Simple Analytical Model Research Articles

The effect of sculpting planets on the steepness of debris-disc inner edges

ABSTRACT Debris discs are our best means to probe the outer regions of planetary systems. Many studies assume that planets lie at the inner edges of debris discs, akin to Neptune and the Kuiper Belt, and use the disc morphologies to constrain those otherwise-undetectable planets. However, this produces a degeneracy in planet mass and semimajor axis. We investigate the effect of a sculpting planet on the radial surface-density profile at the disc inner edge, and show that this degeneracy can be broken by considering the steepness of the edge profile. Like previous studies, we show that a planet on a circular orbit ejects unstable debris and excites surviving material through mean-motion resonances. For a non-migrating, circular-orbit planet, in the case where collisions are negligible, the steepness of the disc inner edge depends on the planet-to-star mass ratio and the initial-disc excitation level. We provide a simple analytic model to infer planet properties from the steepness of ALMA-resolved disc edges. We also perform a collisional analysis, showing that a purely planet-sculpted disc would be distinguishable from a purely collisional disc and that, whilst collisions flatten planet-sculpted edges, they are unlikely to fully erase a planet’s signature. Finally, we apply our results to ALMA-resolved debris discs and show that, whilst many inner edges are too steep to be explained by collisions alone, they are too flat to arise through completed sculpting by non-migrating, circular-orbit planets. We discuss implications of this for the architectures, histories, and dynamics in the outer regions of planetary systems.

Nonlinear analysis model and seismic resilience assessment of LEM-filled CFS residence

Lightweight EPS materials (LEM)-filled cold-formed steel (CFS) shear wall structure is a new type of green, low-carbon and prefabricated rural residence, which has drawn in expanding consideration due to the promotion of the rural revitalization strategy. However, most of the existing research on this type of residence has focused on its behaviours of components, with little attention was paid to its overall response to resist earthquake disasters. During the past two decades, significant advancements have been made in effectively mitigating building collapses and reducing casualties resulting from earthquakes. Thus, the concept of seismic resilience is proposed, and the seismic performance requirements of structural design have been elevated from “safety” to “resilience”. To analyze the seismic resilience of LEM-filled CFS residence, this paper proposed a strut and tie- equivalent spring model to establish the simplified analysis model of a single composite wall, and the precision of the model was confirmed by test results, in which the nonlinear characteristic and the supporting effect of fillers was considered. Subsequently, three LEM-filled CFS residences are designed using the direct displacement-based design method. Then the three-D models are established for nonlinear analysis, and the inter-drift ratio (IDR) and residual inter-drift ratio (RIDR) are adopted to estimate the seismic response of the three archetypes. The seismic resilience of the three archetypes are assessed based on FEMA P58. This paper would provide a guidance for the nonlinear analysis and seismic resilience assessment of this type of residences, and promote the application and popularization of this kind of residence.

Deformation of the Juan de Fuca Plate Beneath the Central Cascadia Continental Margin (44°-45°N) in Response to an Upper Plate Load

A 3D crustal model for the central Cascadia continental shelf and Coast Range between 44°N and 45°N shows that the crystalline crust of the forearc wedge beneath the coastline is characterized by a NW-trending, vertical slab of high-velocity rock interpreted to represent the dike complex that fed the Yachats Basalt, which was intruded into the forearc approximately 37 million years ago. A spatial correlation is observed between downward deflection of the crust of the subducting Juan de Fuca plate, inferred from inversion of PmP arrivals to image the Moho surface, and the high velocity (and consequently high density) anomaly underlying the Yachats Basalt. Apparent subsequent rebound of the subducting plate at greater depth suggests a primarily elastic response of the subducting plate to this load. Calculations for a range of plausible values for the magnitude of the load and the width and depth of the depression indicate that the effective elastic thickness of the subducted Juan de Fuca plate is < 6 km. Although our simple analytical models do not include partial support of the load of the slab by the adjacent upper plate crust or time dependence to account for the motion of the slab beneath the load, incorporation of those effects should decrease rather than increase the apparent strength of the subducted plate. We conclude that the subducted Juan de Fuca plate beneath the central Oregon margin is elastically thin and has the potential to store elastic strain energy before rupturing. Our model of a well-defined, focused and static upper plate load that locally deforms the subducted plate within the nominally seismogenic or transitional part of the Cascadia plate boundary may be unique in providing a relatively straightforward scenario for estimating the mechanical properties of the subducted Juan de Fuca plate. We extrapolate from these results to speculate that elastic deformation of the subducting plate may contribute to the low level of seismicity throughout much of the Cascadia forearc in the inter-seismic period between great earthquakes but note that our local results do not preclude faulting or elasto-plastic deformation of a thin and weak plate as it subducts. These results also suggest that the subducting plate should deform in response to larger scale variations in upper plate thickness and density.

Stiff, Smooth, and Solid? Complex Fracture Hydraulics' Imprint on Oscillatory Hydraulic Testing

AbstractFractured bedrock aquifers, especially deep aquifers, represent increasingly common targets for waste storage and alternative energy development, necessitating detailed quantitative descriptions of fracture hydraulic properties, geometry, and connectivity. Yet, multi‐scale characterization of the physical properties that govern fluid flow through and storage in fractured bedrock remains a fundamental hydrogeologic challenge. Oscillatory hydraulic testing, a novel hydraulic characterization technique, has been showing promise in field experiments to characterize the effective hydraulic properties of bedrock fractures. To date, these characterization efforts utilize simplified diffusive analytical models that conceptualize a non‐deforming, parallel‐plate fracture embedded within impermeable host rock, and have found that the returned fracture hydraulic parameter estimates exhibit an apparent period‐dependence. We conduct synthetic experiments using three different numerical models to examine proposed mechanisms that might contribute to the observed period‐dependence including heterogeneous flow and storage within the fracture (i.e., aperture heterogeneity), fracture‐host rock fluid exchange, and fracture hydromechanics. This work represents the first systematic analysis that seeks to understand the process(es) occurring within a bedrock fracture that might be contributing to this apparent period‐dependence. Our analysis demonstrates that all investigated mechanisms generate period‐dependent effective hydraulic parameter estimates, each with their own potentially diagnostic trends; however, fracture hydromechanics is the only explored mechanism that consistently reproduces period‐dependent trends in parameter estimates that are consistent with existing field investigations. These results highlight the need to develop more complex numerical modeling approaches that account for this hydromechanical behavior when characterizing fractured bedrock aquifers.

Exploring assumptions for air infiltration rate estimates using indoor radon in UK homes

Radon, a known carcinogen, is one of the most commonly monitored indoor contaminants. This paper utilises findings from a previous study on indoor radon measurements in United Kingdom (UK) homes to explore the UK Government’s Standard Assessment Procedure (SAP) assumptions for air infiltration rates. These assumptions are important as they are used to assess the energy performance of dwellings and compliance with building regulations. Indoor radon data is aggregated by 16 combinations of home energy efficiency measures (loft and wall insulation, glazing upgrades and draught proofing) and fitted using a simple analytic radon model. We find indoor radon to be inversely proportional to air change rate and proportional to a fit coefficient, k, of 42.2 ± 3.1 (95% Confidence Interval (CI)). We also show that the assumptions within SAP used to estimate home infiltration rates can be modified to include the impact of home energy efficiency which improves the fit (R 2 from 0.38 to 0.51) to the radon data. This work provides evidence to help improve assumptions regarding the effects of home energy efficiency on infiltration rates.

Analysis of Light Intensity and Charge Holding Time Dependence of Pinned Photodiode Full Well Capacity.

In this paper, the light intensity and charge holding time dependence of pinned photodiode (PD) full well capacity (FWC) are studied for our pixel structure with a buried overflow path under the transfer gate. The formulae for PDFWC derived from a simple analytical model show that the relation between light intensity and PDFWC is logarithmic because PDFWC is determined by the balance between the photo-generated current and overflow current under the bright condition. Furthermore, with using pulsed light before a charge holding operation in PD, the accumulated charges in PD decrease with the holding time due to the overflow current, and finally, it reaches equilibrium PDFWC. The analytical model has been successfully validated by the technology computer-aided design (TCAD) device simulation and actual device measurement.

Generalized Airy theory and its region of quantitative validity

Airy theory has long proved to be a remarkably simple analytical model that describes the various features of the atmospheric rainbow. But the stringent assumptions upon which its derivation is based, prevent it from being quantitatively accurate in practical situations. We derive an analytical generalization of Airy theory for both the transverse electric and magnetic polarizations and for an arbitrary number of internal reflections. This generalized analytical model contains both the Airy integral and its first derivative, multiplied by constants of proportionality that are independent of the scattering angle. We find that, for the primary rainbow, it provides a quantitatively accurate approximation to the exact Lorenz-Mie-Debye theory of the rainbow for a much wider range of sizes of spherical water drops than does the original version of Airy theory, but still has stringent limitations for the second-order rainbow and beyond.

Design of Trench MIS Field Plate Structure for Edge Termination of GaN Vertical PN Diode.

In this study, we developed an analytic model to design a trench metal-insulator-semiconductor (MIS) field plate (FP) structure for the edge termination of a vertical GaN PN diode. The key parameters considered in the trench MIS FP structure include trench depth, MIS dielectric material and thickness, and interface charge density of MIS. The boundary conditions are defined based on the maximum allowed electric field strengths at the dielectric and semiconductor regions. The developed model was validated using TCAD simulations. As an example, a 1 kV GaN vertical PN diode was designed using the optimized FP structure, which exhibited the same breakdown voltage characteristics as an ideal one-dimensional PN diode structure without edge effects. This proposed simple analytic model offers a design guideline for the trench MIS FP for the edge termination of vertical PN diodes, enabling efficient design without the need for extensive TCAD simulations, thus saving significant time and effort.

Experimental and analytical studies on residual flexural behaviour of reinforced alkali-activated slag-based concrete beams after exposure to fire

Understanding the flexural behaviour of reinforced alkali-activated slag-based concrete beams after exposure to a fire is imperative to ensure their safety use and develop adequate retrofitting measures. However, up to this point in time, no relevant investigations on this specific subject have been reported. This paper presents an experimental study comparing the flexural behaviour of alkali-activated slag-based concrete (AAC) and Portland cement concrete (PCC) beams exposed to the standard ISO 834 fire curve. The research considers concrete strength and heating duration as research parameters. The test results revealed that AAC beams displayed a lower temperature field and experienced less mid-span deflection increase compared to PCC beams during heating. Normal-strength AAC and PCC beams exhibited comparable losses in flexural capacity after being heated for 1 h or 1.5 h. However, PCC beam with a concrete strength over 80 MPa experienced more capacity loss due to severe spalling during heating. On the other hand, compared with PCC counterparts, AAC beams exhibited lower residual flexural stiffness and experienced greater stiffness loss, mainly due to the formation of more cracks induced by thermal shrinkage of AAC. The flexural capacity and stiffness loss of AAC beams increased with increasing concrete strength and heating duration after fire exposure. The residual flexural capacities of RC beams were predicted using a simplified analytical model that incorporates heat transfer analysis and the 500 ℃ isotherm method. The predictions demonstrated excellent agreement with the test results.

Effects of vehicle dynamics on small UAS-gust encounters

This study investigates the relative impacts of different gusts on representative small Uncrewed Air Systems through the use of a simple analytical model. The model uses basic vehicle characteristics, including planform area and mass, to account for the altitude gained during gust interactions. This is a missing component from most current fundamental gust studies, both experimental and numerical. The results show that the induced negative effective angle of attack created by the vertical motion of the vehicle has a significant countering effect on the gust and suggests that this effective angle of attack should be accounted for in future gust studies. Efforts are undertaken to determine the relative importance of accounting for this motion. This is done by investigating the impact of the induced negative angle of attack on the altitude trajectory. An equation is found using gust and vehicle characteristics to determine the critical gust ratio at a given gust development rate, which is the minimum gust ratio which will lead to vehicle stall. Lastly, an empirical relationship is derived to allow for the effective gust ratio conversion between fixed-model experiments and flying-vehicle gust interactions.

Deep transfer learning for groundwater flow in heterogeneous aquifers using a simple analytical model

Deep learning models exhibit good interpolating ability, but their performance is often hindered by the scarcity of data in groundwater problems. Analytical models (solutions) provide a first-order physical principle for groundwater flow, but they are only applicable under specific conditions, such as when the aquifer is homogeneous. This study introduces a novel framework for deep transfer learning that integrates the strengths of both methods and overcomes their limitations. Specifically, we propose a deep learning model guided by a simple analytical model to predict groundwater flow in heterogeneous aquifers. It differs from previous deep learning model by incorporating the knowledge from the simple analytical model and utilizing transfer learning technique to improve the prediction in relatively complicated problems where the analytical model is not applicable. The model is tested against the traditional deep learning model Deep Back Propagation Neural Network (DBPNN) in the scenarios with unknown hydraulic conductivity fields. The results show that the proposed model significantly improve the accuracy of hydraulic head predictions by fusing analytical knowledge with neural networks. The hydraulic conductivity mainly affects the parameters of the shallow layers in the neural network, which enables the use of transfer learning techniques in more complex problems. In all test scenarios, the prediction errors of the proposed model are much smaller than those of the DBPNN. Additionally, the proposed model performs satisfactorily even with limited training data.

A Simplified Analytical Model for FRP-Strengthened Curved Brittle Substrates Using the Multi-Linear Bond-Slip Law

The utilization of fiber-reinforced polymer (FRP) composites for building reinforcement has gained widespread acceptance. However, the bond behavior between externally applied composites and strengthened substrates, which are crucial for system efficacy, has primarily focused on flat surfaces. Yet, the challenge of curved substrates, common in masonry arches and vaults, remains less explored. This study introduces a classical analytical model addressing the bond behavior between FRP plates and curved substrates. This classical approach is structured upon a simplified model that concentrates all the non-linearities of the FRP–substrate interface. The interface is described through a universal multi-linear stress–slip relationship, with the influence of the curved substrate being considered by the normal stress that impacts the interface law. Closed-form solutions for distinct bond-slip law stages are derived and verified against the previous study. Through comparisons with existing experimental data and simulations, this approach is able to predict the maximum load, the trends of the global load-slip curves, and give insights into detailed local behavior. Additionally, the exploration of employing neural networks for determining the interface law exhibits promising outcomes.

Surface tension of very small liquid drops

There has been much debate in the literature on the surface tension of very small liquid drops. It would be useful to have a simple analytical model to better understand and predict any changes that occur at the nanoscopic scale. In this work, it is hypothesized that density variation at the interface of liquids due to curvature causes surface tension to deviate from bulk values. Equations were derived to predict that variation in terms of the diameters of the drop and its constituent atoms and molecules. Surface tension is expected to decrease exponentially for drops that have diameters less than a few nanometers and/or that contain less than several thousand atoms or molecules. These findings agree with those from earlier simulation and experimental studies.

Design and analysis of timber-concrete-based civil structures and its applications: A brief review

Abstract Builders, designers, and the research community are becoming interested in incorporating timber and concrete based composite structures because they effectively integrate the structural qualities of timber and concrete. The structure’s stiffness, ductility, and load capacity are all affected by the quality of the timber connections used in construction. However, timber-concrete-based structures are limited due to a lack of design knowledge and the brittle failure behaviour of timber under shear or tensile loading. Experimental, numerical, and analytical methods have been proposed in the literature, and the key parameters influencing the performance of timber-concrete structures have been discussed. This study addresses the current challenges in designing timber-concrete connections and their failure modes and suggests simple performance-based analytical models that determine the failure mode. It looks at some of the best numerical design methods used in the past and tries to determine the best way to use timber as a possible way to use safe design principles for timber–concrete composite structures in the future.

Modelling and scaling laws of the ion emission regime in Taylor cones

This article presents a first-principles model for electrosprays operating in the ion emission regime. The model considers ion emission from a Taylor cone anchored on a tubular emitter, including the fluid dynamics as well as the electrostatic interaction between the liquid, the electrodes and the ion beam. The model accounts for the self-heating of the liquid due to ohmic and viscous dissipation, and the associated variation of the viscosity and electrical conductivity with temperature. The numerical solution reproduces the experimental phenomenology of the ion emission regime (e.g. current levels, the high sensitivity to the ion solvation energy, the proportionality between the emitted current and emitter potential, etc.), and other aspects of the underlying physics such as the coupling between ion emission and self-heating of the liquid. The numerical solution is also used to validate a simpler analytical model that yields scaling laws for the emitted current, and for the characteristic length, current density and electric field of the emission region. The analytical model also provides liquid-dependent criteria for the onset of the ion emission regime.

Effect of IT Alignment on Employee Performance and the Operating Role of Operating Environment

The thesis was about the information technology alignment and employee performance in private service sector a case of Umeme Uganda limited. The study set out to: examine the IT Alignment practices in Umeme (U) Limited; to analyses the relationship between IT Alignment and employee performance; and to examine the moderating role of the operating environment on the relationship between IT Alignment and employee performance. The study was cross-sectional in nature, using both qualitative and quantitative approaches. Data was collected using self-administered questionnaires, and interviews with top management of Umeme limited central Uganda. Out of a population of 290, the study targeted a sample size of 165 respondents. The study applied Statistical Programmed for Social Scientists (SPSS) to test all four hypotheses. The results were presented as descriptive statistics and inferential statistics specifically correlation, regression analysis and hierarchical regression analysis models. The study confirmed a positive significant predictor relationship between information technology alignment and employee performance in Umeme this was done by Exploratory Factor Analysis (EFA).
 The moderating role of the operating environment on the relationship between IT Alignment and employee performance at Umeme (U) Limited Central Uganda using a hierarchical regression analysis where interaction term (ITA*OP) appeared a significant predictor of employee performance The study designed a model, the Information Technology Alignment Innovative Preference Model (ITAIP) to build capacities and conduct research activities that would result in long-term and sustainable improvements in employee performance in private service sector. The study concluded that since ITA influence employee performance, the management of Umeme in support of IT needs to build a dynamic ITAIP, that will enable them cope with continuous improvement for greater efficacy and increased productivity as protocols are more strictly followed when orienting new employees. The study suggests that in order to build and install new IT governance the firm needs a detailed knowledge of how to improve efficiency, Costs optimization, Collaboration, collective decision, commitment, time management, creativity and digital work to release new services to customers, Transformational of ITA and improve the overall quality of the IT services provided in UMEME limited Uganda.
 Purpose: The purpose of this study was to empirically establish the relationship between IT alignment practices and employee performance in the Private Service Sector particularly in Umeme Limited.
 Design/methodology/approach: The study took a cross-sectional descriptive and analytical design. Out of a sample size of 165 employees, a total of 165 usable questionnaires were identified implying a response rate of 100%. The paper applied Statistical Programme for Social Scientists (SPSS) to test four hypotheses. The results are presented in terms of correlation and simple regression analysis models.
 Findings: Results indicate that of the four hypotheses developed in literature review, three were positive and significant predictors of employee performance. IT governance, IT implementation and IT investment were found to be significant positive precursors of employee performance. The authors did not test the Integration of IT activities – employee performance association as Integration of IT activities was eliminated during Exploratory Factor Analysis.
 Practical implications: This study is relevant and useful to private service entities as it provides them with a blue print on how to implement IT alignment practices with the aim of improving employee performance. To policy makers at National level, the study outcomes will be helpful in collecting, analyzing, and disseminating economic data that will serve private decision makers at all levels, on fiscal and monetary policy, business finance and investment strategy, and personal household economic matters.
 Originality/value: This study demonstrates that the proper implementation of IT alignment practices leads to improvements in employee performance in terms of collaboration, collective decision making, commitment, time management, creativity and digital work within the workplace.

Extreme Tidal Stripping May Explain the Overmassive Black Hole in Leo I: A Proof of Concept

A recent study found dynamical evidence of a supermassive black hole of ∼3 × 106 M ⊙ at the center of Leo I, the most distant dwarf spheroidal galaxy of the Milky Way. This black hole, comparable in mass to the Milky Way’s Sgr A*, places the system >2 orders of magnitude above the standard M •–M ⋆ relation. We investigate the possibility, from a dynamical standpoint, that Leo I’s stellar system was originally much more massive and, thus, closer to the relation. Extreme tidal disruption from one or two close passages within the Milky Way’s virial radius could have removed most of its stellar mass. A simple analytical model suggests that the progenitor of Leo I could have experienced a mass loss in the range 32%–57% from a single pericenter passage, depending on the stellar velocity dispersion estimate. This mass-loss percentage increases to the range 66%–78% if the pericenter occurs at the minimum distance allowed by current orbital reconstructions. Detailed N-body simulations show that the mass loss could reach ∼90% with up to two passages, again with pericenter distances compatible with the minimum value allowed by Gaia data. Despite very significant uncertainties in the properties of Leo I, we reproduce its current position and velocity dispersion, as well as the final stellar mass enclosed in 1 kpc (∼5 × 106 M ⊙) within a factor <2. The most recent tidal stream is directed along our line of sight toward Leo I, making it difficult to detect. Evidence from this extreme tidal disruption event could be present in current Gaia data in the form of extended tidal streams.

Breast Cancer Diagnosis Using Extended-Wavelength-Diffuse Reflectance Spectroscopy (EW-DRS)-Proof of Concept in Ex Vivo Breast Specimens Using Machine Learning.

This study aims to investigate the feasibility of using diffuse reflectance spectroscopy (DRS) to distinguish malignant breast tissue from adjacent healthy tissue, and to evaluate if an extended-wavelength range (450-1550 nm) has an advantage over the standard wavelength range (450-900 nm). Multivariate statistics and machine learning algorithms, either linear discriminant analysis (LDA) or support vector machine (SVM) are used to distinguish the two tissue types in breast specimens (total or partial mastectomy) from 23 female patients with primary breast cancer. EW-DRS has a sensitivity of 94% and specificity of 91% as compared to a sensitivity of 40% and specificity of 71% using the standard wavelength range. The results suggest that DRS can discriminate between malignant and healthy breast tissue, with improved outcomes using an extended wavelength. It is also possible to construct a simple analytical model to improve the diagnostic performance of the DRS technique.

Dynamic Buckling Characteristics of Drill String in Horizontal Wells

Buckling may cause drill string damage or even drilling failure. For the 3[Formula: see text]000-m-long horizontal section drill string, a simplified analysis model of drill string in horizontal well is established, and the dynamic response results of axial displacement, angular displacement and contact force are obtained. When buckling, the closer the position of drill string is to the bottom, the later the buckling time, the smaller the buckling deformation degree, the slower the growth rate of axial displacement, and the smaller the attenuation degree of angular displacement and contact force amplitude. After buckling, drill string undergoes tensile deformation and eventually remains stable in the tensile state. After stabilization, from the top of drill string to the bottom of drill string, axial displacement increment increases first, then remains unchanged and then decreases, and the relative torsion angle between different positions gradually decreases. The drill string is always in horizontal contact with the wellbore, resulting in the same contact force values at different locations. The change of well inclination angle does not affect the change law of displacement and contact force. The absolute value of angular displacement is negatively correlated with the change of well inclination angle, and the value of axial displacement increment and contact force is positively correlated with the change of well deviation angle, but the value of contact force is quite close. The research results can provide reference for alleviating the buckling of drill string in horizontal wells.

Analysis of the Relationship between Domestic Savings and Domestic Investment in Saudi Arabia

This study aims to examine the relationship between domestic savings and domestic investment in Saudi Arabia for the period 1980-2019. The study uses annual data and employs the simple linear regression model and EViews program for analysis. The results show a positive direct relationship between domestic savings and domestic investment, with approximately 25% of the total domestic investments in the study period attributed to changes in the volume of Saudi financial savings. The study also reveals that other economic variables contribute more significantly to the levels of domestic investment. The findings suggest that Saudi policymakers should focus on increasing the volume of financial savings and implementing policies that encourage domestic investment to boost economic growth. The study has certain limitations, and future research should explore the impact of other economic variables on domestic investment in Saudi Arabia.