Alternative derivation of the Claerbout equations

Geophysics ◽  
1978 ◽  
Vol 43 (7) ◽  
pp. 1543-1545
Author(s):  
M. R. Foster ◽  
C. E. Laird
Keyword(s):  
Higher Dimensions ◽  
Equation Of Motion ◽  
One Dimension ◽  
Particle Displacement ◽  
Dimensional Theory ◽  
Alternative Derivation ◽  
One Dimensional ◽  
Reflectivity Function ◽  
The One ◽  
Compressional Velocity

This paper is basically an extension to higher dimensions of the one‐dimensional theory developed by Foster (1975). We begin by briefly reviewing these ideas. In one dimension, the equation of motion for the particle displacement u is given by [Formula: see text]where [Formula: see text] is the vertical traveltime, and [Formula: see text] is the reflectivity function. ρ and c are, respectively, the density and compressional velocity.

Forced Motions of Elastic Rods

1954 ◽  
Vol 21 (3) ◽  
pp. 221-224
Author(s):  
G. Herrmann
Keyword(s):  
Equation Of Motion ◽  
Elastic Rod ◽  
Dimensional Theory ◽  
Compressional Waves ◽  
One Dimensional ◽  
Forced Motion ◽  
Lagrange’S Equation ◽  
Rod Theory ◽  
Dependent Variables ◽  
The One

Abstract In a recent paper by Mindlin and Herrmann, a one-dimensional theory of compressional waves in an elastic rod was described. This theory takes into account both radial inertia and radial shear stress and, accordingly, contains two dependent variables instead of the one axial displacement of classical rod theory. The solution of the equations for the case of forced motions thus involves complications not usually encountered. The difficulties may be surmounted in several ways, one of which is presented in this paper. The method described makes use of Lagrange’s equation of motion and reduces the most general problem of forced motion to a free vibration problem and a quadrature.

scholarly journals A Spanner for the Day After

2020 ◽  
Vol 64 (4) ◽  
pp. 1167-1191 ◽  
Author(s):  
Kevin Buchin ◽  
Sariel Har-Peled ◽  
Dániel Oláh
Keyword(s):  
Higher Dimensions ◽  
Black Box ◽  
One Dimension ◽  
Catastrophic Failure ◽  
One Dimensional ◽  
Residual Graph ◽  
The One ◽  
Construction Works

AbstractWe show how to construct a $$(1+\varepsilon )$$ ( 1 + ε ) -spanner over a set $${P}$$ P of n points in $${\mathbb {R}}^d$$ R d that is resilient to a catastrophic failure of nodes. Specifically, for prescribed parameters $${\vartheta },\varepsilon \in (0,1)$$ ϑ , ε ∈ ( 0 , 1 ) , the computed spanner $${G}$$ G has $$\begin{aligned} {{\mathcal {O}}}\bigl (\varepsilon ^{-O(d)} {\vartheta }^{-6} n(\log \log n)^6 \log n \bigr ) \end{aligned}$$ O ( ε - O ( d ) ϑ - 6 n ( log log n ) 6 log n ) edges. Furthermore, for anyk, and any deleted set $${{B}}\subseteq {P}$$ B ⊆ P of k points, the residual graph $${G}\setminus {{B}}$$ G \ B is a $$(1+\varepsilon )$$ ( 1 + ε ) -spanner for all the points of $${P}$$ P except for $$(1+{\vartheta })k$$ ( 1 + ϑ ) k of them. No previous constructions, beyond the trivial clique with $${{\mathcal {O}}}(n^2)$$ O ( n 2 ) edges, were known with this resilience property (i.e., only a tiny additional fraction of vertices, $$\vartheta |B|$$ ϑ | B | , lose their distance preserving connectivity). Our construction works by first solving the exact problem in one dimension, and then showing a surprisingly simple and elegant construction in higher dimensions, that uses the one-dimensional construction in a black-box fashion.

scholarly journals Assessing a Linear Nanosystem's Limiting Reliability from its Components

2008 ◽  
Vol 45 (03) ◽  
pp. 879-887 ◽  
Author(s):  
Nader Ebrahimi
Keyword(s):  
Present State ◽  
Size Range ◽  
Two Dimensions ◽  
The Other ◽  
One Dimension ◽  
Present Moment ◽  
One Dimensional ◽  
The One ◽  
Fixed Moment ◽  
Nanosized Systems

Nanosystems are devices that are in the size range of a billionth of a meter (1 x 10-9) and therefore are built necessarily from individual atoms. The one-dimensional nanosystems or linear nanosystems cover all the nanosized systems which possess one dimension that exceeds the other two dimensions, i.e. extension over one dimension is predominant over the other two dimensions. Here only two of the dimensions have to be on the nanoscale (less than 100 nanometers). In this paper we consider the structural relationship between a linear nanosystem and its atoms acting as components of the nanosystem. Using such information, we then assess the nanosystem's limiting reliability which is, of course, probabilistic in nature. We consider the linear nanosystem at a fixed moment of time, say the present moment, and we assume that the present state of the linear nanosystem depends only on the present states of its atoms.

scholarly journals LOCAL FRACTIONAL SUPERSYMMETRY FOR ALTERNATIVE STATISTICS

1996 ◽  
Vol 11 (11) ◽  
pp. 899-913 ◽  
Author(s):  
N. FLEURY ◽  
M. RAUSCH DE TRAUBENBERG
Keyword(s):  
Group Theory ◽  
Braid Group ◽  
Equation Of Motion ◽  
Coset Space ◽  
One Dimensional ◽  
The One

A group theory justification of one-dimensional fractional supersymmetry is proposed using an analog of a coset space, just like the one introduced in 1-D supersymmetry. This theory is then gauged to obtain a local fractional supersymmetry, i.e. a fractional supergravity which is then quantized à la Dirac to obtain an equation of motion for a particle which is in a representation of the braid group and should describe alternative statistics. A formulation invariant under general reparametrization is given by means of a curved fractional superline.

scholarly journals CFD tool application in predicting the behavior of a centrifugal fan designed by one-dimensional theory

2021 ◽  
Vol 10 (12) ◽  
pp. e412101219653
Author(s):  
Henrique Marcio Pereira Rosa ◽  
Gabriela Pereira Toledo
Keyword(s):  
Velocity Distribution ◽  
Cfd Simulation ◽  
Centrifugal Fan ◽  
Dimensional Theory ◽  
Recovery Coefficient ◽  
Characteristic Curves ◽  
One Dimensional ◽  
Ansys Cfx ◽  
Computational Fluid Dynamics Cfd ◽  
The One

Computational fluid dynamics (CFD) is the most current technology in the fluid flow study. Experimental methods for predicting the turbomachinery performance involve greater time consumption and financial resources compared to the CFD approach. The purpose of this article is to present the analysis of CFD simulation results in a centrifugal fan. The impeller was calculated using the one-dimensional theory and the volute the principle of constant angular momentum. The ANSYS-CFX software was used for the simulation. The turbulence model adopted was the SST. The simulation provided the characteristic curves, the pressure and velocity distribution, and the static and total pressure values at impeller and volute exit. An analysis of the behavior of the pressure plots, and the loss and recovery of pressure in the volute was performed. The results indicated the characteristic curves, the pressure and velocity distribution were consistent with the turbomachinery theory. The pressure values showed the static pressure at volute exit was smaller than impeller exit for some flow rate. It caused the pressure recovery coefficient negative.  This work indicated to be possible design a centrifugal fan applying the one-dimensional theory and optimize it with the CFD tool.

Limit theorems and absorption problems for quantum radom walks in one dimension

2002 ◽  
Vol 2 (Special) ◽  
pp. 578-595
Author(s):  
N. Konno
Keyword(s):  
Random Walks ◽  
Limit Theorems ◽  
The Other ◽  
One Dimension ◽  
Unitary Matrices ◽  
Quantum Random Walks ◽  
One Dimensional ◽  
The Difference ◽  
The One

In this paper we consider limit theorems, symmetry of distribution, and absorption problems for two types of one-dimensional quantum random walks determined by $2 \times 2$ unitary matrices using our PQRS method. The one type was introduced by Gudder in 1988, and the other type was studied intensively by Ambainis et al. in 2001. The difference between both types of quantum random walks is also clarified.

scholarly journals Universality in the One-Dimensional Self-Organized Critical Forest-Fire Model

1994 ◽  
Vol 49 (9) ◽  
pp. 856-860
Author(s):  
Barbara Drossel ◽  
Siegfried Clar ◽  
Franz Schwabl
Keyword(s):  
Size Distribution ◽  
Forest Fire ◽  
Nearest Neighbor ◽  
The Self ◽  
One Dimension ◽  
Fire Model ◽  
One Dimensional ◽  
Self Organized ◽  
Forest Fire Model ◽  
The One

Abstract We modify the rules of the self-organized critical forest-fire model in one dimension by allowing the fire to jum p over holes of ≤ k sites. An analytic calculation shows that not only the size distribution of forest clusters but also the size distribution of fires is characterized by the same critical exponent as in the nearest-neighbor model, i.e. the critical behavior of the model is universal. Computer simulations confirm the analytic results.

Smooth solution to the one-dimensional inhomogeneous non-automorphic Landau–Lifshitz equation

2006 ◽  
Vol 462 (2072) ◽  
pp. 2397-2413 ◽  
Author(s):  
Junyu Lin ◽  
Shijin Ding
Keyword(s):  
Difference Method ◽  
Existence And Uniqueness ◽  
Smooth Solution ◽  
One Dimension ◽  
Initial Value ◽  
One Dimensional ◽  
Uniform Estimates ◽  
Lifshitz Equation ◽  
Orthogonal Base ◽  
The One

Using the differential–difference method and viscosity vanishing approach, we obtain the existence and uniqueness of the global smooth solution to the periodic initial-value problem of the inhomogeneous, non-automorphic Landau–Lifshitz equation without Gilbert damping terms in one dimension. To establish the uniform estimates, we use some identities resulting from the fact and the fact that the vectors form an orthogonal base of the space .

Taylor Cylinder Testing of High Strength Steels for Hard Target Warhead Applications

2009 ◽  
Author(s):  
Rachel Russo ◽  
Nicholas Dutton ◽  
Bart Baker ◽  
Karen Torres ◽  
Stanley E. Jones ◽  
...  
Keyword(s):  
Impact Test ◽  
True Strain ◽  
High Strength Steels ◽  
High Strength ◽  
True Stress ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Cylinder Test ◽  
Taylor Impact ◽  
The One

A one-dimensional analysis of the Taylor impact test [4] has been used to estimate the quasi-static stress for several different alloys. One criticism of this work was the use of Taylor cylinder test data to estimate the quasi-static true stress/true strain compression diagram. The one-dimensional theory does accommodate this estimate. The purpose of this paper is to demonstrate that this process leads to acceptable results by analyzing a series of high, medium, and low strength materials.

τ-D Decomposition to the One Dimensional Delay Differential Equation by Fixed the Coefficient b<0

2013 ◽  
Vol 785-786 ◽  
pp. 1418-1422
Author(s):  
Ai Gao
Keyword(s):  
Differential Equation ◽  
Hopf Bifurcation ◽  
Delay Differential Equation ◽  
Stability Domain ◽  
Transcendental Equation ◽  
One Dimension ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Delay Differential

In this paper, we provide a partition of the roots of a class of transcendental equation by using τ-D decomposition ,where τ>0,a>0,b<0 and the coefficient b is fixed.According to the partition, one can determine the stability domain of the equilibrium and get a Hopf bifurcation diagram that can provide the Hopf bifurcation curves in the-parameter space, for one dimension delay differential equation .

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