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.

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 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.

NUMERICAL STUDIES ON THE VIBRATIONAL SPECTRUM OF FIBONACCI CHAIN: A MULTIFRACTAL ANALYSIS

1991 ◽  
Vol 05 (05) ◽  
pp. 825-841 ◽  
Author(s):  
WLODZIMIERZ SALEJDA
Keyword(s):  
Vibrational Spectrum ◽  
Multifractal Analysis ◽  
Scaling Laws ◽  
Model Parameters ◽  
Local Scaling ◽  
One Dimensional ◽  
Dynamic Matrix ◽  
Numerical Studies ◽  
Wide Range ◽  
The One

A harmonic Hamiltonian modelling the lattice dynamics of the one-dimensional Fibonacci-type quasicrystal is studied numerically. The multifractal analysis of vibrational spectrum is performed. It is found that the integrated normalized density of states [Formula: see text], where x denotes the square of the eigenenergy of the dynamic matrix, exhibits a finite range of scaling indices α (i.e. α min ≤α≤ α max ) describing the local scaling laws of [Formula: see text]. The α-f spectra and the Renyi dimensions [Formula: see text] are calculated in a wide range of model parameters taking into account the next-nearest-neighbour (NNN) interactions of atoms. In particular, we have observed that: (1) The α-f spectra are smooth in the interval [Formula: see text]; (2) If the so-called parameter of quasi-periodicity Q increases, then αmin and the fractal dimension of vibrational spectra [Formula: see text] decrease; (3) If the strength of NNN interactions h grows then α min decreases but D increases.

scholarly journals Inferring Linkage Disequilibrium Between a Polymorphic Marker Locus and a Trait Locus in Natural Populations

Genetics ◽  
2000 ◽  
Vol 156 (1) ◽  
pp. 457-467 ◽  
Author(s):  
Z W Luo ◽  
S H Tao ◽  
Z-B Zeng
Keyword(s):  
Linkage Disequilibrium ◽  
Allele Frequency ◽  
Random Mating ◽  
Natural Populations ◽  
Polymorphic Marker ◽  
Marker Locus ◽  
Model Parameters ◽  
Phenotypic Variance ◽  
Wide Range ◽  
Trait Locus

Abstract Three approaches are proposed in this study for detecting or estimating linkage disequilibrium between a polymorphic marker locus and a locus affecting quantitative genetic variation using the sample from random mating populations. It is shown that the disequilibrium over a wide range of circumstances may be detected with a power of 80% by using phenotypic records and marker genotypes of a few hundred individuals. Comparison of ANOVA and regression methods in this article to the transmission disequilibrium test (TDT) shows that, given the genetic variance explained by the trait locus, the power of TDT depends on the trait allele frequency, whereas the power of ANOVA and regression analyses is relatively independent from the allelic frequency. The TDT method is more powerful when the trait allele frequency is low, but much less powerful when it is high. The likelihood analysis provides reliable estimation of the model parameters when the QTL variance is at least 10% of the phenotypic variance and the sample size of a few hundred is used. Potential use of these estimates in mapping the trait locus is also discussed.

scholarly journals Antifungal Activity of Propyl Disulfide from Neem (Azadirachta indica) in Vapor and Agar Diffusion Assays against Anthracnose Pathogens (Colletotrichum gloeosporioides and Colletotrichum acutatum) in Mango Fruit

2021 ◽  
Vol 9 (4) ◽  
pp. 839
Author(s):  
Muhammad Rafiullah Khan ◽  
Vanee Chonhenchob ◽  
Chongxing Huang ◽  
Panitee Suwanamornlert
Keyword(s):  
Antifungal Activity ◽  
Mycelial Growth ◽  
Colletotrichum Gloeosporioides ◽  
Colletotrichum Acutatum ◽  
Model Parameters ◽  
Pathogenicity Test ◽  
Agar Diffusion ◽  
Wide Range ◽  
Significant Difference ◽  
Diffusion Assay

Microorganisms causing anthracnose diseases have a medium to a high level of resistance to the existing fungicides. This study aimed to investigate neem plant extract (propyl disulfide, PD) as an alternative to the current fungicides against mango’s anthracnose. Microorganisms were isolated from decayed mango and identified as Colletotrichum gloeosporioides and Colletotrichum acutatum. Next, a pathogenicity test was conducted and after fulfilling Koch’s postulates, fungi were reisolated from these symptomatic fruits and we thus obtained pure cultures. Then, different concentrations of PD were used against these fungi in vapor and agar diffusion assays. Ethanol and distilled water were served as control treatments. PD significantly (p ≤ 0.05) inhibited more of the mycelial growth of these fungi than both controls. The antifungal activity of PD increased with increasing concentrations. The vapor diffusion assay was more effective in inhibiting the mycelial growth of these fungi than the agar diffusion assay. A good fit (R2, 0.950) of the experimental data in the Gompertz growth model and a significant difference in the model parameters, i.e., lag phase (λ), stationary phase (A) and mycelial growth rate, further showed the antifungal efficacy of PD. Therefore, PD could be the best antimicrobial compound against a wide range of microorganisms.

scholarly journals A Reinforcement Learning Framework for Spiking Networks with Dynamic Synapses

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Karim El-Laithy ◽  
Martin Bogdan
Keyword(s):  
Reinforcement Learning ◽  
Spike Timing ◽  
Neural Representation ◽  
Model Parameters ◽  
Learning Framework ◽  
Reference Target ◽  
Wide Range ◽  
Spiking Network ◽  
Dynamic Synapses ◽  
Exclusive Or

An integration of both the Hebbian-based and reinforcement learning (RL) rules is presented for dynamic synapses. The proposed framework permits the Hebbian rule to update the hidden synaptic model parameters regulating the synaptic response rather than the synaptic weights. This is performed using both the value and the sign of the temporal difference in the reward signal after each trial. Applying this framework, a spiking network with spike-timing-dependent synapses is tested to learn the exclusive-OR computation on a temporally coded basis. Reward values are calculated with the distance between the output spike train of the network and a reference target one. Results show that the network is able to capture the required dynamics and that the proposed framework can reveal indeed an integrated version of Hebbian and RL. The proposed framework is tractable and less computationally expensive. The framework is applicable to a wide class of synaptic models and is not restricted to the used neural representation. This generality, along with the reported results, supports adopting the introduced approach to benefit from the biologically plausible synaptic models in a wide range of intuitive signal processing.

scholarly journals Modelling the Inflation and Elastic Instabilities of Rubber-Like Spherical and Cylindrical Shells Using a New Generalised Neo-Hookean Strain Energy Function

2021 ◽  
Author(s):  
Afshin Anssari-Benam ◽  
Andrea Bucchi ◽  
Giuseppe Saccomandi
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Limit Point ◽  
Strain Energy ◽  
Cylindrical Shells ◽  
Strain Energy Function ◽  
Model Parameters ◽  
Wide Range ◽  
Cylindrical Tubes ◽  
Gent Model

AbstractThe application of a newly proposed generalised neo-Hookean strain energy function to the inflation of incompressible rubber-like spherical and cylindrical shells is demonstrated in this paper. The pressure ($P$ P ) – inflation ($\lambda $ λ or $v$ v ) relationships are derived and presented for four shells: thin- and thick-walled spherical balloons, and thin- and thick-walled cylindrical tubes. Characteristics of the inflation curves predicted by the model for the four considered shells are analysed and the critical values of the model parameters for exhibiting the limit-point instability are established. The application of the model to extant experimental datasets procured from studies across 19th to 21st century will be demonstrated, showing favourable agreement between the model and the experimental data. The capability of the model to capture the two characteristic instability phenomena in the inflation of rubber-like materials, namely the limit-point and inflation-jump instabilities, will be made evident from both the theoretical analysis and curve-fitting approaches presented in this study. A comparison with the predictions of the Gent model for the considered data is also demonstrated and is shown that our presented model provides improved fits. Given the simplicity of the model, its ability to fit a wide range of experimental data and capture both limit-point and inflation-jump instabilities, we propose the application of our model to the inflation of rubber-like materials.

scholarly journals Study on Friction in Automotive Shock Absorbers Part 1: Friction Simulation Using a Dynamic Friction Model in the Contact Zone of an FEM Model

Vehicles ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 212-232
Author(s):  
Ludwig Herzog ◽  
Klaus Augsburg
Keyword(s):  
Ride Comfort ◽  
Viscous Friction ◽  
Simulation Method ◽  
Friction Model ◽  
Model Parameters ◽  
Dynamic Friction ◽  
Friction Modeling ◽  
Shock Absorbers ◽  
Operation Conditions ◽  
Wide Range

The important change in the transition from partial to high automation is that a vehicle can drive autonomously, without active human involvement. This fact increases the current requirements regarding ride comfort and dictates new challenges for automotive shock absorbers. There exist two common types of automotive shock absorber with two friction types: The intended viscous friction dissipates the chassis vibrations, while the unwanted solid body friction is generated by the rubbing of the damper’s seals and guides during actuation. The latter so-called static friction impairs ride comfort and demands appropriate friction modeling for the control of adaptive or active suspension systems. In this article, a simulation approach is introduced to model damper friction based on the most friction-relevant parameters. Since damper friction is highly dependent on geometry, which can vary widely, three-dimensional (3D) structural FEM is used to determine the deformations of the damper parts resulting from mounting and varying operation conditions. In the respective contact zones, a dynamic friction model is applied and parameterized based on the single friction point measurements. Subsequent to the parameterization of the overall friction model with geometry data, operation conditions, material properties and friction model parameters, single friction point simulations are performed, analyzed and validated against single friction point measurements. It is shown that this simulation method allows for friction prediction with high accuracy. Consequently, its application enables a wide range of parameters relevant to damper friction to be investigated with significantly increased development efficiency.

Coupled Thermo-Hydro-Geochemical Models of Engineered Barrier Systems: The Febex Project

2000 ◽  
Vol 663 ◽  
Author(s):  
J. Samper ◽  
R. Juncosa ◽  
V. Navarro ◽  
J. Delgado ◽  
L. Montenegro ◽  
...  
Keyword(s):  
Large Scale ◽  
Reference Model ◽  
Numerical Models ◽  
Full Scale ◽  
Small Scale ◽  
Model Parameters ◽  
In Situ Test ◽  
Wide Range ◽  
Engineered Barrier

ABSTRACTFEBEX (Full-scale Engineered Barrier EXperiment) is a demonstration and research project dealing with the bentonite engineered barrier designed for sealing and containment of waste in a high level radioactive waste repository (HLWR). It includes two main experiments: an situ full-scale test performed at Grimsel (GTS) and a mock-up test operating since February 1997 at CIEMAT facilities in Madrid (Spain) [1,2,3]. One of the objectives of FEBEX is the development and testing of conceptual and numerical models for the thermal, hydrodynamic, and geochemical (THG) processes expected to take place in engineered clay barriers. A significant improvement in coupled THG modeling of the clay barrier has been achieved both in terms of a better understanding of THG processes and more sophisticated THG computer codes. The ability of these models to reproduce the observed THG patterns in a wide range of THG conditions enhances the confidence in their prediction capabilities. Numerical THG models of heating and hydration experiments performed on small-scale lab cells provide excellent results for temperatures, water inflow and final water content in the cells [3]. Calculated concentrations at the end of the experiments reproduce most of the patterns of measured data. In general, the fit of concentrations of dissolved species is better than that of exchanged cations. These models were later used to simulate the evolution of the large-scale experiments (in situ and mock-up). Some thermo-hydrodynamic hypotheses and bentonite parameters were slightly revised during TH calibration of the mock-up test. The results of the reference model reproduce simultaneously the observed water inflows and bentonite temperatures and relative humidities. Although the model is highly sensitive to one-at-a-time variations in model parameters, the possibility of parameter combinations leading to similar fits cannot be precluded. The TH model of the “in situ” test is based on the same bentonite TH parameters and assumptions as for the “mock-up” test. Granite parameters were slightly modified during the calibration process in order to reproduce the observed thermal and hydrodynamic evolution. The reference model captures properly relative humidities and temperatures in the bentonite [3]. It also reproduces the observed spatial distribution of water pressures and temperatures in the granite. Once calibrated the TH aspects of the model, predictions of the THG evolution of both tests were performed. Data from the dismantling of the in situ test, which is planned for the summer of 2001, will provide a unique opportunity to test and validate current THG models of the EBS.

Comparing different block propagation modelling approaches using the Platrock simulation platform 

2021 ◽  
Author(s):  
Vincent Acary ◽  
Franck Bourrier ◽  
David Toe ◽  
Francois Kneib
Keyword(s):  
Expert Knowledge ◽  
Material Point ◽  
Model Parameters ◽  
Propagation Models ◽  
Rockfall Hazard ◽  
Wide Range ◽  
Natural Terrain ◽  
Block Propagation ◽  
Propagation Modelling ◽  
Modelling Approaches

&lt;p&gt;&lt;br&gt;Block propagation models are routinely used for the quantitative assessment of rockfall hazard. In these models, one of the major di&amp;#64259;culties is the development of physically consistent and &amp;#64257;eld applicable approaches to model the interaction between the block and the natural terrain. For most of propagation models, a thorough calibration of the input parameters is not available over the wide range of configurations encountered in practice. Consequently, the parameters choice is strongly depending on expert knowledge. In addition, most of models exhibit substantial sensitivity to some parameters, i.e. small changes of these parameters entail large differences in the simulation results.&lt;/p&gt;&lt;p&gt;The trajectory analysis platform Platrock, freely available upon request (contact: [email protected]), allows performing 2D and 3D simulations using both material point rebound models and models, based on non-smooth mechanics, that explicitly account for block shape. This platform provides several simulation tools for detailed analyses of block propagation on study sites.&lt;/p&gt;&lt;p&gt;The possibilities of the predictive capabilities of different block propagation modelling approaches integrated into the Platrock platform have been assessed on a well-documented study site, where a benchmark of propagation models has been done in the context of C2ROP research project. This analysis emphasized the capacities of trajectory analyses to traduce block propagation but also demonstrated their substantial sensitivity to model parameters. The results from these simulations cannot be relevantly interpreted if they are not accompanied with calibration proofs, sensitivity analysis, and detailed interpretation of the results from the expert in charge of the study.&lt;/p&gt;

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