Three-dimensional Order Research Articles

An immersed finite element method for elliptic interface problems in three dimensions

This article presents an immersed finite element (IFE) method for solving the typical three-dimensional second order elliptic interface problem with an interface-independent Cartesian mesh. The local IFE space on each interface element consists of piecewise trilinear polynomials constructed by extending polynomials from one subelement to the whole element according to the jump conditions of the interface problem. In this space, the IFE shape functions with the Lagrange degrees of freedom can always be constructed regardless of interface location and discontinuous coefficients. The proposed IFE space is proven to have the optimal approximation capabilities to the functions satisfying the jump conditions. A group of numerical examples with representative interface geometries are presented to demonstrate features of the proposed IFE method.

Chaos and control of a three-dimensional fractional order discrete-time system with no equilibrium and its synchronization

Chaotic systems with no equilibrium are a very important topic in nonlinear dynamics. In this paper, a new fractional order discrete-time system with no equilibrium is proposed, and the complex dynamical behaviors of such a system are discussed numerically by means of a bifurcation diagram, the largest Lyapunov exponents, a phase portrait, and a 0–1 test. In addition, a one-dimensional controller is proposed. The asymptotic convergence of the proposed controller is established by means of the stability theory of linear fractional order discrete-time systems. Next, a synchronization control scheme for two different fractional order discrete-time systems with hidden attractors is reported, where the master system is a two-dimensional system that has been reported in the literature. Numerical results are presented to confirm the results.

On three-dimensional variable order time fractional chaotic system with nonsingular kernel

Abstract We use the Adams-Bashforth-Moulton scheme (ABMS) to determine the approximate solution of a variable order fractional three-dimensional chaotic process. The derivative is defined in the fractional sense of variable order Atangana-Baleanu-Caputo (ABC). Numerical examples show that to solve these variable-order fractional differential equations easily and efficiently, the Adams-Bashforth-Moulton method can be implemented. Lastly, simulation results demonstrate the proposed robust control’s effectiveness.

Nanoarchitecture through Strained Molecules: Cubane-Derived Scaffolds and the Smallest Carbon Nanothreads.

Relative to the rich library of small-molecule organics, few examples of ordered extended (i.e., nonmolecular) hydrocarbon networks are known. In particular, sp3 bonded, diamond-like materials represent appealing targets because of their desirable mechanical, thermal, and optical properties. While many covalent organic frameworks (COFs)-extended, covalently bonded, and porous structures-have been realized through molecular architecture with exceptional control, the design and synthesis of dense, covalent extended solids has been a longstanding challenge. Here we report the preparation of a sp3-bonded, low-dimensional hydrocarbon synthesized via high-pressure, solid-state diradical polymerization of cubane (C8H8), which is a saturated, but immensely strained, cage-like molecule. Experimental measurements show that the obtained product is crystalline with three-dimensional order that appears to largely preserve the basic structural topology of the cubane molecular precursor and exhibits high hardness (comparable to fused quartz) and thermal stability up to 300 °C. Among the plausible theoretical candidate structures, one-dimensional carbon scaffolds comprising six- and four-membered rings that pack within a pseudosquare lattice provide the best agreement with experimental data. These diamond-like molecular rods with extraordinarily small thickness are among the smallest members in the carbon nanothread family, and calculations indicate one of the stiffest one-dimensional systems known. These results present opportunities for the synthesis of purely sp3-bonded extended solids formed through the strain release of saturated molecules, as opposed to only unsaturated precursors.

Frustration between two- and three-dimensional smectic ordering leads to a biaxial nematic phase.

The bola-amphiphilic, T-shaped mesogen CT2 has an aromatic, biphenyl core terminated on both ends by hydrophilic groups and a semi-perfluorinated, aliphatic side chain. Upon cooling from the isotropic phase, the fluorinated tails and the polar, rod-like cores nanophase-segregate to form a fluid lamellar phase. At high temperatures, the biphenyl cores are orientationally disordered in two dimensions (2D) in the lamellar planes but on further cooling the cores order orientationally, giving a biaxial lamellar phase with 2D nematic in-plane ordering. At lower temperature, the aromatic and hydrophilic parts of the cores nanosegregate within the lamellae and 2D smectic correlations of the head groups develop. X-ray diffraction shows that this 2D smectic ordering is incompatible with the initial lamellar structure, with both structures becoming short-ranged, resulting in a 3D biaxial nematic phase with macroscopic orthorhombic symmetry featuring strong smectic correlations in two orthogonal spatial dimensions. Freeze-fracture transmission electron microscopy enables direct visualization of the resulting short-ranged periodic structures.

Active damping of geometrically nonlinear vibrations of smart composite shells using elliptical smart constrained layer damping treatment with fractional derivative viscoelastic layer

In this article, the performance of elliptical smart constrained layer damping treatments on active damping of geometrically nonlinear vibrations of doubly curved smart laminated composite shells is analyzed. The constraining layers of the smart constrained layer damping treatments comprised vertically/obliquely reinforced 1–3 piezoelectric composites, while the constrained layers of isotropic viscoelastic materials are modeled using the three-dimensional fractional order derivative model. A mesh-free model of the smart composite shells is developed for analyzing their nonlinear transient responses within the framework of a layerwise shear and normal deformation theory considering the von Kármán–type geometric nonlinearity. Thin, doubly curved laminated composite shells integrated with elliptical/rectangular smart constrained layer damping patches with different stacking sequences and boundary conditions are considered for presenting the numerical results. The numerical analyses demonstrate the higher effectiveness of the elliptical smart constrained layer damping treatments over the rectangular ones in attenuating the nonlinear vibrations of laminated composite shells.

Revealing the assembly of filamentous proteins with scanning transmission electron microscopy.

Filamentous proteins are responsible for the superior mechanical strength of our cells and tissues. The remarkable mechanical properties of protein filaments are tied to their complex molecular packing structure. However, since these filaments have widths of several to tens of nanometers, it has remained challenging to quantitatively probe their molecular mass density and three-dimensional packing order. Scanning transmission electron microscopy (STEM) is a powerful tool to perform simultaneous mass and morphology measurements on filamentous proteins at high resolution, but its applicability has been greatly limited by the lack of automated image processing methods. Here, we demonstrate a semi-automated tracking algorithm that is capable of analyzing the molecular packing density of intra- and extracellular protein filaments over a broad mass range from STEM images. We prove the wide applicability of the technique by analyzing the mass densities of two cytoskeletal proteins (actin and microtubules) and of the main protein in the extracellular matrix, collagen. The high-throughput and spatial resolution of our approach allow us to quantify the internal packing of these filaments and their polymorphism by correlating mass and morphology information. Moreover, we are able to identify periodic mass variations in collagen fibrils that reveal details of their axially ordered longitudinal self-assembly. STEM-based mass mapping coupled with our tracking algorithm is therefore a powerful technique in the characterization of a wide range of biological and synthetic filaments.

Three-Dimensional Higher Order PML Based on Alternating Direction Implicit Algorithm

Based on the alternating direction implicit finite-difference time-domain (ADI-FDTD) algorithm, a higher order perfectly matched layer (HO-PML) is proposed to solve the problems in a three-dimensional computational domain. The proposed scheme can not only take advantage of the HO-PML for improving the absorbing performance but also has the advantage of the ADI-FDTD algorithm in terms of the unconditional stability. A dielectric resonator antenna example is carried out to validate its effectiveness. The results show that the Courant–Friedrich–Levy limit can be eliminated and the absorbing performance can be further enhanced.

Kinetic modelling of waste wood devolatilization during pyrolysis based on thermogravimetric data and solar pyrolysis reactor performance

Within presented paper complex kinetic analysis of waste wood solar pyrolysis with fuel characterisation has been presented. Thermogravimetric (TGA) data were obtained for heating rates denoted in solar pyrolysis experiments: 5, 10, 15 and 20 K/min. Study presents alternative approach to lignocellulosic biomass kinetics using NETZSCH Kinetics Neo (v. 2.1.2.2) software. TGA data were enriched with the gas analyser indications and experiments results from solar pyrolysis examined on self-designed laboratory reactor. Presented methodology consisted of (1) isoconversional analysis: Friedman, Kissinger-Akahira-Sunose and Ozawa-Flynn-Wall analysis yielding apparent activation energies Eα, varying from 185.37 to 375.56 kJ/mol at reaction extent 0.1–0.9, (2) reaction model identification with generalised master plot method which showed that decomposition was driven by three-dimensional diffusion (D3) with transition to three-dimensional phase boundary (R3) and reaction order based models (F1,F2,Fn) at the end of conversion. Finally, (3) kinetic model construction was performed based on experiments observations, resulting in modelling of 3 main reactions of pyrolysis products formations. The most intensive condensable release was observed between 250 and 440 °C what correlated with CO2 release described by dominant two-step D3-F2 consecutive reaction with activation energies and logarithmic pre-exponential factors 159.92 kJ/mol, 10.44 log(1/s) and 256.78 kJ/mol, 19.05 log(1/s) for first and second step respectively. CO formation obeyed R3 reaction mechanism with activation energy 181 kJ/mol and pre-exponential factor 12.16 log(1/s). Last stage of pyrolysis, charring, was described by two-step consecutive reaction Fn(n = 3.463)-F2 resulting in formation of CH4 and H2 with activation energies and pre-exponential factors of 249.72 kJ/mol, 15.87 log(1/s) and 162 kJ/mol, 6.61 log(1/s) respectively. Kinetic models and isoconversional methods results were tested using Fisher-Snedecor test. Presented methodology was compared with traditional three pseudo-component wood pyrolysis model and discussed.

Global Mittag-Leffler boundedness and synchronization for fractional-order chaotic systems

This paper deals with the issues of the global Mittag-Leffler boundedness and synchronization for three-dimensional fractional order chaotic systems (FOCSs). First, by constructing proper generalized Lyapunov function and using the extremum principle of function, some new 3D ellipsoid estimations and a cylindrical domain estimation of the bounds are derived for the addressed fractional system without existence assumptions, which improve the earlier publications and can deduce some new estimations. Besides, linear feedback control strategies with a single state and one input or two inputs are proposed to achieve synchronization. Some new sufficient synchronization criteria are derived by inequality techniques. Comparison of our results with that of the existing ones shows that the computation of the bounds and the control gain constants is easier and simpler and the controllers here have more simple structures. Simulation results are given to show the validity of the proposed scheme.

CrystaLattE: Automated computation of lattice energies of organic crystals exploiting the many-body expansion to achieve dual-level parallelism.

We present an algorithm to compute the lattice energies of molecular crystals based on the many-body cluster expansion. The required computations on dimers, trimers, etc., within the crystal are independent of each other, leading to a naturally parallel approach. The algorithm exploits the long-range three-dimensional periodic order of crystals to automatically detect and avoid redundant or unnecessary computations. For this purpose, Coulomb-matrix descriptors from machine learning applications are found to be efficient in determining whether two N-mers are identical. The algorithm is implemented as an open-source Python program, CrystaLattE, that uses some of the features of the Quantum Chemistry Common Driver and Databases library. CrystaLattE is initially interfaced with the quantum chemistry package Psi4. With CrystaLattE, we have applied the fast, dispersion-corrected Hartree-Fock method HF-3c to the lattice energy of crystalline benzene. Including all 73 symmetry-unique dimers and 7130 symmetry-unique trimers that can be formed from molecules within a 15 Å cutoff from a central reference monomer, HF-3c plus an Axilrod-Teller-Muto estimate of three-body dispersion exhibits an error of only -1.0 kJ mol-1 vs the estimated 0 K experimental lattice energy of -55.3 ± 2.2 kJ mol-1. The convergence of the HF-3c two- and three-body contributions to the lattice energy as a function of intermonomer distance is examined.

Synthesis-Controlled Polymorphism and Magnetic and Electrochemical Properties of Li3Co2SbO6.

Li3Co2SbO6 is found to adopt two highly distinct structural forms: a pseudohexagonal (monoclinic C2/m) layered O3-LiCoO2 type phase with "honeycomb" 2:1 ordering of Co and Sb, and an orthorhombic Fddd phase, isostructural with Li3Co2TaO6 but with the addition of significant Li/Co ordering. Pure samples of both phases can be obtained by conventional solid-state synthesis via a precursor route using Li3SbO4 and CoO, by controlling particle size, initial lithium excess, and reaction time. Both phases show relatively poor performance as lithium-ion battery cathode materials in their as-made states, but complex and interesting low-temperature magnetic properties. The honeycomb phase is the first of its type to show A-type antiferromagnetic order (ferromagnetic planes, antiferromagnetically coupled) below TN = 14 K. Isothermal magnetization and in-field neutron diffraction below TN show clear evidence for a metamagnetic transition at H ≈ 0.7 T to three-dimensional ferromagnetic order. The orthorhombic phase orders antiferromagnetically below TN = 112 K and then undergoes two more transitions at 80 and 60 K. Neutron diffraction data show that the ground state is incommensurate.

Phosphine-free synthesis of FeTe2 nanoparticles and self-assembly into tree-like nanoarchitectures**Project supported by the National Natural Science Foundation of China (Grant No. 11874027) and the China Postdoctoral Science Foundation (Grant Nos. 2019T120233 and 2017M621198).

Manipulating the self-assembly of transition metal telluride nanocrystals (NCs) creates opportunities for exploring new properties and device applications. Iron ditelluride (FeTe2) has recently emerged as a new class of magnetic semiconductor with three-dimensional (3D) magnetic ordering and narrow band gap structure, yet the self-assembly of FeTe2 NCs has not been achieved. Herein, the tree-like FeTe2 nanoarchitectures with orthorhombic crystal structure have been successfully synthesized by hot-injection solvent thermal approach using phosphine-free Te precursor. The morphology, size, and crystal structure have been investigated using transmission electron microscopy (TEM), high-resolution TEM (HRTEM), and powder x-ray diffraction (XRD). We study the formation process of tree-like FeTe2 NCs according to trace the change of the sample morphology with the reaction time. It was found that the FeTe2 nanoparticles show oriented aggregation and self-assembly behavior with the increase of reaction time, which is attributed to size-dependent magnetism properties of the samples. The magnetic interaction is thought to be the driving force of nanoparticle self-organization.

Coexisting spin resonance and long-range magnetic order of Eu in EuRbFe4As4

Magnetic excitations and magnetic structure of EuRbFe$_4$As$_4$ were investigated by inelastic neutron scattering (INS), neutron diffraction, and random phase approximation (RPA) calculations. Below the superconducting transition temperature $T_\text{c}=36.5$~K, the INS spectra exhibit the neutron spin resonances at $Q_\text{res}=1.27(2)$~$\text{\AA}^{-1}$ and $1.79(3)$~$\text{\AA}^{-1}$. They correspond to the $\mathbf{Q}=(0.5,0.5,1)$ and $(0.5,0.5,3)$ nesting wave vectors, showing three dimensional nature of the band structure. The characteristic energy of the neutron spin resonance is $E_\text{res}=17.7(3)$~meV corresponding to $5.7(1)k_\text{B}T_\text{c}$. Observation of the neutron spin resonance mode and our RPA calculations in conjunction with the recent optical conductivity measurements are indicative of the $s_\pm$ superconducting pairing symmetry in EuRbFe$_4$As$_4$. In addition to the neutron spin resonance mode, upon decreasing temperature below the magnetic transition temperature $T_\text{N}=15$~K, the spin wave excitation originating in the long-range magnetic order of the Eu sublattice was observed in the low-energy inelastic channel. Single-crystal neutron diffraction measurements demonstrate that the magnetic propagation vector of the Eu sublattice is $\mathbf{k}=(0, 0, 0.25)$, representing the three-dimensional antiferromagnetic order. Linear spin wave calculations assuming the obtained magnetic structure with the intra- and inter-plane nearest neighbor exchange couplings of $J_1/k_\text{B}=-1.31$~K and $J_c/k_\text{B}=0.08$~K can reproduce quantitatively the observed spin wave excitation. Our results show that superconductivity and long-range magnetic order of Eu coexist in EuRbFe$_4$As$_4$ whereas the coupling between them is rather weak.

Making It Clear: Exploring Crystal Structures by Constructing and Comparing See-Through Models

Acquiring a basic understanding about the composition of crystal structures and the resulting structure–property relationship is central for chemists and material chemists, enabling the prediction of desired properties and the solution of a wide range of current challenges in sciences, e.g., the development of clean-energy storage. For a deeper understanding of physical and chemical properties of crystals, it is necessary to focus on different global and local structural features that characterize the composition of several atoms or ions as well as the direct environment of single atoms or ions. To improve students’ mental visualization of both global and local features of the three-dimensional order of crystal structures, we developed and implemented a modeling activity with new transparent models. During the activity, students construct and compare models of common crystal structures, like sodium chloride and zinc blend. The usage of clear plastic balls, in particular, allows students to focus on global features such as packing arrangement and lattice structure, as well as on local ones, like coordination number, site occupation, and polyhedral connectivity. The latter features have been difficult to realize so far. We used a design-based research approach to improve the activity and the instructional material, provided herein, through several rounds of evaluation in a course for undergraduate students in materials chemistry. A detailed qualitative analysis of students’ discourse during the activity revealed that students were engaged in various content-related interactions with the models and that it is beneficial to combine a student-centered construction of the models with a subsequent comparison phase.

Chirality-driven ferroelectricity in LiCuVO4

Chirality or the handedness of objects is of prime importance in life science, biology, chemistry, and physics. It is also a major symmetry ingredient in frustrated magnets revealing spin-spiral ground states. Vector-chiral phases, with the twist (either clock- or counter clock-wise) between neighboring spins being ordered, but with disorder with respect to the angles between adjacent spins, have been predicted almost five decades ago. Experimental proofs, however, are rare and controversial. Here, we provide experimental evidence for such a phase in LiCuVO4, a one-dimensional quantum magnet with competing ferromagnetic and antiferromagnetic interactions. The vector-chiral state is identified via a finite ferroelectric polarization arising at temperatures well above the multiferroic phase exhibiting long-range three-dimensional spin-spiral and polar order. On increasing temperatures, spin order becomes suppressed at TN, whereas chiral long-range order still exist, leaving a temperature window with chirality-driven ferroelectricity in the presence of an external magnetic field.

Gait analysis in patients after bilateral versus unilateral total hip arthroplasty

BackgroundGait abnormalities were reported in patients after total hip arthroplasty (THA). One-stage bilateral THA was introduced for bilateral hip pathologies, showing similar clinical and surgical outcome to unilateral procedure. However, no studies analyze the gait features after bilateral THA surgery compared to unilateral THA. Research questionAre there differences in gait characteristics between bilateral and unilateral THA patients and are there differences between these cases and asymptomatic age-matched healthy subjects? MethodsIn this prospective observational study, thirty-five patients with bilateral (n = 18) or unilateral THA (n = 17) and twenty asymptomatic age-matched volunteers were studied. Participants underwent three-dimensional gait analysisin order to detect gait spatial-temporal and kinematic (Gait Variable Score - GVS) parameters. Mobility (Timed Up and Go - TUG), fear of movement (Tampa Scale of Kinesiophobia - TSK) and pain during walking (Numeric Rating Scale - NRS) were also assessed. Patients were evaluated the day before surgery and at seven days, whereas healthy subjects underwent a single evaluation. ANOVA was used to assess differences between the three groups at each time-point and within-group differences in bilateral and unilateral groups. ResultsAt baseline, no differences between the two groups of patients were found. As expected, their gait spatial-temporal and kinematic parameters and functional variables were impaired with respect to healthy subjects, both before and after surgery. After surgery, GVS Pelvic-TILT closer to normative values, longer stance and shorter swing phases were found in bilateral cases compared to unilateral patients. Moreover, a higher NRS score was found in bilateral patients, whereas TUG and TSK revealed no differences between the two groups of patients. SignificanceThe current findings, focusing on short-term effectiveness of bilateral THA, could assist physiotherapists in selecting the best ambulation training and an appropriate rehabilitation approach immediately after surgery.

The smectic phase in semiflexible polymer materials: A large scale molecular dynamics study

Semiflexible polymers in concentrated lyotropic solution are studied within a bead-spring model by molecular dynamics simulations, focusing on the emergence of a smectic A phase and its properties. We systematically vary the density of the monomeric units for several contour lengths that are taken smaller than the chain persistence length. The difficulties concerning the equilibration of such systems and the choice of appropriate ensemble (constant volume versus constant pressure, where all three linear dimensions of the simulation box can fluctuate independently) are carefully discussed. Using HOOMD-blue on graphics processing units, systems containing more than a million monomeric units are accessible, making it possible to distinguish the order of the phase transitions that occur. While in this model the nematic-smectic transition is continuous, the transition from the smectic phase to a related crystalline structure with true three-dimensional long-range order is clearly of first order. Further, both orientational and positional correlations of monomeric units are studied as well as the order parameters characterizing the nematic, smectic A, and crystalline phases. The analogy between smectic order and one-dimensional harmonic crystals with respect to the behavior of the structure factor is also explored. Finally, the results are put in perspective with pertinent theoretical predictions and possible experiments.

Atomic structure and crystallography of joints in SnO2 nanowire networks

Joints of three-dimensional (3D) rutile-type (r) tin dioxide (SnO2) nanowire networks, produced by the flame transport synthesis (FTS), are formed by coherent twin boundaries at (101)r serving for the interpenetration of the nanowires. Transmission electron microscopy (TEM) methods, i.e. high resolution and (precession) electron diffraction (PED), were utilized to collect information of the atomic interface structure along the edge-on zone axes [010]r, [111]r and superposition directions [001]r, [101]r. A model of the twin boundary is generated by a supercell approach, serving as base for simulations of all given real and reciprocal space data as for the elaboration of three-dimensional, i.e. relrod and higher order Laue zones (HOLZ), contributions to the intensity distribution of PED patterns. Confirmed by the comparison of simulated and experimental findings, details of the structural distortion at the twin boundary can be demonstrated.

9,9′-Bifluorenylidene-diketopyrrolopyrrole donors for non-polymeric solution processed solar cells

We have synthesised new materials comprised of 9,9′-bifluorenylidene and dithienodiketopyrrolopyrrole units. While 9,9′-bifluorenylidene has been primarily used in non-fullerene acceptors, when used in combination with the diketopyrrolopyrrole moiety it can form donor materials that can be used in conjunction with fullerene acceptors. The compounds differ in the substituents on the 9,9′-bifluorenylidene (protonated = 1A and dimethoxy = 1B) moiety. The structure of both the neat and blend films with PC70BM were found to be strongly dependent on the processing solvent used. In particular, Grazing Incidence Wide Angle X-ray Scattering measurements of films of 1A or 1B blended with PC70BM prepared from chloroform or chloroform with o-dichlorobenzene as an additive showed that the donor material had no particular ordering. However, when 1,8-diiodooctane was added to the processing solvent the 1A blends showed liquid crystalline ordering while 1B formed well-defined crystallites with three-dimensional ordering. The difference in film structure had a profound effect on the device properties. For 1A the optimised blend ratio with PC70BM was 1:4, but when 1,8-diiodooctane was used as the additive the best ratio of 1A to fullerene was 1:1. The films containing the well-defined crystallites of 1B all performed poorly, which was ascribed to a lack of a percolation pathway for hole extraction. The best performing device was comprised of a 1:1 blend of 1A and PC70BM, which had a power conversion efficiency of 2.6%.