Spherical Model Research Articles

Optimizing waste heat recovery for hydrogen production: Modeling and simulation of ternary size metallic granule flow in a cooling cylinder

In order to recover the waste heat of high temperature metallic granules to produce steam for hydrogen production, a waste heat recovery cooling cylinder with cooling water channel is innovatively developed. The simulation is carried out based on DEM and soft sphere model to study the flow characteristics of ternary size metallic granules. The model of cooling cylinder is established and verified by comparing to the experiment data. The change rule of bed shape in the waste heat recovery cooling cylinder is examined, and the inclination angle, rotational speed and filling rate are assessed to find their influence on the flow characteristics of ternary size metallic granules. The results indicated that, with the increase of inclination angle, the axial velocity increases by 482.76%, which means the reduce of residence time of granules. With the increase of rotational speed, the axial velocity has an increase of 161.54%, the sum velocity increases by 158.49%, leading to a decrease of residence time. As the filling rate increases from 1.5% to 15.5%, the contact number has an increase of 91.53%, which lead to the increase of heat transfer area. The residence time and heat transfer area will directly affect the waste heat recovery efficiency, so a proper arrangement of granule flow is significant for enhancing the heat transfer efficiency.

Resonance scattering generated by rotating bodies

Abstract The scattering of rotating bodies to a polarized plane wave, including the dielectric cylinder and sphere, is studied. The resonance caused by rotation is emphasized. Numerical results prove that the resonance scattering caused by rotation can be realized in the optical range. It is sensitive to the rotation dimensionless parameter γ. The internal Mie mode corresponding to the electromagnetic field intensity changes with γ, and the resonant mode appears when the particle rotates at a specific speed. Moreover, the resonant mode changes with γ. It causes resonance scattering to appear in the same particle at different speeds. Inside particles, resonant rings are composed of a series of array points and are determined by γ. Under resonance conditions, the energy near the rotating cylinder is consistent with its rotation direction. In contrast, the direction of energy flow in the rotating sphere model is opposite to the direction of particle rotation. This work provides a novel idea for the design of ultra-sensitive sensors and resonators. It has promising applications in optical communication, optical microscopy, and optical signal processing.

Ionisation of atoms determined by kappa refinement against 3D electron diffraction data.

Conventional refinement strategies used for three-dimensional electron diffraction (3D ED) data disregard the bonding effects between the atoms in a molecule by assuming a pure spherical model called the Independent Atom model (IAM) and may lead toan inaccurate or biased structure. Here we show that it is possible to perform a refinement going beyond theIAM with electron diffraction data. We perform kappa refinement which models charge transfers between atoms while assuming a spherical model. We demonstrate the procedure by analysing five inorganic samples; quartz, natrolite, borane, lutecium aluminium garnet, and caesium lead bromide. Implementation of kappa refinement improved the structure model obtained over conventional IAM refinements and provided information on the ionisation of atoms. The results were validated against periodic DFT calculations. The work presents an extension of the conventional refinement of 3D ED data for a more accurate structure model which enables charge density information to be extracted.

Correction to: Free Energy Fluctuations of the Bipartite Spherical SK Model at Critical Temperature

Correction to: Free Energy Fluctuations of the Bipartite Spherical SK Model at Critical Temperature

Structural analysis of superparamagnetic colloid aggregates confined in spherical cavities under external magnetic field

In this study, we investigated the behaviour of aggregates composed of superparamagnetic colloids under the influence of an external magnetic field, confined within several spherical cavities. The study included systems of two and three cavities in contact, as well as two cavities separated by a distance d along the direction of the external field. Monte Carlo computer simulations employing a model of hard spheres with central dipoles were realised to explore the behaviour of the magnetic particles, constrained to move within pairs (and trios) of spherical cavities. The primary focus of this investigation was to elucidate the structures formed by magnetic particles within systems presented here. Chains or ribbons primarily form within the central region of the spherical cavities. The aggregates within each cavity are drawn towards one another until they make contact at the closest points of the cavities. This behaviour is replicated when there is a separation distance between the spherical cavities, including cases where three cavities are in contact. This phenomenon may explain the observed attraction between magnetoliposomes as reported in the literature [García-Jimeno et al. Nanoscale. 9 (39), 15131–15143 (2017)].

Prediksi Risiko Emisi Karbon Dioksida Melalui Pemodelan GSTAR Kriging di Wilayah Asia

This study analyzes the variability of carbon dioxide emissions across Asia, revealing that China, India, and Indonesia are the primary contributors with extremely high average emissions and standard deviations. The GSTAR(3;1,1,1) model has been shown to be optimal for forecasting future emissions, based on lower RMSE and MAPE values. Ordinary Kriging analysis using the isotropic spherical semivariogram model provides the most accurate predictions for unobserved areas, with contour maps indicating that the northeastern region of Asia will continue to face high emission concentrations until 2027. While countries such as Brunei and Armenia have managed to keep emission levels low, the instability of emission trends across Asia underscores the need for emission reduction strategies tailored to the specific context of each country.

Theia 456: Tidally Shredding an Open Cluster

The application of clustering algorithms to the Gaia astrometric catalog has revolutionized our census of stellar populations in the milky Way, including the discovery of many new dispersed structures. We focus on one such structure, Theia 456 (COIN-Gaia-13), a loosely bound collection of ∼320 stars spanning ∼120 pc that has previously been shown to exhibit kinematic, chemical, and gyrochronal coherency, indicating a common origin. We obtain follow-up radial velocities and supplement these with Gaia astrometry to perform an in-depth dynamical analysis of Theia 456. By integrating stellar orbits through a Milky Way potential, we find the currently dispersed structure coalesced into a small cluster in the past. Via Bayesian modeling, we derive a kinematic age of 245 ± 3 Myr (statistical), a half-mass–radius of 9 ± 2 pc, and an initial one-dimensional velocity dispersion of 0.14 ± 0.02 km s−1. Our results are entirely independent of model isochrones, details of stellar evolution, and internal cluster dynamics, and the statistical precision in our age derivation rivals that of the most precise age-dating techniques known today, though our imperfect knowledge of the Milky Way potential and simple spherical model for Theia 456 at birth add additional uncertainties. Using posterior predictive checking, we confirm these results are robust under reasonable variations to the Milky Way potential. Such low-density structures that are disrupted by the Galactic tides before virializing may be ubiquitous, signifying that Theia 456 is a valuable benchmark for studying the dynamical history of stellar populations in the Milky Way.

Study on the characteristics particles of coarse grain material in high bench dump

Particle shape is an important factor affecting the strength and deformation of coarse materials in dumps. However, conducting research on particle shape in current laboratory experiments, and there exists no classification standard for the particle shape of the dump. Considering the project on high-bench dump in Jiangxi Province, based on the random particle construction method, this study determined the characteristic particles of coarse grain material in the dumping site by combining field investigation results, large-scale direct shear tests, and numerical analysis. Further, the influence mechanism of coarse grain content and characteristic particles on the mechanical characteristics of the dump were analyzed. The results showed that the increase in coarse grain content enhanced the irregularity of particle shape, increased the internal friction angle between particles, and reduced the cohesion of the dump. Moreover, with increase in the normal stress, the shear strength changed from insignificant to gradually enhanced, although the increasing trend slowed down. The constructed random particle model can well solve the effects of occlusion, nesting, and friction between particles that is neglected by the standard spherical particle model, and the fitting degree is better. The particle characteristics of coarse-grain materials in the dump were primarily block, strip, and flake. The three types of shape characteristics under low normal stress did not affect the mechanical properties of the dump. Further, with the increase in normal stress, the stress-strain curve reflected the shape characteristics and content of the dominant characteristics in the dump. Specifically, the block sample exhibited the dominant characteristics and the most content under the same normal stress, followed by the strip sample, with the flake sample exerting the least influence. The research results provide a theoretical basis for long-term safe operation, disaster monitoring, and early warning of high bench dump.

Time‐lapse inversion of self‐potential data through particle filtering

AbstractIn environmental sciences, comprehending the movement of subsurface contaminants is crucial for formulating effective remediation measures. The self‐potential (SP) method has become a common tool for delineating landfill contamination plumes. Contaminant diffusion or migration represents dynamic processes, with corresponding SP responses evolving over time. However, conventional SP interpretation approaches have predominantly relied on static single‐frame inversion, overlooking the temporal correlation in time‐series SP data and resulting in cumulative errors. To tackle this challenge, we introduce a novel method for time‐lapse inversion of SP data leveraging particle filtering. This approach recursively refines the priori state model through posteriori observations to achieve precise estimations of dynamic models. Specifically, a spherical polarization model is deployed to establish the state equations of underground contaminant diffusion and transport models, whereas the observation model is derived through forward modeling. The proposed method is validated using two synthetic examples and one lab‐measured dataset. The findings demonstrate the efficacy of the time‐lapse inversion algorithm in precisely estimating dynamic models, outperforming static single‐frame inversion based on the particle swarm optimization algorithm. The posteriori distribution of particles approximates a bell‐shaped distribution, with the true state closely positioned near the peak probability. Therefore, we affirm that conducting time‐lapse inversion of time‐series SP data through particle filtering is an effective and dependable approach for accurately estimating dynamic model states.

Bionic Design of High-Performance Joints: Differences in Failure Mechanisms Caused by the Different Structures of Beetle Femur-Tibial Joints.

Beetle femur-tibial joints can bear large loads, and the joint structure plays a crucial role. Differences in living habits will lead to differences in femur-tibial joint structure, resulting in different mechanical properties. Here, we determined the structural characteristics of the femur-tibial joints of three species of beetles with different living habits. The tibia of Scarabaeidae Protaetia brevitarsis and Cetoniidae Torynorrhina fulvopilosa slide through cashew-shaped bumps on both sides of the femur in a guide rail consisting of a ring and a cone bump. The femur-tibial joint of Buprestidae Chrysodema radians is composed of a conical convex tibia and a circular concave femur. A bionic structure design was developed out based on the characteristics of the structure of the femur-tibial joints. Differences in the failure of different joint models were obtained through experiments and finite element analysis. The experimental results show that although the spherical connection model can bear low loads, it can maintain partial integrity of the structure and avoid complete failure. The cuboid connection model shows a higher load-bearing capacity, but its failure mode is irreversible deformation. As key parts of rotatable mechanisms, the bionic models have the potential for wide application in the high-load engineering field.

BEMM-GEN: A Toolkit for Generating a Biomolecular Environment-Mimicking Model for Molecular Dynamics Simulation.

Understanding the influence of the cellular environment on protein conformations is crucial for elucidating protein functions within living cells. In studies using molecular dynamics (MD) simulation, carbon nanotubes and hydrophobic cages have been widely used to emulate the cellular environment inside specific large biomolecules such as ribosome tunnels and chaperones. However, recent studies suggest that these uniform hydrophobic models may not adequately capture the environmental effects inside each biomolecule. Based on these facts, it is necessary to generate spherical and cylindrical models with varied chemical properties corresponding to the components within target biomolecules. We developed a biomolecular environment-mimicking model generator (BEMM-GEN) that generates spherical and cylindrical models with user-specified chemical properties and allows the integration of arbitrary protein conformations into the generated models. BEMM-GEN provides model and protein complex structures, along with the corresponding parameter files for MD simulation (AMBER and GROMACS), and users immediately run their MD simulation based on the generated input files. BEMM-GEN can be freely downloaded and installed via a Python package manager (pip install BEMM-gen). The source code files and a user manual for operation are provided on GitHub (https://github.com/y4suda/BEMM-GEN).

Preferred Distance in Human-Drone Interaction.

In two augmented-reality experiments, we transferred the paradigm of interpersonal distance regulation to human-drone interaction. In the first experiment, we used a simple spherical drone model and explored how both hovering height and approach angle affect the preferred distance. Drone height above the ground had a strong effect. The preferred distance to the drone was larger than that typically found toward human actors, in particular, when the drone trajectory was very high. In the second experiment, we sought to gain a deeper understanding of the factors that may influence this effect. In addition to the simple spherical drone model used in the first experiment, we also varied its appearance and attachment to the ground. Surprisingly, anthropomorphic features increased preferred distances. We, therefore, discuss the extent to which social aspects and subjectively perceived danger influence the preferred distance for interaction with drones, which thus need to be considered in the design of human-drone interaction.

Modeling the elastic–plastic contact forces and deformations of nonrotationally symmetric lunar dust particles

The sharp morphological features of lunar dust particles generate significant elastic–plastic contact forces and deformations upon contact with material surfaces, which considerably affect the mechanical properties of lunar dust particles, including their contact, collision, adhesion, transport, and wear characteristics. Despite these severe effects, valid models considering the contact characteristics of typical sharp-featured lunar dust particles are currently lacking. This study proposes an elastic–plastic contact model for nonrotationally symmetric lunar dust particles showing typical sharp features. Detailed derivations of the expressions for various physical responses observed when lunar dust particles establish normal contacts with elastic and elastic–plastic half-spaces under adhesive conditions are also provided. These include derivations for elastic forces, elastic–plastic forces, contact areas, pull-off forces, residual displacements, and plastic deformation areas. Furthermore, the tangential pull-off force during the tangential loading of lunar dust particles is derived, and the tangential contact characteristics are explored. Comparisons of the results of the proposed model with those of previous experiments reveal that the proposed model shows errors of only 6.06 % and 1.03 % in the maximum indentation depth and residual displacement, respectively. These errors are substantially lower than those of conventional spherical models (60.30 % and 60.13 %, respectively), confirming the superior accuracy of the proposed model. Furthermore, the discrete element method is employed to analyze the effects of normal and tangential contacts, dynamic characteristics, and plastic deformations on the considered lunar dust particles. The results are then compared with those of existing contact models. They reveal that maximum elastic–plastic forces under normal contact conditions are positively correlated with the initial velocity but negatively correlated with the lateral angle. Furthermore, the tangential pull-off force is positively correlated with the normal force and surface energy. In addition, the contact duration of lunar dust particles is positively correlated with their initial velocities, while the residual displacement is negatively correlation. For instance, as the initial velocity increases from 10 to 50 m/s, the maximum elastic–plastic force increases from 37.64 to 321.72 mN. Comparisons of the proposed model with other contact models reveal that the maximum elastic–plastic force of the elastic–plastic triangular pyramid model is only 14.93 % that of the cylindrical model, 34.23 % that of the spherical model, and 76.27 % that of the conical model, indicating significant reductions in the maximum elastic–plastic force owing to the plastic deformations of particles with typical sharp features. Overall, the results of this study offer crucial insights into the mechanical characteristics of nonspherical lunar dust particles under various contact conditions, such as elastic–plastic and adhesive contacts, and can guide in situ resource utilization on the lunar surface and for craft landings.

Determination of particle number concentration for biological particles using AF4-MALS: Dependencies on light scattering model and refractive index

Determining accurate counts and size distributions for biological particles (bioparticles) is crucial in wide-ranging fields, but current methods to this end are susceptible to bias from polydispersity in size. This bias can be mitigated by incorporating a separation step prior to characterization. For this reason, asymmetrical flow field-flow fractionation (AF4) with on-line multiangle light scattering (MALS) has become an important platform for determining particle size. AF4-MALS has also been increasingly used to report particle concentration, particularly for complex biological particles, yet the impact of light scattering models and particle refractive indices (RI) have not been quantitatively evaluated. Here, we develop an analysis workflow using AF4-MALS to simultaneously separate and determine particles sizes and concentrations. The impacts of the MALS particle counting model used to process data and the chosen RI value(s) on particle counts are systematically assessed for polystyrene latex (PSL) particles and bacterial outer membrane vesicles (OMVs) in the 20-500 nm size range. Across spherical models, PSL and OMV particle counts varied up to 13% or 200%, respectively. For the coated-sphere model used in the analysis of OMV samples, the sphere RI value greatly impacts particle counts. As the sphere RI value approaches the RI of the suspending medium, the model becomes increasingly sensitive to the light scattering signal-to-noise ratio ultimately causing erroneous particle counts. Overall, this work establishes the importance of selecting appropriate MALS models and RI values for bioparticles to obtain accurate counts and provides an AF4-MALS method to separate, enumerate, and size polydisperse bioparticles.

An error compensation method for on-machine measuring blade with industrial robot

To achieve the seamless integration of precision grinding blade with timely measured data, an on-machine measurement system employing industrial robot is developed. The limitation to its widespread application lies in the accuracy of measurement, prompting the proposal of an error compensation method to address the measurement error within the implemented blade on-machine measurement system. To address the pre-travel error in the measuring device of the on-machine measurement system, an analysis of the factors influencing the pre-travel error of the contact probe is conducted. Subsequently, pre-travel error data is gathered utilizing the experimental calibration method involving a standard ball, and a prediction model employing the bilinear interpolation algorithm is established to facilitate error compensation. Employing pre-travel error compensation for the analysis of the operating body error in the on-machine measurement system, a spherical center distance constraint error model is derived through closed-loop kinematic calibration of the six-degrees-of-freedom industrial robot. Kinematic parameter error identification is conducted using a hybrid algorithm combining the L-M algorithm and the adaptive factor double-variable DE algorithm. This approach diminishes the spherical center distance measurement error, reducing it from 0.081 mm to 0.016 mm. Subsequently, experiment is conducted to measure blade machining allowances using an on-machine robotic measurement system, comparing the obtained data with measurement from a blue light scanner and a coordinate measuring machine (CMM). The results reveal average absolute deviations of 0.020 mm, 0.015 mm, and 0.016 mm in the three blade cross sections for the on-machine robotic measurement system and the blue light scanner, respectively. Correspondingly, the average absolute deviations for the on-machine robotic measurement system and the CMM in the three blade sections are 0.028 mm, 0.029 mm, and 0.029 mm. Moreover, the on-machine measurement system demonstrates commendable measurement repeatability, with a standard deviation of 0.003 mm.

Effective quantum gravitational collapse in a polymer framework

We study how the presence of an area gap, different than zero, affects the gravitational collapse of a dust ball. The implementation of such discreteness is achieved through the framework of polymer quantization, a scheme inspired by loop quantum gravity (LQG). We study the collapse using variables which represent the area, in order to impose the non-zero area gap condition. The collapse is analyzed for both the flat and spherical Oppenheimer-Snyder models. In both scenarios the formation of the singularity is avoided, due to the inversion of the velocity at finite values of the sphere surface. This happens due to the presence of a negative pressure, with origins at a quantum level. When the inversion happens inside the black hole event horizon, we achieve a geometry transition to a white hole. When the inversion happens outside the event horizon, we find a new possible astrophysical object. A characterization of such hypothetical object is done. Some constraints on the value for the area gap are also imposed in order to maintain the link with our already established physical theories.

Patterns of interaction between peptides of various structures and pyrimidine nucleic bases in a buffered saline medium according to the analysis of thermodynamic parameters

Complexation of cytosine, uracil and thymine with the dipeptides glycyl-glycine, glycyl-l-phenylalanine, alanyl-l-glutamine and with the tripeptide γ-l-glutamyl-l-cysteinyl-glycine in a buffered saline has been studied using dissolution calorimetry. The values of the reaction constant, the change in Gibbs energy, enthalpy, and entropy have been found (log Kr, ΔrG, ΔrH, TΔrS). By analyzing the obtained data together with previous results for other peptides, it was found that peptides bind to pyrimidine nucleic bases in a solution in several important patterns. No pattern depending on the charge of the peptide is observed in the obtained thermodynamic values, which indicates a minor role of electrostatic interaction in their binding by the nucleic base. The effect of the structure of the peptide and the nucleobase on the thermodynamic parameters of complexation is manifested in the fine balance of the enthalpy and entropy factors of the process. The Gibbs energy of complexation depends on the number of potential H-bonding sites of the peptide, which shows the major contribution of H-bonding between the reagents. The reduction in the favorable entropy factor is responsible for the tendency of negative ΔrG values to decrease with increasing number of sites. It was found that positive values of entropy change during complex formation increase with increasing hydrophobicity index of the peptide, which is interpreted within the framework of the overlapping hydration sphere model. Strengthening the hydrophobic properties of the nucleic base from uracil to thymine due to the additional CH3 group slightly changes the enthalpy and entropy of the process of binding the +AlaGln− zwitterion but significantly affects the thermodynamic parameters of binding the anion of peptide +/−GluCysGly−.

Revealing the Structural Intricacies of Biomembrane-Interfaced Emulsions with Small- and Ultra-Small-Angle Neutron Scattering.

Utilizing cell membranes from diverse cell types for biointerfacing has demonstrated significant advantages in enhancing colloidal stability and incorporating biological properties, tailored specifically for various biomedical applications. However, the structures of these materials, particularly emulsions interfaced with red blood cell (RBC) or platelet (PLT) membranes, remain an underexplored area. This study systematically employs small- and ultra-small-angle neutron scattering (SANS and USANS) with contrast variation to investigate the structure of emulsions containing perfluorohexane within RBC (RBC/PFH) and PLT membranes (PLT/PFH). The findings reveal that the scattering length density of RBC and PLT membranes is 1.5 × 10-6Å-2, similar to 30% (w/w) deuterium oxide. Using this solvent as a cell membrane-matching medium, estimated droplet diameters are 770nm (RBC/PFH) and 1.5µm (PLT/PFH), based on polydispersed sphere model fitting. Intriguingly, calculated patterns and invariant analysis reveal native droplet architectures featuring entirely liquid PFH cores, differing significantly from the observed bubble-droplet core system in electron microscopy. This highlights the advantage of SANS and USANS in differentiating genuine colloidal structures in complex dispersions. In summary, this work underscores the pivotal role of SANS and USANS in characterizing biointerfaced colloids and in uncovering novel colloidal structures with significant potential for biomedical applications and clinical translation.

Optimization of Tantalite Ore Dissolution Using Hydrofluoric-sulphuric Acid and Shrinking Core Model

Aim: This study investigates the dissolution of tantalite mineral from granitic pegmatite in Okpella, Northern Edo State, Nigeria. Study Design: Elemental and mineral composition analysis of tantalite ore sample from Okpella was carried out using X-ray fluorescence and X-ray diffraction. Response Surface Methodology (RSM) and the shrinking core model were used in designing the study while the effects of temperature, stirring speed, particle diameter, and mixed acids concentrations were investigated in the dissolution rates of the mineral. Duration of Study: 50 experimental runs were designed using RSM Central Composite Design (CCD) to optimize variables including HF concentration (1-8 M), H2SO4 concentration (0.5-3 M), temperature (32-82°C), stirring speed (0-500 rpm), and particle size (0.1-0.3 mm), with a constant contact time of 240 minutes. Methodology: Pulverized tantalite samples (0.1-0.3 mm) were reacted with varying concentrations of hydrofluoric and sulphuric acids (1-8 M and 0.5-3.0 M, respectively) for 240 minutes, with stirring speeds between 0-500 rpm and temperatures from 32 to 82°C. The mixture was stirred in a water bath with 50 ml of mixed acids solution and 2 g of ore. After the reaction, the solution was decanted, and the residual ore was washed, dried at 60 °C, and weighed. The difference between the initial and final weights indicated the amount of undissolved tantalite ore. Results: Ore characterization results revealed high concentration of tantalum (34.17%), iron (12.55%), niobium (8.38%), and titanium (6.01%), with other elements present in smaller amounts. Optimal conditions were found to be 8 M HF, 0.5 M H2SO4, 82°C, 500 rpm stirring speed, and 0.1 mm particle size, resulting in 97.28% dissolution of tantalite ore. Regression analysis demonstrated model robustness with an F-value of 16.70 and a P-value of 0.0001, indicating HF concentration and stirring speed as the most impactful factors. The model’s R² value of 0.9201 and adjusted R² of 0.8650 confirm its predictive accuracy. Analysis using the shrinking sphere model showed that film diffusion control is the primary limiting step with t/τ=0.999, while reaction control resulted in slightly lower conversion with t/τ=0.973, highlighting film diffusion as the main constraint but with high conversion efficiency. Conclusion: The findings from this investigation not only reveal the dissolution of tantalite ore through a detailed experimental approach, identifying optimal conditions -8 M HF, 0.5 M H2SO4, 82 oC, 500 rpm stirring speed and 0.1 mm particle size- that achieve a 97.28% dissolution, but they also enhance our understanding of mineral processing. These understanding are crucial for mineral dissolution up scaling technologies in industrial applications, which will potentially leads to a more efficient extraction method that could significantly reduce costs and environmental impacts in the mining sector. This research could drive advancements in sustainable resource recovery and contribute to sourcing of critical minerals.

Mass scaling relations for dark halos from an analytic universal outer density profile

Context. The average matter density within the turnaround scale, which demarcates where galaxies shift from clustering around a structure to joining the expansion of the Universe, is an important cosmological probe. However, a measurement of the mass enclosed by the turnaround radius is difficult. Analyses of the turnaround scale in simulated galaxy clusters place the turnaround radius at about three times the virial radius in a ΛCDM universe and at a (present-day) density contrast with the background matter density of the Universe of δ ~ 11. Assessing the mass at such extended distances from a cluster’s center is a challenge for current mass measurement techniques. Consequently, there is a need to develop and validate new mass-scaling relations, to connect observable masses at cluster interiors with masses at greater distances. Aims. Our research aims to establish an analytical framework for the most probable mass profile of galaxy clusters, leading to novel mass scaling relations, allowing us to estimate masses at larger scales. We derive such analytical mass profiles and compare them with those from cosmological simulations. Methods. We used excursion set theory, which provides a statistical framework for the density and local environment of dark matter halos, and complement it with the spherical collapse model to follow the non-linear growth of these halos. Results. The profile we developed analytically showed good agreement (better than 30%, and dependent on halo mass) with the mass profiles of simulated galaxy clusters. Mass scaling relations were obtained from the analytical profile with offset better than 15% from the simulated ones. This level of precision highlights the potential of our model for probing structure formation dynamics at the outskirts of galaxy clusters.