DEM Simulations of Resistance of Particle to Intruders during Quasistatic Penetrations

Based on the discrete element method and hydrostatics theory,an improved Archimedes principle is proposed to study the rules pertaining to resistance changes during the penetration process of an intruder into the particulate materials.The results illustrate the fact that the lateral contribution to the resistance is very small,while the tangential force of the lateral resistance originates from friction effects.Conversely,the resistance of particulate materials on the intruder mainly occurs at the bottom part of the intruding object.Correspondingly,the factors that determine the resistance of the bottom part of the intruding object and the rules pertaining to resistance changes are analyzed.It is found that when the volume density and friction coefficient of the particles and the radius of the bottom surface of the cylindrical intruder are varied,the resistance–depth curve consists of a nonlinear segment and a linear region.The intersection of the two stages occurs at the same location h/˜R=0.15±0.055.The slope of the linear stage is determined by the friction coefficient of the particles.Accordingly,the relationship between the slope and the friction coefficient is quantified.Finally,it is shown that the slope is independent of the geometry of the intruder.

Density Measurements of Na_2WO_4-WO_3-ZnO Melts

Based on Archimedes principle, the densities of Na 2WO 4 WO 3 ZnO melts at a fixed mole ratio of 3.43 of Na 2WO 4 to ZnO were measured. The results indicated that there was a linear relationship between the densities and temperatures at a fixed composition. At a fixed temperature, the linear relationship between densities and compositions showed different slop within different composition regions. The reasons were explained in view of ionic composition changes.

Walking of spider on water surface studied from its leg shadows

Different from sculling forward of water striders with their hairy water-repellent legs, water spiders walked very quickly on water surfaces. By using a shadow method, the walking of water spiders had been studied. The three-dimensional trajectories and the supporting forces of water spider legs during walking forward were achieved. Results showed that the leg movement could be divided into three phases： slap, stroke, and retrieve. Employing an effective strategy to improving walking efficiency, the sculling legs supported most of its body weight while other legs were lifted to reduce the lateral water resistance, which was similar to the strategy of water striders. These findings could help guiding the design of water walking robots with high efficiency.

New Mechanism and Analytical Formula for Understanding the Gravity Constant <i>G</i>

The nature of gravitation and G is not well understood. A new gravitation mechanism is proposed that explains the origin and essence of the gravitational constant, G. Based on general relativity, the vacuum is considered to be a superfluid with measurable density. Rotating bodies drag vacuum and create a vortex with gradient pressure. The drag force of vacuum fluid flow in the arm of the vortex is calculated relative to the static vacuum and a value that is numerically equal to that of G is obtained. Using Archimedes’ principle, it is determined that G is the volume of vacuum displaced by a force equivalent to its weight which is equal to the drag force of the vacuum. It is concluded that the gravitational constant G expresses the force needed to displace a cubic metre of vacuum that weighs one kg in one second. Therefore, G is not a fundamental physical constant but rather is an expression of the resistance encountered by the gravitational force in the vacuum.

How did Archimedes discover the law of buoyancy by experiment？

After Archimedes and Vitruvius era, for more than 2000 years, it has been believed that the displaced water measurement of golden crown is impossible, and at his Eureka moment, Archimedes discovered the law of buoyancy （Proposition 7 of his principles） and proved the theft of a goldsmith by weighing the golden crown in water. A previous study showed that a small amount of displaced water was able to be measured with enough accuracy by the introduced method. Archimedes measured the weight of displaced water. He did not find the law of buoyancy but rather specific gravity of things at the moment. After which, Archimedes continued to measure the specific gravity of various solids and fluids. Through these measurements, he reached the discovery of the law of buoyancy directly by experiment. In this paper, the process to the discovery of Archimedes＇ principle （Proposition 5） is presented.