Infinite Surface Research Articles

The two-phase problem for harmonic measure in VMO and the chord-arc condition

Let Ω + ⊂ R n + 1 \Omega ^+\subset \mathbb {R}^{n+1} be a bounded δ \delta -Reifenberg flat domain, with δ > 0 \delta >0 small enough, possibly with locally infinite surface measure. Assume also that Ω − = R n + 1 ∖ Ω + ¯ \Omega ^-= \mathbb {R}^{n+1}\setminus \overline {\Omega ^+} is an NTA (non-tangentially accessible) domain as well and denote by ω + \omega ^+ and ω − \omega ^- the respective harmonic measures of Ω + \Omega ^+ and Ω − \Omega ^- with poles p ± ∈ Ω ± p^\pm \in \Omega ^\pm . In this paper we show that the condition that log ⁡ d ω − d ω + ∈ VMO ⁡ ( ω + ) \log \dfrac {d\omega ^-}{d\omega ^+} \in \operatorname {VMO}(\omega ^+) is equivalent to Ω + \Omega ^+ being a chord-arc domain with inner unit normal belonging to VMO ⁡ ( H n | ∂ Ω + ) \operatorname {VMO}(\mathcal {H}^n|_{\partial \Omega ^+}) .

Adsorption isotherms and removal of lead (II) and cadmium (II) from aqueous media using nanobiochar and rice husk

Removal of Cd(II) and Pb(II) from aqueous solutions is a challenging task and the search for novel adsorbents is underway. This study examined the efficiency of nanobiochar (NB) and rice husk (RH) in the adsorption and removal of Cd(II) and Pb(II) from water. The effect of various physicochemical parameters such as initial pH, initial Cd and Pb concentration, adsorbent dosage, and contact time were tested. SEM/EDX images confirmed the adsorption of Pb and Cd with surface physical and chemical changes. The maximum Pb removal was noted at pH 6 using NB (96%) and at pH 8 for RH (90%), and the maximum Cd removal by NB was recorded at 8 pH (91%) and by RH at pH 6 (87%). The decline in adsorption intensity at lower pH suggested protonation of the adsorbent surface causing cation-cation repulsion. Most of the adsorption occurred within the initial 60 min. A continuous gradual increase in the adsorption with time suggested multilayer formation. Of the three isotherms, the Freundlich model fits the present data best, implying an infinite surface coverage and indicating the potential for multilayer adsorption of Pb and Cd on the surfaces of RH and NB adsorbents. In conclusion, this study highlights the promising potential of NB as a cost-effective adsorbent for the removal of Cd and Pb ions from aqueous solutions.

Chemical Reaction, Thermal Radiation and Newtonian Heating Impacts on Unsteady MHD Rotating Casson Fluid Flow Past an Infinite Vertical Porous Surface

Chemical Reaction, Thermal Radiation and Newtonian Heating Impacts on Unsteady MHD Rotating Casson Fluid Flow Past an Infinite Vertical Porous Surface

Erosion of surfaces by trapped vortices

Two two-dimensional free boundary problems describing the erosion of solid surfaces by the flow of inviscid fluid in the presence of trapped vortices are considered. The first problem tackles an initially flat, infinite fluid-solid interface with uniform flow at infinity and a vortex in equilibrium above the surface. The second involves flow around a finite body with a trailing Föppl-type vortex pair. The conformal invariance of the complex potential permits both problems to be formulated as a Polubarinova–Galin (PG) type equation in which the time-dependent eroding surface in the physical z-plane is mapped to the fixed boundary of the ζ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\zeta $$\\end{document}-disk. The Hamiltonian governing the equilibrium position of the vortex (or vortex pair in the second problem) is also found from the same map. In each problem, the PG equation giving the conformal map is found numerically and the time-dependent evolution of the interface and vortex location is determined. Different models governing the erosion of the interface are investigated in which the normal velocity of the boundary depends on some given function of the fluid flow velocity at the boundary. Typically, in the infinite surface case, erosion leads to the formation of a symmetric valley beneath the vortex which, in turn, moves downward toward the interface. A finite body undergoes erosion which is asymmetric in the flow direction leading to a flattening of the lee surface of the body so displaying some similarity to the experiments and associated viscous theory of Ristroph et al, Moore et al (Proc Natl Acad Sci 109(48):19606–19609, 2012, Phys Fluids 25(11):116602, 2013).

Quadratic differentials and foliations on infinite Riemann surfaces

Quadratic differentials and foliations on infinite Riemann surfaces

Energetic processes and thermodynamic analysis of the spinning Kiselev black hole with cloud of strings

Here we study the impact of the string clouds, the quintessence dark energy and other spacetime parameters on the center-of-mass energy, Penrose-process and thermodynamic properties of a stationary black hole solution of the Einstein field equations. We observe that the three distinct horizons i.e the Cauchy horizon, the event horizon and the cosmological horizon exist when the spin parameter a of the black hole is less than its extremal value aE. Interestingly we see that the infinite redshift surface of the black hole is not much sensitive to the quintessence parameter γ. It is sensitive to the parameter a and it increases as the parameter a increases. Further, we notice that an increase in the string cloud parameters b, quintessence parameter γ and a make the radius of the ergosphere of the black hole larger. We also notice that a rise in the parameter a makes the innermost stable circular orbits (ISCO) smaller and for an increase in the parameter b and γ the ISCO becomes larger than that for the Kerr spacetime. For the center-of-mass energy of the spinning black hole with quintessence and cloud of strings we observe that it can be arbitrarily high only for the extremal case of the black hole for a specific range of values of the angular momentum of the colliding particles. We notice that the Penrose-process is more efficient for smaller values of the string cloud parameter b and the parameter γ has no significant impact on this process. Moreover we see that an increase in the parameters b, γ and a cause the Helmholtz free energy to increase and opposite is true for the temperature of this type of rotating black hole. We learn that the area and entropy of the black hole are also depend on the parameters b, γ and a, and their effect make the entropy smaller. Interestingly we find a range of the horizon radius for the thermodynamic stability of the black hole. To get more information about the thermodynamic quantities of the rotating black hole with quintessence and cloud of strings, we plot them for different ranges of the spacetime parameters.

Polarization conversion and lateral shifts in multilayered structure with finitely-gapped topological surface states

Abstract The polarizatison conversion and the Goos–Hänchen (GH) shifts of the reflected electromagnetic wave for the multilayered structure made of topological insulator (TI) layers with finite surface energy gap are investigated. The transfer matrix formalism is adopted to analyze the reflection of electromagnetic wave through the multilayered structure, and the influences of surface energy gap, thickness and number of the TI layers are discussed. We find that maximum polarization conversion rate can be obtained with appropriate surface energy gap of TI, and within a certain range of finite energy gap, the polarization conversion effect is stronger than that for the case under the infinite surface energy gap limit. Greater polarization conversion rate for TI with small surface energy gap can be found than that for TI with larger energy gap in some range of layer numbers. At large incident angles the GH shifts vary considerably with the layer number for TI with relatively larger energy gap. Result of the combined influence of surface energy gap and layer number shows that, there exists both the positive and negative enhancement peaks of the GH shifts, and for smaller energy gap, fewer TI layers are required to obtain the transition between positive and negative GH shifts.

Corner- and edge-mode enhancement of near-field radiative heat transfer.

It is well established that near-field radiative heat transfer (NFRHT) can exceed Planck's blackbody limit1 by orders of magnitude owing to the tunnelling of evanescent electromagnetic frustrated and surface modes2-4, as has been demonstrated experimentally for NFRHT between two large parallel surfaces5-7 and between two subwavelength membranes8,9. However, although nanostructures can also sustain a much richer variety of localized electromagnetic modes at their corners and edges10,11, the contributions of such additional modes to further enhancing NFRHT remain unexplored. Here we demonstrate both theoretically and experimentally a physical mechanism of NFRHT mediated by the corner and edge modes, and show that it can dominate the NFRHT in the 'dual nanoscale regime' in which both the thickness of the emitter and receiver, and their gap spacing, are much smaller than the thermal photon wavelengths. For two coplanar 20-nm-thick silicon carbide membranes separated by a 100-nm vacuum gap, the NFRHT coefficient at room temperature is both predicted and measured to be 830W m-2 K-1, which is 5.5 times larger than that for two infinite silicon carbide surfaces separated by the same gap, and 1,400 times larger than the corresponding blackbody limit accounting for the geometric view factor between two coplanar membranes. This enhancement is dominated by the electromagnetic corner and edge modes, which account for 81% of the NFRHT between the silicon carbide membranes. These findings are important for future NFRHT applications in thermal management and energy conversion.

Magnetohydrodynamic influence on fractional nanofluid convection in infinite vertical porous media with constant heat flux

This study investigates the complex dynamics governing free convection flow in nanofluids under Magnetohydrodynamics (MHD) within a porous medium along an infinite vertical surface. We specifically focus on scenarios involving constant and uniform heat flux as well as heat sources. The governing equations, incorporating the Boussinesq approximation, continuity, and momentum equations, are formulated and solved using Caputo-Fabrizio derivatives and Laplace transforms. This comprehensive approach integrates the Boussinesq approximation and Caputo-Fabrizio fractional derivatives, while the use of Laplace transforms enables precise analytical solutions. Additionally, our investigation highlights the significant impact of nanometer-sized copper particles on fluid properties, transforming the behavior from Newtonian (water-like) to non-Newtonian. This transformation profoundly affects thermal conductivity and velocity behavior within the system. Overall, this research establishes a robust foundation for future studies and provides a framework for exploring non-Newtonian nanofluid systems in the context of MHD-driven free convection flow.

Aeroelastic tailoring of stiffened cantilever plate using composites and structural layouts: A parametric study

AbstractThis paper studies the aeroelasticity of a stiffened cantilever plate using composite material and novel structural layouts. A comprehensive parametric study is conducted to determine the influence of different design parameters on the aeroelastic boundaries. Design parameters include plate sweep angle, ply orientation, stringer cross-section and stringer sweep angle. Nastran is used to run the aeroelastic analysis, and the process is automated using ${\rm{Matla}}{{\rm{b}}^{}}$ . The structure of the plate is modelled using laminate elements whereas the stringers are modelled using the Euler-Bernoulli beam elements. The unsteady aerodynamic loads are modelled using doublet-lattice method (DLM) and the structural and aerodynamic meshes are connected using an infinite plate surface (IPS) spline. A mesh sensitivity analysis is conducted to ensure fine meshes for the aerodynamics and structure. The study’s findings demonstrate the benefits of employing forward swept (Fw) stringers since it increases flutter speed by almost 38% compared to the unswept stringers case and prevents divergence. Moreover, the static aeroelastic analysis illustrates that the utilisation of Fw swept stringers can reduce the average tip displacement and tip twist effectively. T-shaped stringers are recommended to stiffen the plate due to their lower impact on the total mass of the plate. In some configurations, the structural layout has a much higher effect on the aeroelastic instabilities when compared to the material effect (ply orientation). However, results suggest combining both for some cases to get balanced washin and washout effects.

Multipole Approach to the Dynamical Casimir Effect with Finite-Size Scatterers.

A mirror subjected to a fast mechanical oscillation emits photons out of the quantum vacuum-a phenomenon known as the dynamical Casimir effect (DCE). The mirror is usually treated as an infinite metallic surface. Here, we show that, in realistic experimental conditions (mirror size and oscillation frequency), this assumption is inadequate and drastically overestimates the DCE radiation. Taking the opposite limit, we use instead the dipolar approximation to obtain a simpler and more realistic treatment of DCE for macroscopic bodies. Our approach is inspired by a microscopic theory of DCE, which is extended to the macroscopic realm by a suitable effective Hamiltonian description of moving anisotropic scatterers. We illustrate the benefits of our approach by considering the DCE from macroscopic bodies of different geometries.

Unsteady dynamical analysis of convective hydromagnetic thermal migration of chemically reacting tiny species with dissipation and radiation in an inclined porous plate

The essence of the current examination is to carry out thermofluid parametric sensitivity with time-varying thermal migration of chemically reactive tiny species across an oscillating infinite plate surface. The impact of thermal motile tiny particles under the influence of many other oscillating flow parameters has yet to be investigated; hence the results obtained in this research are novel. Using a suitable non-dimensional variable, the leading PDEs (partial differential equations) are transmuted into dimensionless PDEs, ensuring equations are numerically solved using the MAPLE built-in approach. The numerical values produced in a limited scenario are linked with the outcomes found in the literature to validate the precision of the numerical approach utilized. The fluctuations in the profiles of the velocity, temperature, and concentration, in addition to the wall friction and rate of thermal and solutal transport, are illustrated via graphs and tables due to the modification of the critical parameters. The endmost results of the study concede that increasing permeability quantity and thermal and solutal buoyancy impellers intensify the fluid velocity. In contrast, a converse tendency is perceived with magnetic parameter and also, wall friction acts opposite to the velocity. The fluid temperature attenuated with dilation of the Prandtl number and radiation parameter, whilst a contrary trend was perceived with Eckert number. The increasing thermo-diffusion helps to develop fluid concentration whilst the Schmidt number and chemical reaction displayed opposite trend. Further, we achieved a tremendous conformity between the current findings and genuine results in the literature.

Two Results on End Spaces of Infinite Type Surfaces

Two Results on End Spaces of Infinite Type Surfaces

An inverse gas chromatography study of the adsorption of organics on zeolite and zeolite/iron oxyhydroxide composite at the infinite and finite surface coverage

The surfaces of natural (NZ) and zeolite/iron oxyhydroxide composite (ZFe) samples were analysed by means of inverse gas chromatography (IGC) using the adsorption data of organic non-polar and polar probes, in the infinite and finite-dilution regimes, in the temperature range 483?513 K. The dispersive components of the free energy of adsorption, ?S, determined by the Gray method, decreased with increasing temperature for both zeolites. The specific interactions were characterised by the specific free adsorption energy change, ?Ga S, the specific enthalpy change of adsorption, ?Ha S, as well as the donor and acceptor interaction parameters (KA, KD) and the basic character of the NZ and ZFe was evidenced. The adsorption isotherms of n-hexane, benzene, chloroform and tetrahydrofuran (THF) were determined under finite surface coverage and used to estimate the specific surface area and the adsorption energy distribution. The adsorption capacity of the ZFe was higher than for NZ for all the investigated adsorbates. The specific surface areas and pore size distributions were also determined using nitrogen adsorption?desorption isotherms, i.e., the BET method. It was observed that the nature of the adsorbate and the properties of the solid surface of the initial and modified samples governed the uptake of adsorbates.

3D Monte Carlo surface-atmosphere radiative transfer modelling with DART

Significant errors can arise if the adjacency effect (i.e., the contribution of neighbouring pixels to the radiance of a pixel) is neglected in the interpretation of remote sensing images. For example, adjacency radiances can account for >30% of the signal at the top of the atmosphere (TOA) of a white sand-lined coastline (Bulgarelli and Zibordi, 2018). This paper shows that 3D radiative transfer (RT) modelling can quantify this phenomenon. It presents a new 3D Monte Carlo surface-atmosphere RT modelling in the DART RT model, and a resulting virtual 3D Earth-Atmosphere laboratory for accurate simulation of atmospheric RT, including the adjacency effect. It was first validated with the atmosphere model SMART-G for 2D scenes: relative difference is 0.20% in TOA directional reflectance of infinite black surface for solar zenith equal to 60°, and 0.03% in TOA nadir reflectance of a black disc inside infinite white Lambertian surface, for solar zenith equal to 0° and 30°. Then, the adjacency effect on the TOA radiance and TOA albedo of a 3D scene was studied for a circular city (radius 2 km) surrounded by a forest (dimension 10 km), for four Sentinel-2A bands (blue, green, red, near infrared). Its contribution to TOA nadir radiance reaches ∼20% in the near infrared band, and increases with viewing zenith angle (VZA): ∼60% if VZA = 80°. The 3D scene TOA albedo was calculated after adapting the DART Bidirectional Reflectance Factor (BRF) camera to simulate TOA radiance for all upward directions at any angular resolution. For Sentinel-2A’s four bands, the adjacency effect influences the TOA albedo of the circular city by up to 10% for the green band and up to 27% for the near infrared band, well above the maximum uncertainty 5% usually required in land surface applications. The adjacency effect of the city neighbourhood 3D structure was studied by replacing it by a Lambertian surface with its albedo. The city nadir TOA radiance changed by up to 1.3% with very small change in TOA albedo (<0.5%). This new modelling greatly improves DART potential for accurate simulation of atmospheric effects. It is in the DART version freely available for research and education (https://dart.omp.eu).

Asymptotic Behavior of a Parametric Algebraic Surface

Starting from the concept of infinite branches and approximation surfaces, we present a method to compute infinite branches and surfaces having the same asymptotic behavior as an input parametric surface. The results obtained in this work represent a breakthrough for the study of surfaces and their applications.

Surface Houghton groups

AbstractFor every $$n\ge 2$$ n ≥ 2 , the surface Houghton group$${\mathcal {B}}_n$$ B n is defined as the asymptotically rigid mapping class group of a surface with exactly n ends, all of them non-planar. The groups $${\mathcal {B}}_n$$ B n are analogous to, and in fact contain, the braided Houghton groups. These groups also arise naturally in topology: every monodromy homeomorphism of a fibered component of a depth-1 foliation of closed 3-manifold is conjugate into some $${\mathcal {B}}_n$$ B n . As countable mapping class groups of infinite type surfaces, the groups $$\mathcal {B}_n$$ B n lie somewhere between classical mapping class groups and big mapping class groups. We initiate the study of surface Houghton groups proving, among other things, that $$\mathcal {B}_n$$ B n is of type $$\text {F}_{n-1}$$ F n - 1 , but not of type $$\text {FP}_{n}$$ FP n , analogous to the braided Houghton groups.

Laminations and 2-filling rays on infinite type surfaces

The loop graph of an infinite type surface is an infinite diameter hyperbolic graph first studied in detail by Juliette Bavard. An important open problem in the study of infinite type surfaces is to describe the boundary of the loop graph as a space of geodesic laminations. We approach this problem by constructing the first examples of 2-filling rays on infinite type surfaces. Such rays have strong filling properties while failing to correspond to points on the boundary of the loop graph. As such they may be thought of as “fake boundary points.” We give multiple constructions using both a hands-on combinatorial approach and an approach using train tracks and automorphisms of flat surfaces. In addition, our approaches are sufficiently robust to describe all 2-filling rays with certain other basic properties as well as to produce uncountably many distinct mapping class group orbits.

Exceptional Spatial Variation of Charge Injection Energies on Plasmonic Surfaces.

Charge injection into a molecule on a metallic interface is a key step in many photoactivated reactions. We employ the many-body perturbation theory and compute the hole and electron injection energies for CO2 molecule on an Au nanoparticle with ∼3,000 electrons and compare it to results for idealized infinite surfaces. We demonstrate a surprisingly large variation of the injection energy barrier depending on the precise molecular position on the surface. Multiple "hot spots," characterized by low energy barriers, arise due to the competition between the plasmonic coupling and the degree of hybridization between the molecule and the substrate. The charge injection barrier to the adsorbate on the nanoparticle surface decreases from the facet edge to the facet center. This finding contrasts with the typical picture in which the electric field enhancement on the nanoparticle edges is considered the most critical factor.

The aesthetic of nomadism and the logic of perception in creative action (Recurrences in the geographies of the sensed)

The artwork was born from the womb of flat surfaces that have neither specific direction nor destination. It emanates from infinite chaotic surfaces, overlapping and contradicting, intertwining and entwining vertically and horizontally in ways that are not subject to logical geometrical norms. Despite all the chaos and emptiness, existence remains steadfast in its elements and its primitive colors because of its interchangeable event. Art does not differ from nature. Perception brings them together in a mixture of colors on the surface of the painting. The artist transfers his infinite perceptions to an expression of what draws man to the world to endless ideas and sensations expressing the instinctive inattentiveness of existence. As it is an artistic event multiplying the desire to seek victory in the world and belief in life in its diversity, dissonance, and multiplicity. It validates life against death, consolidates fun, and exalts joy and forces of nature against transcendence and divine ethics.