The current global production of plastics is over 300 million tons, 20% of which is produced in China. It has been estimated that about 90% of the discarded plastics are not recycled. China was the world's leading importer of waste plastics, while since January 1, 2018, China's import ban on waste plastics has been put into force, which has had a far-reaching effect on global plastic production and solid waste management. Southeast Asian countries like Malaysia have replaced China as the leading importer of plastic wastes. As the main exporter of waste plastics, EU has released strategy and initiative about plastics to restrict the use of micro plastics and single-use plastics. Meanwhile main European counties like UK, German and France have also taken own active measures to realize the control of packaging waste and non-recycled plastic and the recycling of plastic wastes in several years. As For the US, some areas such as Seattle and San Francisco have positively responded to the global trend of plastic ban. However, the controversy over "plastic restriction" in the whole state obstructed the promulgation and implementation of the national plastic ban. On the whole, major companies and more than 60 countries all over the world have introduced levies or bans to combat single-use plastic wastes. The Chinese government began to rectify the domestic waste plastics market and the Ministry of Industry and Information Technology of China has clarified the threshold of waste plastic treatment capacity for key enterprises. In addition to landfill, direct recovery and waste to energy processes are the main disposal methods of waste plastics. Thermoplastics like PE, PP and PET that are sorted out from the waste stream by citizens can be directly recycled to the primary material. The mixed waste plastics can be used as fuel in waste to energy plants, or as feedstock to pyrolysis plants that transform them to high value-added oil or chemical materials, which are more promising disposal methods of waste plastics.

Renewal processes with heavy-tailed power law distributed sojourn times are commonly encountered in physical modelling and so typical fluctuations of observables of interest have been investigated in detail. To describe rare events the rate function approach from large deviation theory does not hold and new tools must be considered. Here we investigate the large deviations of the number of renewals, the forward and backward recurrence time, the occupation time, and the time interval straddling the observation time. We show how non-normalized densities describe these rare fluctuations, and how moments of certain observables are obtained from these limiting laws. Numerical simulations illustrate our results showing the deviations from arcsine, Dynkin, Darling-Kac, Lévy and Lamperti laws. PACS numbers: 02. 50. -r, 05. 20. -y, 05. 40. -a

Recently observation of random walks in complex environments like the cell and other glassy systems revealed that the spreading of particles, at its tails, follows a spatial exponential decay instead of the canonical Gaussian. We use the widely applicable continuous time random walk model and obtain the large deviation description of the propagator. Under mild conditions that the microscopic jump lengths distribution is decaying exponentially or faster i.e., Lévy like power law distributed jump lengths are excluded, and that the distribution of the waiting times is analytical for short waiting times, the spreading of particles follows an exponential decay at large distances, with a logarithmic correction. Here we show how anti-bunching of jump events reduces the effect, while bunching and intermittency enhances it. We employ exact solutions of the continuous time random walk model to test the large deviation theory.

-The mean first exit (passage) time characterizes the average time of a stochastic process never leaving a fixed region in the state space, while the escape probability describes the likelihood of a transition from one region to another for a stochastic system driven by discontinuous (with jumps) Lévy motion. This paper discusses the two deterministic quantities, mean first exit time and escape probability, for the anomalous processes having the tempered Lévy stable waiting times with the tempering index µ > 0 and the stability index 0 < α ≤ 1; as for the distribution of jump lengths (in the CTRW framework) or the type of the noises driving the system (in the Langevin picture), two cases are considered, i.e., Gaussian white noise and non-Gaussian (tempered) β-stable (0 < β < 2) Lévy noise. Firstly, we derive the nonlocal elliptic partial differential equations (PDEs) governing the mean first exit time and escape probability. Based on the derived PDEs, it is observed that the mean first exit time depends strongly on the domain size and the values of α, β and µ; when µ is close to zero, the mean first exit time tends to ∞. In particular, we also find an interesting result that the escape probability of a particle with (tempered) power-law jumping length distribution has no relation with the distribution of waiting times for the model considered in this paper. For the solutions of the derived PDEs, the boundary layer phenomena are observed, which inspires the motivation for developing the boundary layer theory for nonlocal PDEs.Introduction. -Anomalous diffusion phenomena are widely found in natural world; the subdiffusion includes, e.g., motion of lipids on membranes, solute transport in porous media, translocation of polymers; and the superdiffuion is observed in, e.g., turbulent flow, optical materials, motion of predators, human travel, etc [1]. The types of diffusion are usually distinguished by the exponent of the evolution of the second order moment of a stochastic process x(t) with respect to the time t, i.e., x T (t)x(t) ∼ t γ ; when γ = 1, it is normal diffusion; γ < 1 corresponds to subdiffusion and γ > 1 superdiffusion.