Dimensional Calculations Research Articles

Failure pattern in ceramic metallic target under ballistic impact

The ballistic resistance and failure pattern of a bi-layer alumina 99.5% - aluminium alloy 1100-H12 target against steel 4340 ogival nosed projectile has been explored in the present experimental cum numerical study. In the experimental investigation, damage induced in the ceramic layer has been quantified in terms of number of cracks developed and failure zone dimensions. The resultant damage in the backing layer has been studied with variation in the bulge and perforation hole in the backing layer with the varying incidence velocity. The discussion of the experimental results has been further followed by three dimensional finite element computations using ABAQUS/Explicit finite code to investigate the behaviour of different types of bi-layer targets under multi-hit projectile impact. The JH-2 constitutive model has been used to reproduce the behaviour of alumina 99.5% and JC constitutive model has been used for steel 4340 and aluminium alloy 1100-H12. The total energy dissipation has been noted to be of lesser magnitude in case of sub-sequential impact in comparison to simultaneous impact of two projectiles. The distance between the impact points of two projectiles also effected the ballistic resistance of bi-layer target. The ballistic resistance of single tile ceramic front layer and four tile ceramic of equivalent area found to be dependent upon the boundary conditions provided to the target.

GRINN: a physics-informed neural network for solving hydrodynamic systems in the presence of self-gravity

Modeling self-gravitating gas flows is essential to answering many fundamental questions in astrophysics. This spans many topics including planet-forming disks, star-forming clouds, galaxy formation, and the development of large-scale structures in the Universe. However, the nonlinear interaction between gravity and fluid dynamics offers a formidable challenge to solving the resulting time-dependent partial differential equations (PDEs) in three dimensions (3D). By leveraging the universal approximation capabilities of a neural network within a mesh-free framework, physics informed neural networks (PINNs) offer a new way of addressing this challenge. We introduce the gravity-informed neural network (GRINN), a PINN-based code, to simulate 3D self-gravitating hydrodynamic systems. Here, we specifically study gravitational instability and wave propagation in an isothermal gas. Our results match a linear analytic solution to within 1% in the linear regime and a conventional grid code solution to within 5% as the disturbance grows into the nonlinear regime. We find that the computation time of the GRINN does not scale with the number of dimensions. This is in contrast to the scaling of the grid-based code for the hydrodynamic and self-gravity calculations as the number of dimensions is increased. Our results show that the GRINN computation time is longer than the grid code in one- and two- dimensional calculations but is an order of magnitude lesser than the grid code in 3D with similar accuracy. Physics-informed neural networks like GRINN thus show promise for advancing our ability to model 3D astrophysical flows.

Insight into Poly(l-lactic acid) Coexisting Amorphous and Semicrystalline Phases Using FT-IR Imaging and Four Polarization-Three Dimensional Macromolecular Orientation Calculation

Insight into Poly(<scp>l</scp>-lactic acid) Coexisting Amorphous and Semicrystalline Phases Using FT-IR Imaging and Four Polarization-Three Dimensional Macromolecular Orientation Calculation

PLANNING FOR RETAINING WALLS ON THE TANJUNG PAKIS AJI JEPARA VILLAGE ROAD

Retaining walls are a ground control technique that is very necessary to overcome landslides. As happened in the Tanjung Pakis Aji village area. It has steep slopes and there are indications that landslides often occur during the rainy season. The soil parameters that need to be known to plan soil retention walls for testing include specific gravity (Gs); 2.65 kN/m2, void number (e); 33.9, porosity 97.14, shear angle φ ; 29.71 ˚, soil cohesion (c) 24.5 kN/m2, dry soil volume weight (yd ) ; 1.18 kN/m3, wet soil volume weight (yb); 1.87 kN/m3, air content (Wn); 15.29%. Dimensional calculations, stability control, reinforcement of retaining walls are very important in planning retaining walls. The aim of this research is to plan a retaining wall at this location using a cantilever type retaining wall. The results show that the cantilever type retaining wall with dimensions H = 7 m, B = 3 m, T = 0.4 m, Tt and Th = 0.5, Lt = 1, Lh = 1.m, the cantilever is declared safe for the condition of the soil with a safety factor value of Fgs = 4.061 (safe), Fgl = 2.57 (safe), F carrying capacity = 6.62 (safe). From these calculations, reinforcement of types D19-250, D19-200, D19-200 can be obtained, with shrinkage reinforcement D13-100, D13-200.

Determination of local fractal dimension of the catalyst support MgAl2O4 surface

In this paper, a procedure for estimating local fractal dimensionality values for greyscale images was developed. This procedure was tested on synthesised fractal and multifractal Brownian surfaces. The use of the method of detrended fluctuation analysis to determine the Hurst index for samples with a size not exceeding 2000 points was analysed. The optimal values of the sample size and the scale parameter have been obtained, allowing the Hurst index to be calculated with an error of less than 20%. The procedure was also tested on greyscale images, which are 8-bit representations of a synthesised fractal surface. The peculiarities of the application of the procedure for calculating the local fractal dimension for images obtained by scanning electron microscopy have been analysed. The values of the local fractal dimension of the oxide support MgAl2O4 are calculated using SEM images at different magnifications. It has been shown that, taking into account the fractal dimensionality calculation, different morphologies of the particle surface are observed at different scales of image magnification. At the highest magnification, the particle surface is found to consist of embedded smooth micron particles. The surface morphology of the MgAl2O4 particle depends on the micro- and mesopores between the embedded particles, this surface can be characterised by a fractal surface with FD2 = 2.3–2.4.

Mutual Information Guided Diffusion for Zero-Shot Cross-Modality Medical Image Translation.

Cross-modality data translation has attracted great interest in medical image computing. Deep generative models show performance improvement in addressing related challenges. Nevertheless, as a fundamental challenge in image translation, the problem of zero-shot learning cross-modality image translation with fidelity remains unanswered. To bridge this gap, we propose a novel unsupervised zero-shot learning method called Mutual Information guided Diffusion Model, which learns to translate an unseen source image to the target modality by leveraging the inherent statistical consistency of Mutual Information between different modalities. To overcome the prohibitive high dimensional Mutual Information calculation, we propose a differentiable local-wise mutual information layer for conditioning the iterative denoising process. The Local-wise-Mutual-Information-Layer captures identical cross-modality features in the statistical domain, offering diffusion guidance without relying on direct mappings between the source and target domains. This advantage allows our method to adapt to changing source domains without the need for retraining, making it highly practical when sufficient labeled source domain data is not available. We demonstrate the superior performance of MIDiffusion in zero-shot cross-modality translation tasks through empirical comparisons with other generative models, including adversarial-based and diffusion-based models. Finally, we showcase the real-world application of MIDiffusion in 3D zero-shot learning-based cross-modality image segmentation tasks.

Laboratory Scaled-Down Cementitious Concrete Model Used for Estimating the Bearing Capacity of a Bridge Girder Based on the Similitude Theory.

Bridges are structures subjected to multiple types of loads and combinations during their service life. The uncertainties linked with the materials' behavior and manufacturing processes often necessitate the testing of produced elements on a real scale. This is particularly true for bridge concrete precast girders, which are frequently tested to predict the ultimate carrying load. Testing procedures are time-consuming, expensive in terms of both time and money, and involve a large amount of logistics and auxiliary equipment and devices. Thus, testing scaled-down models in laboratory conditions and extrapolating the obtained results with respect to the real-scale element using similitude theory has become a very common alternative method in the last decade. In this paper, experimental data regarding the efficiency of dimensional analysis computation are discussed. The proposed method involves comparing the values at which failure in bending and shear occurs for a 1:10 cementitious concrete bridge beam model with respect to the values computed for the prototype beam. Regarding the obtained results, a very small difference between the test results and the calculated values can be noticed.

High-Gain Design Microstrip Antenna for Weather Radar on Aircraft at the 9.4 GHz Frequency

The use of radar in aviation primarily centers around aircraft weather radar systems, which provide real-time monitoring of weather conditions surrounding the aircraft. Antennas play a crucial role in enabling detection within these radar systems. This article is dedicated to research efforts focused on developing a microstrip antenna design using array techniques to achieve high gain. The research methodology follows Thiagarajan's 4D approach, encompassing the Define, Design, Develop, and Disseminate stages. To optimize performance, the research encompasses the creation of various antenna designs, including single patches, 1x2, 4x4, and 8x4 arrays, employing feed and coaxial insert enumeration methods. Additionally, comparisons are drawn between two substrates, specifically FR-4 and Rogers RT- 5880. Parameters under scrutiny encompass gain, VSWR, return loss, bandwidth, and radiation patterns. The design process for microstrip antennas involves intricate dimensional calculations and array method selection, followed by a detailed application-based design. The results consistently demonstrate VSWR values below 2 and return loss values below -10 dB for microstrip antenna designs on both FR-4 and Rogers RT-5880 substrates. The most significant gains were achieved by an 8 x 4 array design employing the insert feed enumeration method on a Rogers RT-5880 substrate, reaching an impressive 17,979 dBi. The widest bandwidth is observed in the design of the 1x2 array using the Rogers RT-5880 substrate, reaching 651.1 MHz. Moreover, it is evident that an increase in the number of patches in the array corresponds to an increase in gain. Notably, Rogers RT-5880 material demonstrates a superior capacity to produce higher gain compared to FR-4 substrates

Three-Dimensional Quantitative Assessment of Pedicle Screw Accuracy in Clinical Utilization of a New Robotic System in Spine Surgery: A Multicenter Study.

The objective of this study was to evaluate the accuracy of pedicle screw placement in patients undergoing percutaneous pedicle screw fixation with robotic guidance, using a newly developed 3-dimensional quantitative measurement system. The study also aimed to assess the clinical feasibility of the robotic system in the field of spinal surgery. A total of 113 patients underwent pedicle screw insertion using the CUVIS-spine pedicle screw guide system (CUREXO Inc.). Intraoperative O-arm images were obtained, and screw insertion pathways were planned accordingly. Image registration was performed using paired-point registration and iterative closest point methods. The accuracy of the robotic-guided pedicle screw insertion was assessed using 3-dimensional offset calculation and the Gertzbein-Robbins system (GRS). A total of 448 screws were inserted in the 113 patients. The image registration success rate was 95.16%. The average error of entry offset was 2.86 mm, target offset was 2.48 mm, depth offset was 1.99 mm, and angular offset was 3.07°. According to the GRS grading system, 88.39% of the screws were classified as grade A, 9.60% as grade B, 1.56% as grade C, 0.22% as grade D, and 0.22% as grade E. Clinically acceptable screws (GRS grade A or B) accounted for 97.54% of the total, with no reported neurologic complications. Our study demonstrated that pedicle screw insertion using the novel robot-assisted navigation method is both accurate and safe. Further prospective studies are necessary to explore the potential benefits of this robot-assisted technique in comparison to conventional approaches.

Study of micro-scale flow characteristics under surface acoustic waves

As an effective tool for contactless manipulation of submicrometer scale objects, the controllability of acoustic streaming velocity and flow field morphology determines the accuracy of object migration and the completeness of three dimensional (3D) imaging. This paper proposes an equivalent acoustic streaming driving force model that is applicable to both two dimensional (2D) and 3D calculations and constructs a numerical method for submicrometer microsphere migration and rotation velocity in acoustic streaming. The results show that the relationship between the peripheral vortex size Lp/wc and the relative acoustic streaming velocity vas/vf satisfies Lp/wc = 0.125vas/vf0.36 under certain geometrical conditions. Reducing the spatial confinement and increasing the inter-vortex distance will increase the energy release efficiency, reduce the pressure gradient distribution and convective dissipation rates, increase the vortex intensity and radiation range, and consequently, increase the vortex characteristic size. In complex 3D vortex flow fields, suspended objects are affected by velocity distributions and exhibit motions such as cross-flow lines and rotation. For larger vortex structure sizes, full 3D imaging is more favorable due to the increased rotation speed and period of motion along the orbit of the submicrometer microspheres. This study helps us to reveal the modulation mechanism of acoustic streaming field flow characteristics, enrich the basic theory of alternating orbital motion and forces on objects in vortex structures, and provide guidance for acoustic flow-based contactless object manipulation.

A novel allowance evaluation method of blade based on high-precision matching and deviation calculating for 3D points

3D points are increasingly used in evaluating allowance of complex curved blade. However, the error of position-attitude alignment and dimensional deviation calculation between nominal and measured models will reduce accuracy of blade allowance. Therefore, a novel allowance evaluation method is proposed to enhance allowance evaluation accuracy by overcoming above problems. In this method, a point cloud registration algorithm is developed by the inlier correspondences selection methods (PCR-ICS) based on local features of 3D points and rigid geometric consistency. For different sets of point cloud, the registration accuracy with this algorithm is improved by over 30% than that with some typical registration algorithms. Considering unsmooth and missing regions of the measured model, a novel point-to-plane deviation calculation (PTPDC) algorithm is developed by constructing planes in conical region of normal vector of each point in the nominal model. The effectiveness of proposed method is verified by GOM scanning experiments of blades with different sizes and shapes. The allowance evaluation error of these blades all is less than 0.03 mm compared to the results obtained by coordinate measuring machine.

Coupled three-dimensional quantum mechanical wave packet study of proton transfer in H2+ + He collisions on accurate abinitio two-state diabatic potential energy surfaces.

We have carried out fully close-coupled three dimensional quantum mechanical wave packet dynamical calculations for the reaction He+H2+→HeH++H on the ground electronic adiabatic potential energy surface and on the lowest two electronic states of newly constructed abinitio calculated diabatic potential energy surfaces for the system [Naskar et al., J. Phys. Chem. A 127, 3832 (2023)]. With the reactant diatom (H2+) in its roto-vibrational ground state (v = 0, j = 0), the calculations have been carried out in hyperspherical coordinates to obtain the reaction attributes. Convergence profiles of the reaction probability with respect to the total angular momentum quantum number at different collision energies are presented for the title reaction. State-to-state as well as initial state selected integral reaction cross sections are calculated from the fully converged reaction probabilities over a range of collision energies. The integral cross section values computed using the two-state diabatic potential energy surfaces are significantly lower than those obtained using the ground electronic state adiabatic potential energy surface and are in much better agreement with the available experimental results than the latter for total energy greater than 1.1eV. Therefore, it becomes clear that it is important to include the nonadiabatic coupling terms for a quantitative prediction of the dynamical observables.

THREE-COMPONENT LENS ZOOM-AFOCAL TRANSFOCAL SYSTEMS FOR THREAD RANGEFINDER

Problems. Synthesis of zoom zooms, which use zoom-afocal systems together with fixed lenses. Creation of a method of parametric synthesis of a three-component zoom-afocal system of a zoom-zoom based on the requirements for the required range of change in angular magnification, permissible cutting of peripheral beams of rays, the field of view of the system and the external location of the aperture diaphragm.&#x0D; The aim of the study. Development of a method for the synthesis of a three-component zoom-afocal system suitable for computer automation.&#x0D; Methodology of implementation. The theory of optical systems composed of thin components is used. Based on this theory, a system of equations is created in which the distances between the components are unknown. To ensure manufacturability, the first and third components of the system are identical. Using the formulas for angles and heights of zero rays, taking into account the requirements for permissible vignetting of beams and the angles of the zoom field of view, the necessary light diameters of the components are calculated.&#x0D; Research results. The resulting formulas for the overall calculation of the zoom-afocal system allow you to take into account the requirements for the longitudinal and transverse dimensions of the system, the position of the aperture diaphragm, determine the focal lengths of the components and their relative location depending on the angular magnification over the entire range of its change. It is established that a three-component system with identical first and second components has a variable axial length, which is maximal at an angular increase of one.&#x0D; Conclusions. The created method of parametric synthesis of a three-component zoom-afocal system for a zoom-zoom, in which the aperture diaphragm of a fixed lens serves as the aperture diaphragm, allows you to automate the dimensional calculation of the system and determine the laws of linear movement of its components along the optical axis.

Optimized designing of generalized electrodes for aluminum/steel resistance spot welding process based on numerical calculation

This work focused on the effects of using different electrode combinations on the welding process and welding quality during aluminum/steel resistance spot welding (RSW) process. The electrodes used during the RSW process can be classified into two catalogues, planar type (P type) and sphere type(S type). An effective two dimensional (2D) numerical calculation model using finite element method (FEM) was developed. In the model, the friction effects between different contact surfaces were seriously considered, and the accuracy and reliability of the model were verified by means of actual welding experiments. Subsequently, the numerical calculation model was used to determine which type of electrode combination was the best one for welding quality by analyzing corresponding RSW processes using four different electrode combination schemes: PP type, SS type, PS type and SP type for upper and lower electrodes. To guarantee scientific nature of the comparisons and analyses, a constant energy regulation method was introduced for each process. The heat energy generation analyses, intermetallic compound formation and growth analyses, and current density analyses were conducted. Combining with actual experiments, the results showed that the welded joint obtained from RSW process using SP type electrode combination scheme had the best comprehensive performance, not only in the double nugget sizes, but also in the deformations of two types of parent metal sheets. In addition, the optimum sizes of the electrodes in this combination were determined through numerical calculations and experiments. Final result showed that the optimum diameter for S type and P type were respectively 9 mm and 60 mm. The work can supply important references for the dissimilar metal RSW process improvement.

A simple, quantitative expression for understanding and evaluating the yield strength of amorphous alloys based on symbolic regression and dimensional calculation

High strength can be the most important and outstanding mechanical property of amorphous alloys as structural materials. To improve the limitations of current strength models, elucidate the key factors determining the yield strength (σy) of amorphous alloys and formulate an explicit, quantitative expression of σy, herein, we successfully developed an ML-based strength model by employing symbolic regression and dimensional calculation. 10 key descriptors were initially extracted from 22 candidate descriptors using random forest model and SHAP method, and dimensional calculation was simultaneously carried out with numerical calculation to ensure the dimensional consistency of final expression. The results shown that the SR-DC model was superior to SR-GP and SR-BGP models, with its satisfactory combination of accuracy (R2=0.93) and simplicity. Meanwhile, molar volume (Vm), melting point (Tm), Pauling electronegativity (χp), and valence electron density (VED) were identified as the key factors and were used to explicitly express the yield strength of amorphous alloys. The final expression was well verified by further theoretical and experimental verification. This work not only provided a general benchmark for the composition design and development of high-strength amorphous alloys but also demonstrated the great potential of symbolic regression combined with dimensional calculation to develop quantitative composition-structure-property relationship in future designing novel materials.

Dimensional analysis-based head loss calculation for the micro-pressure filtering and washing tank

Abstract Filtering is an important measure for the prevention of emitter clogging in micro-irrigation systems. Head loss and energy consumption are two problems in pressurized irrigation systems. Therefore, a combined filtration device – micro-pressure filtering and washing tank – was designed. In this study, the micro-pressure filtering and washing tank was taken as the research object, and a physical model test of inlet flow and sediment concentration was carried out. The head loss prediction model of the micro-pressure filtering and washing tank under clean water and muddy water conditions was established by dimensional and multiple regression analyses, and the determination coefficients (R2) were 0.987 and 0.953, respectively. In addition, the test data were used to validate the head loss prediction model for muddy water. The average relative error of the predicted values was 3.36%, suggesting that the proposed models are ideal for head loss prediction. The research results can provide technical support for the structure optimization and filtration mechanism of the micro-pressure filtering and washing tank, and enrich the theory of micro-pressure filtration.

Directed flow and global polarization in Au+Au collisions across energies covered by the beam energy scan at RHIC

We study the directed flow of identified particles in Au+Au collisions at $\sqrt{s_\text{NN}}=7.7$ to 62.4 GeV. The Glauber model is extended to include both a tilted deformation of the QGP fireball with respect to the longitudinal direction and a non-zero longitudinal flow velocity gradient in the initial state. By combining this improved initial condition with a (3+1)-dimensional viscous hydrodynamic model calculation, we obtain a satisfactory description of the transverse momentum spectra and the rapidity dependent directed flow coefficient of different hadron species. Our calculation indicates the sensitivity of the hadron directed flow, especially its splitting between protons and antiprotons, to both the initial geometry and the initial longitudinal flow velocity. Therefore, the combination of directed flow of different hadrons can provide a tight constraint on the initial condition of nuclear matter created in heavy-ion collisions. The initial condition extracted from the directed flow is further tested with the global polarization of $\Lambda$ and $\bar{\Lambda}$ within the same theoretical framework, where we obtain a reasonable description of these hyperon polarization observed at different collision energies at RHIC.

Návrh elektrického mechanizmu otáčania výložníka stĺpového žeriava pre manipuláciu s kalovými čerpadlami

The article is a continuation of the issue of the technical solution of the hinge for handling sludge pumps in the Jaslovské Bohunice nuclear power plant. The main goal is the design of the electric jib rotating mechanism. It was based on the previous proposal for placing the boom consisting of a dimensional calculation of the new support column and the proposal for placing the boom on this column. The save consisted of two bonds. The upper support of the boom was solved using a rolling bearing fixed in the upper part of the column. The bottom bearing contains an axial plain bearing and a fixed gear as part of the rotating mechanism. In the next step, it is necessary to design the attachment of the selected electric motor with a planetary gearbox and a pinion for this construction. The priority in the design will be mainly to observe the axial distance of the gears, but also to consider the mounting method given by the manufacturer and the torque generated by the engine. A holder in which the motor is attached and then attached to the structure will be designed. Thanks to this, the axial distance will be fulfilled. In addition to supporting the motor, the holder also serves as a radial bearing lock, preventing the bearing from being accidentally pulled out. The result of calculations and designs will be 2D diagrams and 3D visualization of the new construction.

A new instrumented spherical indentation test methodology to determine fracture toughness of high strength steels

A new instrumented spherical indentation test (ISIT) methodology is proposed to determine fracture toughness of metallic materials that their strain hardening can be adequately described by a power-law function. Firstly, tensile properties, including Young’s modulus (E), yield stress (σy) and strain hardening exponent (n) are determined by an improved representative stress–strain method with the Meyer power-law correction. Secondly, by performing dimensional analysis and finite element computation, a new dimensionless function of critical indentation contact pressure (Pmcr) versus tensile properties is developed. To generalize the above dimensionless function to a broad scale of metallic materials, 100 different combinations of tensile properties have been implemented in the finite element computation of spherical indentation tests. Consequently, Pmcr of various tested metallic materials can be calculated conveniently by substituting the corresponding tensile properties into the dimensionless function. The critical indentation depth (hccr) of metallic materials can then be determined by identifying Pmcr on the curve of mean contact pressure versus indentation depth. Finally, fracture toughness is calculated by the concept of indentation energy to fracture at hccr. To demonstrate the repeatability of the above methodology, it has been applied to predict fracture toughness of three different high strength steels by two research groups, independently. The best measurement capacity of the present approach could be optimized in a relative small error, as ±6 % in tensile properties and ±10 % in fracture toughness, that is close to the conventional standard testing results upon multiple samples of the same group.

A Note on Humphreys’ Conjecture on Blocks

Humphreys’ conjecture on blocks parametrises the blocks of a reduced enveloping algebra of the Lie algebras of a reductive algebraic group over an algebraically closed field of positive characteristic. It is well-known to hold under Jantzen’s standard assumptions. We note here that it holds under slightly weaker assumptions, by utilising the full generality of certain results in the literature. We also provide a new approach to prove the result in type G2 in characteristic 3, a case in which the previously mentioned weaker assumptions do not hold. This approach requires some dimensional calculations for certain centralisers, which we conduct in the Appendix for all the exceptional Lie algebras in bad characteristic.