We apply the alternating direction method of multipliers (ADMM) optimization algorithm to implicit time integration of elastic bodies, and show that the resulting method closely relates to the recently proposed projective dynamics algorithm. However, as ADMM is a general purpose optimization algorithm applicable to a broad range of objective functions, it permits the use of nonlinear constitutive models and hard constraints while retaining the speed, parallelizability, and robustness of projective dynamics. We further extend the algorithm to improve the handling of dynamically changing constraints such as sliding and contact, while maintaining the benefits of a constant, prefactored system matrix. We demonstrate the benefits of our algorithm on several examples that include cloth, collisions, and volumetric deformable bodies with nonlinear elasticity and skin sliding effects.

The Hirota-Satsuma-Ito equation in (2+1)-dimensions passes the three-soliton test. This paper aims to generalize this equation to a new one which still has abundant interesting solution structures. Based on the Hirota bilinear formulation, a symbolic computation with a new class of Hirota-Satsuma-Ito type equations involving general second-order derivative terms is conducted to require having lump solutions. Explicit expressions for lump solutions are successfully presented in terms of coefficients in a generalized Hirota-Satsuma-Ito equation. Three-dimensional plots and contour plots of a special presented lump solution are made to shed light on the characteristic of the resulting lump solutions.

The local fractional Laplace variational iteration method was applied to solve the linear local fractional partial differential equations. The local fractional Laplace variational iteration method is coupled by the local fractional variational iteration method and Laplace transform. The nondifferentiable approximate solutions are obtained and their graphs are also shown.

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In this article, we present a new application for the Yang-Srivastava-Machado fractional derivative without singular kernel to the steady heat flow problem. The Sumudu transform is used to find the analytical solution of the fractional-order heat flow.

Biomimetic antireflective silicon nanocones array is used for analysis of small molecules by mass spectrometry. The role of the absorbed laser energy and its distribution in the laser desorption/ionization process has been investigated by varying the antireflective features precisely. By optimizing the antireflective silicon array, the absorbed laser energy can be channeled completely into the desorption/ionization of analytes. The optimized silicon array exhibits excellent performance to detect peptide, amino acid, drug molecule, and carbohydrate without any interference in the low-mass region.

In this paper, we can obtain curvature estimates for spacelike admissible graphic hypersurfaces in the (n + 1)-dimensional Lorentz-Minkowski space R n+1 1 , and through which the existence of spacelike admissible graphic hypersurfaces, with prescribed 2-th Weingarten curvature and Dirichlet boundary data, defined over a strictly convex domain in the hyperbolic plane H n (1) ⊂ R n+1 1 of center at origin and radius 1, can be proven.

In this work, a three-dimensional, steady state model was developed by combining mechanical equations, Navier-stokes equation, Maxwell-Stefan equation, and Butler-Volmer equation. This model was used to investigate the influences of flow field structure and assembly force on porosity distribution in gas diffusion layer (GDL), species distribution in GDL, and current density distribution in GDL and membrane by extracting uneven porosity in the GDL from mechanical calculation equation to put in mass transfer calculation and electrochemical calculation equation as the known data. The optimum assembly prestress and optimum flow field structure were achieved. The results show combined effect of the assembly force and flow field makes the uneven porosity distribution and remarkable lateral current in the GDL; the channel width/ rib width ratio of flow field has significant effects on the performance of the high temperature proton exchange membrane fuel cells (HT-PEMFC). These results provide the potential to promote the performance and application of HT-PEMFC.