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Our aim in this paper is to study the well-posedness and the dissipativity of higher-order anisotropic conservative phase-field systems. More precisely, we prove the existence and uniqueness of solutions and the existence of the global attractor.
Abstract We present a class of high-order Eulerian–Lagrangian Runge–Kutta finite volume methods that can numerically solve Burgers’ equation with shock formations, which could be extended to general scalar conservation laws. Eulerian–Lagrangian (EL) and semi-Lagrangian (SL) methods have recently seen increased development and have become a staple for allowing large time-stepping sizes. Yet, maintaining relatively large time-stepping sizes post shock formation remains quite challenging. Our proposed scheme integrates the partial differential equation on a space-time region partitioned by linear approximations to the characteristics determined by the Rankine–Hugoniot jump condition. We trace the characteristics forward in time and present a merging procedure for the mesh cells to handle intersecting characteristics due to shocks. Following this partitioning, we write the equation in a time-differential form and evolve with Runge–Kutta methods in a method-of-lines fashion. High-resolution methods such as ENO and WENO-AO schemes are used for spatial reconstruction. Extension to higher dimensions is done via dimensional splitting. Numerical experiments demonstrate our scheme’s high-order accuracy and ability to sharply capture post-shock solutions with large time-stepping sizes.
In this paper, we introduce a new family of spatially co-located field solvers for particle-in-cell applications which evolve the potential formulation of Maxwell’s equations under the Lorenz gauge. Our recent work [2] introduced the concept of time-consistency, which connects charge conservation to the preservation of the gauge at the semi-discrete level. It will be shown that there exists a large family of time discretizations which satisfy this property. Additionally, it will be further shown that for large classes of time marching methods, the satisfaction of the gauge condition automatically implies the satisfaction of Gauss’s law for electricity, with the potential formulation ensuring that that Gauss’s law for magnetism is satisfied by definition. We focus on popular time marching methods including centered differences, backward differences, and diagonally-implicit Runge-Kutta methods, which are coupled to a spectral discretization in space. We demonstrate the theory by testing the methods on a relativistic Weibel instability and a drifting cloud of electrons.
A total of 14 vertical electrical soundings using Schlumberger electrode configuration and the complementary laboratory analysis of aquifer samples were carried out in the Abak Local Government Area of Akwa Ibom State, the coastal region of Nigeria. The study focused on the estimation of geohydrodynamic parameters of the frequently exploited aquifers and the implication of hydrodynamic parameters on the lithostratigraphy and the anticipated exposure of the assessed geologic formation at the shorelines. These parameters were porosity (ϕ), tortuosity (τ), formation factor (F), aquifer water formation resistivity (R{sub w}) and coefficient of permeability/hydraulic conductivity (K). Computation of the effective porosities from the aquifer cuttings was carried out using wet weight–dry weight technique and petrophysical techniques. The F values were computed using the aquifer formation bulk resistivity measured from field 1-D resistivity data analysis, whose interpretation was constrained by nearby borehole information. The formation pore water resistivities were estimated from the laboratory using electrical resistivity metre. The Win RESIST software program was used in interpreting the field data electronically. The results of interpretation gave the primary parameters of saturated and unsaturated units of the coastal regions used in this work. The area generally shows seemingly high porosity with high coefficient of permeability. The primary and secondary parameters have been contoured to model their distributions. Besides, some functional relations have been realized through regression analyses. The contour distribution of the geohydrodynamic parameters indicates the vulnerability of the water repositories to contaminations as well as the vulnerability of the shoreline to waterborne erosion. The seemingly high effective porosity in the compliant laboratory and calculated values indicate that the coastal region is neither lithified nor compacted/consolidated. This signals the possibility of the formation to be easily eroded, weathered or flooded where these units are exposed to water current. With these revelations, the shorelines could be properly managed and conserved by geotechnically reinforcing with hard and water-resistant concrete that can protect the vulnerable and erosion-prone porous sediments.
In this paper, we design a compact finite difference scheme which preserves the original conservative properties to solve the generalized symmetric regularized long-wave equations. The existence of the difference solution is proved by the Brouwer fixed-point theorem. Applying the discrete energy method, the convergence and stability of the difference scheme is obtained, and its numerical convergence order is O(τ{sup 2}+h{sup 4}) in the L{sup ∞}-norm for u and ρ. For computing the nonlinear algebraic system generated by the compact scheme, a decoupled iterative algorithm is constructed and proved to be convergent. Numerical experiment results show that the theory is accurate and the method is efficient and reliable.
Under investigation in this paper is a fifth-order nonlinear Schrödinger equation, which describes the propagation of attosecond pulses in an optical fiber. Based on the Lax pair, infinitely-many conservation laws are derived. With the aid of auxiliary functions, bilinear forms, one-, two- and three-soliton solutions in analytic forms are generated via the Hirota method and symbolic computation. Soliton velocity varies linearly with the coefficients of the high-order terms. Head-on interaction between the bidirectional two solitons and overtaking interaction between the unidirectional two solitons as well as the bound state are depicted. For the interactions among the three solitons, two head-on and one overtaking interactions, three overtaking interactions, an interaction between a bound state and a single soliton and the bound state are displayed. Graphical analysis shows that the interactions between the two solitons are elastic, and interactions among the three solitons are pairwise elastic. Stability analysis yields the modulation instability condition for the soliton solutions.
The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems with exact analytic solutions with the form of Gaussian wave packets. In particular, one-dimensional conservative systems with at most quadratic Hamiltonians are studied.
Highlights: • Determination of the structure of the wild-type LptB in complex with ATP and Mg{sup 2+}. • Demonstrated that ATP binding residues are essential for LptB’s ATPase activity and LPS transport. • Dimerization is required for the LptB’s function and LPS transport. • Revealed relationship between activity of the LptB and the vitality of E. coli cells. - Abstract: Lipopolysaccharide (LPS) is the main component of the outer membrane of Gram-negative bacteria, which plays an essential role in protecting the bacteria from harsh conditions and antibiotics. LPS molecules are transported from the inner membrane to the outer membrane by seven LPS transport proteins. LptB is vital in hydrolyzing ATP to provide energy for LPS transport, however this mechanism is not very clear. Here we report wild-type LptB crystal structure in complex with ATP and Mg{sup 2+}, which reveals that its structure is conserved with other nucleotide-binding proteins (NBD). Structural, functional and electron microscopic studies demonstrated that the ATP binding residues, including K42 and T43, are crucial for LptB’s ATPase activity, LPS transport and the vitality of Escherichia coli cells with the exceptions of H195A and Q85A; the H195A mutation does not lower its ATPase activity but impairs LPS transport, and Q85A does not alter ATPase activity but causes cell death. Our data also suggest that two protomers of LptB have to work together for ATP hydrolysis and LPS transport. These results have significant impacts in understanding the LPS transport mechanism and developing new antibiotics.
The skin consists mostly of extracellular matrix (ECM) composed mainly of collagen, which provides a protective barrier from the environment. The skin continuously experiences harmful stress and damage. As aging progresses, the expression of various genes declines, and physiological functional deterioration occurs. The reduction of collagen accompanying aging impairs the barrier function of the skin and weakens protection from stressors. In the nematode Caenorhabditis elegans, ECM proteins turn over during aging. Older worms of longevity mutants exhibit increased collagen expression, whereas knockdown of collagen genes shortens lifespan. However, it is unclear whether the progression of aging can be delayed by increasing collagen production via an external stimulus. In this study, we examined the effects of collagen tripeptide (CTP), a collagen-derived compound, on lifespan and aging. Our results showed that CTP upregulated collagen genes via the p38 mitogen-activated protein kinase (MAPK)/SKN-1 pathway. Moreover, CTP extended lifespan and delayed aging through p38 MAPK/SKN-1 pathway. In addition, CTP also induced collagen expression via the p38 MAPK pathway in mammals. Our findings supported that external stimuli such as CTP could promote ECM youthfulness using a conserved signaling pathway, thereby contributing to suppression of aging.
The genomes of white-rot fungi hold extended repertoires of enzymes active on virtually all the chemical bonds that intertwine lignocellulose polymers, and several Trametes species have been identified as powerful tools for biorefinery or bioremediation. However, only few studies have addressed the intra-species polymorphism one would expect from fungal strains collected in contrasted environments. We compared the genome sequence of pairs of strains collected in different geographic areas, for each of three fungal species. Using an updated list of the predicted functions for fungal ligno- and cellulolytic enzymes (CAZymes), we observed a high conservation of the gene repertoires among the six strains. We compared the adaptative response of the fungi grown on crystalline cellulose, wheat straw, aspen or pine sawdust by transcriptomics and secretomics. The gene regulation profiles were determined by the species and the substrates, rather than the strain. The secretomes did not show marked differences in the sets of secreted CAZymes after 3 day-growth on the substrates. We identified five transcription factor genes and two sesquiterpenoid synthesis genes induced during growth on lignocellulose. Wider studies using larger sets of strains will be necessary to evaluate the genericity of our findings, and to assess the phenotype diversity one could expect from geographic diversity as compared to taxonomic diversity in Trametes fungi.
Through three-dimensional STORM super-resolution microscopy, we resolve the spectrin-actin-based membrane cytoskeleton of neural stem cells (NSCs) and NSC-derived neurons, astrocytes, and oligodendrocytes. We show that undifferentiated NSCs are capable of forming patches of locally periodic, one-dimensional (1D) membrane cytoskeleton with ~180 nm periodicity. Such periodic structures become increasingly ordered and long-ranging as the NSCs mature into terminally differentiated neuronal and glial cell types, and, during this process, distinct 1D periodic “strips” dominate the flat 2D membranes. Moreover, we report remarkable alignment of the periodic cytoskeletons between abutting cells at axon-axon and axon-oligodendrocyte contacts and identify two adhesion molecules, neurofascin and L1CAM, as candidates to drive this nanoscale alignment. We thus show that a conserved 1D periodic membrane cytoskeletal motif serves as a nanoscale scaffold and ruler to mediate the physical interactions between cell types of the NSC lineage.
Notch is a conserved signaling pathway that is essential for metazoan development and homeostasis; dysregulated signaling underlies the pathophysiology of numerous human diseases. Receptor-ligand interactions result in gene expression changes, which are regulated by the transcription factor RBPJ. RBPJ forms a complex with the intracellular domain of the Notch receptor and the coactivator Mastermind to activate transcription, but it can also function as a repressor by interacting with corepressor proteins. Here, we determine the structure of RBPJ bound to the corepressor SHARP and DNA, revealing its mode of binding to RBPJ. We tested structure-based mutants in biophysical and biochemical-cellular assays to characterize the role of RBPJ as a repressor, clearly demonstrating that RBPJ mutants deficient for SHARP binding are incapable of repressing transcription of genes responsive to Notch signaling in cells. Altogether, our structure-function studies provide significant insights into the repressor function of RBPJ.
Earth system models are composed of coupled components that separately model systems such as the global atmosphere, ocean, and land surface. While these components are well developed, coupling them in a single system can be a significant challenge. Computational efficiency, accuracy, and stability are principal concerns. In this study we focus on these issues. In particular, implicit–explicit (IMEX) tight and loose coupling strategies are explored for handling different time scales. For a simplified model for the air–sea interaction problem, we consider coupled compressible Navier–Stokes equations with an interface condition. Under the rigid-lid assumption, horizontal momentum and heat flux are exchanged through the interface. Several numerical experiments are presented to demonstrate the stability of the coupling schemes. Here, we show both numerically and theoretically that our IMEX coupling methods are mass conservative for a coupled compressible Navier–Stokes system with the rigid-lid condition
Decarboxylation — the release of carbon dioxide (CO 2 ) from a substrate — reduces the carbon yield of bioproduced chemicals. When overlaid onto central carbon metabolism, carbon-conservation networks (CCNs) that reroute flux around CO 2 release can theoretically achieve higher carbon yields for products derived from intermediates that traditionally require CO 2 release, such as acetyl-CoA. Recently, CCNs have started to be implemented in model organisms to produce compounds at higher carbon yields. However, implementation of CCNs in nonmodel hosts may have the greatest impact given their ability to assimilate a larger array of feedstocks, greater environmental tolerance, and unique biosynthetic pathways, ultimately enabling access to a wider range of products. Here, we review recent advances in CCNs with a focus on their application to nonmodel organisms. The differences in central carbon metabolism among different nonmodel hosts reveal opportunities to engineer and apply new CCNs.
We present in this work the implementation of the Energy Conserving Semi-Implicit Method in a parallel code called ECsim. This new code is a three-dimensional, fully electromagnetic particle in cell (PIC) code. It is written in C/C++ and uses MPI to allow massive parallelization. ECsim is unconditionally stable in time, eliminates the finite grid instability, and has the same cycle scheme as the explicit code with a computational cost comparable to other semi-implicit PIC codes. All these features make it a very valuable tool to address situations which have not been possible to analyze until now with other PIC codes. In this work, we show the details of the algorithm implementation and we study its performance in different systems. ECsim is compared with another semi-implicit PIC code with different time and spectral resolution, showing its ability to address situations where other codes fail.
The Boltzmann equation describes the evolution of the phase-space probability distribution of classical particles under binary collisions. Approximations to it underlie the basis for several scholarly fields, including aerodynamics and plasma physics. While these approximations are appropriate in their respective domains, they can be violated in niche but diverse applications which require direct numerical solution of the original nonlinear Boltzmann equation. An expanded implementation of the Galerkin–Petrov conservative spectral algorithm is employed to study a wide variety of physical problems. Enabled by distributed precomputation, solutions of the spatially homogeneous Boltzmann equation can be achieved in seconds on modern personal hardware, while spatially-inhomogeneous problems are solvable in minutes. Here, several benchmarks are presented focusing on accuracy compared to both analytic theoretical predictions and other Boltzmann solvers. These benchmarks span several physical domains including weakly ionized plasma, gaseous fluids, and atomic-plasma interaction.
Local studies of accretion disks and laboratory magnetized plasmas employ analytical coordinate mappings that introduce sheared boundary conditions (BCs). Here, we present a discontinuous Galerkin (DG) algorithm to apply such BCs based on projections and quadrature-free integration. The procedure is high-order accurate, preserves moments exactly and works in multiple dimensions. Tests of increasing complexity are provided, beginning with translations of one and two dimensional fields, followed by 3D and 5D simulations with sheared (twist-shift) BCs. Results show that the algorithm is (p + 1)-order accurate in the DG representation and (p + 2) -order accurate in the cell averages, with p being the order of the polynomial basis. Quantification of the algorithm's hyperdiffusion and discussion of aliasing errors are given. This technique enables conservative local simulations of plasma turbulence with DG, not possible until now.
Chile was one of many countries that initiated environmental impact assessments in the 1990s, and has relied on their use for species conservation and territorial planning without the use of larger-scale environmental and ecological planning. The capacity of Chile's environmental impact assessment system (SEIA) to evaluate resident freshwater fishes and the potential impacts of water projects and aquaculture activities – two categories of projects that create direct threats to freshwater fishes – are assessed. Of the 3997 such submissions to the SEIA, only 0.6% conducted any freshwater fish assessment, and only 0.1% conducted any quantitative assessment of expected impacts from the associated project. The small number of assessments was characterized by poor study design, inconsistent sampling methodology, and species misidentification. Traditional assessments failed to include freshwater fish ecology in the general assessment framework. The new strategic environmental evaluation system only underscores the need for vastly improved field sampling protocols and assessment methodologies.