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We present a model to calculate the resonant energy absorption of a laser with finite number of pulses impinging on a doped porous dielectric slab. Analytical reflection R and transmission T coefficients are first derived as a function of 0 < α ≤ 1 to account for porosity with α = 1 denotes a perfect ideal slab, which are verified using an electromagnetic solver. Based on the Drude model with resonant line due to impurities, we calculate the resonant energy absorption as a function of doping concentration, quality factor of the resonant line, porosity, length of the slab, and laser pulse length. It is important to note that simulating the combined effects of these parameters is challenging using existing models. The energy absorption efficiency is maximized for a certain degree of doping concentration at a given pulse length and also for a certain pulse length at a given doping concentration. At small doping concentration, the absorption efficiency increases with smaller α (high porosity) and the trend is reversed at larger α (low porosity). Dimensionless parameters are constructed, allowing the calculated results to be applicable over a wide range of frequencies and pulse durations. Thus, this model serves as a useful tool to characterize the amount of energy absorption due to these combined effects, which are important for many applications in plasmonics, optoelectronics, high power microwaves breakdown, and organic materials. Some possible experiments are suggested for future verification of the model. [ABSTRACT FROM AUTHOR]

It is known that field emission from random nano-structured surfaces cannot be well characterized with the original field emission model known as the Fowler–Nordheim (FN) law or the Murphy–Good (MG) law. To account for the roughness effects, the traditional approach was to introduce the arbitrary field enhancement factor β in the FN and MG laws. In this paper, by treating the random roughness of field emitters as a fractional dimension object with 0 < α < 1 , fractional models of the FN and MG law, which were formulated recently may serve as alternate characterization tools. At α = 1 , the models will recover the traditional FN and MG laws valid for a perfect flat planar surface. These generalized fractional FN law ( FN α) and the fractional MG law ( MG α) will be used to characterize various field emission experiments by finding the best 0 < α < 1 values to account for the degree of the random roughness. The findings will be compared among the traditional and fractional emission models, where the best-fitting results will be shown for each case. It is found that the fractional field emission models provide more physical and appropriate field emission parameters, i.e., field enhancement factor and field emission area, in comparison with traditional field emission models. [ABSTRACT FROM AUTHOR]

In this study, analytical models for space charge limited current (SCLC) transport in a porous (or disordered) trap-limited dielectric cylindrical configuration are developed. The method used in this paper is first verified by reproducing the well-known analytical results for planar cases developed decades ago based on the traditional approach. By considering the porous solid as a fractional object characterized by a parameter α ≤ 1 , we formulate its fractional capacitance and determine the SCLC transport by using the transit time approach. At α = 1 , it will recover the well-known Mott–Gurney law and Mark–Helfrich law for trap-free and trap-limited cases, respectively. For cylindrical geometry, our findings show an analytical form that is not available from the traditional methods. We anticipate that the proposed analytical model will serve as a useful tool for characterizing the current–voltage measurements in SCLC transport in dielectric breakdown and organic electronics, where spatial porosity of the materials is inevitable. The introduced fractional parameter α extracted from such characterization can facilitate the quantitative determination of the relationship between spatial porosity and charge mobility. [ABSTRACT FROM AUTHOR]

This short report describes the phenomenon of space-charge-limited (SCL) current transport between ballistic and collision-dominated regimes for an inhomogeneous medium with a finite emission area. This intermediate regime can be considered as a weakly collisional regime where the collisional mean free path is comparable to the length of the medium. The SCL current density is calculated as a function of the degree of collision, inhomogeneity of the medium, and the geometrical properties of the emitting area. The inhomogeneity of the medium is characterized by a parameter of (0 < α ≤ 1) , where α = 1 denotes a perfect homogenous medium. The calculated SCL current density is enhanced by finite emission area effects by a factor of 1 + F × G , where F measures the mean position of the electrons in the medium, and G is a geometrical correction factor due to finite emission area. The enhancement is found to be higher in the collisional regime as compared to the ballistic regime. A higher inhomogeneity (with smaller α) also increases the enhancement. Smooth transition between the fully ballistic SCL transport (Child–Langmuir model) and the collision-dominated SCL transport (Mott–Gurney model) is demonstrated and verified, respectively, by the particle-in-cell code and the device simulator. This model is useful for the characterization of high-current SCL transport where the non-ideal conditions (such as inhomogenous medium and weakly collisional regime) cannot be described by the existing SCL models. [ABSTRACT FROM AUTHOR]

In this paper, we model a heterogeneous dielectric medium exhibiting fractal geometry or disordered random structures by applying non-integer dimensions to determine its capacitance between two parallel plates. The capacitance depends on the fractional dimensions of the fractal or disordered dielectric slab, which may be obtained from the theoretical fractal dimension or box-counting method. The findings are verified by CST Studio Suite (Electromagnetic field simulation software), experimental measurements, and the equivalent capacitance method. Five common types of fractals (Cantor bars/plates, Sierpinski carpet, Sierpinski triangle, Haferman carpet, and Menger sponge) and random structures are tested with good agreement. There is also an effective gain of capacitance in using less amount of dielectric materials, which may be useful in material-savings of dielectrics. This research shows a useful tool in modeling the capacitance of heterogeneous materials, where fractals and disordered structures may be commonly encountered in organic materials and any dielectrics where precision and fabrication are not perfect. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to assess unbiased options pricing predictions via ad hoc Black–Scholes model approaches. This paper investigates a number of technical issues when fitted values of implied volatility from linear regression are plugged into the Black–Scholes model, which leads to biased estimation. First, the study observes that the implied volatility linear regression can yield a negative outcome, which is meaningless. Therefore, a logarithmic transformation is applied to the linear function to ensure that the forecast is positive. Second, the retransformation from log to original metric to fitted values of implied volatility and the nonlinearity of Black–Scholes to implied volatility yields biased forecasts. A smearing technique has been applied in this study to correct this bias. Finally, the smearing estimation method also provides biased results if there is heteroscedasticity in the OLS estimation residuals. This study applies the weighted least square regression technique in order to avoid heteroscedasticity. According to the performance measures such as mean bias (MB), mean absolute error (MAE) and mean absolute relative error, the study concludes that the smearing method is the most effective to correct the bias in ad hoc Black–Scholes approaches as well as that an absolute smile approach is better than a relative smile approach without the smearing technique, but with smearing methods, relative smile performs superior to absolute. [ABSTRACT FROM AUTHOR]

Islamic banking came into existence four decades ago and now it is very popular all over the world due to its unique attraction and continuous growth. Muslims accept it because of its religious prospects and its growth trend which is increasing day by day. Islamic banking system increases rapidly not only in Muslim world but other Non-Muslim countries also adopting this system. It is getting more attention now-a-days. Islamic financing is different from Conventional financing in all respect. Ijarah is the one of highly popularize product innovation by Islamic banks. It is also known as AITAB (al Ijarah Thumma Al Bai'). Conventional Banks are using leasing concept which is opposite to the Ijarah financing. Pakistan is among the pioneer countries that embedded Islamic banking concept at early stages. In present scenario Pakistan come into the list of major player of Islamic banking industry. The aim of this study is to understand Islamic banking system and its challenges, and future growth. Further this study investigates the nature and difference of Ijarah financing compared to conventional banks and also sees its growth, challenges and future prospects. [ABSTRACT FROM AUTHOR]