Three-dimensional analytical expressions of strain gauge coefficients of infinitely thick polycrystalline metal films

1980 ◽  
Vol 15 (12) ◽  
pp. 2991-2994 ◽  
Author(s):  
C. R. Pichard ◽  
C. R. Tellier ◽  
A. J. Tosser
Keyword(s):  
Strain Gauge ◽  
Three Dimensional ◽  
Metal Films ◽  
Polycrystalline Metal ◽  
Analytical Expressions

scholarly journals Three Dimensional Analytical Separation of Grain Boundary and Surface Scatterings in Polycrystalline Metal Films in the Case of Non Cubic Grains

1981 ◽  
Vol 9 (2) ◽  
pp. 125-130 ◽  
Author(s):  
C. R. Tellier ◽  
C. R. Pichard ◽  
A. J. Tosser
Keyword(s):  
Grain Boundaries ◽  
Three Dimensional ◽  
Approximate Model ◽  
Metal Films ◽  
Three Dimensional Model ◽  
Polycrystalline Metal ◽  
Fine Grained ◽  
Thin Polycrystalline ◽  
Analytical Separation ◽  
Approximate Expressions

Analytical approximate expressions for the resistivity and its temperature coefficient of thin polycrystalline metal films have been derived by considering separately the contributions of the grain-boundaries perpendicular to thex-,y- andz-axes. Provided that the grain-boundaries act as moderately efficient scatterers reasonable deviations from the three-dimensional model are obtained; an approximate model then seems convenient with which to perform the calculations of the strain coefficients of such fine-grained films.

Three-dimensional strain coefficients of resistivity of thin polycrystalline metal films

1981 ◽  
Vol 16 (8) ◽  
pp. 2281-2286 ◽  
Author(s):  
C. R. Tellier ◽  
C. R. Pichard ◽  
A. J. Tosser
Keyword(s):  
Three Dimensional ◽  
Metal Films ◽  
Polycrystalline Metal ◽  
Thin Polycrystalline

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 Origin and Application of the Twinned Calcite Strain Gauge

Geosciences ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 296
Author(s):  
Richard H. Groshong
Keyword(s):  
Stress Analysis ◽  
Strain Gauge ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Constant Strain Rate ◽  
Axis Orientation ◽  
Order Of Magnitude ◽  
Rate Experiment ◽  
Strain Axis ◽  
Expected Values

This paper is a personal account of the origin and development of the twinned-calcite strain gauge, its experimental verification, and its relationship to stress analysis. The method allows the calculation of the three-dimensional deviatoric strain tensor based on five or more twin sets. A minimum of about 25 twin sets should provide a reasonably accurate result for the magnitude and orientation of the strain tensor. The opposite-signed strain axis orientation is the most accurately located. Where one strain axis is appreciably different from the other two, that axis is generally within about 10° of the correct value. Experiments confirm a magnitude accuracy of 1% strain over the range of 1–12% axial shortening and that samples with more than 40% negative expected values imply multiple or rotational deformations. If two deformations are at a high angle to one another, the strain calculated from the positive and negative expected values separately provides a good estimate of both deformations. Most stress analysis techniques do not provide useful magnitudes, although most provide a good estimate of the principal strain axis directions. Stress analysis based on the number of twin sets per grain provides a better than order-of-magnitude approximation to the differential stress magnitude in a constant strain rate experiment.

Numerical study of the second harmonic generation in FELs

2021 ◽  
Vol 28 (3) ◽  
Author(s):  
A. M. Kalitenko
Keyword(s):  
Second Harmonic Generation ◽  
Harmonic Generation ◽  
Free Electron ◽  
Numerical Study ◽  
Second Harmonic ◽  
Three Dimensional ◽  
X Ray ◽  
Linac Coherent Light Source ◽  
The Individual ◽  
Analytical Expressions

A numerical study of the effect of betatron oscillations on the second harmonic generation in free-electron lasers (FELs) is presented. Analytical expressions for the effective coupling strength factors are derived that clearly distinguish all contributions in subharmonics and each polarization of the radiation. A three-dimensional time-dependent numerical FEL code that takes into account the main FEL effects and the individual contribution of each electron to the second harmonic generation is presented. Also, the X- and Y-polarizations of the second harmonic are analyzed. The second harmonic was detected in experiments at the Advanced Photon Source (APS) Low Energy Undulator Test Line (LEUTL) and Linac Coherent Light Source (LCLS) in the soft X-ray regime. The approach presented in the article can be useful for a comprehensive study and diagnostics of XFELs. In the paper, the LCLS and Pohang Accelerator Laboratory X-ray Free-Electron Laser (PAL-XFEL) experiments are modeled. The simulation results are in a good agreement with the experimental data.

λ-Transition to the Bose-Einstein Condensate

1995 ◽  
Vol 50 (10) ◽  
pp. 921-930 ◽  
Author(s):  
Siegfried Grossmann ◽  
Martin Holthaus
Keyword(s):  
Heat Capacity ◽  
Three Dimensional ◽  
Einstein Condensate ◽  
Einstein Condensation ◽  
Condensation Temperature ◽  
Harmonic Oscillator Potential ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Analytical Expressions ◽  
Grand Canonical

Abstract We study Bose-Einstein condensation of comparatively small numbers of atoms trapped by a three-dimensional harmonic oscillator potential. Under the assumption that grand canonical statis­tics applies, we derive analytical expressions for the condensation temperature, the ground state occupation, and the specific heat capacity. For a gas of TV atoms the condensation temperature is proportional to N1/3, apart from a downward shift of order N-1/3. A signature of the condensation is a pronounced peak of the heat capacity. For not too small N the heat capacity is nearly discon­tinuous at the onset of condensation; the magnitude of the jump is about 6.6 N k. Our continuum approximations are derived with the help of the proper density of states which allows us to calculate finite-AT-corrections, and checked against numerical computations.

Turret Mooring Design Based on Analytical Expressions of Catastrophes of Slow-Motion Dynamics

1998 ◽  
Vol 120 (3) ◽  
pp. 154-164 ◽  
Author(s):  
M. M. Bernitsas ◽  
L. O. Garza-Rios
Keyword(s):  
Parametric Design ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Slow Motion ◽  
Sensitivity Analyses ◽  
Design Parameters ◽  
Mooring Lines ◽  
The Stability ◽  
Fifth Order ◽  
Analytical Expressions

Analytical expressions of the bifurcation boundaries exhibited by turret mooring systems (TMS), and expressions that define the morphogeneses occurring across boundaries are developed. These expressions provide the necessary means for evaluating the stability of a TMS around an equilibrium position, and constructing catastrophe sets in two or three-dimensional parametric design spaces. Sensitivity analyses of the bifurcation boundaries define the effect of any parameter or group of parameters on the dynamical behavior of the system. These expressions allow the designer to select appropriate values for TMS design parameters without resorting to trial and error. A four-line TMS is used to demonstrate this design methodology. The mathematical model consists of the nonlinear, fifth-order, low-speed, large-drift maneuvering equations. Mooring lines are modeled with submerged catenaries, and include nonlinear drag. External excitation consists of time-independent current, wind, and mean wave drift.

More hyperelastic models for rubber-like materials: consistent tangent operators and comparative study

2013 ◽  
Vol 22 (1-2) ◽  
pp. 27-50 ◽  
Author(s):  
Mokarram Hossain ◽  
Paul Steinmann
Keyword(s):  
Large Deformations ◽  
Pure Shear ◽  
Three Dimensional ◽  
Network Models ◽  
Polymeric Materials ◽  
Chain Molecules ◽  
Current Contribution ◽  
Dimensional Network ◽  
Analytical Expressions ◽  
Order Tangent

AbstractRubber-like materials can deform largely and nonlinearly upon loading, and they return to the initial configuration when the load is removed. Such rubber elasticity is achieved due to very flexible long-chain molecules and a three-dimensional network structure that is formed via cross-linking or entanglements between molecules. Over the years, to model the mechanical behavior of such randomly oriented microstructures, several phenomenological and micromechanically motivated network models for nearly incompressible hyperelastic polymeric materials have been proposed in the literature. To implement these models for polymeric material (undoubtedly with widespread engineering applications) in the finite element framework for solving a boundary value problem, one would require two important ingredients, i.e., the stress tensor and the consistent fourth-order tangent operator, where the latter is the result of linearization of the former. In our previous work, 14 such material models are reviewed by deriving the accurate stress tensors and tangent operators from a group of phenomenological and micromechanical models at large deformations. The current contribution will supplement some further important models that were not included in the previous work. For comparison of all selected models in reproducing the well-known Treloar data, the analytical expressions for the three homogeneous defomation modes, i.e., uniaxial tension, equibiaxial tension, and pure shear, have been derived and the performances of the models are analyzed.

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