Full Equations Research Articles

ANISOTROPIC EDDY VISCOSITY A BENCHMARK CASE STUDY IN AN IDEALISED TIDAL ESTUARY

Numerical schemes for solving the full shallow water equations require a turbulence closure model to represent the momentum diffusion caused by turbulence that the velocity fields do not explicitly capture. Typical models include Smagorinsky, depth-U*, Prandlt, and k-epsilon. All of these models predict isotropic eddy viscosity – i.e. the diffusion of momentum acts equally in all directions. However, it is known that when modelling saline transport within an estuary with a 2D scheme, mass dispersion is present in the longitudinal direction due to the depth velocity profile. In a 2D numerical scheme, should diffusion of momentum also be applied anisotropically? In this paper we present a benchmark case study between laboratory measured velocity results and those from numerical simulations using TUFLOW.

The effect of the 5E instructional model on students’ cognitive processes and their attitudes towards chemistry as a subject

The research aim was to examine the effect of the 5E instructional model on students’ cognitive processes and attitudes towards chemistry as a subject. The research was performed at three Slovak grammar schools in the 1st year during the 2nd term of the 2021/2022 school year. This research employed the experimental approach with a quasi-experimental design that involved experimental and control groups. The research sample consisted of 218 students, and it was divided into two groups: the experimental group comprised 114 students (who studied using the 5E model) and the control group comprised 104 students (who studied conventionally). The intervention took place during eight lessons (four two-hour laboratory exercises). A set of inquiry-based activities for the “chemical reactions and equations” thematic unit verified via pilot research was implemented using the 5E model in the experimental group. The research used the following tools: the chemistry concepts test based on the revised Bloom’s taxonomy and a questionnaire to identify the attitudes of students towards chemistry as a subject. The chemistry concepts test results indicated that teaching with the 5E model was more effective than teaching without the 5E model in terms of developing cognitive processes. It affected all the observed cognitive processes (memorization, understanding, application, analysis, and evaluation). After teaching with 5E model, students’ attitudes in experimental group towards learning chemistry as a subject changed significantly. Finally, research presents some recommendations, including conducting more studies on 5E model-based strategy, cognitive processes, and attitudes towards science.

Perivascular pumping of cerebrospinal fluid in the brain with a valve mechanism.

The flow of cerebrospinal fluid (CSF) along perivascular spaces (PVSs) is an important part of the brain's system for clearing metabolic waste. Experiments reveal that arterial motions from cardiac pulsations and functional hyperaemiadrive CSF in the same direction as the blood flow, but the mechanism producing this directionality is unclear. Astrocyte endfeet bound the PVSs of penetrating arteries, separating them from brain extracellular space (ECS) and potentially regulating flow between the two compartments. Here, we present two models, one based on the full equations of fluid dynamics and the other using lumped parameters, in which the astrocyte endfeet function as valves, regulating flow between the PVS and the ECS. In both models, cardiac pulsations drive a net CSF flow consistent with prior experimental observations. Functional hyperaemia, acting with cardiac pulsation, increases the net flow. We also find, in agreement with experiments, a reduced net flow during wakefulness, due to the known decrease in ECS permeability compared to the sleep state. We present in vivo imaging of penetrating arteries in mice, which we use to measure accurately the amplitude of their constrictions and dilations during both cardiac pulsation and functional hyperaemia, an important input for the models. Our models can be used to explore the effects of changes in other input parameters, such as those caused by ageing or disease, as better measurements of these parameters become available.

Subjective well-being in university students: Two psychosocial skills complementing entrepreneurial attitudes

Wide entrepreneurship education (EE), based on constructivist pedagogies and effectual logic, emphasizes the inclusion of entrepreneurial attitudes and personal development as central EE components. Hence, the main aim of this study is examining how entrepreneurial attitudes and subjective well-being (SWB) are related with two additional personal resources necessary to thrive in an unpredictable and demanding labour market. Following constructivist educational recommendations, a full structural equation model was proposed and tested relating entrepreneurial attitudes, psychological capital, and self-care with SWB in a sample of 324 undergraduates. The findings revealed that self-care is a significant mediator, explaining 75.3% of SWB, and fully mediates the impact of psychological capital on SWB. However, self-care did not mediate the relationship between entrepreneurial attitudes and SWB. Intriguingly, a negative effect of entrepreneurial attitudes on SWB was observed. The study suggests mitigating this adverse impact by encouraging activities that foster self-care and psychological capital in university students.

The Quantization of Gravity: The Quantization of the Full Einstein Equations

We quantized the full Einstein equations in a globally hyperbolic spacetime N=Nn+1, n≥3, and found solutions of the resulting hyperbolic equation in a fiber bundle E which can be expressed as a product of spatial eigenfunctions (eigendistributions) and temporal eigenfunctions. The spatial eigenfunctions form a basis in an appropriate Hilbert space while the temporal eigenfunctions are solutions to a second-order ordinary differential equation in R+. In case n≥17 and provided the cosmological constant Λ is negative, the temporal eigenfunctions are eigenfunctions of a self-adjoint operator H^0 such that the eigenvalues are countable and the eigenfunctions form an orthonormal basis of a Hilbert space.

Stoichiometric model of a fully closed bioregenerative life support system for autonomous long-duration space missions

Bioregenerative life support systems (BLSS) are vital for long-duration and remote space missions to increase mission sustainability. These systems break down human waste materials into nutrients and CO2 for plants and other edible organisms, which in turn provide food, fresh water, and oxygen for astronauts. The central idea is to create a materially closed loop, which can significantly reduce mission mass and volume by cutting down or even eliminating disposable waste. In most BLSS studies only a fraction of the resources, such as food, are provided by the system itself, with the rest taken on board at departure or provided through resupply missions. However, for autonomous long-duration space missions without any possibility of resupply, a BLSS that generates all resources with minimal or no material loss, is essential. The goal of this study is to develop a stoichiometric model of a conceptually fully closed BLSS that provides all the metabolic needs of the crew and organisms. The MELiSSA concept of the European Space Agency is used as reference system, consisting of five interconnected compartments, each inhabited by different types of organisms. A detailed review of publicly available MELiSSA literature from 1989 to 2022 revealed that no existing stoichiometric model met the study’s requirements. Therefore, a new stoichiometric model was developed to describe the cycling of the elements C, H, O, and N through all five MELiSSA compartments and one auxiliary compartment. A compact set of chemical equations with fixed coefficients was established for this purpose. A spreadsheet model simulates the flow of all relevant compounds for a crew of six. By balancing the dimensions of the different compartments, a high degree of closure is attained at steady state, with 12 out of 14 compounds exhibiting zero loss, and oxygen and CO2 displaying only minor losses between iterations. This is the first stoichiometric model of a MELiSSA-inspired BLSS that describes a continuous provision of 100% of the food and oxygen needs of the crew. The stoichiometry serves as the foundation of an agent-based model of the MELiSSA loop, as part of the Evolving Asteroid Starships (E|A|S) research project.

The wave stability of solitary waves over a bump for the full Euler equations

The wave stability of solitary waves over a bump for the full Euler equations

Transonic Flow Computation Over A Heat Shield Using Three Dimensional Finite Element Method

A three dimensional finite element method is employed for solution of the transonic full potential equation in mass conservation form. The finite element analysis allows the boundary conditions to be treated in simple and exact manner, without the use of a mapping scheme. The full potential equation is based on the assumption of irrotational flow and density of the fluid is calculated using isentropic relation and it is applicable for upstream local Mach number upto 1.6. The nonlinear full potential equation is reduced to a set of nonlinear algebraic equation using Galerkin’s formulation. An iterative scheme in conjunction with the artificial viscosity term is used to solve the set of algebraic equations. The artificial viscosity term stabilizes the numerical scheme and captures the shock very well. An appropriate grid arrangement is selected in the algorithm to maintain proper and continuous linkage between upstream and downstream of the flow at the centroid of the hexahedral element. The surface pressure distribution in the freestream Mach number range 0.80 - 0.95 and at an angle of incidence 5 degree shows a fairly good agreement with the experimental data. The present finite element discretization can be coupled with the commercially available software.

Forbidden dark matter annihilation into leptons with full collision terms

The standard approach of calculating the relic density of thermally produced dark matter based on the assumption of kinetic equilibrium is known to fail for forbidden dark matter models since only the high momentum tail of the dark matter phase space distribution function contributes significantly to dark matter annihilations. Furthermore, it is known that the computationally less expensive Fokker-Planck approximation for the collision term describing elastic scattering processes between non-relativistic dark matter particles and the Standard Model thermal bath breaks down if both scattering partners are close in mass. This, however, is the defining feature of the forbidden dark matter paradigm. In this paper, we therefore include the full elastic collision term in the full momentum-dependent Boltzmann equation as well as in a set of fluid equations that couple the evolution of the number density and dark matter temperature for a simplified model featuring forbidden dark matter annihilations into muon or tau leptons through a scalar mediator. On the technical side, we perform all angular integrals in the full collision term analytically and take into account the effect of dark matter self-interactions on the relic density. The overall phenomenological outcome is that the updated relic density calculation results in a significant reduction of the experimentally allowed parameter space compared to the traditional approach, which solves only for the abundance. In addition, almost the entire currently viable parameter space can be probed with CMB-S4, next-generation beam-dump experiments or at a future high-luminosity electron-position collider, except for the resonant region where the mediator corresponds to approximately twice the muon or tau mass.

Exploring Students’ Academic Performance, Motivational Orientation and Self-Regulated Learning Strategies towards Chemistry

Chemistry is considered one of the most difficult subjects for college students. Process Oriented Guided Inquiry Learning activities are a student-centered teaching-learning strategy used in classrooms to improve students' academic performance. This study investigates the effectiveness of POGIL activities in teaching Chemistry in the two sections of Bachelor of Industrial Technology (BIT) students enrolled in Chemistry for the first semester of 2022-2023 to determine the academic performance, motivational orientation, and self-regulated learning strategies before and after the intervention. We administered the examination on Stoichiometry and Chemical Equations and Motivated Strategies for Learning Questionnaires before and after the intervention. BIT 1B had the POGIL activities for Stoichiometry, while BIT 1A had the traditional lecture on the same topic. For the second topic, chemical equation, the intervention was switched. BIT 1A had the POGIL activities, while BIT 1B had the traditional lecture. The result showed that most respondents were male since Industrial Technology is a male-dominated course. A significant difference was observed between the post-test scores of the students exposed to POGIL activities and traditional lectures. A significant difference was also observed in the motivational orientation and self-regulated learning strategies after exposure to POGIL activities. Students in a POGIL class perform better than students in a traditional class. It is recommended to use a student-centered teaching strategy such as POGIL, which encourages active learning in teaching Chemistry to improve students' academic performance.

Strengthen the Balancing of Chemical Equations Through an App

Con base en los resultados de las pruebas Saber Valle 2021, aplicada a los estudiantes de grado décimo de la Institución Educativa Jorge Eliécer Gaitán (IEJEG) del Municipio de Restrepo, Valle del Cauca, en el área de química se identifica que la competencia: de resolución de problemas en balanceo de ecuaciones químicas presenta un bajo desempeño. Por este motivo se busca desarrollar una estrategia que permita a los estudiantes alcanzar un mejor desempeño en esta competencia. Para abordar esta situación, se emplea una investigación descriptiva que consiste en analizar y observar detenidamente el grupo de estudio con el fin de registrar su comportamiento en relación con el objetivo planteado. El propósito es obtener datos que puedan ser organizados y cuantificados, con el fin de superar la dificultad identificada. Este enfoque de investigación se basa en el análisis cuantitativo de las pruebas aplicadas y en los resultados obtenidos. Se utiliza un enfoque descriptivo con un método mixto que incluye observación directa, prueba inicial y final del proceso. El objetivo principal de esta propuesta es contribuir a mejorar el proceso de aprendizaje mediante el uso de MIT INVENTOR 2, una aplicación de fácil acceso y gratuita, que no requiere programas sofisticados en su diseño. Como resultado, se crea la aplicación Lin_Poll, la cual permite alcanzar el objetivo general de la investigación. El desarrollo de esta propuesta pedagógica, basada en el uso de las TIC, promueve el aprendizaje de la competencia de resolución de problemas en ecuaciones químicas. Mediante el uso de la aplicación móvil Lin_Poll, se logra un aprendizaje significativo, como se evidencia en los resultados positivos obtenidos en la prueba final, con un promedio del 74,80%. Esto genera una mayor motivación por parte de los estudiantes hacia el aprendizaje, impulsando un cambio positivo en el proceso educativo.

Rendezvous and Proximity Operations in Cislunar Space Using Linearized Dynamics for Estimation

As interest in Moon exploration grows, and efforts to establish an orbiting outpost intensify, accurate modeling of spacecraft dynamics in cislunar space is becoming increasingly important. Contrary to satellites in Low Earth Orbit (LEO), where it takes around 5 ms to communicate back and forth with a ground station, it can take up to 2.4 s to communicate with satellites near the Moon. This delay in communication can make the difference between a successful docking and a catastrophic collision for a remotely controlled satellite. Moreover, due to the unstable nature of trajectories in cislunar space, it is necessary to design spacecraft that can autonomously make frequent maneuvers to stay on track with a reference orbit. The communication delay and unstable trajectories are exactly why autonomous navigation is critical for proximity operations and rendezvous and docking missions in cislunar space. Because spacecraft computational hardware is limited, reducing the computational complexity of navigational algorithms is both desirable and often necessary. By the introduction of a linear system approach to the deputy spacecraft motion, this research avoids the computational burden of integrating the deputy relative equations of motion. In this research, the relative CR3BP equations of motion are derived and linearized using a matrix exponential approximation. This research continues the development of the matrix exponential linearized relative circular restricted three-body problem (CR3BP) equations by applying the dynamics model to estimation and control applications. A simulation is performed to compare state estimation results obtained from using the linearized equations of motion utilizing a Kalman filter and for state estimation utilizing an unscented Kalman filter with the full nonlinear equations of motion. The linearized exponential model is shown to be sufficient for state estimation in the presence of noisy measurements for an example scenario. Additionally, a linear quadratic regulator (LQR) controller was added to optimally control a deputy spacecraft to rendezvous with a chief spacecraft in cislunar space. The contribution of this work is twofold: to provide a proof of concept that the matrix exponential solution for the linearized relative CR3BP equations can be used as the dynamics model for state estimation, as well as to simulate an optimal rendezvous maneuver in the presence of measurement noise.

Multimerizations, Aggregation, and Transfer Reactions of Small Numbers of Molecules.

Chemical equilibria of multimerizations in systems with small numbers of particles exhibit a behavior seemingly at odds with that observed macroscopically. In this paper, we apply the recently proposed expression of equilibrium constant for binding, which includes cross-correlations in reactants' concentrations, to write an equilibrium constant for the formation of clusters larger than two (e.g., trimer, tetramer, and pentamer) as series of two-body reactions. Results obtained by molecular dynamics simulations demonstrate that the value of this expression is constant for all concentrations and system sizes, as well as at an onset of a phase transition to an aggregated state, where densities in the system change discontinuously. In contrast, the value of the commonly utilized expression of equilibrium constant, which ignores correlations, is not constant and its variations can reach few orders of magnitude. Considering different paths for the same multimer formation, with elementary reactions of any order, yields different expressions for the equilibrium constant, yet, with exactly the same value. This is also true for routes with essentially zero probability to occur. Existence of different expressions for the same equilibrium constant imposes equalities between averages of correlated, along with uncorrelated, concentrations of participating species. Moreover, a relation between an average particle number and relative fluctuations derived for two-body reactions is found to be obeyed here as well despite couplings to additional equilibrium reactions in the system. Analyses of transfer reactions, where association and dissociation events take place on both sides of the chemical equation, further indicate the necessity to include cross-correlations in the expression of the equilibrium constant. However, in this case, the magnitudes of discrepancies of the uncorrelated expression are smaller, likely because of partial cancellation of correlations, which exist on both the reactant and product sides.

Global existence and asymptotic stability of the free boundary problem of the primitive equations with heat insulation

In this paper, we deal with the free boundary value problem of the three-dimensional full primitive equations for the large-scale ocean with heat insulation in a bounded domain. The domain is periodic in the horizontal direction and finite in the vertical direction, and its upper boundary is a free surface driven by the fluid and bottom boundary is fixed. We show that the unique strong solution of the free boundary value problem for the three-dimensional full primitive equations exists globally in time and converges to the equilibrium state with exponential decay rate, when the initial data is a small perturbation of the steady state in regular Sobolev space.

An Evolving Spacetime Metric Induced by a ‘Static’ Source

In a series of recent papers we developed a formulation of general relativity in which spacetime and the dynamics of matter evolve with a Poincaré invariant parameter τ. In this paper, we apply the formalism to derive the metric induced by a ‘static’ event evolving uniformly along its t-axis at the spatial origin x=0. The metric is shown to vary with t and τ, as well as spatial distance r, taking its maximum value for a test particle at the retarded time τ=t−r/c. In the resulting picture, an event localized in space and time produces a metric field similarly localized, where both evolve in τ. We first derive this metric as a solution to the wave equation in linearized field theory, and discuss its limitations by studying the geodesic motion it produces for an evolving event. By then examining this solution in the 4+1 formalism, which poses an initial value problem for the metric under τ-evolution, we clarify these limitations and indicate how they may be overcome in a solution to the full nonlinear field equations.

Benchmarking chemical neural ordinary differential equations to obtain reaction network-constrained kinetic models from spectroscopic data

Kinetic model identification relies on accurate concentration measurements and physical constraints to limit solution multiplicity. Not having these measurements and prior knowledge of species and reactions creates considerable challenges that are currently unresolved. We address these by developing a data-driven framework using realtime spectroscopic data, comprising: (i) multivariate curve resolution to deconvolve the spectra of the reacting mixture into those of its pseudocomponents and their corresponding concentrations, which enables species identification without prior information, (ii) Bayesian structure learning among the pseudocomponent spectra to enable hypothesizing reaction pathways, and (iii) neural ordinary differential equations (ODE) that are physically constrained by the hypothesized reaction network and the laws of mass action and temperature dependence to learn kinetic models from the temporal concentration projections of the realtime spectra. The predictive performance of the constrained neural ODEs is limited by the accuracy of spectral deconvolution in the presence of noise, and has been benchmarked against a constrained regression approach by varying signal:noise ratios in the synthetic spectroscopic data of reacting mixtures. Although the hypothesized reaction network differs from the actual reaction template, owing to noise, the network-constrained neural ODEs are seen to result in a 75.2% and 68.15% decrease in the root mean squared error (RMSE) of the concentration profile predictions as compared to the constrained regression method, when trained on time projected concentration data of the synthetic spectra generated at a signal to noise ratio of 35 and 100, respectively.

Development of a Two-Stage Hydrometallurgical Process for Gold-Antimony Concentrate Treatment from the Olimpiadinskoe Deposit.

An integrated two-stage metallurgical process has been developed to process concentrates from the Olimpiadinskoe deposit, which contain high levels of antimony and arsenic. The optimal parameters for the alkaline sulfide leaching process of the initial concentrate from the Olimpiadinskoe deposit were determined to achieve the maximum extraction of antimony at a 99% level. The recommended parameters include an L:S ratio of 4.5:1, a sodium sulfide concentration of 61 g/L, a sodium hydroxide concentration of 16.5 g/L, a duration of 3 h, and a temperature of 50 °C. A synergistic effect of co-processing alkaline sulfide leach cakes with sulfuric and nitric acids was observed. The pre-treatment step reduced the nitric acid composition by converting carbonates into gypsum and increased the arsenic extraction by 15% during subsequent nitric acid leaching. The laboratory research on the nitric acid leaching of decarbonized cake established the key parameters for the maximum iron and arsenic extraction in solution (92% and 98%, respectively), including an L:S ratio of 9:1, a nitric acid concentration of 6 mol/L, and a time of 90 min. Full polynomial equations for the iron and arsenic extraction from the decarbonized cake were derived. The model demonstrated a high relevance, as evidenced by the determination coefficients (R2) of 96.7% for iron and 93.2% for arsenic. The technology also achieved a high gold recovery rate of 95% from the two-stage alkaline sulfide and nitric acid leach cake. Furthermore, the maximum deposition of arsenic from the nitrate leach solution in the form of insoluble As2S3 was determined to be 99.9%. A basic technological flow sheet diagram for processing the flotation gold-antimony concentrate from the Olimpiadinskoe deposit was developed, including two stages: the production of metallic antimony and the gold extraction from the nitric leach cake.

Revisit the causal inference between organizational commitment and job satisfaction: A meta-analysis disentangling its sources of inconsistencies.

Existing theories and studies have exclusively focused on the direct temporal ordering of organizational commitment (OC) and job satisfaction (JS). However, their ordering varies highly across empirical studies. It is unclear whether such high variation is caused by statistical artifacts (i.e., spurious variation) or substantive moderators (i.e., true variation). Therefore, to disentangle artificial and substantial sources of this variation, we adopted traditional and full information meta-analytic structural equation modeling based on 71 independent samples (N = 16,698) with panel designs. After correcting for statistical artifacts, there was moderate heterogeneity in the lagged effects of OC and JS, suggesting that their ordering was not direct or simple but moderated by other variables. Further, the conceptualizations and/or measurements of OC and JS, time lag, and the timing of the investigation (e.g., newcomers vs. nonnewcomers) moderated their ordering. Finally, different specifications of the ordering between OC and JS resulted in differential cross-lagged relationships among JS, OC, and turnover intentions (k = 31, N = 6,876). Our meta-analysis provides new insights into the conceptualizations and/or measurements of OC and JS, adds some theoretical clarification to the dissenting theories by incorporating the time element, nuanced differences in the OC conceptualizations and the timing of the investigation, and raises concern over theory and research informed by studies overlooking alternative orderings of JS and OC. Looking forward, we suggest several promising future directions for explaining the heterogeneous cross-lagged relationships between OC and JS. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Sonic boom propagation over real topography

The effect of elevation variation on sonic boom reflection is investigated using real terrain data. To this end, the full two-dimensional Euler equations are solved using finite-difference time-domain techniques. Numerical simulations are performed for two ground profiles of more than 10 km long, extracted from topographical data of hilly regions, and for two boom waves, a classical N-wave, and a low-boom wave. For both ground profiles, topography affects the reflected boom significantly. Wavefront folding due to terrain depression is notably highlighted. For the ground profile with mild slopes, the time signals of the acoustic pressure at the ground are, however, only slightly modified compared to the flat reference case, and the associated noise levels differ by less than 1 dB. With steep slopes, the contribution due to wavefront folding has a large amplitude at the ground. This results in an amplification of the noise levels: a 3 dB increase occurs at 1% of the positions along the ground surface, and a maximum of 5–6 dB is reached near the terrain depressions. These conclusions are valid for the N-wave and low-boom wave.

The composition of mackinawite

Abstract The composition of a mineral is a defining characteristic. The various compositions listed for mackinawite in current mineralogical databases and reference books, such as Fe(Ni)S and Fe1+xS, are both wrong and misleading. Statistical analyses of over 100 mackinawite compositions reported over the last 50 years show a mean composition of Me1.0S where Me = Fe + Co + Ni + Cu. Mackinawite is stoichiometric FeS. As with many sulfide minerals, Ni-, Co-, and, possibly, Cu-rich varieties occur in addition to the simple iron monosulfide. These varieties are best referred to as nickelian mackinawite, cobaltian mackinawite, and cupriferous mackinawite. The results confirm that these metals substitute for Fe in the mackinawite structure rather than being contained in the interstices between the Fe-S layers. Most compositional data on mackinawites derive from electron probe microanalyses of small grains in magmatic/hydrothermal associations. The result means that there is no dichotomy between the composition of ambient temperature synthetic mackinawite (which is supposed to be equivalent to sedimentary mackinawite) and mackinawites from higher temperature associations. The correct representation of the composition of mackinawite has implications for a wide swathe of fundamental science, including the origin of life, the genesis of magmatic ore deposits, the provenance of meteorites as well as industrial applications such as water treatment and steel corrosion. The stoichiometric formulation permits the mackinawite formula to be balanced electronically using conventional Fe and S ionic species. It also enables simple, balanced chemical equations involving mackinawite.