Particular solutions play a critical role in solving inhomogeneous problems using boundary methods such as boundary element methods or boundary meshless methods. In this short article, we derive the ...closed-form particular solutions for the Laplace and biharmonic operators using the Gaussian radial basis function. The derived particular solutions are implemented numerically to solve boundary value problems using the method of particular solutions and the localized method of approximate particular solutions. Two examples in 2D and 3D are given to show the effectiveness of the derived particular solutions.
•The polynomial-basis-functions-based particular solutions are derived analytically.•The present method is meshless and free from annoying parameters.•This method is accurate and fast, which has huge ...potential for real engineering problems.
The traditional polynomial expansion method is deemed to be not suitable for solving two- and three-dimensional problems. The system matrix is usually singular and highly ill-conditioned due to large powers of polynomial basis functions. And the inverse of the coefficient matrix is not guaranteed for the evaluation of derivatives of polynomial basis functions with respect to the differential operator of governing equations. To avoid these troublesome issues, this paper presents an improved polynomial expansion method for the simulation of plate bending vibration problems. At first, the particular solutions using polynomial basis functions are derived analytically. Then these polynomial particular solutions are employed as basis functions instead of the original polynomial basis functions in the method of particular solutions for the approximated solutions. To alleviate the conditioning of the resultant matrix, we employ the multiple-scale method. Numerical experiments compared with analytical solutions, solutions by the Kansa’s method, and reference solutions in references confirm the efficiency and accuracy of the proposed method in the solution of Winkler and thin plate bending problems including irregular shapes.
A new conjugated polymer based on 5,7-bis(2-ethylhexyl)benzo1,2-c:4,5-c′dithiophene-4,8-dione, named as PBDTBDD, was designed, synthesized, and applied in polymer solar cells (PSCs). A power ...conversion efficiency (PCE) of 6.67% was obtained from the PBDTBDD/PC61BM-based PSC, which is a remarkable result for the PSCs using PC61BM as electron acceptor. The PBDTBDD/PC61BM-based device exhibits a narrow absorption band and excellent quantum efficiency in the range from 500 to 700 nm. Furthermore, PBDTBDD shows a strong aggregation effect in solution state, and the study indicates that although the temperature used in solution preparation has little influence on molecular orientation as well as crystallinity of the D/A blend, it plays an important role in forming proper domain size in the blend. This work provides a good example to reveal the correlation between the morphology of the blend films and the processing temperature of the solution preparation. Furthermore, the study in this work suggests an interesting and feasible approach to modulate domain size without changing crystallinity of the blend films in PSCs.
According to statistical data in Poland, sexual acts of minors account for about 3% of all criminal acts committed by minors and nearly 20% of all acts from the catalogue of crimes against sexual ...freedom and morality. The main objective of the study was to attempt to develop and present characteristics of minors who commit rape with particular cruelty. Taking into account the way the perpetrators act, the motivational background and the circumstances of the crime. In particular, attention was paid to specific individual and family characteristics. Because it is not clear whether juvenile sex offenders are different from non-sex offenders. The aim of this article is an attempt to capture individual, family and environmental differences. The study was also intended to provide information about who the victims are. The study was conducted on the basis of empirical material from court cases in which the basis of liability was Article 1974 of the Penal Code, and the perpetrators or accomplices of the acts were minors who at the time of the act were over 15 years of age but under 17 years of age. The research material consisted of court case files that had been finally completed, including forensic psychological opinions prepared by court experts. Cases from 2015-2020 were analysed. The obtained results allowed to capture some specific features of families in which minors were brought up and the characteristics of juvenile sex offenders themselves. This article raises the difficult issue of juvenile responsibility for sexual crimes, indicates areas in which it is necessary to regulate interactions and areas of possible preventive impacts.
In this paper, the method of particular solutions (MPS) using trigonometric functions as the basis functions is proposed to solve two-dimensional elliptic partial differential equations. The ...inhomogeneous term of the governing equation is approximated by Fourier series and the closed-form particular solutions of trigonometric functions are derived using the method of undetermined coefficients. Once the particular solutions for the trigonometric basis functions are derived, the standard MPS can be applied for solving partial differential equations. In comparing with the use of radial basis functions and polynomials in the MPS, our proposed approach provides another simple approach to effectively solving two-dimensional elliptic partial differential equations. Five numerical examples are provided in this paper to validate the merits of the proposed meshless method.
Fine particular matter (PM2.5) pollution still occurs frequently in China. Despite recognizing the importance of regional joint prevention and control (RJPC) for mitigating haze pollution, there is ...still a limited understanding of scheme design and effectiveness. In this study, with the Fenhe Plain in China serving as the case, the Integrated Source Apportionment Method (ISAM), incorporated into the Community Multiscale Air Quality Modeling System (CMAQ), was used to quantitively identify PM2.5 sources during a typical heavy pollution episode from Jan. 20th to 25th, 2021. Informed by source apportionment, we designed and assessed multiple RJPC scenarios for eliminating heavy pollution, yielding recommended RJPC schemes. Source apportionment results revealed a substantial increase in the contribution percentage of regions within a 350-km radius during the pollution episode compared to the non-polluted period. Sulfate was predominantly contributed from long-distance transport, whereas nitrate was chiefly contributed from closer regions. Ammonium exhibited higher local contributions than nitrate from the Fenhe Plain. Moreover, Taiyuan and Linfen were identified as PM2.5 exporters, whereas Sanmenxia, Jinzhong, and Luliang served as PM2.5 importers, and Yuncheng acted as a comprehensive city. The proposed specific RJPC schemes aimed at eliminating heavy pollution for the Fenhe Plain emphasized the importance of controlling emissions of particulate matter, ammonia, nitrogen oxides, and volatile organic compounds in areas within an approximate 350-km radius outside the Fenhe Plain, in addition to strengthening the local emission control. Nevertheless, only through the comprehensive and in-depth implementation of emission control measures across a larger area can PM2.5 compliance be achieved.
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•A framework for developing regional joint prevention and control (RJPC) schemes was presented.•Typical cities of PM2.5 export and import in the Fenhe Plain were identified.•Areas within an approximate 350-km radius notably contributed to PM2.5 and its components.•Specific RJPC schemes were proposed to eliminate heavy haze pollution episodes.
In this Perspective, we present a unique approach to the design and synthesis of giant molecules based on “nanoatoms” for engineering structures across multiple length scales and controlling their ...macroscopic properties. Herein, “nanoatoms” refer to shape-persistent molecular nanoparticles (MNPs) with precisely defined chemical structures and surface functionalities that can serve as elemental building blocks for the precision synthesis of giant molecules by methods such as sequential “click” approach. Typical “nanoatoms” include those MNPs based on fullerenes, polyhedral oligomeric silsesquioxanes, polyoxometalates, and folded globular proteins. The resulting giant molecules are precisely defined macromolecules. They include, but are not limited to, giant surfactants, giant shape amphiphiles, and giant polyhedra. Giant surfactants are polymer tail-tethered “nanoatoms” where the two components have drastic chemical differences to impart amphiphilicity. Giant shape amphiphiles not only are built up by covalently bonded MNPs of distinct shapes where the self-assembly is driven by chemical interactions but also are largely influenced by the packing constraints of each individual shape. Giant polyhedra are either made of a large MNP or by deliberately placing “nanoatoms” at the vertices of a polyhedron. In general, giant molecules capture the essential structural features of their small-molecule counterparts in many ways but possess much larger sizes. They are recognized in certain cases as size-amplified versions of those counterparts, and often, they bridge the gap between small molecules and traditional macromolecules. Highly diverse, thermodynamically stable and metastable hierarchal structures are commonly observed in the bulk, thin film, and solution states of these giant molecules. Controlled structural variations by precision synthesis further reveal a remarkable sensitivity of their self-assembled structures to the primary chemical structures. Unconventional nanostructures can be obtained in confined environments or through directed self-assembly. All the results demonstrate that MNPs are unique elements for macromolecular science, providing a versatile platform for engineering nanostructures that are not only scientifically intriguing but also technologically relevant.
The availability of the closed-form particular solution for a given differential equation based on a chosen basis function is crucial for solving partial differential equations using the method of ...particular solutions. In general, the derivation of such a closed-form particular solution is by no means trivial, particularly for higher order partial differential equations. In this paper we give a simple algebraic procedure to avoid the direct derivation of the closed-form particular solutions for fourth order partial differential equations. One numerical example is given to demonstrate the effectiveness of our proposed approach.
In recent years, localized methods are proven to be very effective for solving various types of problems in scientific computing. Many researchers have successfully implemented localized approaches ...to solve large-scale problems. Oscillatory radial basis functions collocation method, a global method, is a meshless numerical method in the literature. The novelty of this article is to address the computational efficiency issues of the oscillatory radial basis functions collocation method using a localized approach for solving elliptic partial differential equations in 2D. We carry out a number of experiments to validate our proposed numerical scheme. Numerical results clearly demonstrate that our scheme is highly accurate and computationally efficient.
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