Simple Analytical Model Research Articles

A Simple Neural Network for Estimating Fine Sediment Sources Using XRF and XRD

Suspended sediment (SS) has a wide range of negative effects such as increased water turbidity, altered habitat structures, sedimentation, and effects on hydraulic systems and environmental engineering projects. Nevertheless, the methods for accurately determining SS sources on a basin-scale are poorly understood. Herein, we used a simplified neural network analysis (NNA) model to identify the sources of SS in Japan’s Oromushi River Catchment Basin. Fine soil samples were collected from different locations of the catchment basin, processed, and separately analysed using X-ray fluorescence (XRF) and X-ray diffraction (XRD). The sampling stations were grouped according to the type of soil cover, vegetation type and land-use pattern. The geochemical components of each group were fed into the same neural network layer, and a series of equations were applied to estimate the sediment contribution from each group to the downstream side of the river. Samples from the same sampling locations were also analysed by XRD, and the obtained peak intensity values were used as the input in the NNA model. SS mainly originated from agricultural fields, with regions where the ground is covered with volcanic ash identified as the key sources through XRF and XRD analysis, respectively. Therefore, based on the nature of the surface soil cover and the land use pattern in the catchment basin, NNA was found to be a reliable data analytical technique. Moreover, XRD analysis does not incorporate carbon, and also provides detailed information on crystalline phases. The results obtained in this study, therefore, do not depend on seasonal uncertainty due to organic matter.

Study on the Effect of Soft–Hard Material Interface Differences on Crack Deflection in Nacre-Inspired Brick-and-Mortar Structures

Nacre has excellent balanced strength and toughness. In this paper, the mechanical performance of the typical “brick-and-mortar” structure, including the stress–strain and strain at the interface as well as the stress in the bricks, was calculated by a simplified analytical model of the nacre. This paper proposes a new method to control the crack deflection based on the toughening mechanism of the nacre. The crack extension of the “brick-and-mortar” structure was simulated using cohesive elements based on the traction–separation law with elastic and softening stiffness as variables, and it was found that both stiffness could effectively control the crack extension. The strength and toughness of the models with different stiffness combinations were calculated and plotted as a function of elastic stiffness and softening stiffness, showing that elastic stiffness significantly affects strength and softening stiffness is a determinant of toughness.

Effects of liquid fraction and contact angle on structure and coarsening in two-dimensional foams

Aqueous foams coarsen with time due to gas diffusion through the liquid between the bubbles. The mean bubble size grows, and small bubbles vanish. However, coarsening is little understood for foams with an intermediate liquid content, particularly in the presence of surfactant-induced attractive forces between the bubbles, measured by the interface contact angle where thin films meet the bulk liquid. Rigorous bubble growth laws have yet to be developed, and the evolution of bulk foam properties is unclear. We present a quasistatic numerical model for coarsening in two-dimensional wet foams, focusing on growth laws and related bubble properties. The deformation of bubble interfaces is modelled using a finite-element approach, and the gas flow through both films and Plateau borders is approximated. We give results for disordered two-dimensional wet foams with $256$ to $1024$ bubbles, at liquid fractions from $2\,\%$ to $25\,\%$ , beyond the zero-contact-angle unjamming transition, and with contact angles up to $10^\circ$ . Simple analytical models for the bubble pressures, film lengths and coarsening growth rates are developed to aid interpretation. If the contact angle is non-zero, we find that a prediction of the coarsening rate approaches a non-zero value as the liquid fraction is increased. We also find that an individual bubble's effective number of neighbours determines whether it grows or shrinks to a good approximation.

Capillary filling dynamics in closed-end carbon nanotubes-Defying the classical Lucas-Washburn paradigm.

The emergence of two-dimensional (2D) materials such as carbon nanotubes (CNTs) offers the possibility of exploring new regimes of capillarity and wetting that remained inaccessible with traditional microfluidic and nanofluidic substrates. Here, we bring out the non-intuitive capillary filling regimes in closed-end CNTs using molecular-level investigations. Contrary to the existing understanding of the advancing liquid meniscus getting retarded by the viscous resistance offered by an entrapped vapor phase in a three-dimensional capillary, here the liquid meniscus is shown to accelerate toward the later stages of the dynamic wetting, which is attributed to the modified surface friction due to a 2D interface. This apparently counterintuitive observation is qualitatively linked to the local pressure fluctuations across the meniscus caused by the spontaneous bombardment of the entrapped vapor molecules, which may ramify into hitherto unexplored phenomena of a shape-reversed meniscus advancing in the 2-D pore. We further develop a simple analytical model to represent the essential physics of the resulting capillary filling dynamics, featuring significant deviations from the classical Lucas-Washburn paradigm. These results may turn out to be imperative in realizing new regimes of capillarity in 2D materials in multifarious applications, ranging from energy storage and water filtration to thin film flows in integrated electronics and photonic devices.

Device physics of perovskite light-emitting diodes

Perovskite light-emitting diodes (LEDs) have emerged as a potential solution-processible technology that can offer efficient light emission with high color purity. Here, we explore the device physics of perovskite LEDs using simple analytical and drift-diffusion modeling, aiming to understand how the distribution of electric field, carrier densities, and recombination in these devices differs from those assumed in other technologies such as organic LEDs. High barriers to electron and hole extraction are responsible for the efficient recombination and lead to sharp build-up of electrons and holes close to the electron- and hole-blocking barriers, respectively. Despite the strongly varying carrier distributions, bimolecular recombination is surprisingly uniform throughout the device thickness, consistent with the assumption typically made in optical models. The current density is largely determined by injection from the metal electrodes, with a balance of electron and hole injection maintained by redistribution of electric field within the device by build-up of space charge.

Lateral Response Analysis of a Large‐Diameter Pile Under Combined Horizontal Dynamic and Axial Static Loads in Nonhomogeneous Soil

ABSTRACTThe large diameter piles are widely used in structures such as offshore wind turbines due to their superior lateral load‐bearing capacity. To explore the lateral response of a large‐diameter pile under combined horizontal dynamic and axial static loads in nonhomogeneous soil, a simplified analytical model of the pile–soil interaction is developed. This model represents the pile as a Timoshenko beam resting on the Pasternak foundation, incorporating the double‐shear effect by considering both pile and soil shear. The governing matrix equations for the pile elements are derived from the principle of virtual work. Further, the pile's lateral deformations and internal forces are obtained using the modified finite beam element method (FBEM) and then validated through existing analytical solutions. Finally, the contribution of various properties of pile, soil, and applied load to the pile's lateral vibration response are performed. It is found that both pile and soil shear effects significantly impact the lateral dynamic response of a large‐diameter pile. Additionally, in nonhomogeneous soil, decreasing surface soil strength and dimensionless frequency lead to increased lateral displacements and bending moments of the pile, which are significantly affected by the P‐Δ effect under increasing axial load.

The Impact of Mass-dependent Stochasticity at Cosmic Dawn

The James Webb Space Telescope is unveiling a surprising lack of evolution in the number densities of ultraviolet (UV)-selected galaxies at redshift z ≳ 10. At the same time, observations and simulations are providing evidence for highly bursty star formation in high-z galaxies, resulting in significant scatter in their UV luminosities. Galaxies in low-mass dark matter halos are expected to experience most stochasticity due to their shallow potential wells. Here, we explore the impact of a mass-dependent stochasticity using a simple analytical model. We assume that scatter in the M UV–M h relation increases toward lower halo masses, following the decrease in halo escape velocity, σUV∼Mh−1/3 , independent of redshift. Since low-mass halos are more dominant in the early universe, this model naturally predicts an increase in UV luminosity functions (LFs) at high redshifts compared to models without scatter. We make predictions for additional observables, which would be affected by stochasticity and could be used to constrain its amplitude, finding (i) galaxies are less clustered compared to the no-scatter scenario, with the difference increasing at higher-z; (ii) assuming that star-bursting galaxies dominate the ionizing photon budget implies reionization starts earlier and is more gradual compared to the no-scatter case; (iii) at fixed UV magnitude, galaxies should exhibit wide ranges of UV slopes, nebular emission line strengths, and Balmer breaks. Comparing to observations, the mass-dependent stochasticity model successfully reproduces the observed LFs up to z ∼ 12. However, the model cannot match the observed z ∼ 14 LFs, implying additional physical processes enhance star formation efficiency in the earliest galaxies.

Simplified dynamic modeling and Fuzzy gain scheduled PID control of woodward-governor controlled grid-interactive twin-shaft gas turbine plants

Biomass-integrated gas turbines for electricity generation are competitive with coal and nuclear energy production. Gas turbine-based power generation system looks to be an excellent solution amid the emerging environmental conditions and the increased energy crisis. This paper presents a simplified dynamic analysis model for biomass-based, Woodward governor-controlled, twin-shaft heavy-duty gas turbine (HDGT) plants, alongside an intelligent controller for stability enhancement. Grid-connected HDGTs can become unstable under load disturbances, potentially causing system shutdowns. A simplified model for twin-shaft gas turbines, rated from 18.2 MW to 106.7 MW, has been identified based on control characteristics during startup. The speed controller is dominant, while the acceleration controller is only active at startup, and the temperature controller's effect is minimal during normal operation. This model suits all dynamic studies of twin-shaft gas turbines, regardless of varying power ratings and rotor time constants. For improving the grid stability, a Takagi-Sugeno-Kang (TSK) fuzzy gain scheduling PID controller has been proposed in this work and its behavior is validated with 5001M, 7001Ea, and 9001Ea models. Step response of fuzzy PID controller under load disturbances and set-point variations are compared with fixed gain PID controllers tuned by Ziegler-Nichols (ZN) and performance index-based tuning using the typical gas turbine model. Further the controller behavior is validated with field test-based model parameters as derived from the real-world combustion turbines used in Alaskan Railbelt system. Extensive research simulation and validation results reveal that the fuzzy self-tuning PID controller showed superior adaptability for grid-interactive twin-shaft HDGTs under load variations and set-point variations. Time domain specifications and the performance indices confirms that the proposed fuzzy tuned PID controller ensure reliable and stable operation for the energy management in grid-operative mode. The proposed simplified model and intelligent control logic enable various dynamic studies in grid-connected environments for both simple cycle and combined cycle operations.

Observation of Space-Dependent Rotational Doppler Shifts with a Single Ion Probe.

We present an experiment investigating the rotational Doppler effect using a single trapped ion excited by two copropagating vortex laser beams. The setup isolates the azimuthal gradients of the fields, eliminating longitudinal and curvature effects. We provide a detailed characterization of the phenomenon by deterministically positioning a single ion across the beams and measuring fluorescence spectra with sharp "dark resonances" whose features depend on the angular velocity of the ion and the difference of optical orbital angular momentum between the two beams. The interpretation of the measurements is supported by numerical simulations and by a simplified analytical model. Our results reveal key properties of the rotational Doppler effect, showing that it increases approaching the center of the beam and that it is independent of the waist of the beam. This offers insights into the feasibility of superkicks or super-Doppler shifts for sensing and manipulating atomic motion transverse to the beams' propagation direction.

Incorporating soil‐structure interaction into simplified numerical models for fragility analysis of RC structures

AbstractSimplified building models are a valuable option for seismic assessment at the regional scale. These models often use calibrated springs to model column behaviour, and recent advances have made them suitable for capturing torsional response in Reinforced‐Concrete Moment‐Resisting‐Frames. Nevertheless, their validation is typically achieved using fixed‐base models, which do not include the influence of soil‐structure interaction (SSI). This study introduces a novel approach to quantify the accuracy of a recently developed simplified model while accounting for dynamic SSI, using a newly implemented, refined 3D Finite Element non‐linear soil model in OpenSees. The accuracy of the simplified structural model is assessed by comparing the results of non‐linear dynamic analyses with those of a refined model in terms of (i) a peak structural demand parameter such as the interstorey‐drift ratio and (ii) fragility curves computed from cloud analysis and accounting for collapse cases. The study presents details of the proposed refined approach for 3D soil modelling in OpenSees, focusing on implementing free‐field boundary conditions and structure‐to‐soil connections. Results show that the accuracy of the simplified model is maintained, even in the presence of SSI, and it successfully captures the overall structural response measured at peak demand. For the proposed case study, the difference between the simplified and refined models’ fragility curves’ medians is 4% and 2% for fixed and SSI models, respectively. The simplified structural model, combined with the refined soil model for SSI effects, presents an innovative and conservative, yet computationally efficient, alternative for seismic risk analysis, even in the presence of structural irregularity.

3-Dimensional numerical analysis of geosynthetic double-encased annulus stone columns

A geosynthetic double-encapsulated annulus stone column technique is proposed in this study to overcome limitations associated with conventional stone columns, such as limited lateral load-bearing capacity and potential issues related to aggregate dispersion in soft soils. Geosynthetic double-encapsulated annulus stone columns are consistent with conventional stone columns besides being confined in and around the surrounding soil. The performance of geosynthetic double-encapsulated annulus stone columns is primarily dependent upon their outer-to-inner diameter ratio. For this reason, comprehensive 3-dimensional numerical studies were carried out to evaluate the optimum outer-to-inner diameter ratio of the annulus stone column. The results suggest that the ultimate load-carrying capacity of an annulus stone column increases with an increasing ratio of outer to inner diameter until an optimum value. In addition, the double encapsulation enhances confinement, improving shear stiffness and reducing lateral bulging. However, the load-carrying capacity was substantially reduced beyond the critical outer-to-inner diameter ratio. A simple analytical model extending the theory of thin cylinders is also introduced to estimate the accumulated stresses and strains in the geosynthetic encasement. The proposed model operates within a simplified framework of elastic solutions that facilitate practising engineers to design and optimize geosynthetic encasements for enhanced structural performance.

A simple dynamic time constant model for both summer overheating and winter heating analysis

As new buildings have high levels of insulation it is important to ensure that solar and other internal gains do not make the interiors too hot in summer. This is well known. But assessing overheating at an early design stage is not so easy. The Thermal Mass Parameter (TMP) in the regulations is based on a 24 h cyclic assessment of the depth of heat storage in a material. This paper examines a simpler method using the whole thermal mass, simple steady state calculations and a time constant that can take into account the heat gains over a number of days, such as in a heat wave, not just over 24 h. This simple dynamic time constant model (SDTCM) would be a more realistic model to assess overheating and performance for Future Homes and Buildings Standards, now under consultation in the UK. The model can equally be applied to assess winter heating and for dynamic simulation to consider control strategies. Practical application This paper describes a simple model that can be used for determining heating sizing in winter and overheating in summer. It relates to assessing the thermal mass via the time constant relating to the dynamic response of the building. This will be useful in initial design and possibly regulation.

Magnetising galaxies with cold inflows

High-redshift ($z galaxies accrete circumgalactic gas through cold streams. Recent high-resolution magnetohydrodynamic (MHD) simulations of these streams show a significant amplification of the intergalactic magnetic field in the shear layer around them. For this work we estimated the magnetisation of high-redshift galaxies that would result purely due to the accretion of already magnetised gas from cold streams. We used the mass inflow rates and saturated magnetic field values from cold stream simulations as input to a simple analytic model that calculates the galactic magnetic field purely from mass accretion. Our model predicts average magnetic field strengths that exceed muG values at $z 2-3$ for inflow rates above $0.1 \ yr^ $. For high inflow rates, our model results are consistent with the recent detection of a strong magnetic field in $z 2.6$ galaxies. Within the assumptions of our simple model, magnetised cold streams emerge as a viable mechanism for seeding a dynamically important galactic magnetic field.

H2 Fluorescent Emission from the Diffuse Interstellar Medium

Near-IR spectroscopy, which can now be performed at unprecedented sensitivity with the NIRSpec instrument on JWST, can offer a novel probe of diffuse clouds through the observation of H2 fluorescent emissions. Whereas previous observations of interstellar H2 fluorescent emissions were primarily confined to dense clouds lying close to a source of UV radiation, JWST opens the possibility of detecting such emissions from diffuse molecular clouds exposed to the average radiation field in the Galaxy. A simple analytic model is presented to predict the near-IR H2 fluorescent line intensities emitted by diffuse interstellar clouds with a Plummer density profile. It is applicable to sightlines where the column densities of H and H2 have been measured and the peak gas density can be estimated.

Development and Comparison of Model-Based and Data-Driven Approaches for the Prediction of the Mechanical Properties of Lattice Structures

AbstractLattice structures have great potential for several application fields ranging from medical and tissue engineering to aeronautical one. Their development is further speeded up by the continuing advances in additive manufacturing technologies that allow to overcome issues typical of standard processes and to propose tailored designs. However, the design of lattice structures is still challenging since their properties are considerably affected by numerous factors. The present paper aims to propose, discuss, and compare various modeling approaches to describe, understand, and predict the correlations between the mechanical properties and the void volume fraction of different types of lattice structures fabricated by fused deposition modeling 3D printing. Particularly, four approaches are proposed: (i) a simplified analytical model; (ii) a semi-empirical model combining analytical equations with experimental correction factors; (iii) an artificial neural network trained on experimental data; (iv) numerical simulations by finite element analyses. The comparison among the various approaches, and with experimental data, allows to identify the performances, advantages, and disadvantages of each approach, thus giving important guidelines for choosing the right design methodology based on the needs and available data.

A simplified model for unsteady airflow analysis in ultra-long tunnels based on the resistance compensation method

A simplified model for unsteady airflow analysis in ultra-long tunnels based on the resistance compensation method

Current density–voltage characteristics of exciplex-type organic light-emitting diodes expressed by a simple analytic equation

Exciplex-type bilayer organic light-emitting diodes (OLEDs) with ohmic contacts exhibited current density–voltage (J–V) characteristics that closely matched a simplified analytical model proposed by Nikitenko and Bässler. The analytical model is based on the following key assumptions: (i) complete hole–electron recombination at the interface between a hole transport layer (HTL) and an electron transport layer (ETL), (ii) ohmic contacts at the interfaces between metal electrodes and carrier transport layers, and (iii) electric-field-independent carrier mobilities in both HTL and ETL. The excellent matching shows that the simplified analytical model is sufficient to describe the J–V characteristics of the OLEDs. We also demonstrated that if the carrier mobility of one carrier transport layer is known, that of the other transport layer can be estimated using the equation derived by the simplified analytical model. The simplified analytical model provides a useful method to estimate carrier mobilities within carrier transport layers themselves in OLEDs.

Exploring the connection between AGN radiative feedback and massive black hole spin

We present a novel implementation for active galactic nucleus (AGN) feedback through ultrafast winds in the code GIZMO. Our feedback recipe accounts for the angular dependence of radiative feedback on black hole spin. We self-consistently evolve in time (i) the gas-accretion process from resolved scales to a smaller scale unresolved (subgrid) AGN disk, (ii) the evolution of the spin of the massive black hole (MBH), (iii) the injection of AGN-driven winds into the resolved scales, and (iv) the spin-induced anisotropy of the overall feedback process. We tested our implementation by following the propagation of the wind-driven outflow into an homogeneous medium, and here we present a comparison of the results against simple analytical models. We also considered an isolated galaxy setup, where the galaxy is thought to be formed from the collapse of a spinning gaseous halo, and there we studied the impact of the AGN feedback on the evolution of the MBH and of the host galaxy. We find that: (i) AGN feedback limits the gas inflow that powers the MBH, with a consequent weak impact on the host galaxy characterized by a suppression of star formation by about a factor of two in the nuclear (≲kpc) region; (ii) the impact of AGN feedback on the host galaxy and on MBH growth is primarily determined by the AGN luminosity rather than by its angular pattern set by the MBH spin (i.e., more luminous AGNs more efficiently suppress central star formation (SF), clearing wider central cavities and driving outflows with larger semiopening angles); (iii) the imprint of the angular pattern of AGN radiation emission is detected more clearly at high (i.e., Eddington) accretion rates. At such high rates, the more isotropic angular patterns, as occur for high spin values, sweep away gas in the nuclear region more easily, therefore causing a slower MBH mass and spin growths and a higher quenching of SF. We argue that the influence of spin-dependent anisotropy of AGN feedback on MBH and galaxy evolution is likely to be relevant in those scenarios characterized by high and prolonged MBH accretion episodes and by high AGN wind–galaxy coupling. Such conditions are more frequently met in galaxy mergers and/or high-redshift galaxies.

Effects of Bursty Star Formation on [C ii] Line Intensity Mapping of High-redshift Galaxies

Bursty star formation—a key prediction for high-redshift galaxies from cosmological simulations explicitly resolving stellar feedback in the interstellar medium—has recently been observed to prevail among galaxies at redshift z ≳ 6. Line intensity mapping (LIM) of the 158 μm [C ii] line as a star formation rate (SFR) indicator offers unique opportunities to tomographically constrain cosmic star formation at high redshift, in a way complementary to observations of individually detected galaxies. To understand the effects of bursty star formation on [C ii] LIM, which have remained unexplored in previous studies, we present an analytic modeling framework for high-z galaxy formation and [C ii] LIM signals that accounts for bursty star formation histories induced by delayed supernova feedback. We use it to explore and characterize how bursty star formation can impact and thus complicate the interpretation of the [C ii] luminosity function and power spectrum. Our simple analytic model indicates that bursty star formation mainly affects low-mass galaxies by boosting their average SFR and [C ii] luminosity, and in the [C ii] power spectrum it can create a substantial excess in the large-scale clustering term. This distortion results in a power spectrum shape that cannot be explained by invoking a mass-independent logarithmic scatter. We conclude that burstiness must be accounted for when modeling and analyzing [C ii] data sets from the early Universe, and that in the extreme, the signature of burstiness may be detectable with first-generation experiments such as TIME, CONCERTO, and CCAT-DSS.

Beyond the biting - limited impact of explicit mosquito dynamics in dengue models

Mathematical models play a crucial role in assisting public health authorities in timely disease control decision-making. For vector-borne diseases, integrating host and vector dynamics into models can be highly complex, particularly due to limited data availability, making system validation challenging. In this study, two compartmental models akin to the SIR type were developed to characterize vector-borne infectious disease dynamics. Motivated by dengue fever epidemiology, the models varied in their treatment of vector dynamics, one with implicit vector dynamics and the other explicitly modeling mosquito-host contact. Both considered temporary immunity after primary infection and disease enhancement in secondary infection, analogous to the temporary cross-immunity and the Antibody-dependent enhancement biological processes observed in dengue epidemiology. Qualitative analysis using bifurcation theory and numerical experiments revealed that the immunity period and disease enhancement outweighed the impact of explicit vector dynamics. Both models demonstrated similar bifurcation structures, indicating that explicit vector dynamics are only justified when assessing the effects of vector control methods. Otherwise, the extra equations are irrelevant, as both systems display similar dynamics scenarios. The study underscores the importance of using simple models for mathematical analysis, initiating crucial discussions among the modeling community in vector-borne diseases.