Model Of Density Distribution Research Articles

A tail probability density distribution model of stress amplitude under band-limited stochastic vibration loadings

Resonance of engineering structures under stochastic vibration loadings is a primary cause of fatigue failure. Considering that cyclic loadings below the fatigue limit of the material contribute little to fatigue damage, the portion of the stress amplitude distribution that exceeds the fatigue limit is in focus in this paper, and a tail probability density distribution model of stress amplitude under band-limited stochastic vibration loadings is proposed. First, the response stress power spectral density functions under band-limited loadings are simulated by using the normal distribution and the Weibull distribution, respectively, and then the frequency domain signals are converted into time domain signals by adopting the inverse fast Fourier transform method. A two-parameter Weibull model of tail probability density distribution of stress amplitude is proposed, and the relationship between model parameters and power spectral moment parameters is given. Finally, the comparative analysis of the model accuracy and the vibration fatigue test of aluminum alloy notch specimen are carried out. It is demonstrated that the fatigue life predicted by the presented model is highly coincident with the results of tests and the time domain method.

The 3D Crustal Structure of the Wilkes Subglacial Basin, East Antarctica, Using Variation of Information Joint Inversion of Gravity and Magnetic Data

AbstractDirect geological information in Antarctica is limited to ice free regions along the coast, high mountain ranges, or isolated nunataks. Therefore, indirect methods are required to reveal subglacial geology and heterogeneities in crustal properties, which are critical steps toward interpreting geological history. We present a 3D crustal model of density and susceptibility distribution in the Wilkes Subglacial Basin (WSB) and the Transantarctic Mountains (TAM) based on joint inversion of airborne gravity and magnetic data. The applied “variation of information” technique enforces a coupling between inferred susceptibility and density, relating these quantities to the same gravity and magnetic sources to give an enhanced inversion result. Our model reveals a large body located in the interior of the WSB interpreted as a batholithic intrusive structure, as well as a linear dense body at the margin of the Terre Adélie Craton. Density and susceptibility relationships are used to inform the interpretation of petrophysical properties and the reconstruction of the origin of those crustal bodies. The petrophysical relationship indicates that the postulated batholitic intrusion is granitic, but independent from the Granite Harbor Igneous Complex described previously in the TAM area. Emplacement of a large volume of intrusive granites can potentially elevate local geothermal heat flow significantly. Finally, we present a new conceptual tectonic model based on the inversion results, which includes development of a passive continental margin with seaward dipping basalt horizons and magmatic underplating followed by two distinct intrusive events associated with the protracted Ross Orogen.

An Efficient Algorithm for Gravity Forward Modeling (GFM) with Masses of Arbitrary Shapes and Density Distributions

Summary Currently, gravimetric forward modelling of mass density structures with arbitrary geometries and density distributions typically involves subdividing the mass body into individual geometric elements (such as rectangular prisms), calculating their gravitational contributions that are then summed up to obtain the gravitational attraction of the whole body. To achieve a more accurate approximation of the true geometric shape and density distribution, this rectangular prism model requires fine dividing, which significantly increases computational load and reduces numerical efficiency. To address this issue, we propose the algorithm for gravimetric forward modeling of arbitrary geometric shapes and density distributions in spectral domain that significantly improves numerical efficiency while preserves computational accuracy. The novelty of our proposed algorithm lies in dividing the masses into multiple layers of equal thickness in the vertical direction, providing constant upper and lower bounds. This allows to extended Parker's formulas and apply the Fast Fourier Transform (FFT) to increase numerical efficiency. The algorithm is tested using synthetic models and then used to compute gravitational effects of topography and sediments using real data from Tibet. Results show high accuracy and numerical efficiency than rectangular prism approach.

Method for analysing of wind power wave nature based on kernel density estimation

It is beneficial for improving the accuracy of wind power output prediction by analysing and mastering the inherent laws of the fluctuation characteristics of wind power output, guiding the power grid dispatching department to reasonably arrange power generation plans, and improving the economic efficiency of system operation. In order to characterize the probability density distribution of wind power output fluctuation, two adaptive bandwidth kernel density estimation models are established by correcting the fixed bandwidth obtained from the empirical method and unbiased cross-validation method respectively, and then the two models are combined and optimized, and ultimately, the probability density distribution model of wind power output fluctuation based on Hybrid Adaptive Kernel Density Estimation (HAKDE) is established. A variety of probability density distribution models are used to fit the wind power output fluctuations at different spatial and temporal scales in a province in North China, and the example results show that the hybrid adaptive kernel density estimation model has the best fitting effect, thus verifying the effectiveness of the hybrid adaptive kernel density estimation model.

Exploring building component thermal storage performance for optimizing indoor thermal environment – A case study in Beijing

Optimizing the thermal storage of building components is crucial for improving indoor thermal conditions and reducing heating energy consumption. However, existing studies often overlook the effect of the substantial thermal mass in common building components, each storing different levels of heat. This study finds that considering this thermal mass and its energy during the building design phase can significantly save insulation material costs and heating energy consumption.Our work is built upon the analysis of the thermal behaviors of real buildings. We collected data from 43 representative rooms in cold regions and utilized Multiple Linear Regression models to examine how solar radiation and outdoor temperatures affect thermal mass in external walls, internal walls, and floors. We also used Probabilistic Density Distribution models to study heat transfer within these components. Subsequently, we applied Conduction Transfer Functions with just a 2.08% error rate to derive an optimal passive design strategy for year-round use of building thermal mass.Experimental results show that our strategy saves more energy by 0.78 kWh/m2 without increasing the insulation material cost, exceeding current standards. In cold regions, our study suggests focusing on mitigating the negative effects of building thermal mass, which offers greater energy savings than exploiting its positive aspects. Moreover, our findings can be easily integrated into the optimization of physical properties like thermal capacity and insulation for either improving stock buildings or designing new buildings, further enhancing their energy and material efficiency.

Exploring the Origin of Stars on Bound and Unbound Orbits Causing Tidal Disruption Events

Tidal disruption events (TDEs) provide a clue to the properties of a central supermassive black hole (SMBH) and an accretion disk around it, and to the stellar density and velocity distributions in the nuclear star cluster surrounding the SMBH. Deviations of TDE light curves from the standard occurring at a parabolic encounter with the SMBH depend on whether the stellar orbit is hyperbolic or eccentric and the penetration factor (β, the tidal disruption radius to the orbital pericenter ratio). We study the orbital parameters of bound and unbound stars being tidally disrupted by comparison of direct N-body simulation data with an analytical model. Starting from the classical steady-state Fokker–Planck model of Cohn & Kulsrud, we develop an analytical model of the number density distribution of those stars as a function of orbital eccentricity (e) and β. To do so, fittings of the density and velocity distribution of the nuclear star cluster and of the energy distribution of tidally disrupted stars are required and obtained from N-body data. We confirm that most of the stars causing TDEs in a spherical nuclear star cluster originate from the full loss-cone region of phase space, derive analytical boundaries in eccentricity-β space, and find them confirmed by N-body data. Since our limiting eccentricities are much smaller than critical eccentricities for full accretion or the full escape of stellar debris, we conclude that those stars are only very marginally eccentric or hyperbolic, close to parabolic.

Incorporating the coupled effects of slot opening, armature reaction and saturation in the model of the airgap flux density distribution of permanent magnet synchronous machines

AbstractA new analytic model for calculating of the air‐gap flux density (AGFD) of surface‐mounted permanent magnet synchronous machines (SMPMSMs) is presented. This proposed model is capable to taking into account the effects of magnetic saturation, armature reaction and stator slots opening. Furthermore, the real form of air‐gap distribution and spatial distribution of flux density of the PM poles are considered. The armature reaction effect is modeled using phasor diagram analysis of the motor as a function of the load torque, the armature current amplitude, power factor and the inverse air gap length. Also, saturation phenomenon predicted using the new non‐linear proposed function in connection with the armature reaction effects and the properties of the lamination material. It is shown that the proposed model capable to predicting acceptably the air gap flux density waveform of the SMPMSMs at lagging and leading power factors and with the load torque variation. The presented analytical approach is verified by the two‐dimensional finite‐element analysis (FEA) results.

Simulation Analysis of Dynamic Damage Probability Modelling for Laser Systems

The paper proposes a method that analyses the dynamic damage probability of laser systems to address the shortcomings of the quantitative model for the damage probability of laser systems. Firstly, the far-field energy density distribution model is constructed according to the power spectrum inversion method. Then, the instantaneous on-target spot power density distribution is equivalently portrayed based on the combination of the far-field power density and the missile target characteristics. Next, the instantaneous on-target spot is combined with the tracking and aiming error to obtain the probability distribution of the energy density of the long-period on-target spot. Finally, the temperature probability distribution is obtained by analyzing the relation between the target energy density and the temperature of the inner wall of the warhead. Consequently, the damage probability was calculated. The simulation shows that there is a unique maximum damage probability when the target is flying in a straight line and the laser system strikes the missile sideways. The method can provide support for the shooting timing of high-energy laser systems.

A contribution to the investigation of acoustic interferences in aircraft distributed propulsion

The objective of this work is to better understand the acoustic interferences created by distributed propulsion engines based on an approach that combines RANS simulation results for the aerodynamic prediction and analytical models to calculate acoustics. A multi-propeller configuration without wing is considered for this investigation. The propeller geometry and the operating conditions are realistic for a regional transport airplane. In the first part of the paper, the results obtained by two different and independent prediction methods are compared. One method is well-established and serves as validation for the second, low-order method, which is better suited for design-to-noise applications since it requires less details as input and is computationally faster by several orders of magnitude. The good agreement between both methods, obtained for a single propeller as well as for the distributed propeller configuration, is exploited in the second part of the paper to investigate the role of acoustic interferences. Taking acoustic interferences into account drastically affects the directivity of the tonal emission. Compared to the results obtained by considering the propellers as if they were uncorrelated, the far-field sound pressure levels can be significantly lower at the radiation nodes or amplified up to the theoretical limit of 9 dB calculated for eight propellers. The directivity patterns depend on the relative initial angular positions of the propellers. When these positions are randomly varied according to the uniform probability density distribution model, the mean result (expectation) is the same as if the propellers were considered as uncorrelated. Finally, the results show that the probability that the acoustic level is lower than the mean value is higher than 50% because of the positive skewness of the probability distribution of the resulting pressure amplitude. Even though the propeller–propeller and propeller–wing interactions were not considered, the essence of the findings is expected to remain valid for more complex configurations because those interactions are rotor phase-locked.

Research on the Forward Solving Method of Defect Leakage Signal Based on the Non-Uniform Magnetic Charge Model.

Pipeline magnetic flux leakage inspection is widely used in the evaluation of material defect detection due to its advantages of having no coupling agent and easy implementation. The quantification of defect size is an important part of magnetic flux leakage testing. Defects of different geometrical dimensions produce signal waveforms with different characteristics after excitation. The key to achieving defect quantification is an accurate description of the relationship between the magnetic leakage signal and the size. In this paper, a calculation model for solving the defect leakage field based on the non-uniform magnetic charge distribution of magnetic dipoles is developed. Based on the traditional uniformly distributed magnetic charge model, the magnetic charge density distribution model is improved. Considering the variation of magnetic charge density with different depth positions, the triaxial signal characteristics of the defect are obtained by vector synthesis calculation. Simultaneous design of excitation pulling experiment. The leakage field distribution of rectangular defects with different geometries is analyzed. The experimental results show that the change in defect size will have an impact on the area of the defect leakage field distribution, and the larger the length and wider the width of the defect, the more sensitive the impact on the leakage field distribution. The solution model is consistent with the experimentally obtained leakage signal distribution law, and the model is a practical guide by which to improve the quality of defect evaluation.

A Monte Carlo Density Distribution Model Study to Analyze Galaxy Structure, Mass Distribution, and Dark Matter Phenomena

This research uses the Monte Carlo density distribution model to study the structure and mass distribution of galaxies and the dark matter phenomenon. Through computer simulations, the research developed a mathematical model with parameters such as rho0, rc, beta, and others, to describe the structure and mass distribution of galaxies. The results show that the model can reproduce various galaxy structures, including groups, clusters and filaments, and influence the behavior and characteristics of individual galaxies. This research provides a deeper understanding of dark matter and its impact on the evolution of the universe. It has implications for improving our understanding of dark matter and the use of Monte Carlo density distribution models to study galaxies. This study provides new insights into the evolution of galaxies and their relationship with dark matter in cosmology. Using both physics and mathematical concepts, this research helps to understand the phenomenon of dark matter and the structure of galaxies, and provides a basis for further research on dark matter and galaxy evolution.

Data-constrained Solar Modeling with GX Simulator

To facilitate the study of solar flares and active regions, we have created a modeling framework, the freely distributed GX Simulator IDL package, that combines 3D magnetic and plasma structures with thermal and nonthermal models of the chromosphere, transition region, and corona. Its object-based modular architecture, which runs on Windows, Mac, and Unix/Linux platforms, offers the ability to either import 3D density and temperature distribution models, or to assign numerically defined coronal or chromospheric temperatures and densities, or their distributions, to each individual voxel. GX Simulator can apply parametric heating models involving average properties of the magnetic field lines crossing a given voxel, as well as compute and investigate the spatial and spectral properties of radio, (sub)millimeter, EUV, and X-ray emissions calculated from the model, and quantitatively compare them with observations. The package includes a fully automatic model production pipeline that, based on minimal users input, downloads the required SDO/HMI vector magnetic field data, performs potential or nonlinear force-free field extrapolations, populates the magnetic field skeleton with parameterized heated plasma coronal models that assume either steady-state or impulsive plasma heating, and generates non-LTE density and temperature distribution models of the chromosphere that are constrained by photospheric measurements. The standardized models produced by this pipeline may be further customized through specialized IDL scripts, or a set of interactive tools provided by the graphical user interface. Here, we describe the GX Simulator framework and its applications.

Subsurface Model Of Mt. Sinabung Using The GGM-Plus Satellite Gravity Data And Deconvolution Euler

Mt. Sinabung in Karo Regency, North Sumatra Province, with an altitude of 2450 meters above sea level, became active again in 2010 after a break in volcanic activity for ± 300 years. Since the eruption in 2010 until now, eruptions are still ongoing periodically. The aim of this research is to obtain a model of the subsurface density distribution of Mt. Sinabung. Modeling was carried out using GGM-Plus 2013 satellite gravity data and ERTM2160 topographical data. Bouguer correction and terrain processing use an average density of 2.67 g/cc. After that, the anomaly was separated by using the moving average. Residual anomalies were then analyzed using Euler deconvolution. The results obtained are the existence of a fault structure on the west and three layers of rock obtained which consist of the basement with a density of 2.8 g/cc 3 – 3.3 g/cc, then Toba pyroclastic deposits with a density 1.8 g/cc – 2.3 g/cc and limestone deposits with a density of 2.4 g/cc – 2.7 g/cc.

Hydrogen adsorption in nanopores: Molecule-wall interaction mechanism

Reduction in the utilization of carbon-based fossil energy is the inevitable pathway to fulfill the net-zero CO2 emission target. Hydrogen, one of favorable clean energy sources, becomes a heat topic at present while its safe and efficient storage remains a challenging issue. The majority of related research focus on the hydrogen injection into salt cavern as well as depleted oil/gas reservoirs, where hydrogen is highly compressed under high pressure. In this research, an alternative approach that stores hydrogen into nanopores using the essential adsorption property is investigated, and so does its advantage over traditional high-pressure injection method. First of all, a mechanical model for density distribution of nanoconfined hydrogen is established by the chemical potential equilibrium principle, in which both intermolecular interactions and molecule-wall interactions are taken into account. Additionally, shift of critical properties taking place in nanopores is coupled as well. Then, the nanoconfined hydrogen adsorption behavior is presented, influence of atmosphere parameters, like pressure and temperature, as well as nanopore physical properties, like pore size and strength the pore wall imposes on hydrogen molecules, are identified. The proposed model can reach excellent agreements with hydrogen adsorption data collected from the existed experiments and molecular simulation, clarifying its reliability. Results show that (a) Adsorption phase thickness approaches 0.5 nm, indicating 1–2 adsorption layers are formed, which is insensitive to pressure or temperature variation; (b) Nanoconfined hydrogen density is able to achieve as great as 7 times bulk-hydrogen density at relatively low pressure, suggesting nanopores could store more hydrogen molecules than the traditional high-pressure injection method; (c) Modifying nanopore surface chemistry to intensify molecule-wall interaction strength is a desirable method to dramatically improve nanoconfined hydrogen adsorption capacity. The research lays a fundamental framework to shed light on hydrogen adsorption from a microscopic viewpoint.

The northeastern Algeria hydrothermal system: gravimetric data and structural implication

The Tell Atlas of Algeria has a huge potential for hydrothermal energy from over 240 thermal springs with temperatures up to 98^circ C in the Guelma area. The most exciting region is situated in the northeastern part which is known to have the hottest hydrothermal systems. In this work, we use a high-resolution gravity study to identify the location and origin of the hot water, and how it reaches the surface. Gravimetric data analysis shows the shapes of the anomalies arising due to structures at different subsurface depths. The calculation of the energy spectrum for the data also showcases the depths of the bodies causing anomalies. 3D-Euler deconvolution is applied to estimate the depths of preexisting tectonic structures (faults). These preprocessing steps assist with assessing signal attenuation that impacts the Bouguer anomaly map. The residual anomaly is used in a three-dimensional inversion to provide a subsurface density distribution model that illustrates the locations of the origin of the dominant subsurface thermal systems. Overall, the combination of these standard processing steps applied to the measurements of gravity data at the surface provides new insights about the sources of the hydrothermal systems in the Hammam Debagh and Hammam Ouled Ali regions. Faults that are key to the water infiltrating from depth to the surface are also identified. These represent the pathway of the hot water in the study area.

Jupiter’s cloud-level variability triggered by torsional oscillations in the interior

Jupiter’s weather layer exhibits long-term and quasi-periodic cycles of meteorological activity that can completely change the appearance of its belts and zones. There are cycles with intervals from 4 to 9 years, dependent on the latitude, which were detected in 5-μm radiation, which provides a window into the cloud-forming regions of the troposphere; however, the origin of these cycles has been a mystery. Here we propose that magnetic torsional oscillations arising from the dynamo region could modulate the heat transport and hence be ultimately responsible for the variability of the tropospheric banding. These axisymmetric torsional oscillations are magnetohydrodynamic waves influenced by rapid rotation, which have been detected in Earth’s core, and have been recently suggested to exist in Jupiter by the observation of magnetic secular variations by Juno. Using the magnetic field model JRM33, together with a density distribution model, we compute the expected speed of these waves. For the waves excited by variations in the zonal jet flows, their wavelength can be estimated from the width of the alternating jets, yielding waves with a half-period of 3.2–4.7 years at 14–23° N, consistent with the intervals in the cycles of variability of Jupiter’s North Equatorial Belt and North Temperate Belt identified in the visible and infrared observations. The nature of these waves, including the wave speed and the wavelength, is revealed by a data-driven technique, dynamic mode decomposition, applied to the spatiotemporal data for 5-μm emission. Our results indicate that exploration of these magnetohydrodynamic waves may provide a new window to the origins of quasi-periodic patterns in Jupiter’s tropospheric clouds and to the internal dynamics and the dynamo of Jupiter. Torsional waves extend into the deep interior of Jupiter where they can modulate the outgoing heat flux and couple with Jupiter’s weather layer to generate the observed quasi-periodic oscillations in the cloud deck. Such waves can be used to explore the interior structure of gas giants.

3-D Inversion of Gravity Data of the Central and Eastern Gonghe Basin for Geothermal Exploration

The Gonghe Basin is one of the most important regions for the exploration and development of hot dry rock geothermal resources in China. However, there is still some controversy about the main heat source of hot dry rock geothermal resources in the Gonghe Basin. Combined with previous research results including three-dimensional magnetotelluric imaging and linear inversion of Rayleigh wave group and phase velocity result, we obtained a high-resolution underground spatial density distribution model of the Gonghe Basin based on satellite gravity data by using 3-D gravity focusing inversion method. According to the results, there are widely distributed low density anomalies relative to surrounding rock in the middle crust of the study area. The low-density layer is speculated to be a low-velocity, high-conductivity partial melting layer in the crust of the Gonghe Basin. The inversion result confirms for the first time the existence of a partial melt layer from the gravity point of view, and this high temperature melt layer may be the main heat source of the hot dry rock geothermal resources in the Gonghe Basin. It can provide a new basis for further research on the genesis of the hot dry rock geothermal system in the Gonghe Basin.

Developing a Bone Mineral Density Distribution Model to Reduce the Risk for Postoperative Hip Surgery Complications in Racial Minorities: A Research Protocol

Introduction: Racial minorities, including Black and Hispanic populations, suffer more postoperative hip surgery complications relating to fixations and replacements than White populations. The goal is to use CT scans and 3D projections to create a bone mineral density distribution model for these racial groups. Methods: A preliminary trial of the proposed methods was conducted to ensure reliable data could be obtained. Semi-automatic segmentation of left femurs from decedents was done in 3D Slicer, followed by mean bone mineral density analysis. Discussion: Preliminary trials show that the BMD processing pipeline gives viable results for sample groups of 5 CT scans. Future studies done with this research protocol will involve a larger sample size and the inclusion of machine learning extensions that will reduce the processing time of the CT scans. Confounding variables not considered in the preliminary trial will also be analyzed. Conclusion: The use of the streamlined pipeline in conjunction with other imaging software could provide an alternative to bone mineral density imaging, as well as lead to the development of models for minorities with less representation in medical data.

An Integration Model for Flux Density Distribution Formed by a Heliostat

An accurate flux density calculation is essential for optimizing and designing solar tower systems. Most of the existing methods introduce multiple assumptions, and the accuracy and scope of the application are limited. This paper proposes an integration model used to calculate the flux density distribution after only applying the Gaussian model for solar brightness distribution. It is the first time that multiple reflections and the influence of the optical error transferred from different planes of the glass mirror are considered in order to build an optical model for the flux density of a heliostat. The reflection from two surfaces of the glass mirror used to form three main parts of beams was considered in the present model, and Fresnel’s equations were applied to calculate the energy of the three parts of reflected rays. An elliptic Gaussian model was applied for the optical error distribution of the heliostat. The model error was evaluated using the experimental data of ten heliostats, and the applicability and accuracy of the model were verified through flux distribution and an intercept factor. The average relative prediction error of the present model from the experimental data was only 2.83%, which is less than SolTrace and other models.

A probabilistic model for field density distribution of asphalt pavements

ABSTRACT The field density of as-constructed asphalt pavements usually exhibits considerable variability. Understanding and quantifying this variability is of crucial importance for building more reliable and durable pavements. This study investigates the probability distribution of the field density based on an analytical model of gyratory compaction. The model is derived from mass balance and the transition state theory for the process of aggregate rearrangement. Meanwhile, the variability in the compaction effort is also taken into account. The model is first calibrated by the laboratory gyratory compaction experiments, and is then used to predict the probability distribution of the field density, which is compared with field measurements. It is shown that the probabilistic model can capture the left-skewed and leptokurtic features of the field density distribution. The present model surpasses the commonly used Gaussian distribution for characterising the field density distribution. A parametric study is performed to investigate the effects of the compaction properties of mixture and field compaction effort on the probability distribution of the field density. The model can potentially be used to guide the asphalt mix design for achieving the desired field density.