Horizontal Balance Research Articles

Development of overturning circulation in sloping waterbodies due to surface cooling

Cooling the surface of freshwater bodies, whose temperatures are above the temperature of maximum density, can generate differential cooling between shallow and deep regions. When surface cooling occurs over a long enough period, the thermally induced cross-shore pressure gradient may drive an overturning circulation, a phenomenon called ‘thermal siphon’. However, the conditions under which this process begins are not yet fully characterised. Here, we examine the development of thermal siphons driven by a uniform loss of heat at the air–water interface in sloping, stratified basins. For a two-dimensional framework, we derive theoretical time and velocity scales associated with the transition from Rayleigh–Bénard type convection to a horizontal overturning circulation across the shallower sloping basin. This transition is characterised by a three-way horizontal momentum balance, in which the cross-shore pressure gradient balances the inertial terms before reaching a quasi-steady regime. We performed numerical and field experiments to test and show the robustness of the analytical scaling, describe the convective regimes and quantify the cross-shore transport induced by thermal siphons. Our results are relevant for understanding the nearshore fluid dynamics induced by nighttime or seasonal surface cooling in lakes and reservoirs.

An Empirical Investigation into Alarming Signals Ignored by the U.S. Multi-Brand Retailer J. Crew Incorporation during COVID-19 Pandemic

This study investigated the financial signals that have been ignored or have failed to be controlled by J. Crew Inc. from 2013 until 2019. Exploratory research is carried out with the help of secondary data which was collected from the downloaded formal documents submitted by J. Crew Inc. to the Securities Exchange Commission (SEC). Researchers analyzed these documents and prepared statements on vertical income statement, vertical balance sheet, horizontal income statement, horizontal balance sheet, trend analysis of income statement, and trend analysis of balance sheet, as well as ratio analysis on liquidity, long-term solvency, profitability, and turnover ratios with the help of excel. This paper has identified total of 15 alarming signs that companies either ignored, could not control, or did not act with alertness towards to stop the business being taken out of hands. In this research paper, the establishment of J. Crew Inc. was presented in four sections: Crew Retail Stores, Crew Factory Stores, Crew Mercantile Stores, and Crew Madewell Stores. The results of this study show that it was not the COVID-19 pandemic that pushed this retail giant into bankruptcy, but numerous reasons and financial turbulences. J. Crew’s financial performance gave plenty of alarming signals that the showed the company was not on track, but these were ignored by the company. Right from net profit, operating expenses, total revenue, goodwill, return on assets, liquidity, and solvency, all 15 indicators were not meeting the industry ideal standard for a continuous period of 5 years. Whether or not the organization can rebuild and contend in a post-pandemic world, is not yet clear.

Boundary layer-mediated vorticity generation in currents over sloping bathymetry

AbstractCurrent-topography interactions in the ocean give rise to eddies spanning a wide range of spatial and temporal scales. Latest modeling efforts indicate that coastal and underwater topography are important generation sites for submesoscale coherent vortices (SCVs), characterized by horizontal scales of (0.1 – 10) km. Using idealized, submesoscale and BBL-resolving simulations and adopting an integrated vorticity balance formulation, we quantify precisely the role of bottom boundary layers (BBLs) in the vorticity generation process. In particular, we show that vorticity generation on topographic slopes is attributable primarily to the torque exerted by the vertical divergence of stress at the bottom. We refer to this as the Bottom Stress Divergence Torque (BSDT). BSDT is a fundamentally nonconservative torque that appears as a source term in the integrated vorticity budget and is to be distinguished from the more familiar Bottom Stress Curl (BSC). It is closely connected to the bottom pressure torque (BPT) via the horizontal momentum balance at the bottom and is in fact shown to be the dominant component of BPT in solutions with a well-resolved BBL. This suggests an interpretation of BPT as the sum of a viscous, vorticity generating component (BSDT) and an inviscid, ‘flow-turning ’ component. Companion simulations without bottom drag illustrate that although vorticity generation can still occur through the inviscid mechanisms of vortex stretching and tilting, the wake eddies tend to have weaker circulation, be substantially less energetic, and have smaller spatial scales.

Hyperhomocysteinemia alters cytokine gene expression, cytochrome c oxidase activity and oxidative stress in striatum and cerebellum of rodents

AimsHomocysteine has been linked to neurodegeneration and motor function impairments. In the present study, we evaluate the effect of chronic mild hyperhomocysteinemia on the motor behavior (motor coordination, functional performance, and muscular force) and biochemical parameters (oxidative stress, energy metabolism, gene expression and/or protein abundance of cytokine related to the inflammatory pathways and acetylcholinesterase) in the striatum and cerebellum of Wistar male rats. Main methodsRodents were submitted to one injection of homocysteine (0.03 μmol Hcy/g of body weight) between 30th and 60th postnatal days twice a day. After hyperhomocysteinemia induction, rats were submitted to horizontal ladder walking, beam balance, suspension, and vertical pole tests and/or euthanized to brain dissection for biochemical and molecular assays. Key findingsChronic mild hyperhomocysteinemia did not alter motor function, but induced oxidative stress and impaired mitochondrial complex IV activity in both structures. In the striatum, hyperhomocysteinemia decreased TNF-α gene expression and increased IL-1β gene expression and acetylcholinesterase activity. In the cerebellum, hyperhomocysteinemia increased gene expression of TNF-α, IL-1β, IL-10, and TGF-β, while the acetylcholinesterase activity was decreased. In both structures, hyperhomocysteinemia decreased acetylcholinesterase protein abundance without altering total p-NF-κB, NF-κB, Nrf-2, and cleaved caspase-3. SignificanceChronic mild hyperhomocysteinemia compromises several biochemical/molecular parameters, signaling pathways, oxidative stress, and chronic inflammation in the striatum and cerebellum of rats without impairing motor function. These alterations may be related to the mechanisms in which hyperhomocysteinemia has been linked to movement disorders later in life and neurodegeneration.

Thrust Measurements on the High Efficient and Reliable Vacuum Arc Thruster (HERVAT)

In this work, thrust measurements of the high efficient and reliable vacuum arc thruster (HERVAT) are performed for different pulse energies. The thruster system includes a thruster head together with a newly developed pulse processing unit (PPU). The complete system (HERVAT + PPU) is able to perform more than 1 × 107 pulses. Moreover, the influence of an integrated active magnetic nozzle is investigated. As a result, the thrust to power ratio, the average thrust level and the impulse bit for each configuration are measured and calculated. For the thrust measurements, a highly sensitive horizontal thrust balance with an active force actuator is used and operated in the thrust compensation mode. The investigated system is able to achieve levels from 5 to 40 μN and thrust to power ratios from 1 to 2 μN/W. The experimental results are compared to the data available in literature.

Binocular integration and stereopsis in children with television torticollis

BackgroundTo observe the characteristics of binocular integration and stereopsis in children with television torticollis.MethodsA retrospective study was carried out, where data were collected from 25 children with television torticollis as the disease group after refractive error correction and 25 normal children as the control group. A virtual reality system was used to assess and analyze the characteristics of binocular integration by a contrast balance test and binocular stereopsis.ResultsThe 25 children in the disease group included 17 males and 8 females with an average age of 7.5 ± 1.9 years old and an average binocular spherical equivalent of − 0.35 ± 1.46D. The 25 children in the control group were also 17 males and 8 females with an average age of 7.3 ± 2.2 years old and the average binocular spherical equivalent of − 0.48 ± 0.93D. No significant differences were found in the horizontal bar contrast balance test between the 2 groups at near and far distances. Near-distance vertical bar contrast balance test was normal in 23 subjects and suppressed in 2 subjects in the control group, while it was normal in 13 subjects and suppressed in 12 subjects in the disease group, which showed a statistically significant difference (P = 0.002). Far distance vertical bar contrast balance test was normal in 24 subjects and suppressed in 1 subject in the control group, normal in 7 subjects and suppressed in 18 subjects in the disease group, showing a statistically significant difference (P = 0.000). All subjects in the 2 groups showed 100〞 as near distance stereoacuity. At far distance, the mean stereoacuity was 176.00〞 ± 92.56〞 in the control group, and 352.00〞 ± 270.99〞 in the disease group, with a statistically significant difference (P = 0.011).ConclusionBy using virtual reality technology, defects in binocular visual function were found in children whose television torticollis persisted after regular refractive error correction. Television torticollis may be associated with the deficit of binocular integration for vertical bars and far distance stereopsis.

New Insight Into the Onshore Intrusion of the Kuroshio Into the East China Sea

AbstractThe Kuroshio Current, a vigorous western boundary current in the Pacific, is responsible for bringing high temperature, high salinity, and phosphate‐rich open ocean water into the East China Sea (ECS) when it flows past Taiwan and generates a branch current, known as the Kuroshio Branch Current (KBC), which intrudes onto the continental shelf of the ECS. Based on observations and numerical modeling, a 1.5‐layer reduced‐gravity model is evaluated and modified to simulate the flow pattern of the Kuroshio intrusion (KI) northeast of Taiwan. We revised the analytical solution derived by Hsueh (1992), https://doi.org/10.1029/92JC01401 to conserve the horizontal momentum balance in the along‐shelf and cross‐shelf directions. The new analytical solution not only explains the KI angle but also addresses the KBC recirculation mechanism. To sustain the steady‐state momentum balance in the area adjacent to the shelf break northeast of Taiwan, there must be a recirculation that plays the same role in vorticity dynamics as the combination of the joint effect of baroclinicity and relief, bottom friction, and nonlinear advection. Unlike previous studies, our results agree well with the observations and could account for seasonal variations in the KI direction. Moreover, the new model predicts a reasonable velocity maximum (0.42 m s−1) over the shelf break. Satellite data and numerical results confirm that the new solution reflects a reasonable estimation for KI direction. This theory may potentially be applied to regions with trenches or valleys with completely different flow patterns by using similar analytical methods.

Tissue-scale tensional homeostasis in skin regulates structure and physiological function

Tensional homeostasis is crucial for organ and tissue development, including the establishment of morphological and functional properties. Skin plays essential roles in waterproofing, cushioning and protecting deeper tissues by forming internal tension-distribution patterns, which involves aligning various cells, appendages and extracellular matrices (ECMs). The balance of traction force is thought to contribute to the formation of strong and pliable physical structures that maintain their integrity and flexibility. Here, by using a human skin equivalent (HSE), the horizontal tension-force balance of the dermal layer was found to clearly improve HSE characteristics, such as the physical relationship between cells and the ECM. The tension also promoted skin homeostasis through the activation of mechano-sensitive molecules such as ROCK and MRTF-A, and these results compared favourably to what was observed in tension-released models. Tension-induced HSE will contribute to analyze skin physiological functions regulated by tensional homeostasis as an alternative animal model.

Modified L'Episcopo tendon transfer for isolated loss of active external rotation

Patients with isolated loss of active external rotation (ILER) but preserved active forward elevation have recently been identified as a rare and distinct clinical entity. The modified L'Episcopo procedure attempts to restore horizontal muscle balance and restore active external rotation. A retrospective study was performed for all patients with ILER and preserved forward elevation with Hamada stage ≤2 changes undergoing the modified L'Episcopo tendon transfer. Preoperative rotator cuff fatty infiltration and morphology was reported. Clinical, radiographic, and functional outcomes were recorded preoperatively and compared to postoperative outcomes at a minimum of 24 months' follow-up. Nine patients (8 male, 1 female) with a mean age of 58.4 years(range, 51-67 years) were evaluated at a mean follow-up of 64.3 months (range, 24-126 months). Significant improvement was demonstrated in active external rotation with the arm at the side (mean increase of 47°; range, 30°-60°, P = .004) and at 90° abduction(mean increase of 41°; range, 20°-70°, P = .004). The mean Constant score and pain score significantly improved at final follow-up (P = .004). All patients were either very satisfied or satisfied, with a mean subjective shoulder value of 74% (range, 60%-99%). In appropriately selected patients with ILER and preserved active forward elevation, the modified L'Episcopo procedure can restore horizontal muscle balance and produce significant improvements in active external rotation, Constant score, and pain.

Rossby modes in slowly rotating stars: depth dependence in distorted polytropes with uniform rotation

Context.Large-scale Rossby waves have recently been discovered based on measurements of horizontal surface and near-surface solar flows.Aims.We are interested in understanding why it is only equatorial modes that are observed and in modelling the radial structure of the observed modes. To this aim, we have characterised the radial eigenfunctions ofrmodes for slowly rotating polytropes in uniform rotation.Methods.We followed Provost et al. (1981, A&A, 94, 126) and considered a linear perturbation theory to describe quasi-toroidal stellar adiabatic oscillations in the inviscid case. We used perturbation theory to write the solutions to the fourth order in the rotational frequency of the star. We numerically solved the eigenvalue problem, concentrating on the type of behaviour exhibited where the stratification is nearly adiabatic.Results.We find that for free-surface boundary conditions on a spheroid of non-vanishing surface density,rmodes can only exist forℓ = mspherical harmonics in the inviscid case and we compute their depth dependence and frequencies to leading order. For quasi-adiabatic stratification, the sectoral modes with no radial nodes are the only modes which are almost toroidal and the depth dependence of the corresponding horizontal motion scales asrm. For allrmodes, except the zero radial order sectoral ones, non-adiabatic stratification plays a crucial role in the radial force balance.Conclusions.The lack of quasi-toroidal solutions when stratification is close to neutral, except for the sectoral modes without nodes in radius, follows from the need for both horizontal and radial force balance. In the absence of super- or sub-adiabatic stratification and viscosity, both the horizontal and radial parts of the force balance independently determine the pressure perturbation. The only quasi-toroidal cases in which these constraints on the pressure perturbation are consistent are the special cases whereℓ = mand the horizontal displacement scales withrm.

La sexta ola o era del Estado constitucional democrático, social y ambiental –ECDSA– en Iberoamérica: reconstitucionalización y pluralismo tridimensional

El presente artículo analiza las transformaciones constitucionales de Iberoamérica en los últimos tres decenios y medio con un enfoque en la reconstitucionalización pluralista después del interludio de las autocracias republicanas. Iniciará con una introducción al constitucionalismo comparado según el modelo de las seis olas, para continuar con la conceptuación de la época, preguntando por las ventajas y desventajas de los constructos del neoconstitucionalismo y del ECDSA. En tercer lugar, examinará las dinámicas de transformación y las nuevas normas supremas. El cuarto apartado sondeará las tendencias en el equilibrio horizontal y vertical de poderes. Quinto, se revisará el perfil pluralista y el enfoque en el triángulo de valores liberales, sociales y ambientales. El sexto subcapítulo echará un vistazo a la integración continental y la protección supranacional de valores constitucionales. Para terminar, se formulan algunas observaciones conclusivas sobre constituciones extensas, idealistas, transformadoras y parcialmente normativas.

Special Tax Zones and Proportionality: A New Parameter for the Necessity Test

The judgement of proportionality under the variables of fundamental freedoms and State aid rules is a process that often fails to promote legal certainty with respect to the necessity test, especially when the review involves tax measures of a Special Tax Zone (STZ). The central idea of this article suggests the possibility of a new parameter for the necessity of territorial tax measures in order to limit the discretionality of the EU institutions and contribute in terms of legal certainty. For this purpose, the concept of ‘fiscal residue’ is presented, giving evidence of its possible implementations in the context of STZs as an objective parameter for the necessity test, for both fundamental freedoms and State aid rules. The discussion of the results covers the EU law and national law perspectives as well as the possibility of a system of EU governance for the use of the fiscal residue with respect to STZs. Finally, the new outlook of the necessity test is focused on the equalization of the fiscal residue, opening doors for a more comprehensive idea of European Union, including the value of social cohesion at the territorial level. Special tax zones, EU tax law, Territorial tax incentives, Fundamental freedoms, Regional fiscal aid, Proportionality, Necessity test, Least restrictive alternative, Fiscal residue, Horizontal fiscal balance, Fiscal equalization

New Zealand‐Wide Geodetic Strain Rates Using a Physics‐Based Approach

AbstractWe present a new strain rate map for New Zealand, based on geodetic data acquired from 1995 to 2013. We use a physics‐based approach, which inverts the horizontal GPS velocities for Vertical Derivatives of Horizontal Stress (VDoHS) rates, relying on using elasticity theory and the horizontal force balance equations at the Earth's surface. The VDoHS rates are then integrated to obtain horizontal strain rates. Strain rates derived using this new approach are less spatially smoothed than previous results using conventional methods. In addition to the major plate boundary features in New Zealand, low‐rate zones of deformation are resolved by the strain and VDoHS rates, which bodes well for the utility of this method to reveal processes on hidden or ill‐characterized fault zones. Application of this new method to obtain strain and VDoHS rates provides the highest resolution view to‐date of contemporary deformation in New Zealand.

Test-Retest Reliability and Response Stability of Gaze Stabilization, Postural Sway, and Dynamic Balance Tests in Persons with Multiple Sclerosis and Controls.

Psychometric properties of tests that assess the angular vestibulo-ocular reflex (aVOR) and vestibulospinal reflex function are currently unknown. This study investigated the test-retest reliability and response stability of gaze stabilization, postural sway, and dynamic balance measures in persons with multiple sclerosis (MS) and controls. Nineteen adults with MS and 14 controls performed passive horizontal head impulses, quiet standing, and dynamic balance tests on two separate occasions. Gaze stabilization measures included aVOR gain, number of compensatory saccades (CSs) per head rotation, CS latency, and gaze position error. Postural sway included sway amplitude and total sway path. Dynamic balance measure included the Functional Gait Assessment. Intraclass correlation coefficient, standard error of measurement (SEM, SEM%), and minimal detectable difference at 95% confidence level were calculated. Test-retest reliability for aVOR gain, CSs per head rotation, and gaze position error was moderate and for each postural sway and dynamic balance measure was good. Low error (SEM, SEM%) for aVOR gain, CS latency, postural sway, and dynamic balance variables and low minimal detectable difference values for aVOR gain and Functional Gait Assessment scores were seen, suggestive of acceptable response stability. These results support the utility of some of the gaze and postural measures for examination and treatment efficacy purposes in people with MS.

On the wave-current interaction during the passage of a tropical cyclone in the Bay of Bengal

The impact of waves on currents and vice-versa is an integral part of the complex coastal dynamics. The wave-current interaction is prominent in the coastal shelf-slope regions, particularly during the passage of a tropical cyclone. In the present study, we describe the importance of wave-current interaction in the northern Bay of Bengal (BoB) using a fully coupled three-dimensional Coupled Ocean-Atmosphere-Wave-Sediment Transport (COAWST) modelling system. The COAWST model is applied to the case of a very severe cyclonic storm Phailin that passed over the BoB basin during 10–15 October 2013. To represent the interaction between waves and currents, we utilized the newly implemented vortex-force method in the coupled model. Numerical experiments with different coupling configuration within the COAWST modelling framework were performed to separately identify the effects of wind, tide, and wave-current interaction process. A comparison of model results with the buoy observations of water elevations, currents, and wave measurements shows a good agreement between model and observed data. Various terms of the momentum balance were calculated from the model simulated and diagnosed parameters. A comparison of the horizontal momentum balance term identifies the wave-breaking induced acceleration as one of the leading terms along the storm affected the east coast of India. Further, an increase in the apparent bed roughness caused by waves found to affect the values and distribution of the bottom shear stress. The pressure gradient term showed significant changes to the pure tidal case. The study highlights that the changes in the momentum balance caused by waves includes contributions from the variations in the water level and currents. The most relevant effect on the coastal hydrodynamics was in the form of a wave-induced setup near the location of landfall of the cyclone.

Learning and long-term retention of dynamic self-stabilization skills.

In earlier studies, we had subjects use a joystick to balance themselves when seated in a device programmed to behave like an inverted pendulum. Subjects tested in a vertically oriented roll plane showed rapid learning for dynamically stabilizing themselves about the direction of balance when it corresponded with the direction of gravity. Subjects tested in a horizontally oriented roll plane, unlike the vertical roll plane subjects, did not have gravitational cues to determine their angular positions and showed minimal learning and persistent cyclical drifting. We describe here a training program to enhance learning and performance of dynamic stabilization in the horizontal roll plane based on our previous finding that balance control involves two dissociable components: alignment using gravity-dependent positional cues and alignment using dynamic cues. We hypothesized that teaching subjects to balance in a vertical roll plane to directions of balance that did not correspond with the direction of gravity would enhance the ability to stabilize at the direction of balance in the horizontal roll plane where gravity-dependent cues are absent. All subjects trained in vertical rolllater showed greatly improved performance in horizontal plane balance. Control subjects exposed only to horizontal roll plane balancing showed minimal improvements. When retested 4months later, the training subjects showed further performance improvements during the course of the retest trials whereas the control group showed no further improvement. Our findings indicate that balance control can be enhanced in situations lacking gravitationally dependent position cues as in weightlessness, when initial training occurs with such cues present.

Distributed hydrological-hydraulic modeling of the karst polje water balance

The paper presents developed 3Dnet-HET, a distributed hydrologic model coupled with the discrete channel network concept for groundwater circulation simulation in the karst environment. The hydrologic part is driven by the spatially distributed precipitation input and characteristic air temperatures to produce surface runoff and groundwater infiltration as a result. This represents input for the “horizontal water balance” module in which the groundwater flow is simulated by the system of discrete conduits representing known groundwater paths. In this study, the model is applied for simulation of the Dabarsko polje water balance in Bosnia and Herzegovina, as well as the river Bregava catchment runoff. The model is firstly calibrated based on recorded water levels in the Dabarsko polje and flow discharges at the Bregava spring. Obtained model is utilized to analyze the Dabarsko polje water balance and possible effects of the planned hydropower plant “Dabar”. Results indicate a high flow variation and necessity of integrated real-time water management of the whole Trebisnjica system.

Measuring the Wilson depression of sunspots using the divergence-free condition of the magnetic field vector

Context. The Wilson depression is the difference in geometric height of unit continuum optical depth between the sunspot umbra and the quiet Sun. Measuring the Wilson depression is important for understanding the geometry of sunspots. Current methods suffer from systematic effects or need to make assumptions on the geometry of the magnetic field. This leads to large systematic uncertainties of the derived Wilson depressions. Aims. We aim to develop a robust method for deriving the Wilson depression that only requires the information about the magnetic field that is accessible from spectropolarimetry, and that does not rely on assumptions on the geometry of sunspots or on their magnetic field. Methods. Our method is based on minimizing the divergence of the magnetic field vector derived from spectropolarimetric observations. We have focused on large spatial scales only in order to reduce the number of free parameters. Results. We tested the performance of our method using synthetic Hinode data derived from two sunspot simulations. We find that the maximum and the umbral averaged Wilson depression for both spots determined with our method typically lies within 100 km of the true value obtained from the simulations. In addition, we applied the method to Hinode observations of a sunspot. The derived Wilson depression (∼600 km) is consistent with results typically obtained from the Wilson effect. We also find that the Wilson depression obtained from using horizontal force balance gives 110–180 km smaller Wilson depressions than both, what we find and what we deduce directly from the simulations. This suggests that the magnetic pressure and the magnetic curvature force contribute to the Wilson depression by a similar amount.

Diurnal Evolution of Submesoscale Front and Filament Circulations

AbstractThe local circulation of submesoscale fronts and filaments can be partly understood through a horizontal momentum balance of Coriolis, a horizontal pressure gradient, and vertical diffusivity in a turbulent boundary layer, known as the turbulent thermal wind balance (TTW or T2W). T2W often reproduces the instantaneous relative vorticity and divergence of submesoscale circulations in open-ocean and shelf settings. However, a diurnal cycle in submesoscale vorticity and divergence is characterized by a non-T2W phasing: a maximum in divergence magnitude lags the maximum in vertical diffusivity (with vorticity lagging divergence). Here, an idealized model is used to solve the transient turbulent thermal wind (T3W) equations and to investigate the diurnal evolution of front and filament circulation in a 2D plane. Relative to a steady-state circulation, transient evolution can cause both instantaneous strengthening and a weaker diurnal average of the secondary circulation. The primary mechanisms controlling the diurnal variability exist in a 1D Ekman layer that imprints onto the 2D circulation. In midlatitudes, acceleration during separate phases of the diurnal cycle (from night to day and from day to night) is dominated by distinct inertial oscillation and vertically diffusive mechanisms, respectively. However, the manifestation of these dual accelerations is sensitive to latitude, boundary layer depth, and the strength of the forcing. A simple 1D model predicts the diurnal phasing of submesoscale divergence and vorticity in realistic primitive equation simulations of the southwestern Pacific and coastal California.

T–x–y Diagram of MgO–SiO2–Al2O3 System: Microstructure Design

A computer model of the T–x–y diagram of MgO–SiO2–Al2O3 system is used to show the possibility of analysis of its microstructure constitution in terms of competition between primary and eutectic crystals by means of vertical mass balance diagrams calculated for a given centroid over the whole temperature range. The usefulness of horizontal mass balance diagrams is considered for studying phase relations at a fixed temperature along the chosen isopleth. Mass balances were used to determine the crystallization path at the quasi-peritectic liquidus point with the invariant reaction L + Al2O3 = 3Al2O3 · 2SiO2 + MgO · Al2O3, whose composition was taken into account in giving a rationale to corundum armor element technology.