Supplementary condition for STG-designed speed-independent circuits

1998 ◽  
Vol 34 (7) ◽  
pp. 620 ◽  
Author(s):  
C. Piguet
Keyword(s):  
Supplementary Condition

End Fitting Effect on Stress Evaluation of Tensile Armor Tendons in Unbonded Flexible Pipes Under Axial Tension

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Leilei Dong ◽  
Qi Zhang ◽  
Yi Huang ◽  
Gang Liu ◽  
Zhiyuan Li
Keyword(s):  
Lateral Displacement ◽  
Axial Strain ◽  
Supplementary Condition ◽  
Bending Stress ◽  
Stress Evaluation ◽  
Axial Tension ◽  
Flexible Pipes ◽  
Helical Angle ◽  
The Wire ◽  
Unbonded Flexible Pipes

This paper deals with the effect of termination restraint due to end fitting on the stress evaluation of tensile armors in unbonded flexible pipes under axial tension. The problem is characterized by one single armoring tendon helically wound on a cylindrical supporting surface subjected to traction. The deviation from the initial helical angle is taken to describe the armor wire path as the pipe is stretched. The integral of this angle change gives the lateral displacement of the wire, which is determined by minimizing the energy functional that consists of the strain energy due to axial strain, local bending and torsion, and the energy dissipated by friction, leading to a variational problem with a variable endpoint. The governing differential equation of the wire lateral displacement, together with the supplementary condition, is derived using the variational method and solved analytically. The developed model is verified with a finite element (FE) simulation. Comparisons between the model predictions and the FE results in terms of the change in helical angle and transverse bending stress show good correlations. The verified model is then applied to study the effects of imposed tension and friction coefficient on the maximum bending stress. The results show that the response to tension is linear, and friction could significantly increase the stress at the end fitting compared with the frictionless case.

Inertial Effects in the Dynamics of Martensitic Phase Boundaries

1991 ◽  
Vol 246 ◽  
Author(s):  
Lev Truskinovsky
Keyword(s):  
Traveling Wave ◽  
Classical System ◽  
Interface Structure ◽  
Traveling Wave Solution ◽  
Supplementary Condition ◽  
System Of Equations ◽  
Inertial Effects ◽  
Jump Conditions ◽  
Phase Boundaries ◽  
Material Discontinuities

AbstractLocalized phase transitions, as well as shock waves, can be modeled by material discontinuities satisfying appropriate jump conditions. One can show that the classical system of Rankine-Hugoniot jump conditions is incomplete in the case of subsonic phase boundaries. The supplementary condition which generalizes the condition of phase equilibrium, can be obtained from the traveling wave solution of the truly dynamic system of equations describing the interface structure.

scholarly journals Some properties of non-commutative regular graded rings

1992 ◽  
Vol 34 (3) ◽  
pp. 277-300 ◽  
Author(s):  
Thierry Levasseur
Keyword(s):  
Noetherian Ring ◽  
Global Dimension ◽  
Supplementary Condition ◽  
Graded Rings ◽  
Finitely Generated ◽  
Injective Dimension ◽  
Commutative Case ◽  
Finite Global Dimension ◽  
Image Position ◽  
Dimension One

Let A be a noetherian ring. When A is commutative (of finite Krull dimension), A is said to be Gorenstein if its injective dimension is finite. If A has finite global dimension, one says that A is regular. If A is arbitrary, these hypotheses are not sufficient to obtain similar results to those of the commutative case. To remedy this problem, M. Auslander has introduced a supplementary condition. Before stating it, we recall that the grade of a finitely generated (left or right) module is defined by

THE QUANTIZATION OF CLASSICAL SPIN THEORY

1953 ◽  
Vol 31 (1) ◽  
pp. 1-10 ◽  
Author(s):  
S. Shanmugadhasan
Keyword(s):  
Hamiltonian Dynamics ◽  
Equations Of Motion ◽  
Supplementary Condition ◽  
Poisson Brackets ◽  
Rest System ◽  
Spin Tensor ◽  
Constraint Condition ◽  
Set Up ◽  
Jacobi Equations ◽  
Quantum Formulation

The antisymmetric spin tensor of rank two used to describe the rotational motion of a particle is assumed to satisfy the constraint condition that the velocity 4-vector is orthogonal to it. Since the dipole moment is proportional to the spin tensor, this condition leads always to a purely magnetic dipole in the rest system of the particle. Frenkel has indicated how the action principle for the classical equations of motion can be set up treating the above constraint condition as a supplementary condition. The Hamiltonian dynamics of a system having supplementary conditions and Lagrange undetermined multipliers has been discussed recently by Dirac. Dirac's method and results previously obtained give the required Hamilton–Jacobi equations and Poisson Brackets of the dynamical variables. The cases where the particle behaves like a pure gyroscope and a symmetrical top are treated. When there is an interacting field, it is assumed that the action of the Held is given by the effective 4-vector potential without further specification. The orthogonality of the velocity to the tensor dual to the spin tensor can be imposed as an alternative constraint condition. This possibility is discussed briefly. The quantum formulation is completed with the help of the standard analogy rules.

Molecular quantum electrodynamics

1971 ◽  
Vol 321 (1547) ◽  
pp. 557-572 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Quantum Electrodynamics ◽  
Unitary Transformation ◽  
Charged Particles ◽  
Gauge Condition ◽  
Binding Energies ◽  
Quantum Mechanical ◽  
Supplementary Condition ◽  
Molecular Systems ◽  
Hamiltonian Theory

A comparison is made of the conventional quantum mechanical hamiltonian for the interaction of molecular systems with the electromagnetic field and the alternative multipole formulation given recently (Atkins & Woolley 1970). The conventional hamiltonian is first derived by using Dirac’s generalized hamiltonian theory in which the Coulomb gauge condition is introduced as a supplementary condition. We analyse further the interpretation of the unitary transformation that connects the two hamiltonians in terms of the arbitrariness of the phase of the wavefunctions of charged particles in the presence of the electromagnetic field, and finally examine the problem of exhibiting explicitly the binding energies of the molecular systems.

Sign in / Sign up

Export Citation Format

Share Document