New Numerical Method For Calculation Research Articles

Computation of ESR spectra from the time evolution of the magnetization: Comparison of autocorrelation and Wiener-Khinchin-relation-based methods

To evaluate ESR spectrum at finite temperatures for specified spatial configurations of spins is very important issue to study quantum spin systems. Although a direct numerical estimation of the Kubo formula provides exact data, the application is limited to small size of the system because of the restriction of the computer capacity. The method of the Fourier transform of the autocorrelation function improved the restriction. As an extension of the method, we propose a new method for numerical calculation of the ESR spectrum from the time evolution of the magnetization by making use of the Wiener-Khinchin theorem.

Thermal conductivity of carbon supracrystalline nanotubes

A principally new method of numerical calculation of the surface thermal conductivity of single-layer nanotubes taking into account their monoatomic thickness has been proposed. The method has been tested for graphene and cupracrystalline carbon nanotubes. The results for graphene nanotubes agree with the experimental data.

New Numerical Method for Calculation of Flow in a Long Region with Free Surface

New Numerical Method for Calculation of Flow in a Long Region with Free Surface

Simulation of microfocused image size from a one-bounce glass capillary

A new method of numerical calculation, based on geometrical optics for X-rays rather than ray-tracing, is developed to simulate the focal spot size and intensity gain from an elliptically-tapered one-bounce glass mono-capillary. Numerical results for a capillary designed for protein crystallography are in good agreement with experimental measurements and confirm a capillary slope errors limitation on the image quality.

Electron states in quantum-dot and antidot arrays placed in a strong magnetic field

Quantum electronic states in a dot (antidot) array in the presence of a dc magnetic field are studied. A new method of numerical calculation of the electron spectrum and wave functions in a two-dimensional periodic potential and perpendicular magnetic field is proposed. The magnetic-subband energies, density of electron states, and electron density |ψ(x,y)|2, as well as the amplitude of the potential, and lattice period and degree of anisotropy for different magnetic fields have been found. The calculations were performed for quantum dots in the In0.2Ga0.8As-GaAs and GaAs-Al0.3Ga0,7As systems. The rearrangement of the spectrum with variation of magnetic field and with transition from the tight-binding to weak-binding approximation is studied (ω c is the cyclotron frequency, and V 0 is the periodic-potential amplitude). The calculations show that the two-dimensional lattices epitaxially grown presently on semiconductor surfaces permit observation of quantum effects associated with rearrangement of the spectrum (electron transport and optical absorption) in magnetic fields H⩽1 MG.

Calculation of viscoelastic flow using molecular models: the connffessit approach

A new method for numerical calculation of viscoelastic flow based on simulation of molecular models of polymers is presented. The CONNFFES-SIT ( C alculation o f N on- N ewtonian F low: F inite E lements and S tochastic S imulation T echnique) approach directly combines standard finite element methods as currently used in the calculation of viscoelastic flow with stochastic simulations of polymer dynamics and thus obviates the need for a rheological constitutive equation to describe the fluid. The stresses are obtained from the molecular configurations rather than from constitutive equations. As an illustration of the method, the time development of plane Couette flow is studied for the upper-convected Maxwell, Oldroyd- B, FENE-P and FENE fluids. For the upper-convected Maxwell, Oldroyd- B and FENE-P models comparisons with analytical and existing numerical solutions are presented. Significant deviations between the behavior of the FENE-P and FENE models for the start-up of plane Couette flow are found.

A METHOD OF ESTIMATION OF TURBULENT DIFFUSION IN A CIRCULAR PIPE BASED ON SPATIAL-DEPENDENCE MATRIX

Considering that a scalar quantity (mass or heat) is transported on a turbulent lump where fluid particles show almost same behavior, a new method of numerical calculation for the turbulent diffusion is proposed. This method is based on the spatial-dependence matrix, which is one of the tools of pattern analysis. The usefulness of the method is examined by experiments on the turbulent diffusion of the tracer which is injected into the source point on the pipe axis and it is confirmed that the reasonable feature of turbulent diffusion is estimated by the method.

Theoretical Model and Numerical Simulation of Two-Longitudinal-Mode Oscillation in an Injection-Locked TEA CO2 Laser

Injection locking of a TEA CO2 laser is studied theoretically from the point of view of analyzing its two-longitudinal-mode oscillation (TLMO) observed experimentally. A phenomenological theoretical model and a new method of numerical calculation are developed to simulate TLMO locked with a monochromatic injection field. In the proposed theoretical model, injected radiation is allowed to couple with two neighboring longitudinal modes with assumed coupling coefficients. By making use of the proposed algorithm, rapid temporal variation of population densities and cavity fields can be calculated numerically, maintaining the correct phase relation. The simulation results show good agreement with experimental results and the power-modulated output of the TEA CO2 laser is obtained theoretically.

On the green function calculation for heavy quarkonium potential models

A new method for numerical calculation of the Green functions of the Schrödinger equation is proposed in the case of spherically symmetric potentials. This method can be applied to the potentials describing heavy quarkonium as well as to other problems of quantum mechanics. The case of the Coulomb potential with a running coupling constant is considered in detail.

Correction of differential capacitance profiles for Debye-length effects

Conventional differential capacitance-voltage ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C-V</tex> ) profiling methods are limited in resolution by the method used to convert <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C-V</tex> data to profile data. A new method of numerical calculation of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C-V</tex> data, using cubic finite elements, is presented which allows a more exact relationship between <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C-V</tex> data and profile data to be calculated. This new method of data reduction allows the resolution of differential <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C-V</tex> profiling method to be extended to dimensions near the local extrinsic Debye length.

A new method for numerical calculation of potentials and trajectories in systems of cylindrical symmetry

The charge density method for solving Laplace's equation is treated for a system with cylindrical symmetry, where the electrodes can be represented by smooth curves of arbitrary shape. It is assumed that each electrode has two separate sharp edges, but this is no severe restriction. The singularity in the charge density at the edges is eliminated by approximating the integral equation with Gauss-Chebyshev quadrature. A second singularity, occurring if the potential is evaluated on an electrode, is split off and integrated analytically. The resulting set of linear equations is characterised by a symmetric, positive definite matrix and is solved with the Choleskii method. The potential and the electric field can be calculated anywhere outside the electrodes directly from the charge densities. The equations of motion are solved with the method of rational extrapolation. This allows the tracing of electron rays in the non-paraxial region. Some results are given and their accuracy is discussed. In comparison with existing methods either the accuracy is significantly improved or the computer requirements are considerably reduced.

A new method of numerical calculation for stagnation point flows

Bei der Berechnung von zweidimensionalen inkompressiblen Potentialstromungen um abgerundete und symmetrische Korper erhalt man einen Annaherungswert fur den Bereich nahe dem Staupunkt, indem man annimmt, dass die Stromungsart dieselbe ist wie die um einen Kreiszylinder.