A novel surface-integral-equation formulation for efficient and accurate electromagnetic analyses of near-zero-index structures

We consider accurate and iteratively efficient solutions of electromagnetic problems involving homogenized near-zero-index (NZI) bodies using surface-integral-equation formulations in frequency domain. NZI structures can be practically useful in a plethora of optical applications, as they possess near-zero permittivity and/or permeability values that cannot be found in nature. Hence, numerical simulations are of utmost importance for rigorous design and analyses of NZI structures. Unfortunately, small values of electromagnetic parameters bring computational challenges in numerical solutions of homogeneous models. Conventional formulations available in the literature encounter stability issues that make them inaccurate and/or inefficient as permittivity and/or permeability approach zero. We propose a novel formulation that involves a well-balanced combination of operators and that can provide both accurate and efficient solutions of all NZI cases. Numerical results are presented to demonstrate the superior properties of the developed formulation in comparison to the conventional ones.

Potential Uranium Migration within the Geochemical Gradient of the Opalinus Clay System at the Mont Terri

Transport properties of potential host rocks for nuclear waste disposal are typically determined in laboratory or in-situ experiments under geochemically controlled and constant conditions. Such a homogeneous assumption is no longer applicable on the host rock scale as can be seen from the pore water profiles of the potential host rock Opalinus Clay at Mont Terri (Switzerland). The embedding aquifers are the hydro-geological boundaries, that established gradients in the 210 m thick low permeable section through diffusive exchange over millions of years. Present-day pore water profiles were confirmed by a data-driven as well as by a conceptual scenario. Based on the modelled profiles, the influence of the geochemical gradient on uranium migration was quantified by comparing the distances after one million years with results of common homogeneous models. Considering the heterogeneous system, uranium migrated up to 24 m farther through the formation depending on the source term position within the gradient and on the partial pressure of carbon dioxide pCO2 of the system. Migration lengths were almost equal for single- and multicomponent diffusion. Differences can predominantly be attributed to changes in the sorption capacity, whereby pCO2 governs how strong uranium migration is affected by the geochemical gradient. Thus, the governing parameters for uranium migration in the Opalinus Clay can be ordered in descending priority: pCO2, geochemical gradients, mineralogical heterogeneity.

Heat and water fluxmodeling in an earth dam

This study aims to identify the water flux in an earth dam using heat flux due to convection. Sixteen earth dams model was constructed in a hydraulic flume by varyinggeometrical and flow input parameters to identify heat and water flux.Homogeneous as well was earth dam with the clay core was built-in a hydraulic flume. Temperature measurements were doneto calculate heat flux in the experimental model. A finite element model of the earth dam using Seep/w was developed to obtain water flux,while temp/wwas to obtain heat flux. These results were used as input in Temp/w and Seep/w in Geostudio 2020. Significant reduction of the heat and water fluxwas seen while comparing the homogeneous models with central impervious core models. An increase in the heat and water flux was observed on increasing the downstream filter's length, longitudinal slope,and vice versa with the upstream slope and the thickness of the clay core. Comparing fluxesina homogeneous dam model (model 1) with the clay core model (model 9) with top width 2.4 m and bottom width 18 m in model 9, both water flux and heat flux were reduced78.46%. While comparing it with model 10, with bottom core width of 18 m and top core width of 1.9 m, both water flux and heat flux reduced by 77.72%. Heat flux measurements were found a valuable alternative to detecting water flux and seepage in an earth dam at a reduced cost.

Characterization of Three Complete Mitogenomes of Flatidae (Hemiptera: Fulgoroidea) and Compositional Heterogeneity Analysis in the Planthoppers’ Mitochondrial Phylogenomics

Although sequences of mitogenomes have been widely used for investigating phylogenetic relationship, population genetics, and biogeography in many members of Fulgoroidea, only one complete mitogenome of a member of Flatidae has been sequenced. Here, the complete mitogenomes of Cerynia lineola, Cromna sinensis, and Zecheuna tonkinensis are sequenced. The gene arrangements of the three new mitogenomes are consistent with ancestral insect mitogenomes. The strategy of using mitogenomes in phylogenetics remains in dispute due to the heterogeneity in base composition and the possible variation in evolutionary rates. In this study, we found compositional heterogeneity and variable evolutionary rates among planthopper mitogenomes. Phylogenetic analysis based on site-homogeneous models showed that the families (Delphacidae and Derbidae) with high values of Ka/Ks and A + T content tended to fall together at a basal position on the trees. Using a site-heterogeneous mixture CAT + GTR model implemented in PhyloBayes yielded almost the same topology. Our results recovered the monophyly of Fulgoroidea. In this study, we apply the heterogeneous mixture model to the planthoppers' phylogenetic analysis for the first time. Our study is based on a large sample and provides a methodological reference for future phylogenetic studies of Fulgoroidea.

An essential base of the central types of the convex theory

In this paper, we consider the model-theoretical properties of the essential base of the central types of convex theory. Also shows the connection between the center and Jonsson theory in permissible enrichment signatures. Moreover, the theories under consideration are hereditary. This article is divided into 2 sections: 1) an essential types and an essential base of central types (in this case, the concepts of an essential type and an essential base are defined using the Rudin-Keisler order on the set of central types of some hereditary Jonsson theory in the permissible enrichment); 2) the atomicity and the primeness of ϕ(x)-sets. In this paper, new concepts are introduced: the ϕ(x)-Jonsson set, the AP A-set, the AP A-existentially closed model, the ϕ(x)-convex theory, the ϕ(x)-transcendental theory, the AP A-transcendental theory. One of the ideas of this article refers to the fact that in the work of Mustafin T.G. it was noticed that any universal model of a quasi-transcendental theory with a strong base is saturated, but we generalized this result taking into account that: the concept of quasi-transcendence will be replaced by the ϕ(x)-transcendence, where ϕ(x) defines some Jonsson set; and the notion of a strong base is replaced by the notion of an essential base, but in a permissible enrichment of the hereditary Jonsson theory. The main result of our work shows that the number of fragments obtained under a closure of an algebraic or definable type does not exceed the number of homogeneous models of a some Jonsson theory, which is obtained as a result of a permissible enrichment of the hereditary Jonsson theory.

COVID-19 Dynamics: A Heterogeneous Model

The mathematical model reported here describes the dynamics of the ongoing coronavirus disease 2019 (COVID-19) epidemic, which is different in many aspects from the previous severe acute respiratory syndrome (SARS) epidemic. We developed this model when the COVID-19 epidemic was at its early phase. We reasoned that, with our model, the effects of different measures could be assessed for infection control. Unlike the homogeneous models, our model accounts for human population heterogeneity, where subpopulations (e.g., age groups) have different infection risks. The heterogeneous model estimates several characteristics of the epidemic more accurately compared to the homogeneous models. According to our analysis, the total number of infections and their peak number are lower compared to the assessment with the homogeneous models. Furthermore, the early-stage infection increase is little changed when population heterogeneity is considered, whereas the late-stage infection decrease slows. The model predicts that the anti-epidemic measures, like the ones undertaken in China and the rest of the world, decrease the basic reproductive number but do not result in the development of a sufficient collective immunity, which poses a risk of a second wave. More recent developments confirmed our conclusion that the epidemic has a high likelihood to restart after the quarantine measures are lifted.

The Geometry of Marked Contact Engel Structures

A contact twisted cubic structure$$({\mathcal M},\mathcal {C},{\varvec{\upgamma }})$$ ( M , C , γ ) is a 5-dimensional manifold $${\mathcal M}$$ M together with a contact distribution $$\mathcal {C}$$ C and a bundle of twisted cubics $${\varvec{\upgamma }}\subset \mathbb {P}(\mathcal {C})$$ γ ⊂ P ( C ) compatible with the conformal symplectic form on $$\mathcal {C}$$ C . The simplest contact twisted cubic structure is referred to as the contact Engel structure; its symmetry group is the exceptional group $$\mathrm {G}_2$$ G 2 . In the present paper we equip the contact Engel structure with a smooth section $$\sigma : {\mathcal M}\rightarrow {\varvec{\upgamma }}$$ σ : M → γ , which “marks” a point in each fibre $${\varvec{\upgamma }}_x$$ γ x . We study the local geometry of the resulting structures $$({\mathcal M},\mathcal {C},{\varvec{\upgamma }}, \sigma )$$ ( M , C , γ , σ ) , which we call marked contact Engel structures. Equivalently, our study can be viewed as a study of foliations of $${\mathcal M}$$ M by curves whose tangent directions are everywhere contained in $${\varvec{\upgamma }}$$ γ . We provide a complete set of local invariants of marked contact Engel structures, we classify all homogeneous models with symmetry groups of dimension $$\ge 6$$ ≥ 6 up to local equivalence, and we prove an analogue of the classical Kerr theorem from Relativity.

Revisiting the dust destruction efficiency of supernovae

ABSTRACT Dust destruction by supernovae is one of the main processes removing dust from the interstellar medium (ISM). Estimates of the efficiency of this process, both theoretical and observational, typically assume a shock propagating into a homogeneous medium, whereas the ISM possesses significant substructure in reality. We self-consistently model the dust and gas properties of the shocked ISM in three supernova remnants (SNRs), using X-ray and infrared (IR) data combined with corresponding emission models. Collisional heating by gas with properties derived from X-ray observations produces dust temperatures too high to fit the far-IR fluxes from each SNR. An additional colder dust component is required, which has a minimum mass several orders of magnitude larger than that of the warm dust heated by the X-ray emitting gas. Dust-to-gas mass ratios indicate that the majority of the dust in the X-ray emitting material has been destroyed, while the fraction of surviving dust in the cold component is plausibly close to unity. As the cold component makes up virtually all the total dust mass, destruction time-scales based on homogeneous models, which cannot account for multiple phases of shocked gas and dust, may be significantly overestimating actual dust destruction efficiencies, and subsequently underestimating grain lifetimes.