Cosine Distribution Research Articles

Determination of shear strength of steel shear walls with three different vertical stress distributions for considering the gravity load effect

The gravity load will reduce the shear strength of a steel shear wall (SSW) under a wind load or an earthquake load. However, this effect is not considered in practice and may lead to potential danger. In this work, three assumed distributions of vertical stress due to the gravity load, i.e. 1) cosine distribution, 2) effective width model and 3) three-segment distribution, were considered. The stress throughout the inclined tensile strip, considering the effect of different vertical stress distributions, is determined using the Von Mises yield criterion. The shear strength is calculated by integrating the shear stress along the width. To evaluate the proposed approach with different vertical stress distributions a finite element model using the software LS-DYNA is developed. The results show that the three-segment distribution is able to describe the effect of gravity load of the SSWs of different aspect ratios and slenderness ratios, while that of the cosine distribution and the effective width model will underestimate the shear strength.

A Stress Distribution of Thin Rectangular Steel Wall Under a Uniform Compression

The stress distribution of a steel wall is important in the determination of its shear capacity, e.g. under a wind load or an earthquake load. Since the wall has also to simultaneously carry the gravity load, the influence of this uniform vertical load on the stress distribution is relevant. For a simple-supported thick and square wall, a stress distribution in a cosine form was adequate. However, for an extremely thin wall, a cosine distribution is no longer valid, especially in the post-buckling condition. In this work a three-segment distribution is proposed, i.e. at both edge segments a cosine distribution from edge stress to buckling stress and in the middle segment a constant distribution of buckling stress. To evaluate the proposed distribution, a finite element model using the software ANSYS/LS-DYNA is developed. This model has been verified using the results obtained from own experiments and works done by others. The results show that the proposed stress distribution is able to describe the behavior of thin walls for different aspect ratios and slendernesses. The cosine distribution and the effective width model are also discussed.

P.109 Genome-wide methylation patterns in persistent ADHD and in association with impulsive and callous traits

The solar receiver is considered the cornerstone of the solar tower power system. In particular, it receives high-temperature heat flux rays, and extracts the maximum heat energy to be transferred to the heat transfer fluid, while minimising any thermal and mechanical stresses. Reducing the solar receiver size helps to reduce the loss of spillage; consequently, the thermal stress increases. Using a solar receiver with inserted triangular longitudinal fins enhances the heat transfer as well as strengthens the receiver tube. This study aims to optimise the number of fins, heat flux aiming point, heat transfer fluid, nanoparticle effect with molten salt as the base fluid, and type of receiver material. Non-uniform heat flux with the cosine and Gaussian effects have been considered. When the number of fins (N) increases, the maximum temperature (Tmax) decreases and the heat transfer is enhanced. When N = 20, Tmax = 656.4 K and when N = 1, Tmax = 683.55, while the efficiency for N = 1 is greater by 3% compared to when N = 20. The cosine distribution of heat flux has a higher maximum temperature than the Gaussian distribution by 29% and is 102% higher in receiver efficiency. The thermal efficiency when the heat flux is aimed at the middle point of the receiver is higher by 10% compared with a lower or upper aiming point. Using Al2O3 nanoparticles with a concentration of 0.5 wt.% increases the thermal efficiency by 14% more than when using pure molten salt when Re = 38000. Using liquid sodium is not required to monitor the peak heat flux, and by adding triangular fins the displacement and thermal stress are 6.5 % lower compared to a smooth receiver.

A sinusoidal beam theory for functionally graded sandwich curved beams

To the best of the authors’ knowledge, there is no research work available on FG sandwich curved beams in the whole variety of literature. Therefore, the analysis presented on static behaviour of FG sandwich curved beams in this study is the main contribution and the novelty of the present study. A sinusoidal beam theory considering the effects of transverse normal stress/strain is applied for the bending analysis of FG sandwich beams curved in elevation. The beam has functionally graded skins at top and bottom and isotropic core at the middle. Material properties of FG skins are varied through the thickness according to the power law distribution. The present theory accounts for sinusoidal variation of axial strain and cosine distribution of transverse shear strain through the thickness of the beam. Governing equations of equilibrium are derived using Hamilton’s principle. Analytical solutions for simply supported curved beam are obtained using Navier’s solution procedure. The non-dimensional numerical results are obtained for different radii of curvature and various power law coefficients. The present study contributes many new results on the bending analysis of functionally graded sandwich beams curved in elevation for the reference of future research in this area.

Polarization by light reflection at metallic surfaces observed in the shape of the Balmer-α line of low density plasmas

The degree of linear polarization of light reflected at metallic surfaces is obtained from the shape of the Balmer-α line measured in a low density plasma. The measurements of the polarization properties of metallic surfaces utilize only the high-resolution emission spectra induced by fast reflected H atoms (≈100 eV) in ArH plasmas. The measurements are performed at two different lines-of-sight to the target surfaces of Mo and Cu. Only at the observation angle close to the Brewster one, a significant drop of the measured red-shifted signal is detected for the Mo target: the red-shifted emission reduces by ≈50% depending on whether the transverse (S) or the parallel (P) polarization component of the reflected light is selected. In contrast to this, a very weak change of emission is observed for the Cu surface for the same angle. The spectra measured in front of the Mo target were modeled utilizing the energy and angular distribution of reflected atoms and excitation of the cross section of Ar-H collision combined in a Doppler-shifted emission model. A good agreement with the theoretical calculations is found for polarization components (except for the weak P polarization at 70°). Finally, the undercosine distribution of the reflected atoms with b ≈ 0.2 (b is the power of the cosine distribution) shows the best agreement with the spectra measured at both lines-of-sight.

On a Generalized Raised Cosine Distribution: Some Properties, Characterizations and Applications

Abstract In this paper, we introduced a generalization of the raised cosine distribution. We also provided its several distributional properties and characterizations, including percentiles and some applications.

The surface current method in gray Dancoff factor calculation

The Dancoff correction is important in the calculation of the effective cross section of resonant isotopes in a heterogeneous system. Although the neutron current method is a simple and straightforward approach to estimate the Dancoff factor, its use is limited to the black Dancoff factor. In this paper, we expand the current method used to determine both the black and gray Dancoff factors. The method developed also relies on a neutron transport solver, where a fixed source on a fuel rod surface has an outward direction, a cosine distribution, and a constant shape. The detector is located on the surface of the rods to measure incoming and outgoing currents; therefore, there is no need to calculate the chord length, and the development, validation, and verification of the code can be omitted. The mathematical foundation of the suggested method is derived using the integral transport equation. The effects of the moderator and lattice configuration are followed by a sensitivity analysis of the Dancoff factor for several problems, including pressurized water reactor and cluster fuel assemblies. The maximum and average relative errors of the calculated results are approximately 0.3% and 0.05%, respectively.

Magnetic insulation in a curved vacuum transmission line

The curved structure of a coaxial magnetically insulated transmission line (MITL) causes it to generate a nonuniform azimuthal magnetic field, which can disturb the electron flow and lead to a higher current loss when compared with a straight MITL. In this paper, the current loss mechanism and nonuniformity of the azimuthal magnetic field inherent to curved MITLs are investigated using theoretical analysis and particle-in-cell simulations. Results show that the critical current for magnetic insulation of the curved MITL increases with nonuniformity of the azimuthal magnetic field. The magnitude of the azimuthal magnetic field of the curved MITL can be described by a cosine distribution, lower in the outer region and higher in the inner region of the curved MITL. Nonuniformity of the azimuthal magnetic field decreases as electron current increases. Finally, an empirical expression relating to the structural parameters of curved MITLs is obtained for nonuniformity of the azimuthal magnetic field, which can be used to estimate the critical current for magnetic insulation in curved MITLs. This work extends the understanding of magnetic insulation in curved coaxial transmission lines.

On Static Bending, Elastic Buckling and Free Vibration Analysis of Symmetric Functionally Graded Sandwich Beams

This article presents Navier type closed-form solutions for static bending, elastic buckling and free vibration analysis of symmetric functionally graded (FG) sandwich beams using a hyperbolic shear deformation theory. The beam has FG skins and isotropic core. Material properties of FG skins are varied through the thickness according to the power law distribution. The present theory accounts for a hyperbolic distribution of axial displacement whereas transverse displacement is constant through the thickness i.e effects of thickness stretching are neglected. The present theory gives hyperbolic cosine distribution of transverse shear stress through the thickness of the beam and satisfies zero traction boundary conditions on the top and bottom surfaces of the beam. The equations of the motion are obtained by using the Hamilton’s principle. Closed-form solutions for static, buckling and vibration analysis of simply supported FG sandwich beams are obtained using Navier’s solution technique. The non-dimensional numerical results are obtained for various power law index and skin-core-skin thickness ratios. The present results are compared with previously published results and found in excellent agreement.

Hedge Fund Investing or Mutual Fund Investing: An Application of Multi-Attribute Utility Theory

This paper contrasts high-risk, hedge fund trading, with low-risk, mutual fund trading, in terms of their differing utility functions. We envision hedge funds, led by informed traders who use information to seek out investment opportunities, timing market conditions, with the expectation that prices will move in their favor. Directional hedge funds act to influence prices, while non-directional hedge funds do not act to influence prices. We present utility functions based on steeply-sloping Laplace distributions and hyperbolic cosine distributions, to describe the actions of directional hedge fund traders. Less steeply-sloping lognormal distributions, Coulomb wave functions, quadratic utility functions, and Bessel utility functions are used to describe the investing style of non-directional hedge fund traders. Flatter Legendre utility functions and inverse sine utility functions describe the modest profit-making aspirations of mutual fund traders. The paper’s chief contribution is to develop optimal prices quantitatively, by intersecting utility functions with price distributions. Price distributions for directional hedge fund returns are portrayed as sharp increases and decreases, in the form of jumps, in a discrete arrival Poisson-distributed process. Separate equations are developed for directional hedge fund strategies, including event-driven arbitrage, and global macro strategies. Non-directional strategies include commodity trading, risk-neutral arbitrage, and convertible arbitrage, with primarily lognormal pricing distributions, and some Poisson jumps. Mutual funds are perceived to be Markowitz portfolios, lying on the Capital Market Line, or the International Capital Market Line, tangent to the Efficient Frontier of minimum variance-maximum return portfolios.

Tapered Unit Cell Control of a Sinusoidally Modulated Reactance Surface Antenna

A design procedure for synthesizing the desired beam pattern of the sinusoidally modulated reactance surface (SMRS) antenna is proposed. This methodology is a type of aperture tapering technique, where cosine distribution of aperture illumination was applied to the SMRS antenna. The unit cell of the SMRS antenna allows control of the leakage constant while keeping phase constant almost constant value in some allowable surface impedance modulation range; this characteristic provides the aperture amplitude tapering technique to the SMRS antennas. To verify this proposed concept, a prototype SMRS antenna composed of nine tapered unit cells was implemented using a printed circuit board process. The designed antenna radiates at 35° off broadside at 10 GHz. We obtained 16.6 dBi of measured antenna gain and the normalized sidelobe level was about −14.33 dB.

Buckling load of bending coiled tubing under an injector

When coiled tubing is applied in high oil–gas wells, buckling load of a coiled tubing under the injector is the key for functionality. The coiled tubing is curved, but it is simplified to straight tubing for buckling load solved in the past. These calculations were not sufficient for the problem. In this article, buckling load of a bent coiled tubing is discussed based on the actual details of the exploitation. First, the coiled tubing curvature changes during the working period reaching the shape presented in analysis of the article. To determine the distribution of stress and the zones to failure, a coiled tubing was studied using the theory of curved beam moment, and buckling load of the bending coiled tubing was derived. The study has indicated that the gooseneck curve radius and the yield strength enable to determine the residual curvature of coiled tubing. The axial stress along the convex and concave sides is a half periodic sine and cosine distribution along the length of the coiled tubing, and the maximum axial stress is on the middle of the concave side of the outside diameter of the coiled tubing. There is an inversely proportional relationship between buckling load and length of the tubing, and a proportion of buckling load and the diameter–thickness ratio. Moreover, buckling load was more sensitive to the tubing length than its wall-thickness.

Some characterizations of raised cosine distribution

Some distributional properties of the raised cosine distribution are presented. Based on the distributional properties, several new characterizations of the raised cosine distribution are given.Â

Monte Carlo simulation of gas free molecular flow in turbo molecular pump’s inlet tube

ABSTRACTDue to the beaming effect of inlet tube and reflection effect of turbine cover in the turbo molecular pump, the positional and angular distribution of incident gas molecules (IGM) on the turbine blades would no longer be uniformly distributed. Based on the test particle Monte Caro method, a new self-defining procedure is proposed and it can be more accurate to describe the status of IGM into turbine blades. The results show that the influence of rotor speed on the transmission probability is indistinctive. Meanwhile, the incident density between the tip and root of the blades is distinct. The positional beaming effect and the angular beaming effect are enhanced with the lengthening of the tube and less molecule diverge towards the tube wall. The positive transmission probability of first-stage turbine blades using our new method is different from those obeying the cosine distribution under the same number of incident molecules. The calculation results of new method verified by another procedure are reasonable and accurate.

The Valuation of Currency Put Options

Investors who seek to profit from depreciating currencies may invest in put options. Upon option exercise, the currency is sold at a high price, and then purchased at the lower future currency value, resulting in a gain for the put buyer. A series of such transactions yields a stream of income for the put investor. Alternatively, the investor could short sell the currency, reaping gains from the difference between the high short sale price and the low future purchase price. This paper derives the theoretical formulations for combined short sale and puts purchase strategies for the US dollar, the Euro, the Australian dollar and the New Zealand dollar, and the Mexican peso. Utility functions are based upon an assumption of declining risk aversio with negative rescale factors and positive threshold factors in a hyperbolic cosine distribution. This distribution intersects with the cosine distribution of short sale prices on the U. S. dollar, the lognormal distribution of short sale prices on the Euro, the Weiner process for shorts on the Australian dollar and the New Zealand dollar, and the Laplace currency distribution for peso shorts. Similar utility functions intersect with Levy-Khintchine jump processes to provide put option prices for each type of foreign currency.

Angular and velocity distributions of tungsten sputtered by low energy argon ions

Sputtering by ions with low near-threshold energies is investigated. Experiments and simulations are conducted for tungsten sputtering by low-energy, 85–200 eV Ar atoms. The angular distributions of sputtered particles are measured. A new method for molecular dynamics simulation of sputtering taking into account random crystallographic surface orientation is developed, and applied for the case under consideration. The simulations approximate experimental results well. At low energies the distributions acquire “butterfly-like” shape with lower sputtering yields for close to normal angles comparing to the cosine distribution. The energy distributions of sputtered particles were simulated. The Thompson distribution remains valid down to near-threshold 85 eV case.

The Exact Radiated Power and Directivity of a Scanning Line Source Radiator

The theory for computing the closed-form, exact radiated power of a scanning electric line source is provided for any scan angle (including zenith, nadir, and complex-valued angles of radiation) and for any current distribution of any length (including both electrically short and electrically long line sources). Knowledge of the radiated power pattern is not needed. The theory is couched in terms of three straightforward mathematical operations: an autocorrelation of the current distribution, a modified Helmholtz operation, and a convolution integral. Examples associated with the uniform, triangular, half-wave dipole, cosine, and cosine-squared distributions are provided to showcase the theory. Validation of the theory is established by comparing data obtained from the examples with data obtained via numerical integration of the power pattern. The agreement between data sets is effectively perfect.

Evaluation of different orientation angle distributions within the X-Bragg scattering model for bare soil moisture estimation

ABSTRACTIn this paper, the applicability of three different orientation angle distributions of surface facets within the extended Bragg (X-Bragg) scattering model is investigated for estimation of soil moisture over bare surfaces using both Eigen-based and model-based polarimetric synthetic aperture radar (PolSAR) decomposition techniques. The three distributions considered for investigation in the X-Bragg model are uniform, half cosine, and the Lee distributions. In order to understand the sensitivity of the model using the three orientation angle distributions, key polarimetric parameters, such as scattering entropy (H), scattering anisotropy (A), scattering mechanism (α), cross-pol power (T33), linear T12 coherence (|γ(HH+VV)(HH–VV)|), are simulated and analysed for various widths of distributions. The analysis of the simulated polarimetric parameters show that the Lee distribution has a reduced roughness validity range compared with the uniform and half cosine distributions. DLR E-SAR L-band data from the AgriSAR’2006 campaign over the Demmin test site in Northern Germany are inverted for soil moisture over bare surfaces. The inverted soil moisture from the physics-based X-Bragg model is compared with in situ measured TDR (time domain reflectometry) soil moisture values. The inversion results using the Eigen-based decomposition reveal similar root mean square error (RMSE = 14 vol.%) and inversion rates for three distributions. The model-based decomposition inversion results obtained at various fixed widths of distributions reveal that the Lee distribution shows less RMSE of 8 vol.% and high inversion rates for moderate surface roughness (ks = 0.5) as compared with half cosine and uniform distributions.

Imaging quality evaluation method of pixel coupled electro-optical imaging system

With advancements in high-resolution imaging optical fiber bundle fabrication technology, traditional photoelectric imaging system have become “flexible” with greatly reduced volume and weight. However, traditional image quality evaluation models are limited by the coupling discrete sampling effect of fiber-optic image bundles and charge-coupled device (CCD) pixels. This limitation substantially complicates the design, optimization, assembly, and evaluation image quality of the coupled discrete sampling imaging system. Based on the transfer process of grayscale cosine distribution optical signal in the fiber-optic image bundle and CCD, a mathematical model of coupled modulation transfer function (coupled-MTF) is established. This model can be used as a basis for following studies on the convergence and periodically oscillating characteristics of the function. We also propose the concept of the average coupled-MTF, which is consistent with the definition of traditional MTF. Based on this concept, the relationships among core distance, core layer radius, and average coupled-MTF are investigated.Results show that the coupled-MTF oscillation converges to a fixed value when the deviation between a spatial frequency of input signal and Nyquist frequency is 1% and when the total number of pixels in the coupled system is more than 1000. The minimal frequency deviation corresponds to the slow velocity of the oscillational convergent. The oscillation amplitude of coupled-MTF differs in tangential and sagittal directions in a manner related to the corresponding pixel coupling error. The coupled-MTF periodically oscillates with the alignment error between the coupled pixel. One cycle is equivalent to the diameter of fiber cladding. The observation from the simulations further reveal that the distance between adjacent fiber cores and the dimension of core layer are directly related to the system imaging quality and the signal-to-noise ratio. Moreover, the average coupled-MTF can be used to quantitatively describe the function of related parameters and the imaging quality of the system.

Mechanism of total electron emission yield reduction using a micro-porous surface

Suppression of the total secondary electron yield (TEY) of metal surfaces is important in many areas such as accelerator, satellite, and Hall thruster. Among TEY suppression techniques, micro-porous surfaces have been demonstrated as an effective method. In this work, we developed an analytical model that is able to obtain the contributions of TEY from both the 1st and 2nd generation secondary electrons (SEs). Calculation results show that the TEY contributed by the bottom of the hole dominates the TEY of the micro-porous surface with the aspect ratio we have chosen. Thus, we developed the following design guidance for the improvement of the TEY suppression efficiency of the micro-porous surface: either lower the TEY of the bottom or guide its SEs to the lateral side of the hole. To verify this idea, we performed the following numerical simulations: a micro-hole with its inner surfaces coated with a low TEY material and a micro-hole with nano-triangular grooves or nano-truncated cone pillars embedded at its bottom. Compared with a usual micro-hole, the proposed hybrid micro/nano structures show improved TEY suppression efficiency as expected from the analytical model. The percentage ratios of the 1st and 2nd generation SEs obtained from the simulation agree well with the predictions of the analytical model. What is more, we also present the results of the emitting angle distribution of SEs which represent remarkable deviation from the usual cosine distribution.