The valence force field (VFF) model is a concise physical interpretation of the atomic interaction in terms of the bond and angle variations in the explicit quadratic functional form, while the machine learning (ML) method is a flexible numerical approach to make predictions based on some pre-obtained training data without the need of any explicit functions. We propose a so-called ML-VFF model, by combining the clear physical essence of the VFF model and the numerical flexibility of the ML method. Instead of imposing any explicit functional forms for the atomic interaction, the ML-VFF model predicts the potential and force with the Gaussian regression approach. We take graphene as an example to illustrate the ability of the ML-VFF model to make accurate predictions with relatively low computational expenses. We also discuss some key advantages and drawbacks of the ML-VFF model.

In this letter, we present an extensive study of the linearly forced isotropic turbulence. By using analytical method, we identify two parametric choices, of which they seem to be new as far as our knowledge goes. We prove that the underlying nonlinear dynamical system for linearly forced isotropic turbulence is the general case of a cubic Lienard equation with linear damping. We also discuss a Fokker-Planck approach to this new dynamical system,which is bistable and exhibits two asymmetric and asymptotically stable stationary probability densities.

Pulsating jet is one of the common working modes in electrohydrodynamic printing (EHDP) that process is highly affected by operating parameters and material properties. In this paper, the processes of pulsating jet for liquids with different physical properties were investigated using numerical simulation. An electrohydrodynamic solver was established, and a charge flux restricting step was adopted to ensure a realistic distribution of free charges. Three various ejection regimes were observed in our simulations: oscillating cone (OC), choked jet (CJ), and stable cone-jet (SJ). We found that three dimensionless numbers relating to liquid properties determined the ejection regime: the Ohnesorge number, Q0{\epsilon}r/Q, and Q0/(QRe). Based on those dimensionless numbers, the roles of liquid properties on pulsating jet (OC and CJ) were analyzed. In OC, the break of the jet is due to the significant oscillation of the Taylor cone, which is mainly affected by viscosity and conductivity. In CJ, the jet emission is terminated by the excessive resistant force in the cone-jet transition region. For liquids with low and medium viscosity, the dominant resistant force is the polarization force or viscous force when {\epsilon}rRe is larger or smaller than 1, respectively. For high viscosity liquids, the viscous force always becomes the major resistance. These results further reveal the physical mechanism of pulsating jet and can be used to guide its application.

Eshelby's problems have been generalized to arbitrary shape of polygonal, polyhedral, and ellipsoidal inclusions embedded in an infinite isotropic domain under transient heat transfer, and Eshelby's tensors have been analytically derived to evaluate disturbed thermal fields caused by inclusions with a polynomial-form eigen-fields. Transformed coordinates are applied to arbitrarily shaped inclusions for domain integrals of transient fundamental solutions. This formulation is for general transient heat transfer, and it can recover classic Eshelby's tensor for the ellipsoidal subdomain with explicit expression for the spherical subdomain in the steady state and Michelitsch's solution in the harmonic state. The discontinuity and singularity of domain integral for Eshelby's tensor are investigated and the temporal effects are discussed. The formulation for a polyhedral inhomogeneity is verified with the finite element method results and the classic solution of a spherical inhomogeneity problem when the sphere is divided into many polyhedrons. The generalized formulation for Eshelby's problem enables the simulation and modeling of particulate composites containing arbitrarily shaped particles for steady-state, harmonic and transient heat transfer in both two- and three-dimensional space.

This paper proposes a single-domain dual-reciprocity inclusion-based boundary element method (DR-iBEM) for a three-dimensional fully bonded bi-layered composite embedded with ellipsoidal inhomogeneities under transient/harmonic thermal loads. The heat equation is interpreted as a static one containing time- and frequency-dependent nonhomogeneous source terms, which is similar to eigen-fields but is transformed into a boundary integral by the dual-reciprocity method. Using the steady-state bimaterial Green's function, boundary integral equations are proposed to take into account continuity conditions of temperature and heat flux, which avoids setting up any continuity equations at the bimaterial interface. Eigen-temperature-gradients and eigen-heat-source are introduced to simulate the material mismatch in thermal conductivity and heat capacity, respectively. The DR-iBEM algorithm is particularly suitable for investigating the transient and harmonic thermal behaviors of bi-layered composites and is verified by the finite element method (FEM). Numerical comparison with the FEM demonstrates its robustness and accuracy. The method has been applied to a functionally graded material as a bimaterial with graded particle distributions, where particle size and gradation effects are evaluated.