Simple Lattice Research Articles

Phonon Hall Viscosity of Ionic Crystals.

When time-reversal symmetry is broken, the low-energy description of acoustic lattice dynamics allows for a dissipationless component of the viscosity tensor, the phonon Hall viscosity, which captures how phonon chirality grows with the wave vector. In this work, we show that, in ionic crystals, a phonon Hall viscosity contribution is produced by the Lorentz forces on moving ions. We calculate typical values of the Lorentz force contribution to the Hall viscosity using a simple square lattice toy model, and we compare it with literature estimates of the strengths of other Hall-viscosity mechanisms.

Bounds in simple hexagonal lattice and classification of 11-stick knots

The stick number and the edge length of a knot type in the simple hexagonal lattice (sh-lattice) are the minimal numbers of sticks and edges required, respectively, to construct a knot of the given type in sh-lattice. By introducing a linear transformation between lattices, we prove that for any given knot both values in the sh-lattice are strictly less than the values in the cubic lattice. Finally, we show that the only non-trivial [Formula: see text]-stick knots in the sh-lattice are the trefoil knot ([Formula: see text]) and the figure-eight knot ([Formula: see text]).

Some examples of quasiperiodic tilings obtained with a simple grid method

A grid method using tiling by fundamental domain of simple bi-dimensional lattices is presented. It refers to a previous work done by Stampfli in 1986 using two grids by regular hexagons, one rotated by relatively to the other. This leads to a quasiperiodic structure with a twelvefold symmetry made of regular triangles, squares and rhombuses. The tessellation of the plane by the overlap domains of two hexagons, each belonging to one of the two grids is considered. Vertices of the quasiperiodic tiling are the mid-point of the centers of the two overlapping hexagons. Edges of the quasiperiodic tiling are obtained by a Delaunay triangulation of the set of reference points. This method is extended to two other types of quasiperiodic tilings with other fundamental domains. A first example uses two square grids leading to the octagonal Ammann-Beenker quasiperiodic tiling. The second example is also based on the hexagonal lattice, but with grids defined by the lattice fundamental rhombic cell.

Experimental investigation and thermodynamic calculation of the Co–Zn–Zr ternary system

The phase equilibria of the Co–Zn–Zr ternary system were systematically studied by combining experimental analysis and thermodynamic modelling. The 450 °C isothermal section at the Zn-rich corner and the 600 °C isothermal section of Co–Zn–Zr system were studied by means of scanning electron microscopy, energy dispersive X-ray spectroscopy and X-ray diffraction. Seventeen and ten three-phase regions were obtained at 600 and 450 °C isothermal sections, respectively. Three stable ternary compounds named τ1 (ZrCo2Zn20), τ2 (Zr5Co3Zn12) and τ3 (Zr10Co3Zn7) were found in the 600 °C isothermal section. Among them, the Bravais lattice symmetry of the τ2 phase is a simple tetragonal lattice, and its lattice parameters are a = 8.945 Å, b = 8.945 Å, c = 11.737 Å and α = β = γ = 90°. Based on the comprehensive evaluation of the current experimental results and the data reported in the literature, the thermodynamic description of the system was developed using the CALPHAD technique. A set of self-consistent thermodynamic parameters for the Co–Zn–Zr ternary system was obtained with good agreement between the experimental and calculated results.

Phase-field-based lattice Boltzmann model for simulating thermocapillary flows.

This paper proposes a simple and accurate lattice Boltzmann model for simulating thermocapillary flows, which can deal with the contrast between thermodynamic parameters. In this model, two lattice Boltzmann equationsare utilized to solve the conservative Allen-Cahn equationand the incompressible Navier-Stokes equations, while another lattice Boltzmann equationis used for solving the temperature field, where the collision term is delicately designed such that the influence of the contrast between thermodynamic parameters is incorporated. In contrast to the previous lattice Boltzmann models for thermocapillary flows, the most distinct feature of the current model is that the forcing term used in the present thermal lattice Boltzmann equationis not needed to calculate space derivatives of the heat capacitance or the order parameter, making the scheme much more straightforward and able to retain the main merits of the lattice Boltzmann method. The developed model is first validated by considering the thermocapillary flows in a heated microchannel with two superimposed planar fluids. It is then used to simulate the thermocapillary migration of a two-dimensional deformable droplet, and its accuracy is consistent with the theoretical prediction when the Marangoni number approaches zero. Finally, we numerically study the motion of two recalcitrant bubbles in a two-dimensional channel where the relationship between surface tension and temperature is assumed to be a parabolic function. It is observed that due to the competition between the inertia and thermal effects, the bubbles can move against the liquid's bulk motion and towards areas with low surface tension.

On angular and surface interactions in two-dimensional elastic lattices

This paper deals with two-dimensional elastic lattices which asymptotically converge towards isotropic linear elastic continua. The square lattice composed of central and angular interactions, pioneered by Gazis et al. (1960) for 3D cubic lattices, allows the modelling of isotropic linear elastic continua (in the continuous asymptotic limit) with equivalent Poisson's ratios smaller than 1/3 in a plane stress assumption. This paper presents an alternative or complementary elastic model based on surface elastic interactions, which can be viewed as a complementary lattice model for values of Poisson's ratios greater than 1/3 in plane stress. The physical background of this non-central potential is discussed, basing on the existence of a dual surface pressure. The model can be also introduced from variational arguments. This surface model of Fuchs type is shown to be equivalent to a perimetric elastic model in the linear range. Additionally, this paper explores the possibility of coupling both surface and angular lattice elasticity for square lattices, with the potential to cover a large variety of elastic continua in the asymptotic limit. Gradient elasticity and lattice-based nonlocal elastic continua are constructed, starting from this simple square lattice composed of angular, surface and central interactions. The static behaviour of these square lattices (with central, angular and surface interaction) is investigated in pure compression and pure shear loading, with exact analytical solutions for the discrete displacement field.

Evidence for ground state coherence in a two-dimensional Kondo lattice

Kondo lattices are ideal testbeds for the exploration of heavy-fermion quantum phases of matter. While our understanding of Kondo lattices has traditionally relied on complex bulk f-electron systems, transition metal dichalcogenide heterobilayers have recently emerged as simple, accessible and tunable 2D Kondo lattice platforms where, however, their ground state remains to be established. Here we present evidence of a coherent ground state in the 1T/1H-TaSe2 heterobilayer by means of scanning tunneling microscopy/spectroscopy at 340 mK. Our measurements reveal the existence of two symmetric electronic resonances around the Fermi energy, a hallmark of coherence in the spin lattice. Spectroscopic imaging locates both resonances at the central Ta atom of the charge density wave of the 1T phase, where the localized magnetic moment is held. Furthermore, the evolution of the electronic structure with the magnetic field reveals a non-linear increase of the energy separation between the electronic resonances. Aided by ab initio and auxiliary-fermion mean-field calculations, we demonstrate that this behavior is inconsistent with a fully screened Kondo lattice, and suggests a ground state with magnetic order mediated by conduction electrons. The manifestation of magnetic coherence in TMD-based 2D Kondo lattices enables the exploration of magnetic quantum criticality, Kondo breakdown transitions and unconventional superconductivity in the strict two-dimensional limit.

Simple lattice model explains equilibrium separation phenomena in glassy polymers.

The Robeson bound is a theoretical limit that applies to kinetics-driven membrane separations of gas mixtures. However, this bound does not apply to sorption-driven membrane processes such as CO2/N2 separation, which lacks a theoretical explanation. As a result, we are uncertain about the factors that control the limiting behavior of sorption-driven separations. To address this issue, we employed a simple lattice model and dynamic mean field theory to examine the transport properties of disordered model structures, isolating sorption effects from purely kinetic effects. Our findings indicate that transport effects play a crucial role in sorption-driven processes, and perm-selectivity is consistently lower than sorption selectivity, which is an unattainable limit. We used basic geometric fragments of the structure to explain how transport effects emerge and manifest themselves in sorption-driven processes.

Genetic variability, heritability, and genetic advance for quantitative traits of sorghum [Sorghum Bicolor (L.) Moench] genotypes at Fedis, Eastern Ethiopia

Sorghum is the second most important food crop after teff in Ethiopia. The objective of the study was to estimate the genetic variations, heritability, and expected genetic advances in the selected sorghum genotypes. Sixty-four sorghum genotypes were evaluated for 17 quantitative traits in 8x8 simple lattice designs at the Boko research site. The analysis of variance revealed highly significant differences among genotypes for all traits. The Phenotypic Coefficient Of Variation (PCV) ranged from 4.74% for days to flowering to 24.74% for panicle width, while Genotypic Coefficients Of Variation (GCV) ranged from 3.58% for leaf length to 20.33 % for panicle width. The highest PCV and GCV values were recorded for panicle width, head weight, and harvest index. Moderate PCV and GCV were recorded for grain filling period, grain filling rate, plant height, panicle length, and grain yield; indicating the effectiveness of selection based on the phenotypic performance of the genotypes. Broad sense heritability (H2) ranged from 24.74 % for biomass yield to 96.6% for head weight, whereas GAM ranged from 4.8% for biomass yield to 41.95% for panicle width. High H2 coupled with high GAM was observed for grain filling rate, panicle length, panicle width, head weight, grain yield, and harvest index; indicating that these characters are controlled by additive gene action and phenotypic selection for these characters will be effective. However, the information generated in the current study it can be useful for breeders who want to improve yield and yield contributing traits of sorghum.

Boundary ferromagnetism in zigzag edged graphene

The flat band of edge states that occur in the simple tight-binding lattice model of graphene with a zigzag edge have long been conjectured to take up a ferromagnetic configuration. In this work, we prove that, for a large class of interaction Hamiltonians that can be added to the tight-binding model, and at the first order in perturbation theory, the degeneracy of edge states is resolved in such a way that the ground state is in the maximal, spin j = N/2 representation of the spin symmetry, where N is the number of edge states.

Formulation Development and Evaluation of Apremilast Nanoemulsion

Apremilast is a selective phosphodiesterase 4 inhibitor administered orally in the treatment of moderate-to-severe plaque psoriasis and active psoriatic arthritis. It is classified as class IV drug as per BCS classification so it indicates low solubility and lower permeability through the skin. Therefore the objective of the research is to improve permeability of Apremilast through the skin and improve solubility by using oil and surfactant by formulating Nanoemulsion. Nanoemulsion was prepared by selecting Captex 355, Cremophore RH 40, Labrafil and Propylene glycol as the oil, surfactant,co-surfactant and co-solvent respectively after solubility study. Pseudo-ternary phase diagrams were constructed to find out the optimum ratio of oil: Smix (surfactant: co-Surfactant). Simple lattice design was applied to the optimization of the prepared nanoemulsion. The nanoemulsion was evaluated for Physical parameter, pH, Droplet size, zeta potential, in-vitro diffusion study etc. Results of Droplet size measurements, zeta potential and % drug diffusion indicated A5 batch optimized batch than other formulation of the nanoemulsion. So, optimized formulation further tested for Skin irritation study and stability study.The Apremilast loaded stable Nanoemulsion system was prepared and various process variables were evaluated. Batch A5 was selected as an optimized batch containing 10 % Captex 355, 40 % Smix (Cremophore RH 40 and Labrafil) and 50% water. Optimized batch was found to be stable after three month at ambient condition of temperature and humidity, giving reproducible results when evaluated.

Effect of three cycles of recurrent selection for yield in four Spanish landraces of maize

Landraces of maize (Zea mays L.) have a variability not found in the elite hybrids due to the bottleneck during selection. There is a renewed interest in using that variability, incorporating alleles for specific traits, or widening the general variability of elite germplasm. In Europe, there is also an interest in the direct use of local landraces by farmer’s associations seeking agriculture that preserves crop diversity. Pre-breeding programs are aimed to reduce the yield gap among landraces and improved materials. In the Misión Biológica de Galicia we have carried out three cycles of a S1 recurrent selection program for yield on four local landraces from Northwestern Spain with the objective of obtaining improved populations that might be cultivated by farmers and that could be used as sources of superior inbred lines. One hundred plants were selfed in each landrace and the S1 families were evaluated in a 10 × 10 simple lattice. The 20 S1 families with the highest grain yields were randomly intercrossed to form the selected population of each landrace. After three cycles of selection, each population and its cycles of selection were evaluated in three locations for two years. All the populations had a consistent yield gain in the first cycle of selection. However, the response in later cycles differed among the populations: one population had a continuous increase of 21% per cycle while two populations had a reduced yield in the last cycles. Our results highlight the need to include secondary traits to avoid unintentional indirect effects. We conclude that, in pre-breeding programs, it could be worthy to use large effective numbers to prevent inbreeding depression, particularly when the objective is the direct use of improved landraces. Another conclusion is that recurrent selection does not seem to be as efficient on European germplasm as it is on Corn Belt varieties. Finally, obtaining valuable new germplasm requires a sustained, long-term effort.

Motion of localized disturbances in scalar harmonic lattices.

We present analytical and numerical investigations of energy propagation in systems of massive particles that interact via harmonic (linear) forces. The particle motion is described by a scalar displacement, and the particles are arranged in a simple crystal lattice. For the systems under consideration we prove the conservation of the total energy flux analytically. Then, using a sample case of a square lattice, we confirm the analytical results numerically. We create disturbances of a special kind which can move with a predefined velocity with a minor change in their shape. We show that a clot of energy, associated with each disturbance, moves similarly to a free body of matter in classical mechanics. We also numerically study a simultaneous propagation of a number of energy clots as an analogy to the motion of point masses in the conventional mechanics of particles. The obtained results demonstrate that an energy flow in lattices can be described in terms of numerous separated energy bodies, making a step towards a linkage between lattice dynamics and the kinetic theory of heat transfer in solids.

Exciton dissociation mediated by phonons in organic photovoltaics

It is well known that phonons can overscreen the bare Coulomb electron-electron repulsion, turning it into the effective attraction that binds the Cooper pairs responsible for BCS superconductivity. Here, we use a simple lattice model to prove that the counterpart of this is also possible, whereby phonons overscreen the bare electron-hole attraction and may turn it repulsive at short distances, driving exciton dissociation in certain regions of the parameter space. We argue that this phonon-mediated short-range screening may play an important role in the physics of organic solar cell materials (and other materials with strong electron-phonon coupling) and could point the way to new strategies for optimizing their efficiencies.

Machine learning surrogate modeling toward the design of lattice-structured heat sinks fabricated by additive manufacturing

Metal additive manufacturing (AM) enables the fabrication of lattice-structured heat sinks with enhanced heat transfer properties. The lattice structural features for enhancing heat transfer and suppressing pressure loss need to be clarified. To describe the structural features dominating heat transfer and pressure loss, eleven structural parameters consisting of three groups, namely the area, hydraulic diameter, and effective flow path, are proposed and used as inputs for the neural network (NN) surrogate model. The surrogate model precisely and quickly predicts the heat transfer property and pressure loss simulated by computational fluid dynamics. The random forest feature importance is used to select necessary and sufficient structural features. Four parameters describing the bottleneck in the flow pathway, surface area, and intricate structures are selected. Even when only the selected four parameters are used, the NN model maintains a high prediction performance, suggesting that the four parameters are sufficient for describing the heat transfer and pressure loss. Four parameters are used to discuss the design concept for lattice-structured heat sinks. An appropriately intricate lattice structure exhibits improved heat transfer and reduced pressure loss compared to a simple lattice structure. This study provides new insights into the design of lattice-structured heat sinks fabricated by AM.

Analysis and design of bistable and thermally reversible metamaterials inspired by shape-memory alloys

In this work, we study lattice structures that exhibit a bistable behavior, i. e., they can snap from one stable state to another, and are also completely reversible, capable of reverting back to its original state through a heat treatment. We design this behavior by constructing lattice structures using networks of nonlinear springs that display tension–compression asymmetry and have different thermal expansion coefficients. The mismatch in the thermal expansion coefficients induces residual stresses in the springs which results in the lattice structure exhibiting bistability at low temperatures and monostability at high temperatures. This behavior mimics the crystallographic phase transformations of shape memory alloys, but here artificially introduced in a structural lattice. By analyzing a representative unit cell, we quantify the effect that the stiffness and the thermal expansion coefficient of the springs have on the stability of the structural lattice. In addition, for simple 2D lattices, using the concept of universal unfoldings of singularity theory, we perform a perturbation analysis to identify the key variables of the structure where controlling defects is important, as they lead to drastic changes in the bifurcation behavior of the lattice. Finally, we verify numerically our analytical predictions in both 2D and 3D simulations using continuation techniques. The examples proposed confirm that the bistable and reversible features of the unit cell carry on to the macroscale, opening the route for the design of lattice structures for energy absorption applications that can heal with a heat treatment.

Note on the Chromatic Number of Minkowski Planes: The Regular Polygon Case

The famous Hadwiger–Nelson problem asks for the minimum number of colors needed to color the points of the Euclidean plane so that no two points unit distance apart are assigned the same color. In this note we consider a variant of the problem in Minkowski metric planes, where the unit circle is a regular polygon of even and at most 22 vertices. We present a simple lattice–sublattice coloring scheme that uses 6 colors, proving that the chromatic number of the Minkowski planes above are at most 6. This result is new for regular polygons having more than 8 vertices.

Observation of topological corner states in a D4-symmetric square lattice of split-ring resonators

Topological states offer an increased versatility in disorder-robust localization of electromagnetic waves at the edges and corners of photonic structures. In most of the cases, such properties are achieved due to the appropriate lattice symmetry. Here, by contrast, we explore an alternative design strategy where the topological states in a simple square lattice are tailored due to the orientation of non-centrosymmetric split-ring resonators comprising the meta-structure. We numerically predict the emergence of the nontrivial topological properties and confirm our prediction by fabricating the structure and observing the localized edge and corner states experimentally.

Topological Floquet engineering using two frequencies in two dimensions

Using two-frequency driving in two dimensions opens up new possibilites for Floquet engineering, which range from controlling specific symmetries to tuning the properties of resonant gaps. In this work, we study two-band lattice models subject to two-tone Floquet driving and analyse the resulting effective Floquet bandstructures both numerically and analytically. On the one hand, we extend the methodology of Sandholzer et al. [10.1103/PhysRevResearch.4.013056] from one to two dimensions and find competing topological phases in a simple Bravais lattice when the two resonant drives at $1\omega$ and $2\omega$ interfere. On the other hand, we explore driving-induced symmetry breaking in the hexagonal lattice, in which the breaking of either inversion or time-reversal symmetry can be tuned independently via the Floquet modulation. Possible applications of our work include a simpler generation of topological bands for ultracold atoms, and the realisation of non-linear Hall effects as well as Haldane's parity anomaly in inversion-symmetric parent lattices.

Transverse Hypercrystals Formed by Periodically Modulated Phonon Polaritons

Photonic crystals and metamaterials are two overarching paradigms for manipulating light. By combining these approaches, hypercrystals can be created, which are hyperbolic dispersion metamaterials that undergo periodic modulation and mix photonic-crystal-like aspects with hyperbolic dispersion physics. Despite several attempts, there has been limited experimental realization of hypercrystals due to technical and design constraints. In this work, hypercrystals with nanoscale lattice constants ranging from 25 to 160 nm were created. The Bloch modes of these crystals were then measured directly using scattering near-field microscopy. The dispersion of the Bloch modes was extracted from the frequency dependence of the Bloch modes, revealing a clear switch from positive to negative group velocity. Furthermore, spectral features specific to hypercrystals were observed in the form of sharp density of states peaks, which are a result of intermodal coupling and should not appear in ordinary polaritonic crystals with an equivalent geometry. These findings are in agreement with theoretical predictions that even simple lattices can exhibit a rich hypercrystal bandstructure. This work is of both fundamental and practical interest, providing insight into nanoscale light-matter interactions and the potential to manipulate the optical density of states.