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Fix two positive integers $d\geq3$ and $q$. We give an upper bound for anti-canonical volumes of $d$-dimensional $\frac{1}{q}$-lc toric Fano varieties, which corresponds to an upper bound for the dual normalized volumes of the associated $d$-dimensional $\frac{1}{q}$-lc Fano polytopes. And we also construct examples to show that these upper bounds are optimal. Besides, we provide an optimal upper bound for volumes of $d$-dimensional lattice simplices $S$ such that $\frac{1}{q}S$ has exactly one interior lattice point., Comment: 27 pages,comments are welcome

In additive manufacturing (AM), particularly for laser-based metal AM, process optimization is crucial to the quality of products and the efficiency of production. The identification of optimal process parameters out of a vast parameter space, however, is a daunting task. Despite advances in simulations, the process optimization for specific materials and geometries is developed through a time-consuming trial-and-error approach, which often lacks the versatility to address multiple optimization objectives. Machine learning (ML) provides a powerful tool to accelerate the optimization process, but most current studies focus on simple single-track prints, which hardly translate to manufacturing 3D components for engineering applications. In this study, we develop an Accurate Inverse process optimization framework in laser Directed Energy Deposition (AIDED), based on machine learning models and a genetic algorithm, to aid process optimization in laser DED processes. Using the AIDED, we demonstrate the following: (i) Accurately predict single-track (R2 score 0.995), multi-track (R2 score 0.969), and multi-layer (1.07% and 10.75% error in width and height, respectively) cross-sectional melt pool geometries directly from process parameters; (ii) Determine appropriate hatch spacing and layer thickness for fabricating fully dense (density > 99.9%) multi-track and multi-layer prints; (iii) Inversely identify optimal process parameters directly from customizable application objectives within 1-3 hours. We also validate the effectiveness of the AIDED experimentally by achieving two exemplary targets: fast print speed and fine print resolution. Furthermore, we show the high transferability of the framework from stainless steel to pure nickel. With AIDED, we pave a new way for ''aiding'' the process optimization in the laser-based AM processes that is applicable to a wide range of materials.

Hexagonal boron nitride (h-BN) is brittle, however, its atomic-scale structural engineering can lead to unprecedented physical properties. Here we report the bulk synthesis of high-density crystalline h-BN solids by using high-temperature spark plasma sintering (SPS) of micron size h-BN powders. In addition to the high mechanical strength and ductile response of such materials, we have obtained anomalous values of dielectric constant beyond theoretical limits, high thermal conductivity, and exceptional neutron radiation shielding capability. Through exhaustive characterizations we reveal that SPS induces non-basal plane crystallinity, twisting of layers, and facilitates inter-grain fusion with a high degree of in-plane alignment across macroscale dimensions, resulting in near-theoretical density and anomalous properties. Our findings highlight the importance of material design, via new approaches such as twisting and interconnections between atomically thin layers, to create novel ceramics with properties that could go beyond their intrinsic theoretical predictions., Comment: Authors revised version, 46 pages, 4 figures

In materials science, a wide range of properties of materials are governed by various types of energies, including thermal, physicochemical, structural, and mechanical energies. In 2005, Dr. Frans Spaepen used crystalline face-centered-cubic (fcc) copper as an example to discuss a variety of phenomena that are associated with energies. Inspired by his pioneering work, we broaden our analysis to include a selection of representative pure metals with fcc, hexagonal close-packed (hcp), and body-centered cubic (bcc) structures. Additionally, we extend our comparison to energies between pure metals and equiatomic binary, ternary, and multi-principal element alloys (sometimes also known as high-entropy alloys). Through an extensive collection of data and calculations, we compile energy tables that provide a comprehensive view of how structure and alloying influence the energy profiles of these metals and alloys. We highlight the significant impact of constituent elements on the energies of alloys compared to pure metals and reveal a notable disparity in mechanical energies among materials in fcc-, hcp- and bcc-structured metals and alloys. Furthermore, we discuss the underlying mechanisms behind these patterns and discuss the implications for structural transformations, providing insights into the broader context of these energy variations.

The keyhole phenomenon is widely observed in laser materials processing, including laser welding, remelting, cladding, drilling, and additive manufacturing. Keyhole-induced defects, primarily pores, dramatically affect the performance of final products, impeding the broad use of these laser-based technologies. The formation of these pores is typically associated with the dynamic behavior of the keyhole. So far, the accurate characterization and prediction of keyhole features, particularly keyhole depth, as a function of time has been a challenging task. In situ characterization of keyhole dynamic behavior using a synchrotron X-ray is complicated and expensive. Current simulations are hindered by their poor accuracies in predicting keyhole depths due to the lack of real-time laser absorptance data. Here, we develop a machine learning-aided simulation method that allows us to accurately predict keyhole depth over a wide range of processing parameters. Based on titanium and aluminum alloys, two commonly used engineering materials as examples, we achieve an accuracy with an error margin of 10 %, surpassing those simulated using other existing models (with an error margin in a range of 50-200 %). Our machine learning-aided simulation method is affordable and readily deployable for a large variety of materials, opening new doors to eliminate or reduce defects for a wide range of laser materials processing techniques.

Polar nematic liquid crystals are new classes of condensed-matter states where the inversion symmetry common to the traditional apolar nematics is broken. Establishing theoretical descriptions for the novel phase states is an urgent task. Here, we develop a Landau-type mean-field theory for both the achiral and chiral ferroelectric nematics. In the polar nematic states, the inversion symmetry breaking adds two new contributions: an additional odd elastic term (corresponding to the flexoelectricity in symmetry) to the standard Oseen-Frank free energy and an additional Landau term relating to the gradient of local polarisation. As a general necessity, the coupling between the scalar order parameter and polarisation order is further considered. In the chiral and polar nematic state, we reveal that the competition between the twist elasticity and polarity dictates effective compressive energy arising from the quasi-layer structure. The polarisation gradient is an essential term for describing the ferroelectric nature of the systems. The approaches provide theoretical foundations for testing and predicting polar structures in emerging polar liquid crystals., Comment: 18 pages, 3 figures

Materials-by-design has been historically challenging due to complex process-microstructure-property relations. Conventional analytical or simulation-based approaches suffer from low accuracy or long computational time and poor transferability, further limiting their applications in solving the inverse material design problem. Here, we establish a deep learning and genetic algorithm framework that integrates forward prediction and inverse exploration. This framework provides an end-to-end solution to achieve application-specific mechanical properties by microstructure optimization. In this study, we select the widely used Ti-6Al-4V to demonstrate the effectiveness of this framework by tailoring its microstructure and achieving various yield strength and elastic modulus across a large design space, while minimizing the stress concentration factor. Compared with conventional methods, our framework is efficient, versatile, and readily transferrable to other materials and properties. Paired with additive manufacturing's potential in controlling local microstructural features, our method has far-reaching potential for accelerating the development of application-specific, high-performing materials., Comment: 19 pages, 5 figures

For a real number $0<\epsilon<1/3$, we show that the anti-canonical volume of an $\epsilon$-klt Fano $3$-fold is at most $3200/\epsilon^4$ and the order $O(1/\epsilon^4)$ is sharp., Comment: 15 pages, comments are welcome

Dislocations, line defects in crystalline materials, play an essential role in the mechanical[1,2], electrical[3], optical[4], thermal[5], and phase transition[6] properties of these materials. Dislocation motion, an important mechanism underlying crystal plasticity, is critical for the hardening, processing, and application of a wide range of structural and functional materials[1,7,8]. For decades, the movement of dislocations has been widely observed in crystalline solids under mechanical loading[9-11]. However, the goal of manipulating dislocation motion via a non-mechanical field alone remains elusive. Here, we present real-time observations of dislocation motion controlled solely by an external electric field in single-crystalline zinc sulfide (ZnS). We find that 30{\deg} partial dislocations can move back and forth depending on the direction of the electric field, while 90{\deg} partial dislocations are motionless. We reveal the nonstoichiometric nature of dislocation cores using atomistic imaging and determine their charge characteristics by density functional theory calculations. The glide barriers of charged 30{\deg} partial dislocations, which are lower than those of 90{\deg} partial dislocations, further decrease under an electric field, explaining the experimental observations. This study provides direct evidence of dislocation dynamics under a non-mechanical stimulus and opens up the possibility of modulating dislocation-related properties., Comment: https://www.nature.com/articles/s41563-023-01572-7

Topological spin and polar textures have fascinated people in different areas of physics and technologies. However, the observations are limited in magnetic and solid-state ferroelectric systems. Ferroelectric nematic is the first liquid-state ferroelectric that would carry many possibilities of spatially distributed polarization fields. Contrary to traditional magnetic or crystalline systems, anisotropic liquid crystal interactions can compete with the polarization counterparts, thereby setting a challenge in understating their interplays and the resultant topologies. Here, we discover chiral polarization meron-like structures during the emergence and growth of quasi-2D ferroelectric nematic domains, which are visualized by fluorescence confocal polarizing microscopy and second harmonic generation microscopies. Such micrometre-scale polarization textures are the modified electric variants of the magnetic merons. Unlike the conventional liquid crystal textures driven solely by the elasticity, the polarization field puts additional topological constraints, e.g., head-to-tail asymmetry, to the systems and results in a variety of previously unidentified polar topological patterns. The chirality can emerge spontaneously in polar textures and can be additionally biased by introducing chiral dopants. An extended mean-field modelling for the ferroelectric nematics reveals that the polarization strength of systems plays a dedicated role in determining polarization topology, providing a guide for exploring diverse polar textures in strongly-polarized liquid crystals.

Merkle tree is a widely used tree structure for authentication of data/metadata in a secure computing system. Recent state-of-the art secure systems use a smaller-sized MT, namely Bonsai Merkle Tree (BMT) to protect the metadata such as encryption counters. Common BMT algorithms were designed for traditional Von Neumann architectures with a software-centric implementation in mind, hence they use a lot of recursions and are often sequential in nature. However, the modern heterogeneous computing platforms employing Field-Programmable Gate Array (FPGA) devices require concurrency-focused algorithms to fully utilize the versatility and parallel nature of such systems. Our goal for this work is to introduce HMT, a hardware-friendly BMT algorithm that enables the verification and update processes to function independently and provides the benefits of relaxed update while being comparable to eager update in terms of update complexity. The methodology of HMT contributes both novel algorithm revisions and innovative hardware techniques to implementing BMT. We introduce a hybrid BMT algorithm that is hardware-targeted, parallel and relaxes the update depending on BMT cache hit but makes the update conditions more flexible compared to lazy update to save additional write-backs. Deploying this new algorithm, we have designed a new BMT controller with a dataflow architecture, speculative buffers and parallel write-back engines that allows for multiple concurrent relaxed authentication. Our empirical performance measurements have demonstrated that HMT can achieve up to 7x improvement in bandwidth and 4.5x reduction in latency over baseline in subsystem level tests. In a real secure-memory system on a Xilinx U200 accelerator FPGA, HMT exhibits up to 14\% faster execution in standard benchmarks compared to state-of-the art BMT solution on FPGA.