A theoretical exploration of the effect of fluorine and cyano substitutions in diketopyrrolopyrrole-based polymer donor for organic solar cells

A series of polymer donor materials 1-5 based on diketopyrrolopyrrole and thiophene unit which have been widely used in organic solar cells (OSCs) were investigated based on quantum chemical calculations. The effect of fluorine and cyano substitutions in polymer donor materials was focused on. Based on the investigation on electronic structures and optical properties of the reported molecules 1 and 2 and the analysis on some parameters relevant to charge dissociation ability at donor/acceptor interface constituted by 1 and 2 with PC₆₁BM such as intermolecular charge transfer and recombination, driving force and Coulombic bound energy, we explained why fluorine substitution can improve OPV efficiency through strengthening eletron-withdrawing ability from a theoretical perspective. Then we designed cyano-substituted polymers 3-5 with the aim of obtaining better photovoltaic donor materials. The results reveal that our attempt to design donor materials which can balance large open-circuit voltage (V_oc) and high short-circuit current (J_sc) in OSCs has worked out. It is worth noting that the substitutions of fluorine and cyano groups synergistically reduce energy gap and HOMO energy level of polymers 3 and 4. Moreover, 3/PC₆₁BM and 4/PC₆₁BM heterojunctions show over 10⁷ and 10⁴ times higher than 1/PC₆₁BM on the ratios of intermolecular charge transfer and recombination rates (k_inter-CT/k_inter-CR). Thus, our work here may provide an efficient strategy to design promising donor materials in OPVs and we hope it could be useful in the future experimental synthesis.     

Numerical study on short-circuit current of single layer organic solar cells with Schottkey contacts

The influence of the cathode work function,carriers mobilities and temperature on the short-circuit current of single layer organic solar cells with Schottkey contacts was numerically studied,and the quantitative dependences of the short-circuit current on these quantities were obtained.The results provide the theoretical foundation for experimental study of single layer organic solar cells with Schottkey contacts.     

Analytical and numerical study of the effects of an elastically-linked body on sloshing

In order to investigate the effects of an elastically-linked moving body on liquid sloshing inside a tank, an analytical formulation and a numerical approach were proposed to assess hydrodynamic loads in a partially filled rectangular tank with a body connected to the tank by springs. The analytical approach was developed based on the potential theory to calculate fluid velocity field, and the dynamics of the liquid sloshing coupled to the moving body are described as a mechanical system with two degrees of freedom. The coupling between the fluid and the moving body is given by a damping force calculated based on the body geometry and the fluid velocity field. The proposed numerical approach is based on the Moving Particle Semi-implicit (MPS) method, which is a Lagrangian particle-based method and very effective to model nonlinear hydrodynamics due to fluid–structure interaction. In the numerical approach, the rigid body is modeled as a cluster of particles and the motions are calculated considering its mass, moment of inertia, hydrodynamic loads and springs restoring forces. The elastic link between the body and tank is modeled by applying Hooke’s law. Simple cases of floating body motion were used to validate the numerical method. Finally, analytical and numerical results were compared. Despite its simplicity, the analytical approach proposed in the present work is an efficient approach to provide qualitative understanding and a first estimate of the moving body effects on the sloshing inside the tank. On the other hand, the numerical approach can provide more detailed information about the coupling phenomena, and it is an effective mean for the assessment of the reduction of the sloshing loads due to the moving body with elastic link. Finally, the effectiveness of the concept as a sloshing suppressing device is also investigated.     

Optimal shape for optical absorption in organic thin film solar cells

The power conversion efficiency of organic solar cells can be increased by using light trapping geometries, which enhance the light absorption. In this paper, we analyze the optical performance of organic thin film solar cells using the finite element method solving the Maxwell equations. Shape optimization is then performed with the goal of maximizing the light absorption in the active layer, while keeping its thickness low. The optimization algorithm is based on the gradient of the objective function, where sensitivity is obtained from the adjoint approach. To avoid irregular shapes in the optimized structures, two different shape representation techniques, finite element node based curve representation in conjunction with the Helmholtz filter and B-spline curve representation with varying number of control points are used. Both are demonstrated being effective in smoothing the design shapes. Periodic grating structures are observed in the optimized shapes and significant increase in light absorption is achieved in the active layer with low thickness.     

Analytical resolution and numerical identification of fuzzyrelational systems

Since Sanchez's seminal paper on fuzzy relational equations, both their theories and applications have been continuously exploited by researchers. However, the solvable conditions of a system of fuzzy relational equations, also known as a fuzzy relational system (FRS), are still poorly established and their relationship with the methods for obtaining approximate solutions are unclear. When the FRS is adopted to model a fuzzy system, most of the existing identification algorithms focus on parameter estimation and less on the structure identification. In this paper, these two issues are addressed. New theoretical understandings on solving a system of fuzzy relational equations exactly and approximately are presented and their implications on the use of FRS to encode fuzzy rulebases are highlighted. Based upon the guided evolutionary simulated annealing (GESA) algorithm, an evolutionary identification formulation called EVIDENT capable for both parameter and structure identifications in fuzzy system models is proposed. As demonstrated by the simulation results, the new algorithm not only is effective in determining the structure of the systems, but also identifies a better parametric solution, as compared with that of the existing FRS identification algorithms.     

Analytical and numerical modeling of squeeze-film damping in perforated microstructures

The literature includes a variety of analytical and semi-analytical models to describe squeeze-film damping in MEMS perforated structures. Even if many of them have been validated by means of numerical simulations, nobody seems to have discussed about the accuracy of numerical approaches in this field. In the present paper, we apply both the main analytical models and a commercial finite element software, COMSOL Multiphysics, to solve a good number of squeeze-film problems. They refer to some cases, which were experimentally investigated during the past by different authors. The tested structures are rigid rectangular plates fabricated with different material, different perforation ratio (i.e., the ratio of the hole side to the holes pitch) and different number of perforations. We compare both the analytical and the numerical results with the available experimental data, in order to have an overview about their effectiveness. Numerical simulations offer in all the considered cases valuable agreement with experiments.     

Analytical and numerical results onM-variable generalized Bessel functions

Recently, some multivariable special functions have been obtained by generalizing functions of Bessel type. Here, we continue the treatment of these functions starting fromJ _n (x, y; i), which is of noticeable practical interest. Finally, we consider the cases of functionsJ _n(x₁, x₂,..., x_M) and the related modified version,I _n(x₁, x₂,..., x_M), with two significant physical applications. Calculations of multivariable generalized Bessel functions are discussed and numerical results are given forJ _n(x₁,x₂;i), withn=0, 1, in a region of interest.     

Analytical and numerical simulation of satellite image from space

In this paper, an analytical and numerical formulation for observed satellite radiances from space is provided, allowing for the radiation effect due to the adjacent rugged terrain. Up to now the atmospheric effect on the satellite images has been dealt with in the case of flat terrain. In this present paper, an allowance for the multiple reflection of light by the adjacent mountainous terrain has been taken into account approximately using the mean background albedo. Then, the validity of the numerical approximate solution is discussed for several cases of typical surface reflection examples, with respect to the atmospheric and topographic correction problem.     

Analytical and numerical description for isothermal gas flows in microchannels

Analytical solutions for the pressure and the velocity profiles in a microchannel are derived from the quasi gasdynamic equations (QGD). An expansion method according to a small geometric parameter ɛ is undertaken to obtain the isothermal flow parameters. The deduced expression of the mass flow rate is similar to the analytical expression obtained from the Navier-Stokes equations with a second order slip boundary condition and gives results in agreement with the measurements. The analytical expression of the pressure predicts accurately the measured pressure distribution. The effects of the rarefaction and of the compressibility on pressure distributions are discussed. The numerical calculations based on the full system of the QGD equations were carried out for different sizes of the microchannels and for different gases. The numerical results confirm the validity of the analytical approach.     

Analytical, numerical and experimental investigations of mixing fluids in microchannel

This work presents theoretical analysis, numerical simulation, fabrication and test of a micromixer chip for mixing fluids in microchannel. A three-dimensional analytical model is developed using a different mathematical approach to study passive laminar mixing phenomena and predict concentration distribution in a microchannel. The analytical model is validated by comparing with experimental and simulation results. The process of mixing fluids in a microchannel is simulated by solving the continuity, momentum and mass diffusion equations. The simulation results are validated and then parametric studies are performed to investigate the effects of channel aspect ratio, Reynolds number and diffusion coefficient on the mixing performance. The micromixer chip is fabricated with patterned SU-8 photoresist as the microchannel layer on a PMMA substrate using a combination of photolithography and micro-milling. Experiments are performed with different mixing fluids and the results were compared with that obtained from the theoretical model and simulation results.     

Computational study of diketopyrrolopyrrole-based organic dyes for dye sensitized solar cell applications

Four diketopyrrolopyrrole (DPP)-based organic dyes utilizing the donor–π-acceptor motif were investigated by density functional theory (DFT) and time-dependent DFT (TDDFT) approaches. The four dyes were composed of different donor groups, i.e. indoline, carbazole, triphenylamine, and coumarin. We investigated the effects of the DPP unit and different donors on the spectra and electrochemical properties of the dyes, respectively. In comparison with the model dye which adopts a phenylene unit as the π-spacer, the DPP dyes all display remarkably enhanced spectral responses in the visible region of the solar spectrum. The key to this increase was the incorporation of electron-deficient DPP moieties to the molecular core, which significantly lowers LUMO levels and therefore reduces the band gap. The dye/(TiO₂)₄₆ anatase nanoparticle systems were also simulated to show the electronic structures at the interface. We studied some key properties including absorption spectra, light-harvesting efficiency, molecular orbital distributions, and injection time of electrons from the excited state of dye to the conduction band of TiO_2. The dye DPP-I with indoline moiety as the electron donor demonstrates desirable energetic, electronic, and spectroscopic parameters for dye sensitized solar cells (DSSCs) applications. Our theoretical study is expected to provide valuable insights into the molecular design of novel DPP-based organic dyes for the optimizations of DSSCs.     

Analytical and numerical comparisons of biogeography-based optimization and genetic algorithms

We show that biogeography-based optimization (BBO) is a generalization of a genetic algorithm with global uniform recombination (GA/GUR). Based on the common features of BBO and GA/GUR, we use a previously-derived BBO Markov model to obtain a GA/GUR Markov model. One BBO characteristic which makes it distinctive from GA/GUR is its migration mechanism, which affects selection pressure (i.e., the probability of retaining certain features in the population from one generation to the next). We compare the BBO and GA/GUR algorithms using results from analytical Markov models and continuous optimization benchmark problems. We show that the unique selection pressure provided by BBO generally results in better optimization results for a set of standard benchmark problems. We also present comparisons between BBO and GA/GUR for combinatorial optimization problems, include the traveling salesman, the graph coloring, and the bin packing problems.     

Analytical and numerical solutions for a reliability-based benchmark example

The aim of this elementary reliability-based truss topology example is to serve as a benchmark for checking on the validity, accuracy and convergence of FE-based numerical topology optimization methods. The above problem has been solved analytically by using an extension of the optimal layout theory (Prager and Rozvany) and the solution has been verified numerically by a first order reliability approach (FORM) combined with a material distribution method (SIMP).     

有机半导体太阳能传感器技术研究进展

本文研究了有机半导体太阳能传感器材料和应用进展,包括有机半导体材料和太阳能传感器模型,高品质有机光导体的设计、合成和提纯,有机半导体太阳能传感器的制造和试验等。     

Analytical investigation and numerical verification of Casimir effect on electrostatic nano-cantilevers

In this paper, the two-point boundary value problem (BVP) of the nano-cantilever deflection subjected to Casimir and electrostatic forces is investigated using analytical and numerical methods to obtain the instability point of the nano-beam. In the analytical treatment of the BVP, the nonlinear differential equation of the model is transformed into the integral form by using the Green’s function of the cantilever beam. Then, closed-form solutions are obtained by assuming an appropriate shape function for the beam deflection to evaluate the integrals. The pull-in parameters of the beam are computed under the combined effects of electrostatic and Casimir forces. Electrostatic microactuators and freestanding nanoactuators are considered as special cases of our study. The detachment length and the minimum initial gap of freestanding nanocantilevers, which are the basic design parameters for NEMS switches, are determined. The results of the analytical study are verified by numerical solution of the BVP. The centerline of the beam under the effect of electrostatic and Casimir forces at small deflections and at the point of instability is obtained numerically to test the validity of the shape function assumed for the beam deflection in the analytical investigation. Finally, the large deformation theory is applied in numerical simulations to study the effect of the finite kinematics on the pull-in parameters of nano-canilevers.     

Effects of engine thermal transients on the energy management of series hybrid solar vehicles

The paper focuses on investigating thermal-transients effects, associated to intermittent use of internal combustion engine (ICE), on fuel economy and hydrocarbon (HC) emissions of series hybrid solar vehicles (HSVs). An offline, non-linear constrained optimization is set-up to individuate the ICE power trajectory that simultaneously minimizes fuel consumption, suitably operates the battery and fully exploits daily solar contribution. The results highlight the importance of including thermal transients in HSV energy management. The combined effects of engine, generator and battery losses, along with cranking energy and thermal transients, produce non-trivial solutions for the engine/generator group, which should not necessarily operate at its maximum efficiency.     

Analytical and numerical evaluation of the suppressed fuzzy c-means algorithm: a study on the competition in c-means clustering models

Suppressed fuzzy c-means (s-FCM) clustering was introduced in Fan et al. (Pattern Recogn Lett 24:1607–1612, 2003) with the intention of combining the higher speed of hard c-means (HCM) clustering with the better classification properties of fuzzy c-means (FCM) algorithm. The authors modified the FCM iteration to create a competition among clusters: lower degrees of memberships were diminished according to a previously set suppression rate, while the largest fuzzy membership grew by swallowing all the suppressed parts of the small ones. Suppressing the FCM algorithm was found successful in the terms of accuracy and working time, but the authors failed to answer a series of important questions. In this paper, we clarify the view upon the optimality and the competitive behavior of s-FCM via analytical computations and numerical analysis. A quasi competitive learning rate (QLR) is introduced first, in order to quantify the effect of suppression. As the investigation of s-FCM’s optimality did not provide a precise result, an alternative, optimally suppressed FCM (Os-FCM) algorithm is proposed as a hybridization of FCM and HCM. Both the suppressed and optimally suppressed FCM algorithms underwent the same analytical and numerical evaluations, their properties were analyzed using the QLR. We found the newly introduced Os-FCM algorithm quicker than s-FCM at any nontrivial suppression level. Os-FCM should also be favored because of its guaranteed optimality.     

Extending donor size in D-A-π-A organic dye for dye sensitized solar cells: Anti-aggregation and improving electron injection

We have theoretically designed two D-A-π-A dyes 3 and 4 based on the efficient references 1 and 2 by introducing an extra electron donor unit (D2). Via calculating the electronic structures of isolated dyes, we obtain that dyes 3 and 4 possess stronger light-harvesting efficiency imparted by the fluorescence energy transfer of D2 part, maintain comparable lifetime of excited states, and shorten the electron injection time significantly with regard to 1 and 2. Meanwhile, dye 3 positively shifts the edge of virtual states of TiO₂ in a larger extent compared to its counterparts. Then after considering the alignment morphology of multiple dyes adsorbed on TiO₂ surface, we find that dyes 3 and 4 manifest the capability of anti-aggregation obviously, which is evidenced by the smaller quantity of intermolecular electronic coupling compared to that of dyes 1 and 2, definitively illustrating the prominent performance of novel dyes with the bulky D2 moiety. Finally, dye 3 is screened out as the potential candidate for future application.     

A numerical study of compactons

The Korteweg–de Vries equation has been generalized by Rosenau and Hyman [Compactons: Solitons with finite wavelength, Phys. Rev. Lett. 70(5) (1993) 564] to a class of partial differential equations that has soliton solutions with compact support (compactons). Compactons are solitary waves with the remarkable soliton property that after colliding with other compactons, they re-emerge with the same coherent shape [Rosenau and Hyman, Compactons: Solitons with finite wave length, Phys. Rev. Lett. 70(5) (1993) 564]. In this paper finite difference and finite element methods have been developed to study these types of equations. The analytical solutions and conserved quantities are used to assess the accuracy of these methods. A single compacton as well as the interaction of compactons have been studied. The numerical results have shown that these compactons exhibit true soliton behavior.