Vibrational frequencies of the diced and decorated honeycomb lattices

2019 ◽  
Vol 33 (08) ◽  
pp. 1950058 ◽  
Author(s):  
M. Q. Owaidat
Keyword(s):  
Lattice Dynamics ◽  
Vibrational Mode ◽  
Harmonic Approximation ◽  
Vibrational Frequencies ◽  
Numerical Results ◽  
Two Dimensional ◽  
Classical Lattice

In this paper, the classical lattice dynamics for the two-dimensional diced and decorated honeycomb lattices in the harmonic approximation is studied. The numerical results for the vibrational mode frequencies are presented.

EDF2: A Density Functional for Predicting Molecular Vibrational Frequencies

2004 ◽  
Vol 57 (4) ◽  
pp. 365 ◽  
Author(s):  
Ching Yeh Lin ◽  
Michael W. George ◽  
Peter M. W. Gill
Keyword(s):  
Vibrational Spectra ◽  
Density Functional ◽  
Functional Model ◽  
Harmonic Approximation ◽  
Vibrational Frequencies ◽  
Computational Approach ◽  
Numerical Results ◽  
Harmonic Frequencies ◽  
Anharmonic Frequencies ◽  
Computationally Expensive

The majority of calculations of molecular vibrational spectra are based on the harmonic approximation but are compared (usually after empirical scaling) with experimental anharmonic frequencies. Any agreement that is observed in such cases must be attributable to fortuitous cancellation of errors and it would certainly be preferable to develop a more rigorous computational approach. In this paper, we introduce a new density functional model (EDF2) that is explicitly designed to yield accurate harmonic frequencies, and we present numerical results for a wide variety of molecules whose experimental harmonic frequencies are known. The EDF2 model is found to be significantly more accurate than other DFT models and competitive with the computationally expensive CCSD(T) method.

scholarly journals Onset of Convection in Two-Dimensional Porous Cavities with Open and Conducting Boundaries

2021 ◽  
Vol 136 (3) ◽  
pp. 791-812
Author(s):  
Peder A. Tyvand ◽  
Jonas Kristiansen Nøland
Keyword(s):  
Critical Rayleigh Number ◽  
Numerical Results ◽  
Temperature Perturbation ◽  
Two Dimensional ◽  
Onset Of Convection ◽  
Order Problem ◽  
Fourth Order Problem ◽  
Thermally Conducting ◽  
Perturbation Pressure ◽  
Special Case

AbstractThe onset of thermal convection in two-dimensional porous cavities heated from below is studied theoretically. An open (constant-pressure) boundary is assumed, with zero perturbation temperature (thermally conducting). The resulting eigenvalue problem is a full fourth-order problem without degeneracies. Numerical results are presented for rectangular and elliptical cavities, with the circle as a special case. The analytical solution for an upright rectangle confirms the numerical results. Streamlines penetrating the open cavities are plotted, together with the isotherms for the associated closed thermal cells. Isobars forming pressure cells are depicted for the perturbation pressure. The critical Rayleigh number is calculated as a function of geometric parameters, including the tilt angle of the rectangle and ellipse. An improved physical scaling of the Darcy–Bénard problem is suggested. Its significance is indicated by the ratio of maximal vertical velocity to maximal temperature perturbation.

Numerical Analysis of Two-Phase Pipe Flow of Liquid Helium Using Multi-Fluid Model

2001 ◽  
Vol 123 (4) ◽  
pp. 811-818 ◽  
Author(s):  
Jun Ishimoto ◽  
Mamoru Oike ◽  
Kenjiro Kamijo
Keyword(s):  
Phase Transition ◽  
Gas Phase ◽  
Liquid Helium ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Numerical Results ◽  
Phase Flow ◽  
Two Dimensional ◽  
Two Phase ◽  
Normal Fluid

The two-dimensional characteristics of the vapor-liquid two-phase flow of liquid helium in a pipe are numerically investigated to realize the further development and high performance of new cryogenic engineering applications. First, the governing equations of the two-phase flow of liquid helium based on the unsteady thermal nonequilibrium multi-fluid model are presented and several flow characteristics are numerically calculated, taking into account the effect of superfluidity. Based on the numerical results, the two-dimensional structure of the two-phase flow of liquid helium is shown in detail, and it is also found that the phase transition of the normal fluid to the superfluid and the generation of superfluid counterflow against normal fluid flow are conspicuous in the large gas phase volume fraction region where the liquid to gas phase change actively occurs. Furthermore, it is clarified that the mechanism of the He I to He II phase transition caused by the temperature decrease is due to the deprivation of latent heat for vaporization from the liquid phase. According to these theoretical results, the fundamental characteristics of the cryogenic two-phase flow are predicted. The numerical results obtained should contribute to the realization of advanced cryogenic industrial applications.

Dynamic Stability of Ni FCC Crystal under Isotropic Tension

2013 ◽  
Vol 592-593 ◽  
pp. 47-50
Author(s):  
Petr Řehák ◽  
Miroslav Černý
Keyword(s):  
Dynamic Stability ◽  
Wave Vector ◽  
First Principles ◽  
Lattice Dynamics ◽  
Harmonic Approximation ◽  
Tensile Loading ◽  
The Other ◽  
Other Hand ◽  
Critical Strains

Lattice dynamics and stability of fcc crystal of Ni under isotropic (hydrostatic) tensile loading are studied from first principles using supercell method and a harmonic approximation. According to the results, strength of the crystal is determined by occurrence of an instability related to soft phonons with finite wave vector. On the other hand, the critical strains and stresses associated with such instabilities are only slightly lower than those related to the volumetric instability.

GAP-LABELING PROPERTIES OF THE ENERGY SPECTRUM FOR TWO-DIMENSIONAL FIBONACCI QUASILATTICES

1995 ◽  
Vol 09 (01) ◽  
pp. 55-66
Author(s):  
YOUYAN LIU ◽  
WICHIT SRITRAKOOL ◽  
XIUJUN FU
Keyword(s):  
Energy Spectrum ◽  
Density Of States ◽  
Energy Gap ◽  
Fractional Part ◽  
Numerical Results ◽  
Step Height ◽  
Integrated Density Of States ◽  
Two Dimensional

We have analytically obtained the occupation probabilities on subbands of the hierarchical energy spectrum and the step heights of the integrated density of states for two-dimensional Fibonacci quasilattices. Based on the above results, the gap-labeling properties of the energy spectrum are found, which claim that the step height is equal to {mτ}, where the braces denote the fractional part, and m is an integer that can be used to label the corresponding energy gap. Numerical results confirm these results very well.

On Wall Effects in Cavity Flows

1984 ◽  
Vol 28 (01) ◽  
pp. 70-75
Author(s):  
C. C. Hsu
Keyword(s):  
Numerical Results ◽  
Cavity Flows ◽  
Two Dimensional ◽  
Wall Effects ◽  
Free Jet ◽  
Theoretical Predictions ◽  
Experimental Findings ◽  
Good Agreement

Simple wall correction rules for two-dimensional and nearly two-dimensional cavity flows in closed or free jet water tunnels, based on existing linearized analyses, are made. Numerical results calculated from these expressions are compared with existing experimental findings. The present theoretical predictions are, in general, in good agreement with data.

Numerical simulation of boundary-layer transition and transition control

1989 ◽  
Vol 199 ◽  
pp. 403-440 ◽  
Author(s):  
E. Laurien ◽  
L. Kleiser
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Transition Process ◽  
Numerical Results ◽  
Boundary Layer Transition ◽  
Two Dimensional ◽  
Layer Transition ◽  
Longitudinal Vortices ◽  
Tollmien Schlichting

The laminar-turbulent transition process in a parallel boundary-layer with Blasius profile is simulated by numerical integration of the three-dimensional incompressible Navier-Stokes equations using a spectral method. The model of spatially periodic disturbances developing in time is used. Both the classical Klebanoff-type and the subharmonic type of transition are simulated. Maps of the three-dimensional velocity and vorticity fields and visualizations by integrated fluid markers are obtained. The numerical results are compared with experimental measurements and flow visualizations by other authors. Good qualitative and quantitative agreement is found at corresponding stages of development up to the one-spike stage. After the appearance of two-dimensional Tollmien-Schlichting waves of sufficiently large amplitude an increasing three-dimensionality is observed. In particular, a peak-valley structure of the velocity fluctuations, mean longitudinal vortices and sharp spike-like instantaneous velocity signals are formed. The flow field is dominated by a three-dimensional horseshoe vortex system connected with free high-shear layers. Visualizations by time-lines show the formation of A-structures. Our numerical results connect various observations obtained with different experimental techniques. The initial three-dimensional steps of the transition process are consistent with the linear theory of secondary instability. In the later stages nonlinear interactions of the disturbance modes and the production of higher harmonics are essential.We also study the control of transition by local two-dimensional suction and blowing at the wall. It is shown that transition can be delayed or accelerated by superposing disturbances which are out of phase or in phase with oncoming Tollmien-Schlichting instability waves, respectively. Control is only effective if applied at an early, two-dimensional stage of transition. Mean longitudinal vortices remain even after successful control of the fluctuations.

Recent Numerical Results on the Two-Dimensional Hubbard Model

1989 ◽  
pp. 390-390
Author(s):  
S. Sorella ◽  
S. Baroni ◽  
R. Car ◽  
M. Parrinello ◽  
A. Parola ◽  
...  
Keyword(s):  
Hubbard Model ◽  
Numerical Results ◽  
Two Dimensional

Two-Dimensional Finite Element Analysis of Laboratory Seawall Model

2014 ◽  
Vol 580-583 ◽  
pp. 2134-2140
Author(s):  
Jian Zhang ◽  
Jian Feng Zhai ◽  
Xian Mei Wang ◽  
Jie Chen
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Numerical Analysis ◽  
Numerical Results ◽  
Experimental Results ◽  
Base Layer ◽  
Two Dimensional ◽  
Element Analysis ◽  
Cemented Sand ◽  
Dimensional Finite Element

Two-Dimensional finite element analysis was used to investigate the performance of seawall construction over weak subgrade soil using artificial base layer material consisted of cemented sand cushion comprising geosynthetics materials. Two types of base layer materials pure sand and cemented sand comprising husk rich ash and two types of geosynthetics materials geogrid and geotextile were used. Constitutive models were used to represent different materials in numerical analysis. The competence of two-dimensional numerical analysis was compared with experimental results. Numerical results showed a superior harmony with the experimental results. Finite element analysis model proved to be a great tool to determine the parameters that are difficult to measure in laboratory experiments. In addition, finite element analysis has the benefit of cost and time saving when compared to experimental investigation work. Numerical results showed strain induced in geosynthetics eliminated beyond a distance approximately equal six times of footing width.

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