Lattice Construction Research Articles

On Construction of Tri-Concept Lattices

On Construction of Tri-Concept Lattices

A lattice structure for ancestral configurations arising from the relationship between gene trees and species trees

To a given gene tree topology G and species tree topology S with leaves labeled bijectively from a fixed set X, one can associate a set of ancestral configurations, each of which encodes a set of gene lineages that can be found at a given node of the species tree. We introduce a lattice structure on ancestral configurations, studying the directed graphs that provide graphical representations of lattices of ancestral configurations. For a matching gene tree topology and species tree topology G=S, we present a method for defining the digraph of ancestral configurations from the tree topology by using iterated cartesian products of graphs. We show that a specific set of paths on the digraph of ancestral configurations is in bijection with the set of labeled histories — a well-known phylogenetic object that enumerates possible temporal orderings of the coalescences of a tree. For each of a series of tree families, we obtain closed-form expressions for the number of labeled histories by using this bijection to count paths on associated digraphs. Finally, we prove that our lattice construction extends to nonmatching tree pairs, and we use it to characterize pairs (G,S) having the maximal number of ancestral configurations for a fixed G. We discuss how the construction provides new methods for performing enumerations of combinatorial aspects of gene and species trees.

Catalytic role of high pressure in the graphitization of amorphous carbon

To accelerate the graphitization transformation efficiency, reduce the transformation threshold of graphitization, and explore the transformation process and catalytic mechanism of amorphous carbon structure under high pressure, we performed rapid graphitization of amorphous carbon materials by a high temperature-high pressure synergistic preparation method. The results show that the high pressure intervention can accelerate the graphitization transformation progress of amorphous carbon materials and reduce the graphitization transition temperature threshold. Especially at 2.8 GPa–1300 °C, the graphitization transformation rate is significantly increased, and the catalytic effect of high pressure is remarkable. The graphitization effect of this method is close to that of the conventional graphitization method at 3000 °C. The high temperature and high pressure synergistic effect reduces the graphitization temperature requirement by 56%, 1 MPa can compensate for the energy loss of 2.15 °C, and the preparation time is substantially reduced. Meanwhile, We summarize the important stages of initial lattice construction, microcrystal growth, and rapid formation of graphitic lattice in the transformation of disordered lattice under the synergistic effect of high temperature and high pressure, clearly showing the different evolutionary features in the process of structural transformation.

On Lattice Constructions D and D' from q-ary Linear Codes

Multilevel lattice codes, such as those associated to Constructions $C$, $\overline{D}$, D and D', have relevant applications in communications. In this paper, we investigate some properties of lattices obtained via Constructions D and D' from $q$-ary linear codes. Connections with Construction A, generator matrices, expressions and bounds for the lattice volume and minimum distances are derived. Extensions of previous results regarding construction and decoding of binary and $p$-ary linear codes ($p$ prime) are also presented.

Higher cup products on hypercubic lattices: Application to lattice models of topological phases

In this paper, we derive the explicit formula for higher cup products on hypercubic lattices based on the recently developed geometrical interpretation on the simplicial complexes. We illustrate how this formalism can elucidate lattice constructions on hypercubic lattices for various models and derive them from spacetime actions. In particular, we demonstrate explicitly that the (3 + 1)D SPT S=12∫w22+w14 (where w1 and w2 are the first and second Stiefel-Whitney classes) is dual to the 3-fermion Walker-Wang model constructed on the cubic lattice. Other examples include the double-semion model and also the “fermionic” toric code in arbitrary dimensions on hypercubic lattices. In addition, we extend previous constructions of exact boson-fermion dualities and the Gu-Wen Grassmann integral to arbitrary dimensions. Another result that may be of independent interest is a derivation of a cochain-level action for the generalized double-semion model, reproducing a recently derived action on the cohomology level.

Exploring the ultrahigh rolling contact fatigue life of M50 bearing steel by adjusting the cryogenic sequence

The influence of different cryogenic sequences on the rolling contact fatigue (RCF) life of M50-bearing steel has been studied. The results show that direct cryogenic treatment after quenching can effectively improve RCF life. The L10 life is strikingly 5 times longer than that with cryogenic treatment after tempering. This is caused by the distinct lattice construction of martensite and the transformation of retained austenite. More secondary nanocarbides and fine twins are formed via cryogenic treatment before tempering compared with cryogenic treatment after tempering. The improvement in the RCF life of the steel is attributed to the joint effects of the secondary nanocarbides and twin boundaries with a width of 5–13 nm, which delays significantly crack initiation and propagation. This study highlights a common method to improve the service life of high-carbon and high-alloy steels by adjusting the cryogenic sequence.

Topology-induced chiral photon emission from a large-scale meron lattice

AbstractMerons are a class of topologically protected particle-like structures created in in-plane magnetized magnetic films. The structures can act as information carriers and could be used for magnetic storage. However, the development of such applications is hampered by limitations in the size, thermal stability and magnetic-field requirements of the systems. Here we report the construction of millimetre-scale meron lattices that are stable at room temperature and under zero magnetic field. Our system is based on a trilayer structure composed of a thin iron film sandwiched between films of palladium and magnesium oxide (Pd/Fe/MgO) on a gallium nitride wafer. It is fabricated using a molecular-beam epitaxy approach that is assisted by a high magnetic field, which leads to a strong Dzyaloshinskii–Moriya interaction. The lattices can be used for chirality transfer from merons to electrons and then to photons, and we show that the meron lattices can be used as spin injectors in nitride-based light-emitting diodes. The topology-induced spin light-emitting diode can provide 22.5% circularly polarized electroluminescence at room temperature and under zero magnetic field.

High-temperature graphitization characteristics of vitrinite and inertinite

In order to explore the graphitization characteristic differences between vitrinite and inertinite in coal, this study conducted high-temperature thermal simulation experiments (at five temperature points: 1800°C, 2100°C, 2400°C, 2700°C, and 3000°C) using inertinite-rich and vitrinite-rich samples as graphitization precursors. The quantitative comparison for the evolution characteristics of their graphite lattice was carried out using high-resolution transmission electron microscopy (HRTEM), X-ray diffractometer (XRD), and Raman spectroscopy (Raman) techniques. HRTEM revealed that an evident increase in carbon layer numbers and degree of extension was observed with increasing treatment temperature, XRD showed the variation of lattice parameters (d002/La/Lc) with temperature, Raman data revealed the variation of lattice defects (R2/R3) with temperature. It was discussed about the differences of graphite lattice construction processes between inertinite and vitrinite, throughout the entire temperature range of the experiment, the d002 spacing of inertinite was always smaller than that of vitrinite, indicating a higher degree of graphitization. vitrinite exhibited a uniform and smooth evolution state throughout the entire heating process, while inertinite exhibited an “inert” state between 1800°C and 2100°C (d002 values stagnated near at 0.3440 nm). With increasing simulated temperature, the defect level (R2 and R3) of vitrinite rapidly decreased below that of inertinite, throughout the entire temperature range, vitrinite demonstrated superior defect healing ability in terms of both rate and capability compared to inertinite. Under high-temperature thermal simulation, the three-dimensional lattice construction and defect elimination of vitrinite exhibited synchronous evolution characteristics. On the other hand, the formation of the graphite lattice in inertinite showed an evolutionary trend of “first three-dimensional lattice construction, followed by gradual defect elimination”.

Heptagonal quasicrystals: Construction of 2D lattices and demonstrations using laser pointers – Concluding part

Photographic slides of an aperiodic heptagonal tiling were used as two-dimensional diffraction gratings (as a standard approach) to describe and demonstrate the basic properties of dodecagonal quasicrystals. The paper completes our earlier two publications dealing with (1) Penrose (decagonal) and Ammann (octagonal) quasicrystals and (2) dodecagonal quasicrystals, the diffraction gratings of which were constructed and presented in an analogous manner.

Higher-group structure in lattice Abelian gauge theory under instanton-sum modification

We consider the U(1) gauge theory on a four-dimensional torus, where the instanton number is restricted to an integral multiple of p. This theory possesses the nontrivial higher-group structure, which can be regarded as a generalization of the Green–Schwarz mechanism, between mathbb {Z}_q 1-form and mathbb {Z}_p 3-form symmetries. Here, mathbb {Z}_q is a subgroup of the center of U(1). Following the recent study of the lattice construction of the U(1)/mathbb {Z}_q principal bundle, we examine how such a structure is realized on the basis of lattice regularization.

Lattice defective and N, S co-doped carbon nanotubes for trifunctional electrocatalyst application

Multifunctional electrocatalysts are desirable for overall water splitting and zinc-air batteries. In this work, N, S co-doped carbon nanotubes (CNT-NS) with a plentiful of defects were obtained through a novel molecular-level codoped and lattice defect construction method. Thiamine hydrochloride and thiocarbamide were adopted as new precursors in situ doping N and S into multi-walled CNTs surfaces, and lattice defects were constructed by in situ chemical etching using ammonium chloride and ammonium bicarbonate. These surface defects and N,S biatom co-doping synergistic effects can accumulate the CNT-NS to exhibit the superior behavior for electrocatalysis of water splitting and zinc-air batteries. The overpotential for overall water splitting was 1.61 V and the specific capacity for zinc-air batteries was 781 mA h g−1, which was superior to previous works. According to the Operando Raman spectroscopy measurements, the S atoms can serve as the intrinsic catalytic sites for HER and OER, and the defective CNT structures could enhance the catalytic kinetics by the electron-transfer process. Further, density functional theory (DFT) results also indicated the contribution of binary atoms co-doping for low ΔGH∗ values. Therefore, this work provides the valuable reference for rational design/construction for metal-free catalysts of overall water splitting.

Robotic arm three-dimensional printing and modular construction of a meter-scale lattice façade structure

Recent advances in additive manufacturing have made the construction of large-scale 3D-printed structures possible. However, most case studies so far have primarily used concrete as the building material and regular geometries as structural forms. In this work, we present a recently built structural art installation located in Shanghai that is composed of lattice panels with regular and irregular shapes enabled by robotic arm 3D printing. To fabricate the spatial lattice structure, we developed a customized end effector for extrusion-based additive manufacturing using a robotic arm. With the developed printing head and printing path control algorithm, the modular lattice structural panels were printed using ABS material via an industrialized robotic arm and then assembled on the site as a facade. This study showcases the potential to use such modular 3D-printed lattice structures with more freedom in form and partially replace labor with robotic arms for accelerated construction and reduced cost.

The Effect of Inositol Hexakisphosphate on HIV-1 Particle Production and Infectivity can be Modulated by Mutations that Affect the Stability of the Immature Gag Lattice

The assembly of an HIV-1 particle begins with the construction of a spherical lattice composed of hexamer subunits of the Gag polyprotein. The cellular metabolite inositol hexakisphosphate (IP6) binds and stabilizes the immature Gag lattice via an interaction with the six-helix bundle (6HB), a crucial structural feature of Gag hexamers that modulates both virus assembly and infectivity. The 6HB must be stable enough to promote immature Gag lattice formation, but also flexible enough to be accessible to the viral protease, which cleaves the 6HB during particle maturation. 6HB cleavage liberates the capsid (CA) domain of Gag from the adjacent spacer peptide 1 (SP1) and IP6 from its binding site. This pool of IP6 molecules then promotes the assembly of CA into the mature conical capsid that is required for infection. Depletion of IP6 in virus-producer cells results in severe defects in assembly and infectivity of wild-type (WT) virions. Here we show that in an SP1 double mutant (M4L/T8I) with a hyperstable 6HB, IP6 can block virion infectivity by preventing CA-SP1 processing. Thus, depletion of IP6 in virus-producer cells markedly increases M4L/T8I CA-SP1 processing and infectivity. We also show that the introduction of the M4L/T8I mutations partially rescues the assembly and infectivity defects induced by IP6 depletion on WT virions, likely by increasing the affinity of the immature lattice for limiting IP6. These findings reinforce the importance of the 6HB in virus assembly, maturation, and infection and highlight the ability of IP6 to modulate 6HB stability.

Free complex Banach lattices

The construction of the free Banach lattice generated by a real Banach space is extended to the complex setting. It is shown that for every complex Banach space E there is a complex Banach lattice FBLC[E] containing a linear isometric copy of E and satisfying the following universal property: for every complex Banach lattice XC, every operator T:E→XC admits a unique lattice homomorphic extension Tˆ:FBLC[E]→XC with ‖Tˆ‖=‖T‖. The free complex Banach lattice FBLC[E] is shown to have analogous properties to those of its real counterpart. However, examples of non-isomorphic complex Banach spaces E and F can be given so that FBLC[E] and FBLC[F] are lattice isometric. The spectral theory of induced lattice homomorphisms on FBLC[E] is also explored.

Mesojunction-Based Design Paradigm of Structural DNA Nanotechnology.

Mesojunctions were introduced as a basic type of crossover configuration in the early development of structural DNA nanotechnology. However, the investigations of self-assembly from multiple mesojunction complexes have been overlooked in comparison to their counterparts based on regular junctions. In this work, we designed standardized component strands for the construction of complex mesojunction lattices. Three typical mesojunction configurations with three and four arms were showcased in the self-assembly of 1-, 2-, and 3-dimensional lattices constructed from both a scaffold-free tiling approach and a scaffolded origami approach.

Stability of antenna support belts

Introduction. The article deals with the issues of stability of compressed belts of lattice construction, as systems in the form of continuous rods consisting of panel elements. Currently, the estimated length of compressed elements is established by design standards for calculating stability without taking into account variability due to the influence of numerous random and systemic factors. This approach does not encourage the improvement of design solutions, the quality of their execution and the control of the structure. And most importantly, it does not allow to realize the reserves of the bearing capacity of structures laid down by the norms. The purpose of this study is to identify and substantiate the reserves of the bearing capacity of antenna supports of a lattice structure according to the criterion of stability of compressed belts.Materials and methods. It is shown that the values of the calculated length coefficient are set by norms with a margin, due, in particular, to ensuring the reliability of structural systems of compressible elements. It is proposed to consider the estimated length of compressed elements as a random variable. The problem of probabilistic estimation of the free (calculated) length of a centrally compressed element as a parameter of the critical force of loss of stability is solved. The possible normative and calculated values of the calculated length coefficient are given, ensuring the reliability of the calculation of compressed antenna support belts, adopted in the current design standards. To assess the variability of stability indicators, the task is to conduct experimental studies, in particular, with the measurement of vibration frequencies of full-scale structures. By controlling the variability indicators of the calculated length coefficient, it is possible to regulate not only reliability, but also the load-bearing capacity reserves provided for by design standards.Conclusions. The proposed approach to the calculation of stability allows to control the calculated values of the calculated length coefficient by controlling statistical variability (coefficient of variation). If there are available methods for measuring indicators, the approach described in the article to calculating compressed elements for stability can be an effective means and tool for improving design solutions, the quality of their execution and control of the structure.

Mechanical characterization of 3D-printed Kelvin cell with varying infill densities

Over the past few years, 3D-printed cellular lattice structures have had a considerable impact on a variety of engineering applications, including their potential for load carrying and crash resistance. The intricate construction of Kelvin cell lattices makes it difficult to manufacture them using conventional production techniques. Such structures can be easily manufactured using fused deposition modelling (FDM). Polylactic acid (PLA) material is used here to print these components. This study compares the mechanical performance of various infill densities in kelvin cell lattices under uniaxial compression. To maintain uniformity throughout the tests, the 10 mm/min compression speed is always maintained when compressing all the lattices. A cylindrical shell which holds the lattice inside has a radius of 3 mm more than kelvin cell lattice which is developed for experimentation. This reduces the difficulty of adding and removing support structures and increases energy absorption capabilities. Using simulations and a Stress–strain graph (based on Force vs. Displacement graph), a thorough comparative analysis is done to describe the varied mechanical behaviours and energy absorption capacities of the components. According to the experimental findings, it is noticed that elastic modulus and plateau stress rise as the infill density does.

Construction of two-dimensional arbitrary shape <sup>87</sup>Rb atomic array based on spatial light modulator

The ultra-cold atomic system is a clean and highly controllable quantum system, which can be used for quantum simulation of important physical problems in many fields such as condensed matter physics, high-energy physics, astrophysics, and chemical reactions. The constructions of optical lattices with different configurations are an important prerequisite for simulating diverse complex quantum systems, especially solid materials. In this work, we use weighted Gerchberg-Saxton algorithm to generate holograms. By using liquid crystal spatial light modulator and high-resolution imaging system, holograms (in momentum space) are transformed into images in real space for constructing various two-dimensional (2D) optical trap arrays, such as simple triangular, hexagonal, square lattice and more complex honeycomb lattice. We load <sup>87</sup>Rb ultra-cold atoms into the 2D optical trap arrays with a minimal spacing of 3 μm in between. This method is versatile and flexible, which is helpful in expanding the application scope of quantum simulation with optical lattices.

Maximum Likelihood Estimation in Mixed Integer Linear Models.

We consider the maximum likelihood (ML) parameter estimation problem for mixed integer linear models with arbitrary noise covariance. This problem appears in applications such as single frequency estimation, phase contrast imaging, and direction of arrival (DoA) estimation. Parameter estimates are found by solving a closest lattice point problem, which requires a lattice basis. In this letter, we present a lattice basis construction for ML parameter estimation and conclude with simulated results from DoA estimation and phase contrast imaging.

Generalisation and longitudinal extension of the Genetic Lattice Construction (GLC) algorithm

The GLC algorithm [1] allows the construction of efficient transfer lines with defined imaging properties using a minimum number of quadrupole elements. This work describes a generalisation of this algorithm to make it applicable to the use of arbitrary beam optical elements. This includes an extension to longitudinal phase space.