Localization of Vibration Propagation in Two-Dimensional Systems With Multiple Substructural Modes

2003 ◽  
Vol 70 (1) ◽  
pp. 119-128
Author(s):  
W.-C. Xie
Keyword(s):  
Two Dimensional ◽  
Regular Perturbation ◽  
Matrix Formulation ◽  
One Dimensional ◽  
Weakly Coupled ◽  
Exponential Rates ◽  
Rates Of Growth ◽  
The Given ◽  
Localization Behavior ◽  
Localization Of Vibration

Localization of vibration propagation in randomly disordered weakly coupled two-dimensional cantilever-mesh-spring arrays, in which multiple substructural modes are considered for each cantilever, is studied in this paper. A method of regular perturbation for a linear algebraic system is applied to determine the localization factors, which are defined in terms of the angles of orientation and characterize the average exponential rates of growth or decay of the amplitudes of vibration in the given directions. Iterative formulations are derived to determine the amplitudes of vibration of the cantilevers. In the diagonal directions, a transfer matrix formulation is obtained. For a given direction of orientation, the localization behavior is similar to that of a one-dimensional cantilever-spring-mesh chain. The effect of the stiffnesses and the disorder in the stiffnesses of the cantilevers on the localization behavior of the system is investigated.

Vibration Mode Localization in Randomly Disordered Weakly Coupled Two-Dimensional Systems

1997 ◽  
Author(s):  
Wei-Chau Xie
Keyword(s):  
Eigenvalue Problems ◽  
Vibration Mode ◽  
Numerical Approach ◽  
Logarithmic Scale ◽  
Two Dimensional ◽  
Regular Perturbation ◽  
Mode Localization ◽  
Weakly Coupled ◽  
Exponential Rates ◽  
Rates Of Decay

Abstract In this paper, a general method of regular perturbation for linear eigenvalue problems is presented, in which the orders of perturbation terms are extended to infinity. The method of regular perturbation is applied to study vibration mode localization in randomly disordered weakly coupled two-dimensional cantilever-spring arrays. Localization factors, which characterize the average exponential rates of decay or growth of the amplitudes of vibration, are defined in terms of the angles of orientation. First-order approximate results of the localization factors are obtained using a combined analytical-numerical approach. For the systems under consideration, the direction in which vibration is originated corresponds to the smallest localization factor; whereas the “diagonal” directions correspond to the largest rate of decay or growth of the amplitudes of vibration. When plotted in the logarithmic scale, the vibration modes are of a hill shape with the amplitudes of vibration decaying linearly away from the cantilever at which vibration is originated.

scholarly journals Three Spirostanol Glycosides from the Seeds of Hyoscyamus Niger L.

2006 ◽  
Vol 1 (1) ◽  
pp. 100-103
Author(s):  
Irina Lunga ◽  
Pavel Kintia ◽  
Stepan Shvets ◽  
Carla Bassarelo ◽  
Cosimo Pizza ◽  
...  
Keyword(s):  
Spectroscopic Methods ◽  
Two Dimensional ◽  
Hyoscyamus Niger ◽  
One Dimensional ◽  
Steroidal Glycosides ◽  
Ms Analysis ◽  
The Given ◽  
First Time ◽  
Chemical Evidence

Three steroidal glycosides of spirostane series have been isolated from the seeds of Hyoscyamus niger L.(Solanaceae). Their structures were determined on the basis of chemical evidence and extensive spectroscopic methods including one-dimensional, two-dimensional NMR and MS analysis. In the genus Hyoscyamus the given compounds have been found out for the first time.

scholarly journals Two-Dimensional Electronic Transport in Rubrene: The Impact of Inter-Chain Coupling

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 233 ◽  
Author(s):  
Ahmed Missaoui ◽  
Jouda Khabthani ◽  
Guy Trambly de Laissardière ◽  
Didier Mayou
Keyword(s):  
Transport Properties ◽  
Electronic Transport ◽  
Ac Conductivity ◽  
Electronic Devices ◽  
Tight Binding ◽  
Two Dimensional ◽  
One Dimensional ◽  
Weakly Coupled ◽  
The Impact ◽  
1D Chains

Organic semi-conductors have unique electronic properties and are important systems both at the fundamental level and also for their applications in electronic devices. In this article we focus on the particular case of rubrene which has one of the best electronic transport properties for application purposes. We show that this system can be well simulated by simple tight-binding systems representing one-dimensional (1D) chains that are weakly coupled to their neighboring chains in the same plane. This makes in principle this rubrene system somehow intermediate between 1D and isotropic 2D models. We analyse in detail the dc-transport and terahertz conductivity in the 1D and in the anisotropic 2D models. The transient localisation scenario allows us to reproduce satisfactorily some basics results such as mobility anisotropy and orders of magnitude as well as ac-conductivity in the terahertz range. This model shows in particular that even a weak inter-chain coupling is able to improve notably the propagation along the chains. This suggest also that a strong inter-chain coupling is important to get organic semi-conductors with the best possible transport properties for applicative purposes.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

The Convex Polytopes and Homogeneous Coordinate Rings of Bivariate Polynomials

2019 ◽  
Vol 16 (2) ◽  
pp. 1
Author(s):  
Shamsatun Nahar Ahmad ◽  
Nor’Aini Aris ◽  
Azlina Jumadi
Keyword(s):  
Convex Polytopes ◽  
Polynomial Systems ◽  
Matrix Formulation ◽  
Bivariate Polynomials ◽  
Homogeneous Coordinates ◽  
The Matrix ◽  
Projective Vector ◽  
Coordinate Rings ◽  
Resultant Matrix ◽  
The Given

Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of a certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven.

State-of-the-Art of Modeling Surface Water Impoundments

1982 ◽  
Vol 14 (1-2) ◽  
pp. 241-261 ◽  
Author(s):  
P A Krenkel ◽  
R H French
Keyword(s):  
Water Quality ◽  
Surface Water ◽  
State Of The Art ◽  
Rate Coefficients ◽  
Two Dimensional ◽  
One Dimensional ◽  
Integral Energy ◽  
Range Of Values ◽  
Dimensional Integral ◽  
Water Impoundment

The state-of-the-art of surface water impoundment modeling is examined from the viewpoints of both hydrodynamics and water quality. In the area of hydrodynamics current one dimensional integral energy and two dimensional models are discussed. In the area of water quality, the formulations used for various parameters are presented with a range of values for the associated rate coefficients.

The formation of gas hydrates under shock wave impact on the bubble media (two-dimensional case)

2010 ◽  
Vol 7 ◽  
pp. 90-97
Author(s):  
M.N. Galimzianov ◽  
I.A. Chiglintsev ◽  
U.O. Agisheva ◽  
V.A. Buzina
Keyword(s):  
Shock Wave ◽  
Gas Hydrates ◽  
Hydrate Formation ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Wave Impact ◽  
Bubble Liquid ◽  
One Dimensional ◽  
Bubble Media ◽  
Main Factors

Formation of gas hydrates under shock wave impact on bubble media (two-dimensional case) The dynamics of plane one-dimensional shock waves applied to the available experimental data for the water–freon media is studied on the base of the theoretical model of the bubble liquid improved with taking into account possible hydrate formation. The scheme of accounting of the bubble crushing in a shock wave that is one of the main factors in the hydrate formation intensification with increasing shock wave amplitude is proposed.

Modifications of the Godunov method for computing disturbance propagation in an elastic body

2016 ◽  
Vol 11 (1) ◽  
pp. 119-126 ◽  
Author(s):  
A.A. Aganin ◽  
N.A. Khismatullina
Keyword(s):  
Elastic Body ◽  
Godunov Method ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Order Accuracy ◽  
One Dimensional ◽  
Disturbance Propagation ◽  
Linear Waves ◽  
Longitudinal And Shear Waves ◽  
Contact Discontinuities

Numerical investigation of efficiency of UNO- and TVD-modifications of the Godunov method of the second order accuracy for computation of linear waves in an elastic body in comparison with the classical Godunov method is carried out. To this end, one-dimensional cylindrical Riemann problems are considered. It is shown that the both modifications are considerably more accurate in describing radially converging as well as diverging longitudinal and shear waves and contact discontinuities both in one- and two-dimensional problem statements. At that the UNO-modification is more preferable than the TVD-modification because exact implementation of the TVD property in the TVD-modification is reached at the expense of “cutting” solution extrema.

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