In this paper, we exploit the use of peridynamics theory for graphical animation of material deformation and fracture. We present a new meshless framework for elastoplastic constitutive modelling that contrasts with previous approaches in graphics. Our peridynamics‐based elastoplasticity model represents deformation behaviours of materials with high realism. We validate the model by varying the material properties and performing comparisons with finite element method (FEM) simulations. The integral‐based nature of peridynamics makes it trivial to model material discontinuities, which outweighs differential‐based methods in both accuracy and ease of implementation. We propose a simple strategy to model fracture in the setting of peridynamics discretization. We demonstrate that the fracture criterion combined with our elastoplasticity model could realistically produce ductile fracture as well as brittle fracture. Our work is the first application of peridynamics in graphics that could create a wide range of material phenomena including elasticity, plasticity, and fracture. The complete framework provides an attractive alternative to existing methods for producing modern visual effects.

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This paper is concerned with the periodic solutions for a class of Nicholson-type delay systems with nonlinear density-dependent mortality terms. By using coincidence degree theory, some criteria are obtained to guarantee the existence of positive periodic solutions of the model. Moreover, an example and a numerical simulation are given to illustrate our main results.

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Abstract. In this paper, we study entire solutions of some nonlinear difference equations and transcendental meromorphic solutons of some nonlinear differential equations. Our results generalize the results due to [11], [17].

High frequency ultrasonic radiation technology was developed as a novel and efficient means of regenerating spent biological activated carbon (BAC) used in drinking water treatment plants (DWTPs). The results of this study indicated that high frequency ultrasonic treatment could recover the spent BAC, to some extent, with the following optimal conditions: a frequency of 400 kHz, sonication power of 60 W, water temperature of 30 °C, and sonication time of 6 min. Under the above conditions, the iodine value increased from 300 mg/g to 409 mg/g, the volume of total pores and micropores increased from 0.2600 cm/g and 0.1779 cm/g to 0.3560 cm/g and 0.2662 cm/g, respectively; the specific surface area of micropores and the mean pore diameter expanded from 361.15 m/g and 2.0975 nm to 449.92 m/g and 2.1268 nm, respectively. The biological activity increased from 0.0297 mgO/gC·h to 0.0521 mgO/gC·h, while the biomass decreased from 203 nmolP/gC to 180 nmolP/gC. The results of high throughput 16S rRNA gene amplicon sequencing showed that microorganisms such as Clostridia and Nitrospira were markedly decreased due to high frequency ultrasound. The method used in this study caused the inhibition of certain carbon-attached microbials resulting in a negative effect on the removal rate of ammonia-N during the initial stage of the long-term reuse operation. The removal of UV254 and atrazine were restored from 8.1% and 55% to 21% and 76%, respectively.

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