One-dimensional Complex Research Articles

Beyond large complex structure: quantized periods and boundary data for one-modulus singularities

We study periods in an integral basis near all possible singularities in one-dimensional complex structure moduli spaces of Calabi-Yau threefolds. Near large complex structure points these asymptotic periods are well understood in terms of the topological data of the mirror Calabi-Yau manifold. The aim of this work is to characterize the period data near other boundaries in moduli space such as conifold and K-points. Using results from Hodge theory, we provide the general form of these periods in a quantized three-cycle basis. Based on these periods we compute the prepotential and related physical couplings of the underlying supergravity theory. Moreover, we elucidate the meaning of the model-dependent coefficients that appear in these expressions: these can be identified with certain topological and arithmetic numbers associated to the singular geometry at the moduli space boundary. We illustrate our findings by studying a wide set of examples.

Scaling regimes of the one-dimensional phase turbulence in the deterministic complex Ginzburg-Landau equation.

We consider the one-dimensional deterministic complex Ginzburg-Landau equationin the regime of phase turbulence, where the order parameter displays a defect-free chaotic phase dynamics, which maps to the Kuramoto-Sivashinsky equation, characterized by negative viscosity and a modulational instability at linear level. In this regime, the dynamical behavior of the large wavelength modes is captured by the Kardar-Parisi-Zhang (KPZ) universality class, determining their universal scaling and their statistical properties. These modes exhibit the characteristic KPZ superdiffusive scaling with the dynamical critical exponent z=3/2. We present numerical evidence of the existence of an additional scale-invariant regime, with the dynamical exponent z=1, emerging at scales which are intermediate between the microscopic ones, intrinsic to the modulational instability, and the macroscopic ones. We argue that this new scaling regime belongs to the universality class corresponding to the inviscid limit of the KPZ equation.

A brief introduction to one-dimensional complex dynamics

A brief introduction to one-dimensional complex dynamics

Structural elucidation and interpretation of 2D‒3D supramolecular assemblies featuring lone-pair···π interaction in two Cu(II)‒PDA complexes: Experimental and computational assessment

The structural study of two synthesized Cu-PDA (Cu = Copper(II), PDA = deprotonated Pyridine-2,6-dicarboxylic acid) complexes has been carried out using single-crystal X-ray diffraction where complex (1) [Cu(PDA)(H2O)2] exhibits one-dimensional (1D) and two-dimensional (2D) supramolecular assemblies and complex (2) [Cu(PDA)(H2PDA)]·H2O exhibits 1D, 2D, and 3D (three-dimensional) supramolecular networks in their solid-state structure with the aid of intermolecular noncovalent interactions. Lone pair···π/π···lone pair networks are exclusively found in both complex (1) and (2). The intermolecular interactions are characterized through Hirshfeld surface analysis and quantified by 2D fingerprint plot. The noncovalent interactions are further characterized by Bader's theory of ‘Atoms in Molecules’ (AIM) and ‘noncovalent interaction’ (NCI) plot and the topological parameters at bond critical points (BCPs) have been evaluated. Therefore, the energetic factors to the stabilization of the crystal structure observed experimentally have been obtained by the computational calculations.

Preparation, structure and properties of a novel one-dimensional erbium (III) complex

A novel one-dimensional erbium complex [ErL2(NO3)(H2O)2]n (HL = 2-picolinic acid) was synthesized by hydrothermal methods, and its crystal structure was determined by single crystal x-ray diffraction. The complex crystallize in monoclinic system, space group C2/c with a = 15.7525(5) Å, b = 11.4958(4) Å, c = 9.7977(3) Å, β = 102.862(3) º, V = 1729.72(10) Å3, C12H10ErN3O9, Mr = 507.49, Z = 4, Dc = 1.949 g•cm-3, F(000) = 972,  = 4.901 mm-1, S= 1.119, λ(MoKα) = 0.071073 nm, R = 0.0239 and wR = 0.0668. The 2-picolinic acid ligand adopts bidentate bridging coordination mode to connect adjacent erbium ions to form a one-dimensional chain structure. A series of properties of the complex were measured by solid-state photoluminescence, solid-state diffuse reflection and differential scanning calorimetry.

Syntheses, structures and magnetic properties of three dinuclear, one-dimensional and two-dimensional dysprosium(iii) complexes based on naphthalene diimide salicylic acid

Three new dysprosium(iii) complexes with dinuclear, one-dimensional chain and two-dimensional network structures were synthesized and characterized.

3,5-Bis(4-pyridyl)-1,2,4-oxadiazole: An Unsymmetric Bidentate Ligand, Polymeric Silver Complex and Antimicrobial Activity Study

1,2,4-Oxadiazole based unsymmetric bidentate ligand, 3,5-bis-(4-pyridyl)-1,2,4-oxadiazole has been employed for complexation with silver nitrate; this ligand has been used for the first time for preparation of any coordination complex. A polymeric array of one-dimensional silver-ligand complex is formed where each metal ion is coordinated to two 4-pyridyl groups of two different ligands and two O-atoms of a nitrate ion. Single crystal X-ray data shows presence of hydrogen bonding and π-π stacking between each one-dimensional array which leads to formation of channels in its solid state. The hydrogen bonding interactions have also been verified by Hirsfeld surface analysis plots. Antimicrobial property study of ligand 3,5-bis-(4-pyridyl)-1,2,4-oxadiazole has been performed with Lactobacillus plantarum and it inhibits the growth at 12.5 μg mL-1.

Ferrocenyl-substituted nitronyl nitroxide in the design of one-dimensional magnets.

By the reaction of M(hfac)2 (M = Mn(II), Co(II), Cu(II), and Zn(II); hfac is the hexafluoroacetylacetonate anion) and ferrocenyl-substituted nitronyl nitroxide (L), we succeeded in the synthesis of stable heterospin complexes: mononuclear [Zn(hfac)2L], trinuclear {[Cu(hfac)2]3L2} and chain polymer [Mn(hfac)2L]n and [Co(hfac)2L]n. The specific steric bulkiness of the ferrocenyl substituent leads to the formation of trans-type coordination polyhedra in the [Mn(hfac)2L]n and [Co(hfac)2L]n chains. The introduction of the ferrocene substituent leads to an effective weakening of intermolecular or interchain magnetic exchange coupling. Ferrimagnetic ordering was observed for one-dimensional complexes [M(hfac)2L]n (M = Mn(II), Co(II)). [Co(hfac)2L]n exhibits features of single-chain magnet behaviour: slow relaxation of magnetization below 13 K is associated with a high coercive field (54 kOe at 2 K).

Wave beams, packets and pulses in inhomogeneous non-Hermitian media with dispersive gain or damping

Wave beams, packets or pulses are known to be subject to a drift if the properties of the medium change across their extension. This effect is often analyzed considering the dispersive properties of the oscillation, related to the real part of the dispersion relation. The evolution of Gaussian beams/packets/pulses in nonuniform media in the presence of gain or damping is investigated in detail, with particular emphasis on the role of dispersion on both the real and the imaginary part of the dispersion relation. In the paraxial limit, the influence of a non-Hermitian medium on the evolution of the wave can be treated employing the equations derived by Graefe and Schubert in the frame of non-Hermitian quantum mechanics (Phys. Rev. A 83 060101(R)). Analytic solutions of the corresponding paraxial equations are obtained here for a one-dimensional complex dispersion relation characterized by a linear or quadratic dependence on the transverse coordinate (a space coordinate for beams and packets, the time in the co-moving frame for a pulse). In the presence of a constant gradient in both the real and the imaginary part of the dispersion relation, the contribution of the latter can lead to a faster or slower propagation with respect to the Hermitian case, depending on the parameters. In focusing media, a constant gain can counteract dispersive or inhomogeneous damping producing packets of asymptotically constant shape. The analytic formulas derived in this paper offer a way to predict or control the properties of beams/packets/pulses depending on their initial conditions and on the characteristics of the medium.

Low complexity subspace approach for unbiased frequency estimation of a complex single-tone

We propose a single-tone frequency estimator of a one-dimensional complex signal in complex white Gaussian noise. The estimator is based on the subspace approach and the unitary transformation. Due to its low space and time-complexity, we name the estimator as Low complexity Unitary Principal-singular-vector Utilization for Model Analysis (LUPUMA). Regardless of the observation length, LUPUMA provides a uniform estimation variance over the whole frequency range, while achieving the lowest time-complexity among subspace methods. The proposed estimator asymptotically reaches the Cramér-Rao Lower Bound. For short observations, the signal-to-noise ratio threshold of LUPUMA corresponds to the threshold of the maximum likelihood estimator. The low space and time-complexity along with the stable and state-of-the-art estimation performance for short observations make LUPUMA an ideal candidate for applications with a limited number of signal samples, limited computational power, limited memory, and for applications that require rapid processing time (low latency).

One-dimensional polymer of copper with salicylic acid and pyridine linkers: Synthesis, characterizations, solid state assembly investigation by hirshfeld surface analysis, and computational studies

A new one-dimensional polymeric copper complex [Cu(DNSA)py] with salicylic acid and pyridine was synthesized and characterized by many techniques, including FT-IR, UV–Visible, elemental, TGA/DSC, and single crystal XRD analysis. In the crystal structure, two 3,5-dinitrosalicylic ligands were chelated by the copper cation, in which one ligand was coordinated by the carbonyl O-atom and one of the carboxylate O-atoms, while another symmetry-related ligand was coordinated by the O-atoms of the carboxylate group to form distorted square pyramidal geometry. Thus, a one-dimensional polymer structure is formed, extending along the b-axis. The solid-state assembly was stabilized by various intermolecular interactions, as examined through Hirshfeld surface analysis. Voids analysis was carried out to predict the response of the crystal under external pressure. The most stable structure of the [Cu(DNSA)py] monomer resulted from density functional theory (DFT) using the B3LYP/def2-TZVPP. The 6–311G(d,p) level of theory demonstrated that the Cu atom adapts distorted square pyramidal geometry. The MEP surface and Mulliken charge distribution identified the Cu monomer atoms suitable for electrophilic and nucleophilic attacks. Frontier molecular orbital (FMO) analyses were conducted to anticipate the stability and chemical reactivity of the [Cu(DNSA)py] monomer and its ligand (DNSA). Furthermore, the quantum chemical descriptors of the title compound were obtained from EHOMO and ELUMO energy values.

Nonlinear dissipative wave trains in a system of self-propelled particles

The paper addresses the existence of modulated nonlinear periodic wave trains in a system of self-propelled particles (SPPs). The reductive perturbation method reduces the model hydrodynamics equations to a one-dimensional (1D) complex Ginzburg-Landau (CGL) equation. The modulational instability (MI) phenomenon is studied, where an expression for the instability growth rate is proposed. The latter is used to discuss regions of parameters where trains of solitonic waves are likely to be obtained. This is highly influenced by the values of the variances of Gaussian noise in self-diffusion and binary collision. Solutions for the CGL equations are also studied via the Porubov technique, using a combination of Jacobi and Weierstrass elliptic functions. Wave propagation in the self-propelled particles flock includes modulated nonlinear wave trains, nonlinear spatially localized periodic patterns, and continuous waves.

Continuous families of non-Hermitian surface solitons.

We show that surface solitons form continuous families in one-dimensional complex optical potentials of a certain shape. This result is illustrated by non-Hermitian gap-surface solitons at the interface between a uniform conservative medium and a complex periodic potential. Surface soliton families are parameterized by a real propagation constant. The range of possible propagation constants is constrained by the relation between the continuous spectrum of the uniform medium and the bandgap structure of the periodic potential.

Investigation of Charge-Ordered Barium Iron Fluorides with One-Dimensional Structural Diversity and Complex Magnetic Interactions.

Three mixed-valence barium iron fluorides, Ba7Fe7F34, Ba2Fe2F9, and BaFe2F7, were prepared through hydrothermal redox reactions. The characteristic structures of these compounds feature diverse distributions of FeIIF6 octahedra and FeIIIF6 groups. Ba7Fe7F34 contained one-dimensional infinite ∞[FeIIFeIII6F34]14- double chains, comprising cis corner-sharing octahedra along the b direction; Ba2Fe2F9 contained one-dimensional ∞[Fe2F9]4- double chains, consisting of cis corner-sharing octahedra along the chain (a-axis direction) and trans corner-sharing octahedra vertical to the chain, while BaFe2F7 revealed three-dimensional (3D) frameworks that consist of isolated edge-sharing dinuclear FeII2F10 units linked via corners by FeIIIF6 octahedra. Magnetization and Mössbauer spectroscopy measurements revealed that Ba7Fe7F34 exhibits an antiferromagnetic phase transition at ∼11 K, where ferrimagnetic ∞[FeIIFeIII6F34]14- double chains are arranged in a paralleling manner, while Ba2Fe2F9 shows canted antiferromagnetic ordering at ∼32.5 K, leading to noncollinear spin ordering.

The Dynamics of Interacting Multi-pulses in the One-dimensional Quintic Complex Ginzburg–Landau Equation

The Dynamics of Interacting Multi-pulses in the One-dimensional Quintic Complex Ginzburg–Landau Equation

All meromorphic traveling waves of cubic and quintic complex Ginzburg-Landau equations

For both cubic and quintic nonlinearities of the one-dimensional complex Ginzburg-Landau evolution equation, we prove by a theorem of Eremenko the finiteness of the number of traveling waves whose squared modulus has only poles in the complex plane, and we provide all their closed form expressions. Among these eleven solutions, five are provided by the method used. This allows us to complete the list of solutions previously obtained by other authors.

Nine-Coordinate LnIII-Based One-Dimensional Complexes: Synthesis and Magnetic Properties

Three isostructural one-dimensional lanthanide complexes with formulae of [Dy(H2L)(H2O)2]·Cl·6H2O (1), [Dy0.067Y0.933(H2L)(H2O)2]·Cl·6H2O (1′,) and [Gd(H2L)(H2O)2]·Cl·6H2O (2), where H2L2– is the dianion of the bis-hydrazone (N′,N‴E,N′,N‴E)-N′,N‴-(pyridine-2,6-diylbis(methanylylidene))bis(2-hydroxybenzohydrazide), were synthesized and structurally characterized. Single-molecule magnet (SMM) behavior was observed for the DyIII compound under an applied dc field, which is rarely seen for a nine-coordinate DyIII compound with a hula-hoop coordination geometry. The SMM behavior is ascribed to the single-ion properties of DyIII, which is proved by comparison of the ac magnetic susceptibilities of 1 and the Y/Dy diluted complex 1′. Magnetic studies indicate that the GdIII analogue shows a magnetocaloric effect with a maximum entropy change −ΔSm of 21.32 J kg–1 K–1 at ΔH = 7 T and 3 K.

Synthesis, Structures, and Magnetism of Four One-Dimensional Complexes Using [Ni(CN)4]2- and Macrocyclic Metal Complexes.

Four one-dimensional complexes, denoted as [NiL1][Ni(CN)4] (1), [CuL1][Ni(CN)4] (2), [NiL2][Ni(CN)4]·2H2O (3), and [CuL2][Ni(CN)4]·2H2O (4) (L1 = 1,8-dimethyl-1,3,6,8,10,13-hexaaza-cyclotetradecane; L2 = 1,8-dipropyl-1,3,6,8,10,13-hexaazacyclotetradecane) were synthesized by reacting nickel/copper macrocyclic complexes with K2[Ni(CN)4]. Subsequently, the synthesized complexes were characterized using elemental analysis, infrared spectroscopy analysis, thermogravimetric analysis, and X-ray powder diffraction. Single-crystal structure analysis revealed that the Ni(II)/Cu(II) atoms were coordinated by two nitrogen atoms from [Ni(CN)4]2- with four nitrogen atoms from a macrocyclic ligand, forming a six-coordinated octahedral coordination geometry. Nickel/copper macrocyclic complexes were bridged by [Ni(CN)4]2- to construct one-dimensional chain structures in 1-4. The characterization results showed that the four complexes obeyed the Curie-Weiss law with a weak antiferromagnetic exchange coupling.

Synthesis and Characterization of a One-Dimensional Malleable Spin-Crossover Polymer Complex Modified by Methoxy Polyethylene Glycol.

A novel one-dimensional malleable spin-crossover (SCO) complex {[Fe(MPEG-trz)3](BF4)2} has been successfully synthesized by molecular self-assembly between 4-amino-1,2,4-triazoles (MPEG-trz) grafted with a long flexible chain methoxy polyethylene glycol (MPEG) and metallic complex Fe(BF4)2•6H2O. The detailed structure information was illustrated by using FT-IR and 1H NMR measurements, while the physical behaviors of the malleable SCO complexes were systematically investigated by using magnetic susceptibility measurements using superconductivity quantum interference device (SQUID) and differential scanning calorimetry (DSC). This new metallopolymer exhibits a remarkable spin crossover transition behavior, between two spin quantum states (Fe2+ ions): high spin (HS) state (quintet state) and low spin (LS) state (singlet state), at a specific critical temperature with a slender hysteresis loop of 1 K. DFT computations revealed the partial rules of HOMO-LUMO energy levels and spin density distributions of different four-position substituted [Fe(1,2,4-triazole)3]2+ derivatives with different length of repeat units in polymer complexes. This can go a step further to depict the spin and magnetic transition behaviors of SCO polymer complexes. Furthermore, the coordination polymers possess an excellent processability due to an outstanding malleability, which can be easily shaped into a polymer film with spin magnetic switching properties.

A novel DyIII-based metal-organic framework as the multi-responsive luminescent sensor for acetylacetone and salicylaldehyde

A novel DyIII-based metal-organic framework, namely [(H3O)Dy(BTDB)2(DMF)(H2O)]n (JXUST-24, H2BTDB ​= ​4,4′-(benzo[c][1,2,5]thiadiazole-4,7-diyl)dibenzoic acid), was prepared and structurally characterized. Single-crystal structure determination reveals that JXUST-24 is a one-dimensional chain-based complex. JXUST-24 is a excellent luminescent sensor to identify acetylacetone (acac) by the fluorescence enhancement and blue-shift effect with the detection limit of 14.7 ​ppm, and salicylaldehyde (SA) by the fluorescence quenching effect with the detection limit of 17.9 ​ppm, respectively. The sensing process is mainly attributed to the formation of exciplex and charge transfer for acac and photoinduced electron transfer and competitive absorption mechanism for SA. Importantly, JXUST-24 can be reused after five cycles, indicating the good cyclic performance.