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This paper investigates the tracking problem of fractional-order multi-agent systems. Both the order and parameters of the leader are unknown. Firstly, based on the positive system approach, the asymptotically stable criteria for incommensurate linear fractional-order systems are derived. Secondly, the models of incommensurate heterogeneous multi-agent systems are introduced. To cope with incommensurate and heterogeneous situations among followers and the leader, radial basis function neural networks (RBFNNs) and a discontinuous control method are used. Thirdly, the consensus criteria are derived by using the Vector Lyapunov Function method. Finally, a numerical example is presented to illustrate the effectiveness of the proposed theoretical method. [ABSTRACT FROM AUTHOR]

This paper describes how moiré plasmonic nanoparticle lattices can exhibit lasing action over a broad wavelength and wavevector range. Moiré nanolithography is combined with the PEEL (Photolithography, Etching, Electron‐beam deposition, and Lift‐off) process to fabricate in‐plane incommensurate lattices with optical properties beyond the restricted geometries of Bravais lattices. Because of increased rotational symmetry, moiré lattices support a larger number of transverse electric and transverse magnetic modes relative to their periodic base lattices. It is found that multidirectional lasing characteristics can be predicted by the symmetry of the moiré reciprocal lattice. Incommensurate moiré plasmonic lattices combine advantages of the dense band structures observed in aperiodic lattices with that of predicted modes in Bravais lattices for light‐based technologies in coherent light sources and multiplexed data transfer. [ABSTRACT FROM AUTHOR]

This paper investigates the tracking problem of fractional-order multi-agent systems. Both the order and parameters of the leader are unknown. Firstly, based on the positive system approach, the asymptotically stable criteria for incommensurate linear fractional-order systems are derived. Secondly, the models of incommensurate heterogeneous multi-agent systems are introduced. To cope with incommensurate and heterogeneous situations among followers and the leader, radial basis function neural networks (RBFNNs) and a discontinuous control method are used. Thirdly, the consensus criteria are derived by using the Vector Lyapunov Function method. Finally, a numerical example is presented to illustrate the effectiveness of the proposed theoretical method.

The high-ordered crystal structure of a thermoelectric material does not delimit the phonon conductivity but shows improved electrical properties. Disordered crystal structures act as scattering centers for phonon, but at the expense of the electrical properties of the material. Hence, a diminished thermal (phonon) conductivity and improved electronic conductivity can be obtained from an incommensurate (IC) phase structure. This paper reports that TlBiSe 2 polycrystal material exhibits incommensurate (IC) phase (disordered structure). The 'Tl+' connecting chains and the disordered structure inherent in the IC phase enhance the TE properties in TlBiSe 2. The crystalline phase was confirmed for TlBiSe 2 by X-ray diffraction (XRD). These polycrystals have shown their characteristic Raman modes and micro flake-like morphology, as observed by Raman spectroscopy and field emission scanning electron microscopy (FESEM). X-ray photoelectron spectroscopy confirmed the IC phase formation by observing the characteristic binding energy shift of 'Tl' and 'Se' states. The parallel plane symmetry break in the IC phase has resulted in a hall carrier concentration (n) of 3.49 × 1020 cm−3 and mobility (μ) of 8.27 m2V−1s−1. Further, Seebeck coefficient showed 80 μV/K; the Wiedemann Franz law calculation reserved a lower electronic thermal conductivity of 0.003381 Wm−1K−1 and a power factor of 2.956 μW/m K2 has been attained. [ABSTRACT FROM AUTHOR]

Incommensurate charge order in hole-doped oxides is intertwined with exotic phenomena such as colossal magnetoresistance, high-temperature superconductivity, and electronic nematicity. Here, we map, at atomic resolution, the nature of incommensurate charge-lattice order in a manganite using scanning transmission electron microscopy at room temperature and cryogenic temperature ([Formula: see text]93 K). In diffraction, the ordering wave vector changes upon cooling, a behavior typically associated with incommensurate order. However, using real space measurements, we discover that the ordered state forms lattice-locked regions over a few wavelengths interspersed with phase defects and changing periodicity. The cations undergo picometer-scale ([Formula: see text]6 pm to 11 pm) transverse displacements, suggesting that charge-lattice coupling is strong. We further unearth phase inhomogeneity in the periodic lattice displacements at room temperature, and emergent phase coherence at 93 K. Such local phase variations govern the long-range correlations of the charge-ordered state and locally change the periodicity of the modulations, resulting in wave vector shifts in reciprocal space. These atomically resolved observations underscore the importance of lattice coupling and phase inhomogeneity, and provide a microscopic explanation for putative "incommensurate" order in hole-doped oxides.

Incommensurate charge order in hole-doped oxides is intertwined with exotic phenomena such as colossal magnetoresistance, high-temperature superconductivity, and electronic nematicity. Here, we map, at atomic resolution, the nature of incommensurate charge-lattice order in a manganite using scanning transmission electron microscopy at room temperature and cryogenic temperature ([Formula: see text]93 K). In diffraction, the ordering wave vector changes upon cooling, a behavior typically associated with incommensurate order. However, using real space measurements, we discover that the ordered state forms lattice-locked regions over a few wavelengths interspersed with phase defects and changing periodicity. The cations undergo picometer-scale ([Formula: see text]6 pm to 11 pm) transverse displacements, suggesting that charge-lattice coupling is strong. We further unearth phase inhomogeneity in the periodic lattice displacements at room temperature, and emergent phase coherence at 93 K. Such local phase variations govern the long-range correlations of the charge-ordered state and locally change the periodicity of the modulations, resulting in wave vector shifts in reciprocal space. These atomically resolved observations underscore the importance of lattice coupling and phase inhomogeneity, and provide a microscopic explanation for putative "incommensurate" order in hole-doped oxides.

Herein, we present a topical review of the advances and the mechanisms involved in achieving superlubricity - the regime of friction in which the coefficient of friction (COF) is less than 0.01. In light of the race towards achieving superlubricity on an industrial scale, this review gives a brief overview of the friction dissipating mechanisms at an atomic scale and the atomistic models devised over the years to explain the phenomena of superlubricity. Furthermore, specific emphasis is given to the mechanisms discovered yet to achieve superlubricity on both micro and macro scales in accordance with their physical fundamentals. Additionally, a brief overview of certain obstacles in the course of the same to guide the emerging directions of research is also discussed in the later section. This review provides better guidance for understanding the basics and advancements over the years in the domain of superlubricity facilitating, its transition from laboratories to engineering scale applications.

Rare-earth element Gd doped CoSi, Co1-xGd x Si ( x = 0.01), is investigated using x-ray diffraction and magnetization. It crystallizes in B20 cubic structure with lattice parameter of a = 4.4429 Å. The alloy exhibits two antiferromagnetic transitions AFM-I at 38.44 K and AFM-II at 21.87 K followed by an upturn of magnetization belowTut= 9.79 K as illustrated through the temperature-magnetic field T-H phase diagram. AFM-I state is incommensurate. AFM-II state is weakly correlated as inferred from field-induced transition to AFM-I state. Further, AFM-I state is reported to transform to ferromagnetic state in high magnetic fields. The present study stimulates an approach to derive novel and exotic magnetic materials by substituting rare-earth in transition metal monosilicides., (© 2024 IOP Publishing Ltd.)

Superlubricity can cancel energy loss caused by friction and wear, and holds great promise for moving machine parts and carbon neutrality. However, the superlubricity under particularly on steel surface in an open atmosphere is an essential precondition for industrial use remaining a challenge. A novel strategy was proposed in this work the hybride system of a-C:H-ammonium tetrathiomolybdate in situ decomposed into MoS 2 layers and sulfur monomer (S 8) via flash heating induced by the friction force. The first principles calculations with van der Waals interaction considered confirming the increase in the interlayer spacing from the value of 0.65 nm for pristine bilayer to 1.07 nm for MoS 2 interfaces with S 8 sandwiched, in accordance well with detailed experimental results. A reduction in the interlayer binding energy and in the energy barriers for sliding the MoS 2 layers on basel planes by more than 65%. Further, a reduction in the interfacial sliding energy barrier for S 8 sandwiched between MoS 2 from that of MoS 2 layers with H 2 O sandwiched. Therefore, the superlubricity in the ambient condition is attributed to the incommensurate contact of S 8 /MoS 2 /a-C:H that the presence of S 8 that increases the interlayer spacing of MoS 2 with low E B. [Display omitted] • A hybrid system of (NH 4) 2 MoS 4 and a-C:H film on steel surface was constructed for realizing superlubricity. • In-situ decompose of (NH 4) 2 MoS 4 into S 8 sandwiched into MoS 2 lower the energy and achieve incommensurate contact. • Friction and shear force induced flash heating is the reason of decompose of (NH 4) 2 MoS 4 into S 8 sandwiched into MoS 2. [ABSTRACT FROM AUTHOR]

We report the experimental determination of the magnetic exchange parameter (J/kB= 2.88 ± 0.02 K) for the Spin-3/2 ferromagnetic (FM) Kagomé lattice system: Co 3 V 2 O 8 using the temperature dependence of dc-magnetic susceptibility χ ( T ) data by employing the fundamental Heisenberg linear chain model. Our results are quite consistent with the theoretically reported nearest neighbor dominant FM exchange coupling strengthJex-NN∼2.45 K. Five different magnetic phase transitions (6.2-11.2 K) and spin-flip transitions (9.6-7.7 kOe) have been probed using the∂(χT)/∂Tvs. T , heat capacity ( C P - T ) and differential isothermal magnetization curves. Among such sequence of transitions, the prominent ones being incommensurate antiferromagnetic (AFM) state at 11.2 K, commensurate AFM state at 8.8 K, and commensurate FM state across 6.2 K. All the successive magnetic phase transitions have been mapped onto a single H-T plane through which one can easily distinguish the above-mentioned different phases. The magnetic contribution of the C P - T near T N (11.2 K) has been analyzed using the power-law expressionCM=A|T-TN|-αresulting in the critical exponent α = 0.18 ± 0.01 (0.15 ± 0.003) for T < T N ( T > T N ), respectively for the Co 3 V 2 O 8 . It is interesting to note that non-Debye type dipole relaxation is quite prominent in Co 3 V 2 O 8 and was evident from the Kohlrausch-Williams-Watts analysis of complex modulus and impedance spectra (0⩽β⩽1). Mott's variable-range hopping of charge carriers process is evident through the resistivity analysis (ρac- T -1/4) in the temperature range 275  ∘ C-350  ∘ C. Moreover, the frequency-dependent analysis ofσac( ω ) follows Jonscher's power law yielding two distinct activation energies (Ea∼0.37 and 2.29 eV) between the temperature range 39  ∘ C-99  ∘ C and 240  ∘ C-321  ∘ C., (© 2024 IOP Publishing Ltd.)

Controversy in the description/identification of so‐called intermediate phase(s) in PbHfO3, stable in the range ∼420–480 K, has existed for a few decades. A synchrotron diffraction experiment on a partially detwinned crystal allowed the structure to be solved in the superspace group Imma(00γ)s00 (No. 74.2). In contrast to some previously published reports, in the pure compound only one distinct phase was observed between Pbam PbZrO3‐like antiferroelectric and Pm3m paraelectric phases. The modulation vector depends only slightly on temperature. The major structure modulation is associated with the displacement of lead ions, which is accompanied by a smaller amplitude modulation for the surrounding O atoms and tilting of HfO6 octahedra. Tilting of the octahedra results in a doubling of the unit cell compared with the parent structure. [ABSTRACT FROM AUTHOR]

Controversy in the description/identification of so‐called intermediate phase(s) in PbHfO3, stable in the range ∼420–480 K, has existed for a few decades. A synchrotron diffraction experiment on a partially detwinned crystal allowed the structure to be solved in the superspace group Imma(00γ)s00 (No. 74.2). In contrast to some previously published reports, in the pure compound only one distinct phase was observed between Pbam PbZrO3‐like antiferroelectric and Pm3m paraelectric phases. The modulation vector depends only slightly on temperature. The major structure modulation is associated with the displacement of lead ions, which is accompanied by a smaller amplitude modulation for the surrounding O atoms and tilting of HfO6 octahedra. Tilting of the octahedra results in a doubling of the unit cell compared with the parent structure. [ABSTRACT FROM AUTHOR]

Macromolecular crystal structure determination can be complicated or brought to a halt by crystal imperfections. These issues motivated us to write up what we affectionately call 'The Definitive Hitchhiker's Guide to Pathological Macromolecular Crystals: Lattice Disorders and Modulations'. Perhaps the most challenging imperfections are lattice order–disorder phenomena and positional modulations. Many of these types of crystals have been solved, and progress has been made on the more challenging forms. Diagnostic tools and how to solve many of these problem crystal structures are reviewed. New avenues are provided for approaching the solution of incommensurately modulated crystals. There are a good number of case studies in the literature of lattice order–disorder phenomena and crystallographic modulations that make it timely to write a review. This review concludes with a projected pathway for solving incommensurately modulated crystals, personal views of future directions and needs of the crystallographic community. [ABSTRACT FROM AUTHOR]

In this paper, a new method is proposed for the reduced-order model approximation of commensurate/incommensurate fractional order (FO) systems. For integer order approximation, the model order is determined via Hankel singular values of the original system; while the order of FO approximations is determined via optimization. Unknown parameters of the reduced model are obtained by minimizing a fitness function via the genetic algorithm (GA). This fitness function is the weighted sum of differences of Integral Square Error (ISE), steady-state errors, maximum overshoots, and ISE of the magnitude of the frequency response of the FO system and the reduced-order model. Therefore, both time and frequency domain characteristics of the system considered in obtaining the reduced-order model. The stability criteria of the reduced-order systems were obtained in various cases and added to the cost function as constraints. Three fractional order systems were approximated by the proposed method and their properties were compared with famous approximation methods to show the out-performance of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract Spin chain oxides with different incommensurate hexagonal composite structures have been obtained for a same cationic composition according to the formula Sr 3 CaMn 2 CoO 9+δ by varying the thermal treatments in air. The cell parameters of these oxides, a∼9.5 Å, c 1 ∼2.5 Å and c 2 ∼3.8 Å, decrease as the deviation from commensurability increases, i.e. as γ = c 1/ c 2 decreases and falls away from 2/3. All the investigated samples exhibit a signature typical of single-ion magnet (SIM), as well as a competition between single-chain magnet (SCM) and short-range ordering (SRO) responses. The balance between the latter two features turns out to be clearly affected by the thermal treatment. The sample quenched at 1450 °C, which structure is almost commensurate (γ = 0.6659, close to 2/3), exhibits a SCM behavior without sizeable indication of SRO, whereas, for the samples annealed at 1300 °C or furnace cooled from 1400 °C with an incommensurate structure (γ = 0.6622–0.6631), the SRO character is strongly reinforced. These changes in the magnetic response are assumed to originate from incorporation of extra oxygen into the commensurate stoichiometric Sr 3 CaMn 2 CoO 9 oxide, leading to the replacement of some trimeric units built up of two octahedra and one trigonal prism (Oh 2 Tp) by tetrameric units (Oh 3 Tp) containing one additional octahedron, with a concomitant appearance of cationic vacancies in the trigonal prismatic sites. Highlights • Effect of thermal treatment on spin chain oxide Sr 3 CaMn 2 CoO 9 is investigated. • Different incommensurate hexagonal composite structures are obtained for Sr 3 CaMn 2 CoO 9. • All samples exhibit a signature typical of single-ion magnet (SIM). • There is competition between single-chain magnet (SCM) and short-range ordering (SRO). • Incorporation of extra oxygen into lattice influences magnetism of Sr 3 CaMn 2 CoO 9+δ. [ABSTRACT FROM AUTHOR]

Various single elements form incommensurate crystal structures under pressure, where a zeolite-type "host" sublattice surrounds a "guest" sublattice comprising 1D chains of atoms. On "chain melting," diffraction peaks from the guest sublattice vanish, while those from the host remain. Diffusion of the guest atoms is expected to be confined to the channels in the host sublattice, which suggests 1D melting. Here, we present atomistic simulations of potassium to investigate this phenomenon and demonstrate that the chain-melted phase has no long-ranged order either along or between the chains. This 3D disorder provides the extensive entropy necessary to make the chain melt a true thermodynamic phase of matter, yet with the unique property that diffusion remains confined to 1D only. Calculations necessitated the development of an interatomic forcefield using machine learning, which we show fully reproduces potassium's phase diagram, including the chain-melted state and 14 known phase transitions. [ABSTRACT FROM AUTHOR]

The death of a child is typically seen as incommensurate, a limit-experience defying articulation and comprehension. In her most recent book, Literature in the Ashes of History (2013), the literary critic and trauma theorist Cathy Caruth theorizes a history that inscribes itself in and through its own (self-conscious, and traumatic) self-effacement; what is striking is that her attempt to theorize and initiate what she calls ‘a new kind of language’, produced ‘After the End’ (as she titles the second part of the book), must thus be understood not only in relation to the post-Holocaust world, but also in the context of the more personal, individual trauma of the loss of a child. This article seeks to explore Caruth’s notion of a different kind of language through analysis of two French fictional representations of the death of a child published in this century: Marie Darrieussecq’s novel Tom est mort, and Hélène Cixous’s autofictional novel, Le Jour où je n’étais pas là (2000). I read these texts (which both explicitly locate writing ‘after the end’) alongside Caruth’s Literature in the Ashes of History to contemplate what it might mean to write ‘after the end’. Tom est mort, I argue, experiments with linguistic form, self-consciously stammering — in a manner curiously similar to Caruth’s — in its attempt to express the impact of the death of a child on the mother (and on her language). Cixous’s text, by contrast, gives voice to the mother’s impossible mourning through figures of absence and lack. The ‘new language’ announced by Caruth is in these texts not a new language in itself, rather a language that is articulated in and through its own erasure, disintegration and absence, that ‘undoes’ its subject even as it gives voice to it, and locates itself after an end that cannot be defined. [ABSTRACT FROM AUTHOR]

Friction and wear are important factors which limit the development of Micro-electromechanical Systems (MEMS). Therefore, the research and preparation of wear-resistant micro and nano-functional structures in the field of MEMS has profound importance. Structural superlubricity micro/nano-components (the atomic layers are in incommensurate contact, which means that the friction and wear rate is nearly zero when the layers slide) are expected to be the basic micro and nano functional structures for fabricating ultra wear-resistant MEMS. At present, there is a lack of research on the properties of structural superlubricity micro/nano-components on the surface of silicon, which is known to be the most mainstream base material for MEMS. In this paper, the electronic properties and the atomic-scale friction of the silicon-based surface structural superlubricity micro/nano-components are simulated using first-principles calculations based on the Density functional theory (DFT). By analyzing the silicon-based surface structural superlubricity micro/nano-component with adhesion performances and superlubricity characteristics. The calculation shows that the binding energy value of its lower graphene layer is larger than that of the upper layer during the slip process, and it is found that the friction force of the silicon-based structure can reach the range of 10−3 nN and the average friction coefficient can reach the range of 10−3 in the incommensurate state. Throughout the sliding process, electrostatic repulsion plays an important role in the tribological properties. The larger the electrostatic repulsion, the smoother the potential energy fluctuation, indicating less friction, while the analysis of the charge mechanism further justifies the conclusion. [ABSTRACT FROM AUTHOR]

The compound Y3Ru2−x was synthesized from the elements and the structure was solved from single crystal synchrotron data. The high quality of the data allowed the determination of the incommensurate ordering of the compound, previously reported as disordered, with respect to the second subsystem. The compound crystallizes in the super space group X-3(00γ)0 with the q-vector axial along c*, q = 00γ, λ = 0.4276(7) and the centering vectors (1/3 2/3 0 1/3), (2/3 1/3 0 2/3).

Layered materials, e.g., graphene and transition metal (di)chalcogenides, holding great promises in nanoscale device applications have been extensively studied in fundamental chemistry, solid state physics and materials research areas. In parallel, layered oxides (e.g., Aurivillius and Ruddlesden-Popper phases) present an attractive class of materials both because of their rich physics behind and potential device applications. In this work, we report a novel layered oxide material with self-assembled layered supercell structure consisting of two mismatch-layered sublattices of [Bi3O3+d] and [MO2]1.84 (M = Al/Mn, simply named BAMO), i.e., alternative layered stacking of two mutually incommensurate sublattices made of a three-layer-thick Bi-O slab and a one-layer-thick Al/Mn-O octahedra slab in the out-of-plane direction. Strong room-temperature ferromagnetic and piezoelectric responses as well as anisotropic optical property have been demonstrated with great potentials in various device applications. The realization of the novel BAMO layered supercell structure in this work has paved an avenue toward exploring and designing new materials with multifunctionalities. [ABSTRACT FROM AUTHOR]

The incommensurately modulated structures of three intermediate plagioclase feldspars with compositions of ~An51 are determined by single-crystal X-ray diffraction analyses. The samples selected cover a range of different cooling rate, from relatively fast to extremely slow. The structures show various ordering states that are directly correlated with the cooling histories of the samples. The slowest cooled sample shows an e1 structure with strong density modulation, along with nanoscale exsolution lamellae. The fastest cooled sample displays an e2 structure, without second-order satellite reflections ( f-reflections) and density modulation. The sample with intermediate cooling rate shows a less ordered e1 structure with weak density modulation, but the modulation period and orientation are the same as in e2 structure. The comparison of the structures with the same composition reveals the ordering process and phase transitions during the cooling of plagioclase within the compositional range of Bøggild intergrowth. New parameters from modulation waves can be used for quantifying the ordering state of plagioclase feldspars. Proposed phase relationship and T-T-T diagram for ~An51 plagioclase feldspars are illustrated for explaining the relationship among C, e1 and e2 structures, and relative cooling rates of their host rocks. [ABSTRACT FROM AUTHOR]

We prove that the electronic density of states (DOS) for two-dimensional incommensurate layered structures, where Bloch theory does not apply, is well-defined as the thermodynamic limit of finite clusters. In addition, we obtain an explicit representation formula for the DOS as an integral over local configurations. Next, based on this representation formula, we propose a novel algorithm for computing electronic structure properties in incommensurate heterostructures, which overcomes limitations of the common approach to artificially strain a large supercell and then apply Bloch theory. [ABSTRACT FROM AUTHOR]

Intermediate plagioclase feldspars are the most abundant minerals in the Earth's crust. Their incommensurately modulated structure has puzzled geologists and crystallographers for decades since the phenomenon in a labradorite was reported in 1940. Solving the structure is a necessary step toward mapping the complex subsolidus phase relations of plagioclase solid solution. The structure of a homogeneous labradorite (An51) single crystal from a metamorphic rock is solved and refined from single-crystal X-ray diffraction. The result structure can be simplified as alternating I1-like lamellae domains related by inversion twins. The inversion boundary shows an anorthite-like structure with symmetry and is richer in Ca than the neighboring domains with opposite polarity. No albite-like subunits appear in the e-plagioclase structure. The modulated structure displays a unique Al-Si ordering pattern. A density modulation with a variation of 17 mol% in composition is also observed and can be properly described only by applying second-order harmonic waves for the atomic modulation functions. The modulated structure reveals details that cannot be observed from refinement with only main reflections and may be used to assess the ordering state and cooling rate of its host rock. The homogeneity of the crystal indicates the closure of the solvus for Bøggild intergrowth at low temperature. The highly ordered modulation supports the thermodynamic stability of e-plagioclase. Both Al-Si ordering and Ca-Na ordering are the driving force for formation of the incommensurately modulated structure. [ABSTRACT FROM AUTHOR]

In this paper, a fractional-order (and an integer-order) memristor-based system with the flux-controlled memristor characterized by smooth quadratic nonlinearity is proposed and detailed dynamical analysis is carried out by means of theoretical and numerical methods. To be more specific, stability of each equilibrium point in the equilibrium set is analyzed for the integer-order memristive system. Meanwhile, dynamical behavior depending on the initial states of the memristor is investigated and dynamical bifurcation depending on the slope of the memductance function is also considered. The bifurcation analysis is verified by numerical methods, including phase portraits, bifurcation diagrams, Lyapunov exponents spectrum, and Poincaré mappings. For the fractional-order case, based on the fractional-order stability theory, stability analysis is carried out just for a certain equilibrium point. Moreover, bifurcation behavior depending on the incommensurate order is discussed by virtue of numerical methods based on the Adams–Bashforth–Moulton algorithm. This paper indicates how the fractional order model and the initial state of the memristor extend the dynamical behaviors of the traditional chaotic systems. [ABSTRACT FROM AUTHOR]

One-dimensional nanoscale epitaxial arrays serve as a great model in studying fundamental physics and for emerging applications. With an increasing focus laid on the Cs-based inorganic halide perovskite out of its outstanding material stability, we have applied vapor phase epitaxy to grow well aligned horizontal CsPbX3 (X: Cl, Br, or I or their mixed) nanowire arrays in large scale on mica substrate. The as-grown nanowire features a triangular prism morphology with typical length ranging from a few tens of micrometers to a few millimeters. Structural analysis reveals that the wire arrays follow the symmetry of mica substrate through incommensurate epitaxy, paving a way for a universally applicable method to grow a broad family of halide perovskite materials. The unique photon transport in the one-dimensional structure has been studied in the all-inorganic Cs-based perovskite wires via temperature dependent and spatially resolved photoluminescence. Epitaxy of well oriented wire arrays in halide perovskite would be a promising direction for enabling the circuit-level applications of halide perovskite in high-performance electro-optics and optoelectronics. [ABSTRACT FROM AUTHOR]

Plagioclase feldspars are the most abundant mineral in the Earth's crust. Intermediate plagioclase feldspars commonly display incommensurately modulated or aperiodic structures. Z-contrast images show both Ca-Na ordering and density modulation. The local structure of lamellae domains has I1-like symmetry. The neighboring lamellae domains are in an inversion twinning relationship.With a state-of-the-art X-ray diffraction unit, second-order satellite reflections (f-reflections) are observed for the first time in andesine (An45), a Na-rich e-plagioclase. The f-reflections indicate a structure with a density modulation which is close to a Ca-rich e-plagioclase. The similarity between this e-andesine structure and previously solved e-labradorite structure is confirmed. Refinement of the structure shows density modulation of ~ 7 mol% in compositional variation of the anorthite (An) component. The results from Zcontrast imaging and low-temperature single X-ray diffraction (XRD) provide a structure consistent with density modulation. The discovery of f-reflections in Na-rich e-plagioclase extends the composition range of e1 structure with density modulation to as low as at least An45, which is the lower end of the composition range of Bǿggild intergrowth. The new result supports the loop-shaped solvus for Bǿggild intergrowth, below which is a homogenous stable area for e1 structure in the phase diagram. The phase transition between e2 structure without density modulation and e1 structure with density modulation should happen at low temperature. There is a change in modulation period accompanying the phase transition, as well as higher occupancy of Al in the T1o site. The andesine with density modulation also indicates extremely slow cooling of its host rock. [ABSTRACT FROM AUTHOR]

Legal orders of international investment law and European Union law both provide remedies for investors. This article does not consider whether these remedies are available to the same actors in relation to the same conduct. The argument is limited to comparison of remedies under investment law, almost exclusively compensatory in character and implemented through investor-State arbitration, with remedies under EU law, particularly State liability claims in domestic courts. This comparison at the level of legal principle is not nonsensical - concepts of attribution, breach, rights, and causality do evoke somewhat similar considerations - but ultimately the extent of systemic differences as well as lack of information about crucial aspects of remedies make these matters incommensurable. It is not obvious that comparison of experience of States that have been addressees of both kinds of remedies is more illuminating than the comparison of principle. [ABSTRACT FROM AUTHOR]

The stability of a class of commensurate and incommensurate nonlinear fractional-order systems is studied. First, two comparison inequalities for incommensurate fractional-order systems are proposed. Based on that, a stability criterion regarding a class of incommensurate fractional-order system is given. And then, three stability criteria are presented concerning a typical class of commensurate nonlinear fractional-order systems. After that, two global stability criteria concerning commensurate and incommensurate nonlinear fractional-order systems are provided, respectively. Finally, the fractional-order Liu system and the fractional-order Chen system are taken as examples to show how to apply the proposed results to stabilization problems. [ABSTRACT FROM AUTHOR]

Millimeter sized crystals of six oxides of approximate composition Ba 4 M z Pt 3- z O 9 (M=Co, Ni, Cu, Zn, Mg, Pt) were grown from molten K 2 CO 3 fluxes and found to crystallize in a 2H hexagonal perovskite-related structure type. The compositions of these incommensurate structures, which belong to the A 3 n +3 m A′ n B 3 m +n O 9 m +6 n family of 2H hexagonal perovskite related oxides, were characterized by X-ray diffraction, energy dispersive spectroscopy, and magnetic susceptibility measurements. The specific synthetic considerations, crystal growth conditions, and magnetic susceptibility measurements are discussed. [ABSTRACT FROM AUTHOR]

A Raman study of a twisted bilayer graphene grown by chemical vapor deposition (CVD) and transferred on SiO 2 substrate is presented. The Raman spectra show the G and 2D peaks at 1582 cm −1 and 2683 cm −1 respectively. The presence of the interlayer Raman band (I band) in the range 1374 cm −1 - 1440 cm −1 and of the R band at 1484 cm −1 , as well as the single-Lorentzian line shape of the 2D peak, reveals the incommensurate stacking of the two graphene layers. From the R band, we determined that the twist angle (θ = 13.9°) is close to the critical angle θ c (11.9° for the excitation photon energy of 2.33 eV). The effect of annealing at 1050 °C of the incommensurate twisted bilayer graphene (ItBLG) structure is then studied. The analysis of the Raman spectra allows us to directly quantify the effects of doping and of strain on each graphene layer. [ABSTRACT FROM AUTHOR]

The Type II phase in the Bi1 − xW xO1.5 + 1.5 x system is shown to have a (3 + 3)-dimensional modulated δ-Bi2O3-related structure, in which the modulation vector ɛ `locks in' to a commensurate value of 1/3. The structure was refined in a 3 × 3 × 3 supercell against single-crystal Laue neutron diffraction data. Ab initio calculations were used to test and optimize the local structure of the oxygen sublattice around a single mixed Bi/W site. The underlying crystal chemistry was shown to be essentially the same as for the recently refined (3 + 3)-dimensional modulated structure of Type II Bi1 − xNb xO1.5 + x (Ling et al., 2013), based on a transition from fluorite-type to pyrochlore-type via the appearance of W4O18 `tetrahedra of octahedra' and chains of corner-sharing WO6 octahedra along 〈110〉F directions. The full range of occupancies on this mixed Bi/W site give a hypothetical solid-solution range bounded by Bi23W4O46.5 ( x = 0.148) and Bi22W5O48 ( x = 0.185), consistent with previous reports and with our own synthetic and analytical results. [ABSTRACT FROM AUTHOR]

The electron behavior in incommensurate phase in Sn2P2Se6 has been considered as the motion in the Mathieu potential. A simple model of effective potential change under a transition incommensurate - domain-like structure has been proposed. A behavior of the obtained localized levels system versus the model parameters has been investigated.

NiBr 2 is a multiferroic material with an incommensurate magnetic ground state that has easy-plane anisotropy. This manuscript reports how the magnetic properties evolve with Fe substitution in Ni 1 − x Fe x Br 2 single crystals for 0 ≤ x ≤ 0.17. A particular emphasis is placed on the x = 0.055 crystal, for which H v s. T magnetic phase diagrams were developed on the basis of anisotropic magnetization measurements. The observed phase evolution reveals a phase transition in the x = 0.055 crystal that is not present in NiBr 2. The data also demonstrate that the easy-plane anisotropy of NiBr 2 is altered by Fe substitution, with a finite easy-axis anisotropy developing at even the low concentration of x = 0.055. These results demonstrate that Fe substitution enables a fine-tuning of the magnetism in NiBr 2 , especially the magnetic anisotropy, and may therefore promote complex magnetic phases. • Fe-substitution induces an out-of-plane moment in the incommensurate ground state. • Additional phase transitions are identified in Fe-containing NiBr 2. compounds. • Complex magnetic phase diagrams are observed for 5.5% Fe in NiBr 2. [ABSTRACT FROM AUTHOR]

Stoichiometric spin chain "Mn4+-Co2+" oxides [Sr 4 Mn 2 CoO 9 ] n [Sr 5 Mn 3 CoO 12 ] have been synthesized for n ​= ​1, 2, 3, 4, 5, ∞. The X-ray powder diffraction study of these oxides also formulated Sr 1+x (Mn 1-x Co x)O 3 , shows that their hexagonal aperiodic structure (a≈9.6 ​Å, c 1 ​~ ​2.6 ​Å, c 2 ​~ ​3.9 ​Å; modulation vector q ​= ​γc 1 ∗, with γ ​= ​c 1 /c 2) consists of blocks of multiple (n) Mn 2 CoO 9 trimeric units that alternate with single Mn 3 CoO 12 tetrameric units. Competition between single ion (SIM) and single chain magnetism (SCM) is established from ac-susceptibility magnetic measurements: introduction of tetrameric units in trimeric chains hinders SIM signal which decreases with n and disappears for n ​= ​1. A model is proposed for the origin of SIM based on the presence of [Mn4+ 2 Co2+Mn4+ 2 O 18 ]18−groups in the structure. This scheme is supported by the SIM signal observed for the n ​= ​∞ member Sr 2 Ca 2 Mn 2 Co 0.5 Zn 0.5 O 9 that contains a majority of isolated [Mn4+ 2 Co2+Mn4+ 2 O 18 ] groups. [Display omitted] • Stoichiometric Mn4+ - Co2+ aperiodic spin chain oxides have been synthetized. • Competition between single ion (SIM) and single chain (SCM) in spin chain oxides ​« ​Mn–Co » is clearly established. • A model for origin of SIM signal in spin chain oxides ​« ​Mn–Co » is proposed. [ABSTRACT FROM AUTHOR]

To identify the relation between torque and superlubric motion, we investigate the interlayer sliding behavior of two graphene disks with numerical computation methods. The potential energy, lateral force and torque between the top and bottom graphene disks, which are associated with misfit angle, translational displacement and interlayer distance, are analyzed. The results show that the rotation of the top disk is feeble for commensurate state, but it is difficult to realize superlubricity due to the lateral force fluctuating remarkably. For incommensurate state, the flake exhibits vanishing torque approaching to zero only for partial sliding directions. The superlubricity between the top and bottom disks will be eliminated due to torque-induced reorientation along other sliding directions. Whether for commensurate or incommensurate contact, the amplitudes of the lateral force (516 pN and 13 pN, respectively) are in qualitative agreement with experimental observation (typically 250 pN and 50 pN, respectively). It shows that the interlayer torque is insensitive to the top disk size with incommensurate contact. The results suggest that the superlubric motion of graphene disk can be controlled by adjusting the torque. [ABSTRACT FROM AUTHOR]

139La broadline NMR and HRTEM is used in order to unveil the interplay between local Jahn-Teller (JT) lattice distortions and the magnetic structure in the La1-xCaxMnO3 family of manganites. By increasing x, i.e. diluting the JT active Mn3+ ions, a variety of novel phases is observed, with most spectacular the low T solitonic (stripe) spin arrangement for x≥0.5.

Oscillators composed of incommensurate graphene sheets have been investigated by molecular dynamics simulations. The oscillation frequencies can reach tens of gigahertz range and depend on the surface energy of the bilayer graphene and the oscillatory amplitude. We demonstrate the tunability of such an oscillator in terms of frequency and friction by its varying geometric parameters. Exploration of the damping mechanism by combining the autocorrelation function theory and the direct atomistic simulations reveals that the friction force is proportional to the velocity of oscillatory motion. The results should help optimize the design of graphene-based nanoelectromechanical devices. [ABSTRACT FROM AUTHOR]

Abstract: Objectives: To measure contrast-response functions (CRFs) for 9 visual field (VF) regions and nonlinear interactions between regions using a multifocal steady-state VEP (MSV). Methods: Ten normal adults were tested (51.7±16.9yr, 5 females). Stimuli resembling those of the Frequency Doubling Technology (FDT) perimeter were presented in 9 VF regions simultaneously, which were modulated at incommensurate temporal frequencies (mean 19.7Hz). Responses were recorded to 11 contrasts from 3% to 89%, using 8 scalp electrodes. Two repeats of a 20s duration stimulus were averaged for each contrast. Results: The CRFs were log-linear except for a depression near 7% contrast (p =0.0008), which was prominent in the central VF. The effects of VF region, stimulus frequency and recording electrode were significant (all p <0.016). Significant responses at frequencies corresponding to interactions between VF regions also appeared. Electrodes that were best for the interactions and second harmonic responses differed, suggesting different cortical sources. Conclusions: Despite short recording durations the saturating CRFs meant that significant responses could be measured to low contrasts, and be distinguished from nonlinear interactions. Significance: Recording MSVs to low contrast FDT-like stimuli might be useful for quantifying damage by glaucoma and other visual disorders. [Copyright &y& Elsevier]

Recently, the fractional-order Chen-Lee system was proven to exhibit chaos by the presence of a positive Lyapunov exponent. However, the existence of chaos in fractional-order Chen-Lee systems has never been theoretically proven in the literature. Moreover, synchronization of chaotic fractional-order systems was extensively studied through numerical simulations in some of the literature, but a theoretical analysis is still lacking. Therefore, we devoted ourselves to investigating the theoretical basis of chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen-Lee systems in this paper. Based on the stability theorems of fractional-order systems, the necessary conditions for the existence of chaos and the controllers for hybrid projective synchronization were derived. The numerical simulations show coincidence with the theoretical results. [ABSTRACT FROM AUTHOR]