Non-uniform Geometry Research Articles

Neural operators for hydrodynamic modeling of underground gas storage facilities

Objectives. Much of the research in deep learning has focused on studying mappings between finite-dimensional spaces. While hydrodynamic processes of gas filtration in underground storage facilities can be described by partial differential equations (PDE), the requirement to study the mappings between functional spaces of infinite dimension distinguishes this problem from those solved using traditional mapping approaches. One of the most promising approaches involves the construction of neural operators, i.e., a generalization of neural networks to approximate mappings between functional spaces. The purpose of the work is to develop a neural operator to speed up calculations involved in hydrodynamic modeling of underground gas storages (UGS) to an acceptable degree of accuracy.Methods. In this work, a modified Fourier neural operator was built and trained for hydrodynamic modeling of gas filtration processes in underground gas storages.Results. The described method is shown to be capable of successful application to problems of three-dimensional gas filtration in a Cartesian coordinate system at objects with many wells. Despite the use of the fast Fourier transform algorithm in the architecture, the developed model is also effective for modeling objects having a nonuniform grid and complex geometry. As demonstrated not only on the test set, but also on artificially generated scenarios with significant changes made to the structure of the modeled object, the neural operator does not require a large training dataset size to achieve high accuracy of approximation of PDE solutions. A trained neural operator can simulate a given scenario in a fraction of a second, which is at least 106 times faster than a traditional numerical simulator.Conclusions. The constructed and trained neural operator demonstrated efficient hydrodynamic modeling of underground gas storages. The resulting algorithm reproduces adequate solutions even in the case of significant changes in the modeled object that had not occurred during the training process. The model can be recommended for use in planning and decision-making purposes regarding various aspects of UGS operation, such as optimal control of gas wells, pressure control, and management of gas reserves.

Analysis of the geometric non-uniformity effect on the free vibration characteristic of graphene reinforced axially functionally graded nano-composite beam

In this research work, an axially functionally graded (AFG) Nano-composite beam is modeled to observe the free vibration behavior beamfor non-uniform geometry. The beam is mathematically modeled as an Euler-Bernoulli beam using MATLAB code. Where the graphene Nanoplatelets (GPL) are axially reinforced with A and V type functions. The geometry nonuniformity in the beam is introduced with an exponential function, where the exponent of the equation governs the cross-section of the geometry. The material modulus and other properties at each section along the beam axis are modeled as particulate fiber randomly oriented composite with the help of Halpin Tsai theory and rule of mixture. The finite element method (FEM) is used for the solution and analysis of the model. The model is first validated for uniform geometry results then the non-dimensional fundamental frequency of the AFG beam is obtained for various parameter combinations. The results for various combinations are plotted and it is noted that the free vibration characteristic of the model is strongly dependent on non-uniformity in geometry, end-support constraints,and slenderness ratios (L/h0) combination of the model. This research contributes significantly to the understanding of advanced composite structures and offers potential benefits for the design and optimization of these materials in various engineering applications. The study reveals significant variations in natural frequencies depending on the A type & V type GPL distribution pattern and geometric parameters, which are crucial for the structural integrity and performance of nano composite beams.

Displacement-potential analysis of ply-stresses in a partially guided non-uniform short-column of hybrid laminated composites

Reliable and accurate analysis of local stresses in structural problems of fiber-reinforced laminated composites involving nonuniform geometry is of utmost practical importance, especially when they are subjected to local loads and supports. In this research, a new study of ply stresses in a partially guided, nonuniform, short composite column of hybrid laminates, subjected to an eccentrically distributed loading is conducted using an efficient computational scheme. The analytical modeling of the present mixed-boundary-value problem of laminated structure is realized in terms of a single scalar function of space variables (called as displacement-potential function), which is defined by the displacement components of plane elasticity, and is governed by a single fourth-order partial-differential equation of equilibrium. In this modeling approach, the original three-dimensional symmetric laminated column is reduced to a plane-stress scalar-field problem of an equivalent imaginary lamina in an attempt to obtain the corresponding strain field (global laminate strain), which is then used to determine the stress fields of individual plies through the respective transformed reduced stiffness matrices. A finite-difference based computational scheme is developed to solve the representative nonuniform equivalent lamina in terms of the displacement-potential function, which is however well capable of dealing with different ply materials as well as fiber orientations, together with the associated mixed and changeable physical conditions along the boundaries of the column. A 28-ply balanced hybrid laminate composed of boron-epoxy and glass-epoxy plies with various fiber orientation is considered as the structural material for the present column. The stress fields obtained for individual plies as well as the overall laminate are analyzed in the perspective of a number of practical issues of structural design, which include material hybridization, eccentricity of loading and attachment of partial guides to the column. The design stresses of the nonuniform laminated column are identified to be affected significantly by the material and orientation of fibers as well as the laminate hybridization. An attempt is also made to verify the soundness and accuracy of the present computational scheme through the comparison of the present potential-function solutions with those obtained by the conventional computational method.

Analysis of free vibration characteristics of non-uniform graphene-reinforced axially functionally graded nanocomposite beam

This paper presents the changing effect on the free vibration behaviour of graphene-reinforced axially functionally graded nanocomposite (Gr-AFG) beam with non-uniform geometry. A generalized finite element method (GFEM) and Euler Bernoulli’s theory have been used for parametric analysis and the subsequent formulation of governing differential equations. The proposed approach (for uniform geometry) has been compared with the existing gradation schemes, e.g. ‘X’, ‘O’, ‘UD’, ‘A’, and ‘V’, and found to be well in agreement. Furthermore, a new harmonic ‘M’ function has been introduced in the current analysis, and the non-uniformity in the geometry has been implemented by varying the cross-section along the axial direction of the beam. The ‘M’ gradation in the axial direction results in an increase in the natural frequency with an increase in the slenderness ratio for the first four modes. Compared to uniform geometry, the non-uniform AFG-M beam with exponential geometry variation shows a lower fundamental frequency for all values of the slenderness ratio of the beam with an increase in the value of the exponent under C–S and C–C end support conditions.

A comparative study of exact and neural network models for wave‐induced multiphase flow in nonuniform geometries: Application of Levenberg–Marquardt neural networks

AbstractMultiphase fluids exhibit immiscible, heterogeneous structures like emulsions, foams, and suspensions. Their complex rheology arises from relative phase proportions, interfacial interactions, and component properties. Consequently, they demonstrate nonlinear effects—shear‐thinning, viscoelasticity, and yield stress. Peristalsis generates fluid flow by propagating contraction waves along channel walls. This mechanism can effectively transport multiphase and non‐Newtonian fluids in microsystems. Accurate modeling requires considering evolving phase relations, variable viscosity, slip, and particle migration anomalies, using approaches like homogenization theory or volume‐averaging. Applications include peristaltic pumping of emulsified biopharmaceuticals, microscale mixing/separating of multiphase constituents, and enhancing porous media fluid flow in oil reservoirs. Analytical and computational approaches to modeling multiphase fluid flows in peristaltic conduits provide an enhanced understanding of their complex dynamics, toward innovating engineering systems. An analytical approach is taken to model non‐Newtonian Ree‐Eyring fluid flows in asymmetric, peristaltic systems. Governing differential equations incorporate key parameters and yield closed‐form solutions for velocity, flow rate, and permeability. Suitable assumptions of long wavelength, and low Reynolds number provide accuracy. In parallel, an artificial neural network (ANN) is developed using supervised learning to predict permeability. The inputs consist of channel asymmetry, Reynolds number, amplitude ratio, and other physical factors. Outcomes validate both methodologies—analytical equations derive precise relationships from first principles, while ANNs reliably learn the system patterns from input‐output data. Additionally, ANNs can tackle more complex fluid dynamics problems with speed and adaptability. Their promising role is highlighted in developing new fluid models, improving the efficiency of simulations, and designing control systems. Side‐by‐side analytical and ANN simulation plots will further highlight ANN capabilities in emulating the system characteristics. This paves the path for employing machine learning to investigate multifaceted flows in flexible, peristaltic systems at scale. Performing a graphical examination of the engineering skin friction coefficient across a range of parameters, encompassing volume fraction, first and second order slip, Ree–Eyring fluid attributes, and permeability.

DFT and experimental investigations on Pr substituted WO3 for electronic, thermoelectric and optical applications

The properties of Pr-doped WO3 thin films were studied to examine the optical, thermoelectric, and electrical response for optoelectronic and photovoltaic applications. The thin films were synthesized using the spin coating technique. The various properties were explored by employing the DFT approach. The X-ray diffraction analysis showed the cubic phase crystalline structure of pure and Pr-doped compositions. The morphology contained uniform rod-like uniform features of WO3 thin films which changed to the un-even and non-uniform geometry with increased width in maximum Pr-doped compositions. The projected density of states revealed the major contribution of O-p in valance and W-d in the conduction band while Pr-f orbital showed an additional significant contribution in the Pr-doped compositions. The thermoelectric properties were significantly changed with the increase in Pr doping contents. The highest values of real epsilon and refractive index were found approximately 8.8 and 3.5 for maximum Pr-doped contents. The absorption coefficient and optical conductivity displayed an increasing trend with increment of Pr-doping contents suggesting the suitability with enhanced photovoltaic and optoelectronic properties. A reduction in the band gap of WO3 was observed with Pr-doping content.

An Iterative 3D Correction plus 2D Inversion Procedure to Remove 3D Effects from 2D ERT Data along Embankments.

This paper addresses the problem of removing 3D effects as one of the most challenging problems related to 2D electrical resistivity tomography (ERT) monitoring of embankment structures. When processing 2D ERT monitoring data measured along linear profiles, it is fundamental to estimate and correct the distortions introduced by the non-uniform 3D geometry of the embankment. Here, I adopt an iterative 3D correction plus 2D inversion procedure to correct the 3D effects and I test the validity of the proposed algorithm using both synthetic and real data. The modelled embankment is inspired by a critical section of the Parma River levee in Colorno (PR), Italy, where a permanent ERT monitoring system has been in operation since November 2018. For each model of the embankment, reference synthetic data were produced in Res2dmod and Res3dmod for the corresponding 2D and 3D models. Using the reference synthetic data, reference 3D effects were calculated to be compared with 3D effects estimated by the proposed algorithm at each iteration. The results of the synthetic tests showed that even in the absence of a priori information, the proposed algorithm for correcting 3D effects converges rapidly to ideal corrections. Having validated the proposed algorithm through synthetic tests, the method was applied to the ERT monitoring data in the study site to remove 3D effects. Two real datasets from the study site, taken after dry and rainy periods, are discussed here. The results showed that 3D effects cause about ±50% changes in the inverted resistivity images for both periods. This is a critical artifact considering that the final objective of ERT monitoring data for such studies is to produce water content maps to be integrated in alarm systems for hydrogeological risk mitigation. The proposed algorithm to remove 3D effects is thus a rapid and validated solution to satisfy near-real-time data processing and to produce reliable results.

Evaluation of Lost Circulation Material Sealing for Geothermal Drilling

Lost circulation is a pervasive problem in geothermal wells that can create prohibitive costs during drilling. The main issue with treatment is that the mechanism of plug formation is poorly understood. Here we applied two experimental approaches to characterize the clogging effectiveness of different materials. Fracture flow tests with different geometries were conducted with various individual materials and mixtures at relevant conditions. A high-temperature flow loop system was also developed to inject single- and mixed-material plugs into a gravel pack with a non-uniform geometry to compare with the fracture tests. The fracture tests revealed that single materials tended to form no plug or an unstable plug, while mixtures of materials were uniformly better at sealing fractures. Gravel pack tests at high temperatures show most of the materials are intact but degraded. The fibrous materials can create partial or unstable plugs in the gravel pack, but mixed-material plugs are far more effective at clogging. Both test types suggest that (1) mixed materials are more effective at blocking fluid flow and (2) fibrous materials seal fracture openings better, while granular materials seal inside fractures or pore throats better. Further research is needed to study the long-term stability of different plug configurations.

Flow of an Oldroyd-B fluid in a slowly varying contraction: theoretical results for arbitrary values of Deborah number in the ultra-dilute limit

Pressure-driven flows of viscoelastic fluids in narrow non-uniform geometries are common in physiological flows and various industrial applications. For such flows, one of the main interests is understanding the relationship between the flow rate $q$ and the pressure drop $\Delta p$ , which, to date, is studied primarily using numerical simulations. We analyse the flow of the Oldroyd-B fluid in slowly varying arbitrarily shaped, contracting channels and present a theoretical framework for calculating the $q-\Delta p$ relation. We apply lubrication theory and consider the ultra-dilute limit, in which the velocity profile remains parabolic and Newtonian, resulting in a one-way coupling between the velocity and polymer conformation tensor. This one-way coupling enables us to derive closed-form expressions for the conformation tensor and the flow rate–pressure drop relation for arbitrary values of the Deborah number ( $De$ ). Furthermore, we provide analytical expressions for the conformation tensor and the $q-\Delta p$ relation in the high-Deborah-number limit, complementing our previous low-Deborah-number lubrication analysis. We reveal that the pressure drop in the contraction monotonically decreases with $De$ , having linear scaling at high Deborah numbers, and identify the physical mechanisms governing the pressure drop reduction. We further elucidate the spatial relaxation of elastic stresses and pressure gradient in the exit channel following the contraction and show that the downstream distance required for such relaxation scales linearly with $De$ .

Study on the Seismic Response of a Water-Conveyance Tunnel Considering Non-Uniform Longitudinal Subsurface Geometry and Obliquely Incident SV-Waves

The longitudinal seismic response characteristics of a shallow-buried water-conveyance tunnel under non-uniform longitudinal subsurface geometry and obliquely incident SV-waves was studied using the numerical method, where the effect of the non-uniform longitudinal subsurface geometry due to the existence of a local one-sided rock mountain on the seismic response of the tunnel was focused on. Correspondingly, a large-scale three-dimensional (3D) finite-element model was established, where different incidence angles and incidence directions of the SV-wave were taken into consideration. Also, the non-linearity of soil and rock and the damage plastic of the concrete lining were incorporated. In addition, the wave field of the site and the acceleration response as well as damage of the tunnel were observed. The results revealed the following: (i) a local inclined subsurface geometry may focus an obliquely incident wave due to refraction or total reflection; (ii) a tunnel in a site adjacent to a rock mountain may exhibit a higher acceleration response than a tunnel in a homogeneous plain site; and (iii) damage in the tunnel in the site adjacent to a rock mountain may appear in multiple positions, and the effect of the incidence angle on the mode of compressive deformation and damage of the lining is of significance.

Performance of self-healing mortar containing bacteria immobilized in alginate coated alkali activated lightweight aggregate

Among possible bacteria carriers available on the market, lightweight aggregate (LWA) shows great potential, as it is compatible with the mortar matrix and can retain high amounts of bacteria in the pores. However, the high energy needs to produce commercial LWA is a point of consideration in terms of producing sustainable mortar. Furthermore, the need of increasing the use of fly ash in countries, such as Indonesia, that rely for their electricity on coal power plants is still high. Therefore, LWA generated by cold bonding of fly ash was introduced here as an alternative bacteria carrier. Due to the high open porosity, a coating is needed to protect the bacteria and prevent leakage. Sodium alginate was applied as a coating on expanded clay and fly-ash based LWA containing cells or spores of Bacillus Sphaericus. The viability of spores and cells after encapsulation, and the compressive strength, the healing efficiency and the sealing efficiency of resulting mortar were investigated. The results show that the cells and spores of B. sphaericus are still viable and can actively decompose urea after encapsulation into both LWA types coated with sodium alginate. The strength decreased up to 11% in all mortar samples containing LWA coated with sodium alginate compared to mortar containing LWA without alginate coating. The sodium alginate coating improved the healing efficiency of mortar when cracks were created at 90 days. However high variability occurred for the sealing efficiency, due to the non-uniform crack geometry. In conclusion, fly ash based LWA as a bacterial carrier provides adequate healing performance, similar to commercial expanded clay, but slightly decreased the mechanical properties of resulting mortar.

Impact of urban street geometry on outdoor pedestrian thermal comfort during heatwave in Nagpur city

Rapid urbanization poses challenges to sustainable transportation, impacting walking as a common mode for accessing transit stations. The Urban Heat Island (UHI) effect, exacerbated by the built environment's heat-absorbing properties, intensifies urban heat stress, hindering outdoor activities and reducing walkability. Urban street geometry impacts thermal comfort through its influences on microclimate. This study aims to investigate the relationship between urban street geometry and pedestrian thermal comfort (PTC), examining how different geometries impact microclimatic conditions and thermal comfort along walking routes in Nagpur city during May 2022. It focuses on four streets with non-uniform urban geometries to investigate their impact on PTC. Field surveys were conducted to collect data at four different hours, from 9:00 a.m. to 6:00 p.m., utilizing MS 6252B Digital Anemometer to measure microclimatic parameters. Using RayMan Pro-software, Sky View Factor (SVF), Mean Radiant Temperature, and modified Physiologically Equivalent Temperature (mPET) were simulated. Correlation analysis revealed that SVF significantly influences PTC, with varying effects throughout the day. Results highlight temporal and spatial variations in microclimate and thermal comfort along street sides. Optimizing street orientation, aspect Ratio, and vegetation improves PTC. The study provides quantitative insights, emphasizing the importance of urban street geometry parameters in enhancing overall PTC.

The influence of tympanic-membrane orientation on acoustic ear-canal quantities: A finite-element analysis.

Assuming plane waves, ear-canal acoustic quantities, collectively known as wideband acoustic immittance (WAI), are frequently used in research and in the clinic to assess the conductive status of the middle ear. Secondary applications include compensating for the ear-canal acoustics when delivering stimuli to the ear and measuring otoacoustic emissions. However, the ear canal is inherently non-uniform and terminated at an oblique angle by the conical-shaped tympanic membrane (TM), thus potentially confounding the ability of WAI quantities in characterizing the middle-ear status. This paper studies the isolated possible confounding effects of TM orientation and shape on characterizing the middle ear using WAI in human ears. That is, the non-uniform geometry of the ear canal is not considered except for that resulting from the TM orientation and shape. This is achieved using finite-element models of uniform ear canals terminated by both lumped-element and finite-element middle-ear models. In addition, the effects on stimulation and reverse-transmission quantities are investigated, including the physical significance of quantities seeking to approximate the sound pressure at the TM. The results show a relatively small effect of the TM orientation on WAI quantities, except for a distinct delay above 10 kHz, further affecting some stimulation and reverse-transmission quantities.

Study of Current Distribution over a Power Cable Presenting Non-Uniform Geometry using the Partial Differential Equations Approach

This paper presents a theoretical study of the currents and voltages characteristics transmission over an energy cable (Power Line Transmission PLT). The geometry of line is non-uniform. The proposed approach is based on the Distributed Network model, where the lumped parameters vary as the line's geometry. Most of the numerical methods applied use a frequency approach. However, other techniques are available in the time domain that are more applicable when the perturbation is transitory or an impulse. The partial differential equations (PDE) of telegraphers with variable coefficients are used in order to model the transmission over non-uniform lines. This paper presents the adaptation and application of the FDTD method to solve the problem of transmission of an electric wave over a transmission line whose electromagnetic topology is non-uniform. As an example, the final part of the paper proposes the modeling of the transmission of a transitory wave over an electric power cable. We present an application in the case of the propagation of lightning on an energy cable composed of three twisted wires. The validation of the proposed method will be set by comparing the obtained results with those obtained from a simulation in the frequency domain followed by an IFFT.

A Study of Geometrical Effects on Permeability Estimation in Three-dimensional Fractures Using the Lattice Boltzmann Method

This study investigates the effect of geometry on permeability estimation in three-dimensional fractures using the Lattice Boltzmann Method. Fractures have irregular and complex shapes, which can significantly impact their permeability. Anisotropy of permeability is important as it indicates the influence of changes in fracture orientation on the flow and transport properties of fluids. To examine the relationship between permeability and fracture geometry, we generated three-dimensional fracture geometries using fractal Brownian motion with a Hurst exponent to describe the roughness on the fracture surface. The fractures in this study have varying mean aperture, ranging from narrow to wide, with surface roughness that can be either uniform or non-uniform. The Lattice Boltzmann Method was performed to calculate permeability and investigate the relationship between permeability and geometric parameters of fractures, such as mean aperture and surface roughness. Our results were in good agreement with previous studies on two-dimensional fractures. We found a clear relationship between permeability and mean aperture. Both in uniform and non-uniform geometry have the same trend as the mean aperture increased, permeability generally increased, while rougher surface roughness permeability generally decreased but in non-uniform geometry the data on the graph appears more random and irregular. We extended our investigation to real fractures by digital rock portal data. The analysis revealed that the geometry of the real fractures closely resembled non-uniform geometry, and the permeability exhibited anisotropic behaviour. In addition, the anisotropy of permeability and computation time were also investigated; and it was found that both can be influenced by the three-dimensional fracture geometry.

Analysis of implementing a rail-based maintenance system into a HELIAS 5-B device

This paper reports on the analysis of potential rail-based maintenance systems when implemented into a Helical Advanced Stellarator (HELIAS) 5-B device. The main purpose of such a system would be to handle and exchange the internal vessel components, namely the breeding blanket segments, which are expected to be the largest and heaviest components within the vessel. Other rail-based maintenance systems for tokamak devices, particularly the ITER Blanket Remote Handling System (BRHS), were studied, and their suitability when introduced to the differing constraints of a HELIAS device was determined. Rail-based systems envisaged for DEMO and CFETR devices were also studied. An ITER-like handling system was shown to be unsuitable for a HELIAS device of this scale. This is due to significantly higher blanket masses with an in-vessel operating space no larger than that of ITER, but with the additional complication of longer toroidal lengths and non-uniform vessel geometry. Movement of large components on rails like those found in DEMO and CFETR was shown to be more applicable to the HELIAS device. The main obstacle to the implementation of such rails would be the non-uniform geometry which complicates the selection of a rail path that avoids collisions with other in-vessel components, remote handling equipment, or the vessel structure itself.

Designing a Geodesic Faceted Acoustical Volumetric Array Using a Novel Analytical Method

We present a novel analytical method as an efficient approach to design a geodesic-faceted array (GFA) for achieving a beam performance equivalent to that of a typical spherical array (SA). GFA is a triangle-based quasi-spherical configuration, which is conventionally created using the icosahedron method imitated from the geodesic dome roof construction process. In this conventional approach, the geodesic triangles have nonuniform geometries due to some distortions that occur during the random icosahedron division process. In this study, we took a paradigm shift from this approach and adopt a new technique to design a GFA that is based on uniform triangles. The characteristic equations that relate the geodesic triangle with a spherical platform were first developed as functions of the operating frequency and geometric parameters of the array. Then, the directional factor was derived to calculate the beam pattern associated with the array. A sample design of GFA for a given underwater sonar imaging system was synthesized through an optimization process. The GFA design was compared with that of a typical SA, and a reduction of 16.5% in the number of array elements was recorded in the GFA at a nearly equivalent performance. Both arrays were modeled, simulated, and analyzed using the finite element method (FEM) to validate the theoretical designs. Comparison of the results showed a high degree of compliance between the FEM and the theoretical method for both arrays. The proposed novel approach is faster and requires fewer computer resources than the FEM. Moreover, this approach is more flexible than the traditional icosahedron method in adjusting geometrical parameters in response to desired performance outputs.

An Investigation of Influence of Windshield Configuration and Train Length on High-Speed Train Aerodynamic Performance

The aerodynamic performance of four train models with different windshield configurations (i.e., internal and/or external) in three train marshalling modes (i.e., 3, 6 and 8-car groups) was numerically investigated in this study. The train's airflow characteristics at Re=2.25×106 were determined using the shear stress transport (SST) k- turbulence model. The results were validated by comparing the pressure distributions and drag forces on the streamlined heads with experimental data. The difference in windshield configuration and train length has a substantial influence on the train’s flow field and surface pressure distribution. For the trains with internal windshields, due to non-uniform geometry, the flow is separated and vortices are formed at the windshield area. The boundary layer profile increases with the increased train length, and its thickness varies with windshield configurations. Asymmetric vortices are formed in the wake at a distance close to the tail car’s nose, except for trains with external windshields. The reduction of the flow velocity as the train length increases causes a reduction of the low pressure near the tail car’s streamline transition, thus causing a decrease in the tail car’s drag and lift forces. Consequently, for trains with external windshields, the head car’s drag increases, whereas the total train drag reduces significantly as the train length increases. Therefore, employing external windshields in all the inter-carriage gap sections, irrespective of the train length, demonstrates a good ability to reduce future train’s aerodynamic drag.

Relativistic space-charge field calculation by interpolation-based treecode

Space-charge effects are of great importance in particle accelerator physics. In the computational modeling, tree-based methods are increasingly used because of their effectiveness in handling non-uniform particle distributions and/or complex geometries. However, they are often formulated using an electrostatic force which is only a good approximation for low energy particle beams. For high energy, i.e., relativistic particle beams, the relativistic interaction kernel may need to be considered and the conventional treecode fails in this scenario. In this work, we formulate a treecode based on Lagrangian interpolation for computing the relativistic space-charge field. Two approaches are introduced to control the interpolation error. In the first approach, a modified admissibility condition is proposed for which the treecode can be used directly in the lab-frame. The second approach is based on the transformation of the particle beam to the rest-frame where the conventional admissibility condition can be used. Numerical simulation results using both methods will be compared and discussed.

Physical, Nutritional, and Bioactive Properties of Mandacaru Cladode Flour (Cereus jamacaru DC.): An Unconventional Food Plant from the Semi-Arid Brazilian Northeast.

In this study, we evaluated the physical, nutritional, and bioactive properties of mandacaru cladode flour (Cereus jamacaru DC.). The granulometric profile revealed particles with non-uniform geometry, flakiness, a rectangular tendency, and a non-homogeneous surface, with particle sizes ranging from 20 to 60 µm. The flour presented low water activity (0.423), a moisture content of 8.24 g/100 g, high ash (2.82 g/100 g), protein (5.18 g/100 g), and total carbohydrate contents (74.48 g/100 g), and low lipid contents (1.88 g/100 g). Mandacaru flour is an excellent source of insoluble dietary fiber (48.08 g/100 g), calcium (76.33%), magnesium (15.21%), and potassium (5.94%). Notably, 1H NMR analysis revealed the presence of N-methyltyramine. Using HPLC chromatography, glucose was identified as the predominant sugar (1.33 g/100 g), followed by four organic acids, especially malic acid (9.41 g/100 g) and citric acid (3.96 g/100 g). Eighteen phenolic compounds were detected, with relevant amounts of kaempferol (99.40 mg/100 g), myricetin (72.30 mg/100 g), and resveratrol (17.84 mg/100 g). The total phenolic compounds and flavonoids were 1285.47 mg GAE/100 g and 15.19 mg CE/100 g, respectively. The mean in vitro antioxidant activity values were higher using the FRAP method (249.45 µmol Trolox TEAC/100 g) compared to the ABTS•+ method (0.39 µmol Trolox TEAC/g). Finally, the ascorbic acid had a content of 35.22 mg/100 g. The results demonstrate the value of mandacaru as a little-explored species and an excellent matrix for the development of flours presenting good nutritional value and bioactive constituents with excellent antioxidant potential.