Stellar models with like-Tolman IV complexity factor

In this work, we construct stellar models based on the complexity factor as a supplementary condition which allows to close the system of differential equations arising from the Gravitational Decoupling. The assumed complexity is a generalization of the one obtained from the well known Tolman IV solution. We use Tolman IV, Wyman IIa, Durgapal IV and Heintzmann IIa as seeds solutions. Reported compactness parameters of SMC X-1 and Cen X-3 are used to study the physical acceptability of the models. Some aspects related to the density ratio are also discussed.

Circular motion and the innermost stable circular orbit for spinning particles around a charged Hayward black hole background

The circular orbits of a spinning test particle moving around a charged Hayward black hole is investigated by using the Mathisson–Papapetrou–Dixon equations together with the Tulczyjew spin-supplementary condition. By writing the equations of motion, the effective potential for the description of the test particle is obtained to study the properties of the Innermost Stable Circular Orbit (ISCO). The results show that the ISCO radii for spinning particles moving in the charged Hayward background differ from those obtained in the corresponding Schwarzschild or Reissner–Nordstrom spacetimes, depending on the values of the electric charge and the length-scale parameter of the metric. When the spin of the particle and its orbital angular momentum are aligned, an increase in the spin produces a decrease in the ISCO radius, while in the case in which the spin of the particle and its orbital angular momentum are anti-aligned, an increase in the spin results in an increase of the radius of the ISCO.

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

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.

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

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 lateral displacement of the wire, which is determined by minimization of the energy functional 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 validated with a finite element simulation. Comparisons between the model predictions and the finite element results in terms of the change in helical angle and transverse bending stress show good correlations. The validated 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.

PERSISTENCE OF THE NORMALIZED EIGENVECTORS OF A PERTURBED OPERATOR IN THE VARIATIONAL CASE

Let H be a real Hilbert space and denote by S its unit sphere. Consider the nonlinear eigenvalue problem Ax + ε B(x) =δ x, where A: H → H is a bounded self-adjoint (linear) operator with nontrivial kernel Ker A, and B: H → H is a (possibly) nonlinear perturbation term. A unit eigenvector x0 ∈ S∩ Ker A of A (thus corresponding to the eigenvalue δ=0, which we assume to be isolated) is said to be persistent, or a bifurcation point (from the sphere S∩ Ker A), if it is close to solutions x ∈ S of the above equation for small values of the parameters δ ∈ ℝ and ε ≠ 0. In this paper, we prove that if B is a C1 gradient mapping and the eigenvalue δ=0 has finite multiplicity, then the sphere S∩ Ker A contains at least one bifurcation point, and at least two provided that a supplementary condition on the potential of B is satisfied. These results add to those already proved in the non-variational case, where the multiplicity of the eigenvalue is required to be odd.

Some properties of non-commutative regular graded rings

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

Inertial Effects in the Dynamics of Martensitic Phase Boundaries

Localized 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.