Ray Optical Scattering from Uniform Reflective Cylindrical Metasurfaces using Surface Susceptibility Tensors

A ray optical methodology based on the uniform theory of diffraction is proposed to model electromagnetic field scattering from curved metasurfaces. The problem addressed is the illumination of a purely reflective uniform cylindrical metasurface by a line source, models the surface with susceptibilities and employs a methodology previously used for cylinders coated in thin dielectric layers [1]. The approach is fundamentally based on a representation of the metasurface using the General Sheet Transition Conditions (GSTCs) which characterizes the surface in terms of susceptibility dyadics. An eigenfunction description of the metasurface problem is derived considering both tangential and normal surface susceptibilities, and used to develop a ray optics (RO) description of the scattered fields; including the specular geometrical optical field, surface diffraction described by creeping waves and a transition region over the shadow boundary. The specification of the fields in the transition region is dependent on the evaluation of the Pekeris caret function integral and the method follows [1]. The proposed RO-GSTC model is then successfully demonstrated for a variety of cases and is independently verified using a rigorous eigenfunction solution (EF-GSTC) and full-wave Integral Equation method (IE-GSTC), over the entire domain from the deep lit to deep shadow.

Ray Optical Scattering from Uniform Reflective Cylindrical Metasurfaces using Surface Susceptibility Tensors

A ray optical methodology based on the uniform theory of diffraction is proposed to model electromagnetic field scattering from curved metasurfaces. The problem addressed is the illumination of a purely reflective uniform cylindrical metasurface by a line source, models the surface with susceptibilities and employs a methodology previously used for cylinders coated in thin dielectric layers [1]. The approach is fundamentally based on a representation of the metasurface using the General Sheet Transition Conditions (GSTCs) which characterizes the surface in terms of susceptibility dyadics. An eigenfunction description of the metasurface problem is derived considering both tangential and normal surface susceptibilities, and used to develop a ray optics (RO) description of the scattered fields; including the specular geometrical optical field, surface diffraction described by creeping waves and a transition region over the shadow boundary. The specification of the fields in the transition region is dependent on the evaluation of the Pekeris caret function integral and the method follows [1]. The proposed RO-GSTC model is then successfully demonstrated for a variety of cases and is independently verified using a rigorous eigenfunction solution (EF-GSTC) and full-wave Integral Equation method (IE-GSTC), over the entire domain from the deep lit to deep shadow.

Influence of Texture Portion and Dimple Area Density on the Tribological Characteristics of Dimple Textured Hydrodynamic Journal Bearing

There is a growing interest towards the textured bearings. The normal surface texture has the shape of micro-dimples with preselected diameter, area density and depth. The use of different amount of texturing and dimple area density, can be an effective way to improve tribological properties of textured bearing. In the present study, the tribological properties, of the dimple textured journal bearing of L/D = 2, such as attitude angle, load carrying capacity, friction variable and flow coefficient are estimated for different texture portion and dimple area density. The computationally efficient Progressive mesh densification method is implemented for the numerical solution. The governing Reynolds equation is discretized with the finite difference scheme and then solved using Gauss Seidel method coupled with Successive over relaxation scheme. The numerical results show that the flow coefficient and attitude angle has been improved significantly with texture portion variation. Similarly, when the dimple area density is varied, there is significant improvement in flow coefficient and attitude angle resulting in the maximum flow coefficient at the dimple area density of 0.25 and minimum attitude angle, at the eccentricity ratios from 0.5 to 0.7, for the dimple area density of 0.20. However, the texture portion and dimple area density have no positive influence on the load carrying capacity and friction variable.

When Activator and Inhibitor of PPARα Do the Same: Consequence for Differentiation of Human Intestinal Cells

Peroxisome proliferator-activated receptor α (PPARα) is a ligand-dependent transcription factor that plays a role in various processes including differentiation of several cell types. We investigated the role of PPARα in the differentiation of intestinal cells using HT-29 and Caco2 cell lines as a model as well as human normal colon and colorectal carcinoma tissues. We detected a significant increase in PPARα expression in differentiated HT-29 cells as well as in normal surface colon epithelium where differentiated cells are localised. Thus, it seems that PPARα may play a role in differentiation of intestinal cells. Interestingly, we found that both PPARα activators (fenofibrate and WY-14643) as well as its inhibitor (GW6471) regulated proliferation and differentiation of HT-29 cells in vitro in the same way. Both compounds led to a decrease in proliferation accompanied by a significant increase in expression of villin, intestinal alkaline phosphatase (differentiation markers). Moreover, the same trend in villin expression was observed in Caco2 cells. Furthermore, villin expression was independent of subcellular localisation of PPARα. In addition, we found similar levels of PPARα expression in colorectal carcinomas in comparison to adjacent normal epithelium. All these findings support the hypothesis that differentiation of intestinal epithelium is PPARα-independent.

The Abel map for surface singularities III: Elliptic germs

The present note is part of a series of articles targeting the theory of Abel maps associated with complex normal surface singularities with rational homology sphere links (Nagy and Némethi in Math Annal 375(3):1427–1487, 2019; Nagy and Némethi in Adv Math 371:20, 2020; Nagy and Némethi in Pure Appl Math Q 16(4):1123–1146, 2020). Besides the general theory, by the study of specific families we wish to show the power of this new method. Indeed, using the general theory of Abel maps applied for elliptic singularities in this note we are able to prove several key properties for elliptic singularities (e.g. the statements of the next paragraph), which by ‘old’ techniques were not reachable. If $$({\widetilde{X}},E)\rightarrow (X,o)$$ ( X ~ , E ) → ( X , o ) is the resolution of a complex normal surface singularity and $$c_1:{\mathrm{Pic}}({\widetilde{X}})\rightarrow H^2({\widetilde{X}},{\mathbb {Z}})$$ c 1 : Pic ( X ~ ) → H 2 ( X ~ , Z ) is the Chern class map, then $${\mathrm{Pic}}^{l'}({\widetilde{X}}):= c_1^{-1}(l')$$ Pic l ′ ( X ~ ) : = c 1 - 1 ( l ′ ) has a (Brill–Noether type) stratification $$W_{l', k}:= \{{\mathcal {L}}\in {\mathrm{Pic}}^{l'}({\widetilde{X}})\,:\, h^1({\mathcal {L}})=k\}$$ W l ′ , k : = { L ∈ Pic l ′ ( X ~ ) : h 1 ( L ) = k } . In this note we determine it for elliptic singularities together with the stratification according to the cycle of fixed components. E.g., we show that the closure of any $$W(l',k)$$ W ( l ′ , k ) is an affine subspace. For elliptic singularities we also characterize the End Curve Condition and Weak End Curve Condition in terms of the Abel map, we provide several characterization of them, and finally we show that they are equivalent.

Moderately Discontinuous Homotopy

We introduce a metric homotopy theory, which we call moderately discontinuous homotopy, designed to capture Lipschitz properties of metric singular subanalytic germs. It matches with the moderately discontinuous homology theory recently developed by the authors and E. Sampaio. The $k$-th MD homotopy group is a group $MDH^b_{\bullet }$ for any $b\in [1,\infty ]$ together with homomorphisms $MD\pi ^b\to MD\pi ^{b^{\prime}}$ for any $b\geq b^{\prime}$. We develop all its basic properties including finite presentation of the groups, long homotopy sequences of pairs, metric homotopy invariance, Seifert van Kampen Theorem, and the Hurewicz Isomorphism Theorem. We prove comparison theorems that allow to relate the metric homotopy groups with topological homotopy groups of associated spaces. For $b=1$, it recovers the homotopy groups of the tangent cone for the outer metric and of the Gromov tangent cone for the inner one. In general, for $b=\infty $, the $MD$-homotopy recovers the homotopy of the punctured germ. Hence, our invariant can be seen as an algebraic invariant interpolating the homotopy from the germ to its tangent cone. We end the paper with a full computation of our invariant for any normal surface singularity for the inner metric. We also provide a full computation of the MD-homology in the same case.

Local dynamics of non-invertible maps near normal surface singularities

We study the problem of finding algebraically stable models for non-invertible holomorphic fixed point germs f : ( X , x 0 ) → ( X , x 0 ) f\colon (X,x_0)\to (X,x_0) , where X X is a complex surface having x 0 x_0 as a normal singularity. We prove that as long as x 0 x_0 is not a cusp singularity of X X , then it is possible to find arbitrarily high modifications π : X π → ( X , x 0 ) \pi \colon X_\pi \to (X,x_0) such that the dynamics of f f (or more precisely of f N f^N for N N big enough) on X π X_\pi is algebraically stable. This result is proved by understanding the dynamics induced by f f on a space of valuations associated to X X ; in fact, we are able to give a strong classification of all the possible dynamical behaviors of f f on this valuation space. We also deduce a precise description of the behavior of the sequence of attraction rates for the iterates of f f . Finally, we prove that in this setting the first dynamical degree is always a quadratic integer.

A Modified Helmholtz Equation Least Squares Method for Reconstructing Vibroacoustic Quantities on an Arbitrarily Shaped Vibrating Structure

A modified Helmholtz equation least-square (HELS) method is developed to reconstruct vibroacoustic quantities on an arbitrarily shaped vibrating structure. Unlike the traditional nearfield acoustical holography that relies on the acoustic pressures collected on a hologram surface at a short stand-off distance to a target structure, this modified HELS method takes the partial normal surface velocities and partial acoustic pressures as the input data. The advantages of this approach include but not limited to: (1) The normal surface velocities that represent the nearfield effects are collected directly, which lead to a more accurate reconstruction of the normal surface velocity distribution; (2) The field acoustic pressures are also measured, which leads to a more accurate reconstruction of the acoustic pressure on the source surface as well as in the field; and (3) There is no need to measure the normal surface velocities over the entire surface, which makes this approach quite appealing in practice because most vibrating structures do not allow for measuring the normal surface velocities over the entire source surface as there are always obstacles or constrains around a target structure. Needless to say, regularization is necessary in reconstruction process since all inverse problems are mathematically ill-posed. To validate this approach, both numerical simulations and experimental results are presented. An optimal reconstruction scheme is developed via numerical simulations to achieve the most cost-effective reconstruction results for practical applications.

Controlling the adhesive pull-off force via the change of contact geometry

A first-order asymptotic analysis of the Griffith energy balance in the Johnson–Kendall–Roberts model of adhesive contact under non-symmetric perturbation of the contact geometry is presented. The pull-off force is evaluated in explicit form. A particular case of adhesive contact between a relatively stiff sphere and an elastic half-space is considered under the assumption that the sphere geometry is changed by the application of an arbitrary lateral normal surface loading. The effect of the sphere Poisson’s ratio on controlling the adhesive pull-off force is considered. This article is part of a discussion meeting issue ‘A cracking approach to inventing new tough materials: fracture stranger than friction’.

Stratospheric influence on the predictability of cold spells

<p>The weather-dependent planning and decision-making benefit greatly from subseasonal to seasonal (S2S) weather predictions made for up to six weeks ahead. At this timescale anomalies in the extratropical stratospheric circulation, which can last for several weeks in the Northern Hemisphere during winter, are known to affect climate at the surface and can extend the predictability of tropospheric weather conditions. The downward influence of the stratospheric circulation anomalies on the troposphere is projected by the Northern Annular Mode (NAM). Because of the long persistence of stratospheric anomalies beyond typical weather timescale, the increase in forecast skill is possible for the regions influenced by the atmospheric circulation variability associated with NAM based on the stratospheric predictor.</p><p>In this study, we investigate the predictability of the Eurasian severe and persistent cold spells during winter and its dependence on the state of the stratosphere. We first detected the below-normal surface temperature events over northern Eurasia (cold spells) in the ERA5 re-analysis. Then, to assess the predictability of these cold spells and to evaluate the skill in the probabilistic re-forecasts we divided them into groups associated with different stratospheric circulation anomalies which took place prior to the below-normal temperature events. When the stratospheric vortex is strong it is not expected to favor cold air outbreaks in this region. Therefore, in these cases, the cold air outbreaks result from internal tropospheric dynamics and their predictability is limited by the chaotic behavior of the weather systems. On the other hand, the weakening of the vortex is characterized by a more negative NAM index. This weakening is often followed by an equatorward shift of the tropospheric jets, an increase in the frequency of occurrence of tropospheric blocking, and cold air outbreaks over northern Eurasia. In these cases, the stratospheric vortex weakening can lead to the statistically significant improvement of the skill of cold air outbreak forecasts in case if the forecast model is capable of properly representing the coupling between the stratosphere and the troposphere. We show that the predictability of cold spells in the European Centre for Medium-range Weather Forecasts (ECMWF) model is enhanced under weak vortex conditions starting from week 3 before the event. We also evaluate how the surface predictability is affected by model imperfections by comparing the predictability across different S2S models.</p>