Least-squares finite-element lattice Boltzmann method

A new numerical model of the lattice Boltzmann method utilizing least-squares finite element in space and Crank-Nicolson method in time is presented. The new method is able to solve problem domains that contain complex or irregular geometric boundaries by using finite-element method’s geometric flexibility and numerical stability, while employing efficient and accurate least-squares optimization. For the pure advection equation on a uniform mesh, the proposed method provides for fourth-order accuracy in space and second-order accuracy in time, with unconditional stability in the time domain. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow and Couette flow

Quantitative x-ray scattering of free molecules

Advances in x-ray free electron lasers have made ultrafast scattering a powerful method for investigating molecular reaction kinetics and dynamics. Accurate measurement of the ground-state, static scattering signals of the reacting molecules is pivotal for these pump-probe x-ray scattering experiments as they are the cornerstone for interpreting the observed structural dynamics. This article presents a data calibration procedure, designed for gas-phase x-ray scattering experiments conducted at the Linac Coherent Light Source x-ray Free-Electron Laser at SLAC National Accelerator Laboratory, that makes it possible to derive a quantitative dependence of the scattering signal on the scattering vector. A self-calibration algorithm that optimizes the detector position without reference to a computed pattern is introduced. Angle-of-scattering corrections that account for several small experimental non-idealities are reported. Their implementation leads to near quantitative agreement with theoretical scattering patterns calculated with ab-initio methods as illustrated for two x-ray photon energies and several molecular test systems

Imaging valence electron rearrangement in a chemical reaction using hard X-ray scattering

We have observed the signatures of valence electron rearrangement in photoexcited ammonia using ultrafast hard X-ray scattering. Time-resolved X-ray scattering is a powerful tool for imaging structural dynamics in molecules because of the strong scattering from the core electrons localized near each nucleus. Such core-electron contributions generally dominate the differential scattering signal, masking any signatures of rearrangement in the chemically important valence electrons. Ammonia represents an exception to the typically high core-to-valence electron ratio. We measured 9.8 keV X-ray scattering from gas-phase deuterated ammonia following photoexcitation via a 200 nm pump pulse to the 3s Rydberg state. We observed changes in the recorded scattering patterns due to the initial photoexcitation and subsequent deuterium dissociation. Ab initio calculations confirm that the observed signal is sensitive to the rearrangement of the single photoexcited valence electron as well as the interplay between adiabatic and nonadiabatic dissociation channels. The use of ultrafast hard X-ray scattering to image the structural rearrangement of single valence electrons constitutes an important advance in tracking valence electronic structure in photoexcited atoms and molecules

Isochronous Gaussian Sampling: From Inception to Implementation

Gaussian sampling over the integers is a crucial tool in lattice-based cryptography, but has proven over the recent years to be surprisingly challenging to perform in a generic, efficient and provable secure manner. In this work, we present a modular framework for generating discrete Gaussians with arbitrary center and standard deviation. Our framework is extremely simple, and it is precisely this simplicity that allowed us to make it easy to implement, provably secure, portable, efficient, and provably resistant against timing attacks. Our sampler is a good candidate for any trapdoor sampling and it is actually the one that has been recently implemented in the Falcon signature scheme. Our second contribution aims at systematizing the detection of implementation errors in Gaussian samplers. We provide a statistical testing suite for discrete Gaussians called SAGA (Statistically Acceptable GAussian). In a nutshell, our two contributions take a step towards trustable and robust Gaussian sampling real-world implementations

Least-squares finite-element scheme for the lattice Boltzmann method on an unstructured mesh

A numerical model of the lattice Boltzmann method (LBM) utilizing least-squares finite-element method in space and the Crank–Nicolson method in time is developed. This method is able to solve fluid flow in domains that contain complex or irregular geometric boundaries by using the flexibility and numerical stability of a finite-element method, while employing accurate least-squares optimization. Fourth-order accuracy in space and second-order accuracy in time are derived for a pure advection equation on a uniform mesh; while high stability is implied from a von Neumann linearized stability analysis. Implemented on unstructured mesh through an innovative element-by-element approach, the proposed method requires fewer grid points and less memory compared to traditional LBM. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow, Couette flow, and flow past a circular cylinder. Finally, the proposed method is applied to estimate the permeability of a randomly generated porous media, which further demonstrates its inherent geometric flexibility

Stochastic Modeling of the Permeability of Randomly Generated Porous Media

Permeability of porous media in subsurface environments is subject to potentially large uncertainties due to the heterogeneity of natural systems. In this study, a first-order reliability method (FORM) is combined with a lattice Boltzmann method (LBM) to estimate the permeability of randomly generated porous media. The proposed procedure provides an increased ease of addressing complex pore structures by employing LBM to model fluid flow, while inheriting the computational efficiency from FORM. Macroscale- equivalent permeability can thus be estimated with significantly reduced computational efforts, while maintaining a connection to the complex microscale fluid dynamics within a pore structure environment. Implemented on several randomly generated porous media domains, the proposed method provides 13–120 times the efficiency compared to Monte Carlo methods

Development of a Web-Based Mass Transfer Processes Laboratory: System Development and Implementation

A web-based environment is utilized as a means to introduce advanced mass transfer processes concepts in environmental engineering and science courses. System development and implementation is presented, including detailed descriptions of the techniques employed to link software written in high level computer languages such as C++ and FORTRAN to an internet-based, user-friendly graphical user interface for both program input and output