Some Double Sequence Spaces Generated by Four-Dimensional Pascal Matrix

The purpose of this paper is to discover and examine a four-dimensional Pascal matrix domain on Pascal sequence spaces. We show that they are spaces and also establish their Schauder basis, topological properties, isomorphism and some inclusions.

Binding Mechanism of the Matrix Domain of HIV-1 Gag on Lipid Membranes

Aggregation of the HIV-1 Gag protein onto the plasma membrane (PM) enables viral budding and infection propagation. Gag assembly at the membrane interface is mediated by its matrix domain (MA), the Myristoylated (Myr) N-terminus. MA targets the PM through electrostatic interactions, mainly at its highly-basic-region (HBR). The mechanism of Myr insertion and its role in protein-membrane dynamics remains unclear. Using all-atom molecular dynamics, we examined an MA unit in the vicinity of lipid bilayers that model different characteristics of the PM. Interaction with PIP2 and PS lipids is highly favored around the HBR, and is enough to keep the protein bound. Additionally, we simulated three MA units near our bilayers and quantified the collective effects of free monomers vs. formed trimers on Myr insertion events. Micro-second-long trajectories allowed us to observe Myr insertion, propose a mechanism, quantify specific interactions with lipids, and examine the response of the local membrane environment.

Nonlinear Finite Volume Method for 3D Discrete Fracture-Matrix Simulations

Summary We present a lower dimensional discrete fracture-matrix (DFM) model for general nonorthogonal meshes populated by anisotropic permeability tensors in 3D spatial dimension. The discrete fractures are represented as 2D planes embedded in a 3D matrix domain and serve as internal boundaries for conforming meshing of the entire computational domain. The nonlinear finite volume method (FVM) is used to derive flux for both matrix-matrix connections and fracture-fracture connections to account for permeability anisotropy in the matrix and inside the fracture planes, whereas the linear two-point flux approximation (TPFA) is used to couple the matrix and fracture together. The nonlinear method proceeds by first constructing two one-sided fluxes for a connection, and then a unique flux is obtained by a convex combination of the two one-sided fluxes. Construction of one-sided fluxes requires introducing the so-called harmonic averaging points as auxiliary points. While the nonlinear FVM can be applied to derive the flux for matrix-matrix connections in a straightforward way, difficulties arise for fracture-fracture connections because of the presence of fracture intersections. Therefore, to construct the one-sided fluxes for fracture-fracture connections, we first present a novel generalization of the concept of harmonic averaging point so that auxiliary points can be calculated at fracture intersections. Unique nonlinear fluxes are then derived for fracture-fracture connections and fracture intersections. Results of the numerical examples demonstrate that the linear TPFA coupling of matrix and fracture seems to be adequate even for relatively strong anisotropy on a non-K-orthogonal grid, and the new DFM model can accurately capture the permeability anisotropy effect inside the fracture planes as well as the permeability anisotropy in the matrix domain compared with the equidimensional models in which the fractures are gridded explicitly. Finally, the DFM model is applied successfully to deal with complex fracture networks embedded in a heterogeneous matrix domain or fracture network with challenging geometric features.

The relevance of preferential flow in catchment scale simulations

<p>Despite experimental evidence preferential flow is rarely included in hydrologic catchment scale models. This is, at least partly, due to the challenge of deriving preferential flow parameters. Here, we successfully used the optimization algorithm DREAM to calibrate a 3D physics-based dual-permeability model directly at the catchment scale. We limited the number of parameters to be calibrated to the ones being most influential for the simulation of discharge, and we also calibrated parameters of the matrix domain and the macropore domain with a fixed parameter ratio between soil layers. During calibration, saturated hydraulic conductivities of the macropore domain and of the matrix domain converged to very similar values. The dual-permeability parameter sets also did not outperform a calibrated single-domain reference model scenario. We conclude that the incorporation of vertical preferential flow as represented by the dual-permeability approach was not advantageous for reproducing the hydrometric response reasonably well in the studied catchment.</p>