LATTICE DYNAMICS OF THE BINARY APERIODIC CHAINS OF ATOMS III: PROPERTIES OF VIBRATIONAL EIGENVECTORS

1995 ◽  
Vol 09 (12) ◽  
pp. 1475-1501 ◽  
Author(s):  
WŁODZIMIERZ SALEJDA
Keyword(s):  
Elastic Energy ◽  
Lattice Dynamics ◽  
Quantitative Agreement ◽  
Model Parameters ◽  
Harmonic Model ◽  
Energy Field ◽  
Qualitative And Quantitative ◽  
Phonon Spectra ◽  
Multifractal Spectra ◽  
Optical Region

We numerically study the localization and multifractal properties of normalized vibrational eigenvectors (NVEV), denoted by U, of the microscopic harmonic model of lattice dynamics in Thue-Morse (TM), generalized Fibonacci, octagonal, dodecagonal, Severin, circle and Rudin-Shapiro (RS) binary chain of atoms. Eigenvalues and NVEV are determined with the help of the Dean and Wu-Zheng algorithm, respectively, with free end boundary conditions for chains containing 103<N<104 atoms. The first FM(L) and second SM(L) moment, and the reduced participation ratios Λ red (L) are derived at 1≤L≤N for varying model parameters. All the chains studied show sinusoidal-like and packet-like extended NVEV with Λred(L)≃1, FM(L)≃N/2 and [Formula: see text] The new extended eigenstates called dimmerized NVEV have been found out in the case of the TM chain. The surface localized NVEV with Λred(L)≪1, FM(L)≃1 or FM(L)≃N and the strong tendency to localization of NVEV in RS chain have been observed. The critical NVEV, which dominate in the optical region of phonon spectra, are objects with a broad multifractal (αmin, αmax) spectra. If magnitudes of model parameters are increased then, first, [Formula: see text] and [Formula: see text] at L≪N and, second, [Formula: see text] and [Formula: see text] at L≃N. It is numerically shown that the multifractal spectra α′—f′ characterizing the curdling of the elastic energy field ε(L) are in excellent qualitative and quantitative agreement with the multifractal spectra of the critical NVEV.

LATTICE DYNAMICS OF THE BINARY APERIODIC CHAINS OF ATOMS II: MULTIFRACTALITY OF PHONON SPECTRA

1995 ◽  
Vol 09 (12) ◽  
pp. 1453-1474 ◽  
Author(s):  
WŁODZIMIERZ SALEJDA
Keyword(s):  
Lattice Dynamics ◽  
Energy Spectra ◽  
Legendre Transformation ◽  
Model Parameters ◽  
Local Scaling ◽  
Multifractal Formalism ◽  
Phonon Spectra ◽  
Wide Range ◽  
Multifractal Spectra ◽  
Density Of Phonon States

The curdling of the phonon eigenvalues (PEV) on energy spectra of the binary generalized Fibonacci and non-Fibonaccian chains of atoms are numerically studied. A multifractal formalism based upon a new numerically efficient Legendre transformation from (q, τ) to (α, f) variables is proposed. The multifractal spectra of the normalized integrated density of phonon states (NIDOPS) for aperiodic chains of atoms are calculated in a wide range of model parameters. It is found out that the interval (α min , α max ) of magnitudes of the exponent α, determining the local scaling of the NIDOPS, shows a considerable shift to smaller values. This tendency is most pronounced for the NIDOPS of the so-called copper-mean, nickel-mean, structural circle and Rudin-Shapiro chain, where 0<α min <0.1. It is verified numerically that this effect is a manifestation of a strong curdling of PEV which take place in optical regions of the phonon spectra.

Model of vortex flow of charge in a vessel with turbine impeller

1987 ◽  
Vol 52 (8) ◽  
pp. 1888-1904
Author(s):  
Miloslav Hošťálek ◽  
Ivan Fořt
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Theoretical Data ◽  
Eddy Diffusion ◽  
Quantitative Agreement ◽  
Creeping Flow ◽  
Model Parameters ◽  
Mean Flow ◽  
Two Dimensional Flow ◽  
Vorticity Transport

A theoretical model is described of the mean two-dimensional flow of homogeneous charge in a flat-bottomed cylindrical tank with radial baffles and six-blade turbine disc impeller. The model starts from the concept of vorticity transport in the bulk of vortex liquid flow through the mechanism of eddy diffusion characterized by a constant value of turbulent (eddy) viscosity. The result of solution of the equation which is analogous to the Stokes simplification of equations of motion for creeping flow is the description of field of the stream function and of the axial and radial velocity components of mean flow in the whole charge. The results of modelling are compared with the experimental and theoretical data published by different authors, a good qualitative and quantitative agreement being stated. Advantage of the model proposed is a very simple schematization of the system volume necessary to introduce the boundary conditions (only the parts above the impeller plane of symmetry and below it are distinguished), the explicit character of the model with respect to the model parameters (model lucidity, low demands on the capacity of computer), and, in the end, the possibility to modify the given model by changing boundary conditions even for another agitating set-up with radially-axial character of flow.

LATTICE DYNAMICS OF THE BINARY APERIODIC CHAINS OF ATOMS I: FRACTAL DIMENSION OF PHONON SPECTRA

1995 ◽  
Vol 09 (12) ◽  
pp. 1429-1451 ◽  
Author(s):  
WŁODZIMIERZ SALEJDA
Keyword(s):  
Fractal Dimension ◽  
Lattice Dynamics ◽  
Nearest Neighbor ◽  
Average Distance ◽  
Local Maximum ◽  
Fractal Dimensions ◽  
Dimension Formula ◽  
Phonon Spectra ◽  
Wide Range ◽  
Silver Mean

The microscopic harmonic model of lattice dynamics of the binary chains of atoms is formulated and studied numerically. The dependence of spring constants of the nearest-neighbor (NN) interactions on the average distance between atoms are taken into account. The covering fractal dimensions [Formula: see text] of the Cantor-set-like phonon spec-tra (PS) of generalized Fibonacci and non-Fibonaccian aperiodic chains containing of 16384≤N≤33461 atoms are determined numerically. The dependence of [Formula: see text] on the strength Q of NN interactions and on R=mH/mL, where mH and mL denotes the mass of heavy and light atoms, respectively, are calculated for a wide range of Q and R. In particular we found: (1) The fractal dimension [Formula: see text] of the PS for the so-called goldenmean, silver-mean, bronze-mean, dodecagonal and Severin chain shows a local maximum at increasing magnitude of Q and R>1; (2) At sufficiently large Q we observe power-like diminishing of [Formula: see text] i.e. [Formula: see text], where α=−0.14±0.02 and α=−0.10±0.02 for the above specified chains and so-called octagonal, copper-mean, nickel-mean, Thue-Morse, Rudin-Shapiro chain, respectively.

Computer Simulation of a Press Feed Mechanism and Experimental Confirmation

1994 ◽  
Vol 116 (1) ◽  
pp. 248-256 ◽  
Author(s):  
C. Chassapis ◽  
G. G. Lowen
Keyword(s):  
Computer Simulation ◽  
Data Acquisition System ◽  
Quantitative Agreement ◽  
Drive Shaft ◽  
Strain Gages ◽  
Motion Equations ◽  
Qualitative And Quantitative ◽  
Bending Strain ◽  
Out Of Plane ◽  
Set Up

An experimentally verified simulation of the elastic-dynamic behavior of a lever-type feed mechanism is presented. Based on a combination of experimental and analytical findings, simplified motion equations could be introduced. In the experimental set-up, the motion of the mechanism is monitored by three angular encoders, which are attached to the drive shaft, the rocker-link shaft, and the feed roller shaft, respectively. Their output, which is stored in a specially designed data acquisition system, allows the correlation of the instantaneous rotations of the feed roller and the rocker shafts to that of the drive shaft. Strain gages provide in and out-of-plane bending-strain histories of the bent coupler. Experiment and theory, for different loading conditions, are correlated by way of the coupler strain, the clutch windup angle and the total feed length. Good qualitative and quantitative agreement between computed and experimental results was found.

CFD Study of an Autonomous Submarine in Extraterrestrial Seas

2017 ◽  
Author(s):  
S. Carberry Mogan ◽  
P. Sawicki ◽  
C. J. Bernardo ◽  
D. Chen ◽  
I. Sahin ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Computational Study ◽  
Liquid Hydrocarbon ◽  
Quantitative Agreement ◽  
Near Surface ◽  
Surface Conditions ◽  
Qualitative And Quantitative

A computational study is conducted to evaluate the performance of an extraterrestrial submarine operating in the liquid hydrocarbon seas of Saturn’s largest moon, Titan. To simulate the flow around the submarine and offer a prediction for thrust and power requirements, Computational Fluid Dynamics tools, ANSYS© FLUENT© and DualSPHysics, are utilized for the deeply submerged and near-surface conditions, respectively. Several operational scenarios are investigated and comparisons are made with other available results with a good qualitative and quantitative agreement.

Experiments on strong interactions between solitary waves

1978 ◽  
Vol 85 (3) ◽  
pp. 417-431 ◽  
Author(s):  
P. D. Weidman ◽  
T. Maxworthy
Keyword(s):  
Shallow Water ◽  
Solitary Waves ◽  
Water Waves ◽  
Vries Equation ◽  
Rectangular Channel ◽  
Quantitative Agreement ◽  
Strong Interactions ◽  
Shallow Water Waves ◽  
Qualitative And Quantitative ◽  
The Waves

Experiments on the interaction between solitary shallow-water waves propagating in the same direction have been performed in a rectangular channel. Two methods were devised to compensate for the dissipation of the waves in order to compare results with Hirota's (1971) solution for the collision of solitons described by the Kortewegde Vries equation. Both qualitative and quantitative agreement with theory is obtained using the proposed corrections for wave damping.

Qualitative and Quantitative Analysis of Stacking Disorder in α-and β-SiC by X-ray Diffraction and Structure Modeling

1995 ◽  
Vol 410 ◽  
Author(s):  
Bogdan Palosz ◽  
Svetlana Stel'makh ◽  
Stanislaw Gierlotka
Keyword(s):  
Quantitative Analysis ◽  
Model Parameters ◽  
Qualitative And Quantitative Analysis ◽  
X Ray Diffraction ◽  
X Ray ◽  
Qualitative And Quantitative ◽  
Poisson Function ◽  
Diffraction Patterns ◽  
Computer Generation ◽  
Stacking Disorder

ABSTRACTA method of analysis of disordering in α- and β-SiC polycrystals by numerical modeling, and a simulation of X-ray diffraction profiles are presented. The diffraction patterns of nonperiodic structures were simulated for models of 2000 layer fragments of the structure. Computer generation of the models was based on the Poisson function describing the size distribution of the domains of basic polytypes and faults. The models were quantified by a set of input probability parameters describing relative frequencies of the occurrence of the domains of polytypes and faults. Implementation of a correlation parameter that characterizes coherence of sequential domains of a given polytype assures a good reproducibility of the simulated diffraction profiles obtained for the same set of the model parameters. Based on this method, a quantitative analysis of disordering in polycrystals of SiC annealed in the temperature range 1100–2200 °C was performed.

Phonon spectra of ortho -dinitrotetramethylbenzene crystals

1987 ◽  
Vol 65 (9) ◽  
pp. 2122-2125 ◽  
Author(s):  
Paolo Sgarabotto ◽  
Mario Braghetti ◽  
Rosario Sergio Cataliotti ◽  
Giulio Paliani ◽  
Salvatore Sorriso ◽  
...  
Keyword(s):  
Group Theory ◽  
Phase Transitions ◽  
Solid State ◽  
Melting Point ◽  
Nitro Group ◽  
Vibrational Spectra ◽  
Lattice Dynamics ◽  
Solid Phase ◽  
Methyl Group ◽  
Phonon Spectra

We have studied the vibrational spectra and thermal behaviour of ortho-dinitrotetramethylbenzene (o-DNTMB) to learn more about its molecular and lattice dynamics. The molecule undergoes two solid–solid phase transitions, close to the melting point, which could be explained by the relaxation of forces hindering the methyl-group and nitro-group free rotations. We have deduced the nature of the solid state vibrational motions, particularly those of lattice phonons, using group theory.

Raman phonon spectra and lattice dynamics of 7-methoxycoumarin under pressure

1995 ◽  
Vol 246 (6) ◽  
pp. 619-625
Author(s):  
A. Brillante ◽  
R.G. Della Valle ◽  
E. Venuti
Keyword(s):  
Lattice Dynamics ◽  
Phonon Spectra
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