The motion of the atoms in a molecule may be described as a superposition of translational motion of the molecular center-of-mass, rotational motion about the principal molecular axes, and an intramolecular motion that may be associated with vibrations and librations as well as molecular conformational changes. We have constructed projection operators that use the atomic coordinates and velocities at any two times, t=0 and a later time t, to determine the molecular center-of-mass, rotational, and intramolecular motions in a molecular dynamics simulation. This model-independent technique facilitates characterization of the atomic motions within a system of complex molecules and is important for the interpretation of experiments that rely on time correlation functions of atomic and molecular positions and velocities. The application of the projection operator technique is illustrated for the inelastic neutron scattering functions and for the translational and rotational velocity autocorrelation functions.

This is the first part of direct numerical simulation (DNS) of double-diffusive convection in a slim rectangular enclosure with horizontal temperature and concentration gradients. We consider the case with the thermal Rayleigh number of 10⁵, the Pradtle number of 1, the Lewis number of 2, the buoyancy ratio of composition to temperature being in the range of [0,1], and height-to-width aspect ration of 4. A new 7th-order upwind compact scheme was developed for approximation of convective terms, and a three-stage third-order Runge-Kutta method was employed for time advancement. Our DNS suggests that with the buoyancy ratio increasing form 0 to 1, the flow of transition is a complex series changing from the steady to periodic, chaotic, periodic, quasi-periodic, and finally back to periodic. There are two types of periodic flow, one is simple periodic flow with single fundamental frequency (FF), and the other is complex periodic flow with multiple FFs. This process is illustrated by using time-velocity histories, Fourier frequency spectrum analysis and the phase-space trajectories.

We develop a new formulation of the integral equation (IE) method for three-dimensional (3D) electromagnetic (EM) field computation in large-scale models with multiple inhomogeneous domains. This problem arises in many practical applications including modeling the EM fields within the complex geoelectrical structures in geophysical exploration. In geophysical applications, it is difficult to describe an earth structure using the horizontally layered background conductivity model, which is required for the efficient implementation of the conventional IE approach. As a result, a large domain of interest with anomalous conductivity distribution needs to be discretized, which complicates the computations. The new method allows us to consider multiple inhomogeneous domains, where the conductivity distribution is different from that of the background, and to use independent discretizations for different domains. This reduces dramatically the computational resources required for large-scale modeling. In addition, using this method, we can analyze the response of each domain separately without an inappropriate use of the superposition principle for the EM field calculations. The method was carefully tested for the modeling the marine controlled-source electromagnetic (MCSEM) fields for complex geoelectric structures with multiple inhomogeneous domains, such as a seafloor with the rough bathymetry, salt domes, and reservoirs. We have also used this technique to investigate the return induction effects from regional geoelectrical structures, e.g., seafloor bathymetry and salt domes, which can distort the EM response from the geophysical exploration target.

For numerical simulation of one-dimensional diffraction gratings both in TE and TM polarization, an enhanced adaptive finite element method is proposed in this paper. A modified perfectly matched layer (PML) formulation is proposed for the truncation of the unbounded domain, which results in a homogeneous Dirichlet boundary condition and the corresponding error estimate is greatly simplified. The a posteriori error estimates for the adaptive finite element method are provided. Moreover, a lower bound is obtained to demonstrate that the error estimates obtained are sharp.

In this paper, a multilevel domain decomposition approach based on multigrid methods for obtaining fast solutions for coupled engineering flow applications arising on complex domains is presented. The proposed technique not only allows solutions to be computed efficiently at the element level but also helps us to achieve proper accuracy, load balancing and computational efficiency. Numerical results presented demonstrate the robustness of the proposed technique.

We present a parallel Schwarz type domain decomposition preconditioned recycling Krylov subspace method for the numerical solution of stochastic indefinite elliptic equations with two random coefficients. Karhunen-Loève expansions are used to represent the stochastic variables and the stochastic Galerkin method with double orthogonal polynomials is used to derive a sequence of uncoupled deterministic equations. We show numerically that the Schwarz preconditioned recycling GMRES method is an effective technique for solving the entire family of linear systems and, in particular, the use of recycled Krylov subspaces is the key element of this successful approach.

In this paper, we simulate the pressure driven fluid flow at the pore scale level through 2-D porous media, which is composed of different curved channels via the lattice Boltzmann method. With this direct simulation, the relation between the tortuosity and the permeability is examined. The numerical results are in good agreement with the existing theory.

This work presents a finite difference technique for simulating three-dimensional free surface flows governed by the Upper-Convected Maxwell (UCM) constitutive equation. A Marker-and-Cell approach is employed to represent the fluid free surface and formulations for calculating the non-Newtonian stress tensor on solid boundaries are developed. The complete free surface stress conditions are employed. The momentum equation is solved by an implicit technique while the UCM constitutive equation is integrated by the explicit Euler method. The resulting equations are solved by the finite difference method on a 3D-staggered grid. By using an exact solution for fully developed flow inside a pipe, validation and convergence results are provided. Numerical results include the simulation of the transient extrudate swell and the comparison between jet buckling of UCM and Newtonian fluids.

We use a generalized scaling invariance of the dispersion-managed nonlinear Schrödinger equation to derive an approximate function for strongly dispersion-managed solitons. We then analyze the regime in which the approximation is valid. Finally, we present a method for extracting the underlying soliton part from a noisy pulse, using the resulting approximate formula.

The Unsteady Adaptive Stochastic Finite Elements (UASFE) approach is a robust and efficient uncertainty quantification method for resolving the effect of random parameters in unsteady simulations. In this paper, it is shown that the underlying Adaptive Stochastic Finite Elements (ASFE) method for steady problems based on Newton-Cotes quadrature in simplex elements is extrema diminishing (ED). It is also shown that the method is total variation diminishing (TVD) for one random parameter and for multiple random parameters for first degree Newton-Cotes quadrature. It is proven that the interpolation of oscillatory samples at constant phase in the UASFE method for unsteady problems results in a bounded error as function of the phase for periodic responses and under certain conditions also in a bounded error in time. The two methods are applied to a steady transonic airfoil flow and a transonic airfoil flutter problem.