Simple Analytical Model Research Articles

Stability analysis of heavy machinery moving on weak subsoil. 3D FEM model vs. analytical models

In this paper, the authors present an extension of the scope of the previously conducted research to the full three-dimensional computer simulation (using the finite element method), which takes into account the interaction between: heavy caterpillar tracks system – working platform – weak subsoil. The article presents a computer model considering two caterpillars, resting on elastic-plastic sub-soil, with standard Mohr-Coulomb yield conditions, allowing for computer simulation of the behavior of the system up to achievement of ultimate limit state. The results of the above model are treated as the reference for a simplified Analytical Models of estimating the limit state, which might be used in design procedures. In turn, these Analytical Models are enhancements of previously presented one. The most important results concluding form the Analytical Model are simple interaction formulas, in the space of moments acting on the machine-subsoil system, limiting a domain of safety in given soil conditions.

First Sagittarius A* Event Horizon Telescope Results. VIII. Physical Interpretation of the Polarized Ring

In a companion paper, we present the first spatially resolved polarized image of Sagittarius A* on event horizon scales, captured using the Event Horizon Telescope, a global very long baseline interferometric array operating at a wavelength of 1.3 mm. Here we interpret this image using both simple analytic models and numerical general relativistic magnetohydrodynamic (GRMHD) simulations. The large spatially resolved linear polarization fraction (24%–28%, peaking at ∼40%) is the most stringent constraint on parameter space, disfavoring models that are too Faraday depolarized. Similar to our studies of M87*, polarimetric constraints reinforce a preference for GRMHD models with dynamically important magnetic fields. Although the spiral morphology of the polarization pattern is known to constrain the spin and inclination angle, the time-variable rotation measure (RM) of Sgr A* (equivalent to ≈46° ± 12° rotation at 228 GHz) limits its present utility as a constraint. If we attribute the RM to internal Faraday rotation, then the motion of accreting material is inferred to be counterclockwise, contrary to inferences based on historical polarized flares, and no model satisfies all polarimetric and total intensity constraints. On the other hand, if we attribute the mean RM to an external Faraday screen, then the motion of accreting material is inferred to be clockwise, and one model passes all applied total intensity and polarimetric constraints: a model with strong magnetic fields, a spin parameter of 0.94, and an inclination of 150°. We discuss how future 345 GHz and dynamical imaging will mitigate our present uncertainties and provide additional constraints on the black hole and its accretion flow.

A simple analytical model for turbulent kinetic energy dissipation for self-similar round turbulent jets

This work presents a simple analytical model for the streamwise and radial variations of turbulent kinetic energy dissipation in an incompressible round turbulent jet. The key assumptions in the model are: similarity in the axial velocity profile with a Gaussian shape, axisymmetric flow and the dominance of radial derivatives of the mean velocity over axial direction derivatives (similar to boundary layer theory). Initially, a simplified eddy-viscosity relation for turbulent stresses is derived using the algebraic stress model by Gatski & Speziale (J. Fluid Mech., vol. 254, 1993, pp. 59–78). Subsequently, with this eddy-viscosity relation, the relation for variations of turbulent kinetic energy dissipation is formulated using the conservation of turbulent kinetic energy. To extract the necessary constants of the model, experimental velocity statistics for round jets are obtained through particle image velocimetry measurements. The experimental results of the mean entrainment coefficient for turbulent jets are also analysed. When comparing the radial variation of turbulent kinetic energy dissipation from the model with experimental results at Reynolds number $1.4\times 10^5$ and numerical results at Reynolds number $1200$ from the available literature, we observe a maximum error of $10\,\%$ and $15\,\%$ , respectively. Finally, using the validated model, we analyse the impact of mean velocity evolution parameters on the behaviour of turbulent kinetic energy dissipation and discuss its potential significance in future studies.

Cold and dense perturbative QCD in a very strong magnetic background

We compute the pressure from first principles within perturbative QCD at finite baryon density and very high magnetic fields up to two-loops and with physical quark masses. The region of validity for our framework is given by ms≪μq≪eB, where ms is the strange quark mass, μq is the quark chemical potential, e is the fundamental electric charge, and B is the magnetic field strength. We include the effects of the renormalization scale in the running coupling, αs(μq,eB), and running strange quark mass. We also discuss the simplifications that come about in the chiral limit. The effectively negligible contribution of the exchange diagram allows for building a simple analytic model for the equation of state for pure quark magnetars and computing their mass and radius at very large values of B. These results provide constraints on the behavior of the maximum mass and associated radius from perturbative QCD. We also discuss the magnetic bag model for extreme magnetic fields. Published by the American Physical Society 2024

Absorption of collimated incident radiation in a semitransparent strongly scattering medium: Computational analysis and explanation of red algae blooming in snow

The study of directional radiation absorption in weakly absorbing and strongly scattering media is of interest for a variety of important applications, including laser hyperthermia of human tumors in a therapeutic window of transparency, determination of the optical and thermal properties of highly porous ceramics, and calculations of the deep solar heating of snow cover in polar regions and mountains. In such problems, multiple scattering of radiation can lead to a non-monotonic variation of the absorbed radiation power with distance from the illuminated surface of the medium and to the appearance of the absorption maximum at some depth below the surface. This effect has a known physical explanation and can be predicted using the suggested analytical solution based on the transport approximation for the scattering phase function and the two-flux approximation for the diffuse component of the radiation intensity. The range of illumination angles at which the absorption maximum inside an optically thick medium is observed is determined. The position and magnitude of this maximum are also obtained. In the present work, the verification of this approximate solution using reference numerical calculations is carried out for the first time. It is shown that the simple analytical model is acceptable for regular calculations. Computational results for pure snow illuminated by the Sun showed that red light gives the strongest absorption maximum at a small distance from the snow surface. This is a basis of the presented physical explanation for the intense photosynthesis of red microalgae responsible for the well-known ``snow blood'' phenomenon.

Mechanical Properties and Fracture Toughness Prediction of Ductile Cast Iron under Thermomechanical Treatment

Temperature has a great influence on the mechanical properties of ductile cast iron or nodular cast iron. A thermomechanical treatment was carried out at various elevated temperatures of 450 °C, 750 °C and 850 °C using a universal testing machine with a tub furnace. Specimens were held at these temperatures for 20 min to ensure a homogeneous temperature distribution along the entire length of the specimen, before a tensile load was applied. Specimens were deformed to various levels of uniform strain (0%, 25%, 50%, 75%, and 100%). These degrees of deformation were measured with a dial gauge attached to a movable cross plate. Three strain rates were used for each specimen and temperature: 1.8×10−4 s−1, 9×10−4 s−1 and 4.5×10−3 s−1. A simple analytical model was extracted based on the CT tensile test geometry and yield stress and a 0.2% offset strain to measure the fracture toughness (JIC). To validate the analytical model, an extended finite element method (XFEM) was implemented for specimens tested at different temperatures, with a strain rate of 1.8×10−4 s−1. The model was then extended to include the tested specimens at other strain rates. The results show that increasing strain rates and temperature, especially at 850 °C, increased the ductility of the cast iron and thus its formability. The largest percentage strains were 1 and 1.5 at a temperature of 750 °C and a strain rate of 1.8×10−4 s−1 and 9×10−4 s−1, respectively, and reached their maximum value of 1.7 and 2.2% at 850 °C and a strain rate of 9×10−4 s−1 and 4.5×10−3 s−1, respectively. In addition, the simple and fast analytical model is useful in selecting materials for determining the fracture toughness (JIC) at various elevated temperatures and different strain rates.

A bi-phasic numerical approach for non-linear response and stiffness recovery related to residual thermal stress in UHTCMCs

The tensile properties of sintered Cf-ZrB2/SiC UHTCMCs were investigated for different lamination sequences, revealing ultimate strengths of 570 MPa (0°/0°), 120 MPa (0°/90°), and 40 MPa (90°/90°). The results facilitated modeling the material’s non-linear tensile response, characterized by a remarkably prolonged plateau with pseudo-plastic behavior, followed by stiffness recovery before ultimate failure. A simplified analytical model was developed to predict this behavior originated by residual thermal stresses and inelastic phenomena. A complete constitutive law was then developed and implemented in a FE model, utilizing a bi-phasic approach including Drucker-Prager plasticity and orthotropic ductile damage. Two-step analyses were performed, starting with a thermal step to represent the buildup of a self-equilibrating RTS state in the material phases, followed by a mechanical simulation. This demonstrated the model's efficacy in capturing the non-linear response in both homogeneous and cross-ply lay-ups, contributing to advancements in materials engineering and the design of UHTCMCs-based hot structures.

Cost-Effectiveness of 2 Models of Pessary Care for Pelvic Organ Prolapse: Findings From the TOPSY Randomized Controlled Trial

ObjectivesPelvic organ prolapse is the descent of one or more reproductive organs from their normal position, causing associated negative symptoms. One conservative treatment option is pessary management. This study aimed to to investigate the cost-effectiveness of pessary self-management (SM) when compared with clinic-based care (CBC). A decision analytic model was developed to extend the economic evaluation. MethodsA randomized controlled trial with health economic evaluation. The SM group received a 30-minute SM teaching session, information leaflet, 2-week follow-up call, and a local helpline number. The CBC group received routine outpatient pessary appointments, determined by usual practice. The primary outcome for the cost-effectiveness analysis was incremental cost per quality-adjusted life year (QALY), 18 months post-randomization. Uncertainty was handled using nonparametric bootstrap analysis. In addition, a simple decision analytic model was developed using the trial data to extend the analysis over a 5-year period. ResultsThere was no significant difference in the mean number of QALYs gained between SM and CBC (1.241 vs 1.221), but mean cost was lower for SM (£578 vs £728). The incremental net benefit estimated at a willingness to pay of £20 000 per QALY gained was £564, with an 80.8% probability of cost-effectiveness. The modeling results were consistent with the trial analysis: the incremental net benefit was estimated as £4221, and the probability of SM being cost-effective at 5 years was 69.7%. ConclusionsResults suggest that pessary SM is likely to be cost-effective. The decision analytic model suggests that this result is likely to persist over longer durations.

The initial trajectory of a ball released from uniform circular motion

This short paper presents a simple analytical model for the abrupt termination of circular motion, as discussed in the ‘The Most Mind-Blowing Aspect of Circular Motion’. The model confirms that when a string is released, a ball at the far end of the string continues to move in a near-circular motion for a short time.

Assessing the Fate of Benzophenone-Type UV Filters and Transformation Products during Soil Aquifer Treatment: The Biofilm Compartment as Bioaccumulator and Biodegrader in Porous Media.

The fate of selected UV filters (UVFs) was investigated in two soil aquifer treatment (SAT) systems, one supplemented with a reactive barrier containing clay and vegetable compost and the other as a traditional SAT reference system. We monitored benzophenone-3 (BP-3) and its transformation products (TPs), including benzophenone-1 (BP-1), 4,4'-dihydroxybenzophenone (4DHB), 4-hydroxybenzophenone (4HB), and 2,2'-dihydroxy-4-methoxybenzophenone (DHMB), along with benzophenone-4 (BP-4) and avobenzone (AVO) in all involved compartments (water, aquifer sediments, and biofilm). The reactive barrier, which enhances biochemical activity and biofilm development, improved the removal of all detected UVFs in water samples. Among monitored UVFs, only 4HB, BP-4, and AVO were detected in sediment and biofilm samples. But the overall retained amounts were several orders of magnitude larger than those dissolved. These amounts were quantitatively reproduced with a specifically developed simple analytical model that consists of a mobile compartment and an immobile compartment. Retention and degradation are restricted to the immobile water compartment, where biofilm absorption was simulated with well-known compound-specific Kow values. The fact that the model reproduced observations, including metabolites detected in the biofilm but not in the (mobile) water samples, supports its validity. The results imply that accumulation ensures significant biodegradation even if the degradation rates are very low and suggest that our experimental findings for UVFs and TPs can be extended to other hydrophobic compounds. Biofilms act as accumulators and biodegraders of hydrophobic compounds.

Numerical investigation on the effect of extra-feedback target position on the fringe visibility in a dual optical feedback interferometry system.

Optical feedback interferometry (OFI) exhibits good potential in laboratory and engineering applications as an interferometric measurement technology with unique structure. One challenge of this technology is that the OFI signals may be feeble, and the OFI fringe visibility is low when the optical feedback strength is weak. It has been demonstrated that the OFI fringe amplitude can be enhanced by introducing an extra-feedback into an OFI system. At the same time, it has been confirmed that the position of the extra-feedback target must be strictly controlled as it will directly affect the fringe amplitude. However, the details of how the extra-feedback positions affect the OFI fringe amplitude, and its underpinning mechanism still needs to be unveiled. In this paper, we aim to theoretically investigate the influence of the extra-feedback target position on the OFI fringe amplitude and explore the underpinning mechanism. Firstly, a simplified analytical model for characterizing a dual-channel optical feedback interferometry (DOFI) system in steady state was derived from the Lang-Kobayashi equations. A method of solving the analytical model was developed to further explore the nature of a DOFI system. On top of that, the influence of the extra-feedback target position on the OFI fringe amplitude and its underpinning mechanism was explored, based on which the criteria for how to achieve large fringe amplitudes were summarized. The obtained results provide helpful guidance in constructing a DOFI system with enhanced fringe visibility, and further promote the practical applications of OFI technology.

Nonstationary recharge responses to a drying climate in the Gnangara Groundwater System, Western Australia

The response of groundwater recharge to climate change needs to be understood to enable sustainable management of groundwater systems today and in the future, yet observations of recharge over long-enough time periods to reveal responses to climate trends are scarce. Here we present a meta-analysis of 60 years of recharge studies over the Gnangara Groundwater System of South-West Western Australia, covering a period of sustained drying consistent with climate change projections. The recharge process in the area is defined by a wet winter during which rain saturates a deep, highly permeable soil profile with very low water storage capacity. Measurements of recharge since the 1960s show near-linear reductions in potential recharge of 50%, in response to a 20% reduction in rainfall. For the best-represented land cover in the dataset (Banksia woodland), the reduction in potential recharge was closer to 70%. A simple analytical model suggests that reductions in the duration of winter, coupled with a decreased frequency of winter storms, were most responsible for these declines, and reveals the potential for nonlinear relationships between the recharge fraction (recharge/precipitation) and climatic variables such as mean storm frequency, mean storm depth, and the length of the winter wet season. Overall, results suggest that recharge declines in drying Mediterranean groundwater systems are likely to outstrip the declines in rainfall, and that leveraging existing observation networks worldwide to characterise recharge responses to changing climate is needed to overcome existing interpretation challenges created by inconsistent sites, methods and durations of recharge estimation.

In-plane and out-of-plane one-way vertical bending behavior interaction analysis of unreinforced masonry walls with newly developed load capacity interaction curve

The structural behavior of unreinforced masonry (URM) walls under in-plane (IP) or out-of-plane (OOP) loading in masonry buildings has been extensively investigated in the public literature. However, studies focusing on the URM walls subjected to concurrent IP and OOP loadings are limited. Neglecting IP and OOP interaction effects may lead to unsafe design practices. As such, this study conducts a comprehensive numerical investigation into the behavior of URM walls under combined IP and OOP loading, focusing on the influences of aspect ratio (i.e., height-to-length ratio), slenderness ratio (i.e., height-to-thickness ratio), and pre-compression load levels. To capture the possible failure modes of URM walls under various loading scenarios, the simplified micro modeling approach is employed. The analysis results indicate that the presence of OOP loading leads to a substantial reduction in IP capacities. Longer walls, characterized by smaller AR, exhibit more pronounced IP and OOP interaction effects. Additionally, highly slender walls show significant additional moments due to second-order effects under OOP loading, thereby negatively affecting the IP capacity. Low-level pre-compression loads are beneficial in diminishing capacity interaction effects, while high pre-compression loads exert a negative influence. To facilitate the consideration of IP and OOP capacity interaction effects in an efficient manner, a simplified analytical model is developed through curve fitting, in which the effects of aspect ratio, slenderness ratio, and pre-compression load are incorporated.

Electromagnetic analysis of a wound rotor synchronous machine using an improved subdomain technique considering finite permeability of the core

This study proposed an improved analytical method for electromagnetic field analysis of a wound rotor synchronous machine (WRSM) considering the permeability of soft magnetic materials. A simplified analytical model considering the magnetic permeability of each region is presented. The governing equations of each region are derived from Maxwell’s equations and the electromagnetic field theory, and a general solution is derived by using mathematical techniques. The analytical solutions of all domains are derived by calculating the boundary conditions. To validate the proposed analytical method, the radial and circumferential magnetic flux densities are compared with finite element analysis (FEA) results. In addition, electromagnetic performance parameters such as flux linkage, back-electromotive force, and torque are determined using electromagnetic theories. In particular, the magnetic saturation of the soft magnetic material is due to field and armature current, and the superiority of the proposed method is demonstrated by comparing the improved analytical method considering the global saturation of each region with the nonlinear FEA result considering local saturation. The proposed analytical method can be widely used in the initial and optimal design of WRSM because it can consider saturation of the core due to changes in field and armature current.

3D Diffusion of Water in Melt Inclusion‐Bearing Olivine Phenocrysts

AbstractOlivine‐hosted melt inclusions are an important archive of pre‐eruptive processes such as magma storage, mixing and subsequent ascent through the crust. However, this record can be modified by post‐entrapment diffusion of H+ through the olivine lattice. Existing studies often use spherical or 1D models to track melt inclusion dehydration that fail to account for complexities in geometry, diffusive anisotropy and sectioning effects. Here we develop a finite element 3D multiphase diffusion model for the dehydration of olivine‐hosted melt inclusions that includes natural crystal geometries and multiple melt inclusions. We use our 3D model to test the reliability of simplified analytical and numerical models (1D and 2D) using magma ascent conditions from the 1977 eruption of Seguam volcano, Alaska. We find that 1D models underestimate melt inclusion water loss, typically by ∼30%, and thus underestimate magma decompression rates, by up to a factor of 5, when compared to the 3D models. An anisotropic analytical solution that we present performs well and recovers decompression rates within a factor of 2, in the situations in which it is valid. 3D models that include multiple melt inclusions show that inclusions can shield each other and reduce the amount of water loss upon ascent. This shielding effect depends on decompression rate, melt inclusion size, and crystallographic direction. Our modeling approach shows that factors such as 3D crystal geometry and melt inclusion configuration can play an important role in constraining accurate decompression rates and recovering water contents in natural magmatic systems.

Multi-Performance Economical Optimization of Base Isolation System with Tuned Inerter Negative Stiffness Damper Subjected to Non-Stationary Seismic Excitation

Base isolation proves to be an effective vibration control strategy for buildings. However, the base-isolation floor (BIF) may undergo substantial displacements. To improve the seismic performance of base-isolation system, this paper proposes a multi-performance economical optimization procedure (MPEOP) for exploring the optimal parameters of base isolation system with tuned inerter negative stiffness damper (BIS-TINSD) subjected to non-stationary seismic excitation. The simplified analysis model for BIS-TINSD is developed, followed by the formulation of the state-space representation. The non-stationary seismic excitation is represented as a stationary Gaussian process with a time-modulating function based on the Clough–Penzien spectrum, and combining the equations of motion with seismic excitation results in the augmented state-space representation of structure-damper-excitation, followed by the formulation of differential Lyapunov equation. The multi-objective performance economical index is proposed, in which the performance optimization objective is defined as a weighted combination of base isolation floor displacement and superstructure acceleration, and the economic optimization objective is set as the support stiffness. The Pareto optimal fronts (POF) are adopted to deal with optimal objectives. The examination of optimal design parameters is extended under real earthquake records. The results demonstrate the effectiveness of the MPEOP, and indicate the advantages of the BIS-TINSD compared with the inerter amplify damper (IAD) and negative stiffness inerter damper (NSID).

Seismic performance investigation on self-centering friction frames: Collapse capacity and post-earthquake recovery

Self-centering technology is a promising approach to enhance seismic resilience of frame structures. Despite extensive experimental and theoretical research on various self-centering components, there has been relatively limited quantitative study on the collapse and post-earthquake recovery capabilities of self-centering frame structures. Therefore, this paper introduces a self-centering friction beam-column joint (SCFJ) and develops a simplified analytical model for the joint. Then a series of RC frames with SCFJ are designed, and their seismic resilience and post-earthquake recovery performance are conducted. Finally, this study quantitatively investigates the contribution of SCFJ to the seismic safety and post-earthquake recovery capabilities of RC frames with varying stories. The results indicate that under maximum considered earthquake, the peak floor accelerations and inter-story drift ratio of self-centering friction frames (SCFF) are comparable to those of ordinary RC frames (ORCF). However, the overall residual deformation of the SCFFs can be reduced by 85%–94%. Furthermore, their seismic collapse resistance is improved by 8%–23%. Immediate occupancy and reparability of SCFFs are enhanced by 41%–72% and 29%–35%, respectively. Notably, the enhancement in collapse capacity and post-earthquake recovery performance of SCFFs becomes more pronounced as the number of stories increases.

THE INFLUENCE OF THE STANDARD OF LIVING ON BREAST CANCER MORBIDITY AND MORTALITY IN EUROPE IN THE PERIOD BETWEEN 2017 AND 2019

This paper explores the hypothesis that there is a connection between the standard of living (expressed by the Human Development Index) and the standardised rates of breast cancer incidence and mortality in the female population of Europe. The examination whether the standard of living has an impact on breast cancer incidence and mortality is based on the use of bivariate correlation, as the simplest form of quantitative analysis of two variables which seeks to determine the empirical relationship between them. The second part of the analysis involves the determination of linear relationships using simple linear regression analysis models testing the average impact of the Human Development Index on the standardised breast cancer incidence and mortality rates. The analysis takes into account the importance of yet another socioeconomic factor – response to screening, which can have a major impact on breast cancer mortality.

Gravitational wave mergers of accreting binary black holes in AGN discs

ABSTRACT Binary black hole (BBH) evolution in the discs of active galactic nuclei (AGNs) is a promising channel for gravitational wave (GW)-driven mergers. It is, however, unclear whether binaries interacting with the surrounding disc undergo orbital contraction or expansion. We develop a simple analytical model of accreting BBHs in AGN discs to follow the orbital evolution from the disc-dominated regime at large separations into the GW-driven regime at small separations (the coupled ‘disc + GW’-driven evolution). We obtain that accreting binaries expand in thick discs with aspect ratio greater than a critical value (>hcrit); whereas accreting binaries contract and eventually merge in thin discs (<hcrit). Interestingly, accreting BBHs can experience faster mergers compared to non-accreting counterparts, with a non-monotonic dependence on the disc aspect ratio. The orbital contraction is usually coupled with eccentricity growth in the disc-dominated regime, which lead to accelerated inspirals in the GW-driven regime. We quantify the resulting BBH merger time-scales in AGN discs (τmerger ∼ 105–107 yr) and estimate the associated GW merger rates ($\mathcal {R} \sim (0.2 {\small --} 5) \, \text{Gpc}^{-3} \text{yr}^{-1}$). Overall, accreting binaries may efficiently contract and merge in thin discs, hence this particular BBH-in-AGN channel may provide a non-negligible contribution to the observed GW merger event rate.

A shear stress parametrization for arbitrary wind farms in conventionally neutral boundary layers

In the context of large off-shore wind farms, power production is influenced greatly by the turbine array's interaction with the atmospheric boundary layer. One of the most influencing manifestations of such complex interaction is the increased level of shear stress observed within the farm. This leads to higher momentum fluxes that affect the wind speed at the turbine locations and in the cluster wake. At the wind farm entrance, an internal boundary layer (IBL) grows due to the change in effective roughness imposed by the wind turbines, and for large enough clusters, this can reach the unperturbed boundary layer height in what is referred to as the fully developed regime. Downwind, a second IBL starts growing, while the shear stress profile decays exponentially to its unperturbed state. In the present study, we propose a simple analytical model for the vertical profile of the horizontal shear stress components in the three regions identified above. The model builds upon the top-down model of Meneveau (J. Turbul., vol. 13, 2012, N7), and assumes that the flow develops in a conventionally neutral boundary layer. The proposed parametrization is verified successfully against large-eddy simulations, demonstrating its ability to capture the vertical profile of horizontal shear stress, and its evolution both inside and downwind of the wind farm. Our findings suggest that the developed model can prove extremely useful to enhance the physical grounds on which new classes of coupled wind farm engineering models are based, leading to a better estimation of meso-scale phenomena affecting the power production of large turbine arrays.