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

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

Phosphorylation of Jak2 on Ser(523) Inhibits Jak2-Dependent Leptin Receptor Signaling

The leptin receptor, LRb, and other cytokine receptors are devoid of intrinsic enzymatic activity and rely upon the activity of constitutively associated Jak family tyrosine kinases to mediate intracellular signaling. In order to clarify mechanisms by which Jak2, the cognate LRb-associated Jak kinase, is regulated and mediates downstream signaling, we employed tandem mass spectroscopic analysis to identify phosphorylation sites on Jak2. We identified Ser(523) as the first-described site of Jak2 serine phosphorylation and demonstrated that this site is phosphorylated on Jak2 from intact cells and mouse spleen. Ser(523) was highly phosphorylated in HEK293 cells independently of LRb-Jak2 activation, suggesting a potential role for the phosphorylation of Ser(523) in the regulation of LRb by other pathways. Indeed, mutation of Ser(523) sensitized and prolonged signaling by Jak2 following activation by the intracellular domain of LRb. The effect of Ser(523) on Jak2 function was independent of Tyr(570)-mediated inhibition. Thus, the phosphorylation of Jak2 on Ser(523) inhibits Jak2 activity and represents a novel mechanism for the regulation of Jak2-dependent cytokine signaling