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The source-network, the dynamic trophic level and the energy are incorporated into a "unified" model that describes both micro- and macroevolutions within a single theoretical framework. This model describes the microevolution in details by accounting for the birth, ageing, and natural death of individual organisms as prey-predator interactions on a hierarchical dynamic food web. It also provides a natural description of random mutations and speciation of species as well as their extinctions. The distribution of lifetimes of species follows an approximate power law only over a limited regime, and the distribution of trophic level follows an exponential attenuation.

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.

A solid–solid contact model of a rough surface with a single peak was established to explore the thermal effect of interfacial friction. From the perspective of friction force, temperature and energy, the law of the thermal effect was revealed. The results showed that the temperature of the asperities gradually increased during the shearing process, and a stress concentration formed in the shearing zone. After contact, the asperities had undergone unrecoverable plastic deformation. At each indentation depth, as the rotation angle of the crystal increased, the friction force, average temperature, and the sum of the changes in thermal kinetic and thermal potential energy first increased and then decreased; the trends of the three parameters changing with the rotation angle of the crystal were consistent. The average decreases in the friction force, average temperature, and the sum of the changes in thermal kinetic and thermal potential energy were 52.47%, 30.91% and 56.75%, respectively, for a crystal structure with a rotation angle of 45^∘ compared to a crystal structure with a rotation angle of 0^∘. The methods used in this study provide a reference for the design of frictional pairs and the reduction of the thermal effect of interfacial friction.

In this paper, we introduce fractal interpolation functions (FIFs) and linear FIFs on a post critically finite (p.c.f. for short) self-similar set K. We present a sufficient condition such that linear FIFs have finite energy and prove that the solution of Dirichlet problem -Δ_μ u = f,u|_∂K = 0 is a linear FIF on K if f is a linear FIF.

Noise plays a major role in the behavior of various physical and biological systems, its effects being increasingly pronounced with decrease in system size. While it is jeopardizing the future development of several nanotechnologies, such as magnetic data storage, noise can also play a constructive role in many nonlinear systems, activating a resonance response. In this paper, it is proven that various hysteretic systems can exhibit such coherent behavior — a phenomenon that is generally known as coherence resonance when is solely induced by noise, and stochastic resonance when an external oscillatory signal is present. The quantity used to characterize the regularity of the stochastic output is the power spectrum, which displays a maximum at the resonance frequency. The calculation of the spectral densities for the outputs of hysteretic systems is performed in the framework of stochastic processes defined on graphs. The case of hysteretic systems described by rectangular loops is discussed and analytical expressions for the output power spectra are derived. These theoretical results suggest that hysteretic systems can be used by nanotechnology for concentrating the energy of a flat, noisy input into a short bandwidth frequency region.

In this paper, a new method for global interconnects optimization in nanoscale VLSI circuits using unequal repeater (buffer) partitioning technique is presented. The optimization is performed with the energy-delay product minimization at 65, 90, and 130 nm technology nodes and various loads, using the genetic algorithm (GA) of MATLAB. The results show more improvements of the total propagation delay with respect to the traditional equal buffer partitioning technique. This improvement is obvious for 90 and 130 nm, and with increasing capacitive load, the improvement will be achieved for 65 nm.

Regardless of the state of matter, such as solids, liquids, and gases, the smaller the matter size from bulk to nano-scale, especially in the quantum region, the more rapid is the energy increase. To this end, this study introduces the concept of a group system, in which atoms behave as one, and this system is reinterpreted as that comprising temperature–entropy (TS) energy in thermodynamic data. Based on this concept, water was passed through various mesh-like dissolved tubes, where the size and energy of the water group system were observed to change. Thereafter, as the scale and number of the meshes increased, the ozone, chlorine, and oxygen constituents, which are closely related to sterilization and washing, are generated, changing the basic water composition. Thus, this nano-size impact is not limited to solids and could facilitate in revolutionizing the future applications in fluids.