The Buffon needle problem for Lévy distributed spacings and renewal theory

What is the probability that a needle dropped at random on a set of points scattered on a line segment does not fall on any of them? We compute the exact scaling expression of this hole probability when the spacings between the points are independent identically distributed random variables with a power-law distribution of index less than unity, implying that the average spacing diverges. The theoretical framework for such a setting is renewal theory, to which the present study brings a new contribution. The question posed here is also related to the study of some correlation functions of simple models of statistical physics.

DESIGN AND PARAMETER OPTIMIZATION OF LAYERED FERTILIZATION OPENER FOR WHEAT, BASED ON EDEM

Applying different types of fertilizers to different depths of soil according to demand is advantageous in that it can optimize the distribution of nutrients in arable soil, adjust the nutrient supply of each growth stage of wheat, and increase grain yield. In the study, a layered fertilization opener that could realize the layered fertilization was developed. The interaction model between the opener, fertilizer and soil was established using EDEM simulation software. A response surface analysis was used to determine the optimal parameters of the opener. Specifically, the horizontal distance between the fertilizer drop openings was 140 mm, the machine speed was 1.05 m/s, and the angle of the opener was 37°. Furthermore, field experiments demonstrated that the average depth of upper layer was 8.39 cm, the average depth of middle layer was 16.465 cm, the average depth of lower layer was 24.025 cm, the average spacing of upper layer was 8.075 cm, and the average spacing of lower layer was 7.6 cm. The corresponding findings demonstrated that the layering effect of the opener met the requirements of the fertilization standard.

Comparison of quasi-biennial oscillations of stratospheric winds and atmospheric temperatures at different altitudes

During 1959-89, the 12-month running means of 50 hPa zonal winds, the average atmospheric temperatures in the northern and southern hemisphere at four altitude slabs (950 hPa, 850- 300 hPa, 300-100 hPa and 100-50 hPa), Pacific and Atlantic sea surface temperature (SST) and-30hPa temperatures at North Pole and average for (10°-90° N), all showed quasi-biennial oscillations (QBO). However, whereas the wind QBO had an average spacing of 29 months, only temperatures at 300-100 hPa and Atlantic SST had similar average spacing. Other temperatures as also SO index (represented by Tahiti minus Darwin atmospheric pressure) had larger average spacing. Spectral analysis showed that whereas wind QBO had only one prominent peak at T=2.33 years, other parameters had weak QBOs near T=2.5-2.6 years except Pacific SST and 30 hPa North Pole temperature which had small peaks near T=2.3 years. All the temperatures had prominent peaks in the 3-6 year region which matched with similar peaks in the SO index. There is some indication that stratospheric wind QBO had some relation with parameters at all altitudes in tropics and with North Pole, while ENSO had considerable influence at other latitudes/altitudes.

Effect of High Pressure and Temperature on the Evolution of Si Phase and Eutectic Spacing in Al-20Si Alloys

The microstructure of the Si phase in Al-20Si alloys solidified under high pressure was investigated. The results demonstrate that the morphology of Si phase transformed (bulk→short rod→long needle) with the increase of superheat temperature under high pressure. At a pressure of 3 GPa and a superheat temperature of 100 K, a microstructure with a uniform distribution of fine Si phases on the α-Al matrix was obtained in the Al-20Si alloy. In addition, a mathematical model was developed to analyze the spacing variation of the lamellar Al-Si eutectics under the effect of pressure. The lamellar Al-Si eutectics appeared at 2 GPa and superheat temperatures of 70–150 K, and at 3 GPa and superheat temperatures of 140–200 K. With the increase of pressure from 2 GPa to 3 GPa, the average spacing of lamellar Al-Si eutectics decreased from 1.2–1.6 μm to 0.9–1.1 μm. In binary alloys, the effect of pressure on the eutectic spacing is related to the volume change of the solute phase from liquid to solid. When the volume change of the solute phase from liquid to solid is negative, the lamellar eutectic spacing decreases with increasing pressure. When it is positive, the eutectic spacing increases with increasing pressure.

Study Effect the Shear Spacing and Width of Beam on Behavour of Reinforced Concrete Wide Beams

This paper presented an experimental study of the behaviour of wide reinforced concrete beams with different shear spacing and beam width. Eight specimens in two groups, the group one contains four specimens with the dimensions of (200x500x1600mm) and shear reinforcement spacing (d/2, 0.65d, 3/4d and 1.0d), the group two contains four specimens with the dimensions of (200x600x1600mm) and shear reinforcement spacing (d/2, 0.55d, 3/4d and 1.0d), Variables studied in this study shear reinforcement spacing and width of wide beam, the increasing of shear reinforcement spacing gives close results in RC wide beam, increased shear reinforcement spacing decreased the ultimate loud by 6.6% and when increasing width of beam the ultimate loud decreased by 9.5%, The ultimate deflection decreased by 16.5% and when increasing width of beam decreased by 7.2 %,The number of flexural cracks was equal in all beams, when increasing width of beam the number of flexural crack increased by 2 cracks, The average spacing between shear cracks decreased by 7%, when increasing width of beam average spacing between shear cracks decreased by 19%.

Refinement on the Solidification Structure of H13 tool steel under Multi-Rotational Speeds Super-Gravity Field

In this paper, the effect of multi-rotational speeds super-gravity field on the grain refinement and tensile properties of as-cast H13 steel were investigated systematically. The experimental results revealed that the as-cast grains of H13 steel can be significantly refined in multi-rotational speeds supergravity field. In conventional supergravity field, with the decrease of rotational radius, the secondary dendrite average spacing (SDAS) and the austenite grain average size (AGAS) increase, and the maximum values of SDAS and AGAS are 90 µm and 55 µm, respectively. while in multi-speeds supergravity fields, at the range of increasing rotational speeds, SDAS and AGAS decrease as the rotational radius decreases. In three-rotational speeds supergravity field, the maximum values of SDAS and AGAS are 80 µm and 50 µm. In five-rotational speeds supergravity field, the maximum values of SDAS and AGAS are reduced to 58 µm and 34 µm. Accordingly, both the tensile strength and the plasticity are enhanced with the increasing the number of rotational speeds in supergravity field, especially for the inner position of supergravity sample. The ultimate tensile strengths at outer, middle, and inner positions of H13 steel solidified in conventional supergravity field are 1445 MPa, 1378 MPa, and 1023 MPa, corresponding elongations of 2%, 1.5%, and 0.5%, while in the five-rotational speeds supergravity field, they are 1408 MPa, 1443 MPa, and 1453 MPa, corresponding elongations of 1.8%, 3.9%, and 2.2%. The mechanism for the grain refinement is that multi-speeds super-gravity can reduce the critical nucleation work of austenite, and the tangential force produced by changing the rotational speeds breaks dendrites at the solidification front, refining solidification structure.

Effect of Sanding Processes on the Surface Properties of Modified Poplar Coated by Primer Compared with Mahogany

The surface roughness, static and dynamic liquid wettability of modified poplar wood were measured by different surface treatment of brushing primer and sanding. With the increase of the number of grinding paper, the depth parameters Ra, Ry, Rz and Rp of surface roughness of modified poplar decreased, and the density parameter Sm (the average spacing of micro unevenness of contour) decreased at first and then increased. With the increase of number of the grinding paper, the contact angle of water and glycerol for modified poplar wood decreased at first and then increased. After the modified poplar wood was brushed with the primer and sanded with 240# sandpaper, the density parameter Sm was 0.307, the equilibrium contact angle of distilled water was 34.88, and the equilibrium contact angle of glycerin was 36.46, all of which were the lowest number. At this time, the surface roughness was improved, and the modified poplar has the good wettability that is greater than the mahogany wood wettability. Compared with mahogany, the rough depth parameters of the modified poplar are smaller to those of mahogany, but the Sm of modified poplar wood is greater than that of the mahogany. After the same surface pretreatment, the wetting speed of glycerol on the surface of mahogany is higher than that of the modified poplar.

Development and Evaluation of Inclined Plate Metering Mechanism for the Sowing of Maize (Zea mays L) Seed

Maize (Zea mays L) is the third most imperative food cash crop after wheat and rice in India. Inclined plate seed metering mechanism was developed and evaluated in the laboratory for singulation and uniform placement of maize seeds with three varieties (PMH-1, PIONEER-3396, PMH-10). Metering device was tested at three inclinations of 45°, 50° and 55° using three types of metering plates (P1, P2, P3) having 24 groove number cells. The average spacing between seeds at 3 km/h forward speed with metering plate P1, with angle of inclination 50° was 18.35 cm, 17.67 cm and 17.98 cm for PMH-1, PIONEER-3396 and PMH-10 seeds, respectively. The overall quality of feed index obtained with the parameters are 83.38%, 87.20% and 85.40% for PMH-1, PIONEER-3396 and PMH-10 seeds, respectively, which was higher than other parameters and seed rate of (6.70, 6.75 and 6.70) kg/acre for PMH-1, PIONEER-3396 and PMH-10 seeds, respectively.

Discerning the diets of sweep-feeding eurypterids: assessing the importance of prey size to survivorship across the Late Devonian mass extinction in a phylogenetic context

Eurypterids are generally considered to comprise a mixture of active nektonic to nektobenthic predators and benthic scavenger-predators exhibiting a mode of life similar to modern horseshoe crabs. However, two groups of benthic stylonurine eurypterids, the Stylonuroidea and Mycteropoidea, independently evolved modifications to the armature of their anterior appendages that have been considered adaptations toward a sweep-feeding life habit, and it has been suggested the evolution toward sweep-feeding may have permitted stylonurines to capture smaller prey species and may have been critical for the survival of mycteropoids during the Late Devonian mass extinction. There is a linear correlation between the average spacing of feeding structures and prey sizes among extant suspension feeders. Here, we extrapolate this relationship to sweep-feeding eurypterids in order to estimate the range of prey sizes that they could capture and examine prey size in a phylogenetic context to determine what role prey size played in determining survivorship during the Late Devonian. The mycteropoid Cyrtoctenus was the most specialized sweep-feeder, with comblike appendage armature capable of capturing mesoplankton out of suspension, while the majority of stylonurines possess armature corresponding to a prey size range of 1.6–52 mm, suggesting they were suited for capturing small benthic macroinvertebrates such as crustaceans, mollusks, and wormlike organisms. There is no clear phylogenetic signal to prey size distribution and no evolutionary trend toward decreasing prey sizes among Stylonurina. Rather than prey size, species survivorship during the Late Devonian was likely mediated by geographic distribution and ability to capitalize on the expanding freshwater benthos.

Деформация памяти формы и микрорельеф поверхности монокристаллов сплавов Ni-Fe-Ga-Co и Cu-Al-Ni

We present the results of experimental studies of the return of Ni–Fe–Ga–Co and Cu–Al–Ni single crystals to the initial form at the macro- and microlevels after their deformation by compression and subsequent restorative heating. It is found that the geometric dimensions of the sample are reproduced with high accuracy (up to 20 μm). The microrelief appearing on the initially polished surface during crystal compression (the arithmetic mean profile deviation R _ a ≈ 0.25–0.75 μm, the average spacing of local protrusions of the profile S ≈ 0.027–0.11 mm) is not removed by subsequent heating and remains with further multiple repetition of deformation–restoration cycles.