Rotated Lattice Research Articles

Elastic properties of rotated Ti6Al4V gyroid lattices

Benefitting from the similar microstructure morphology and macroscopic equivalent mechanical properties to the human bone, the Ti6Al4V gyroid lattice is widely applied in implant. Incompatibility of the elastic modulus between the bone and the implant results in the stress shielding. The anisotropy of lattice intensifies the uncontrollability the stress shielding. The anisotropy of lattice is reproduced experimentally and numerically in this work. A method for determining material parameters of representative volume unit is proposed, which successfully weakens the stress shielding in multiple directions. From the numerical results, the following findings are obtained. A method to increase the lattice elastic modulus without changing the volume fraction is proposed. The mechanical properties of the model with certain angle describing the rotated gyroid lattice is closer to isotropy. Several models with volume fractions of 20%–50% are more compatible with the elastic/shear modulus of human bone.

An Adaptive Mesh Refinement–Rotated Lattice Boltzmann Flux Solver for Numerical Simulation of Two and Three-Dimensional Compressible Flows with Complex Shock Structures

An adaptive mesh refinement–rotated lattice Boltzmann flux solver (AMR-RLBFS) is presented to simulate two and three-dimensional compressible flows with complex shock structures. In the method, the RLBFS, which has a strong shock-capturing capability and can effectively eliminate the shock instability phenomenon, is applied to solve the flow filed by reconstructing the fluxes at each cell interface adaptively with the mesoscopic lattice Boltzmann model. To locally and dynamically improve the resolution of intricate shock structures and optimize the required computational resources, a block-structured adaptive mesh refinement (AMR) technique is introduced. The validity and effectiveness of the proposed method are confirmed through a range of two and three-dimensional numerical cases, including the shock tube problem, the four-wave Riemann problem, explosion within a rectangular box, and the vorticity induced by a shock. The results obtained using the AMR-RLBFS exhibit excellent agreement with published data and demonstrate high accuracy in capturing complex shock structures. The computational efficiency of the AMR-RLBFS can be also improved significantly compared to the RLBFS on uniform grids. Furthermore, the numerical outcomes underscore the capability of the AMR-RLBFS to eliminate shock instability effects while efficiently capturing a broader spectrum of small-scale vertical structures. These findings highlight the ability of AMR-RLBFS to improve the computational efficiency and capture intricate shock structures effectively, making it a valuable tool for studying a wide range of compressible flows from aerodynamics to astrophysics.

Development of three-dimensional rotated lattice Boltzmann flux solver for the simulation of high-speed compressible flows

A three-dimensional (3D) Rotated Lattice Boltzmann Flux Solver (RLBFS) is proposed and analyzed with matrix-based linear stability theory for simulating compressible flows in a wide range of Mach numbers. The 3D RLBFS applies the finite volume method to discrete the Navier-Stokes equations and evaluates its fluxes at each cell interface. To improve numerical stability, the convective fluxes are obtained in a hybrid way by using the D1Q4 lattice Boltzmann model in two perpendicular directions decomposed by the outer normal vector of each cell interface. The viscous fluxes are computed in a conventional way using the second-order central scheme. The stability performance and order accuracy of the proposed 3D RLBFS are examined by using the matrix-based stability theory and L2 errors on different meshes respectively. It is shown that the 3D RLBFS is stable even at high Mach number and has the second-order accuracy in space. The reliability and capability of the proposed method is further evaluated by simulating several challenging compressible flow problems, including subsonic flow over the DLR-F4, transonic flow over the ONERA M6 wing, supersonic flow around NACA0012 wing, hypersonic flow over the Viking lander capsule, hypersonic flow over a hemisphere and hypersonic flow around a blunt nose double cone. The obtained numerical results are in good agreement with experimental and/or numerical data published in the literature, indicating that the present method provides a reliable and effective tool for simulating practical three-dimensional compressible flow problems in aeronautics and astronautics.

A rotated lattice Boltzmann flux solver with improved stability for the simulation of compressible flows with intense shock waves at high Mach number

A rotated lattice Boltzmann flux solver with improved stability for the simulation of compressible flows with intense shock waves at high Mach number

Understanding Tribocorrosion of Aluminum at the Crystal Level

Aluminum (Al) and its alloys are excellent corrosion-resistant materials due to their sustained passivity in neutral aqueous solutions. However, tribocorrosion remains a major threat to the integrity of Al, during which corrosion and wear work synergistically to accelerate material degradation. In this work, a combined experimental and computational investigation was carried out using Al single crystals to develop a crystal-based tribocorrosion modeling framework that accounts for the effects of lattice reorientation and dislocations on surface corrosion. Specifically, the mechanical, corrosion, and tribocorrosion properties of Al (100), (110), and (111) single crystals were measured experimentally, followed by characterization of lattice rotation and dislocation density via electron backscattered diffraction (EBSD). Unlike the mechanical and corrosion properties that are orientation-dependent, the tribocorrosion rate was found to be insensitive to the initial orientations of the crystals. Using the experimental results as inputs and validations, a multiphysics finite element model was developed that successfully predicted the depassivation and repassivation currents during tribocorrosion by mapping the local corrosion kinetics as a function of passivation state, crystallographic orientation, and dislocation density. It was found that lattice rotation, rather than dislocations, dominates the overall tribocorrosion behavior. Finally, the decrease of orientation-dependence during tribocorrosion was explained in terms of the coupling between the un-rotated lattice in the unworn region and the rotated lattice from the worn region.

Design of Beam-Steerable Aperiodic Linear Array Antenna With Improved Peak SLL Using Strip-Projection Method

This article discusses the design of the beam-steerable aperiodic linear array antenna with improved sidelobe level (SLL), using the strip-projection method. The strip projection method uses the area of rotated higher-dimensional lattice and projects it to lower dimensions to generate an aperiodic array. This article describes the modeling and analysis of such an array and its optimization for the desired far-field performance. The aperiodic arrays are also generated using various evolutionary optimization algorithms, namely genetic algorithm (GA), particle swarm optimization (PSO), and Jaya algorithms. The far-field performance of the generated aperiodic arrays is compared with the conventional periodic array. The proposed 21-element aperiodic array is also populated with a X-band electromagnetically coupled patch antenna and phase shifter designed using varying width of the high dielectric material. The aperiodic patch array antenna is also developed and characterized for various beam scan angles. A significant improvement of 5.72 dB in peak SLL is achieved at ±30° beam scan angle.

A Construction of Rotated Lattices via Totally Real Subfields of the Cyclotomic Field Q(z_p)

The theory of lattices have shown to be useful in information theory and rotated lattices with high modulations diversity have been extensively studied as an alternative approach for transmission over a Rayleigh-fading channel, where the performance of this modulation schemes essentially depends of the modulation diversity and of the minimum product distance to achieve substantial coding gains. The maximum diversity of a rotated lattice is guaranteed when we use totally real number fields and the minimum product distance is optimized by considering fields with minimum discriminant. In this paper, we present a construction of rotated lattice for the Rayleigh fading channel in Euclidean spaces with full diversity, where this construction is through a totally real subfield K of the cyclotomic field Q(z_p), where p is an odd prime, obtained by endowing their ring of integers.

Constructions of rotated lattice constellations in dimensions power of 3

In this paper, we present the constructions of rotated [Formula: see text]-lattices, where [Formula: see text] is a positive integer, via [Formula: see text]-modules of the ring of the integers [Formula: see text]. Our focus is on totally real number fields since the associated lattices have full diversity and then may be suitable for signal transmission over both Gaussian and Rayleigh fading channels. Lower bounds for the minimum product distances of such construction are also presented.

Adsorbing staircase polygons subject to a force

We study several models of staircase polygons on the rotated square lattice, which interact with an impenetrable surface while also being pushed towards or pulled away from the surface by a force. The surface interaction is governed by a fugacity a and the force by a fugacity y. Staircase polygons are simplifications of more general self-avoiding polygons, a well-studied model of interacting ring polymers. For this simplified case we are able to exactly determine the limiting free energy in the full a-y plane, and demonstrate that staircase polygons exhibit four different phases, including a ‘mixed’ adsorbed-ballistic phase.

Transport gap in vertical devices made of incommensurately misoriented graphene layers

By means of atomistic tight-binding calculations, we investigate the transport properties of vertical devices made of two incommensurately misoriented graphene layers. For a given transport direction (Ox-axis), we define two classes of rotated graphene lattice distinguished by difference in lattice symmetry and, hence, in Brillouin zone. In particular, these two classes correspond to two different cases where the position of their Dirac cones in the ky-axis is determined differently, i.e. or (Ly is the periodic length along the Oy axis). As a consequence, in devices made of two layers of different lattice classes, the misalignment of Dirac cones between the left and right graphene sections opens a finite energy-gap of conductance that can reach a few hundreds of meV. We also show that strain engineering can be used to further enlarge the transport gap and to diminish the sensitivity of the gap on the twist angle and on the commensurateness of the layer stack.

Entanglement of an alternating bipartition in spin chains: relation with classical integrable models

We study the entanglement properties of a class of ground states defined by matrix product states, which are generalizations of the valence bond solid (VBS) state in one dimension. It is shown that the transfer matrix of these states can be related to representations of the Temperley–Lieb algebra, allowing an exact computation of Renyi entropy. For an alternating bipartition, we find that the Renyi entropy can be mapped to an eight vertex model partition function on a rotated lattice. We also show that for the VBS state, the Renyi entropy of the alternating partition is described by a critical field theory with central charge c = 1. The generalization to SU(n) VBS and its connection with a dimerization transition in the entanglement Hamiltonian is discussed.

The critical surface fugacity of self-avoiding walks on a rotated honeycomb lattice

In a recent paper by Beaton et al, it was proved that a model of self-avoiding walks on the honeycomb lattice, interacting with an impenetrable surface, undergoes an adsorption phase transition when the surface fugacity is . Their proof used a generalization of an identity obtained by Duminil-Copin and Smirnov, and confirmed a conjecture of Batchelor and Yung. We consider a similar model of self-avoiding walk adsorption on the honeycomb lattice, but with the lattice rotated by π/2. For this model there also exists a conjecture for the critical surface fugacity, made in 1998 by Batchelor, Bennett-Wood and Owczarek. Using similar methods to Beaton et al, we prove that this is indeed the critical fugacity.

The critical surface fugacity for self-avoiding walks on a rotated honeycomb lattice

In a recent paper with Bousquet-Mélou, de Gier, Duminil-Copin and Guttmann (2012), we proved that a model of self-avoiding walks on the honeycomb lattice, interacting with an impenetrable surface, undergoes an adsorption phase transition when the surface fugacity is 1+√2. Our proof used a generalisation of an identity obtained by Duminil-Copin and Smirnov (2012), and confirmed a conjecture of Batchelor and Yung (1995). Here we consider a similar model of self-avoiding walk adsorption on the honeycomb lattice, but with the impenetrable surface placed at a right angle to the previous orientation. For this model there also exists a conjecture for the critical surface fugacity, made by Batchelor, Bennett-Wood and Owczarek (1998). We adapt the methods of the earlier paper to this setting in order to prove the critical surface fugacity, but have to deal with several subtle complications which arise. This article is an abbreviated version of a paper of the same title, currently being prepared for submission.

Surface code quantum computing by lattice surgery

In recent years, surface codes have become a leading method for quantum error correction in theoretical large-scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural two-dimensional nearest-neighbour (2DNN) structure make them an obvious choice for large scale designs in experimentally realistic systems. While fundamentally based on the toric code of Kitaev, there are many variants, two of which are the planar- and defect-based codes. Planar codes require fewer qubits to implement (for the same strength of error correction), but are restricted to encoding a single qubit of information. Interactions between encoded qubits are achieved via transversal operations, thus destroying the inherent 2DNN nature of the code. In this paper we introduce a new technique enabling the coupling of two planar codes without transversal operations, maintaining the 2DNN of the encoded computer. Our lattice surgery technique comprises splitting and merging planar code surfaces, and enables us to perform universal quantum computation (including magic state injection) while removing the need for braided logic in a strictly 2DNN design, and hence reduces the overall qubit resources for logic operations. Those resources are further reduced by the use of a rotated lattice for the planar encoding. We show how lattice surgery allows us to distribute encoded GHZ states in a more direct (and overhead friendly) manner, and how a demonstration of an encoded CNOT between two distance-3 logical states is possible with 53 physical qubits, half of that required in any other known construction in 2D.

Hard Squares for z = –1

The hard square model in statistical mechanics has been investigated for the case when the activity z is −1. For cyclic boundary conditions, the characteristic polynomial of the transfer matrix has an intriguingly simple structure, all the eigenvalues x being zero, roots of unity, or solutions of x 3 = 4cos2(πm/N). Here we tabulate the results for lattices of up to 12 columns with cyclic or free boundary conditions and the two obvious orientations. We remark that they are all unexpectedly simple and that for the rotated lattice with free or fixed boundary conditions there are obvious likely generalizations to any lattice size.

The Rotated Hexagonal Lattice Model for Pedestrian Flows

Various research efforts have been studied on the topic of pedestrian traffic flow. At the beginning of pedestrian research, the modeling and simulation method for the vehicular traffic flow was simply applied to pedestrian traffic flow. Recently, CA based simulation models are frequently applied to pedestrian flow analysis. Initially, the square lattice model (SLM) is a base model for applying to pedestrians of counterflow and then hexagonal lattice model (HLM) improves its network as a hexagonal cell for more realistic movement of the avoidance of pedestrian conflicts. In this paper, the authors suggest the rotated hexagonal lattice model (RHLM) to take the advantages of SLM and HLM for more realistic pedestrian motion. Two simulation models such as SLM and RHLM are compared by the speed, density, and flow. The comparison shows that RHLM can simulate pedestrian flow more realistically from various perspectives.

In-plane magnetoresistance and magnetization reversal of cobalt antidot arrays

Cobalt antidot arrays defined within a Hall bar mesa have been fabricated using electron-beam lithography. The diameter of the circular antidots was fixed at 1μm with the antidot edge-to-edge spacing varying from 2to0.5μm in a square lattice and 0.4μm in a rotated square lattice. In-plane magnetoresistance measurements were carried out to investigate the magnetization reversal properties. Antidots greatly modify the domain configuration and work as domain wall pinning sites. As a result, the switching and saturation fields increase while the magnetoresistance ratio decreases with the inclusion of antidots and also with increasing antidot areal density. Micromagnetic simulations show that the magnetization reversal of antidot arrays proceeds with the formation and annihilation of domain walls, which is manifested as Barkhausen jumps in the transition regions of the magnetoresistance curves.

Lamination microstructure in shear deformed copper single crystals

We investigate the formation of microscopic patterns in a copper single crystal deformed in a shear experiment. Using high-resolution electron backscatter diffraction imaging, we find a band-like microstructure consisting of confined areas in the sample with rotated lattice. Digital image correlation allows us to exactly determine the macroscopic state of deformation of the sample. This data can be used as a side condition to calculate the lamination parameters from the theory of kinematically compatible lamination of separate material regions, each deforming in single slip. The parameters given by the theory agree with the measured properties, i.e. a lattice rotation of 3° and a lamination normal rotated 7° counterclockwise from a 〈111〉 direction.

Sphere Lower Bound for Rotated Lattice Constellations in Fading Channels

We study the error probability performance of rotated lattice constellations in frequency-flat Nakagami-m block-fading channels. In particular, we use the sphere lower bound on the underlying infinite lattice as a performance benchmark. We show that the sphere lower bound has full diversity. We observe that optimally rotated lattices with largest known minimum product distance perform very close to the lower bound, while the ensemble of random rotations is shown to lack diversity and perform far from it.

Transport properties and structures of vortex matter in layered superconductors

In this paper we analyze the structure, phase transitions, and some transport properties of the vortex system when the external magnetic field lies parallel to the planes in layered superconductors. We show that experimental results for resistivity are qualitatively consistent with numerical simulations that describe the melting of a commensurate rotated lattice. However, for some magnetic fields, the structure factor indicates the occurrence of smectic peaks at an intermediate temperature regime.