Optimal Packing Research Articles

Multispectral Filter Array Design by Optimal Sphere Packing.

Multispectral imaging (MSI) collects a datacube of spatio-spectral information of a scene. Many acquisition methods for spectral imaging use scanning, preventing its widespread usage for dynamic scenes. On the other hand, the conventional color filter array (CFA) method often used to sample color images has also been extended to snapshot MSI using a Multispectral Filter Array (MSFA), which is a mosaic of selective spectral filters placed over the Focal Plane Array (FPA). However, even state-of-the-art MSFAs coding patterns produce artifacts and distortions in the reconstructed spectral images, which might be due to the nonoptimal distribution of the spectral filters. To reduce the appearance of artifacts and provide tools for the optimal design of MSFAs, this paper proposes a novel mathematical framework to design MSFAs using a Sphere Packing (SP) approach. By assuming that each sampled filter can be represented by a sphere within the discrete datacube, SP organizes the position of the equal-size and disjoint spheres's centers in a cubic container. Our method is denoted Multispectral Filter Array by Optimal Sphere Packing (MSFA-OSP), which seeks filter positions that maximize the minimum distance between the spheres's centers. Simulation results show an image quality improvement of up to 2 dB and a remarkable boost in spectral similarity when using our proposed MSFA design approach for a variety of reconstruction algorithms. Moreover, MSFA-OSP notably reduces the appearance of false colors and zipper effect artifacts, often seen when using state-of-the-art demosaicking algorithms. Experiments using synthetic and real data prove that the proposed MSFA-OSP outperforms state-of-the-art MSFAs in terms of spatial and spectral fidelity. The code that reproduces the figures of this article is available at https://github.com/nelson10/DemosaickingMultispectral3DSpherePacking.git.

Non-fundamental trunc-simplex tilings and their optimal hyperball packings and coverings in hyperbolic space I. For families F1-F4

Supergroups of some hyperbolic space groups are classified as a continuation of our former works. Fundamental domains will be integer parts of truncated tetrahedra belonging to families F1 - F4, for a while, by the notation of E. Moln?r et al. in 2006. Our paper relies basically on this work. As an application, optimal congruent hyperball packings and coverings to the truncation base planes with their very good densities are computed. This covering density is better than the conjecture of L. Fejes T?th for balls and horoballs in 1964.

Substituted tetrazoles with N-oxide moiety: critical assessment of thermochemical properties.

Modeling of the structure of molecules and simulation of crystal structure followed by the calculation of the enthalpies of formation for 21 salts of three high-energy tetrazole 1N-oxides: 5-nitro-1-hydroxy-1H-tetrazole 1a-1g, 5-trinitromethyl-1-hydroxy-1H-tetrazole 2a-2g and 6-amino-3-(1-hydroxy-1H-tetrazol-5-yl)-1,2,4,5-tetrazine 1,5-dioxide 3a-3g was performed. The methods of quantum chemistry and the method of atom-atom potentials were used. Structural search for optimal crystal packings was carried out in 11 most common space symmetry groups. The enthalpies of formation were obtained and analyzed using two different approaches: VBT and MICCM methods, which allowed to evaluate the quality of these calculation methods. In addition, the results obtained indicate high values of thermochemical characteristics for some of the considered compounds, which have a positive effect on their explosive properties and unveil their future application potential.

Research on improving the spreadability of viscous powder in additive manufacturing

The cohesive effect between particles is crucial in influencing the quality of the powder layer in additive manufacturing (AM), which will induce low reproducibility of the subsequent particle fusion process and degrade the performance of final products. In this work, the phenomenon and mechanism of interparticle cohesive effect were investigated through numerical simulations, based on which the methods that may reduce the negative effects of high cohesive interactions were proposed, assessed, and optimized. Results indicated that increasing the particle size could weaken the cohesion and effectively improve the packing fraction of the powder layer, but the surface roughness becomes worse due to the serious boundary effect of large particles under the blade. Besides, the spreading of viscous powders at low velocity and high deposition height could facilitate dense powder layers to some extent, while it contradicts the rapid fabrication and thin layer thickness required by AM. In contrast, the methods of increasing the friction resistance of substrate and optimizing the blade geometry could recover the powder layer quality under multiple indicators through limiting the scattered motion of particles and facilitating powder downward deposition, respectively. Consequently, the optimal approach was preferentially proposed to reduce the cohesive effect during spreading and obtain the powder layer with optimum packing fraction, uniformity, and surface roughness. On this basis, the operation window was further extended to high velocity and low deposition height, which can provide effective references for the practical AM process. • Cohesive effects on spreading of Ti6Al4V powders were numerically investigated. • Methods that reducing the cohesive effects on powder spreading were proposed. • Effectiveness/adaptability of these methods were assessed from parametric studies. • The underlying mechanisms were analyzed and corresponding solutions were provided.

A NEURO-GAME MODEL OF STRATEGY ANALYSIS DURING THE DYNAMIC INTERACTION OF PHISHING ATTACK PARTICIPANTS

Cloud computing is a dynamically evolving computing paradigm. The demand for cloud applications and technologies has especially increased during the CoVID-19 pandemic and martial law in Ukraine. The main purpose of using cloud applications and technologies is to free users of cloud resources from managing hardware and software. One of the challenges in designing a private university cloud is estimating the required number of virtualization cluster nodes. These hosts host virtual machines (VMs) of users. These VMs can be used by students and teachers to complete academic assignments as well as scientific work. The second task is to optimize the placement of VMs in the computer network (CN) of the university, which makes it possible to reduce the number of CN nodes without affecting functionality. And this ultimately helps to reduce the cost of such a solution to deploy a private university cloud, which is not unimportant for Ukrainian universities under martial law. The article proposes a model for estimating the required number of virtualization cluster nodes for a private university cloud. The model is based on a combined approach that involves jointly solving the problem of optimal packing and finding, using a genetic algorithm, the configuration of server platforms of a private university cloud.

Coverings with congruent and non-congruent hyperballs generated by doubly truncated Coxeter orthoschemes

After the investigation of the congruent and non-congruent hyperball packings related to doubly truncated Coxeter orthoscheme tilings [Acta Univ. Sapientiae, Mathematica, 11, 2 (2019), 437–459], we consider the corresponding covering problems. In Non-fundamental trunc-simplex tilings and their optimal hyperball packings and coverings in hyperbolic space the authors gave a partial classification of supergroups of some hyperbolic space groups whose fundamental domains will be integer parts of truncated tetrahedra, and determined the optimal congruent hyperball packing and covering configurations belonging to some of these classes. In this paper, we complement these results with the investigation of the non-congruent covering cases and the remaining congruent cases. We prove, that between congruent and non-congruent hyperball coverings the thinnest belongs to the $\{7,3,7\}$ Coxeter tiling with density $\approx 1.26829$. This covering density is smaller than the conjectured lower bound density of L. Fejes Tóth for coverings with balls and horoballs. We also study the local packing arrangements related to $\{u,3,7\}$ $(6< u < 7, ~ u\in \mathbb{R})$ doubly truncated orthoschemes and the corresponding hyperball coverings. We prove, that these coverings are achieved their minimum density at parameter $u\approx 6.45953$ with covering density $\approx 1.26454$ which is smaller than the above record-small density, but this hyperball arrangement related to this locally optimal covering can not be extended to the entire $\mathbb{H}^3$. Moreover, we see that in the hyperbolic plane $\mathbb{H}^2$ the universal lower bound of the congruent circle, horocycle, hypercycle covering density $\sqrt{12}/\pi$ can be approximated arbitrarily well also with non-congruent hypercycle coverings generated by doubly truncated Coxeter orthoschemes.

Review on Battery Packing Design Strategies for Superior Thermal Management in Electric Vehicles

In the last decades of electric vehicle (EV) development, battery thermal management has become one of the remaining issues that must be appropriately handled to ensure robust EV design. Starting from researching safer and more durable battery cells that can resist thermal exposure, battery packing design has also become important to avoid thermal events causing an explosion or at least to prevent fatal loss if the explosion occurs. An optimal battery packing design can maintain the battery cell temperature at the most favorable range, i.e., 25–40 °C, with a temperature difference in each battery cell of 5 °C at the maximum, which is considered the best working temperature. The design must also consider environmental temperature and humidity effects. Many design strategies have been reported, including novel battery pack constructions, a better selection of coolant materials, and a robust battery management system. However, those endeavors are faced with the main challenges in terms of design constraints that must be fulfilled, such as material and manufacturing costs, limited available battery space and weight, and low energy consumption requirements. This work reviewed and analyzed the recent progress and current state-of-the-art in designing battery packs for superior thermal management. The narration focused on significant findings that have solved the battery thermal management design problem as well as the remaining issues and opportunities to obtain more reliable and enduring batteries for EVs. Furthermore, some recommendations for future research topics supporting the advancement of battery thermal management design were also discussed.

Robust optimization and data-driven modeling of tissue paper packing considering cargo deformation

This paper considers the container loading problem (CLP) for efficient packing of low density tissue paper products, for which, volume, instead of weight, is the key driver for logistic decision-making. Tissue products are susceptible to deformation during the packing process. However, this aspect is usually overlooked when defining the optimal packing policy. In this work, we take this aspect into account and develop a novel methodology for CLP optimization of tissue paper products. The deformation is modeled as a function of known product characteristics and packing process variables using data-driven models. Several modeling approaches are compared, including those based on variable selection, regularization and projection to latent variables. The data-driven model is then included into a Mixed Integer Non Linear Programming (MINLP) CLP. A worst-case robust optimization approach is considered, resulting in solutions that are robust against data-driven model uncertainty. The methodology is applied to a real case study from a portuguese tissue paper mill concerning the packing of toilet paper rolls in wood shipping pallets. Predicted results show an average gain of 4 to 7% in load density in the worst-case scenario, compared to current practice. The deformation model is validated experimentally on the industrial site, by testing optimal configurations which show gains in load density up to 40%. The methodology can be easily extended to other tissue paper products as well as any low density product showing reversible deformation during packing.

Numerical Investigations of Non-equal Mass and Non-equal Spacing Packing of Planetary Bodies

We study the optimal packing of non-equally massed and non-equally spaced multi-planet systems through numerical N-body simulations. Previous studies have generally assumed that a system of equal mass planets will be optimally packed if they are also equally spaced, i.e., if the semi-major axis ratios between planet pairs is a constant. We explicitly test this assumption by obtaining the stability timescales of 5-planet systems around a Sun-like star (with masses varying from 3 Earth masses to 3 Jupiter masses) with increasing degrees of non-uniform-spacing represented by the parameter k. Such systems are simulated using N-body integrations until they reach the point of gravitationally unstable close encounters. For planets with equal masses, a value of k = 1 corresponds to equal spacing, whereas a value of k < 1 leads to the inner planets being more widely spaced than outer planets. We study the optimal value of k for optimal planet packing (i.e., longest stability time) under both equal mass and non-equal mass scenarios and find evidence that k = 1 is optimal under most (but not all) initial conditions; we discuss the scenarios where k < 1 may be preferable. We also study the role that distance to mean-motion resonances (MMRs) play in determining the configurations of optimal planet packing.

Adversarial Bandits with Knapsacks

We consider Bandits with Knapsacks (henceforth, BwK ), a general model for multi-armed bandits under supply/budget constraints. In particular, a bandit algorithm needs to solve a well-known knapsack problem : find an optimal packing of items into a limited-size knapsack. The BwK problem is a common generalization of numerous motivating examples, which range from dynamic pricing to repeated auctions to dynamic ad allocation to network routing and scheduling. While the prior work on BwK focused on the stochastic version, we pioneer the other extreme in which the outcomes can be chosen adversarially. This is a considerably harder problem, compared to both the stochastic version and the “classic” adversarial bandits, in that regret minimization is no longer feasible. Instead, the objective is to minimize the competitive ratio : the ratio of the benchmark reward to algorithm’s reward. We design an algorithm with competitive ratio O (log T ) relative to the best fixed distribution over actions, where T is the time horizon; we also prove a matching lower bound. The key conceptual contribution is a new perspective on the stochastic version of the problem. We suggest a new algorithm for the stochastic version, which builds on the framework of regret minimization in repeated games and admits a substantially simpler analysis compared to prior work. We then analyze this algorithm for the adversarial version, and use it as a subroutine to solve the latter. Our algorithm is the first “black-box reduction” from bandits to BwK: it takes an arbitrary bandit algorithm and uses it as a subroutine. We use this reduction to derive several extensions.

Preservice Mathematics Teachers’ Ability to Perform the Mathematizing Process: The Cylinder Packing Problem

The present study aims to examine the preservice middle school mathematics teachers’ ability to perform the process of mathematizing and to identify their competencies within this context. For this purpose, the study was conducted with 43 preservice teachers attending a state university. The research method used is descriptive research. As the data collection tool, a real-life problem called "cylinder packing problem" was presented to preservice teachers, with a view to finding the optimal and lowest-cost packing scheme for a hazelnut grower. The solutions presented by the preservice teachers were subjected to content analysis as well as descriptive analysis. The preservice teachers’ competencies were examined to see their level of effectiveness in the use of notations that are indicators of mathematizing, in achieving mathematical results in the process of problem-solving. The research findings indicate that the preservice teachers generally lacked sufficient comprehension of the problem in the real-life contexts and could not perform the requirements of important skills such as using notations, mathematical models and generalization method which are important in making abstract inferences in the mathematizing process. In light of these findings, further studies to contribute to preservice teachers’ mathematical sophistication levels are recommended in order to improve their competencies in mathematizing.

(Digital Presentation) Using Simulations to Determine the Effects of the Lithium-Ion Battery Pack Sizes on Performance of Electric Vehicles

Internal combustion engine (ICE) vehicles have a longer driving range with a full tank of gas than lithium-ion battery-powered electric vehicles (EVs). Alongside having a higher purchase cost and a lack of charging infrastructure, the range of EVs is a large deterrent to potential buyers. One solution to increasing the range of EVs is using a battery pack with a higher capacity. However, increasing the capacity typically involves an increase in lithium-ion battery cells, which leads to a higher weight, higher vehicle cost, lower energy efficiency, and higher battery charging time. In addition, regenerative braking recovers the vehicle's kinetic energy which is related to speed and weight. To find the optimal battery pack size, a numeric road test simulation can be used to determine how battery pack size affects energy efficiency, driving range, charging time, and cost. This is more optimal than a real-life road test since inconsistent variables like traffic conditions and weather can be controlled. This paper applies work-energy mathematic modeling of an electric vehicle under different EPA dynamometer driving schedules to investigate the problem proposed above, using an EV model with 21700 type lithium-ion cells. In addition, total vehicle weight, motor efficiency, wheel sizes/weight, and the weight of passengers will also be considered. The simulation revealed that when the total vehicle weight reaches a certain point, it can regenerate significant kinetic energy back to the battery pack to increase the range. Figure 1

Spatial Structure of NanoFAST in the Apo State and in Complex with its Fluorogen HBR-DOM2.

NanoFAST is a fluorogen-activating protein and can be considered one of the smallest encodable fluorescent tags. Being a shortened variant of another fluorescent tag, FAST, nanoFAST works nicely only with one out of all known FAST ligands. This substantially limits the applicability of this protein. To find the reason for such a behavior, we investigated the spatial structure and dynamics of nanoFAST, both in the apo state and in the complex with its fluorogen molecule, using the solution NMR spectroscopy. We showed that the truncation of FAST did not affect the structure of the remaining part of the protein. Our data suggest that the deleted N-terminus of FAST destabilizes the C-terminal domain in the apo state. While it does not contact the fluorogen directly, it serves as a free energy reservoir that enhances the ligand binding propensity of the protein. The structure of nanoFAST/HBR-DOM2 complex reveals the atomistic details of nanoFAST interactions with the rhodanine-based ligands and explains the ligand specificity. NanoFAST selects ligands with the lowest dissociation constants, 2,5-disubstituted 4-hydroxybenzyldienerhodainines, which allow the non-canonical intermolecular CH–N hydrogen bonding and provide the optimal packing of the ligand within the hydrophobic cavity of the protein.

Optimization of hollow fiber membrane module for vacuum membrane distillation (VMD) via experimental study

Membrane distillation (MD) is an attractive desalination technology for treating high salt concentration water/wastewater. Nonetheless, developing membrane modules with high flux and fouling resistance but low energy consumption for industrial application remains a critical challenge. In this work, a novel vacuum membrane distillation (VMD) module with a central perforated tube was developed. The variation of vapor pressure on the shell side was monitored to analyze the relationship between the mass transfer driving force and the permeate flux. The energy consumption of each piece of equipment in the VMD device was evaluated. The heater, chiller, and vacuum pump consumed about 1/3 of the total energy for the VMD system. The central perforated tube suction decreased the mean vapor pressure better than the shell suction. Double suction enabled more uniform pressure distribution on the shell side. The permeate flux under double suction was 50–70 % higher than that under single suction. Consequently, the optimal length, packing fraction, and suction mode were proposed based on energy saving. Our results that include the first report on the generation of superheated vapor in VMD can guide engineers in designing the relevant modules and system scale-up and process optimization for industrial applications.

Self-Assembly of Optimally Packed Cylindrical Clusters inside Spherical Shells.

Systems with short-range attraction and long-range repulsion can form ordered microphases in bulk and under confinement. Using grand canonical Monte Carlo simulations, we study a colloidal system with competing interactions under confinement in narrow spherical shells at thermodynamic conditions at which the hexagonal phase of cylindrical clusters is stable in bulk. We observe spontaneous formation of different ordered structures. The results of the simulations are in a very good agreement with the predictions of a simple mathematical model based on the geometry and optimal packing of colloidal clusters. The results of the simulations and the explanation provided by a relatively simple geometric model may be helpful in manufacturing copolymer nanocapsules and may indicate possible ways of coiling DNA strands on spherical objects.

Flow and transport in a pleated filter

A pleated membrane filter consists of a porous membrane layer, which is surrounded by two supporting layers, and the whole structure is pleated and placed into a cylindrical cartridge. Pleated membrane filters are used in a variety of industrial applications, since they offer more surface area to volume ratio that is not found in equivalent flat filters. In this work, we introduce a novel three-dimensional model of a pleated membrane filter that consists of an empty region, a pleated region, and a hollow region. The advection diffusion equation is used to model contaminant concentration in the membrane pores along with Darcy's law to model the flow within the membrane and support layers, while the Stokes equation is used for the flow in the empty region and the hollow region. We further use the key assumptions of our model based on small aspect ratios of the filter cartridge and the pleated membrane to simplify the governing equations, which can be easily solved by numerical methods. By performing these steps, we seek to discover an optimal pleat packing density to find the optimum filter performance, while not exceeding a threshold for the particle concentration at the filter outlet.

Numerical study on the thermodynamic performance of a packed bed cryogenic energy storage system

• Developed a 3-D porous media model for cryogenic energy storage in a packed bed. • Studied the influence of key factors on cold charging performance of the packed bed. • Operating conditions of cryogenic gas charged packed bed were analyzed. Cold energy storage devices improve the round-trip efficiency of cryogenic energy storage systems, where a solid packed bed for cold energy storage (PBCES) is widely utilized. In this study, a three-dimensional transient porous media packed bed model was developed using computational fluid dynamics software ANSYS Fluent 2020 to study the thermodynamic characteristics of a solid PBCES system with cryogenic nitrogen as the working medium during the cold charging process. The effects of the superficial mass flow rate ( G in ), inlet temperature of nitrogen, packing materials, porosity on the packed bed temperature distribution, pressure drop, cold storage efficiency ( η s ), and cold exergy efficiency ( η Ex ) were investigated carefully. The results showed that the axial temperature distribution is a typical thermocline. The system performance is predominantly affected by the criterion of the complete charging (the minimum temperature difference between Face-2 and Face-1, Δ T F2-F1,min ) and the G in . The thermocline thickness decreased with a decrease in the G in . The η s and η Ex increased significantly with an increase in the Δ T F2-F1,min . The maximum η s and η Ex were 77.69% and 75.21% at the G in was 0.1 kg/(m 2 ·s) when the Δ T F2-F1,min was 100 K. The change in porosity had a limited influence on the cryogenic storage performance but considerably influenced the pressure drop; Basalt was recommended as the optimal packing material in the present study. The superficial mass flow rate of working medium and the complete charging indicator (Δ T F2-F1,min ) should be carefully determined to achieve high performance in a practical CES system. The developed simulation model would be promising and useful for the design and optimization of a practical packed bed for CES systems.

Infinite families of optimal systems of biangular lines related to representations of [formula omitted

A line packing is optimal if its coherence is as small as possible. Most interesting examples of optimal line packings are achieving equality in some of the known lower bounds for coherence. In this paper two infinite families of real and complex biangular line packings are presented. New packings achieve equality in the real or complex second Levenshtein bound respectively. Both infinite families are constructed by analyzing well known representations of the finite groups SL(2,Fq). Until now the only known infinite families meeting the second Levenshtein bounds were related to the maximal sets of mutually unbiased bases (MUB). Similarly to the line packings related to the maximal sets of MUBs, the line packings presented here are related to the maximal sets of mutually unbiased weighing matrices. Another similarity is that the new packings are projective 2-designs. The latter property together with sufficiently large cardinalities of the new packings implies some improvement on largest known cardinalities of real and complex biangular tight frames.

Properties and microstructure of packing-optimised recycled aggregate concrete with different cement paste or sand contents

This paper investigates the influences of cement paste volume (CPV) and sand-to-aggregate volume ratio (Bs) on the properties and microstructure of recycled aggregate concrete (RAC). The recycled concrete aggregates (RCAs) in an optimal packing status were utilised to fully replace the natural coarse aggregates. The workability and mechanical properties of RAC were first examined, followed by characterisation of the interfacial transition zones and the pore structure inside RAC by using microhardness test and X-ray computed tomography, respectively. The results indicate that the slump of RAC increases with the CPV in a growing rate, which is mainly attributed to the increased lubrication effect of fresh paste on the aggregates. Under the constant CPV and water-to-cement ratio, increasing the Bs decreases the slump of RAC due to the reduced cement paste film thickness. Increasing the CPV decreases the macroporosity of RAC as it reduces the amount of RCAs with pores in old mortars, thereby enhancing its compressive strength and Young's modulus. However, excessive CPV increases the porosity and thickness of interfacial transition zones, which subsequently weakens the mechanical properties of RAC. The increase of Bs first enhances the granular skeleton by optimising the particle packing status, which is beneficial to RAC properties. However, excessive sand (i.e., high Bs) increases the macroporosity and mean pore size inside RAC, degrading the mechanical properties of RAC. Nonetheless, the flexural strength of RAC is marginally influenced by the CPV or Bs. This study guides the selection of CPV and Bs in the mix design of packing-optimised RAC to refine its microstructure and mechanical properties.

Exploring optimal multimode vibronic pathways in singlet fission of azaborine analogues of perylene.

The development of new singlet fission chromophores is a vibrant area of research to explore the possibility of efficient photovoltaic devices. Using high-level ab-initio density matrix renormalization group calculations, we present a systematic analysis of BN-doped perylenes for their potential application as singlet fission candidates. Four singlet fission chromophores are identified considering the monomer-based properties and their excitonic characters are further analyzed in a dimer configuration optimized in a six-dimensional space for local maxima of fission rates. Furthermore, a multistate multimode vibronic Hamiltonian is employed to identify intra- and interstate vibrational pathways for excitation energy modulation. Several photophysical properties such as Davydov splitting, activation energy and vibronic admixture of multiexcitonic and charge-transfer states are calculated for physically accessible dimers. The optimal dimer packing results in appropriate vibrational relaxation of singlet fission states and promotes significant population transfer which would be more attenuated without such couplings. This work not only identifies potential singlet fission systems with favorable electronic properties but also highlights the sensitivity of dimer packings with respect to the substitution patterns in singlet fission chromophores.