Optimal Dual Schemes for Adaptive Grid Based Hexmeshing

Hexahedral meshes are a ubiquitous domain for the numerical resolution of partial differential equations. Computing a pure hexahedral mesh from an adaptively refined grid is a prominent approach to automatic hexmeshing, and requires the ability to restore the all hex property around the hanging nodes that arise at the interface between cells having different size. The most advanced tools to accomplish this task are based on mesh dualization. These approaches use topological schemes to regularize the valence of inner vertices and edges, such that dualizing the grid yields a pure hexahedral mesh. In this article, we study in detail the dual approach, and propose four main contributions to it: (i) We enumerate all the possible transitions that dual methods must be able to handle, showing that prior schemes do not natively cover all of them; (ii) We show that schemes are internally asymmetric, therefore not only their construction is ambiguous, but different implementative choices lead to hexahedral meshes with different singular structure; (iii) We explore the combinatorial space of dual schemes, selecting the minimum set that covers all the possible configurations and also yields the simplest singular structure in the output hexmesh; (iv) We enlarge the class of adaptive grids that can be transformed into pure hexahedral meshes, relaxing one of the tight topological requirements imposed by previous approaches. Our extensive experiments show that our transition schemes consistently outperform prior art in terms of ability to converge to a valid solution, amount and distribution of singular mesh edges, and element count. Last but not least, we publicly release our code and reveal a conspicuous amount of technical details that were overlooked in previous literature, lowering an entry barrier that was hard to overcome for practitioners in the field.

Sharp Interface Capturing in Compressible Multi-Material Flows with a Diffuse Interface Method

Compressible multi-materialflows are encountered in a wide range of natural phenomena and industrial applications, such as supernova explosions in space, high speed flows in jet and rocket propulsion, underwater explosions, and vapor explosions in post accidental situations in nuclear reactors. In the numerical simulations of these flows, interfaces play a crucial role. A poor numerical resolution of the interfaces could make it difficult to account for the physics, such as material separation, location of the shocks and contact discontinuities, and transfer of the mass, momentum and heat between different materials/phases. Owing to such importance, sharp interface capturing remains an active area of research in the field of computational physics. To address this problem in this paper we focus on the Interface Capturing (IC) strategy, and thus we make use of a newly developed Diffuse Interface Method (DIM) called Multidimensional Limiting Process-Upper Bound (MLP-UB). Our analysis shows that this method is easy to implement, can deal with any number of material interfaces, and produces sharp, shape-preserving interfaces, along with their accurate interaction with the shocks. Numerical experiments show good results even with the use of coarse meshes.

Directional Proton Conductance in Bacteriorhodopsin Is Driven by 2 Concentration Gradient, Not Affinity Gradient

It is widely spread that microorganisms can harvest energy from sun light to establish electrochemical potential across cell membrane by pumping protons outward. Light driven proton pumping against a transmembrane gradient entails exquisite electronic and conformational reconfiguration at fs to ms time scales. However, transient molecular events along the photocycle of bacteriorhodopsin are difficult to comprehend from noisy electron density maps obtained from multiple experiments when the intermediate populations coexist and evolve as a function of 13 decades of time. Here I report an in-depth meta-analysis of the recent time-resolved datasets collected by several consortiums. This analysis deconvolutes the observed mixtures, thus substantially improves the quality of the electron density maps, and provides a clear visualization of the isolated intermediates from I to M. The primary photoproducts revealed here suggest a proton transfer uphill against 15 pH units is accomplished by the same physics that governs the tablecloth trick. While the Schiff base is displaced at the beginning of the photoisomerization within ~30 fs, the proton stays due to its inertia. This affinity-independent early deprotonation builds up a steep proton concentration gradient that drives the directional proton conductance toward the extracellular medium. This mechanism fundamentally deviates from the widely adopted assumption based on equilibrium processes driven by light-induced changes of proton affinities. The method of a numerical resolution of concurrent events from mixed observations is also generally applicable.

Directional proton conductance in bacteriorhodopsin is driven by concentration gradient, not affinity gradient

It is widely spread that microorganisms can harvest energy from sun light to establish electrochemical potential across cell membrane by pumping protons outward. Light driven proton pumping against a transmembrane gradient entails exquisite electronic and conformational reconfiguration at fs to ms time scales. However, transient molecular events along the photocycle of bacteriorhodopsin are difficult to comprehend from noisy electron density maps obtained from multiple experiments when the intermediate populations coexist and evolve as a function of 13 decades of time. Here I report an in-depth meta-analysis of the recent time-resolved datasets collected by several consortiums. This analysis deconvolutes the observed mixtures, thus substantially improves the quality of the electron density maps, and provides a clear visualization of the isolated intermediates from I to M. The primary photoproducts revealed here suggest a proton transfer uphill against 15 pH units is accomplished by the same physics that governs the tablecloth trick. While the Schiff base is displaced at the beginning of the photoisomerization within ~30 fs, the proton stays due to its inertia. This affinity-independent early deprotonation builds up a steep proton concentration gradient that drives the directional proton conductance toward the extracellular medium. This mechanism fundamentally deviates from the widely adopted assumption based on equilibrium processes driven by light-induced changes of proton affinities. The method of a numerical resolution of concurrent events from mixed observations is also generally applicable.

Directional proton conductance in bacteriorhodopsin is driven by concentration gradient, not affinity gradient

It is widely spread that microorganisms can harvest energy from sun light to establish electrochemical potential across cell membrane by pumping protons outward. Light driven proton pumping against a transmembrane gradient entails exquisite electronic and conformational reconfiguration at fs to ms time scales. However, transient molecular events along the photocycle of bacteriorhodopsin are difficult to comprehend from noisy electron density maps obtained from multiple experiments when the intermediate populations coexist and evolve as a function of 13 decades of time. Here I report an in-depth meta-analysis of the recent time-resolved datasets collected by several consortiums. This analysis deconvolutes the observed mixtures, thus substantially improves the quality of the electron density maps, and provides a clear visualization of the isolated intermediates from I to M. The primary photoproducts revealed here suggest a proton transfer uphill against 15 pH units is accomplished by the same physics that governs the tablecloth trick. While the Schiff base is displaced at the beginning of the photoisomerization within ~30 fs, the proton stays due to its inertia. This affinity-independent early deprotonation builds up a steep proton concentration gradient that drives the directional proton conductance toward the extracellular medium. This mechanism fundamentally deviates from the widely adopted assumption based on equilibrium processes driven by light-induced changes of proton affinities. The method of a numerical resolution of concurrent events from mixed observations is also generally applicable.

Shortcuts for biomonitoring programs of stream ecosystems: Evaluating the taxonomic, numeric, and cross-taxa congruence in phytoplankton, periphyton, zooplankton, and fish assemblages

Different biological groups can be used for monitoring aquatic ecosystems because they can respond to variations in the environment. However, the evaluation of different bioindicators may demand multiple financial resources and time, especially when abundance quantification and species-level identification are required. In this study, we evaluated whether taxonomic, numerical resolution and cross-taxa can be used to optimize costs and time for stream biomonitoring in Central Brazil (Cerrado biome). For this, we sampled different biological groups (fish, zooplankton, phytoplankton, and periphyton) in stream stretches distributed in a gradient of land conversion dominated by agriculture and livestock. We used the Mantel and Procrustes analyses to test the association among different taxonomic levels (species to class), the association between incidence and abundance data (numerical resolution), and biological groups. We also assessed the relative effect of local environmental and spatial predictors on different groups. The taxonomic levels and numerical resolutions were strongly correlated in all taxonomic groups (r > 0.70). We found no correlations among biological groups. Different sets of environmental variables were the most important to explain the variability in species composition of distinct biological groups. Thus, we conclude that monitoring the streams in this region using bioindicators is more informative through higher taxonomic levels with occurrence data than abundance. However, different biological groups provide complementary information, reinforcing the need for a multi-taxa approach in biomonitoring.

Directional proton conductance in bacteriorhodopsin is driven by concentration gradient, not affinity gradient

It is widely spread that microorganisms can harvest energy from sun light to establish electrochemical potential across cell membrane by pumping protons outward. Light driven proton pumping against a transmembrane gradient entails exquisite electronic and conformational reconfiguration at fs to ms time scales. However, transient molecular events along the photocycle of bacteriorhodopsin are difficult to comprehend from noisy electron density maps obtained from multiple experiments when the intermediate populations coexist and evolve as a function of 13 decades of time. Here I report an in-depth meta-analysis of the recent time-resolved datasets collected by several consortiums. This analysis deconvolutes the observed mixtures, thus substantially improves the quality of the electron density maps, and provides a clear visualization of the isolated intermediates from I to M. The primary photoproducts revealed here suggest a proton transfer uphill against 15 pH units is accomplished by the same physics that governs the tablecloth trick. While the Schiff base is displaced at the beginning of the photoisomerization within ~30 fs, the proton stays due to its inertia. This affinity-independent early deprotonation builds up a steep proton concentration gradient that drives the directional proton conductance toward the extracellular medium. This mechanism fundamentally deviates from the widely adopted assumption based on equilibrium processes driven by light-induced changes of proton affinities. The method of a numerical resolution of concurrent events from mixed observations is also generally applicable.

Photoinduced isomerization sampling of retinal in bacteriorhodopsin

Photoisomerization of retinoids inside a confined protein pocket represents a critical chemical event in many important biological processes from animal vision, non-visual light effects, to bacterial light sensing and harvesting. Light driven proton pumping in bacteriorhodopsin entails exquisite electronic and conformational reconfigurations during its photocycle. However, it has been a major challenge to delineate transient molecular events preceding and following the photoisomerization of the retinal from noisy electron density maps when varying populations of intermediates coexist and evolve as a function of time. Here I report several distinct early photoproducts deconvoluted from the recently observed mixtures in time-resolved serial crystallography. This deconvolution substantially improves the quality of the electron density maps hence demonstrates that the all-trans retinal undergoes extensive isomerization sampling before it proceeds to the productive 13-cis configuration. Upon light absorption, the chromophore attempts to perform trans-to-cis isomerization at every double bond coupled with the stalled anti-to-syn rotations at multiple single bonds along its polyene chain. Such isomerization sampling pushes all seven transmembrane helices to bend outward, resulting in a transient expansion of the retinal binding pocket, and later, a contraction due to recoiling. These ultrafast responses observed at the atomic resolution support that the productive photoreaction in bacteriorhodopsin is initiated by light-induced charge separation in the prosthetic chromophore yet governed by stereoselectivity of its protein pocket. The method of a numerical resolution of concurrent events from mixed observations is also generally applicable.