Self-buckling is an interesting phenomenon that is easily found around us, either in nature or in objects made by human. Palm fronds which initially directed upward when they were short and turned into bending after appreciably longer is an example of the self-buckling phenomenon. We report here that the self-buckling of columns can be treated as a process of second-order phase transition by considering the straight column as "disorder state", the bending column as "order state", and the temperature as the inverse of column length. The "critical temperature" corresponds to the inverse of critical length for buckling, 1/L cr , and the deviation angle made by column free end relative to vertical direction satisfies a scaling relationship with a scaling power of 0.485. Changing of the column geometry from the vertically upward to the bending state can be considered as a transition from disorder state to order state.
We propose a novel method for estimating the elastic modulus of several materials by processing the bending image of cantilever material sheets. The calculated results (tested for five samples) were consistent with data obtained by direct measurement using a tensile strength device. By placing the cantilever sheets in an environment inside of which the temperature could be controlled, we were able to obtain the temperature dependence of elastic modulus. We identified a drastic drop of elastic modulus at a certain temperature and assumed this temperature corresponds to glass transition temperature. We also introduced an equation for describing the elastic modulus around that critical temperature and were able to estimate the glass transition temperature for all tested polymer materials. Surprisingly, the estimated glass transition temperatures conform to data obtained by direct measurement using a DTA device. Since the elastic modulus changes suddenly around the glass transition temperature, the proposed method might be more accurate than measurement using a DTA device where the glass transition temperature corresponds to the location of a weak peak at the DTA curve. This is the first attempt for estimating the glass transition temperature of polymer based on bending of cantilever slender beam, and seems to be the simplest method. The method is very potential for developing new equipment for determining the glass transition temperature of polymeric materials.
ABTRACTWe demonstrated the stability of tunnels made of granular matters is strongly dependent on the grain size, tunnel diameter, and water content in the granules. Larger tunnel radius, larger grain size, and too much water content tend to destabilize the tunnel. We also develop a model to describe such findings. We indentified a phase diagram of stability which greatly controlled by granular bond order. For granular bond order of larger than unity, we can alwaysmade a stable tunnel. However, for granular bond order of less than unity, we obtain a general expression for maximum tunnel thickness that can be made. To best of our knowledge, this is the first exploration regarding the granular tunnel stability.
An investigation of how coconut palm tree withstands gale force winds has been performed. When observed carefully, the motion of the stalks and leaves affected the wind resistance. The stalks and leaves move randomly when the wind blows continously. Although this is such an interesting phenomenon, there is still no report on the physical modelling. This paper proposes a simple mathematical model to analyze the phenomenon. A simple tool was also designed to retrieve data using Video Tracker. The experiments were conducted on several types of springs. The model showed that the theoretical prediction accurately explained the phenomenon.
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