Compact Surface Research Articles

The Moduli Space of Twisted Laplacians and Random Matrix Theory

Abstract Rudnick recently proved that the spectral number variance for the Laplacian of a large compact hyperbolic surface converges, in a certain scaling limit and when averaged with respect to the Weil–Petersson measure on moduli space, to the number variance of the Gaussian Orthogonal Ensemble of random matrix theory. In this article we extend Rudnick’s approach to show convergence to the Gaussian Unitary Ensemble for twisted Laplacians that break time-reversal symmetry, and to the Gaussian Symplectic Ensemble for Dirac operators. This addresses a question of Naud, who obtained analogous results for twisted Laplacians on high degree random covers of a fixed compact surface.

Types of connected components of the singular locus of the moduli space of compact Riemann surfaces

AbstractIn 2012 G. Bartolini and M. Izquierdo showed that all equisymmetric strata of Broughton’s stratification, corresponding to the actions of groups of order 2 and 3 on Riemann surfaces of genus g are contained in the same connected component $$\mathcal {C}_g^{2,3}$$ C g 2 , 3 of the singular locus $$\mathcal {S}_g$$ S g . The other components that were known to the literature were those composed of points of certain single strata. This motivated the question of whether the singular locus can contain connected components different from $$\mathcal {C}_g^{2,3}$$ C g 2 , 3 and being the union of at least two strata. The existence of such components was proved for infinitely many genera by G. Gromadzki and the author. In this paper, we will describe and classify all types of connected components of the singular locus. In particular, we prove that every connected component different than $$\mathcal {C}_g^{2,3}$$ C g 2 , 3 coincides with some Cornalba component, and we give necessary and sufficient conditions for a cyclic action to define such a component.

Investigation into the swelling and dissolution behaviour of Polymer-Excipient blends of PEO Utilising dissolution imaging

The use of dissolution imaging in analysing the behaviourof hydrophilic matrices and various types of excipients is examined in this study.The main aim was to investigate how different ratios of excipients with different solubility properties, such as lactose, microcrystalline cellulose, and dicalcium phosphate impact on the swelling properties and propranolol hydrochloride (PPN) release characteristics of polyethylene oxide matrix compacts. The surface properties of the compacts were investigated using a focus variation microscope after which dissolution studies were conducted to determine compact swelling and drug release properties. Smr2, a surface parameter representing the percentage of deeper valley structures on the surface, was used to calculate the proportion of the compact surface available for retaining lubrication (dissolution media in this case). Smr2 values of 83 and 84 were measured for the 1:1 and 1:3 PEO lactose compacts, respectively. This parameter utilised in this experiment gives an indication of the compact surface available for the initial hydration process and suggests a higher rate of hydration for the 1:1 and 1:3 PEO lactose compacts. The swelling studies revealed that a higher PEO ratio (3:1) resulted in more extensive gel layer formation as compared to the 1:3 compacts. All PEO:excipient compacts exhibited faster drug release than the compacts comprising PEO as the sole excipient. The quantity of PEO present was thus crucial in influencing the capacity of the matrix to control the release of PPN. This study underscores the potential for modifying drug release by altering the quantity of the matrix gel-former (PEO in this case) as well as the type or ratio of excipient used. The study also highlights the novelty of using UV dissolution imaging to image and quantify swelling and drug dissolution processes as well as providing qualitative observations such as channel formation which can support formulation optimisation and mechanistic understanding.

Indium Nanoparticle‐Decorated Graphite Felt Electrodes for Efficient and Long‐Cycle Zinc‐Bromine Flow Batteries

AbstractZinc‐bromine flow batteries (ZBFBs) offer the potential for large‐scale, low‐cost energy storage; however, zinc dendrite formation on the electrodes presents challenges such as short‐circuiting and diminished performance. Herein, an indium nanoparticle‐decorated graphite felt composite electrode for ZBFBs is proposed to mitigate zinc dendrite formation, improve performance, and prolong operational longevity. Using a facile in situ electrodeposition method, indium nanoparticles are uniformly and densely distributed on the carbon fiber surface, demonstrating exceptional efficacy in regulating zinc deposition. Thus, a higher prevalence of Zn (002) crystal planes and a smoother and more compact surface morphology are obtained, compared with those of thermally treated graphite felt. Furthermore, integration of the composite electrode into the negative side of a ZBFB yielded substantial improvements in cell performance, achieving an energy efficiency of 66.83% ± 0.45% at 120 mA cm−2, significantly surpassing the performance of batteries utilizing thermally treated graphite felt (52.64% ± 1.50%). Notably, the cycle life of the battery is extended by more than five‐fold with the composite electrode, underscoring the remarkable zinc deposition‐regulating capabilities of the indium nanoparticles.

Physical states and transition amplitudes in piecewise flat quantum gravity

In this paper, we show how the path integral for gravity and matter on a piecewise flat spacetime can be used to define the physical quantum gravity states and the related transition amplitudes. The physical states are given by the path integrals for open manifolds from a certain topological class, while the corresponding transition amplitudes are obtained by gluing two such open manifolds into a closed one and calculating the corresponding path integral. We also solve the problem of how to associate a quantum gravity state to an effective action. This is done by using the path integral for a closed manifold from the transition-amplitude topological class so that the state which corresponds to the effective action can be chosen to be the Hartle–Hawking or the Vilenkin wavefunction for the vacuum manifold component of the transition-amplitude manifold.

Casimir energy of hyperbolic orbifolds with conical singularities

In this article, we obtain the explicit expression of the Casimir energy for compact hyperbolic orbifold surfaces in terms of the geometrical data of the surfaces with the help of zeta-regularization techniques. The orbifolds may have finitely many conical singularities. In computing the contribution to the energy from a conical singularity, we derive an expression of an elliptic orbital integral as an infinite sum of special functions. We prove that this sum converges exponentially fast. Additionally, we show that under a natural assumption known to hold asymptotically on the growth of the lengths of primitive closed geodesics of the (2, 3, 7)-triangle group orbifold, its Casimir energy is positive (repulsive).

On the biggest purely non-free conformal actions on compact Riemann surfaces and their asymptotic properties

A continuous action of a finite group G on a closed orientable surface X is said to be gpnf (Gilman purely non-free) if every element of G has a fixed point on X. We prove that the biggest order μ(g), of a gpnf-action on a surface of even genus g≥2, is bounded below by 8g and that this bound is sharp for infinitely many even g as well. This provides, for even genera, a gpnf-action analog of the celebrated Accola-Maclachlan bound 8g+8 for arbitrary finite continuous actions. We also describe the asymptotic behavior of μ. We define M as the set of values of the formμ˜(g)=μ(g)g+1, and its subsets M+ and M− corresponding to even and odd genera g. We show that the set M+d, of accumulation points of M+, consists of a single number 8. If g is odd, then we prove that 4g≤μ(g)<8g. We conjecture that this lower bound is sharp for infinitely many odd g. Finally, we prove that this conjecture implies that 4 is the only element of M−d, leading to Md={4,8}.

On the Gromov–Hausdorff limits of compact surfaces with boundary

In this work we investigate Gromov–Hausdorff limits of compact surfaces carrying length metrics. More precisely, we consider the case where all surfaces have the same Euler characteristic. We give a complete description of the limit spaces and study their topological properties. Our investigation builds on the results of a previous work which treats the case of closed surfaces.

Fixed point index bounds for self-maps on surfacelike complexes

For a certain family of aspherical 2-complexes it is shown that a pair of inequalities, known as hyperbolic index bounds, involving fixed point indices are satisfied for all fixed point minimal self-maps. As a corollary we verify the hyperbolic index bounds for the Nielsen fixed point classes of self-maps f:X→X, when X is a finite wedge of compact surfaces each having non-positive Euler characteristic.

Electron-Surface Scattering from First-Principles.

Electron-surface scattering is important for many transport phenomena and practical applications. Particularly, the downscaling of microelectronics demands higher electrical conductivity for interconnects, which are currently based on Cu, which suffers from strong surface scattering. However, much is still unclear, such as which surface orientation causes stronger scattering. Existing theories require phenomenological parameters whose values are unknown unless fitted to experimental data or based on assumptions, thereby limiting their accuracy and predictive power. Here we present an accurate, parameter-free approach that enables an accurate calculation of electronic transport with surface scattering. Then we apply it to study the conductivities of Cu films with different surface orientations. Contrary to the common belief that a more compact surface should have higher conductivity, we find that (111) is less conductive than (001). This can be explained by the symmetry of the electronic structure. Furthermore, we propose a phenomenological model that has a better fit to the first-principles results than the conventional one. Our work offers insights into electronic transport and enables accurate calculation, understanding, and prediction for a broad range of systems where surface scattering matters.

Asymptotic mapping class groups of Cantor manifolds and their finiteness properties (with an appendix by Oscar Randal-Williams)

We prove that the infinite family of asymptotic mapping class groups of surfaces defined by Funar–Kapoudjian and Aramayona–Funar are of type F_{\infty} , thus answering a problem of Funar–Kapoudjian–Sergiescu and a question of Aramayona–Funar. This result is a specific case of a more general theorem which allows us to deduce that asymptotic mapping class groups of certain Cantor manifolds , also introduced in this paper, are of type F_{\infty} . As important examples, we obtain type F_{\infty} asymptotic mapping class groups that contain, respectively, the mapping class group of every compact surface with non-empty boundary, the automorphism group of every free group of finite rank, or infinite families of arithmetic groups.In addition, for certain types of manifolds, the homology of our asymptotic mapping class groups coincides with the stable homology of the relevant mapping class groups, as studied by Harer and Hatcher–Wahl.

Improved mechanical and thermal performance of bacterial cellulose paper through cationic cassava starch addition

Cationic particles are commonly used as wet-end additives in papermaking processes. This study evaluates the effects of cationic cassava starch (CCS) on the mechanical strength of paper made from bacterial cellulose (BC). Acetobacter xylinum was utilised in the production of bacterial cellulose (BC) paper, whereas 3‑chloro-2-hydroxypropyl trimethyl ammonium chloride (CHPTAC) was employed in the etherification process of cassava starch to synthesize CCS. Papers containing CCS displayed a more compact surface structure compared to traditional wood-based papers, reaching a brightness level of 97.3 and improving thermal and mechanical characteristics, such as higher tensile strength and is suitable for use as a separator in battery fabrication processes. The results emphasise the possibility of using CCS as a sustainable option in paper production, offering enhanced environmental and mechanical efficiency.

Jacobian varieties with group algebra decomposition not affordable by Prym varieties

The action of a finite group G on a compact Riemann surface X naturally induces another action of G on its Jacobian variety J(X). In many cases, each component of the group algebra decomposition of J(X) is isogenous to a Prym varieties of an intermediate covering of the Galois covering πG:X→X/G; in such a case, we say that the group algebra decomposition is affordable by Prym varieties. In this article, we present an infinite family of groups that act on Riemann surfaces in a manner that the group algebra decomposition of J(X) is not affordable by Prym varieties; namely, affine groups Aff(Fq) with some exceptions: q=2, q=9, q a Fermat prime, q=2n with 2n−1 a Mersenne prime and some particular cases when X/G has genus 0 or 1. In each one of this exceptional cases, we give the group algebra decomposition of J(X) by Prym varieties.

Polarization-insensitive compact frequency selective surface with higher angular stability for GSM applications

This article proposes a highly compact, angularly stable, and polarization-insensitive frequency selective surface (FSS) based bandstop filter geometry for shielding electromagnetic (EM) radiations across the GSM band. Each of the unit cells (having dimensions of 10 mm × 10 mm) is made of convoluted meander patterns, which are orthogonally printed on both sides of a dielectric substrate to design this highly compact FSS (the unit cell size is 0.029λ0· 0.029λ0, where λ0 corresponds to the resonance frequency). The metallic pattern on the top layer of the substrate selectively reflects the EM wave for one particular polarization around 890 MHz but transmits the orthogonally polarized wave. In contrast, the pattern printed on the bottom layer behaves oppositely (allowing one polarization and reflecting other polarization), thereby the overall structure exhibiting a bandstop filter response with a 3-dB stop bandwidth ranging from 800 MHz to 960 MHz under dual polarizations. In addition, the geometry exhibits a high angularly stable response till 80° angle of incidence under both transverse electric (TE) mode and transverse magnetic (TM) mode. Good agreement is also observed between the simulated and measured responses for various cases.

Preparation and characterization of ZnS/metal/ZnS transparent conductive multilayer films with different metal layers

ZnS/metal/ZnS transparent conductive multilayer films were deposited on quartz glass by pulsed laser deposition at room temperature with Au, Ag and Cu as the metal layers, and annealed in air at 100, 200 and 300℃ for 1 h. XRD patterns show that β -ZnS(111) diffraction peak of ZnS/Au/ZnS is stronger and sharper than the other two samples, indicating that its crystalline quality is the best. SEM images show the good structural homogeneity of the samples with smooth and compact film surfaces. When the annealing temperature increases from 100 to 300℃, the sheet resistance decreases first and then increases, while the carrier concentration changes in the opposite trend. The maximum transmittance (~85%) for ZnS/Au/ZnS in the visible light region is observed when the sample is annealed at 200℃. The figure of merit is calculated, and the best sample suitable for transparent conductive electrode is determined.

Enhancement the performance of MAPbI3 perovskite solar cells via germanium sulfide doping

In this study, we successfully doped Germanium sulfide (GeS) particles in methylammonium lead triiodide (CH3NH3PbI3) films to create highly efficient inverted perovskite solar cells (PSC). Various characterization methodologies were employed to examine the impact of GeS on the morphological, structural, and compositional properties of the CH3NH3PbI3 perovskite. The X-ray diffraction and Raman spectroscopy analyses of the synthesized products demonstrated that the crystallinity was enhanced, and tetragonal perovskite structures were generated without any impurities when GeS was used at a high concentration. The surface morphology results indicated that the CH3NH3PbI3 perovskite possessed thin coatings with compact, uniform, and smooth surfaces, with large grain size. The production of a high-quality CH3NH3PbI3 film from the CH3NH3PbI3: GeS phase results in improved carrier lifetime, decreased charge-trap density, and nonradiative recombination of the perovskite films. Band gap was observed to be correlated with grain size and crystallinity, which was accompanied by an increase in GeS concentration. We attained a maximum conversion efficiency of 17.46 % by fabricating solar cells with the following structure: soda-lime glass FTO/TiO2/CH3NH3PbI3: GeS/spiro-oMeTAD/Au. Based on our findings, we believe that the doping of GeS is a promising method for improving the properties of perovskite solar cells that are based on CH3NH3PbI3 thin films.

On the geometry at infinity of manifolds with linear volume growth and nonnegative Ricci curvature

We prove that an open noncollapsed manifold with nonnegative Ricci curvature and linear volume growth always splits off a line at infinity. This completes the final step to prove the existence of isoperimetric sets for given large volumes in the above setting. We also find that under our assumptions, the diameters of the level sets of any Busemann function are uniformly bounded as opposed to a classical result stating that they can have sublinear growth when the end is collapsing. Moreover, some equivalent characterizations of linear volume growth are given. Finally, we construct an example to show that for manifolds in our setting, although their limit spaces at infinity are always cylinders, the cross sections can be nonhomeomorphic.

Effect of Lipid-soluble rosemary (Rosmarinus Officinalis L.) extract (carnosic acid) on properties of microcrystalline cellulose/corn starch composite films

The development of biodegradable bioactive films is crucial due to the environmental pollution caused by petroleum-based materials and the food spoilage. Microcrystalline cellulose (MCC)/corn starch (CS) composite films containing lipid-soluble rosemary extract (carnosic acid) (RE) (1 %∼7 %, w/w) were prepared and the effect of RE on the structural, physicochemical, antimicrobial and antioxidant properties of MCC/CS composite films was investigated. The incorporation of lower RE content (1 %) promoted the interactions between film components, thus forming a compact and smooth surface and cross structures. The incorporation of RE changed the long-range order structure of MCC/CS composite film, strengthened the intermolecular interaction between film components, and improved thermal stability. The tensile strength increased from 8.35 MPa to 10.53 MPa and the water vapor permeability decreased from 0.63 to 0.58 g.mm.h-1.m-2.KPa-1. Moreover. Antibacterial (Escherichia coli and Staphylococcus aureus) and antioxidant activity were upsurged as RE contents increased. TOPSIS method indicated the MCC/CS-3 % film and MCC/CS-5 % film were the best films. The above results indicated that an effective use of RE as an enhancer and bacteriostatic agent showed a promising application in food packaging.

Stable twisted cohomology of the mapping class groups in the unit tangent bundle homology

AbstractWe compute the stable cohomology groups of the mapping class groups of compact orientable surfaces with one boundary, with twisted coefficients given by the rational homology of the unit tangent bundles of the surfaces. These coefficients define a covariant functor over the classical category associated to mapping class groups, rather than a contravariant one, and are thus out of the scope of the traditional framework to study twisted cohomological stability. A remarkable property is that the computed stable twisted cohomology is not free as a module over the stable cohomology algebra with constant rational coefficients. For comparison, we also compute the stable cohomology group with coefficients in the first rational cohomology of the unit tangent bundle of the surface, which fits into the traditional framework.

Insulating Material with Scale Components for High-Temperature and High-Pressure Water Applications.

Accurately measuring water holdup in horizontal wells is crucial for effectively using heavy oil reservoirs. The capacitance method is among the most widely used and accurate techniques. However, the absence of suitable insulating materials at high temperatures and pressures limits the effectiveness of capacitive water holdup measurement in heavy oil thermal recovery. This study introduces a new composite material based on an aviation-grade, special glass glaze as the insulating medium doped with inorganic components (CaSO4, MgSO4, Ca(OH)2, and SiO2). This new composite material demonstrates outstanding insulating performance under high-temperature and high-pressure conditions in water. A water environment with a high temperature of 350 °C and a pressure of 12 MPa considerably enhances the composite material's insulation. After 72 h of continuous use, the insulation performance remains 0.3 MΩ. The layers exhibit improved insulation and stability, maintaining integrity through five consecutive temperature shocks in 500 °C air and 20 °C water. XRD, IR, SEM, and TEM analyses reveal that the new composite material is amorphous after firing and that the addition of inorganic components improves the bonding between the glass glaze components and contributes to a denser structure. Simultaneously, SEM and TEM analyses indicate that adding inorganic components results in a smoother, crack-free, and more compact surface of the special glass glaze. This enhancement is crucial for the material's long-term stability in high-temperature and high-pressure water environments.