Nonlinear and dissipative constitutive equations for coupled first-order acoustic field equations that are consistent with the generalized Westervelt equation

2006 ◽  
Author(s):  
Martin D. Verweij
Keyword(s):  
Acoustic Field ◽  
Constitutive Equations ◽  
Field Equations ◽  
First Order ◽  
Westervelt Equation

On Conformally Covariant Spinor Field Equations

1972 ◽  
Vol 50 (18) ◽  
pp. 2100-2104 ◽  
Author(s):  
Mark S. Drew
Keyword(s):  
Minkowski Space ◽  
Invariant Mass ◽  
Spinor Field ◽  
Dimensional Space ◽  
Flat Space ◽  
Field Equations ◽  
First Order ◽  
Conformally Invariant ◽  
Spinor Fields

Conformally covariant equations for free spinor fields are determined uniquely by carrying out a descent to Minkowski space from the most general first-order rotationally covariant spinor equations in a six-dimensional flat space. It is found that the introduction of the concept of the "conformally invariant mass" is not possible for spinor fields even if the fields are defined not only on the null hyperquadric but over the entire manifold of coordinates in six-dimensional space.

Topics in Finite Elasticity: Hyperelasticity of Rubber, Elastomers, and Biological Tissues—With Examples

1987 ◽  
Vol 40 (12) ◽  
pp. 1699-1734 ◽  
Author(s):  
Millard F. Beatty
Keyword(s):  
Constitutive Equations ◽  
Mechanical Energy ◽  
Finite Elasticity ◽  
Physical Nature ◽  
Decomposition Theorem ◽  
Elastic Stability ◽  
Biological Tissues ◽  
Field Equations ◽  
Energy Principle ◽  
Hyperelastic Materials

This is an introductory survey of some selected topics in finite elasticity. Virtually no previous experience with the subject is assumed. The kinematics of finite deformation is characterized by the polar decomposition theorem. Euler’s laws of balance and the local field equations of continuum mechanics are described. The general constitutive equation of hyperelasticity theory is deduced from a mechanical energy principle; and the implications of frame invariance and of material symmetry are presented. This leads to constitutive equations for compressible and incompressible, isotropic hyperelastic materials. Constitutive equations studied in experiments by Rivlin and Saunders (1951) for incompressible rubber materials and by Blatz and Ko (1962) for certain compressible elastomers are derived; and an equation characteristic of a class of biological tissues studied in primary experiments by Fung (1967) is discussed. Sample applications are presented for these materials. A balloon inflation experiment is described, and the physical nature of the inflation phenomenon is examined analytically in detail. Results for the different materials are compared. Two major problems of finite elasticity theory are discussed. Some results concerning Ericksen’s problem on controllable deformations possible in every isotropic hyperelastic material are outlined; and examples are presented in illustration of Truesdell’s problem concerning analytical restrictions imposed on constitutive equations. Universal relations valid for all compressible and incompressible, isotropic materials are discussed. Some examples of non-uniqueness, including that of a neo-Hookean cube subject to uniform loads over its faces, are described. Elastic stability criteria and their connection with uniqueness in the theory of small deformations superimposed on large deformations are introduced, and a few applications are mentioned. Some previously unpublished results are presented throughout.

Strength of the Poincaré gauge field equations in first order formalism

1989 ◽  
Vol 139 (1-2) ◽  
pp. 21-26 ◽  
Author(s):  
Michael Sué ◽  
Eckehard W. Mielke
Keyword(s):  
Gauge Field ◽  
Field Equations ◽  
First Order

WEAK SOLUTIONS FOR WEAK SINGULARITIES

2002 ◽  
Vol 17 (20) ◽  
pp. 2769-2769
Author(s):  
B. C. NOLAN
Keyword(s):  
Existence And Uniqueness ◽  
Finite Measure ◽  
Generalized Solutions ◽  
Functions Of Bounded Variation ◽  
Field Equations ◽  
Finite Radius ◽  
Locally Finite ◽  
Naked Singularities ◽  
First Order ◽  
Bounded Functions

We revisit the problem of the development of singularities in the gravitational collapse of an inhomogeneous dust sphere. As shown by Yodzis et al1, naked singularities may occur at finite radius where shells of dust cross one another. These singularities are gravitationally weak 2, and it has been claimed that at these singularities, the metric may be written in continuous form 2, with locally L∞ connection coefficients 3. We correct these claims, and show how the field equations may be reformulated as a first order, quasi-linear, non-conservative, non-strictly hyperbolic system. We discuss existence and uniqueness of generalized solutions of this system using bounded functions of bounded variation (BV) 4, where the product of a BV function and the derivative of another BV function may be interpreted as a locally finite measure. The solutions obtained provide a dynamical extension to the future of the singularity.

Influence of Relaxation Frequency on Acoustic Wave in Unconsolidated Sands and Acoustic Logging Simulation

2018 ◽  
Vol 26 (02) ◽  
pp. 1850014
Author(s):  
Chongwang Yue ◽  
Xiaopeng Yue
Keyword(s):  
Acoustic Field ◽  
Acoustic Waves ◽  
Relaxation Frequency ◽  
S Wave ◽  
Field Equations ◽  
Acoustic Logging ◽  
Reflected Waves ◽  
Unconsolidated Sands ◽  
Bulk Relaxation ◽  
Shear Relaxation

Apart from consolidated rocks, the effect of relaxation on acoustic propagation in unconsolidated sands cannot be neglected. In this paper, we study the influence of relaxation frequency on the propagation of acoustic waves. We compute the frequency-dependent velocities and attenuation of P1-wave, P2-wave, and S-wave at different bulk or shear relaxation frequency for plane wave. In addition, we derive the integral solutions of acoustic field equations in cylindrical coordinate system to simulate acoustic logging. The reflected acoustic waveforms in a borehole are calculated at different bulk or shear relaxation frequency. Calculation results show that the increase of bulk relaxation frequency will cause the velocity of P1-wave to decrease slightly, and the velocity of P2-wave to decrease substantially. The change of bulk relaxation frequency has no effect on the velocity of S-wave. The increase of bulk relaxation frequency will cause the attenuation of P1-wave or P2-wave to decrease or increase in different wave frequency range. The change of bulk relaxation frequency has no effect on the attenuation of S-wave. The increase of shear relaxation frequency will cause the velocity of P1-wave to increase slightly, and the velocity of P2-wave or S-wave to decrease substantially. The increase of the shear relaxation frequency will cause the attenuation of P1-wave, P2-wave or S-wave to decrease. For acoustic field in a borehole surrounded by unconsolidated sands, the effect of bulk or shear relaxation frequency on the velocity of reflected waves in a borehole is negligible at the dimension of the distance from a logging source. The increase of bulk or shear relaxation frequency will cause the amplitude of the reflected waveforms from the borehole wall to increase.

Pair creation of neutral Dirac particle in (1 + 2)d noncommutative spacetime

2018 ◽  
Vol 33 (03) ◽  
pp. 1850017 ◽  
Author(s):  
B. Hamil
Keyword(s):  
Neutral Particle ◽  
Pair Creation ◽  
Dirac Particle ◽  
Bogoliubov Transformation ◽  
Quantum Fields ◽  
Field Equations ◽  
First Order ◽  
Noncommutative Spacetime

In this paper, we study the influence of the noncommutativity on the pairs creation of neutral particle–antiparticle in (1 + 2)d. Using the Seiberg–Witten maps, the modified Euler–Lagrange field equations up to first-order in the noncommutativity, parameter [Formula: see text] is obtained and the Nikishov method based on Bogoliubov transformation is applied to calculate the density number of created neutral fermions. It is shown that the noncommutativity amplifies the density number N. In addition, when [Formula: see text], we obtain the known results corresponding to the undeformed quantum fields.

scholarly journals On GLM curl cleaning for a first order reduction of the CCZ4 formulation of the Einstein field equations

2020 ◽  
Vol 404 ◽  
pp. 109088 ◽  
Author(s):  
Michael Dumbser ◽  
Francesco Fambri ◽  
Elena Gaburro ◽  
Anne Reinarz
Keyword(s):  
Order Reduction ◽  
Einstein Field Equations ◽  
Field Equations ◽  
First Order
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