Analytical expressions for the permeability of random two-dimensional Poisson fracture networks based on lattice percolation and equivalent media theories

1991 ◽  
Vol 28 (5) ◽  
pp. 280
Keyword(s):  
Two Dimensional ◽  
Fracture Networks ◽  
Analytical Expressions

CALCULATION OF THE DEPENDENCE OF THE DISTANCE TO THE LOCATED OBJECT FROM THE CORNER POSITION OF THE VEHICLE LINE

2018 ◽  
pp. 14-18
Author(s):  
V. V. Artyushenko ◽  
A. V. Nikulin
Keyword(s):  
Real Time ◽  
Statistical Physics ◽  
Angular Position ◽  
Three Dimensional ◽  
Line Of Sight ◽  
Two Dimensional ◽  
Radar Station ◽  
Flight Mode ◽  
Vector Algebra ◽  
Analytical Expressions

To simulate echoes from the earth’s surface in the low flight mode, it is necessary to reproduce reliably the delayed reflected sounding signal of the radar in real time. For this, it is necessary to be able to calculate accurately and quickly the dependence of the distance to the object being measured from the angular position of the line of sight of the radar station. Obviously, the simplest expressions for calculating the range can be obtained for a segment or a plane. In the text of the article, analytical expressions for the calculation of range for two-dimensional and three-dimensional cases are obtained. Methods of statistical physics, vector algebra, and the theory of the radar of extended objects were used. Since the calculation of the dependence of the range of the object to the target from the angular position of the line of sight is carried out on the analytical expressions found in the paper, the result obtained is accurate, and due to the relative simplicity of the expressions obtained, the calculation does not require much time.

scholarly journals Dielectric Function of a Quantum-Confined Thin Film with a Modified Pöschel–Teller Potential

2018 ◽  
Vol 63 (12) ◽  
pp. 1109 ◽  
Author(s):  
Kh. A. Gasanov ◽  
J. I. Guseinov ◽  
I. I. Abbasov ◽  
F. I. Mamedov ◽  
D. J. Askerov
Keyword(s):  
Dielectric Permittivity ◽  
Electron Gas ◽  
Two Dimensional ◽  
Quantum Nanostructures ◽  
Carrier Scattering ◽  
Scattering Potential ◽  
Quantum Confined ◽  
Charge Carrier Scattering ◽  
First Time ◽  
Analytical Expressions

The spatial and time dispersions of the dielectric permittivity of an electron gas in quasi-two-dimensional quantum nanostructures are studied. The screening of the charge-carrier scattering potential in a quantum-confined film with a modified P¨oschel–Teller potential is considered for the first time. Analytical expressions for the dielectric permittivity are obtained.

scholarly journals Frequency-Dependent Tensile and Compressive Effective Moduli of Elastic Solids With Randomly Distributed Two-Dimensional Microcracks

2015 ◽  
Vol 82 (8) ◽  
Author(s):  
Youxuan Zhao ◽  
Yanjun Qiu ◽  
Laurence J. Jacobs ◽  
Jianmin Qu
Keyword(s):  
Wave Attenuation ◽  
Two Dimensional ◽  
Effective Moduli ◽  
The Finite Element Method ◽  
Elastic Solids ◽  
Frequency Dependent ◽  
Micromechanics Models ◽  
Dynamic Case ◽  
Crack Faces ◽  
Analytical Expressions

This paper develops micromechanics models to estimate the tensile and compressive elastic moduli of elastic solids containing randomly distributed two-dimensional microcracks. The crack faces are open under tension and closed under compression. When the crack faces are closed, they may slide against one another following the Coulomb's law of dry friction. The micromechanics models provide analytical expressions of the tensile and compressive moduli for both static and dynamic cases. It is found that the tensile and compressive moduli are different. Further, under dynamic loading, the compressive and tensile moduli are both frequency dependent. As a by-product, the micromechanics models also predict wave attenuation in the dynamic case. Numerical simulations using the finite element method (FEM) are conducted to validate the micromechanics models.

UNBOUNDED SETS OF ATTRACTION

2000 ◽  
Vol 10 (06) ◽  
pp. 1437-1469 ◽  
Author(s):  
GIAN-ITALO BISCHI ◽  
CHRISTIAN MIRA ◽  
LAURA GARDINI
Keyword(s):  
Functional Equation ◽  
Two Dimensional ◽  
Elementary Functions ◽  
Theoretical Methods ◽  
One Dimensional ◽  
Zero Measure ◽  
Analytical Expressions

In this paper we show that unbounded chaotic trajectories are easily observed in the iteration of maps which are not defined everywhere, due to the presence of a denominator which vanishes in a zero-measure set. Through simple examples, obtained by the iteration of one-dimensional and two-dimensional maps with denominator, the basic mechanisms which are at the basis of the existence of unbounded chaotic trajectories are explained. Moreover, new kinds of contact bifurcations, which mark the transition from bounded to unbounded sets of attraction, are studied both through the examples and by general theoretical methods. Some of the maps studied in this paper have been obtained by a method based on the Schröoder functional equation, which allows one to write closed analytical expressions of the unbounded chaotic trajectories, in terms of elementary functions.

Field Computation for Two-Dimensional Array Transducers with Limited Diffraction Array Beams

2005 ◽  
Vol 27 (4) ◽  
pp. 237-255 ◽  
Author(s):  
Jian-Yu Lu ◽  
Jiqi Cheng
Keyword(s):  
Continuous Wave ◽  
Weighting Function ◽  
Near Field ◽  
Bessel Beam ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Computationally Efficient ◽  
Annular Array ◽  
Array Transducer ◽  
Analytical Expressions

A method is developed for calculating fields produced with a two-dimensional (2D) array transducer. This method decomposes an arbitrary 2D aperture weighting function into a set of limited diffraction array beams. Using the analytical expressions of limited diffraction beams, arbitrary continuous wave (cw) or pulse wave (pw) fields of 2D arrays can be obtained with a simple superposition of these beams. In addition, this method can be simplified and applied to a 1D array transducer of a finite or infinite elevation height. For beams produced with axially symmetric aperture weighting functions, this method can be reduced to the Fourier-Bessel method studied previously where an annular array transducer can be used. The advantage of the method is that it is accurate and computationally efficient, especially in regions that are not far from the surface of the transducer (near field), where it is important for medical imaging. Both computer simulations and a synthetic array experiment are carried out to verify the method. Results (Bessel beam, focused Gaussian beam, X wave and asymmetric array beams) show that the method is accurate as compared to that using the Rayleigh-Sommerfeld diffraction formula and agrees well with the experiment.

scholarly journals Capacity of Inhomogeneous Hybrid Wireless Networks in Three-Dimensional Space

2015 ◽  
Vol 11 (9) ◽  
pp. 47
Author(s):  
Feng Wu ◽  
Jiang Zhu ◽  
Yilong Tian ◽  
Zhipeng Xi
Keyword(s):  
Sensor Node ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Network Capacity ◽  
Throughput Capacity ◽  
Two Dimensional ◽  
Hybrid Wireless Networks ◽  
Node Distribution ◽  
Analytical Expressions ◽  
Three Dimensional Space

Network capacity has been widely studied in recent years. However, most of the literatures focus on the networks where nodes are distributed in a two-dimensional space. In this paper, we propose a 3D hybrid sensor network model. By setting different sensor node distribution probabilities for cells, we divide all the cells in the network into dense cells and sparse cells. Analytical expressions of the aggregate throughput capacity are obtained. We also find that suitable inhomogeneity can increase the network throughput capacity.

Stresses at the Surface of a Flat Three-Dimensional Ellipsoidal Cavity

1976 ◽  
Vol 98 (2) ◽  
pp. 164-172 ◽  
Author(s):  
L. Mirandy ◽  
B. Paul
Keyword(s):  
Stress Intensity ◽  
Applied Stress ◽  
Surface Stress ◽  
Fracture Criterion ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Ellipsoidal Cavity ◽  
Isotropic Elastic Medium ◽  
Analytical Expressions

The stress field associated with a thin ellipsoidal cavity in an isotropic elastic medium with arbitrary tractions at distant boundaries is needed to generalize Griffith’s two-dimensional fracture criterion. Such a solution is given here. It is first formulated for a general ellipsoidal cavity having principal semiaxes a, b, and c, and then it is reduced to the specific case of a “flat” ellipsoid for which a and b are very much greater than c. An explicit solution of the general problem is possible but the results are somewhat unwieldy. The dominant terms of an asymptotic solution for small c/b, however, are shown to provide remarkably simple expressions for the stresses everywhere on the surface of the cavity. The applied normal stress parallel to the c axis and the shears lying in a plane perpendicular to it were found to produce surface stresses proportional to (b/c) × applied stress, with the amplification of other components of applied stress being negligible in comparison. Analytical expressions for the location and magnitude of the maximum surface stress are developed along with stress intensity factors for the elliptical crack (c = 0). Three dimensional effects due to ellipsoidal planform aspect ratio (b/a) and Poisson’s ratio are reported.

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