Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model

A two-dimensional variable-order fractional nonlinear reaction-diffusion model is considered. A second-order spatial accurate semi-implicit alternating direction method for a two-dimensional variable-order fractional nonlinear reaction-diffusion model is proposed. Stability and convergence of the semi-implicit alternating direct method are established. Finally, some numerical examples are given to support our theoretical analysis. These numerical techniques can be used to simulate a two-dimensional variable order fractional FitzHugh-Nagumo model in a rectangular domain. This type of model can be used to describe how electrical currents flow through the heart, controlling its contractions, and are used to ascertain the effects of certain drugs designed to treat arrhythmia.

The role of tunnel junction resistances and defects on electron transport mechanism in networks of two-dimensional disordered conductors

The effect of tunnel junction resistances on the electronic property and the magneto-resistance of few-layer graphene sheet networks is investigated. By decreasing the tunnel junction resistances, transition from strong localization to weak localization occurs and magneto-resistance changes from positive to negative. It is shown that the positive magneto-resistance is due to Zeeman splitting of the electronic states at the Fermi level as it changes with the bias voltage. As the tunnel junction resistances decrease, the network resistance is well described by 2D weak localization model. Sensitivity of the magneto-resistance to the bias voltage becomes negligible and diminishes with increasing temperature. It is shown 2D weak localization effect mainly occurs inside of the few-layer graphene sheets and the minimum temperature of 5 K in our experiments is not sufficiently low to allow us to observe 2D weak localization effect of the networks as it occurs in 2D disordered metal films. Furthermore, defects inside the few-layer graphene sheets have negligible effect on the resistance of the networks which have small tunnel junction resistances between few-layer graphene sheets

Two-dimensional coordination polymeric structures in caesium complexes with ring-substituted phenoxyacetic acids

The two-dimensional polymeric structures of the caesium complexes with the phenoxyacetic acid analogues (4-fluorophenoxy)acetic acid, (3-chloro-2-methylphenoxy)acetic acid and the herbicidally active (2,4-dichlorophen­oxy)acetic acid (2,4-D), namely poly[[5-(4-fluorophenoxy)acetato][4-(4-fluorophenoxy)acetato]dicaesium], [Cs2(C8H6FO3)2]n, (I), poly[aqua[5-(3-chloro-2-methylphenoxy)acetato]caesium], [Cs(C9H8ClO3)(H2O)]n, (II), and poly[[7-(2,4-di­chlorophenoxy)acetato][(2,4-dichlorphenoxy)acetic acid]caesium], [Cs(C8H5Cl2O3)(C8H6Cl2O3)]n, (III), are described. In (I), the Cs+ cations of the two individual irregular coordination polyhedra in the asymmetric unit (one CsO7 and the other CsO8) are linked by bridging carboxylate O-atom donors from the two ligand molecules, both of which are involved in bidentate chelate Ocarboxy,Ophenoxy interactions, while only one has a bidentate carboxylate O,O'-chelate inter­action. Polymeric extension is achieved through a number of carboxylate O-atom bridges, with a minimum CsCs separation of 4.3231 (9) Å, giving layers which lie parallel to (001). In hydrated complex (II), the irregular nine-coordination about the Cs+ cation comprises a single monodentate water molecule, a bidentate Ocarboxy,Ophenoxy chelate interaction and six bridging carboxylate O-atom bonding interactions, giving a CsCs separation of 4.2473 (3) Å. The water mol­ecule forms intralayer hydrogen bonds within the two-dimensional layers, which lie parallel to (100). In complex (III), the irregular centrosymmetric CsO6Cl2 coordination environment comprises two O-atom donors and two ring-substituted Cl-atom donors from two hydrogen bis[(2,4-dichlorophenoxy)acetate] ligand species in a bidentate chelate mode, and four O-atom donors from bridging carboxyl groups. The duplex ligand species lie across crystallographic inversion centres, linked through a short O-HO hydrogen bond involving the single acid H atom. Structure extension gives layers which lie parallel to (001). The present set of structures of Cs salts of phenoxyacetic acids show previously demonstrated trends among the alkali metal salts of simple benzoic acids with no stereochemically favourable interactive substituent groups for formation of two-dimensional coordination polymers.

Exact ground state and kink-like excitations of a two-dimensional Heisenberg antiferromagnet

A rare example of a two-dimensional Heisenberg model with an exact dimerized ground state is presented. This model, which can be regarded as a variation on the kagome' lattice, has several features of interest: it has a highly (but not macroscopically) degenerate ground state; it is closely related to spin chains studied by earlier authors; in particular, it exhibits domain-wall-like "kink" excitations normally associated only with one-dimensional systems. In some limits it decouples into noninteracting chains; unusually, this happens in the limit of strong, rather than weak, interchain coupling. [S0163-1829(99)50338-X].

Supramolecular control of the magnetic anisotropy in two-dimensional high-spin Fe arrays at a metal interface

Magnetic atoms at surfaces are a rich model system for solid-state magnetic bits exhibiting either classical(1,2) or quantum(3,4) behaviour. Individual atoms, however, are difficult to arrange in regular patterns(1-5). Moreover, their magnetic properties are dominated by interaction with the substrate, which, as in the case of Kondo systems, often leads to a decrease or quench of their local magnetic moment(6,7). Here, we show that the supramolecular assembly of Fe and 1,4-benzenedicarboxylic acid molecules on a Cu surface results in ordered arrays of high-spin mononuclear Fe centres on a 1.5nm square grid. Lateral coordination with the molecular ligands yields unsaturated yet stable coordination bonds, which enable chemical modification of the electronic and magnetic properties of the Fe atoms independently from the substrate. The easy magnetization direction of the Fe centres can be switched by oxygen adsorption, thus opening a way to control the magnetic anisotropy in supramolecular layers akin to that used in metallic thin films.

Two-dimensional self-assembly of a symmetry-reduced tricarboxylic acid

Investigations of the self-assembly of simple molecules at the solution/solid interface can provide useful insight into the general principles governing supramolecular chemistry in two dimensions. Here, we report on the assembly of 3,4′,5-biphenyl tricarboxylic acid (H3BHTC), a small hydrogen bonding unit related to the much-studied 1,3,5-benzenetricarboxylic acid (trimesic acid, TMA), which we investigate using scanning tunneling microscopy (STM) and density functional theory (DFT) calculations. STM images show that H3BHTC assembles by itself into an offset zigzag chain structure that maximizes the surface molecular density in favor of maximizing the number density of strong cyclic hydrogen bonds between the carboxylic groups. The offset geometry creates “sticky” pores that promote solvent coadsorption. Adding coronene to the molecular solution produces a transformation to a high-symmetry host–guest lattice stabilized by a dimeric/trimeric hydrogen bonding motif similar to the TMA flower structure. Finally, we show that the H3BHTC lattice firmly immobilizes the guest coronene molecules, allowing for high-resolution imaging of the coronene structure.

Analytical studies of gain optimization in CO2-N2 gasdynamic lasers employing two-dimensional wedge nozzles

An analytical method has been proposed to optimise the small-signaloptical gain of CO2-N2 gasdynamic lasers (gdl) employing two-dimensional (2D) wedge nozzles. Following our earlier work the equations governing the steady, inviscid, quasi-one-dimensional flow in the wedge nozzle of thegdl are reduced to a universal form so that their solutions depend on a single unifying parameter. These equations are solved numerically to obtain similar solutions for the various flow quantities, which variables are subsequently used to optimize the small-signal-gain. The corresponding optimum values like reservoir pressure and temperature and 2D nozzle area ratio also have been predicted and graphed for a wide range of laser gas compositions, with either H2O or He as the catalyst. A large number of graphs are presented which may be used to obtain the optimum values of small signal gain for a wide range of laser compositions without further computations.

Two-dimensional phase transitions at electrochemical interfaces

A two-state Ising model has been applied to the two-dimensional condensation of tymine at the mercury-water interface. The model predicts a quadratic dependence of the transition potential on temperature and on the logarithm of the adsorbate concentration. Both predictions have been confirmed experimentally.

Two-dimensional solidification in a cylindrical mold with imperfect mold contact

A two-dimensional axisymmetric problem of solidification of a superheated liquid in a long cylindrical mold has been studied in this paper by employing a new embedding technique. The mold and the melt has an imperfect contact and the heat transfer coefficient has been taken as a function of space and time. Short-time exact analytical solutions for the moving boundary and temperature distributions in the liquid, solid and mold have been obtained. The numerical results indicate that with the present solution, for some parameter values, substantial solidified thickness can be obtained. The method of solution is simple and straightforward, and consists of assuming fictitious initial temperatures for some suitable fictitious extensions of the actual regions. Sufficient conditions for the commencement of the solidification have been discussed.

Magnetic properties of quasi-two-dimensional La2NiO4

Magnetic susceptibility studies on single crystals of nearly stoichiometric La2NiO4 with the applied field both parallel and perpendicular to the c axis show a transition at 204 K below which two-dimensional canted antiferromagnetic order seems to exist. This oxide also undergoes a transition from isotropic to anisotropic susceptibility near 100 and 250 K.

Use of 45° pulse pair as a filter for pure-phase two-dimensional NMR spectroscopy

Conventionally two-dimensional NMR spectra are recorded in the absolute-intensity mode (1-4). It has recently been demonstrated that absorption-mode 2D spectra have much higher resolution and are the preferred mode of presentation, especially for 2D spectra of biomolecules (5-7). Indeed, any experimental scheme which yields phasemixed lineshapes is subject to modification to yield pure-phase spectra, even at the expense of intensity and anomalous multiplet structure (8-10). For this purpose two types of filters are already known: the z filter (9, 20) and the purging pulse (8, 10). In this note, we propose a 45” pulse pair as a filter for obtaining pure-phase 2D spectra, mainly for experiments in which the above filters do not yield pure-phase spectra.

Testing approximate theories of first-order phase transitions on the two-dimensional Potts model

The two-dimensional,q-state (q>4) Potts model is used as a testing ground for approximate theories of first-order phase transitions. In particular, the predictions of a theory analogous to the Ramakrishnan-Yussouff theory of freezing are compared with those of ordinary mean-field (Curie-Wiess) theory. It is found that the Curie-Weiss theory is a better approximation than the Ramakrishnan-Yussouff theory, even though the former neglects all fluctuations. It is shown that the Ramakrishnan-Yussouff theory overestimates the effects of fluctuations in this system. The reasons behind the failure of the Ramakrishnan-Yussouff approximation and the suitability of using the two-dimensional Potts model as a testing ground for these theories are discussed.

Coherence transfer via longitudinal spin order generalized pulse pair filtering for pure phase two-dimensional NMR spectroscopy

A generalized pulse pair has been suggested in which the longitudinal spin order is retained and the transverse components cancelled by random variation of the interval between pulses, in successive applications of the two-dimensional NMR algorithm. This method leads to pure phases and has been exploited to provide a simpler scheme for two-spin filtering and for pure phase spectroscopy in multiple-quantum-filtered two-dimensional NMR experiments.

On a Two-Dimensional Problem in the End-Block Design of Post-Tensioned Prestressed Concrete Beams

Abstract is not available.