Irregular Lattice Research Articles

Optimization‐based pore network modeling approach for determination of hydraulic conductivity function of granular soils

AbstractA wide range of applications of unsaturated hydraulic conductivity is well known in geotechnical, hydrological, and agricultural engineering fields. The standard prediction models for hydraulic conductivity function overlook the complexity of soil pore structure and employ a simplistic approach based on the bundle of capillary tubes. This study proposes an alternative approach employing pore network models calibrated to match soil water retention data to predict the hysteretic hydraulic conductivity function of granular soils. A novel approach to constructing a multidirectional pore network built on an irregular lattice with variable coordination numbers is presented for the realistic representation of soil voids. The geometric and topological parameters of the pore network model are optimized using the genetic algorithm, and adequate pore‐scale processes (piston‐like advance and corner flow during drainage and piston‐like advance, pore body filling, and snap‐off during imbibition) are modeled to get reasonable predictions of hysteretic hydraulic conductivity functions over the entire suction range of granular soils. Comparisons between the pore network model results, standard physically based models, and measured data for a variety of granular soils show that the proposed pore network has a superior performance over other models and compares favorably to the experimental data.

Topological Anderson phases in heat transport

Topological Anderson phases (TAPs) offer intriguing transitions from ordered to disordered systems in photonics and acoustics. However, achieving these transitions often involves cumbersome structural modifications to introduce disorders in parameters, leading to limitations in flexible tuning of topological properties and real-space control of TAPs. Here, we exploit disordered convective perturbations in a fixed heat transport system. Continuously tunable disorder-topology interactions are enabled in thermal dissipation through irregular convective lattices. In the presence of a weak convective disorder, the trivial diffusive system undergos TAP transition, characterized by the emergence of topologically protected corner modes. Further increasing the strength of convective perturbations, a second phase transition occurs converting from TAP to Anderson phase. Our work elucidates the pivotal role of disorders in topological heat transport and provides a novel recipe for manipulating thermal behaviors in diverse topological platforms.

Deformation mechanics of generalized missing rib chiral lattice structures

The planar missing rib lattice topology is generalized to construct a family of regular and irregular tetra-chiral periodic lattices. The geometry of a lattice in the family is completely defined by a set of six parameters. Using a unified energy based approach, the constitutive model and all effective elastic properties of the resulting lattice structures are determined from the unit periodic element of the lattice. Straightforward analytical expressions of the effective properties are obtained for some special geometries, which for the general case may be lengthy. In the latter case, the compliance tensor can easily be obtained numerically. The proposed approach involves accurate determination of the strain tensor and the compliance tensor for which a minimum error norm method is used. The results from the analytical expressions are compared with those obtained from Finite Element Analysis (FEA), and a very good match is observed. To draw a parity with experimental determination of the elastic properties and address the observation of auxeticity (negative Poisson’s ratio) in such lattice structures, the concept of empirical Young’s modulus and Poisson’s ratio is introduced. Using this idea, for the conventional chiral lattice, some disagreement in the existing literature is resolved.

Lattice-Disordered High-Entropy Alloy Engineered by Thermal Dezincification for Improved Catalytic Hydrogen Evolution Reaction.

A disordered crystal structure is an asymmetrical atomic lattice resulting from the missing atoms (vacancies) or the lattice misarrangement in a solid-state material. It has been widely proven to improve the electrocatalytic hydrogen evolution reaction (HER) process. In the present work, due to the special physical properties (the low evaporation temperature of below 900 °C), Zn is utilized as a sacrificial component to create senary PtIrNiCoFeZn high-entropy alloy (HEA) with highly disordered lattices. The structure of the lattice-disordered PtIrNiCoFeZn HEA is characterized by the thermal diffusion scattering (TDS) in transmission electron microscope. Density functional theory calculations reveal that lattice disorder not only accelerates both the Volmer step and Tafel step during the HER process but also optimizes the intensity and distribution of projected density of states near the Fermi energy after the H2O and H adsorption. Anomalously high alkaline HER activity and stability are proven by experimental measurements. This work introduces a novel approach to preparing irregular lattices offering highly efficient HEA and a TDS characterization method to reveal the disordered lattice in materials. It provides a new route toward exploring and developing the catalytic activities of materials with asymmetrically disordered lattices.

In-in correlators and scattering amplitudes on a causal set

Causal set theory is an approach to quantum gravity in which spacetime is fundamentally discrete at the Planck scale and takes the form of an irregular Lorentzian lattice, or “causal set,” from which continuum spacetime emerges in a large-scale (low-energy) approximation. In this work, we present new developments in the framework of interacting quantum field theory on causal sets. We derive a diagrammatic expansion for in-in correlators in local scalar field theories with finite polynomial interactions. We outline how these same correlators can be computed using the double-path integral, which acts as a generating functional for the in-in correlators. We modify the in-in generating functional to obtain a generating functional for in-out correlators. We define a notion of scattering amplitudes on causal sets with noninteracting past and future regions and verify that they are given by S-matrix elements (matrix elements of the time-evolution operator). We describe how these formal developments can be implemented to compute early Universe observables under the assumption that spacetime is fundamentally discrete. Published by the American Physical Society 2024

Large‐Area, High‐Numerical‐Aperture, Freeform Metasurfaces

AbstractNanophotonic devices are optical platforms capable of unprecedented wavefront control. To push the limits of experimental device performance, scalable design methodologies that combine the simplicity and fabricability of conventional design paradigms with the extended capabilities of freeform optimization are required. A novel gradient‐based design framework for large‐area freeform metasurfaces is introduced in which nonlocal interactions between simply shaped nanostructures, placed on an irregular lattice, are tailored to produce high‐order hybridized modes that support customizable large‐angle scattering profiles. Utilizing this approach, multifunctional super‐dispersive metalenses are designed and experimentally demonstrated. The approach to high‐numerical‐aperture radial metalenses capable of diffraction limited focusing and the generation of donut‐shaped point spread functions is also extended. It is anticipated that these concepts will have utility in super‐resolution microscopy, particle trapping, additive manufacturing, and metrology applications that require ultra‐high numerical apertures.

3D-Printed Personalized Lattice Implant as an Innovative Strategy to Reconstruct Geographic Defects in Load-Bearing Bones.

Geographic defect reconstruction in load-bearing bones presents formidable challenges for orthopaedic surgeon. The use of 3D-printed personalized implants presents a compelling opportunity to address this issue. This study aims to design, manufacture, and evaluate 3D-printed personalized implants with irregular lattice porous structures for geographic defect reconstruction in load-bearing bones, focusing on feasibility, osseointegration, and patient outcomes. This retrospective study involved seven patients who received 3D-printed personalized lattice implants for the reconstruction of geographic defects in load-bearing bones. Personalized implants were customized for each patient. Randomized dodecahedron unit cells were incorporated within the implants to create the porous structure. The pore size and porosity were analyzed. Patient outcomes were assessed through a combination of clinical and radiological evaluations. Tomosynthesis-Shimadzu metal artifact reduction technology (T-SMART) was utilized to evaluate osseointegration. Functional outcomes were assessed according to the Musculoskeletal Tumor Society (MSTS) 93 score. Multiple pore sizes were observed in porous structures of the implant, with a wide distribution range (approximately 300-900 um). The porosity analysis results showed that the average porosity of irregular porous structures was around 75.03%. The average follow-up time was 38.4 months, ranging from 25 to 50 months. Postoperative X-rays showed that the implants matched the geographic bone defect well. Osseointegration assessments according to T-SMART images indicated a high degree of bone-to-implant contact, along with favorable bone density around the implants. Patient outcomes assessments revealed significant improvements in functional outcomes, with the average MSTS score of 27.3 (range, 26-29). There was no implant-related complication, such as aseptic loosening or structure failure. 3D-printed personalized lattice implants offer an innovative and promising strategy for geographic defect reconstruction in load-bearing bones. This approach has the potential to match the unique contours and geometry of the geographic bone defect and facilitate osteointegration.

The cellular Potts model on disordered lattices.

The cellular Potts model, also known as the Glazier-Graner-Hogeweg model, is a lattice-based approach by which biological tissues at the level of individual cells can be numerically studied. Traditionally, a square or hexagonal underlying lattice structure is assumed for two-dimensional systems, and this is known to introduce artifacts in the structure and dynamics of the model tissues. That is, on regular lattices, cells can assume shapes that are dictated by the symmetries of the underlying lattice. Here, we developed a variant of this method that can be applied to a broad class of (ir)regular lattices. We show that on an irregular lattice deriving from a fluid-like configuration, two types of artifacts can be removed. We further report on the transition between a fluid-like disordered and a solid-like hexagonally ordered phase present for monodisperse confluent cells as a function of their surface tension. This transition shows the hallmarks of a first-order phase transition and is different from the glass/jamming transitions commonly reported for the vertex and active Voronoi models. We emphasize this by analyzing the distribution of shape parameters found in our state space. Our analysis provides a useful reference for the future study of epithelia using the (ir)regular cellular Potts model.

Unraveling fluorescent mechanism of biomass-sourced carbon dots based on three major components: Cellulose, lignin, and protein

The complexity of biomass components leads to significant variations in the performance of biomass-based carbon dots (CDs). To shed light on this matter, this study presents a comparative analysis of the fluorescence properties of CDs using pure cellulose, lignin, and protein as models. Three CDs showed different fluorescent properties, resulting from the structure difference and carbonization behavior in the hydrothermal. The relatively gentle thermal degradation of proteins allows the macromolecular structure of amino acids to be preserved. This preservation results in a more regular lattice structure, a larger sp2 domain size, and N-doping, which contribute to the highest quantum yield (QY) of 8.7% of the CDs. In contrast, cellulose undergoes more severe thermal degradation with large amounts of small molecules generated, resulting in the CDs with fewer surface defects, more irregular lattice structures, and lower QY. These results provide a guideline for the design of carbon dots from different biomass.

Acoustic valley Hall topological insulators with controllable band gap

In recent years, numerous studies have investigated the impact of imperfections on topological insulators, and certain defects have been observed. Former topological insulators have a limited range of topological transport bands and an irregular lattice structure, which hampers their usefulness in technological applications. Here, it’s implemented the topological transport of sonic waves in a phononic crystal array structure. This paper has shown that changing the rotating scatterer's angle can alter the topological phase, resulting in lattice band inversion. This establishes a topological channel that enables acoustic conduction. It is feasible to create multifarious channel structures and devise acoustic transmission systems with varying positions. The introduction of rotating scatterers enables the regulation of the influx of acoustic waves into targeted channels. And the robustness of its edge states was verified by using the finite element method. These outcomes furnish the sound wave control mechanism with a novel formation and urge the development of programmable sound wave regulation. Based on these properties, the technique of regulating topological wave propagation through the use of a topological insulator can also be extended to other systems, including filters and acoustic devices.

Optimal mechanical properties of Hydroxyapatite gradient Voronoi porous scaffolds for bone applications — A numerical study

Irregular Voronoi-based lattice (IVL) structures in tissue engineering (TE) have significant potential for bone regeneration. These scaffolds can mimic natural human bone interconnectivity by gradually altering strut thickness (ST) and seed point space (PS), which affects both mechanical and biological characteristics. This paper investigates the impact of design parameters, ST and PS, on Hydroxyapatite (HA) ILV structures’ mechanical properties (elastic modulus (E) and maximum compressive strength (MCS)) and geometrical characteristics (pore number, size, and distribution, surface area (SA), and surface area-to-volume ratio (SA/VR)). Four types of IVL scaffolds were designed; PC-TC (Constant PS-Constant ST), PC-TG (Constant PS-Gradient ST), PG-TC (Gradient PS-Constant ST), and PG-TG (Gradient PS-Gradient ST). The study, conducted through linear static structural finite element analysis (FEA) with maximum stress criteria, underscores the profound impact of irregularity and morphology on mechanical performance and geometrical features. Regarding SA and SA/VR, a comparison between PC-TC with other proposed scaffolds showed a minor improvement for PC-TG, while higher significant improvements were found for both PG-TG and PG-TC. In terms of pores distribution and number, no noticeable improvement was observed for the PC-TG scaffold compared to PC-TC. In contrast, PG-TC and PG-TG lattices demonstrated a variety of pore distributions and approximately doubled pore numbers. Studying mechanical properties, considering E and MCS, showcases substantial gains for PG-TC. It, however, revealed that for the rest of the scaffolds, no enhancement was observed regarding E. Based on these results, gradient PS proved to be more effective than gradient ST in enhancing mechanical performance and geometrical properties. Due to these improvements, this study holds promise for expediting bone regeneration and reducing postoperative complications in bone replacement applications.

An Automated Parametric Surface Patch-Based Construction Method for Smooth Lattice Structures with Irregular Topologies

Additive manufacturing enables the realization of complex component designs that cannot be achieved with conventional processes, such as the integration of cellular structures, such as lattice structures, for weight reduction. To include lattice structures in component designs, an automated algorithm compatible with conventional CAD that is able to handle various lattice topologies as well as variable local shape parameters such as strut radii is required. Smooth node transitions are desired due to their advantages in terms of reduced stress concentrations and improved fatigue performance. The surface patch-based algorithm developed in this work is able to solidify given lattice frames to smooth lattice structures without manual construction steps. The algorithm requires only a few seconds of sketching time for each node and favours parallelisation. Automated special-case workarounds as well as fallback mechanisms are considered for non-standard inputs. The algorithm is demonstrated on irregular lattice topologies and applied for the construction of a lattice infill of an aircraft component that was additively manufactured.

Explicit Phase-Field Regularized Voronoi-Based Lattice Model for Quasi-Brittle Fracture and Its Finite Element Implementation

In this study, the conventional Voronoi-based irregular lattice model is regularized by the phase-field method, which effectively introduces a characteristic length parameter to overcome the mesh-size dependent solution. To circumvent the local instability (snap-back) which generally requires sophisticated arc-length control, the so-called phase-field regularized Voronoi-based lattice (PHL) model is realized using an explicit finite element solver. Furthermore, the constitutive law of quasi-brittle materials is embraced when establishing the PHL model, which is proven length-scale insensitive. We show that the PHL model with an explicit solver is very robust and computationally efficient, provided with proper parameters and parallel computing. Moreover, the necessary fine mesh size in the implicit phase-field method is greatly released in the explicit PHL model, of which accurate results could be obtained with the coarser mesh size. Several experiments are adopted to demonstrate the model, including the size effect and mix-mode bending of concrete specimens. Cracks’ initiation, propagation, and coalescence could be automatically captured without any tracking algorithms. In addition, it is noteworthy that the model could easily be extended to coupled mechanical and transportation problems.

Inhomogeneous percolation on the Bethe lattice with critical exponents and its application

This manuscript explores the critical exponents for three-dimensional irregular Bethe lattice (TDIBL) and their closer association with real-life applications. In the current investigation, we evaluate the CEs for TDIBL using several percolating variables, including the cluster size distribution (CSD), percolating probability (PP), mean cluster size (MCS), characteristic cluster size (CCS), and characteristic generation size (CGS). The CEs for TDIBL findings illustrate that the percolation model accomplishes enormous universal classes and is connected with a complicated fractal and resizing structure of underlying geometric characteristics, which will contribute to the system’s mean degree in the percolating method. Additionally, sensitivity analysis and numerical simulation will further enhance our appraisal of the percolating procedure graphically. Furthermore, we address the novel coronavirus 2019 (COVID-19) transmission behavior in the database using our methodology. Utilizing this data type to develop predictions by conveying policy-using courtesy groups with varying infection and recovery probabilities is also feasible. We acknowledge that our revolutionary endeavor will be intriguing, and we will inquire about scientific researchers collaborating with various percolation methods of investigation.

Study the Physical Properties PVT of Polyethylene Glycol usıng the Sımha-Somcynsky Theory

In this study, the structure of polyethylene glycol polymer with different molecular weights was investigated, and the physical properties were studied in terms of pressure, volume and temperature using a theory called Simha-Somcynsky (SS). which shows irregular lattice structure in terms of the hole fraction depending on which thermodynamic quantities are expressed in the statistical thermodynamics of polymers. Therefore, it is necessary to determine the hole fraction and occupied site fraction y. Thermodynamic properties and hole fraction were investigated in the range of temperature between 283-450 K, and at a pressure up to 150 MP. Average error and maximum error in specific volume were determined as 0.036% and 0.28%, respectively, as the highest error in peg302. The other important determination was that the polyethylene glycol had glass transition temperatures ranging from 55 to 60 K.

Nematically Templated Vortex Lattices in Superconducting FeSe.

New pathways to controlling the morphology of superconducting vortex lattices─and their subsequent dynamics─are required to guide and scale vortex world-lines into a computing platform. We have found that the nematic twin boundaries align superconducting vortices in the adjacent terraces due to the incommensurate potential between vortices surrounding twin boundaries and those trapped within them. With the varying density and morphology of twin boundaries, the vortex lattice assumes several distinct structural phases, including square, regular, and irregular one-dimensional lattices. Through concomitant analysis of vortex lattice models, we have inferred the characteristic energetics of the twin boundary potential and furthermore predicted the existence of geometric size effects as a function of increasing confinement by the twin boundaries. These findings extend the ideas of directed control over vortex lattices to intrinsic topological defects and their self-organized networks, which have direct implications for the future design and control of strain-based topological quantum computing architectures.

Generation mechanism and motion behavior of sliver defect in single crystal Ni-based superalloy

Sliver is a common but easily neglected defect in single crystal Ni-based superalloy castings. To date, there is still no unified viewpoint on its formation mechanism and generation causes. In this work, the orientation discontinuity and motion behavior of sliver defects were studied through experiments and numerical simulations. The ultrathin wedge-shaped specimen containing the grain boundary of the sliver and the matrix was prepared at the initial position of the sliver defect for the observation of equal thickness fringes. The discontinuity of equal thickness fringes on both sides of the grain boundary was observed through a transmission electron microscope, which directly confirms the abrupt change in the orientation between the sliver and matrix from the nanoscale. The crystal lattices at the smooth area and the bulging area of the grain boundary were found to have unusually different arrangements. The irregular lattice arrangement at the bulging area shows that the grain boundary has experienced high-stress deformation. Statistical results of sliver orientation deviation with a further composition analysis show the micro protuberance of the mold shell has a noticeable inductive effect on the sliver generation. Furthermore, a self-developed three-dimensional phase-field simulation model coupled with the spatial topology algorithm is established to simulate the orientation deflection behavior and orientation deviation threshold of fractured dendrites. The simulation results indicated that there is an upper limit of the cross-section solid fraction at the fracture position for the motion of the fractured dendrites. When the cross-section solid fraction at the fracture position is higher than this upper limit, it will be difficult to produce large deviation slivers due to the structural limitation of surrounding dendrites. This upper limit does not change with the solidification temperature gradient.

Toward matter dynamics in spin foam quantum gravity

Any approach to pure quantum gravity must eventually face the question of coupling quantum matter to the theory. In the past, several ways of coupling matter to spin foam quantum gravity have been proposed, but the dynamics of the coupled matter-gravity system is challenging to explore. To take first steps towards uncovering the influence quantum matter has on spin foam models, we couple free, massive scalar lattice field theory to a restricted, semi-classical 4d spin foam model, called quantum cuboids. This model can be understood as a superposition of hypercuboidal (and thus irregular) lattices. Both theories are coupled by defining scalar lattice field theory on irregular lattices via discrete exterior calculus and then superimposing these theories by summing over spin foam configurations. We compute expectation values of geometric and matter observables using Markov Chain Monte Carlo techniques. From the observables, we identify a regime in parameter space, in which the spin foam possesses a finite total volume and looks on average like a regular lattice with an emergent lattice spacing dependent on the mass of the scalar field. We also measure the 2-point correlation function and correlation length of the scalar field in relation to the geodesic distance encoded in the spin foam. Our results are consistent with the correlation function of ordinary scalar lattice field theory defined on a fixed regular lattice with the emergent lattice spacing and the same mass. We conclude that in this regime of the model, the scalar field is not sensitive to the fluctuations of the spin foam and effectively behaves as if it is defined on a fixed regular lattice.

Исследование асимптотической последовательности высот правильных симплексов при увеличении размерности евклидова пространства

The problem of spherical packing and the problem of the distribution of points on a sphere are well-known unsolved mathematical problems. In particular, the problem of the distribution of points on a sphere is included in the well-known list of unsolved mathematical problems of Steve Smale. Accordingly, a significant interest for the study is both the direct search for solutions to problems and research in areas related to known problems. In particular, the problem of spherical dense packing and coating packing is directly related to the study of regular, irregular and layered lattices, problems of noise-resistant coding, synthesis and analysis of broadband signals, mathematical research of multidimensional spaces, crystallography, methods for solving differential equations and calculating n-dimensional integrals, and many other particular problems and entire fields of knowledge. The paper presents the results of studies of some properties of n-dimensional regular simplex in Euclidean space. The vectors forming the n-dimensional regular simplex define the fundamental basis of the hexagonal lattice. The subject of the study is some properties and regularities of a vector object forming a regular simplex in n-dimensional Euclidean space, the novelty of the results lies in a formulated and proven theorem, several formulas that allow recursive and non-recursive calculations of some characteristics of n-dimensional regular simplex and spherical hexagonal packages. The object of the study is an n-dimensional regular simplex. Main results a theorem on the asymptotic character of the sequence of heights of regular simplex with increasing dimension of space is formulated and proved, the consequences of the theorem and remarks supplementing the theorem are formulated. The conclusion of the article contains additions and numerical examples with comments for some research results. The practical significance lies in the proposed mathematical tools that contribute to the development of the theory of spherical packing and the study of the properties of geometric objects in n-dimensional Euclidean space.

Estimation of Asymmetric Spatial Autoregressive Dependence on Irregular Lattices

In spatial econometrics, we usually assume that the spatial dependence structure is known and that all information about it is contained in a spatial weights matrix W. However, in practice, the structure of W is unknown a priori and difficult to obtain, especially for asymmetric dependence. In this paper, we propose a data-driven method to obtain W, whether it is symmetric or asymmetric. This is achieved by calculating the area overlap of the adjacent regions/districts with a given shape (a pizza-like shape, in our case). With W determined in this way, we estimate the potentially asymmetric spatial autoregressive dependence on irregular lattices. We verify our method using Monte Carlo simulations for finite samples and compare it with classical approaches such as Queen’s contiguity matrices and inverse-distance weighting matrices. Finally, our method is applied to model the evolution of sales prices for building land in Brandenburg, Germany. We show that the price evolution and its spatial dependence are mainly driven by the orientation towards Berlin.