Full Lattice Research Articles

Effect of sample dimensions on the stiffness of PA12 Lattice materials fabricated using Powder Bed Fusion

Powder Bed Fusion fabrication techniques, including selective laser sintering, have made the fabrication of lattice meta-materials consisting of periodic cells formed by interconnected struts possible. It is generally observed that cell size has a strong influence on the lattice’s effective Young’s modulus, following in the case of typical polymers used for printing a trend of the smaller the softer. However, there is no clear understanding of the origin of the effective elastic modulus reduction with lattice cell size. In this paper, an integrated study is performed to unravel the reasons behind this effect. The analysis performed encompasses mechanical characterization (compression tests and nanoindentation), microstructure characterization (X-ray tomography, DSC, SAXS, and WAXS), and numerical analysis of the effect of defects (FFT and Finite element simulations of cells with roughness and defects) of PA12 printed single cells of different sizes and full lattice specimens containing many cells. It is found that the effect of porosity and roughness is not enough to explain the reduction of the effective elastic modulus with the cell size, suggesting that this effect is necessarily a combination of the defects, incomplete melting of particles and the changes of PA12 nanostructure induced by the different printing conditions as function of full specimen size . The results of the micro- and nanostructure characterization validate this assumption.

Strong–strong beam–beam simulations with lattices of circular e+e- colliders

Strong–strong beam–beam simulations for circular colliders are very time-consuming. Thus far, such simulations have predominantly utilized a linear transfer matrix to represent the full nonlinear lattice. Otherwise, when nonlinear lattices were included, beam–beam interactions were usually studied by using weak–strong or quasi-strong–strong numerical models. The next-generation circular colliders, including FCC-ee at CERN, CEPC in China, and the Super Tau-Charm Factories in China and Russia, will leverage the crab waist collision scheme with a large Piwinski angle. This scheme has already been employed in the two currently operational colliders, DAFNE and SuperKEKB. Accurate predictions of the performance of such colliders call for strong–strong beam–beam simulations, taking into account the interplay of the beam–beam interaction with lattice nonlinearities, impedances, and other collective effects. To answer this call, a novel code APES-T that allows integrating the direct strong–strong beam–beam simulations with element-by-element nonlinear tracking has been developed. To overcome the limitations in computing time, APES-T employs parallelization techniques. Specifically, the beam–beam module is parallelized using MPI programming, while the element-by-element tracking modules are parallelized using GPU programming. In this paper, we present the development of the APES-T code, its benchmark against the SAD code, and its application to the CEPC in investigating the interplay between beam–beam interaction, beamstrahlung, and lattices.

The Full Non-linear Vortex Tube-Vorton Method: the pre-stall condition

The present hybrid vortex tube-vorton method is based entirely on the Full Multi-wake Vortex Lattice Method (FMVLM) concepts, which means detaching vorticity with precise vortex strength and orientation along all separation lines between each discretized element of a shell-body, including all external edges. Since the classic Vortex Particle Method (VPM) is unstable by itself because it does not conserve the total amount of circulation as time evolves (Kelvin’s circulation theorem), an isolated Vortex (regularized) Filament Method (VFM) approach is implemented to obtain advection of vorticity, while the induced velocity field is obtained through its corresponding full vorton cloud. Further, a novel vortex squeezing/stretching scheme for such a vortex cylinder-sphere approach is proposed based on variation in time for vortex volumes in order to precisely (zero residual) conserve both circulation and vorticity at each time step (for each detached vortex element), while the viscous effect can be accounted for via the Core Spreading Method (CSM).

Lattice Path Matroids and Quotients

We characterize the quotients among lattice path matroids (LPMs) in terms of their diagrams. This characterization allows us to show that ordering LPMs by quotients yields a graded poset, whose rank polynomial has the Narayana numbers as coefficients. Furthermore, we study full lattice path flag matroids and show that—contrary to arbitrary positroid flag matroids—they correspond to points in the nonnegative flag variety. At the basis of this result lies an identification of certain intervals of the strong Bruhat order with lattice path flag matroids. A recent conjecture of Mcalmon, Oh, and Xiang states a characterization of quotients of positroids. We use our results to prove this conjecture in the case of LPMs.

Detectable gravitational waves from preheating probes nonthermal dark matter

We describe the challenges and pathways when probing inflaton as dark matter with the stochastic gravitational waves (GWs) signal generated during the (p)reheating. Such scenarios are of utmost interest when no other interaction between the visible and dark sectors is present, therefore having no other detectability prospects. We consider the remnant energy in the coherently oscillating inflaton’s zeroth mode to contribute to the observed relic dark matter density in the Universe. To fully capture the nonlinear dynamics and the effects of backreactions during the oscillation, we resort to full nonlinear lattice simulation with pseudospectral methods to eliminate the differencing noises. We investigate for models whose behavior during the reheating era is of mΦ2Φ2 type and find the typical primordial stochastic GWs backgrounds spectrum from scatterings among highly populated inflaton modes behaving like matter. We comment on the challenges of constructing viable inflationary models such that the inflaton will account for the total dark matter of the Universe while the produced GWs are within the future GWs detectors e.g., BBO, DECIGO, PTA, AION-MAGIS, and CE. We also describe the necessary modifications to the standard perturbative reheating scenario to prevent the depletion of residual inflaton energy via perturbative decay. Published by the American Physical Society 2024

Bottom-hadron production in high-energy pp and heavy-ion collisions

The hadro-chemistry of bottom quarks produced in hadronic collisions encodes valuable information on the mechanism of color-neutralization in these reactions. We first compute the chemistry of bottom-hadrons in high-energy pp collisions employing statistical hadronization with a largely augmented set of states beyond the currently measured spectrum. This enables a comprehensive prediction of fragmentation fractions of weakly decaying bottom hadrons for the first time and a satisfactory explanation of the existing measurements in pp collisions at the LHC. Utilizing the bottom hadro-chemistry thus obtained as the baseline, we then perform transport simulations of bottom quarks in the hot QCD matter created in PbPb collisions at the LHC energy and calculate the pertinent bottom-hadron observables. The transverse momentum (pT) dependent modifications of the bottom baryon-to-meson ratio (Λb0/B-) relative to their pp counterparts are highlighted as a result of bottom quark diffusion and hadronization in the Quark-Gluon Plasma (QGP). We finally summarize the heavy quark (charm vs bottom) diffusion coefficients as extracted from transport simulations and compare them to result from recent full lattice QCD computations.

The Full Multi-wake Vortex Lattice Method: a detached flow model based on Potential Flow Theory

One of the main issues concerning the standard Vortex Lattice Method is its application to partially or fully detached flow conditions, where non-linear aerodynamic characteristics appear as the angle of attack increases and/or the aspect ratio decreases. In order to solve such limitations, a pure numerical approach based entirely on the Vortex Lattice Method concepts has been developed. The so-called steady “Full Multi-wake Vortex Lattice Method” comes from the main hypothesis that each discretized element on the body’s surface detaches their own wakes downstream. The obtained results match for lift, drag and moment coefficients for the entire aspect ratio range configurations (under straight wakes and inviscid assumptions). Future unsteady versions of such a multi-wake approach could improve the current results obtained through Vortex Element Methods (as vortons or isolated vortex filaments).

On the effective dynamic mass of mechanical lattices with microstructure

We present a general formalism for the analysis of mechanical lattices with microstructure using the concept of effective dynamic mass. We first revisit a classical case of microstructure being modeled by a spring-interconnected mass-in-mass cell. The frequency-dependent effective dynamic mass of the cell is the sum of a static mass and of an added mass, in analogy to that of a swimmer in a fluid. The effective dynamic mass is derived using three different methods: momentum equivalence, dynamic condensation, and action equivalence. These methods are generalized to mechanical systems with arbitrary microstructure. As an application, we calculate the effective dynamic mass of a 1D composite lattice with microstructure modeled by a chiral spring-interconnected mass-in-mass cell. A reduced (condensed) model of the full lattice is then obtained by lumping the microstructure into a single effective dynamic mass. A dynamic Bloch analysis is then performed using both the full and reduced lattice models, which give the same spectral results. In particular, the frequency bands follow from the full lattice model by solving a linear eigenvalue problem, or from the reduced lattice model by solving a smaller nonlinear eigenvalue problem. The range of frequencies of negative effective dynamic mass falls within the bandgaps of the lattice. Localized modes due to defects in the microstructure have frequencies within the bandgaps, inside the negative-mass range. Defects of the outer, or macro stiffness yield localized modes within each bandgap, but outside the negative-mass range. The proposed formalism can be applied to study the odd properties of coupled micro-macro systems, e.g., active matter.

Ab Initio Spin Hamiltonian and Topological Noncentrosymmetric Magnetism in Twisted Bilayer CrI3.

Twist engineering of van der Waals magnets has emerged as an outstanding platform for manipulating exotic magnetic states. However, the complicated form of spin interactions in the large moiré superlattice obstructs a concrete understanding of such spin systems. To tackle this problem, for the first time, we developed a generic ab initio spin Hamiltonian for twisted bilayer magnets. Our atomistic model reveals that strong AB sublattice symmetry breaking due to the twist introduces a promising route to realize the novel noncentrosymmetric magnetism. Several unprecedented features and phases are uncovered including the peculiar domain structure and skyrmion phase induced by noncentrosymmetricity. The diagram of those distinctive magnetic phases has been constructed, and the detailed nature of their transitions analyzed. Further, we established the topological band theory of moiré magnons relevant to each of these phases. By respecting the full lattice structure, our theory provides the characteristic features that can be detected in experiments.

Role of structural disorder in the vibrational spectra of sol–gel [formula omitted] and [formula omitted]-Al[formula omitted]O[formula omitted] nanoparticles

Alumina nanopowders belonging to the γ and δ transition phases have been characterized by infrared and Raman spectroscopies. A quantitative interpretation of their vibrational spectra has been provided and related to their crystal structure, with particular emphasis on structural disorder and features not predicted by group-theoretical considerations. Both phases show very similar infrared dielectric functions, but with clear instances of mode-splitting in the δ phase, which are related to ordering in the tetrahedral Al positions. Raman spectroscopy was unable to resolve any modes in the sample identified as γ phase, but the full lattice vibrational region could be measured for the δ sample under UV and red excitation lines. Raman spectra are more complex than those obtained by infrared spectroscopy and cannot be completely explained by factor group analysis, in the absence of dedicated theoretical studies. Finally, the luminescent properties of these materials have been qualitatively explored and linked to disorder and substitutional impurities. In general, the results contained in this work prove that vibrational spectroscopies are powerful tools for quantitative analyses of these disordered nanomaterials and suggest the need for more theoretical work to understand their vibrational properties.

Semi-flexible Trimers on the Square Lattice in the Full Lattice Limit

Trimers are chains formed by two lattice edges, and therefore three monomers. We consider trimers placed on the square lattice, the edges belonging to the same trimer are either colinear, forming a straight rod with unitary statistical weight, or perpendicular, a statistical weight $$\omega$$ being associated to these angular trimers. The thermodynamic properties of this model are studied in the full lattice limit, where all lattice sites are occupied by monomers belonging to trimers. In particular, we use transfer matrix techniques to estimate the entropy of the system as a function of $$\omega$$ . The entropy $$s(\omega )$$ is a maximum at $$\omega =1$$ and our results are compared to earlier studies in the literature for straight trimers ( $$\omega =0$$ ) and angular trimers ( $$\omega \rightarrow \infty$$ ) and for mixtures of equiprobable straight and angular trimers ( $$\omega =1$$ ).

First Theoretical Realization of a Stable Two-Dimensional Boron Fullerene Network

Successful experimental realizations of two-dimensional (2D) C60 fullerene networks have been among the most exciting latest advances in the rapidly growing field of 2D materials. In this short communication, on the basis of the experimentally synthesized full boron B40 fullerene lattice, and by structural minimizations of extensive atomic configurations via density functional theory calculations, we could, for the first time, predict a stable B40 fullerene 2D network, which shows an isotropic structure. Acquired results confirm that the herein predicted B40 fullerene network is energetically and dynamically stable and also exhibits an appealing thermal stability. The elastic modulus and tensile strength are estimated to be 125 and 7.8 N/m, respectively, revealing strong bonding interactions in the predicted nanoporous nanosheet. Electronic structure calculations reveal metallic character and the possibility of a narrow and direct band gap opening by applying the uniaxial loading. This study introduces the first boron fullerene 2D nanoporous network with an isotropic lattice, remarkable stability, and a bright prospect for the experimental realization.

Lusztig Factorization Dynamics of the Full Kostant–Toda Lattices

We study extensions of the classical Toda lattices at several different space-time scales. These extensions are from the classical tridiagonal phase spaces to the phase space of full Hessenberg matrices, referred to as the Full Kostant-Toda Lattice. Our formulation makes it natural to make further Lie-theoretic generalizations to dual spaces of Borel Lie algebras. Our study brings into play factorizations of Loewner-Whitney type in terms of canonical coordinatizations due to Lusztig. Using these coordinates we formulate precise conditions for the well-posedness of the dynamics at the different space-time scales. Along the way we derive a novel, minimal box-ball system for Full Toda that doesn't involve any capacities or colorings, as well as an extension of O'Connell's ODEs to Full Toda.

Design, Simulation, and Mechanical Testing of 3D-Printed Titanium Lattice Structures

Lattice structure topology is a rapidly growing area of research facilitated by developments in additive manufacturing. These low-density structures are particularly promising for their medical applications. However, predicting their performance becomes a challenging factor in their use. In this article, four lattice topologies are explored for their suitability as implants for the replacement of segmental bone defects. The study introduces a unit-cell concept for designing and manufacturing four lattice structures, BCC, FCC, AUX, and ORG, using direct melt laser sintering (DMLS). The elastic modulus was assessed using an axial compression strength test and validated using linear static FEA simulation. The outcomes of the simulation revealed the disparity between the unit cell and the entire lattice in the cases of BCC, FCC, and AUX, while the unit-cell concept of the full lattice structure was successful in ORG. Measurements of energy absorption obtained from the compression testing revealed that the ORG lattice had the highest absorbed energy (350 J) compared with the others. The observed failure modes indicated a sudden collapsing pattern during the compression test in the cases of BCC and FCC designs, while our inspired ORG and AUX lattices outperformed the others in terms of their structural integrity under identical loading conditions.

Fabrication of a lattice structure with periodic open pores through three-dimensional printing for bone ingrowth

Lattice structures for implants can be printed using metal three-dimensional (3D)-printing and used as a porous microstructures to enhance bone ingrowth as orthopedic implants. However, designs and 3D-printed products can vary. Thus, we aimed to investigate whether targeted pores can be consistently obtained despite printing errors. The cube-shaped specimen was printed with one side 15 mm long and a full lattice with a dode-thin structure of 1.15, 1.5, and 2.0 mm made using selective laser melting. Beam compensation was applied, increasing it until the vector was lost. For each specimen, the actual unit size and strut thickness were measured 50 times. Pore size was calculated from unit size and strut thickness, and porosity was determined from the specimen’s weight. The actual average pore sizes for 1.15, 1.5, and 2.0 mm outputs were 257.9, 406.2, and 633.6 μm, and volume porosity was 62, 70, and 80%, respectively. No strut breakage or gross deformation was observed in any 3D-printed specimens, and the pores were uniformly fabricated with < 10% standard deviation. The actual micrometer-scaled printed structures were significantly different to the design, but this error was not random. Although the accuracy was low, precision was high for pore cells, so reproducibility was confirmed.

Anatomically and Biomechanically Relevant Monolithic Total Disc Replacement Made of 3D-Printed Thermoplastic Polyurethane.

Various implant treatments, including total disc replacements, have been tried to treat lumbar intervertebral disc (IVD) degeneration, which is claimed to be the main contributor of lower back pain. The treatments, however, come with peripheral issues. This study proposes a novel approach that complies with the anatomical features of IVD, the so-called monolithic total disc replacement (MTDR). As the name suggests, the MTDR is a one-part device that consists of lattice and rigid structures to mimic the nucleus pulposus and annulus fibrosus, respectively. The MTDR can be made of two types of thermoplastic polyurethane (TPU 87A and TPU 95A) and fabricated using a 3D printing approach: fused filament fabrication. The MTDR design involves two configurations—the full lattice (FLC) and anatomy-based (ABC) configurations. The MTDR is evaluated in terms of its physical, mechanical, and cytotoxicity properties. The physical characterization includes the geometrical evaluations, wettability measurements, degradability tests, and swelling tests. The mechanical characterization comprises compressive tests of the materials, an analytical approach using the Voigt model of composite, and a finite element analysis. The cytotoxicity assays include the direct assay using hemocytometry and the indirect assay using a tetrazolium-based colorimetric (MTS) assay. The geometrical evaluation shows that the fabrication results are tolerable, and the two materials have good wettability and low degradation rates. The mechanical characterization shows that the ABC-MTDR has more similar mechanical properties to an IVD than the FLC-MTDR. The cytotoxicity assays prove that the materials are non-cytotoxic, allowing cells to grow on the surfaces of the materials.

Quarks and triality in a finite volume

In order to understand the puzzle of the free energy of an individual quark in QCD, we explicitly construct ensembles with quark numbers $N_V\neq 0\!\mod 3$, corresponding to non-zero triality in a finite subvolume $V$ on the lattice. We first illustrate the basic idea in an effective Polyakov-loop theory for the heavy-dense limit of QCD, and then extend the construction to full Lattice QCD, where the electric center flux through the surface of $V$ has to be fixed at all times to account for Gauss's law. This requires introducing discrete Fourier transforms over closed center-vortex sheets around the spatial volume $V$ between all subsequent time slices, and generalizes the construction of 't Hooft's electric fluxes in the purge gauge theory. We derive this same result from a dualization of the Wilson fermion action, and from the transfer matrix formulation with a local $\mathbb Z_3$-Gauss law to restrict the dynamics to sectors with the required center charge in $V$.

Refinements for Bragg coherent X-ray diffraction imaging: electron backscatter diffraction alignment and strain field computation.

Bragg coherent X-ray diffraction imaging (BCDI) allows the 3D measurement of lattice strain along the scattering vector for specific microcrystals. If at least three linearly independent reflections are measured, the 3D variation of the full lattice strain tensor within the microcrystal can be recovered. However, this requires knowledge of the crystal orientation, which is typically attained via estimates based on crystal geometry or synchrotron microbeam Laue diffraction measurements. Presented here is an alternative method to determine the crystal orientation for BCDI measurements using electron backscatter diffraction (EBSD) to align Fe-Ni and Co-Fe alloy microcrystals on three different substrates. The orientation matrix is calculated from EBSD Euler angles and compared with the orientation determined using microbeam Laue diffraction. The average angular mismatch between the orientation matrices is less than ∼6°, which is reasonable for the search for Bragg reflections. The use of an orientation matrix derived from EBSD is demonstrated to align and measure five reflections for a single Fe-Ni microcrystal via multi-reflection BCDI. Using this data set, a refined strain field computation based on the gradient of the complex exponential of the phase is developed. This approach is shown to increase accuracy, especially in the presence of dislocations. The results demonstrate the feasibility of using EBSD to pre-align BCDI samples and the application of more efficient approaches to determine the full lattice strain tensor with greater accuracy.

Diquark properties from full QCD lattice simulations

We study diquarks on the lattice in the background of a static quark, in a gauge-invariant formalism with quark masses down to almost physical mπ. We determine mass differences between diquark channels as well as diquark-quark mass differences. The lightest and next-to-lightest diquarks have “good” scalar, {overline{3}}_F , {overline{3}}_c , JP = 0+, and “bad” axial vector, 6F, {overline{3}}_c , JP = 1+, quantum numbers, and a bad-good mass difference for ud flavors, 198(4) MeV, in excellent agreement with phenomenological determinations. Quark-quark attraction is found only in the “good” diquark channel. We extract a corresponding diquark size of ∼ 0.6 fm and perform a first exploration of the “good” diquark shape, which is shown to be spherical. Our results provide quantitative support for modeling the low-lying baryon spectrum using good light diquark effective degrees of freedom.

Anharmonic effects and EXAFS of hcp crystals studied based on high-order expanded Debye-Waller factors including dispersion effects

The anharmonic effects and extended X-ray absorption fine structure (EXAFS) of hcp crystals have been studied based on the high-order expanded Debye-Waller factors. The theory is derived based on the many-body perturbation approach and cumulant expansion up to the fourth order with using the linear anharmonic oscillator model to account for the dispersion involving more contributions of phonons from the first Brillouin zone. The derived anharmonic effective potential includes the many-body effect by a simple measure avoiding the intensive full lattice dynamical calculations. The Morse potential is assumed to describe the single-pair atomic interaction. The derived analytical expressions for cumulants describe the anharmonic effects and are applied to the anharmonic EXAFS contributing to the accurate structural determination. The advantages and efficiencies of the present theory are illustrated by good agreement of numerical results for all considered quantities of Zn in hcp phase with experiment.