Elementary Model Research Articles

Effect of Initial Conditions and Numerical Investigation of Instability Developed during Synthesis of TiC via Vortex Combustion at Moderate Temperatures. Model of Vortex Combustion

Despite the fact that the classical theory of combustion (CTC) operates with the simplest, elementary objects and concepts, such as: flat or slightly curved combustion fronts, elementary combustion models and potential flows. there are some problems that the CTC is only facing with a sufficiently strong curvature of the front. For example, Markstein's solution in the problem of hydrodynamic instability of a plane combustion front. In the work presented by the authors, the problem of stabilizing the titanium carbide synthesis front at moderate temperatures, which cannot be plane due to the thermo physical features of the system under consideration (Le<<1, Ze=6.03 at Тad=3300К), is similarly solved. A model of vortex combustion with a spirally curved front is proposed, the numerical analysis of which showed the stability of similar front of the TiC synthesis in the field of vortex hydrodynamic currents. The resulting solution can serve as a complete alternative to the mode of spiral spin combustion (or rather, to its branch with a low orbital speed and a low combustion temperature) of such systems, not only considered conditionally unstable in CTC, but also actually manifesting this instability during numerical calculations of the area of the existence of a spinal spot with a small radius and great curvature.

An Elementary Kinetic Model for the LSCF and LSCF-CGO Electrodes of Solid Oxide Cells: Impact of Operating Conditions and Degradation on the Electrode Response

An elementary kinetic model was developed to predict the electrochemical response of porous LSCF and LSCF-CGO electrodes. The model was validated thanks to experiments performed on symmetrical cells using a three-electrode setup. After the model calibration on polarization curves, it has been shown that the model is able to simulate accurately the experimental impedance diagram at OCP and under polarization without additional fitting. Moreover, the evolution of the electrode polarization resistance with the oxygen partial pressure is well reproduced by the model. The electrodes reaction mechanism was thoroughly analyzed and it has been shown that the transition from the bulk path to the surface path depends on the temperature, the polarization and the oxygen partial pressure. The rate-determining steps for the LSCF electrode have been identified at OCP as function of the oxygen partial pressure. Finally, a sensitivity analysis has been performed to study the impact of LSCF demixing on the electrode performances. For a given decomposition, it has been highlighted that the surface passivation would be more impacting than the decrease of the ionic conductivity. Moreover, the impact of the LSCF decomposition would be more detrimental for the electrode performances evaluated in electrolysis mode. List of symbols Roman Symbols: Surface double layer capacitance(F m−2) Double layer capacitance at the LSCF/CGO interface(F m−2) Maximum concentration of neutral oxygen atoms in LSCF(mol m−3) Vacancies concentration in LSCF(mol m−3) Vacancies concentration in LSCF at equilibrium(mol m−3) Bulk oxygen chemical diffusion coefficient in LSCF(m2 s−1) Effective diffusion for the i-th species(m2 s−1) Oxygen vancancies self-diffusion coefficient(m2 s−1) Knudsen diffusion coefficient(m2 s−1) Molecular diffusion coefficient(m2 s−1) Diffusion coefficient of the oxygen ad-ions(m2 s−1) Diffusion coefficient of the oxygen ad-atoms(m2 s−1) Diffusion coefficient of the oxygen ad-molecules(m2 s−1) Local electrode potential(V) Activation energy for the i-th species(kJ mol−1) Faraday’s constant(C mol−1) Total inlet gas flow rate(mol s−1) Hole defect in LSCF(–) Ionic current density in CGO/Electronic current density in LSCF(A m−2) Thermodynamic equilibrium constant for the i-th species(–) Forward reaction kinetic constants for R1 for the LSCF(*) or LSCF-CGO(**) electrode (*) (mol m−1 s−1) or (**) (mol m−2 s−1) Forward reaction kinetic constants for R2(m3 mol−1 s−1) Forward reaction kinetic constants for R3 for the LSCF(*) or LSCF-CGO(**) electrode (*) (m s−1) or (**) (s−1) Forward reaction kinetic constants for R4(s−1) Forward reaction kinetic constants for R5(mol2 m−1 s−1) Forward reaction kinetic constants for R6(s−1) Electrode thickness(μm) CGO Electrolyte thickness(μm) Molar mass for the i-th species(g mol−1) m Reaction order(–) Molar flux of the i-th species(mol·m−2·s−1) Oxygen atom in the LSCF lattice(–) Oxygen atom in the CGO lattice(–) Oxygen ad-ion on LSCF surface(–) Oxygen ad-atom on LSCF surface(–) Oxygen ad-molecule on LSCF surface(–) O 2 Gaseous oxygen molecule(–) Oxygen partial pressure(atm) Total pressure(atm) Mean pore radius(m) universal gas constant(J mol−1 K−1) Serial resistanceΩ cm2 Polarization resistanceΩ cm2 Adsorption site on LSCF surface(–) Specific surface area between CGO and LSCF for the LSCF(*) or LSCF-CGO(**) electrode (*) (–) or (**) (m−1) Specific surface area between LSCF and gas phase(m−1) Electrode surface(cm2) Absolute temperature(K) Fuller’s volume for the i-th species(–) Oxygen vacancy in the LSCF lattice(–) Oxygen vacancy in the CGO lattice(–) Molar fraction of species i-th species(–)Greek Symbols: Charge transfer coefficient for oxidation or reduction for the reaction Ri(–) Surface density of available sites on LSCF(mol m−2) ε X Phase volume fraction for the phase X(–) η Overpotential(V) Coverage of oxygen ions on LSCF(–) Coverage of oxygen atoms on LSCF(–) Coverage of oxygen molecules on LSCF(–) Free sites on the LSCF surface(–) Coverage rate of oxygen ions on LSCF at equilibrium(–) Coverage rate of oxygen atoms on LSCF at equilibrium(–) Coverage rate of oxygen molecules on LSCF at equilibrium(–) Free site on LSCF at equilibrium(–) Kinetic rate of chemical/electrochemical reaction (i) in the electrode(*) or at the electrolyte interface(**) (*) (mol m−3 s−1) or (**) (mol m−2 s−1) Electrochemical potential(J mol−1) Density of triple phase boundary lengths for the LSCF(*) or LSCF-CGO(**) electrode (*) (m−1) or (**) (m−2) Electronic conductivity of LSCF(S m−1) Ionic conductivity of CGO(S m−1) Effective conductivity for th i-th species(S m−1) φ i Potential(V) χ Surface electrostatic potential(V) τ X Tortuosity factor for the phase X(–)

Numerical simulation of ground‐penetrating radar data for studying the geometry of fault zone

ABSTRACTPalaeoseismology studies the footprints of ancient earthquakes to improve the knowledge about the modern seismicity of the territory. A ground‐penetrating radar (GPR), among other geophysical methods, is used for quick determination of shallow stratigraphy – displaced, oblique layers within the fault zone. GPR data interpretation from diverse and complex reflection patterns of the fault zone heavily depends on the interpreter's experience. The range of different fault zone parameters in which this method can be successfully applied has not yet been investigated. We used a numerical simulation of GPR data to determine how GPR images the elements of faults (fault plane, hanging wall, footwall) in comparison with other reflections. Furthermore, we studied which parameters have the most significant impact on GPR wave patterns. We performed a series of numerical models of a fault, changing its geometry with increasing complexity from elementary models to realistic ones. The resulting synthetic profiles allowed finding specific GPR signatures from the fault plane, the hanging wall and the footwall. We collected field GPR data from two different fault zones and examined them for verification.

Enhancement of Photovoltaic Current through Dark States in Donor‐Acceptor Pairs of Tungsten‐Based Transition Metal Di‐Chalcogenides

AbstractAs several photovoltaic materials experimentally approach the Shockley–Queisser limit, there has been a growing interest in unconventional materials and approaches with the potential to cross this efficiency barrier. One such candidate is dark state protection induced by the dipole–dipole interaction between molecular excited states. This phenomenon has been shown to significantly reduce carrier recombination rate and enhance photon‐to‐current conversion, in elementary models consisting of few interacting chromophore centers. Atomically thin 2D transition metal di‐chalcogenides (TMDCs) have shown great potential for use as ultra‐thin photovoltaic materials in solar cells due to their favorable photon absorption and electronic transport properties. TMDC alloys exhibit tunable direct bandgaps and significant dipole moments. In this work, the dark state protection mechanism has been introduced to a TMDC based photovoltaic system with pure tungsten diselenide (WSe2) as the acceptor material and the TMDC alloy tungsten sulfo‐selenide (WSeS) as the donor material. Our numerical model demonstrates the first application of the dark state protection mechanism to a photovoltaic material with a photon current enhancement of up to 35% and an ideal photon‐to‐current efficiency exceeding the Shockley–Queisser limit.

Mathieu unit cell as a template for low emittance lattices

The multi-bend achromat (MBA), which often serves as a building block for modern low-emittance storage rings, is composed of a repetition of unit cells with optimized optical functions for low emittance in the achromat center, as well as end cells for dispersion and optics matching to insertion devices. In this work, we describe the simplest stable class of unit cells that are based on a longitudinal Fourier expansion, transforming Hill equations to Mathieu equations. The resulting cell class exhibits continuously changing dipolar and quadrupolar moments along the beam path. Although this elementary model is defined by only three parameters, it captures a significant amount of notions that are applied in the design of MBAs. This is especially interesting as Mathieu cells can be viewed as an elementary extension of Christofilos' original model of alternating-gradient focusing, while their sinusoidal bending and focusing functions lend themselves to future applications in undulator-like structures. Mathieu cells can be used to estimate the range of reasonable cell tunes and put an emphasis on the combination of longitudinal gradient bending and reverse bending, as well as on strong horizontal focusing to reach emittances lower than the classic theoretical minimum emittance cell. Furthermore, the lowest emittances in this model are accompanied by small absolute momentum compaction factors.

A fresh look at the Hind Ubbelohde approach: Simple yet effective modification

Viscosity plays an essential role in the study of intermolecular interactions in liquid mixtures. Prediction of properties has gained a lot of significance in the past few months in light of the COVID pandemic, wherein most of the research laboratories are under lockdown and experimental work has come to a standstill. A study of literature shows that for past several years Hind Ubbelohde equation has been considered as a very basic and an elementary predictive model for viscosity prediction. In this investigation we have made an attempt to tweak the Hind Ubbelohde approach. The testing of present model has been carried out on 170 binary, more than 25 multicomponent liquid mixtures over a broad range of temperatures. A comparative study has been carried out employing established predictive equations using Average Absolute Percentage Deviation (AAPD) as the criterion. Grand AAPDs clearly indicate the superiority of the proposed approach in comparison to its original counterpart.

Stagnant peaked free surface released at a sloping beach

A stagnant free-surface flow is an instantaneous flow field of pure acceleration with zero velocity and a deformed surface. There exists a potential-flow acceleration field. With zero velocity and the acceleration field given, there is a limiting free-surface position which possesses one peak at its point of highest elevation. By complex analysis, it can be shown that the surface peak has a right angle. We elaborate on an elementary model of two-dimensional stagnant free-surface flow with a peak. Our model may serve to describe a situation of maximal single-wave run-up with a given energy at a uniformly sloping beach. The highest possible run-up of an incoming solitary wave corresponds to zero kinetic energy. It encompasses an idealized situation where the kinetic wave energy is converted into potential energy in a water mass piling up along the slope to become stagnant at one single moment. Multipoles with singularities outside the fluid domain may give rise to a smooth and gradual deceleration needed for a non-breaking run-up process. A pair of dipoles with an orientation perpendicular to a given slope represents the stagnant acceleration fields with the highest surface peak spatially concentrated along the slope. Thereby, a one-parameter family of surface shapes is constituted, only dependent on the slope angle. The initial flow field, the initial free surface, the initial isobars and the geometric parameters are all calculated for different slope angles.

Нечеткие фазовые траектории волновых твердотельных гироскопов

The paper considers elementary fuzzy oscillator models represented by hard and fuzzy second-order differential equations with hard and fuzzy initial conditions. Linear models describe wave processes in ring resonators of hemispherical resonator gyroscopes.We show that in the case 1 (a hard model with fuzzy initial conditions), when there is no internal friction (model 1), phase trajectories appear as a fuzzy centre shaped as an elliptical ring. When internal friction is present (model 2), phase trajectories appear as a fuzzy focus shaped as a circular logarithmic spiral. In the case 2, for a fuzzy hemispherical resonator gyroscope model with hard initial conditions, when there is no internal friction (model 1), a representative point of a fuzzy phase trajectory does not stop or increase its oscillations with time, meaning that the system is asymptotically unstable, while for the model 2 the origin singularity is a fuzzy stable focus. In the case 3, for a fuzzy hemispherical resonator gyroscope model with fuzzy initial conditions, when there is no internal friction (model 1), there is a fuzzy asymptotic instability in the model 1 of a hemispherical resonator gyroscope, while in the presence of internal friction (model 2), the phase trajectory is also a function of time and controls the asymptotic stability of the fuzzy model 2 of a hemispherical resonator gyroscope. Asymptotic stability is determined for all cases and models

Dynamics of an Atom Cavity Field System in Interacting Fock Space

In this paper, we investigate one-time passing of a V -type three-level atom through a single-mode interacting field in a cavity. We extend the idea of elementary Jaynes-Cummings model by assuming that the field vector belongs to interacting Fock space. In the process, we arrive at a state vector which will be analyzed to study the nonclassicality of the evolved state of the system.

3D Numerical Modeling of Rigid Inclusion-Improved Soft Soils Under Monotonic and Cyclic Loading—Case of a Small-Scale Laboratory Experiment

This paper is based on small-scale laboratory tests (1:10) of a rigid inclusion-improved soil under normal gravity. A low area improvement ratio (2.4%) under monotonic and cyclic loading was used. 3D numerical calculations are performed to model these tests. The proposed numerical modeling is performed by the finite element method (FEM) using the ABAQUS software. A representative elementary volume model is suggested for reducing the calculation time. A hypoplastic constitutive model (HYP model) is applied for the load transfer platform (LTP). A total of three geometrical configuration cases of the experimental tests are numerically considered including a rigid slab over a mattress of 100 mm on the reinforced soil, a mattress of 100 mm on the reinforced soil, and a rigid slab over a mattress of 50 mm on the reinforced soil. The proposed numerical results are compared to the experimental data and the previous numerical results of Houda. The cyclic response of the systems is shown in terms of soil arching and settlements. The decrease in pile efficacy and the cumulative settlements are exhibited. The HYP model allows to better simulate the soil arching mechanisms inside the LTP than the CYsoil model used in the Houda’s research work. A good concordance between the proposed numerical results and the experimental data was obtained.

Pore-scale simulation of salt fingers in porous media using a coupled iterative source-correction immersed boundary-lattice Boltzmann solver

In the conventional representative elementary volume-scale models, details of fluid movement, thermal transfer and mass transport in the porous media are relatively hard to capture, while the understanding of them is crucial in many diverse engineering and environmental applications such as running nuclear power facilities or pollutant diffusion in soil environment. In this paper, a pore-scale lattice Boltzmann method (LBM) modeling of double diffusion systems in saturated porous media is developed to investigate the role played by pore structure in the behavior of salt finger phenomena together with their fluid flow mechanism. An iterative source-correction immersed boundary method is developed to describe the solid skeleton with different boundary conditions for velocity field, heat transfer, and mass transport, respectively. The natural convection in a vertical annulus and the conjugate heat transfer problem in a two-layer horizontal annulus are employed to verify the accuracy and the applicability of the immersed boundary method for Dirichlet-type, Neumann-type and conjugate heat transfer boundary conditions, respectively. Comparisons between the present results and existing investigation show a very good agreement and demonstrate that the double diffusive process in porous media can be predicted with a good accuracy by the proposed model. Subsequently, the instability evolution process of salt finger-type of double diffusive convection in porous media is investigated, with a focus on the structure and behavior of salt fingers and the kinetic energy evolution. The obtained simulation results show that in saturated porous media, relatively large vertical mass fluxes can be generated even if the density distribution is of dynamical stability.

Elementary example of exact effective-Hamiltonian computation

We present an exact computation of effective Hamiltonians for an elementary model obtained from the Yukawa theory by going to the limit of bare fermions being infinitely heavy and bare bosons being at rest with respect to the fermions that emit or absorb them. The coupling constant can be arbitrarily large. The Hamiltonians are computed by solving the differential equation of the renormalization group procedure for effective particles (RGPEP). Physical fermions, defined in the model as eigenstates of the effective Hamiltonians, are obtained in the form of an effective fermion dressed with a coherent state of effective bosons. The model computation illustrates the method that can be used in perturbative computations of effective Hamiltonians for realistic theories. It shows the mechanism by which the perturbative expansion and Tamm-Dancoff approximation increase in accuracy along the RGPEP evolution.

RENT—Repeated Elastic Net Technique for Feature Selection

Feature selection is an essential step in data science pipelines to reduce the complexity associated with large datasets. While much research on this topic focuses on optimizing predictive performance, few studies investigate stability in the context of the feature selection process. In this study, we present the Repeated Elastic Net Technique (RENT) for Feature Selection. RENT uses an ensemble of generalized linear models with elastic net regularization, each trained on distinct subsets of the training data. The feature selection is based on three criteria evaluating the weight distributions of features across all elementary models. This fact leads to the selection of features with high stability that improve the robustness of the final model. Furthermore, unlike established feature selectors, RENT provides valuable information for model interpretation concerning the identification of objects in the data that are difficult to predict during training. In our experiments, we benchmark RENT against six established feature selectors on eight multivariate datasets for binary classification and regression. In the experimental comparison, RENT shows a well-balanced trade-off between predictive performance and stability. Finally, we underline the additional interpretational value of RENT with an exploratory post-hoc analysis of a healthcare dataset.

Anharmonicity in light nuclei near drip lines

Single-particle energy levels of nucleons moving in an anisotropic harmonic oscillator potential along with a spin-orbit and an orbit-orbit interaction have been calculated. The model proposed herein incorporates shapes generated by higher multipolar anisotropies other than the quadruple one. The gaps among the energy levels are strongly dependent on the degree of anisotropy and hence, affect the nucleonic separation energies. For large anisotropies, this characteristic disturbs the occurrences of the usual magic numbers and the sequential ordering of the shells characterized by principal quantum number, N, associated with the elementary shell model. For large asymmetries, the states characterized by higher N, may come down and lie below the energies of the states with lower N and vice versa. This feature of the model provides a natural explanation of intruder states or the island of inversion observed experimentally. For certain choices of the parameters, the large gaps in single nucleonic separation energies could occur at neutron numbers, 10,18,30, and 32 as observed, respectively, in 20Ne, 28Ne, 52Ti, and 54Ti. For neutron as well as proton number 14, the magnitude of this energy gap depends strongly on the choice of the strength of the spin-orbit and orbit-orbit terms. The model provides a simple understanding of the observed fact that some nuclei with proton or neutron number 14 sometimes exhibit this gap but not others. It also provides an interesting insight of having a low-laying (1/2 − ) state in 7He, and confirms the ground state spin and parity of 11Be to be (1/2+) and those of 9He to be (1/2+), both of which have been contentious. This investigation indicated the density distribution, i.e., the shapes of many of nuclei near drip line to be anisotropic having a symmetry about their body-fixed z-axis.

Optimal Capacity Allocation for Heavy-Traffic Fixed-Cycle Traffic-Light Queues and Intersections

Setting traffic light signals is a classical topic in traffic engineering, and important in heavy-traffic conditions when green times become scarce and longer queues are inevitably formed. For the fixed-cycle traffic-light queue, an elementary queueing model for one traffic light with cyclic signaling, we obtain heavy-traffic limits that capture the long-term queue behavior. We leverage the limit theorems to obtain sharp performance approximations for one queue in heavy traffic. We also consider optimization problems that aim for optimal division of green times among multiple conflicting traffic streams. We show that inserting heavy-traffic approximations leads to tractable optimization problems and close-to-optimal signal prescriptions.

Hierarchical model of competition under uncertainty

Oligopoly is a basic concept in the theory of competition. This structure is the central object of research in the economics of markets. There are many mathematical models of the market that are formalized in the form of an oligopoly in economic theory. The Cournot oligopoly is an elementary mathematical model of competition. The principle of equilibrium formalizes the non-cooperative nature of the conflict. Each player chooses the equilibrium strategy of behavior that provides the greatest profit, provided that the other competitors adhere to their equilibrium strategies. The Stackelberg model describes a two-level hierarchical model of firm competition. The top-level player (center, leader) chooses his strategy, assuming reasonable (optimal) decision-making by the lower-level players. Lower-level players (agents, followers) recognize the leadership of the center. They consider the center's strategies known. These players choose their strategies, wanting to maximize their payoff functions. This hierarchical structure is from a game point of view a case of a hierarchical game Gamma1. The indefinite uncontrolled factors (uncertainties) are the values for which only the range of possible values is known in this paper. Recently, studies of game models under uncertainty have been actively conducted. In particular, non-coalitional games under uncertainty are investigated. The concepts of risk and regret are formalized in various ways in the theory of problems with uncertainty. At the same time, the decision-maker takes into account both the expected losses and the possibility of favorable actions of factors beyond his control.\nThis article examines the two-level hierarchical structure of decision-making in the problem of firm competition. A linear-quadratic model with two levels of hierarchy is considered. This model uses the concepts of Cournot and Stackelberg under uncertainty. Uncontrolled factors (uncertainties) are identified with the actions of the importing company. The Wald and Savage principles are used to formalize the solution. According to Wald's maximin criterion, game with nature is seen as a conflict with a player who wants to harm the decision-maker as much as possible.\n\nSavage's minimax regret criterion, when choosing the optimal strategy, focuses not on winning, but on regret. As an optimal strategy, the strategy is chosen in which the amount of regret in the worst conditions is minimal. A new approach to decision-making in the game with nature is formalized. It allows you to combine the positive features of both principles and weaken their negative properties. The concept of U-optimal solution of the problem in terms of risks and regrets is considered.\nThe problems of formalization of some types of optimal solutions for a specific linear-quadratic problem with two levels of hierarchy are solved.

Parameter estimation from ICC curves

Incidence vs. Cumulative Cases (ICC) curves are introduced and shown to provide a simple framework for parameter identification in the case of the most elementary epidemiological model, consisting of susceptible, infected, and removed compartments. This novel methodology is used to estimate the basic reproduction ratio of recent outbreaks, including those associated with the ongoing COVID-19 pandemic.

Construction of an elementary school disaster prevention education class model that incorporates the concept of ESD

Construction of an elementary school disaster prevention education class model that incorporates the concept of ESD

Comparative analysis of the stress-strain state of standard and individual reconstructive plates

The aim of the study was to analyze a three-dimensional finite element model of a post-resection defect of the lower jaw, design and producing of an individual reconstructive plate, compare the stress-strain of this plate using standard reconstructive «CONMET» plate for stabilizing the lower jaw segments through a simulation of the chewing load. The study was carried out on two identical finite elementary models with bone defects in the body of the lower jaw by fixing with a standard reconstructive «CONMET» plate and designed reconstructive plate. In order to simulate the biomechanical loads on the plates when chewing, an impact of force during the occlusal contact of the incisor was applied. The magnitude of the vertical load was equal to 150 N. The condylar processes were fixed in all three directions to prevent reaction forces in the temporomandibular joint. Comparative analysis of two fixation methods showed higher value of equivalent Von Mises stress in individual reconstructive plate than in standard plate. Individual reconstructive plate has better strength characteristics compared to the standard reconstructive «CONMET» plate.

Subgroups of elliptic elements of the Cremona group

Abstract The Cremona group is the group of birational transformations of the complex projective plane. In this paper we classify its subgroups that consist only of elliptic elements using elementary model theory. This yields in particular a description of the structure of torsion subgroups. As an application, we prove the Tits alternative for arbitrary subgroups of the Cremona group, generalizing a result of Cantat. We also describe solvable subgroups of the Cremona group and their derived length, refining results from Déserti.