Search Results (6)

We study a class of fractional stochastic differential equations (FSDEs) with coefficients that may not satisfy the linear growth condition and non-Lipschitz diffusion coefficient. Using the Lamperti transform, we obtain conditions for positivity of solutions of such equations. We show that the trajectories of the fractional CKLS model with $\beta >1$ are not necessarily positive. We obtain the almost sure convergence rate of the backward Euler approximation scheme for solutions of the considered SDEs. We also obtain a strongly consistent and asymptotically normal estimator of the Hurst index $H>1/2$ for positive solutions of FSDEs. Full article

In the present study we describe a straightforward and highly replicable methodology to assess the anthropogenic sediment budget within a coastal system (the Northern Tuscany littoral cell, Italy), specifically selected in a partially natural and partially highly urbanized coastal area, characterized by erosion and accretion processes. The anthropogenic sediment budget has been here calculated as an algebraic sum of sediment inputs, outputs and transfer (m³) within a 40 year time interval (1980–2020). Sediment management strongly influences the sediment budget and, even if its evaluation is crucial to assess the efficiency of a coastal management policy, it is often difficult to quantify the anthropogenic contribution to sedimentary processes. Different types of intervention are carried out by a variety of competent authorities over time (Municipalities, Marinas, Port Authorities), and the correct accountability of sediment budget is no longer known, or possible, for the scientific community. In the Northern Tuscany littoral cell, sedimentation is concentrated in a convergent zone and updrift of port structures, which have determined a series of actions, from offshore dumping and disposal into confined facilities (sediment output), to bypassing and redistribution interventions (sediment transfer); conversely, river mouths and coastal areas protected by groins and barriers are subjected to severe erosion and coastline retreat, resulting in many beach nourishments (sediment input). The majority of coastal protection interventions were carried out to redistribute sand from one site to another within the study area (2,949,800 m³), while the sediment input (1,011,000 m³) almost matched the sediment output (1,254,900 m³) in the considered time interval. A negative anthropogenic sediment budget (−243,900 m³) is here documented. Full article

The mathematical structure of some natural phenomena of nonlinear physical and engineering systems can be described by a combination of fuzzy differential equations that often behave in a way that cannot be fully understood. In this work, an accurate numeric-analytic algorithm is proposed, based upon the use of the residual power series, to investigate the fuzzy approximate solution for a nonlinear fuzzy Duffing oscillator, along with suitable uncertain guesses under strongly generalized differentiability. The proposed approach optimizes the approximate solution by minimizing a residual function to generate r-level representation with a rapidly convergent series solution. The influence, capacity, and feasibility of the method are verified by testing some applications. Level effects of the parameter r are given graphically and quantitatively, showing good agreement between the fuzzy approximate solutions of upper and lower bounds, that together form an almost symmetric triangular structure, that can be determined by central symmetry at r = 1 in a convex region. At this point, the fuzzy number is a convex fuzzy subset of the real line, with a normalized membership function. If this membership function is symmetric, the triangular fuzzy number is called the symmetric triangular fuzzy number. Symmetrical fuzzy estimates of solutions curves indicate a sense of harmony and compatibility around the parameter r = 1. The results are compared numerically with the crisp solutions and those obtained by other existing methods, which illustrate that the suggested method is a convenient and remarkably powerful tool in solving numerous issues arising in physics and engineering. Full article

The formations of micro-droplets are strongly influenced by the local geometries where they are generated. In this paper, through experimental research, we focus on the roles of microchannel tapering in the liquid paraffin/ethanol coaxial flows in their flow patterns, flow regimes, and droplet parameters, i.e., their sizes and forming frequencies. For validity, the non-tapering coaxial flows (the convergence angle $\alpha =0^{\circ }$ ) are investigated, the experimental methods and experimental data are examined and analyzed by contrasting the details with previous works, and consistent results are obtained. We consider a slightly tapering microchannel (the convergence angle $\alpha ={2.8}^{\circ }$ ) and by comparison, the experiments show that the tapering has significant effects on the flow patterns, droplet generation frequencies, and droplet sizes. The regimes of squeezing, dripping, jetting, tubing, and threading are differentiated to shrink toward the coordinate origin of the $C{a}_c$ – $W{e}_d$ space. The closer it is to the origin, the less variations will occur. For the adjacent regimes of the origin, i.e., dripping and squeezing, slight changes have occurred in both flow patterns, as well as the droplet characters. In the dripping and squeezing modes, the liquid droplets are generated near the orifice of the inner tube. Their forming positions (geometry) and flow conditions are almost the same. Therefore, the causes of minute changes in such regimes are physically understandable. While in the jetting regimes, the droplets shrink in size and their forming frequencies increase. The droplet sizes and the frequencies are both linearly related to those of the non-tapering cases with the corresponding relations derived. Furthermore, the threading and the tubing patterns almost did not emerged in the non-tapering data, as it seemed easier to form elongated jets, thinning or widening, in the tapered tubes. This can be explained by the stable analysis of the coaxial jets, which indicates that the reductions in the microchannel diameters can suppress the development of the interface disturbances. Full article

Iterative methods were employed to obtain solutions of linear and non-linear systems of equations, solutions of differential equations, and roots of equations. In this paper, it was proved that s-iteration with error and Picard–Mann iteration with error converge strongly to the unique fixed point of Lipschitzian strongly pseudo-contractive mapping. This convergence was almost $\mathrm{F}$ -stable and $\mathrm{F}$ -stable. Applications of these results have been given to the operator equations $\mathrm{F}x=\mathrm{f}$ and $x+\mathrm{F}x=\mathrm{f},$ where $\mathrm{F}$ is a strongly accretive and accretive mappings of $\mathrm{X}$ into itself. Full article