Singular Properties Research Articles

Sustainable Nitrogen Photofixation Promoted by Carbon Nitride Supported Bimetallic RuPd Nanoparticles under Mild Conditions

In this work, we developed a sustainable catalytic system based on bimetallic RuPd nanoparticles (4.6 ± 1.1 nm) supported on graphitic carbon nitride for the photofixation of nitrogen to ammonia in water at 25 °C. The ammonia production rates, expressed in terms of the NH4+ formed, reached up to 1389.84 μmol·g–1·h–1, which was much superior to those observed for the monometallic ones. This excellent result can be attributed to the beneficial synergism between the two metals that leads to singular catalytic properties. Also, the bimetallic nanoparticles seem to offer a suitable condition to trap the photoexcited electrons from the semiconductor support, favoring the photoreaction. In addition, ethanol, a renewable biomass-derived compound, was used as an environment-friendly sacrificial agent, which afforded even better ammonia production when compared to previously reported studies applying methanol, a common agent chosen in the N2 photofixation process.

Climbing three-Reggeon ladders: Four-loop amplitudes in the high-energy limit in full color

We show that an iterative solution of rapidity evolution equations with a leading-order kernel renders the entire signature-odd tower of next-to-next-to-leading logarithmic (NNLL) contributions to partonic $2\ensuremath{\rightarrow}2$ amplitudes in the Regge limit computable in full color. The result, which universally holds in any gauge theory, corresponds to a set of three-Reggeon ladder diagrams. In this setting we compute the NNLL amplitude to four loops in dimensional regularization through finite corrections. Furthermore, by contrasting the result with the exponentiation properties of soft singularities we determine the four-loop correction to the soft anomalous dimension at this logarithmic accuracy. The latter features quartic Casimir contributions beyond those appearing in the cusp anomalous dimension. Finally, in the case of $\mathcal{N}=4$ super Yang-Mills, we also determine the finite hard function at four loops through NNLL in full color.

A new survey to the nonlinear electrical transmission line model

In this paper, we find new travelling wave solutions to the nonlinear electrical transmission line model. Exponential function method is applied. This model is used to the voltage behaviors in electrical transmission lines. Under a suitable choice of control parameters, we plot the figures along with contour surfaces of new solutions by using computational programs such as Mathematica, Maple and Matlab. Some information about the behavior of voltage on the electrical lines is extracted. The hyperbolic, periodic or singular properties are reported.

Discrete soliton solutions of the fractional discrete coupled nonlinear Schrödinger equations: Three analytical approaches

The fractional discrete coupled nonlinear Schrödinger equations are solved on account of the modified Riemann–Liouville fractional derivative and Mittag–Leffler function. By using the fractional generalized Riccati method, generalized Mittag–Leffler function method and fractional generalized tanh–sech function method, some new analytical discrete solutions constructed by generalized trigonometric and hyperbolic functions are obtained, including discrete fractional bright soliton, dark soliton, combined soliton, and periodic solutions. In order to illustrate the effect of fractional order parameter on dynamics of fractional discrete soliton, some results in this study are illustrated graphically. Results indicate that although the combined wave is made up of singular coth function, it does not exhibit the singular property in the discrete case. Moreover, two kinds of scalar soliton solutions are found. These results could be of great significance to further study complex nonlinear discrete physical phenomena.

Padé approximant approach to singular properties of quantum gases: the ideal cases

In this paper, we show how to recover the low-temperature and high-density information of ideal quantum gases from the high-temperature and low-density approximation by the Padé approximant. The virial expansion is a high-temperature and low-density expansion and in practice, often, only the first several virial coefficients can be obtained. For Bose gases, we determine the BEC phase transition from a truncated virial expansion. For Fermi gases, we recover the low-temperature and high-density result from the virial expansion.

Controlling Heat Conduction with Nonlinear-Transformation Cloaking

Recently, coordinate transformation method can be used to design invisibility cloaks for many types of waves, including heat conduction. The main difficulties encountered implementing the cloaking devices may be due to singular and anisotropic thermodynamic properties after coordinate transformation. This paper designs a nonlinear cloak with tunable thermodynamic parameters from a thermal diffusion path perspective to control thermal conduction. A theory of nonlinear-transformation thermodynamics is given and a nonlinear thermal diffusion path equation for thermal conduction is derived. A broadband thermal cloak is constructed with layered homogeneous and isotropic materials based on a nonlinear transformation. The cloaking performance of the nonlinear-transformation cloak can be adjusted by varying a design parameter, which affects thermal diffusion in the inner region of the cloak. Both the cloaks can exhibit detouring thermal diffusion around the inclusion, while the cloak designed in this paper has more flexibility in guiding heat conduction by changing the value of the design parameter. Numerical simulations demonstrate that the nonlinear-transformation cloak is effective in shielding the heat diffusion from outer region of the cloak. The methodology developed in this paper provides a useful approach to flexibly adjusting the thermal diffusion path according to different engineering requirements.

Initial Morphology and Feedback Effects on Laser-Induced Periodic Nanostructuring of Thin-Film Metallic Glasses.

Surface nanostructuring by femtosecond laser is an efficient way to manipulate surface topography, creating advanced functionalities of irradiated materials. Thin-film metallic glasses obtained by physical vapor deposition exhibit microstructures free from grain boundaries, crystallites and dislocations but also characterized by a nanometric surface roughness. These singular properties make them more resilient to other metals to form laser-induced nanopatterns. Here we investigate the morphological response of Zr65Cu35 alloys under ultrafast irradiation with multipulse feedback. We experimentally demonstrate that the initial columnar microstructure affects the surface topography evolution and conditions the required energy dose to reach desired structures in the nanoscale domain. Double pulses femtosecond laser irradiation is also shown to be an efficient strategy to force materials to form uniform nanostructures even when their thermomechanical properties have a poor predisposition to generate them.

Zn(ferulate)-LSH Systems as Multifunctional Filters.

Excessive UV solar radiation exposure causes human health risks; therefore, the study of multifunctional filters is important to skin UV protective ability and also to other beneficial activities to the human organism, such as reduction of reactive oxygen species (ROS) responsible for cellular damages. Potential multifunctional filters were obtained by intercalating of ferulate anions into layered simple metal hydroxides (LSH) through anion exchange and precipitation at constant pH methods. Ultrasound treatment was used in order to investigate the structural changes in LSH-ferulate materials. Structural and spectroscopic analyses show the formation of layered materials composed by a mixture of LSH intercalated with ferulate anions, where carboxylate groups of ferulate species interact with LSH layers. UV-VIS absorption spectra and in vitro SPF measurements indicate that LSH-ferulate systems have UV shielding capacity, mainly UVB protection. The results of reactive species assays show the ability of layered compounds in capture DPPH•, ABTS•+, ROO•, and HOCl/OCl− reactive species. LSH-ferulate materials exhibit antioxidant activity and singular optical properties that enable their use as multifunctional filters.

A Singularly P-Stable Multi-Derivative Predictor Method for the Numerical Solution of Second-Order Ordinary Differential Equations

In this paper, a symmetric eight-step predictor method (explicit) of 10th order is presented for the numerical integration of IVPs of second-order ordinary differential equations. This scheme has variable coefficients and can be used as a predictor stage for other implicit schemes. First, we showed the singular P-stability property of the new method, both algebraically and by plotting the stability region. Then, having applied it to well-known problems like Mathieu equation, we showed the advantage of the proposed method in terms of efficiency and consistency over other methods with the same order.

Symmetry between the anisotropic N behavior in the lattice under high pressures and the formation of expanded austenite

The nitrogen expanded austenite (γN or the S-phase), easily attainable by nitriding processes of FCC chromium-containing materials such as stainless steel (SS), Ni-based superalloys and CoCr alloys, discloses singular properties such as strong anisotropic expansion and crystal direction-dependent diffusion. These fundamental aspects were undertaken here from an experimental-theoretical approach. The S-phase was produced by plasma nitriding on SS 316L powder grains, and the material was submitted to quasi-hydrostatic compression-decompression experiments up to 30 GPa with in situ structural analyses. The experimental results agreed very well with a solid mechanics-based analysis. With this methodology – that was effective for modified surfaces – the anisotropic nitrogen reallocation in the lattice was found to obey a same linear relation during both compression (the S-phase decay) and nitriding (the S-phase formation). The transition from austenite with low nitrogen content – CN (the first-order expansion) to the S-phase (colossal saturated second-order) was featured by inversion of relative magnitudes, between 111 and 100, of the K〈ϕ〉=E〈ϕ〉31−2ν〈ϕ〉, elastic moduli E〈ϕ〉 and Poisson's ratios ν〈ϕ〉 (ϕ=hkl), all of them dependent on the orientation factor Γ[ϕ]. Rates of compression/expansion between 111 and 100 were affected accordingly. Such phenomena was concluded to arise from the inversion of the anisotropy factor, from Aγ>1 to AγN<1, which is an intrinsic property of the nitrided austenite and rules the aforementioned anisotropy inversions. Stress-induced nitrogen redistribution among crystal directions (at constant temperature) promoted changes in CN and affected elastic constants (Sij). It let the elastic modulus evolve with stresses applied on the solid. The elastic properties Sij and E〈ϕ〉 of the S-phase were determined at different pressure ranges, including pressures close to the atmospheric condition.

Porosity and permeability variability across a chalk reservoir in the Danish North Sea: Quantitative impacts of depositional and diagenetic processes

Abstract The Upper Cretaceous to Lower Paleocene Chalk Group in the North Sea comprises important reservoir targets for hydrocarbon and energy storage. The quantitative impacts of mineralogy, chalk diagenesis and oil saturation on petrophysics are often based on general trends that cannot be directly applied to reservoir engineering. The present study aims at identifying quantitatively the individual effects of mineralogy, compaction and cementation, and oil saturation on porosity and permeability by means of detailed samplings and mineralogical and petrophysical analyses from base to top of the Kraka reservoir. Special attention is brought to the visual inspection of the rock fabric and its variations across the reservoir in order to better constrain interpretations and establish relationships within an otherwise scattered dataset. Porosity and permeability variations are categorised into two trends, a mineralogical and diagenetic trend, which can both form tight rock. For chalk containing >7% quartz and > 4% clay, porosity decreases linearly from 35% to 21% and permeability from 0.5 mD to 0.07 mD with increasing quartz content. The amount of quartz rather than clay appears as an effective tool to estimate the petrophysical properties of impure chalk. Below 7% quartz and 4% clay, compaction and cementation decrease porosity and permeability in two steps along transects from oil- to water-bearing intervals. A first step of predominantly mechanical compaction reducing porosity and permeability from >41% to 37% and from 3 to 3.5 mD to 1.5–2.5 mD, respectively, is followed by a phase of chemical compaction and cementation that further deteriorates petrophysical properties. In Ekofisk Fm., stylolitised chalk and deposits located adjacent to chert horizons display singular petrophysical properties that do not fit the observed trends. The outliers likely result from phases of local chemical compaction and early cementation associated with chert formation. Porosity-permeability functions and uncertainty analyses are also proposed for the different controlling factors and at different scales of observation. The proposed petrophysical relationships are instrumental in building more realistic reservoir models and can assist geoscientists in interpreting and upscaling the large amount of geological data collected in chalk fields.

Polarization singularities in light scattering by small particles

Using full-wave numerical simulations and analytical multipole expansions we investigated the properties of real-space polarization singularities that emerge in light scattering by subwavelength particles. We considered spherical and torus particles made of dielectric or perfect-electric-conductor material. We determined the topological indices and the trajectories of electric-field polarization singularities in both the near-field and far-field regions. In the far-field region, a total of four singularities are identified and the sum of their polarization topological indices is two, independent of the particle's geometric shape. In the near-field region, the polarization singularities strongly depend on the particle's shape and the polarization of incident light, and their index sum is not governed by the Poincar\'e-Hopf theorem anymore due to the non-transverse nature of the fields. From near field to far field, a flipping of sign can happen to the polarization topological indices of the C lines. The far-field properties of the singularities can be well explained by the interference of the excited multipoles, but their near-field properties can be strongly affected by the evanescent fields that are not captured by the multipole expansions. Our work uncovers the important relationship between particles' geometric properties and the polarization singularities of their scattering field. The results can be applied to manipulate polarization singularities in nanophotonic systems and could generate novel applications in optical sensing.

Dimers, orientifolds and anomalies

We study 4d mathcal{N} = 1 gauge theories engineered via D-branes at orientifolds of toric singularities, where gauge anomalies are cancelled without the introduction of non-compact flavor branes. Using dimer model techniques, we derive geometric criteria for establishing whether a given singularity can admit anomaly-free D-brane configurations purely based on its toric data and the type of orientifold projection. Our results therefore extend the dictionary between geometric properties of singularities and physical properties of the corresponding gauge theories.

A Unified Mathematical Formalism for First to Third Order Dielectric Response of Matter: Application to Surface-Specific Two-Colour Vibrational Optical Spectroscopy

To take advantage of the singular properties of matter, as well as to characterize it, we need to interact with it. The role of optical spectroscopies is to enable us to demonstrate the existence of physical objects by observing their response to light excitation. The ability of spectroscopy to reveal the structure and properties of matter then relies on mathematical functions called optical (or dielectric) response functions. Technically, these are tensor Green’s functions, and not scalar functions. The complexity of this tensor formalism sometimes leads to confusion within some articles and books. Here, we do clarify this formalism by introducing the physical foundations of linear and non-linear spectroscopies as simple and rigorous as possible. We dwell on both the mathematical and experimental aspects, examining extinction, infrared, Raman and sum-frequency generation spectroscopies. In this review, we thus give a personal presentation with the aim of offering the reader a coherent vision of linear and non-linear optics, and to remove the ambiguities that we have encountered in reference books and articles.

Generation of multi-contour plane curves using vortex beams

We propose a simple method for the generation of multi-contour plane curves based on vortex beam illumination of an optical element calculated using the Whittaker integral and parametric curve definition. The effect of splitting the contour of the curve into several lines is based on the optical fulfillment of the differentiation. Spiral phase plates can be used to perform the radial Hilbert transformation as an analog of the differentiation operation independent of the direction. In this paper, we use the invariance property of the vortex phase singularity of a laser beam both during propagation in free space and when passing through lens systems. Thus, when a vortex beam illuminates an optical element designed to form a focal curve, two operations are simultaneously performed: splitting the contour of the light curve and introducing a phase gradient along this curve. The splitting of the contour is applied in optical capture and manipulation of opaque particles. A split contour of the light curve can serve as light barriers for opaque particles, as well as for capturing several transparent microparticles simultaneously. Phase gradient generation is also in demand in various applications, since a transverse energy flow is generated in a certain direction.

Beyond Erdős-Kunen-Mauldin: Shift-compactness properties and singular sets

The Kestelman-Borwein-Ditor Theorem asserts that a non-negligible subset of R which is Baire (= has the Baire property, BP) or measurable is shift-compact: it contains some subsequence of any null sequence to within translation by an element of the set. Here effective proofs are recognized to yield (i) analogous category and Haar-measure metrizable generalizations for Baire groups and locally compact groups respectively, and (ii) permit under V=L construction of co-analytic shift-compact subsets of R with singular properties, e.g. being concentrated on Q, the rationals.

Concepts of methodology for digitalization of additional education of children and youth

The preconditions for the research are based on sustained trends of the influence of development rates of digital economy, information space in Belarus on dynamics of digital transformation of additional education of children and youth (AECY). Analysis of AECY digital transformation revealed specific properties of didactic singularity of information education environment, network clustering of resources, dynamics of media environment contour, e-technologization of didactics. The established preconditions of stability of AECY digitization as a constant of transfer to regulations predetermined the aim of this work: development, substantiation of methodological concepts of AECY digitization. The research methods included theoretical and empirical analysis, expert appraisals, simulation, forecasting. The results are comprised of development of a set of organizational and network, environmental, instrumental, technological, institutional concepts of scientific methodology of AECY digitization. The obtained results were verified in the project titled “Implementation of Republican methodological cluster as a resource of development of additional education of children and youth” (2017-2020) on the premises of National Center of Artistic Activity of Children and Youth (Minsk) in accordance with the Program of innovations of the Ministry of Education, Belarus. The novelty of the results is in introduction of the following categories into scientific usage of pedagogical science: didactic singularity of information and education environment, structure of media environment contour. The novelty of the results is reflected in authentic intelligent product of scientific and practical significance in the context of Belarus National Strategy of Sustainable Social and Economic Development–2030.

Screening method of mildronate and over 300 doping agents by reversed-phase liquid chromatography-high resolution mass spectrometry

Considering the huge amount of substances associated with athletic performance improvement, current doping control analysis requires a comprehensive screening method, which leads to the detection of prohibited substances of different physico-chemical properties. This comprehensiveness associated with instrumental approaches based on high resolution mass spectrometry has allowed the development of extremely sensitive and selective detection methods. Furthermore, it is desirable the method to be simple, fast and straightforward. Mildronate is a highly polar quaternary amine, classified as metabolic modulator by the World Anti-Doping Agency (WADA). The inclusion of mildronate in the screening strategy is a challenge considering its singular physicochemical properties, compared to numerous doping agents of low and medium polarity. For this purpose, a method combining solid-phase extraction (SPE) and dilute-and-shoot approach has been developed and validated, allowing the detection of mildronate and other 332 prohibited substances. In the sample preparation protocol, the enzymatic deconjugation step and SPE conditions were stressed to enable the recovery of mildronate without jeopardizing the detection of other doping agents. The C18/18% SPE cartridge without any type of ionic interaction, associated with the dilute-and-shoot approach proved to be effective for all monitored substances. The instrumental method employed was based on liquid chromatography using a reversed-phase column in a 12-minute gradient coupled to a high-resolution mass spectrometry in full scan with positive and negative switching and fragmentation in the positive mode, for the most critical detection compounds. The performance of the method was evaluated regarding selectivity, precision, recovery, carry-over, limit of detection and stability, following the recommendations of WADA.

High accurate pseudo-spectral Galerkin scheme for pantograph type Volterra integro-differential equations with singular kernels

Spectral and pseudo-spectral Galerkin techniques, by using the standard Jacobi polynomials, are implemented to calculate numerically the solutions of pantograph type Volterra delay integro-differential equations that have kernels with the property of weak singularity. Because of the complex structure of the considered problems, pseudo-spectral Galerkin approaches are more desirable with respect to the spectral Galerkin approaches, since they have the property of integral approximator by using high order convergent Gauss quadrature formulas. A deep and detailed analysis of convergence of the numerical solutions to the exact solutions are given under some mild conditions such as smoothness of the solutions. Some test problems are illustrated and efficiency of the suggested numerical approach is investigated with respect to a recently proposed Jacobi pseudo-spectral collocation technique via some figures and tables experimentally.

On singularity properties of convolutions of algebraic morphisms ‐ the general case

Let $K$ be a field of characteristic zero, $X$ and $Y$ be smooth $K$-varieties, and let $G$ be a algebraic $K$-group. Given two algebraic morphisms $\varphi:X\rightarrow G$ and $\psi:Y\rightarrow G$, we define their convolution $\varphi*\psi:X\times Y\to G$ by $\varphi*\psi(x,y)=\varphi(x)\cdot\psi(y)$. We then show that this operation yields morphisms with improved smoothness properties. More precisely, we show that for any morphism $\varphi:X\rightarrow G$ which is dominant when restricted to each absolutely irreducible component of $X$, by convolving it with itself finitely many times, one can obtain a flat morphism with reduced fibers of rational singularities, generalizing the main result of our previous paper. Uniform bounds on families of morphisms are given as well. Moreover, as a key analytic step, we also prove the following result in motivic integration; if $\{f_{\mathbb{Q}_{p}}:\mathbb{Q}_{p}^{n}\rightarrow\mathbb{C}\}_{p\in\mathrm{primes}}$ is a collection of functions which is motivic in the sense of Denef-Pas, and $f_{\mathbb{Q}_{p}}$ is $L^{1}$ for any $p$ large enough, then in fact there exists $\epsilon>0$ such that $f_{\mathbb{Q}_{p}}$ is $L^{1+\epsilon}$ for any $p$ large enough.