Chemical Bond. III. A One‐Dimensional Theory of the Energetics and Ionic Character of the Hydrogen Bond

1959 ◽  
Vol 31 (2) ◽  
pp. 294-299 ◽  
Author(s):  
Paul C. McKinney ◽  
Gordon M. Barrow
Keyword(s):  
Hydrogen Bond ◽  
Chemical Bond ◽  
Ionic Character ◽  
Dimensional Theory ◽  
One Dimensional

scholarly journals Quantitative Experimental and Theoretical Investigations on the Interaction of Shock Waves with Magnetic Fields

1969 ◽  
Vol 24 (10) ◽  
pp. 1449-1457
Author(s):  
H. Klingenberg ◽  
F. Sardei ◽  
W. Zimmermann
Keyword(s):  
Magnetic Fields ◽  
Shock Waves ◽  
Physical Model ◽  
Spectroscopic Method ◽  
Experimental Results ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Theoretical Investigations ◽  
Theoretical Predictions ◽  
Interaction Of Shock Waves

Abstract In continuation of the work on interaction between shock waves and magnetic fields 1,2 the experiments reported here measured the atomic and electron densities in the interaction region by means of an interferometric and a spectroscopic method. The transient atomic density was also calculated using a one-dimensional theory based on the work of Johnson3 , but modified to give an improved physical model. The experimental results were compared with the theoretical predictions.

The Exact One-Dimensional Theory for End-Loaded Fully Anisotropic Beams of Narrow Rectangular Cross Section

2001 ◽  
Vol 68 (6) ◽  
pp. 865-868 ◽  
Author(s):  
P. Ladeve`ze ◽  
J. G. Simmonds
Keyword(s):  
Cross Section ◽  
Plane Stress ◽  
Rectangular Cross Section ◽  
Dimensional Theory ◽  
Explicit Formulas ◽  
Cross Sectional ◽  
Rectangular Shape ◽  
One Dimensional ◽  
Anisotropic Elastic ◽  
Derivatives Of

The exact theory of linearly elastic beams developed by Ladeve`ze and Ladeve`ze and Simmonds is illustrated using the equations of plane stress for a fully anisotropic elastic body of rectangular shape. Explicit formulas are given for the cross-sectional material operators that appear in the special Saint-Venant solutions of Ladeve`ze and Simmonds and in the overall beamlike stress-strain relations between forces and a moment (the generalized stress) and derivatives of certain one-dimensional displacements and a rotation (the generalized displacement). A new definition is proposed for built-in boundary conditions in which the generalized displacement vanishes rather than pointwise displacements or geometric averages.

A Study of a Sharp 90 Degree Curved Flow

1992 ◽  
Author(s):  
R. H. Kim
Keyword(s):  
Turbulence Model ◽  
Ideal Gas ◽  
Radius Of Curvature ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Algebraic Stress Model ◽  
Finite Difference Technique ◽  
Curved Tube ◽  
Kinetic Energy Loss ◽  
The Ideal

Abstract An investigation of air flow along a 90 degree elbow-like tube is conducted to determine the velocity and temperature distributions of the flow. The tube has a sharp 90 degree turn with a radius of curvature of almost zero. The flow is assumed to be a steady two-dimensional turbulent flow satisfying the ideal gas relation. The flow will be analyzed using a finite difference technique with the K-ε turbulence model, and the algebraic stress model (ASM). The FLUENT code was used to determine the parameter distributions in the passage. There are certain conditions for which the K-ε model does not describe the fluid phenomenon properly. For these conditions, an alternative turbulence model, the ASM with or without QUICK was employed. FLUENT has these models among its features. The results are compared with the result computed by using elementary one-dimensional theory including the kinetic energy loss along the passage of the sharp 90 degree curved tube.

On shock-induced light-fluid-layer evolution

2021 ◽  
Vol 933 ◽  
Author(s):  
Yu Liang ◽  
Xisheng Luo
Keyword(s):  
Layer Thickness ◽  
Coupling Effect ◽  
Fluid Layer ◽  
Nonlinear Models ◽  
Interfacial Instability ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Helium Gas ◽  
Wave Patterns ◽  
Thickness Variations

Shock-induced light-fluid-layer evolution is firstly investigated experimentally and theoretically. Specifically, three quasi-one-dimensional helium gas layers with different layer thicknesses are generated to study the wave patterns and interface motions. Six quasi-two-dimensional helium gas layers with diverse layer thicknesses and amplitude combinations are created to explore the Richtmyer–Meshkov instability of a light-fluid layer. Due to the multiple reflected shocks reverberating inside a light-fluid layer, the speeds of the two interfaces gradually converge, and the layer thickness saturates eventually. A general one-dimensional theory is adopted to describe the two interfaces’ motions and the layer thickness variations. It is found that, for the first interface, the end time of its phase reversal determines the influence of the reflected shocks on it. However, the reverberated shocks indeed lead to the second interface being more unstable. When the two interfaces are initially in phase, and the initial fluid layer is very thin, the two interfaces’ spike heads collide and stabilise the two interfaces. Linear and nonlinear models are successfully adopted by considering the interface-coupling effect and the reverberated shocks to predict the two interfaces’ perturbation growths in all regimes. The interfacial instability of a light-fluid layer is quantitatively compared with that of a heavy-fluid layer. It is concluded that the kind of waves reverberating inside a fluid layer significantly affects the fluid-layer evolution.

Vibrations of beams with a breathing crack and large amplitude displacements

2015 ◽  
Vol 230 (1) ◽  
pp. 34-54 ◽  
Author(s):  
Gonçalo Neves Carneiro ◽  
Pedro Ribeiro
Keyword(s):  
Time Domain ◽  
Equations Of Motion ◽  
Shape Functions ◽  
Breathing Crack ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Time Histories ◽  
Linear Effects ◽  
Fourier Spectra ◽  
The Time Domain

The vibrations of beams with a breathing crack are investigated taking into account geometrical non-linear effects. The crack is modeled via a function that reduces the stiffness, as proposed by Christides and Barr (One-dimensional theory of cracked Bernoulli–Euler beams. Int J Mech Sci 1984). The bilinear behavior due to the crack closing and opening is considered. The equations of motion are obtained via a p-version finite element method, with shape functions recently proposed, which are adequate for problems with abrupt localised variations. To analyse the dynamics of cracked beams, the equations of motion are solved in the time domain, via Newmark's method, and the ensuing displacements, velocities and accelerations are examined. For that purpose, time histories, projections of trajectories on phase planes, and Fourier spectra are obtained. It is verified that the breathing crack introduce asymmetries in the response, and that velocities and accelerations can be more affected than displacements by the breathing crack.

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