under a radial thermal gradient originating due to braking action as estimated by FEM analysis. The steady state creep behavior of the discs under stresses developing due to rotation has been determined following Sherby's law. Based on the developed model, the distributions of stresses and strain rates have been obtained and compared for various functionally graded material (FGM) discs containing the same average amount (20 vol per cent) of dispersoid. The creep response of a composite disc with uniform SiCP content of 20 vol per cent and operating under a radial thermal gradient has also been computed for comparison with the results obtained for FGM discs.FindingsThe study reveals that the distribution of stresses and strain rates in a rotating composite disc operating under a radial thermal gradient are significantly affected by different particle distributions with in the disc. The creep stresses and steady state creep rates in a rotating FGM disc can be significantly reduced by employing more SiCP particles in the middle compared to the inner and the outer radii.Originality/valueThe study provides an understanding of the required tailoring of composition in order to control creep stresses and creep rates in a rotating FGM disc operating under a radial thermal gradient.

Measurements of normal stress distributions experienced by rigid liquid composite moulding tools

Mould tools used for LCM processes such as Resin Transfer Moulding (RTM) and Injection/Compression Moulding (I/CM) must withstand local forces due to compaction of the fibre reinforcement, and due to resin pressure generated within the laminate. A series of RTM and I/CM experiments have been carried out, with the focus placed on measurement of normal stress distributions exerted on the mould surface. In addition, total mould clamping force and injection gate pressure histories have been recorded. I/CM experiments using force-controlled secondary compaction were also undertaken, and compared to the velocity-controlled cases. Observed fluid pressure fields showed good agreement with theory, namely a logarithmic distribution during fluid injection and a quadratic distribution during the compression driven filling phase of I/CM. Significant spatial variation in normal stress due to reinforcement compaction was observed. The influence of the fluid pressure on the total stress experienced by the mould was observed to be a function of both the fibre volume fraction of the part and the applied injection pressure, the latter being more pronounced at lower part volume fractions.

Dual affine connections on a quadratic hyperband distribution in a projective-metric space and their applications

In this paper, we develop fundamentals of the dual theory of quadratic hyperband distributions H of m-dimensional line elements in a projective-metric space Kn (m < n − 1). In particular, we show that, on a dual normalized distribution H, there are induced two dual affine connections and indicate some applications of these connections to the geometry of m-webs on H.

Diode end pumped Nd:YAG laser at 946 nm with high pulse energy limited by thermal lensing

Diode lasers with peak powers in the kW range and pulse durations of micro- to milli-seconds have been available since several years. Pumping solid state lasers with such sources yield high output pulse energies in spiking or Q-switched operation. The output energy is limited by the thermal lens effects, which are measured and calculated. The time dependent heat conduction equation in the laser crystal is solved numerically to predict the overall temperature rise and thermal lensing. The thermally induced optical path difference is approximated by a quadratic distribution to obtain the focal length f of the thermal lens. The thermal lens coefficient K=1/(f⋅Pav), which depends only weakly on the heat transfer coefficient H of the laser crystal to the heat sink, decreases exponentially with increasing pump frequency until the steady state is reached. Experiments were done with a Nd:YAG crystal at different pump frequencies up to 100 Hz. The thermal lens coefficients obtained by the power maxima of asymmetric flat-flat resonators agree with our calculations.

Effects of Yearly Change in Nut Fruiting on Autumn Home-range Use by Macaca fuscata on Kinkazan Island, Northern Japan

Temporal changes in food availability affect foraging success and ultimately reproductive success of animals. They include both seasonal and annual changes. Although many researchers have investigated food availability and the corresponding ranging behavior of primates, studies of yearly changes have been limited. We studied the effects of the fruiting of nuts of Fagus crenata, Zelkova serrata, and Torreya nucifera on the ranging behavior of Japanese macaques (Macaca fuscata) in autumn on Kinkazan Island, northern Japan, for 5 yr between 2000 and 2005 (excluding 2003). We divided the study area (3.3 km2) into 100 × 100-m quadrats to assess the distribution of nut-rich quadrats that contained high densities of nut-producing species. The home ranges of the monkeys contained more nut-rich quadrats than expected, and the difference was significant for 3 of 5 yr. Autumn home-range use was also affected by the distribution of nut production, although the effect differed by year: monkeys frequently used nut-rich quadrats in a Zelkova-year (2000) and in 1 Torreya-year (2001), whereas they nonselectively used nut-rich quadrats in 2 Fagus-years (2002 and 2005) and in another Torreya-year (2004). Thus, Japanese macaques flexibly change their autumn ranging behavior according to yearly changes in distribution of nut production.

Several Modeling Methods for Representation of AC Magnetic Properties of Electrical Steel Sheets Taking Account of Skin Effect

Several homogenized models are compared for accurate representation of ac magnetic properties of silicon steel sheets. Two of them are generalized Pry and Bean models that have a parameter for the frequency dependence of eddy-current loss. The third model assumes a quadratic distribution of magnetic flux density along the thickness direction. The other model is an extension of linear magnetization model. Numerical simulations show that the third model yields inaccurate BH loops whereas the other models accurately represent BH loops.