Regular Band Research Articles

Practical approaches for evaluating radiative heat from high pressure hydrogen flame

As the construction of hydrogen stations and other hydrogen-related facilities progresses, it becomes increasingly crucial for safety designs to account for scenarios where leaked hydrogen might ignite. Since a hydrogen flame is usually invisible, detection must rely on radiative heat or temperature. While it is possible to predict accurate radiative heat flux from a high pressure hydrogen jet flame through detailed numerical calculations of hydrogen combustion with its radiation, the objective of this study is to provide a simpler and more accurate prediction method. Previous experimental data of radiative heat flux, Qr from high pressure hydrogen jet flames were compiled, and a simple experimental equation Qr=1463.3(Lo/Lf)−2.32 was derived, where Lf and Lo represent the flame length and the distance perpendicular to the flame axis from the midpoint of the flame length to the observer, respectively. Radiative heat fluxes were computed through detailed numerical simulations using three types of water vapor radiation models: Goody's narrow random band model, the exponential broad band model by Edward and Elsasser's narrow regular band model. The temperature and water vapor partial pressure distributions obtained from numerical simulations were used as input conditions. The results were found to be in good agreement with the experimental equation. Moreover, a simple diagram representing the radiative heat flux from a hydrogen flame was derived using the method of cylinder-like approximation. The results of this study show that if the hydrogen pressure and leakage aperture diameter are given, the radiative heat flux at a certain distance can be predicted with high accuracy. Additionally, the average value of emissivity for the hydrogen diffusion flame was found to be on the order of 0.03.

Effect of Preheating on the Mechanical Workability Improvement of High-Strength Electrical Steels during Tandem Cold Rolling

Cold-rolled silicon steel strip products are widely used as the main soft magnetic components in cores of electrical motors, generators, and transformers. In the case of rotating electrical machines, the so-called non-oriented electro-technical steels are normally applied. They are characterized by a similar behaviour to the induced magnetic field found in all sheet plane directions. The kind of soft magnetic alloys that defined herein not only possess an isotropy of electromagnetic properties, but also high mechanical strength; such alloys are called high-strength electro-technical (HSET) steels. These commercially produced HSET steels contain a high silicon content in the range of 3–4 wt.%. However, if the silicon content exceeds 3%, the machinability of Fe–Si alloys is dramatically reduced and they become much more brittle as a consequence. According to this, regular hot band brittle damage occurs during cold deformation at a high-speed tandem rolling mill. In accordance with these reasons, the production of thin high-strength silicon steel grades using the traditional methods of cold rolling deformation is extremely problematic and it is characterised by a high degree of steel sheet mechanical damage. In this scientific work, the effect of preheating hot-rolled strips on their mechanical workability improvement during tandem cold rolling was investigated. The results of this study indicate that the cold rolling of hot bands at elevated temperatures increases their resistance to brittle failure and mechanical plasticity. Moreover, the mathematical simulation clearly demonstrates that residual stress is distributed relatively homogeneously across the thickness of samples, which were cold rolled at 100 °C in contrast to the same ones deformed at room temperature.

Left regular bands of groups and the Mantaci–Reutenauer algebra

We develop the idempotent theory for algebras over a class of semigroups called left regular bands of groups (LRBGs), which simultaneously generalize group algebras of finite groups and left regular band (LRB) algebras. Our techniques weave together the representation theory of finite groups and LRBs, opening the door for a systematic study of LRBGs in an analogous way to LRBs. We apply our results to construct complete systems of primitive orthogonal idempotents in the Mantaci–Reutenauer algebra MRn[G] associated to any finite group G. When G is abelian, we give closed form expressions for these idempotents, and when G is the cyclic group of order two, we prove that they recover idempotents introduced by Vazirani.

Investigation of the multi-spectral line output characteristics of a multi-atmospheric CO2 pulsed laser

We have investigated the multi-spectral line output characteristics of a CO2 pulsed laser at multi-atmospheric pressure. The pulse waveforms, wavelengths, and energies of the output spectral lines and the small-signal gains of the full spectrum were measured at 3, 4, and 6 atm. To explain the experimental results and predict the output at higher pressure, a modified six-temperature multi-frequency dynamic model of the regular and sequence band lines was developed. The output spectrum varying from the 10P to 9R band with the increase of pressure was studied theoretically and experimentally. In addition, the gains of the 9R(16), 9P(16), 10R(16), and 10P(16) lines at 3 to 14 atm were simulated and measured, providing insights into variation regulation of the four band gains as pressure increases.

Lasing at a stationary inflection point

The concept of lasers based on the frozen mode regime in active periodic optical waveguides with a 3rd-order exceptional point of degeneracy (EPD) is advanced. The frozen mode regime in a lossless and gainless waveguide is associated with a stationary inflection point (SIP) in the Bloch dispersion relation, where three Bloch eigenmodes coalesce forming the frozen mode. As a practical example, we consider an asymmetric serpentine optical waveguide (ASOW). An ASOW operating near the SIP frequency displays a large group delay of a non-resonant nature that scales as the cube of the waveguide length, leading to a strong gain enhancement when active material is included. Therefore, a laser operating in the close vicinity of an SIP has a gain threshold that scales as a negative cube of the waveguide length. We determine that this scaling law is maintained in the presence of small distributed losses, such as radiation associated with waveguide bends and roughness. In addition, we show that although gain causes a distortion in the modes coalescing at the SIP, the properties of the frozen mode are relatively resistant to such small perturbations and we still observe a large degree of exceptional degeneracy for gain values that bring the system above threshold. Finally, our study also reveals that lasing near an SIP is favored over lasing near a photonic band edge located in close proximity to the SIP. In particular, we observe that an SIP-induced lasing in an ASOW displays lower gain threshold compared to lasing near the photonic regular band edge (RBE), even though the SIP resonance has a lower quality factor than the RBE resonance.

Right Clifford restriction semigroups

Right C-restriction semigroups are the common generalizations of right C-rpp semigroups and right C-lpp semigroups. The structure of such a semigroup is established in terms of the [Formula: see text]-product of a right regular band and a C-restriction semigroup. As its applications, we give the structures of right C-rpp semigroups and right C-lpp semigroups. Also, we give the dual wreath product structure of right C-restriction semigroups. These results extend the related results in (Semigroup Forum 68 (2004) 280–292) and (Algebra Colloquium 14 (2007) 285–294).

Degenerate Distributed Feedback Photonic Structure With Two Gratings Exhibiting Degenerate Band Edge

We propose a degenerate version of the Bragg condition, associated to a degenerate band edge (DBE). A standard Bragg condition can be implemented using a periodic grating that operates at the regular band edge. The structure we propose to realize a DBE is made of two stacked identical gratings that form two coupled periodic waveguides with broken mirror symmetry. The occurrence of the DBE is verified by using both an eigenmode solver and the calculations of scattering parameters, using full-wave simulations. The proposed structure is a good candidate to conceive a degenerate distributed feedback lasers operating at the DBE.

Cu(II)-Metallized Three-Layered Cu–8HQ Complex with Hierarchical Crystallite Morphologies Synthesized via Reaction–Diffusion

Self-organization of regular band patterns of the precipitate via a reaction-diffusion (RD) framework is called Liesegang phenomenon. This non-equilibrium system is emerging as an efficient method for synthesizing materials with unique morphologies that may have desired properties. The formation of continuous precipitation inside a band with poor control over the shape and size of sparingly soluble salts has been well documented. However, only a few reports on forming organic-inorganic bonds are available. In the present work, we demonstrate the formation of 2D frameworks of bis-(8-hydroxyquinoline) copper(II) in the agar gel via RD. The macroscopic particles were dumbbell-shaped, with aspect ratios ranging from 2.7 (inner bands) to 0.7 (outer bands). The particles were composed of ribbon-shaped crystallites at the microscopic level, each with three layers of parallelogram prismatic monoclinic sheets stacked over one another, which could easily be exfoliated. The powder X-ray diffraction patterns at low angles and the surface areas of the crystallites indicated the formation of metal-organic frameworks. It was observed that the sizes of the particles could be tuned by controlling the extent of diffusion using reactant concentrations. Since such heterostructures have energy storage capacity, the cyclic voltammograms of the unexfoliated and exfoliated materials showed that they fall in the pseudocapacitor category with potential application as the electrode material. The frameworks were further characterized by techniques such as optical and electron microscopy, X-ray diffraction, IR spectroscopy, and UV-visible spectrophotometry.

Economic ordering quantity inventory model with verhulst’s demand under fuzzy uncertainty for geographical market

Inventory plays an important role in the production process. One of the primary reasons why inventory management modeling is essential for the industry is because it will suffer immensely if there are insufficient food products to stock during the shutdown period. By determining the combined optimal cost of the retailers and wholesalers, this research significantly improves the service of the supply chain from wholesaler to retailer. The stochastic number for the imperfect perishable items is provided in this inventory study. By altering the parameter values, the uniform distribution is used to calculate these damaged items. This approach identifies the backordering quantity for both regular and uncertain fish band circumstances. The cost of maintaining the inventory will rise significantly of increased wastage due to a rise in deteriorating, which will result in the loss of perishable food items. The primary goal of this research paper is to transport them without being destroyed until they reach their desired consumers. By determining the back ordering quantity during a shutdown, one can decrease the overall expenses incurred by the retailers. These computational complexity measures are proven in a fuzzy uncertain environment. The main goal of this paper is to analyze the variation of demand during the unanticipated period and find the optimum total cost of the perishable products. The growth of production in a particular area at a particular time, interconnect with another large number of products in the same area and is calculated by Verhulst’s demand with time depended on proficiency rate. Concerning the existing Verhulst’s demand pattern for the production process, this paper introduced that for perishable items in a fuzzy unanticipated situation. A bountiful system analysis is performed to find the cost function under fuzzy environment and the sensitivity analysis is carried out to perform the key representation constant.

Triple Ladder Lumped Circuit With Sixth Order Modal Exceptional Degeneracy

We introduce a circuit topology based on a simple triple-ladder circuit realized with lumped reactive components that provides a sixth order degenerate band-edge (6DBE). The 6DBE is a special kind of sixth-order exceptional point of degeneracy in a lossless and gainless periodic ladder. This degeneracy provides a very flat band edge in the phase-frequency dispersion diagram. The proposed topology exhibits unique structured resonance features associated with a high loaded Q-factor. We investigate the Floquet-Bloch modes in an infinite-length periodic triple-ladder and their dispersion relation using the S parameter formalism. We also provide the approximate analytic expressions of the eigenmodes and dispersion relation around the degenerate point based on the Puiseux series expansion. We investigate the filtering characteristics of a finite-length structure terminated with loads to highlight the special properties of the 6DBE compared to ladders with regular band edge (RBE) and fourth order degenerate band edge (DBE). The circuit framework introduced here with a 6DBE can be exploited in designing novel high Q-factor oscillators, filters, sensors, and pulse shaping networks.

Cell complexes, poset topology and the representation theory of algebras arising in algebraic combinatorics and discrete geometry

In recent years it has been noted that a number of combinatorial structures such as real and complex hyperplane arrangements, interval greedoids, matroids and oriented matroids have the structure of a finite monoid called a left regular band. Random walks on the monoid model a number of interesting Markov chains such as the Tsetlin library and riffle shuffle. The representation theory of left regular bands then comes into play and has had a major influence on both the combinatorics and the probability theory associated to such structures. In a recent paper, the authors established a close connection between algebraic and combinatorial invariants of a left regular band by showing that certain homological invariants of the algebra of a left regular band coincide with the cohomology of order complexes of posets naturally associated to the left regular band. The purpose of the present monograph is to further develop and deepen the connection between left regular bands and poset topology. This allows us to compute finite projective resolutions of all simple modules of unital left regular band algebras over fields and much more. In the process, we are led to define the class of CW left regular bands as the class of left regular bands whose associated posets are the face posets of regular CW complexes. Most of the examples that have arisen in the literature belong to this class. A new and important class of examples is a left regular band structure on the face poset of a CAT(0) cube complex. Also, the recently introduced notion of a COM (complex of oriented matroids or conditional oriented matroid) fits nicely into our setting and includes CAT(0) cube complexes and certain more general CAT(0) zonotopal complexes. A fairly complete picture of the representation theory for CW left regular bands is obtained.

Extensions of left regular bands by $${\mathcal {R}}$$-unipotent semigroups

In this paper we describe \({\mathcal {R}}\)-unipotent semigroups being regular extensions of a left regular band by an \(\mathcal {R}\)-unipotent semigroup T as certain subsemigroups of a wreath product of a left regular band by T. We obtain Szendrei’s result that each E-unitary \({\mathcal {R}}\)-unipotent semigroup is embeddable into a semidirect product of a left regular band by a group. Further, specialising the first author’s notion of \(\lambda \)-semidirect product of a semigroup by a locally \({\mathcal {R}}\)-unipotent semigroup, we provide an answer to an open question raised by the authors in [Extensions and covers for semigroups whose idempotents form a left regular band, Semigroup Forum 81 (2010), 51-70].

Finite Submonoids of Free Left Regular Bands with Unit

We deal with subsemigroups of a free left regular band Fn of rank n. It is proved that any finite, right hereditary, left regular band with a linearly ordered support semilattice is embedded in Fn for some n.

Compaction Banding in High‐Porosity Carbonate Rocks: 2. A Gradient‐Dependent Plasticity Model

AbstractBased on the experimental study on Saint‐Maximin limestone presented in a companion paper (Abdallah et al., 2020), a gradient‐dependent plasticity model is developed to account for the key role of porosity heterogeneity in the formation and propagation of compaction bands. The constitutive law, developed in the frame of a micromorphic continuum theory, contains two hardening variables: the porosity and its second gradient. A calibration method for the additional micromechanical parameters is proposed. Data from the companion paper are used in a four‐step calibration procedure. First, the standard Cauchy component is calibrated by means of the macroscopic stress‐strain curves. An Asymmetric Cam‐Clay (ACC) model is adopted for the yield surface. The dominant wavelength of the porosity heterogeneity of the material is evaluated by applying the fast Fourier transformation (FFT) on several porosity profiles obtained on samples before loading. This wavelength is interpreted as the material length that appears in the model. In addition to the deformation maps computed from digital volume correlation (DVC), a method that evaluates the second gradient of porosity is developed to calibrate the hardening laws. A linear stability analysis (LSA) is performed to calibrate the higher‐order elastic modulus. The constitutive model is implemented in a finite element code, and triaxial loading experiments are simulated. The numerical results are consistent with the experimental data in terms of the onset of compaction bands, their thickness, and plastic strain. The size effect of the sample is explored, and a regular band spacing, comparable to the band thickness, is obtained.

Mechanism of ice-band pattern formation caused by resonant interaction between sea ice and internal waves in a continuously stratified ocean

In polar oceans, ice-band patterns are frequently observed around the ice edge in the winter, where sea ice production and melting continually occur. A better understanding of such fundamental processes in marginal ice zones (MIZs) may be key to accurate predictions of sea-ice evolution. Ice bands exhibit approximately 10-km-scale regular band spacings, and their long axes turn to the counter-clockwise (clockwise) with respect to the wind direction in the Northern (Southern) Hemisphere. We formulate a theory that is relevant for a continuously stratified ocean and compare the theoretical results with the numerical-model results and satellite observations. The numerical results quantitatively agree well with the theory. In particular, resonance condition, on which the phase speed of internal wave matches with the ice-band propagation speed, is always satisfied even if wind speed becomes slow. This is because there are an infinite number of baroclinic modes in continuously stratified ocean. We also show that an ice-band pattern emerges from a random initial ice concentration even though the wind is homogeneous. Plume-like ice bands along ice edge, which are frequently observed by satellites, are well explained by the pattern formation from random noise. Various effects of the ice-band formation were explored with respect to the relationship between the initial ice concentration and the wind direction, ice roughness, ice thickness, temporal variation of wind, and the Coriolis parameter.

Noncommutative inclusion–exclusion, representations of left regular bands and the Tsetlin library

We find a semigroup [Formula: see text], whose category of partial representations contains the representation category [Formula: see text] of the free left regular band [Formula: see text]. We use this to construct a resolution for the absolute kernel of a representation of [Formula: see text], for which the kernel [Formula: see text] of the Markov operation in the Tsetlin library model is a prominent example. We obtain a formula for the dimension of the absolute kernel, generalizing the equality of the dimension of [Formula: see text] to the number of derangements of order [Formula: see text].

Photoluminescence evolutions and physical mechanism discussions of Sr1.95-(Ca/Ba) MgSi2O7:Eu2+ phosphors

Abstract With Ca and Ba substitutions for Sr, the photoluminescence evolution of Sr2MgSi2O7:0.05Eu2+ has been investigated and discussed. With spectra and crystal structure analysis, the photoluminescence intensity variation, the emission band shift, the chromaticity coordinate evolution and the thermal stability changes have been revealed. The corresponding physical mechanisms have been discussed. With Ca/Ba substitution, the emission spectra show entire red/blue shift; while the photoluminescence intensity are both quenched. The crystal structure and lattice parameter variations were refined. Based on the reflection spectra measurements, the forbidden band gap of the series of Sr1.95-x(Ca/Ba)xMgSi2O7:0.05Eu2+ phosphors were calculated. Both for Ca and Ba substitution, the forbidden band gap is elevated. The regular emission band red/blue shifts are ascribed to the increased/decreased crystal splitting of the Eu2+ 5d electron. Based on the estimation of the crystal splitting intensity and the calculation of the forbidden band gap, the Eu2+ 5d electron transition process and the Ca/Ba substitution tuning process are illustrated. The thermal stability of Sr2MgSi2O7: Eu2+ is promoted with Ca/Ba substitution. The thermal quenching mechanism of this phosphor can be confirmed to self-ionization. This work proves cation substitution is a suitable route to tune the photoluminescence property of the phosphors. The revealed physical mechanisms are in favor of understanding the tuning process of the phosphors.

Modeling of a picosecond CO2 amplifier with electrical and optical pumping.

As a long-wavelength laser with strong energy storage capacity and large scale of amplification, the CO2 laser is considered an effective amplifier in the next-generation picosecond terawatt infrared laser system, but the pulse splitting effect caused by its discrete gain spectrum limits its behavior. In this paper, we have developed a specific model of a CO2 amplifier, which is optically and electrically pumped at the same time. The model is based on gas discharge that is combined with photon absorption, temperature, and wave equation. The proposed hybrid pumped CO2 amplifier scheme can increase the gain proportion of the sequence band transition (0002-1001, 0003-1002, etc.) from 12% to nearly 50% of the regular band and broaden the bandwidth of each line by over 15.8% by the overlap of the sequence band and regular band. The relative energy concentration of the first subpulse can be increased by up to 190% when the amplification factor reaches 103. The study on the model of a picosecond CO2 amplifier with electrical and optical pumping may contribute to the amplification of an ultrafast mid-infrared pulse to the terawatt or higher region.

Scanning tunneling spectroscopic study of monolayer 1T-TaS2 and 1T-TaSe2

The isostructural and isoelectronic transition-metal-dichalcogenides 1T-TaS2 and 1T-TaSe2 are layered materials with intricate electronic structures. Combining the molecular beam epitaxy growth, scanning tunneling microscopy measurements and first-principles calculations, we prepare monolayer 1T-TaS2 and TaSe2 and explore their electronic structures at the atomic scale. Both two-dimensional (2D) compounds exhibit commensurate charge density wave phase at low temperature. The conductance mapping identifies the contributions from different Ta atoms to the local density of states with spatial and energy resolution. Both 1T-TaS2 and 1T-TaSe2 monolayer are shown to be insulators, while the former has a Mott gap and the latter is a regular band insulator.

The Effect of Jazz Improvisation Instruction on Measures of Executive Function in Middle School Band Students

Research investigating links between academic achievement and active music instruction has not previously differentiated between different types of instruction. In the current study, 155 seventh- and eighth-grade middle school band students were divided into two groups. Both groups received 2 months of instruction in jazz phrasing, scales, and vocabulary, but only the experimental group was taught to improvise. All instruction was part of the warm-up routine in regular band classes. All students were tested before and after instruction on the Wisconsin Card Sorting Task (cognitive flexibility) and the classic Stroop task (inhibitory control). At posttest, eighth-grade students in the experimental group scored significantly better on cognitive flexibility with a smaller percentage of perseverative errors, whereas the treatment had no effect on seventh-grade students on this outcome. Seventh graders, but not eighth graders, in the experimental group increased their posttest scores for inhibitory control, though this result was only marginally significant. In relation to previous research, the current results strongly suggest that far-transfer effects of active music participation depend on the nature of the instruction. Results of prior and future studies should therefore be interpreted in light of the type of music-making engaged by participants.