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Draw-down time for a stochastic process is the first passage time of a draw-down level that depends on the previous maximum of the process. In this paper we study the draw-down-related Parisian ruin problem for spectrally negative Lévy risk processes. Intuitively, a draw-down Parisian ruin occurs when the surplus process has continuously stayed below the dynamic draw-down level for a fixed amount of time. We introduce the draw-down Parisian ruin time and solve the corresponding two-sided exit problems via excursion theory. We also find an expression for the potential measure for the process killed at the draw-down Parisian time. As applications, we obtain new results for spectrally negative Lévy risk processes with dividend barrier and with Parisian ruin.

The present study outlines major concerns and potential environmental consequences of the proposed Pancheshwar high dam in Uttarakhand (Central Himalaya), India. We evaluate the risks associated with the project in the light of environmental impact observed for the Tehri project in the region and the geological understanding developed over the years. Three major factors and their likely impacts analysed relate to (i) sediment mobilization from glacial–paraglacial zones and unstable slopes, (ii) infrastructure development, and (iii) seismicity. We highlight the need to reassess geo-environmental implications of the project in the ecologically sensitive Kaliganga valley.

Climate change and the related increases in evapotranspiration threaten to make northern peatlands drier. The carbon sink function in peatlands is based on the delicate balance between the photosynthesis and decomposition. However, little is known about how existing and invading plant species will photosynthesize under drier conditions. The aim of this study is to quantify the long-term consequences of climate change-induced drying for peatland photosynthesis in the level of individual species and vegetation community. We measured the species-level photosynthesis of vascular plants and mosses characteristic for the three peatland types (rich fen, poor fen, bog) within a 16-year water level drawdown (WLD) experiment. Measurements were made in the laboratory from mesocosms collected from the field within the same day. We applied nonlinear mixed-effects models to test the impact of WLD on hyperbolic photosynthetic light response curve parameters. The model was then used to upscale photosynthesis to site-level. WLD impacted site-level photosynthesis through two mechanisms: species turnover and changes in species-level photosynthesis rate. The rich fen was the most sensitive and underwent major changes through both mechanisms; the vascular plant community shifted to woody plant dominance with higher rate of photosynthesis than the pre-treatment vegetation, and the rate of species-level photosynthesis increased significantly. The bog had a stable plant community with little change in photosynthesis, while the poor fen was an intermediate of the three peatland types. Our results suggest that vascular plants are the main drivers of site-level productivity changes, while mosses are more resistant to change. The change seems proportional to the availability of mineral nutrients, with higher nutrient status supporting vascular plant expansion.

For spectrally negative Lévy processes, we prove several fluctuation results involving a general draw-down time, which is a downward exit time from a dynamic level that depends on the running maximum of the process. In particular, we find expressions of the Laplace transforms for the two-sided exit problems involving the draw-down time. We also find the Laplace transforms for the hitting time and creeping time over the running-maximum related draw-down level, respectively, and obtain an expression for a draw-down associated potential measure. The results are expressed in terms of scale functions for the spectrally negative Lévy processes.

Rapid Draw-Down (RDD) in an earthfill dam has serious implications for dam safety regarding slope stability issues. The evaluation of reservoir draw-down impact on slope stability was carried out with the Limit Equilibrium Method (LEM) and stress-based Finite Element Method (FEM), using GeoStudio. The time-dependent Factor of Safety (FOS) and nonlinear behavior were evaluated considering 8 h of RDD. The resulting FOS values of 1.28 and 1.27 using LEM and stress-based FEM were classified as unsafe. The minimum allowable draw-down factor of safety value is 1.3, as per the guideline. The suggested two designs, with upstream horizontal filters and increased upstream dam permeability, provided an adequate FOS. However, the nonlinear analysis with coupled FEM has shown that the upstream slope is unstable in all three cases (i.e., as-built design, increased upstream dam shell permeability, and suggested application of horizontal filter layers) considering 8 h of RDD. Several gradual draw-down rates were also tested and it has been found that the FOS increases with decreased draw-down rates. FOS charts, pressure fluctuation, and flow measurements in the upstream dam shell have revealed that slope stability is highly influenced by pore water pressure and draw-down rate. The safe allowable draw-down rate of 20 h was identified, considering the as-built design of the dam.

Coupled FEM–DEM simulations enable the direct analysis of the load, the deformation and the stresses inside machine parts which interact with bulk materials. The analysis of large deformations of elastic parts is interesting as the deformation will significantly influence the bulk material behaviour. In this paper a bidirectional coupling method for the FEM software ANSYS ® Classic and the DEM software LIGGGHTS ® is presented. The coupling algorithm was verified and validated using a modified draw down test rig. The results from the experimental investigations and the FEM–DEM simulations are compared. A very good correlation between experiments and simulations could be found.

In this paper, we prove several results involving a general draw-down time from the running maximum for refracted spectrally negative Lévy processes. Using an approximation method, which is excursion theory at its heart, we find expressions for the Laplace transforms for the two-sided exit problems which are related to the draw-down time and an expression for the associated potential measure. The results are expressed in terms of scale functions.

Evaluation of pore water pressure in conditions of a rapid draw-down of a reservoir water level is one of the most vital issues in the stability embankment dams. The purpose of this study is to investigate seepage flow and slope stability during the rapid draw-down of the reservoir water level for the Doiraj embankment dam. This dam is located in Ilam province, Iran. The finite element method and limit equilibrium method approaches were used. Numerical simulations were carried out for transient unsaturated flows. It is shown that increasing the draw-down decreases the factor of safety. The minimum critical factor of safety decreases with increase in the reservoir water level draw-down rate. This study also reveals that the acceptable water level draw-down rate for this dam could be greater than the recommended water level draw-down rate of the United States Army Corps of Engineers. The critical factor of safety value for the reservoir water level draw-down of 1.20 m/day in the investigated embankment dam was 1.835, which is higher than the minimum standard value of 1.50; hence, the upstream slope is stable even for water level draw-down rates up to this value.

For application of polymer nanofibers (e.g., sensors, and scaffolds to study cell behavior) it is important to control the spatial orientation of the fibers. We compare the ability to align and pattern fibers using shear force fiber spinning, i.e. contacting a drop of polymer solution with a rotating collector to mechanically draw a fiber, with electrospinning onto a rotating drum. Using polystyrene as a model system, we observe that the fiber spacing using shear force fiber spinning was more uniform than electrospinning with the rotating drum with relative standard deviations of 18% and 39%, respectively. Importantly, the approaches are complementary as the fiber spacing achieved using electrospinning with the rotating drum was ~10 microns while fiber spacing achieved using shear force fiber spinning was ~250 microns. To expand to additional polymer systems, we use polymer entanglement and capillary number. Solution properties that favor large capillary numbers (>50) prevent droplet breakup to facilitate fiber formation. Draw-down ratio was useful for determining appropriate process conditions (flow rate, rotational speed of the collector) to achieve continuous formation of fibers. These rules of thumb for considering the polymer solution properties and process parameters are expected to expand use of this platform for creating hierarchical structures of multiple fiber layers for cell scaffolds and additional applications.

In this paper, we consider the problem of computing different types of finite time survival probabilities for a Markov-Modulated risk model and a Markov-Modulated risk model with reinsurance, both with varying premium rates. We use the multinomial approximation scheme to derive an efficient recursive algorithm to compute finite time survival probabilities and finite time draw-down survival probabilities. Numerical results show that by comparing with MCMC approximation, discretize approximation and diffusion approximation methods, the proposed scheme performs accurate results in all the considered cases and with better computation efficiency.