This work introduces a methodology for the statistical mechanical analysis of polymeric chains under tension controlled by optical or magnetic tweezers at thermal equilibrium with an embedding fluid medium. The response of single bonds between monomers or of entire groups of monomers to tension is governed by the activation of statistically interacting particles representing quanta of extension or contraction. This method of analysis is capable of describing thermal unbending of the freely-jointed or worm-like chain kind, linear or nonlinear contour elasticity, and structural transformations including effects of cooperativity. The versatility of this approach is demonstrated in an application to double-stranded DNA undergoing torsionally unconstrained stretching across three regimes of mechanical response including an overstretching transition. The three-regime forceextension characteristic, derived from a single free-energy expression, accurately matches empirical evidence. (c) J τ J J (b) (d) (a) FIG. 1: (Color online) Schematic representations for a chain of N = 7 monomers of (a) the reference state, (b) a state under tension with extension particles activated, (c) a state under tension and torque with twist-contraction particles activated, and (d) a state under tension with extension particles and contact particles activated.

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Composite materials have become a highly preferred technology nowadays in the industry with their advantages such as superior mechanical performance and weight loss for aerospace applications, especially due to the combination of different components and the formation of new products. In addition, with nanocomposites, this technology skips a step further and allows more effective products to be produced. Nanocomposites are produced using carbon allotropes such as graphene and carbon nanotubes, which have the title of being one of the strongest materials that have been the subject of academic studies in recent years.

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Objective: The ongoing COVID-19 pandemic, which was initially identified in December 2019 in the city of Wuhan in China, poses a major threat to the worldwide health care. By August 04, 2020, there were globally 6958481 deaths. 57651 of them come from Turkey. As a result, various governments and their respective populations have taken strong measures to control the spread of the pandemic. In this study, a model that is by construction able to describe both government actions and individual reactions in addition to the well known exponential spread is presented. Moreover, the influence of the weather is included. This approach demonstrates a quantitative method to track these dynamic influences. This makes it possible to numerically estimate the influence that various private or state measures which were put into effect due the purpose of containing the pandemic had at time t. This might serve governments across the world by allowing them to plan their actions based on quantitative data in order to minimize the social and economic consequences of their containment strategies. Methods: A compartmental model based on SEIR that includes the risk perception of the population by an additional differential equation and uses an implicit time-dependent transmission rate is constructed. Within this model, the transmission rate depends on temperature, population and government actions which in turn depend on time. The model was tested using different scenarios, with the different dynamic influences being mathematically switched on and off. In addition, the real data of infected coronavirus cases in Turkey were compared with the results of the model. Results: The mathematical study of the influence of the different parameters is presented through different scenarios. Remarkably, the last scenario is also an example of a theoretical mitigation strategy that shows its maximum in August 2020. In addition, the results of the model are compared with the real data from Turkey using conventional fitting that shows good agreement. Conclusions: Although most countries activated their pandemic plans, significant disruptions in health care systems occurred. The framework of this model seems to be valid for a numerical analysis of dynamic processes that occur during the COVID-19 outbreak due to weather and human reactions. As a result, the effects of the measures introduced could be better planned in advance by use of this model.