Simple Periodic Boundary Conditions Research Articles

Simple periodic boundary conditions for molecular simulation of uniaxial flow

We present rotating periodic boundary conditions (PBCs) for the simulation of nonequilibrium molecular dynamics (NEMD) under uniaxial stretching flow (USF) or biaxial stretching flow (BSF). Such nonequilibrium flows need specialized PBCs since the simulation box deforms with the background flow. The technique builds on previous models using one or two lattice remappings, and is simpler than the PBCs developed for the general three dimensional flow. For general three dimensional flows, Dobson [1] and Hunt [2] proposed schemes which are not time-periodic since they use more than one automorphism remapping. This paper presents a single automorphism remapping PBCs for USF and BSF which is time periodic up to a rotation matrix and has better minimum lattice spacing properties.

Space-time asymptotic expansion method for transient thermal conduction in the periodic composite with temperature-dependent thermal properties

Space-time asymptotic expansion method (AEM) is a rigorous method for solving the multiscale transient thermal conduction problem in periodic composites. However, the AEM is still difficult to model the thermal behavior in composites when temperature-dependent material properties are taken into account. Besides, its complex and costly implementation also restricts the usage of AEM. A space–time AEM for multiscale transient thermal analysis is comprehensively studied in this study to address these issues properly. After the constitutive equation of temperature-dependent characteristic temperature tensor and effective thermal properties in the transient thermal conduction is deduced from the solid theoretical base, a new implementation approach comprised of both homogenization and localization is developed. It can directly model the characteristic temperature tensor within a representative volume element model under simple periodic boundary conditions and linear temperature loads, differing from conventional AEM, which requires complex location-related heat flux loads. Moreover, a new characteristic heat flux tensor is proposed to replace the characteristic temperature tensor in the localization of heat flux. All these contributions simplify the localization in the new implementation. The thermal behavior of A fiber-reinforced composite during the forming process is investigated using the space–time AEM and multiscale finite element method. The comparison results between space–time AEM and multiscale finite element method indicate that the space–time AEM is accurate and efficient as the differences of local temperature and heat flux are 0.0051 °C and 7.2 × 10-5 W/mm2, and the total nodes in space–time AEM is only about half of the multiscale finite element method.

Internal- and rho-axis systems of molecules with one large amplitude internal motion: The geometry of rho.

The internal-axis system (IAS) of molecules with a large amplitude internal motion (LAM) is determined by integrating the kinematic equation of the IAS by Lie-group and Lie-algebraic methods. Numerical examples on hydrogen peroxide, nitrous acid, and acetaldehyde demonstrate the methods. By exploiting the special product structure of the solution matrix, simple methods are devised for calculating the transformation to the rho-axis system (RAS) along with the value of the parameter ρ characterizing a RAS rotational-LAM kinetic energy operator. The parameter ρ so calculated agrees exactly with that one obtained by the Floquet method as shown in the example of acetaldehyde. Geometrical interpretation of ρ is given. The advantageous property of the RAS over the IAS in retaining simple periodic boundary conditions is numerically demonstrated.

Ising lines: Natural topological defects within ferroelectric Bloch walls

Phase-field simulations demonstrate that the polarization order-parameter field in the Ginzburg-Landau-Devonshire model of rhombohedral ferroelectric ${\mathrm{BaTiO}}_{3}$ allows for an interesting linear defect, stable under simple periodic boundary conditions. This linear defect, here called the Ising line, can be described as an about 2-nm-thick intrinsic paraelectric nanorod acting as a highly mobile borderline between finite portions of Bloch-like domain walls of opposite helicity. These Ising lines play the role of domain boundaries associated with the Ising-to-Bloch domain-wall phase transition.

Modifications to a Turbulent Inflow Generation Method for Boundary-Layer Flows

NUMERICAL simulations of turbulent boundary layers require inflow/outflow boundary conditions. Downstream flow is particularly sensitive to the inlet boundary condition; it is necessary to provide a realistic, coherent series of time-varying velocity components to avoid wasteful and potentially costly readjustment behavior. Simple periodic boundary conditions (where downstream flow is reapplied at the inlet), while suitable for channel or pipe flow simulations, are poorly suited to spatially developing flows such as flat-plate boundary layers [1]. Lund et al. [2] (LWS) developed a quasi-periodic approach using an accurate scaling technique. This method used recycling of the downstream data to provide the inlet boundary condition on the inflow simulation (illustrated in Fig. 1). It has been successfully applied in both incompressible and compressible boundary-layer simulations [3–5]. Despite the wealth of publications that have successfully applied this method, a number of studies [5–10] have indicated that some aspects of LWS method can prove difficult to implement. Hurdles include spurious periodicity, error accumulation, and initial conditions. The main objective of this Technical Note is to propose simple modification to the original LWS formulation to address these issues, and also to avoid use of the 99% boundary-layer thickness.

FDTD Analysis of Periodic Structures With Arbitrary Skewed Grid

An efficient finite-difference time-domain (FDTD) algorithm with a simple periodic boundary condition (PBC) is developed to analyze general periodic structures with arbitrary skewed grids. The algorithm is easy to implement and efficient in both memory usage and computation time. The stability criterion of the algorithm is angle independent and therefore it is suitable for implementing incidence with angle close to grazing as well as normal incidence. The validity of this algorithm is verified through several numerical examples such as dipole and Jerusalem cross frequency selective surfaces (FSS) with various skew angles.

A simple and efficient FDTD/PBC algorithm for scattering analysis of periodic structures

An efficient finite difference time domain (FDTD) algorithm with a simple periodic boundary condition (PBC) is developed to analyze reflection and transmission properties of general periodic structures with arbitrary incident angles. In this new approach, the FDTD simulation is performed by setting a constant horizontal wave number instead of a specific incident angle. The principle of the FDTD/PBC algorithm is discussed and two important implementation issues are addressed, namely, the excitation of plane wave and the suppression of horizontal resonance. The validity of the approach is demonstrated through several numerical examples on dielectric slabs and frequency selective surfaces.

Drude Weight of the Two-Dimensional Hubbard Model –Reexamination of Finite-Size Effect in Exact Diagonalization Study–

The Drude weight of the Hubbard model on the two-dimensional square lattice is studied by the exact diagonalizations applied to clusters up to 20 sites. We carefully examine finite-size effects by consideration of the appropriate shapes of clusters and the appropriate boundary condition beyond the limitation of employing only the simple periodic boundary condition. We successfully capture the behavior of the Drude weight that is proportional to the squared hole doping concentration. Our present result gives a consistent understanding of the transition between the Mott insulator and doped metals. We also find, in the frequency dependence of the optical conductivity, that the mid-gap incoherent part emerges more quickly than the coherent part and rather insensitive to the doping concentration in accordance with the scaling of the Drude weight.

On the streamfunction–vorticity formulation in sliding bi-period frames: Application to bulk behavior for polymer blends

The Lees–Edwards description of bi-periodic boundary conditions has been extended to the streamfunction and streamfunction–vorticity formulation in sliding bi-periodic frames. The required compatibility conditions are formulated and uniqueness of the solution is shown. The model has been implemented in a spectral element method context to describe bulk shear behavior far away from walls, where no simple periodic boundary conditions can be used. In the numerical model a Lagrangian multiplier is introduced to couple the shearing boundaries. The proposed method has been validated for a mathematical test problem; convergence is shown and the influence of the order of approximation of the Lagrangian multiplier is studied. Finally, results are presented for drop coalescence across the boundaries of the bi-periodic frame.