Occupied-orbital fast multipole method for efficient exact exchange evaluation

We present an efficient algorithm for computing the exact exchange contributions in the Hartree-Fock and hybrid density functional theory models on the basis of the fast multipole method (FMM). Our algorithm is based on the observation that FMM with hierarchical boxes can be efficiently used in the exchange matrix construction, when at least one of the indices of the exchange matrix is constrained to be an occupied orbital. Timing benchmarks are presented for alkane chains (C400H802 and C150H302), a graphene sheet (C150H30), a water cluster [(H2O)100], and a protein Crambin (C202H317O64N55S6). The computational cost of the far-field exchange evaluation for Crambin is roughly 3% that of a self-consistent field iteration when the multipoles up to rank 2 are used

Differences of weighted composition operators between the Fock spaces

We study some important topological properties such as boundedness, compactness and essential norm of differences of weighted composition operators between Fock spacesComment: 10 page

Weighted composition operators between different Fock spaces

We study weighted composition operators acting between Fock spaces. The following results are obtained: (1) Criteria for the boundedness and compactness; (2) Characterizations of compact differences and essential norm; (3) Complete descriptions of path connected components and isolated points of the space of composition operators and the space of nonzero weighted composition operators

Frames and operators in Schatten classes

Let $T$ be a compact operator on a separable Hilbert space $H$. We show that, for $2\le p<\infty$, $T$ belongs to the Schatten class $S_p$ if and only if $\{\|Tf_n\|\}\in \ell^p$ for \emph{every} frame $\{f_n\}$ in $H$; and for $0<p\le2$, $T$ belongs to $S_p$ if and only if $\{\|Tf_n\|\}\in\ell^p$ for \emph{some} frame $\{f_n\}$ in $H$. Similar conditions are also obtained in terms of the sequence $\{\}$ and the double-indexed sequence $\{\}$.Comment: 27 page

Development of a Chemically Reacting Flow Solver on the Graphic Processing Units

The focus of the current research is to develop a numerical framework on the Graphic Processing Units (GPU) capable of modeling chemically reacting flow. The framework incorporates a high-order finite volume method coupled with an implicit solver for the chemical kinetics. Both the fluid solver and the kinetics solver are designed to take advantage of the GPU architecture to achieve high performance. The structure of the numerical framework is shown, detailing different aspects of the optimization implemented on the solver. The mathematical formulation of the core algorithms is presented along with a series of standard test cases, including both nonreactive and reactive flows, in order to validate the capability of the numerical solver. The performance results obtained with the current framework show the parallelization efficiency of the solver and emphasize the capability of the GPU in performing scientific calculations. Distribution A: Approved for public release; distribution unlimited. PA #1117

Automated Discovery of Candidate Simulation Models for Steering Behavior Simulation

Steering behavior of autonomous agents plays important roles in many simulation applications, such as simulation of pedestrian crowds, simulation of evacuation scenarios, simulation of ecosystems, simulation of autonomous robots, and simulation of artificial life in virtual environments used in computer games. It is desirable to have an approach that can automatically discover multiple candidate models for steering behavior simulation besides manual approach (trial-and-error fashion) and data-driven approach. Towards this goal, this work presents an approach that searches for candidate models of steering behavior in an automated way. The proposed framework includes two components. A model space specification provides a formal specification for a general structure from which various models can be constructed, and a search method to search for a set of candidate models based on requirements. To support more complex scenarios, we further add three major extensions including: (1) Activation component assign dynamic priorities for behaviors depending on surround environments. (2) Multiple search stages are provided to assist the evolutionary search algorithm to distribute computational resources better. (3) A special type of entity called space entity to assist agents receive information not only from other entities (agents, obstacles), but also from surrounding empty space. The approach is able to discover multiple candidate models for three basic steering behaviors including the leader- following ( Bleader_following), personal space maintenance ( Bpersonal_space), and mobile obstacle avoidance ( Bobstacle_avoidance). The results show that different possibilities of steering behavior support modelers to have a better understanding of the problem under study, hence assist modelers to develop more advanced models by testing different combinations of the basic steering behaviors. We evaluate all combinations between three basic steering behaviors including: (1) Bleader_following + Bobstacle_avoidance, (2) Bobstacle_avoidance + Bpersonal_space, (3) Bleader_following + Bpersonal_space, and (4) Bleader_following + Bobstacle_avoidance + Bpersonal_space. We further test the approach with two variations of scenario 4: (5) The leader surrounding + Bpersonal_space, (6) Hall-way evacuation with an obstacle in the middle. The results show that the framework is also able to discover multiple models for each of these composite steering behaviors, and several of them have good scalability and robustness