Discrete Density Research Articles

A comparative analysis of 3D woven honeycomb-based aircrew helmet liners against Nomex and Aluminum alternatives

This study investigates the energy dissipation efficiency of an aircrew helmet liner developed using 3D woven honeycomb structural composites compared to different commercially available honeycomb liner materials such as Nomex, and Aluminium. In contrast to liners with discrete density differences, the use of a honeycomb-based liner reduces the concern about delamination, back face deformation and fracture propagation. The research involves comparing several parameters related to crashworthiness, such as specific energy absorption (SEA), crush force efficiency (CFE), and margin of safety, which are crucial for head protection and ensuring helmet injury tolerance. These parameters play a vital role in assessing the ability of different configurations of the honeycomb liner during impacts. Flatwise compression and dynamic impact tests were conducted to evaluate the helmet liner’s performance while maintaining consistency in the helmet shell component. Finite element analysis (FEA) and 3D x-ray Tomography techniques were utilized to analyse the back face deformation (BFD) at high-velocity impact and the internal damage resulting from impacts on the helmet liners, respectively. The results revealed that the 3D woven honeycomb liner configuration performs optimally in terms of energy absorption by demonstrating sufficient and balanced competency across these three critical factors. Additionally, the simulation result revealed that the 3D woven honeycomb liner exhibits wave propagation. This phenomenon enhances its energy absorption capacity and reduces back-face deformation attributed to its crushing behaviour. This research offers valuable insights for improving the performance of aircrew helmet liners, with a particular focus on utilizing 3D woven honeycomb liners featuring 3D woven solid structure to maintain exceptional structural integrity.

Feature-preserving shrink wrapping with adaptive alpha

Recent advancements in shrink-wrapping-based mesh approximation have shown tremendous advantages for non-manifold defective meshes. However, these methods perform unsatisfactorily when maintaining the regions with sharp features and rich details of the input mesh. We propose an adaptive shrink-wrapping method based on the recent Alpha Wrapping technique, offering improved feature preservation while handling defective inputs. The proposed approach comprises three main steps. First, we compute a new sizing field with the capability to assess the discretization density of non-manifold defective meshes. Then, we generate a mesh feature skeleton by projecting input feature lines onto the offset surface, ensuring the preservation of sharp features. Finally, an adaptive wrapping approach based on normal projection is applied to preserve the regions with sharp features and rich details simultaneously. By conducting experimental tests on various datasets including Thingi10k, ABC, and GrabCAD, we demonstrate that our method exhibits significant improvements in mesh fidelity compared to the Alpha Wrapping method, while maintaining the advantage of manifold property inherited from shrink-wrapping methods.

Design and implementation of English vocabulary orthographical revision application based on Matlab

Apropos of English learning, vocabulary learning is one of the most essential parts. Thanks to modern technology, recent years has witnessed scads of vocabulary learning apps springing in the app market which include greatly comprehensive functions. However, among those popular apps, some universal handicaps still exist in the design of the review section, for example, the absence of the freedom for the users to classify the cognitive or priority grade of vocabulary and the low effect of some reviewing methods that could not satisfy the need of the language learners to fully master the orthography of words. This paper aims at contriving an app serving as a supplementary part of English vocabulary learning in order to remedy those inadequacies of mainstream applications or other self-learning methods. In this paper, literature study, graphology, and mathematical modelling are involved. Based on Matlab GUI/App Designer, this paper presents a new method to review English words in which users could customize their lexicon, as well as define the priority of each word and practice spelling of vocabulary on an hourly-based system instead of a daily-based one that most of the existing online platforms adopted. Through creating a discrete probability density function for each word, this app could forward a random word in the glossary for users to practice orthography, obeying the probability density distribution that has a mathematical relationship with familiarity and priority of the words as well as the time factor (Ebbinghaus forgetting curve). Thus, users could thoroughly grasp the orthography of target words.

Data-driven classification of sheared stratified turbulence from experimental shadowgraphs

We propose a dimensionality reduction and unsupervised clustering method for the automatic classification and reduced-order modeling of density-stratified turbulence in laboratory experiments. We apply this method to 113 long shadowgraph movies collected in a “stratified inclined duct” experiment, where turbulence is generated by instabilities arising from a sheared buoyancy-driven counterflow at Reynolds numbers Re≈300–5000, tilt angles θ=1∘–6∘, and Prandtl number Pr≈700. The method automatically detects edges representative of discrete density interfaces, extracts a low-dimensional vector of statistics representative of their morphology, projects these statistics onto a two-dimensional phase space of principal coordinates, and applies a clustering algorithm. Five clusters are detected and interpreted physically based on their typical interface morphology and an examination of representative frames, revealing distinct types of turbulence and mixing: laminarizing, braided, overturning, granular, and unstructured, as well as some intermediate types. The ratio of time spent in each cluster varies gradually across the (Re,θ) space. At intermediate values of Reθ, intermittent turbulence cycles between clusters in phase space and reveals at least two distinct routes to stratified turbulence. These insights demonstrate the potential of this method to reveal the underlying physics of complex turbulent systems from large experimental datasets. Published by the American Physical Society 2024

Variational implicit solvation with Legendre-transformed Poisson–Boltzmann electrostatics

The variational implicit-solvent model (VISM) is an efficient approach to biomolecular interactions, where electrostatic interactions are crucial. The total VISM free energy of a dielectric boundary (i.e. solute–solvent interface) consists of the interfacial energy, solute–solvent interaction energy and dielectric electrostatic energy. The last part is the maximum value of the classical and concave Poisson–Boltzmann (PB) energy functional of electrostatic potentials, with the maximizer being the equilibrium electrostatic potential governed by the PB equation. For the consistency of energy minimization and computational stability, here we propose alternatively to minimize the convex Legendre-transformed Poisson–Boltzmann (LTPB) electrostatic energy functional of all dielectric displacements constrained by Gauss’ Law in the solute region. Both integrable and discrete solute charge densities are treated, and the duality of the LTPB and PB functionals is established. A penalty method is designed for the constrained minimization of the LTPB functional. In application to biomolecular interactions, we minimize the total VISM free energy iteratively, while in each step of such iteration, minimize the LTPB energy. Convergence of such a min–min algorithm is shown. Our numerical results on the solvation of a single ion indicate that the LTPB performs better than the PB formulation, providing possibilities for efficient biomolecular simulations.

Investigating Load Calculation for Broken Ice and Cylindrical Structures Using the Discrete Element Method

Ice loads are critical forces that impact the structural integrity of offshore equipment in high-latitude sea areas and play a pivotal role in the design of structures in ice-prone regions. The primary objective of this study is to investigate both experimental and numerical approaches to analyze ice loads on marine structures, elucidate their characteristics and patterns, and offer technical support for the design of structures in ice-prone areas. To achieve this goal, an ice model was built using polypropylene material, and experiments were conducted in a wave flume at room temperature to measure the ice resistance on cylindrical structures. Structural loads were assessed at various ice velocities while maintaining a fixed ice concentration. Furthermore, a high-performance discrete element technology was employed to develop a numerical simulation method for calculating ice resistance on cylindrical structures. Sensitivity analysis was conducted to evaluate the influence of discrete element density on the resistance outcomes. The predicted structural resistance for ice velocities corresponding to the experimental conditions was compared with the results obtained from the model experiment. The research findings indicate that the primary cause of ice resistance is the interaction between the structure and fragmented ice, which leads to collisions, friction, rotation, and local ice accumulation. To quantify the resistance, ice resistance coefficients were defined using an average resistance formula, representing different statistical values. These coefficients were found to remain relatively constant at varying sailing speeds. The results obtained through the discrete element method for ice resistance demonstrated a remarkable agreement with the experimental findings, both in terms of observed phenomena and numerical values. This agreement serves as evidence substantiating the effectiveness of the numerical approach. These methods offer efficient and accurate load prediction solutions for the design of structures in cold regions.

Learning of discrete models of variational PDEs from data.

We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train a neural network model of a discrete Lagrangian density such that the discrete Euler-Lagrange equations are consistent with the given training data. We, thus, obtain a structure-preserving machine learning architecture. Lagrangian densities are not uniquely defined by the solutions of a field theory. We introduce a technique to derive regularizers for the training process which optimize numerical regularity of the discrete field theory. Minimization of the regularizers guarantees that close to the training data the discrete field theory behaves robust and efficient when used in numerical simulations. Further, we show how to identify structurally simple solutions of the underlying continuous field theory such as traveling waves. This is possible even when traveling waves are not present in the training data. This is compared to data-driven model order reduction based approaches, which struggle to identify suitable latent spaces containing structurally simple solutions when these are not present in the training data. Ideas are demonstrated on examples based on the wave equation and the Schrödinger equation.

Visualization-Driven Illumination for Density Plots.

We present a novel visualization-driven illumination model for density plots, a new technique to enhance density plots by effectively revealing the detailed structures in high- and medium-density regions and outliers in low-density regions, while avoiding artifacts in the density field's colors. When visualizing large and dense discrete point samples, scatterplots and dot density maps often suffer from overplotting, and density plots are commonly employed to provide aggregated views while revealing underlying structures. Yet, in such density plots, existing illumination models may produce color distortion and hide details in low-density regions, making it challenging to look up density values, compare them, and find outliers. The key novelty in this work includes (i) a visualization-driven illumination model that inherently supports density-plot-specific analysis tasks and (ii) a new image composition technique to reduce the interference between the image shading and the color-encoded density values. To demonstrate the effectiveness of our technique, we conducted a quantitative study, an empirical evaluation of our technique in a controlled study, and two case studies, exploring twelve datasets with up to two million data point samples.

Effect of discrete Cr nano-nuclei on stripping property and resistivity of ultrathin Cu foil

An electrochemical deposition strategy for discrete Cr nano-nuclei to achieve ultrathin Cu foil stripping was proposed. The results indicated that this method could be utilized to prepare Cu foils with a thickness of about 1.34 μm. The Cr discrete nucleus density directly affects the stripping performance, surface roughness, and resistivity of Cu foils. Under our experimental conditions, the stripping performance of Cu foil was the best at a Cr discrete nucleus density of 15.7×109 cm−2 and resistivity of 4.95×10−7 Ω·m, 9.2% lower than that of conventional Cr coating of 0.67 μm in thickness and 15.8% lower than that of the coating with potassium dichromate, and the tensile strength exceeds 248.80 MPa.

МЕЛКОМАСШТАБНОЕ МОДЕЛИРОВАНИЕ ДИНАМИКИ ВОД НА ШЕЛЬФЕ И КОНТИНЕНТАЛЬНОМ СКЛОНЕ В АНТАРКТИКЕ

The use of the Fluidity-ICOM model in a full non-hydrostatic formulation makes it possible to correctly investigate fine-scale water dynamics and water transformations on the Antarctic shelf and continental slope. A possibility of solving problems with high spatial resolution in models is provided by the use of the three-dimensional adaptive unstructured mesh with automatic refinement to given scales. The modernization of the graphical model output made it possible to reliably visualize the detailed development of simulated hydrophysical processes, to obtain numerical estimates of parameters of these processes, and to verify them against unique field observation data. An original three-dimensional numerical experiment was held in the area of polynya with an open water surface on the shelf. In this case, the real salt (buoyancy) flux is specified, which is caused by the in-water ice formation in the polynya and is obtained from the actual atmospheric forcing. As a result, the convective circulation was correctly simulated as a process of formation of dense water on the shelf, which then flows down the shelf and continental slope in the form of discrete density currents. Similarity of the model geometric, dynamic, and hydrophysical characteristics of cascading with the typical ones obtained from the analysis of field observations was found.

On nature-inspired design optimization of antenna structures using variable-resolution EM models

Numerical optimization has been ubiquitous in antenna design for over a decade or so. It is indispensable in handling of multiple geometry/material parameters, performance goals, and constraints. It is also challenging as it incurs significant CPU expenses, especially when the underlying computational model involves full-wave electromagnetic (EM) analysis. In most practical cases, the latter is imperative to ensure evaluation reliability. The numerical challenges are even more pronounced when global search is required, which is most often carried out using nature-inspired algorithms. Population-based procedures are known for their ability to escape from local optima, yet their computational efficiency is poor, which makes them impractical when applied directly to EM models. A common workaround is the utilization of surrogate modeling techniques, typically in the form of iterative prediction-correction schemes, where the accumulated EM simulation data is used to identify the promising regions of the parameter space and to refine the surrogate model predictive power at the same time. Notwithstanding, implementation of surrogate-assisted procedures is often intricate, whereas their efficacy may be hampered by the dimensionality issues and considerable nonlinearity of antenna characteristics. This work investigates the benefits of incorporating variable-resolution EM simulation models into nature-inspired algorithms for optimization of antenna structures, where the model resolution pertains to the level of discretization density of an antenna structure in the full-wave simulation model. The considered framework utilizes EM simulation models which share the same physical background and are selected from a continuous spectrum of allowable resolutions. The early stages of the search process are carried out with the use of the lowest fidelity model, which is subsequently automatically increased to finally reach the high-fidelity antenna representation (i.e., considered as sufficiently accurate for design purposes). Numerical validation is executed using several antenna structures of distinct types of characteristics, and a particle swarm optimizer as the optimization engine. The results demonstrate that appropriate resolution adjustment profiles permit considerable computational savings (reaching up to eighty percent in comparison to high-fidelity-based optimization) without noticeable degradation of the search process reliability. The most appealing features of the presented approach—apart from its computational efficiency—are straightforward implementation and versatility.

CryoEM structure of a post-assembly MS-ring reveals plasticity in stoichiometry and conformation.

The flagellar motor supports bacterial chemotaxis, a process that allows bacteria to move in response to their environment. A central feature of this motor is the MS-ring, which is composed entirely of repeats of the FliF subunit. This MS-ring is critical for the assembly and stability of the flagellar switch and the entire flagellum. Despite multiple independent cryoEM structures of the MS-ring, there remains a debate about the stoichiometry and organization of the ring-building motifs (RBMs). Here, we report the cryoEM structure of a Salmonella MS-ring that was purified from the assembled flagellar switch complex (MSC-ring). We term this the 'post-assembly' state. Using 2D class averages, we show that under these conditions, the post-assembly MS-ring can contain 32, 33, or 34 FliF subunits, with 33 being the most common. RBM3 has a single location with C32, C33, or C34 symmetry. RBM2 is found in two locations with RBM2inner having C21 or C22 symmetry and an RBM2outer-RBM1 having C11 symmetry. Comparison to previously reported structures identifies several differences. Most strikingly, we find that the membrane domain forms 11 regions of discrete density at the base of the structure rather than a contiguous ring, although density could not be unambiguously interpreted. We further find density in some previously unresolved areas, and we assigned amino acids to those regions. Finally, we find differences in interdomain angles in RBM3 that affect the diameter of the ring. Together, these investigations support a model of the flagellum with structural plasticity, which may be important for flagellar assembly and function.

Homogenisation of dynamical optimal transport on periodic graphs

This paper deals with the large-scale behaviour of dynamical optimal transport on mathbb {Z}^d-periodic graphs with general lower semicontinuous and convex energy densities. Our main contribution is a homogenisation result that describes the effective behaviour of the discrete problems in terms of a continuous optimal transport problem. The effective energy density can be explicitly expressed in terms of a cell formula, which is a finite-dimensional convex programming problem that depends non-trivially on the local geometry of the discrete graph and the discrete energy density. Our homogenisation result is derived from a Gamma -convergence result for action functionals on curves of measures, which we prove under very mild growth conditions on the energy density. We investigate the cell formula in several cases of interest, including finite-volume discretisations of the Wasserstein distance, where non-trivial limiting behaviour occurs.

Discrete density evolution and LDPC codes designwith asymmetric channels

为了设计非对称信道下的低密度奇偶校验(low-density parity-check, LDPC)码并分析其性能,本文提出了可实现的基于偏移最小和译码的非对称离散密度进化方法.首先推导了低复杂度的非对称信道离散密度进化迭代公式;应用该迭代公式,进一步对采用偏移最小和译码的LDPC码编码进行优化设计,得到了在非对称信道下不同量化范围和步长的LDPC 码的最佳度分布及其性能;最后获得了在高精度量化下的最佳偏移值.结果表明在非对称信道下,改进的基于偏移最小和译码的非对称密度进化方法复杂度比原方法成数量级降低;当码率固定,规则码变量节点度越小其性能越好,最佳偏移值越小.对非规则LDPC码,使用差分进化算法找到了最佳度分布与偏移值.码率固定时,最大变量节点度越大,非规则码性能越好.

Multinomial distribution as part of valuation of the number of failures

Abstract. Aim. The paper aims to examine the application of a multinomial distribution as part of valuation of the number of an object’s failures. It is assumed that the valuation is “based on past experience” (a statistical sample of the number of an object’s failures accumulated over several preceding evaluation periods).Methods. The paper uses methods of system analysis, probability theory and mathematical statistics. The author analyses the primary indicators used to define the applied dependability indicators. It is noted that the valuation of such indicators based on statistical data for complex systems appears to be promising. The problem of valuation of the number of failures using a statistical sample is examined. The primary disadvantages of the used approaches are identified that are associated with errors in defining the average values of series, variation coefficients and asymmetry. It is shown that it is possible to solve the problem using the well-known combinatorics problem “on balls and boxes”, which leads to the use of a multinomial distribution. The paper examined the definition of probabilities for compositions and partitions of the number n into m parts, as well as the probabilities of a given number of balls being in a box with their maximum number. The author also considered formulas and algorithms that allow reducing the number of calculations in case of machine computation of the probabilities of a multinomial distribution. The feasibility of approximating a discrete distribution function by the Gumbel distribution is estimated. The paper demonstrates the feasibility of valuating the number of failures for a “segment” corresponding to a part (fraction) of an object’s dimension considered on a certain part (fraction) of the time interval. It also examines examples of valuating the number of failures for an object as a whole over a 1-month evaluation interval and for ½ of an object over a 12-month evaluation interval, while the total interval for which the statistical sample is accumulated is 72 months. The paper sets forth limitations on the application of the presented method and notes some of its possible advantages. In particular, it is noted that the statistical sample is only one implementation of the multinomial distribution, so it can be said that when applying the proposed method, the results of valuation are no longer affected by the presence of unlikely combinations of series values in the statistical sample. It is also noted that when applying the proposed method of valuating the number of failures, the obtained acceptable value will never be less than or equal to the average value of the statistical sample.Results. Formulas have been obtained for calculating, based on partitions, of the discrete density number and the maximum distribution function of a multinomial distribution. The paper presents the results of algorithm analysis for machine computation. The results of applying some algorithms are presented. A formula is proposed for approximating the distribution function of the maximum of a multinomial distribution using the Gumbel distribution (for the largest values) using the method of moments. The author recommends a range of values of the estimated interval, in which the proposed method provides acceptable reliability of the results. The task of further research is defined.

Investigation of the Effect of Laser Fluence on Microstructure and Martensitic Transformation for Realizing Functionally Graded NiTi Shape Memory Alloy via Laser Powder Bed Fusion

Nowadays, additive manufacturing (AM) of NiTi shape memory alloy is a challenging topic for the realization of 3D functional parts. Particularly, Laser Powder Bed Fusion (LPBF) of NiTi powder is one of the most challenging processes belonging to AM, thanks to its best performances in terms of productivity and precision of geometrical complexity. The control of the functional performances in NiTi components requires a strong interaction between technological and metallurgical approaches. In fact, a strong correlation among the process conditions, the microstructure, and the final functional performances, beyond the defects associated with the process are needed to be understood and analyzed. In the present work, the correlation between the feasibility map of processability and the obtained microstructure, which can be tailored according to the use of different energy density values, of Ni-rich NiTi powder processed with LPBF is investigated. In detail, discrete energy density values, in the range 60–300 J/mm3, were correlated to microstructure, Ni:Ti ratio, and transformation temperatures of the martensitic transformation, analyzed with SEM, EBSD, EDX, and DSC characterizations, respectively. An increase in laser energy density was found to promote Ni evaporation, which induced a change of the microstructure from austenite to martensite at room temperature. A consequent shift of the transformation temperatures to higher values and a change in microstructural texture was achieved. These achievements can support the identification of the feasibility range for manufacturing functionally graded NiTi SMA, requiring tailored functional properties located in selected positions in the 3D parts.

Discrete quasiprobability distributions involving Bernoulli polynomials

<abstract><p>The aim of this short paper is to present a new family of discrete densities with two parameters based on Bernoulli numbers and polynomials. We use the properties of such numbers in order to compute the first moments and the density of a finite sum of such independent variables.</p></abstract>

A new non-gradient-based topology optimization algorithm with black–white density and manufacturability constraints

Topology optimization (TO) is one of the growing research fields, and nongradient-based TO (NGTO) is a promising method. This is due to the algorithm’s ability to avoid local minima and solve TO with no gradient information. Furthermore, the NGTO deals better with manufacturability constraints. In this work, we propose a new NGTO algorithm using the simulated annealing (SA) algorithm, with connectivity criteria and black–white discrete density. The connectivity criterion analyzes the neighborhood of an element and checks if the neighboring elements have the same density, penalizing checkerboard solutions. The results showed that the algorithm converges to an optimized structure with compliance values similar or even enhanced compared to those found in the literature. Taking into account the advantages of being non-gradient and the ease of application, the proposed algorithm presents itself as a promising algorithm in the field of TO research. Since checkerboards are the main limit in the manufacturing of designed parts with topology optimization, the manufacturability constraints applied in the proposed algorithm. The binary non-gradient topology optimization with checkerboard-free structure is the main contribution of the proposed method.

Lattice Boltzmann method with nonreflective boundary conditions for low Mach number combustion

The paper presents a lattice Boltzmann (LB) method for premixed and nonpremixed combustion simulations with nonreflective boundary conditions, in contrast to Navier–Stokes solvers or hybrid schemes. The current approach employs different sets of distribution functions for flow, temperature and species fields, which are fully coupled. The discrete equilibrium density distributions are obtained from the Hermite expansions thus thermal compressibility is included. The coupling among the momentum, energy and species transport enables the model to be applicable for reactive flows with chemical heat release. The characteristic boundary conditions are incorporated into the LB scheme to avoid numerical reflections. The multi-relaxation-time collision schemes are applied to all the LB solution procedures to improve numerical stability. With detailed thermodynamics and chemical mechanisms for hydrogen-air, the LB modelling framework is validated against both premixed flame propagation and nonpremixed counterflow diffusion flame benchmarks. Simulations of circular expanding premixed flames further demonstrate the capability of the new reactive LB method. The developed LB methodology retains the advantages of classic LB methods and extends the LB capability to low Mach number combustion with potential applications in mesoscale and microscale combustors, catalysis, fuel cells, batteries and so on.

A computationally efficient implementation of continuum dislocation dynamics: Formulation and application to ultrafine-grained Mg polycrystals

Continuum dislocation dynamics (CDD) represents the evolution of systems of curved and connected dislocation lines in terms of density-like field variables which include the volume density of loops (or ’curvature density’) as an additional field. Since dislocation curvature represents a spatial derivative of the underlying discrete dislocation density tensor, the curvature field evolution equation of necessity contains numerically inconvenient higher-order derivatives of the density fields. We propose a simple approximation to express curvature in terms of density fields, and demonstrate its application to a benchmark problem in deformation of Mg polycrystals.