Narrow Results

The triangular-type Ising nanowire is constructed on the Bethe lattice (BL) by using the core-shell structure consisting of spin-3/2 atoms as the core and spin-1/2 atoms as the triangular shell. Each triangular plaquette of spins forms a nanoparticle which is connected to upper and lower plaquettes symmetrically. The additions of the plaquettes continue indefinitely until the thermodynamic limit to construct the nanowire. The inter- and intra-bilinear interaction parameters (J) are assumed to be positive or negative to simulate the ferromagnetic (FM) or antiferromagnetic (AFM) interactions, respectively. The crystal field for spin-3/2 and external magnetic field for all sites are also included into the model. After obtaining the formulation of the model in terms of exact recursion relations (ERRs), the thermal variations of magnetizations are studied in detail to obtain the phase diagrams. It is found that the model leads to different types of FM and AFM regions with various forms of phase transitions. It is also interesting that the model presents random or oscillatory magnetization behavior regions for the appropriate values of our system parameters.

An "adaptive" variant of Ruppert's Algorithm for producing quality triangular planar meshes is introduced. The algorithm terminates for arbitrary Planar Straight Line Graph (PSLG) input. The algorithm outputs a Delaunay mesh where no triangle has minimum angle smaller than about 26.45° except "across" from small angles of the input. No angle of the output mesh is smaller than arctan [(sin θ*)/(2-cos θ*)] where θ* is the minimum input angle. Moreover no angle of the mesh is larger than about 137°, independent of small input angles. The adaptive variant is unnecessary when θ* is larger than 36.53°, and thus Ruppert's Algorithm (with concentric shell splitting) can accept input with minimum angle as small as 36.53°. An argument is made for why Ruppert's Algorithm can terminate when the minimum output angle is as large as 30°.

In this paper, four three-node triangular finite element models which can readily be incorporated into the standard finite element program framework are devised via a multi-field variational functional for the bounded plane Helmholtz problem. In the models, boundary and domain fields are independently assumed. The former is constructed by nodal interpolation and the latter comprises nonsingular solutions of the Helmholtz equation. The equality of the two fields are enforced along the element boundary. Among the four devised models, the most accurate one is 1/3 to 1/2 less erroneous than the conventional single-field model in most examples.

A non-extra pixel interpolation NPI is introduced for efficient image upscaling purposes. The NPI algorithm uses extended-triangular and linear scaling functions to match the pixel coordinates. The triangular function uses a modulo-operator with only two variables representing image pixels and scaling ratio. Every two variables of the linear scaling function represent the source/destination image pixels and scaling ratio. The traditional ceil function is used to round off non-integer pixel coordinates. The circshift and padarray functions are used to circularly shift the elements in array output by $k$-amount in each dimension and pad elements of the $d$th columns/rows by g-padsize in the shifted array, respectively. The $k$, $d$ and $g$ values are determined with respect to integer scaling ratios by a vector of $n$-elements. The Exactness, Peak Signal-to-Noise Ratio, Signal-to-Noise Ratio and Discrete Fourier Transform techniques were used for objective evaluation purposes. Experiments demonstrated comparable results as well as the need for further researches.

By assuming a hierarchical interaction with the environments within the Houtappel approximation, decoherence effects on a Quantum Information System (QIS) are studied. In order to avoid a harmful "always on" effect it is assumed that such interaction happens in a single one step. As a result the decoherence times are quantized and inversely proportional to the strength of the couplings of the QIS with the environment. The decoherence is manifested as a liberated heat by the QIS. By Landauer's principle this effect erases the information. Our theoretical results are applied to three different Nuclear Magnetic Resonance systems. Bounds to the probability of erasing the information are imposed for these systems.

This paper presents the torsional analysis of isotropic, orthotropic, and functionally graded material (FGM) triangular and rectangular sections. The formulation of the governing equation of the torsion problem is done using the Saint–Venant torsion theory. Classical power law has been considered for the modeling of FGM material. A meshfree technique based on various radial basis functions is used for the solution of the governing differential equation. MATLAB code is developed to solve the discretized partial differential equations. To demonstrate the effectiveness and accuracy of this technique, convergence study and numerical examples are presented by varying the various parameters. The torsional rigidity factors and shear stress factors are obtained for different new conditions. The solution presented here is validated from the analytical and numerical results along with some new results, which shows the satisfactory performance of the present method.

A novel fused two-dimensionally π-expanded triangular porphyrinoid has been designed. The synthesis is based on facile hexaazatrinaphthalene chemistry in combination with well-established condensation procedures to simultaneously close three porphyrinic cavities. A series of different functionalized π-expanded triangular derivatives were synthesized and their optical and electrochemical properties, as well as their supramolecular organization investigated. Low lying HOMO‒LUMO energy gaps between 1.11–1.32 eV were found for the highly π-conjugated planar triangular hexaazatrinaphthalene derivatives which organize into discotic liquid crystalline columnar stacks. Thereby, derivatives with alkoxy substituents reveal significantly higher order due to their improved flexibility in comparison to their alkyl counterparts.