Narrow Results

The rise of empires can be elucidated by treating them as living organisms, and the celebrated Verhulst or Lotka–Volterra dynamics can be used to understand the growth mechanisms of empires. The fast growth can be expressed by an exponential function as in the case of Macedonian empire of the Alexander the Great whereas a sigmoidal growth can be expressed by power-law equation as in the case of Roman and Ottoman empires. The superpowers Russia and the USA follow somehow different mechanisms, Russia displays two different exponential growth behaviors whereas the USA follows two different power-law behaviors. They did not disturb and mobilize their social capacity much during the course of their rise. The decline and the collapse of an empire occur through a kind of fragmentation process, and the consequently formed small states become rather free in their behavior. The lands of the new states formed exhibit a hierarchical pattern, and the number of the states having an area smaller than the largest one can be given either by an exponential or power-law function. The exponential distribution pattern occurs when the states are quite free in their pursuits, but the power-law behavior occurs when they are under the pressure of an empire or a strong state in the region. The geological and geographical conditions also affect whether there occurs exponential or power-law behavior. The new unions formed such as the European Union and the Shanghai Cooperation increase the power-law exponent implying that they increase the stress in the international affairs. The viscoelastic behavior of the empires can be found from the scattering diagrams, and the storage $(G^{\prime })$and loss modulus $(G^{\prime \prime })$, and the associated work-like and heat-like terms can be determined in the sense of thermodynamics. The $G^{\prime }$ of Ottomans was larger than that of Romans implying that they confronted severe resistance during their expansion. The $G^{\prime }$ of Russia is also larger than that of the USA; in fact the USA did not face severe resistance as they had an overwhelming superiority over native Americans. The $G^{\prime }>G^{\prime \prime }$ indicates solidity in the social structure and Romans, Ottomans, and Russians all have $G^{\prime }$ larger than $G^{\prime \prime }$. The $G^{\prime }$ is slightly larger than $G^{\prime \prime }$ for the USA indicating that they have had a very flexible social structure. By the same token the ratio of the work-like term to the internal energy is larger for Ottomans than that of Romans, and larger for the USA than that of Russia. That means the fraction of the total energy allocated to improve the social capacity is larger for Romans than that of Ottomans, and is larger for Russians than that of the USA.

Rheological properties of Cholesteryl n-valerate, Cholesteryl decanoate and Cholesteryl myristate which are esters of cholesterol have been studied. Phase transition temperatures and rheological parameters such as viscosity, elastic modulus G${}^{\prime }$, loss modulus G${}^{″}$ as functions of temperature, shear rate and time are investigated. In frequency sweep test, a higher transition crossover region has occurred for Cholesteryl myristate, whereas for Cholesteryl n-valerate a frequency-independent plateau prevailed for both the moduli. The occurrence of blue phase in Cholesteryl decanoate during temperature sweep measurements is an indication for the rheological support. The results for steady state have informed that cholesteric esters are having non-Newtonian flow behavior in their respective cholesteric phases. The power-law model has explained well the shear rate dependence of shear stress. A few practical applications of these esters as lubricant additives are discussed, too.

The mechanical properties of eggshell membrane (ESM) are comparable to those of human patellar tendon or skin. This paper, based on static and dynamic nanoindentation technique, studied the time-dependent behavior, i.e., creep and relaxation of the ESM. The effect of loading level, loading rate and holding time on viscoelastic behavior were discussed by using the static measurement method of nanoindentation. The storage modulus, loss modulus and loss factor were obtained as a function of frequency. It was found that the outer membrane (OM) exhibits more apparent relaxation properties and stronger capacity to resist creep deformation than that of the inner membrane (IM). In addition, the loss factor of the IM is larger than that of the OM which caused a larger viscous damping of IM. This work can contribute to the bioinspired applications of ESM.