Inhomogeneous Crystals Research Articles

Global well-posedness of strong solutions to the two-dimensional inhomogeneous biaxial nematic liquid crystal flow with vacuum

This paper considers the inhomogeneous biaxial nematic liquid crystal flow in a smooth bounded domain Ω⊂R2, where the velocity u and the orthogonal unit vector fields (m,n) admit the Dirichlet and Neumann boundary condition, respectively. By applying piecewise estimate and continuity method, we get the global existence of strong solutions, provided that the basic energy is suitably small. Our result may be regarded as an extension and improvement of Gong-Lin (2022) and Li-Liu-Zhong (2017) to the Neumann boundary condition, where the initial vacuum is allowed. Some new techniques are developed in order to deal with integral estimates caused by the boundary condition, and more complicated model.

Electromagnetic transmission of two-dimensional inhomogeneous plasma photonic crystal

A 2D tunable plasma photonic crystal (PPC) was constructed and implemented experimentally over a frequency range of 1 GHz–12 GHz within the electromagnetic spectrum. The PPC was simulated using an inhomogeneous model of a plasma tube based on microwave diagnostics and numerical simulations. The simulation results were found to be in good agreement with the experimental results. The data indicates that for TM polarization, localized plasmons will be excited at various positions within the tube, which does not rely on an interface with the medium, resulting in a broad forbidden band due to plasma inhomogeneity. The bandwidth of this band is consistent with the plasma frequency range. Furthermore, a lattice resonance band is observed, which is related to the incident angle. The cutoff effect of inhomogeneous PPC for TE polarization can be predicted by averaging the plasma parameters. The structure or plasma parameters can be adjusted to tune all the bands mentioned above. These findings can be used as a reference for applications in communication and microwave devices, and could potentially be utilized as a diagnostic tool for plasma parameters.

The Hybridization of Fabry–Perot and Tamm Modes in a Spatially Inhomogeneous Magneto-Photonic Crystal

The Hybridization of Fabry–Perot and Tamm Modes in a Spatially Inhomogeneous Magneto-Photonic Crystal

Three-dimensional flat Landau levels in an inhomogeneous acoustic crystal

When electrons moving in two dimensions (2D) are subjected to a strong uniform magnetic field, they form flat bands called Landau levels (LLs). LLs can also arise from pseudomagnetic fields (PMFs) induced by lattice distortions. In three-dimensional (3D) systems, there has been no experimental demonstration of LLs as a type of flat band thus far. Here, we report the experimental realization of a flat 3D LL in an acoustic crystal. Starting from a lattice whose bandstructure exhibits a nodal ring, we design an inhomogeneous distortion corresponding to a specific pseudomagnetic vector potential (PVP). This distortion causes the nodal ring states to break up into LLs, including a zeroth LL that is flat along all three directions. These findings suggest the possibility of using nodal ring materials to generate 3D flat bands, allowing access to strong interactions and other attractive physical regimes in 3D.

A blow-up criterion for the strong solutions to the two-dimensional non-isothermal inhomogeneous liquid crystal flow with density-dependent viscosity

A blow-up criterion for the strong solutions to the two-dimensional non-isothermal inhomogeneous liquid crystal flow with density-dependent viscosity

Transmission functions of transmissive multilayer inhomogeneous holographic photopolymer liquid crystal diffraction structures

A new analytical model of diffraction of quasimonochromatic light beams on spatially inhomogeneous multilayer diffraction structures formed in photopolymer material with nematic liquid crystals having smooth optical inhomogeneity in the thickness of layers is presented. It is shown that when an applied electric field isapplied to diffraction layers containing a photopolymer composition with a high proportion of liquid crystalline component, a transformation of the selective response with a significant shift in angular selectivity occurs

Electric polarization in inhomogeneous crystals

We derive the charge density up to second order in spatial gradient in inhomogeneous crystals using the semiclassical coarse graining procedure based on the wave packet method. It can be recast as divergence of polarization, whose first-order contribution consists of three parts, a perturbative correction to the original Berry connection expression, a topological part that can be written as an integral of the Chern-Simons 3-form, and a previously-unknown, quadrupolelike contribution. The topological part can be related to the quantized fractional charge carried by a vortex in two-dimensional systems. We then generalize our results to the multiband case and show that the quadrupolelike contribution plays an important role, as it makes the total polarization gauge-independent. Finally, we verify our theory in several model systems.

Zak phases of chiral photonic crystals designed via transformation optics

We study a class of inhomogeneous chiral photonic crystals with topologically nontrivial bands and edge modes using the approach of non-coordinate transformation optics. By transforming the chiral photonic crystals into achiral binary photonic crystals, the closed-form solutions to the photonic bands of the chiral photonic crystals are obtained. We show that the topological edge modes of these chiral photonic crystals can be accurately predicted by the Zak phases developed from the topological band theory for achiral binary photonic crystals.

A remark on global strong solution of two‐dimensional inhomogeneous nematic liquid crystal flows in a bounded domain

AbstractWe study an initial boundary value problem of two‐dimensional (2D) inhomogeneous incompressible nematic liquid crystal flows with nonnegative density. It is proved that there exists a unique global strong solution provided that the initial orientation satisfies a geometric condition.

FMX - the Frontier Microfocusing Macromolecular Crystallography Beamline at the National Synchrotron Light Source II.

Two new macromolecular crystallography (MX) beamlines at the National Synchrotron Light Source II, FMX and AMX, opened for general user operation in February 2017 [Schneider et al. (2013). J. Phys. Conf. Ser. 425, 012003; Fuchs et al. (2014). J. Phys. Conf. Ser. 493, 012021; Fuchs et al. (2016). AIP Conf. Proc. SRI2015, 1741, 030006]. FMX, the micro-focusing Frontier MX beamline in sector 17-ID-2 at NSLS-II, covers a 5-30 keV photon energy range and delivers a flux of 4.0 × 1012 photons s-1 at 1 Å into a 1 µm × 1.5 µm to 10 µm × 10 µm (V × H) variable focus, expected to reach 5 × 1012 photons s-1 at final storage-ring current. This flux density surpasses most MX beamlines by nearly two orders of magnitude. The high brightness and microbeam capability of FMX are focused on solving difficult crystallographic challenges. The beamline's flexible design supports a wide range of structure determination methods - serial crystallography on micrometre-sized crystals, raster optimization of diffraction from inhomogeneous crystals, high-resolution data collection from large-unit-cell crystals, room-temperature data collection for crystals that are difficult to freeze and for studying conformational dynamics, and fully automated data collection for sample-screening and ligand-binding studies. FMX's high dose rate reduces data collection times for applications like serial crystallography to minutes rather than hours. With associated sample lifetimes as short as a few milliseconds, new rapid sample-delivery methods have been implemented, such as an ultra-high-speed high-precision piezo scanner goniometer [Gao et al. (2018). J. Synchrotron Rad. 25, 1362-1370], new microcrystal-optimized micromesh well sample holders [Guo et al. (2018). IUCrJ, 5, 238-246] and highly viscous media injectors [Weierstall et al. (2014). Nat. Commun. 5, 3309]. The new beamline pushes the frontier of synchrotron crystallography and enables users to determine structures from difficult-to-crystallize targets like membrane proteins, using previously intractable crystals of a few micrometres in size, and to obtain quality structures from irregular larger crystals.

Statistical mechanics of dislocation pileups in two dimensions.

Dislocation pileups directly impact the material properties of crystalline solids through the arrangement and collective motion of interacting dislocations. We study the statistical mechanics of these ordered defect structures embedded in two-dimensional crystals, where the dislocations themselves form one-dimensional lattices. In particular, pileups exemplify a new class of inhomogeneous crystals characterized by spatially varying lattice spacings. By analytically formulating key statistical quantities and comparing our theory to numerical experiments using an intriguing mapping of dislocation positions onto the eigenvalues of recently studied random matrix ensembles, we uncover two types of one-dimensional phase transitions in dislocation pileups: A thermal depinning transition out of long-range translational order from the pinned-defect phase, due to a periodic Peierls potential, to a floating-defect state, and finally the melting out of a quasi-long-range ordered floating-defect solid phase to a defect liquid. We also find the set of transition temperatures at which these transitions can be directly observed through the one-dimensional structure factor, where the delta function Bragg peaks, at the pinned-defect to floating-defect transition, broaden into algebraically diverging Bragg peaks, which then sequentially disappear as one approaches the two-dimensional melting transition of the host crystal. We calculate a set of temperature-dependent critical exponents for the structure factor and radial distribution function, and obtain their exact forms for both uniform and inhomogeneous pileups using random matrix theory.

Effect of sucrose ester S370 on interfacial layers and fat crystals network of whipped cream

The effect of sucrose ester S370 on the interfacial layers and fat crystals network of whipped cream has been studied in this work. The addition of S370 showed a little effect on the droplets size, interfacial protein concentration and viscosity of emulsion samples before whipping. However, the addition of S370, as a heterogeneous nucleating agent, could induce nucleation and lead to the formation of more small crystals in the bulk mixture and emulsions. These small crystals, which were not able to pierce the interface of fat droplets effectively, would retard fat coalescence during whipping process. The addition of S370 resulted in lower degree of fat coalescence, lower interfacial protein concentration, shorter optimum whipping time (top) and lower overrun of whipped cream. At lower S370 concentration (<0.05 wt%), large-size crystals and inhomogeneous fat crystals network led to lower firmness and less bubbles stability of whipped cream samples. At 0.05 wt% S370 concentration, homogeneous crystals network, resulted in whipped cream with high firmness and bubbles stability. However, lower interfacial protein concentration and small-size crystals were observed at higher concentration of S370 (>0.05 wt%). As a result, the aerated structure was not strong enough to stabilize whipped cream.

General liquid-crystal theory for anisotropically shaped molecules: Symmetry, orientational order parameters, and system free energy.

A general theory of liquid crystals is presented, starting from the group-theory symmetry analysis of the constituting molecules. A particular attention is paid to the type of elastic free-energies and their relationships with the molecular symmetries. The orientational order-parameter tensors are identified for each molecular symmetry, in a consideration of consistently keeping the leading, characteristic elastic free energies in a model. The order parameters are expressed in terms of symmetric traceless tensors, some of high orders, for all major molecular symmetries, including seven groups of axial symmetries and seven groups of polyhedral symmetries. For spatially inhomogeneous liquid crystals, the couplings of these tensors in the elastic energies are derived by expanding the interaction energies between these molecules. The aim is to provide a general view of the molecular symmetries of individual molecules, orientational order parameters characterizing the orientational distribution functions, and the elastic free energies, all under one single group-theory approach.

Global regularity to the 2D non-isothermal inhomogeneous nematic liquid crystal flows

ABSTRACT In this paper, we prove the global strong solutions for the Cauchy problem of two-dimensional (2D) incompressible non-isothermal nematic liquid crystal flows, if the initial orientation satisfies a geometric condition. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states. When d is a constant vector and , we also extend the corresponding result in Wang Y. [Global strong solution to the two dimensional nonhomogeneous incompressible heat conducting Navier–Stokes flows with vacuum. Discrete Contin Dyn Syst B. doi:10.3934/dcdsb.2020099.] to the whole space , where the global strong solution of 2D inhomogeneous incompressible heat conducting Navier–Stokes flows is established on bounded domain.

Umbilical defect dynamics in an inhomogeneous nematic liquid crystal layer.

Electrically driven nematic liquid crystals layers are ideal contexts for studying the interactions of local topological defects, umbilical defects. In homogeneous samples the number of defects is expected to decrease inversely proportional to time as a result of defect-pair interaction law, so-called coarsening process. Experimentally, we characterize the coarsening dynamics in samples containing glass beads as spacers and show that the inclusion of such imperfections changes the exponent of the coarsening law. Moreover, we demonstrate that beads that are slightly deformed alter the surrounding molecular distribution and attract vortices of both topological charges, thus, presenting a mainly quadrupolar behavior. Theoretically, based on a model of vortices diluted in a dipolar medium, a 2/3 exponent is inferred, which is consistent with the experimental observations.

Global well-posedness of non-isothermal inhomogeneous nematic liquid crystal flows

In this paper, we consider the initial-boundary value problem to the non-isothermal incompressible liquid crystal system with both variable density and temperature. Global well-posedness of strong solutions is established for initial data being small perturbation around the equilibrium state. As the tools in the proof, we establish the maximal regularities of the linear Stokes equations and parabolic equations with variable coefficients and a rigid lemma for harmonic maps on bounded domains. This paper also generalizes the result in [ 5 ] to the inhomogeneous case.

Revealing photonic Lorentz force as the microscopic origin of topological photonic states

Abstract Charged particles like electrons moving in a magnetic field encounter Lorentz force, which governs the formation of electronic topological edge states in quantum Hall effect systems. Here we show that photons transporting in magneto-optical materials and structures also encounter a physical effect called photonic Lorentz force via the indirect interaction with the magneto-optical medium assisted effective magnetic field. This effect can induce half-cycle spiral motion of light at the surface of a homogeneous metallic magneto-optical medium and inhomogeneous magneto-optical photonic crystals, and it governs the intriguing one-way transport properties of robustness and immunity against defects, disorders, and obstacles. Thus, photonic Lorentz force serves as the fundamental microscopic origin of macroscopic photonic topological states, much the same as classical Lorentz force does to electronic topological states.

Manganiakasakaite-(La) and Ferriakasakaite-(Ce), Two New Epidote Supergroup Minerals from Piedmont, Italy

Two new monoclinic (P21/m) epidote supergroup minerals manganiakasakaite-(La) and ferriakasakaite-(Ce) were found in the small Mn ore deposit of Monte Maniglia, Bellino, Varaita Valley, Cuneo Province, Piedmont, Italy. Manganiakasakaite-(La) occurs as subhedral grains embedded in pyroxmangite. Its empirical formula is A(1)(Ca0.62Mn2+0.38) A(2)(La0.52Nd0.08Pr0.07Ce0.07Y0.01Ca0.25) M(1)(Mn3+0.52Fe3+0.28Al0.18V3+0.01) M(2)Al1.00 M(3)(Mn2+0.60Mn3+0.27Mg0.13) T(1−3)(Si2.99Al0.01) O12 (OH), corresponding to the end-member formula CaLaMn3+AlMn2+(Si2O7)(SiO4)O(OH). Unit-cell parameters are a = 8.9057(10), b = 5.7294(6), c = 10.1134(11) Å, β = 113.713(5)°, V = 472.46(9) Å3, Z = 2. The crystal structure of manganiakasakaite-(La) was refined to a final R1 = 0.0262 for 2119 reflections with Fo &gt; 4σ(Fo) and 125 refined parameters. Ferriakasakaite-(Ce) occurs as small homogeneous domains within strongly inhomogeneous prismatic crystals, where other epidote supergroup minerals coexist [manganiandrosite-(Ce), “androsite-(Ce)”, and epidote]. Associated minerals are calcite and hematite. Its empirical formula is A(1)(Ca0.64Mn2+0.36) A(2)(Ce0.37La0.17Nd0.06Pr0.03Ca0.35□0.02) M(1)(Fe3+0.61Al0.39) M(2)Al1.00 M(3)(Mn2+0.64Mn3+0.33Fe3+0.02Mg0.01) T(1−3)Si3.01 O12 (OH), the end-member formula being CaCeFe3+AlMn2+(Si2O7)(SiO4)O(OH). Unit-cell parameters are a = 8.9033(3), b = 5.7066(2), c = 10.1363(3) Å, β = 114.222(2)°, V = 469.66(3) Å3, Z = 2. The crystal structure of ferriakasakaite-(Ce) was refined to a final R1 = 0.0196 for 1960 unique reflections with Fo &gt; 4σ(Fo) and 124 refined parameters.

Revealing the crystallization process and realizing uniform 1.8 eV MA-based wide-bandgap mixed-halide perovskites via solution engineering

Wide-bandgap perovskites are recently drawing tremendous attention in the community for high-efficiency all-perovskite tandem solar cells. However, the formamidinium (FA+) and methylammonium (MA+) based wide-bandgap mixed halide perovskites suffered from high density of traps and pin-holes, respectively. Fundamental understanding on the crystallization and film formation processes are keys to overcome those challenges but not yet clearly understood. In this study, an in-situ photoluminescence technique was used to investigate the perovskite crystallization during the thermal annealing process. It is found that the crystallization of a mixed halide perovskite with bromide (Br−) and iodine (I−) ions following the Ostward ripening crystal growth. Interestingly, it is found that the initial nucleation reaction is quickly completed in the first few seconds, however, leaving the small crystals with inhomogeneous composition. The different aggregation affinities of such inhomogeneous small crystals provoke the formation of pin-holes during the thermal annealing process. By engineering the precursor solution to control the nucleation rate, the chemical composition of the small crystals has become homogenous. Uniform pin-hole free high Br−composited wide-bandgap MA0.9Cs0.1Pb(I0.6Br0.4)3 perovskite films with bandgap energy of 1.8 eV have been realized. The corresponding photovoltaic devices have achieved an encouraging device efficiency of 15.1% with superb photostability.

Применение сканирующей емкостной силовой микроскопии для выявления примесных фаз в сегнетоэлектрике триглицинсульфат

The results of the study of inhomogeneous ferroelectric triglycine sulfate single crystal with a growth periodic impurity structure TGS - TGS + Cr are presented. The impurity distribution was investigated with scanning capacitance force microscopy (SCFM). The peculiarities of the capacitance variations imaging on a doubled and tripled resonant frequency of electrostatic force are considered. The piezoelectric response, surface potential and surface topography were studied. It is shown that capacitive contrast is formed both at the domain boundaries and in the TGS and TGS + Cr bands. It was shown that SCFM allowed one to observe the impurity spatial distribution in the ferroelectric structure at the difference in the chromium concentration about 0.02-0.08 wt%.