Yongxing Shen

Dielectric behavior of three-phase percolative Ni–BaTiO3/polyvinylidene fluoride composites

A three-phase percolative composite with a ferroelectric phase (BaTiO3) and metallic inclusions (Ni) embedded into polyvinylidene fluoride matrix was prepared by using a simple blending and hot-molding technique. Effective medium approximations and percolation theory were employed in order to design and describe the dielectric behavior of such three-phase composites. Our experimental results showed that the static dielectric constant of such a three-phase composite can reach above 800 when the Ni concentration is close to its percolation threshold. Such composites have a potential to become capacitors and can be easily fabricated into various shapes due to its flexibility.

Simulating and interpreting Kelvin probe force microscopy images on dielectrics with boundary integral equations

Kelvin probe force microscopy (KPFM) is designed for measuring the tip-sample contact potential differences by probing the sample surface, measuring the electrostatic interaction, and adjusting a feedback circuit. However, for the case of a dielectric (insulating) sample, the contact potential difference may be ill defined, and the KPFM probe may be sensing electrostatic interactions with a certain distribution of sample trapped charges or dipoles, leading to difficulty in interpreting the images. We have proposed a general framework based on boundary integral equations for simulating the KPFM image based on the knowledge about the sample charge distributions (forward problem) and a deconvolution algorithm solving for the trapped charges on the surface from an image (inverse problem). The forward problem is a classical potential problem, which can be efficiently solved using the boundary element method. Nevertheless, the inverse problem is ill posed due to data incompleteness. For some special cases, we have developed deconvolution algorithms based on the forward problem solution. As an example, this algorithm is applied to process the KPFM image of a gadolinia-doped ceria thin film to solve for its surface charge density, which is a more relevant quantity for samples of this kind than the contact potential difference (normally only defined for conductive samples) values contained in the raw image.

Metastable phase formation in the immiscible Cu-Co system studied by thermodynamic, molecular dynamics and ab initio calculations together with ion beam mixing

For the equilibrium immiscible Cu?Co system with a positive heat of formation of +10?kJ?mol?1, ab initio calculations were used to predict the physical properties of the metastable D019 and L12 structures for the Cu75Co25 phases and the D019 structure for the Cu25Co75 alloy. Based on the ab initio calculation results, an n-body Cu?Co potential was constructed and proven to be realistic. Applying the constructed Cu?Co potential, molecular dynamics simulations predict that the amorphous phase could be obtained at around Cu60Co40 and its atomic distribution could be inhomogeneous. Experimentally, by using ion beam mixing with 200?keV Xe+ ions, an amorphous Cu60Co40 phase with inhomogeneous morphology was indeed obtained at a dose of 1 ? 1015?Xe+?cm?2. Increasing the irradiation dose to 4 ? 1015?Xe+?cm?2, a mixture of Cu-rich and Co-rich metastable phases was obtained. Besides, a mixture of FCC and HCP structures was observed in the Cu82Co18 multilayered sample and an HCP structure was observed in the Cu26Co74 multilayered sample. It was found that the lattice constants of the FCC and HCP phases determined by diffraction analysis were quite compatible with those predicted by the ab initio calculations.

A family of discontinuous Galerkin mixed methods for nearly and perfectly incompressible elasticity

We introduce a family of mixed discontinuous Galerkin (DG) finite element methods for nearly and perfectly incompressible linear elasticity. These mixed methods allow the choice of polynomials of any order k 2: 1 for the approximation of the displacement field, and of order k or k - 1 for the pressure space, and are stable for any positive value of the stabilization parameter. We prove the optimal convergence of the displacement and stress fields in both cases, with error estimates that are independent of the value of the Poissons ratio. These estimates demonstrate that these methods are locking-free. To this end, we prove the corresponding inf-sup condition, which for the equal-order case, requires a construction to establish the surjectivity of the space of discrete divergences on the pressure space. In the particular case of near incompressibility and equal-order approximation of the displacement and pressure fields, the mixed method is equivalent to a displacement method proposed earlier by Lew et al. [29]. The absence of locking of this displacement method then follows directly from that of the mixed method, including the uniform error estimate for the stress with respect to the Poissons ratio. We showcase the performance of these methods through numerical examples, which show that locking may appear if Dirichlet boundary conditions are imposed strongly rather than weakly, as we do here.

Collocation mesh-free method to solve the gray phonon Boltzmann transport equation

ABSTRACT The phonon Boltzmann transport equation (BTE) is an important governing equation for phonon transport at the subcontinuum scale. Numerically solving the BTE can help to study the heat transfer phenomena at microscale and nanoscale, for example, in electronic devices or nanocomposites. In this work, we developed a collocation mesh-free method to solve the BTE for different heat transfer regimes. The proposed numerical scheme does not require meshing the domain or performing numerical integration, and is thus advantageous for problems with complicated geometries. A few case studies show that our method can yield comparable results with semianalytical and finite volume methods.

Analytic perturbation solution to the capacitance system of a hyberboloidal tip and a rough surface

The capacitance system of a hyperboloidal tip and a rough surface is usually encountered in analyzing electrostatic force microscopy images. In this letter, a perturbation approach has been applied to solve for the electric potential of this system, in which the rough surface is treated as perturbation from a flat one. For the first-variation solution, the boundary value problem is represented in the prolate-spheroidal coordinate system and solved in terms of a generalized Fourier series involving conical functions. Based on this solution, the tip-surface Coulombic interaction can be computed. Sample calculations have been applied to sinusoidal surface profiles.

An Elrod–Adams-model-based method to account for the fluid lag in hydraulic fracturing in 2D and 3D

An efficient method to model the fluid lag in hydraulic fracturing has been developed based on the Elrod–Adams model. The main feature of this method is the absence of the need to explicitly track the free end of the fracturing fluid, but rather, the fluid front is obtained by solving the pressure field (zero for the lag) and an auxiliary field for the entire fracture. An important advantage of this method is that no change of formulation, and hence no contact detection, is needed when the fluid reaches the fracture tip. Moreover, the method works for both the injection phase and the liquid withdrawal phase. Based on the latter case studies can be developed to investigate the quantity of the remaining fluid after the fracturing process in order to assess the environmental impact of fracturing. The method applies to both 2D and 3D problems.

Modeling and Experimental Validation of the Electron Beam Selective Melting Process

Abstract Electron beam selective melting (EBSM) is a promising additive manufacturing (AM) technology. The EBSM process consists of three major procedures: ① spreading a powder layer, ② preheating to slightly sinter the powder, and ③ selectively melting the powder bed. The highly transient multi-physics phenomena involved in these procedures pose a significant challenge for in situ experimental observation and measurement. To advance the understanding of the physical mechanisms in each procedure, we leverage high-fidelity modeling and post-process experiments. The models resemble the actual fabrication procedures, including ① a powder-spreading model using the discrete element method (DEM), ② a phase field (PF) model of powder sintering (solid-state sintering), and ③ a powder-melting (liquid-state sintering) model using the finite volume method (FVM). Comprehensive insights into all the major procedures are provided, which have rarely been reported. Preliminary simulation results (including powder particle packing within the powder bed, sintering neck formation between particles, and single-track defects) agree qualitatively with experiments, demonstrating the ability to understand the mechanisms and to guide the design and optimization of the experimental setup and manufacturing process.

A VARIATIONAL FORMULATION OF DISCONTINUOUS-GALERKIN TIME INTEGRATORS

Abstract. Variational integrators provide a way to design structure-preserving time integrators for problems presenting a Lagrangian structure. The basic idea consists in obtaining algorithms from a discrete analogue of Hamilton’s variational principle. Then, the discrete trajectories are stationary points of a discrete analogue of the action functional. The resulting methods enjoy a number of remarkable properties: i) they exactly conserves the momenta associated to the symmetries of a discrete version of the Lagrangian, ii) they define a discrete symplectic flow on the phase space and iii) they show an error in the total energy that remains bounded for exponentially long periods of time. A particularly interesting family of such methods is given by the so called Galerkin variational integrators. Their construction is based on approximating the trajectory of the system by means of piecewise continuous polynomials and providing suitable quadrature rules to approximate the action functional. Then, increasing the order of the interpolating polynomials and the accuracy of the quadrature rules allow to obtain higher order time integrators. In this work we extend the Galerkin methods to the discontinuous case yielding to a family of discontinuous-Galerkin (dG)-methods. To this end, we resort to using two key ingredients: 1) the trajectory of the system is approximated by means of piecewise polynomials which may presents a finite number of discontinuities across time interval boundaries and 2) we approximate the velocity of the system by means of an appropriate dG-time-derivative of the trajectory following some ideas presented in [1, 2] for static problems in elasticity. The resulting algorithms corresponds to a family of discontinuous-symplectic Runge-Kutta methods.