Arbitrary Tension Research Articles

Study of reactions of the sensorimotor system in adolescents during and after surgical correction of spinal deformity

BACKGROUND: Little attention has been paid to the study of delayed sensory and motor reactions in adolescents with spinal deformities after surgical treatment.
 AIM: To study the reactions of the sensorimotor system of adolescents after surgical correction of spinal deformity.
 MATERIALS AND METHODS: The state of the sensory and motor spheres was analyzed in the immediate postoperative period in 21 adolescents with idiopathic scoliosis and in 13 with congenital deformities of the spine. A complex of methods involving global and stimulation electroneuromyography was used. The amplitude of motor, reflex potentials and interference electromyogram was evaluated at the maximum arbitrary tension of the lower limb muscles. Using an esthesiometer, thermal pain sensitivity in Th1S2 dermatomes was explored. In the process of surgical correction, intraoperative neuromonitoring was performed with registration of motor evoked potentials of the lower limb muscles.
 RESULTS: At the beginning of surgical intervention, high-amplitude, well-reproducible motor evoked potentials were obtained in all patients. In the group of patients with idiopathic scoliosis, compared with those with congenital deformities, smooth flow of surgery prevailed (p 0.05) without significant changes in motor potentials relative to the baseline (p 0.05). The number of observations of motor potentials decreased in the both groups and did not exceed 10%; the differences were not significant (p 0.05). The study of the reactions of the sensorimotor system in the immediate postoperative period triggered an increase in the amplitude of M-responses of m. rectus femoris, m. flexor digitorum brevis, m. gastrocnemius, and a decrease in the amplitude of the total EMG of m. rectus femoris. Values of H-reflexes remained at the preoperative level. The analysis of thermal pain sensitivity demonstrated the presence of a more pronounced reaction than that of the motor component. Changes in indicators of this type of sensitivity in groups of adolescents with idiopathic and congenital scoliosis were opposite. In idiopathic scoliosis, negative dynamics of the values prevailed, while in adolescents with congenital deformities of the spine, positive dynamics prevailed. This was because the amount of correction of the main and compensatory curves of the deformity in the group with idiopathic scoliosis was 48% greater (p = 0.0004) and 51% greater (p = 0.011), respectively.
 CONCLUSIONS: After surgical correction of spinal deformities in adolescents, the reactions of the sensory system of thermal pain sensitivity were more pronounced than those of the motor sphere.

De Giorgi\u2019s inequality for the thresholding scheme with arbitrary mobilities and surface tensions

We provide a new convergence proof of the celebrated Merriman–Bence–Osher scheme for multiphase mean curvature flow. Our proof applies to the new variant incorporating a general class of surface tensions and mobilities, including typical choices for modeling grain growth. The basis of the proof are the minimizing movements interpretation of Esedoḡlu and Otto and De Giorgi’s general theory of gradient flows. Under a typical energy convergence assumption we show that the limit satisfies a sharp energy-dissipation relation.

Evolution of FLRW spacetime after the birth of a cosmic string

We consider the evolution of an initially FLRW universe after the formation of a long, straight, cosmic string with arbitrary tension and mass per unit length. The birth of the string sources scalar and tensor-type perturbations in the background metric and both density and velocity perturbations in the background fluid, which compensate for the string mass and maintain energy conservation. The former generate the deficit angle within the light cone of the string and a gravitational shock front at the cosmological horizon, whereas the latter are confined within the sound cone. We study the properties of the metric within each region of the resulting spacetime and give the explicit coordinate transformations which demonstrate non-violation of causality. This paper generalizes the work of previous studies for the Nambu-Goto string.

Derivation of a crack opening deflection relationship for fibre reinforced concrete panels using a stochastic model: Application for predicting the flexural behaviour of round panels using stress crack opening diagrams

This study is aimed at proposing a simple analytical model to investigate the post-cracking behaviour of FRC panels, using an arbitrary tension softening, stress crack opening diagram, as the input. A new relationship that links the crack opening to the panel deflection is proposed. Due to the stochastic nature of material properties, the random fibre distribution, and other uncertainties that are involved in concrete mix, this relationship is developed from the analysis of beams having the same thickness using the Monte Carlo simulation (MCS) technique. The softening diagrams obtained from direct tensile tests are used as the input for the calculation, in a deterministic way, of the mean load displacement response of round panels. A good agreement is found between the model predictions and the experimental results.

Generating black strings

It is generated a five dimensional solution of vacuum Einstein equations, with three free parameters, by means of equipping the Zipoy-Voorhees solution with a scalar field then lifting it to a fifth dimension. This solution presents as particular cases the black string with arbitrary tension and the Gregory-Laflamme black string.The trapped surfaces, mass, tension and the condition of spherical symmetry of the solution are studied.

GENERATING BLACK STRINGS IN HIGHER DIMENSIONS

Starting with a Zipoy–Voorhees line element, we construct and study the three-parameter family of solutions describing a deformed black string with arbitrary tension.

The Validity Range of Low Fidelity Structural Membrane Models

Three classes of structural models can be considered for the characterization of thin extensible pressurized membranes. A low-fidelity, linear model assumes that all of the membrane’s resistance to a transverse pressure is provided from geometric stress-stiffening, and that movement along the membrane is purely out-of-plane. A medium-fidelity model can include geometric nonlinearity (finite strains, non-conservative pressure loads); while the highest level of membrane modeling assumes material nonlinearity: specifically, hyperelasticity. Common modeling applications such as performance prediction, failure prevention, and structural optimization all require repeated function evaluations. As computational cost is proportional to model fidelity, what is the validity range of the two lower fidelity models discussed above? The presence of a large pre-tension within the membrane is known to lessen the role of nonlinear elastic effects: the range of linear transverse deformation increases with pre-tension. Conversely, very low pre-tensions require the use of a nonlinear model, as the linear model becomes unbounded. This work studies the Hencky–Campbell problem for model validation purposes: hydrostatic inflation of a thin flat circular membrane, clamped along its boundary, with an arbitrary initial tension. A full-field, non-contact visual image correlation system is used to estimate the material properties of the rubber membrane, measure the state of pre-tension in the circular sheet, and document the displacement and strain fields as a function of applied pressure. The resulting data set is then compared directly with numerical simulations, in order to estimate the location of the surface of data points wherein a particular low fidelity model (either linear or geometrically nonlinear) loses its predictive capability.

Quasinormal modes of a black hole localized on a codimension-two brane of finite tension

We calculate the quasinormal modes of black holes localized on a 3-brane of finite tension embedded in six-dimensional flat spacetime. Using the WKB approximation, we obtain the frequencies of scalar and gravitational perturbations both analytically and numerically for arbitrary brane tension. We thus extend earlier analytical results which were derived for a brane of small tension.

Black-string solutions with arbitrary tension

We consider $1+4$ dimensional black-string solutions which are invariant under translation along the fifth direction. The solutions are characterized by the two parameters, mass and tension, of the source. The Gregory-Laflamme solution is shown to be characterized by the tension whose magnitude is one half of the mass per unit length of the source. A general class of black-string solutions with arbitrary tension is presented and the spacetime properties of the solutions are discussed.

An efficient parallel computation of unsteady incompressible viscous flow with elastic moving and compliant boundaries on unstructured grids

This paper presents the development and validation of a parallel unstructured-grid fluid–structure interaction (FSI) solver for the simulation of unsteady incompressible viscous flow with long elastic moving and compliant boundaries. The Navier–Stokes solver on unstructured moving grid using the arbitrary Lagrangian Eulerian formulation is based on the artificial compressibility approach and a high-order characteristics-based finite-volume scheme. Both unsteady flow and FSI are calculated with a matrix-free implicit dual time-stepping scheme. A membrane model has been formulated to study fluid flow in a channel with an elastic membrane wall and their interactions. This model can be employed to calculate arbitrary wall movement and variable tension along the membrane, together with a dynamic mesh method for large deformation of the flow field. The parallelization of the fluid–structure solver is achieved using the single program multiple data programming paradigm and message passing interface for communication of data. The parallel solver is used to simulate fluid flow in a two-dimensional channel with and without moving membrane for validation and performance evaluation purposes. The speedups and parallel efficiencies obtained by this method are excellent, using up to 16 processors on a SGI Origin 2000 parallel computer. A maximum speedup of 23.14 could be achieved on 16 processors taking advantage of an improved handling of the membrane solver. The parallel results obtained are compared with those using serial code and they are found to be identical. Copyright © 2005 John Wiley & Sons, Ltd.

Spheres, deficit angles and the cosmological constant

We consider compactifications of six-dimensional gravity in four-dimensional Minkowski or de Sitter space times a two-dimensional sphere, S2. As has been pointed out recently, it is possible to introduce 3-branes in these backgrounds with arbitrary tension without affecting the effective four-dimensional cosmological constant, since its only effect is to induce a deficit angle in the sphere. We show that if a monopole-like configuration of a 6D U(1) gauge field is used to produce the spontaneous compactification of the two extra dimensions in a sphere, a fine-tuning between brane and bulk parameters is reintroduced once the quantization condition for the gauge field is taken into account, so the 4D cosmological constant depends on the brane tension. This problem is absent if instead of the monopole we consider a 4-form field strength in the bulk to obtain the required energy–momentum tensor. Also, making use of the 4-form field, we generalize the solution to an arbitrary number of dimensions (≥6), keeping always four noncompact dimensions and compactifying the rest in an n-dimensional sphere. We show that an (n + 1)-brane with arbitrary tension can be introduced in this background without affecting the effective 4D cosmological constant.

Supersymmetric branes with (almost) arbitrary tensions

We present a supersymmetric version of the two-brane Randall-Sundrum scenario, with arbitrary brane tensions T_1 and T_2, subject to the bound |T_{1,2}| \leq \sqrt{-6\Lambda_5}, where \Lambda_5 < 0 is the bulk cosmological constant. Dimensional reduction gives N=1, D=4 supergravity, with cosmological constant \Lambda_4 in the range \half\Lambda_5 \leq \Lambda_4 \leq 0. The case with \Lambda_4 = 0 requires T_1 = -T_2 = \sqrt{-6\Lambda_5}. This work unifies and generalizes previous approaches to the supersymmetric Randall-Sundrum scenario. It also shows that the Randall-Sundrum fine-tuning is not a consequence of supersymmetry.

FRIEDMANN EQUATION AND CARDY FORMULA CORRESPONDENCE IN BRANE UNIVERSES

We study the brane with arbitrary tension σ on the edge of various black holes with AdS asymptotics. We investigate Friedmann equations governing the motion of the brane universes and match the Friedmann equation to Cardy entropy formula.

Cosmological solutions of supergravity in singular spaces

We study brane-world solutions of five-dimensional supergravity in singular spaces. We exhibit a self-tuned four-dimensional cosmological constant when five-dimensional supergravity is broken by an arbitrary tension on the brane-world. The brane-world metric is of the FRW type corresponding to a cosmological constant Ω Λ=5/7 and an equation of state ω=−5/7 which are consistent with experiment.

Solving the hierarchy problem in two-brane cosmological models

We analyze cosmological solutions in the class of two-brane models with arbitrary tensions which contain matter with general equations of state. We show that the mass hierarchy between the two branes is determined by the ratio of the lapse functions evaluated on the branes. This ratio can be sufficiently small without fine-tuning the brane separation, once the transverse dimension is stabilized. For suitably large interbrane separations, both brane tensions are positive. We also find that the cosmological evolution obeys the standard four-dimensional Friedman equation up to small corrections.

On the existence of surface waves and the propagation of plate waves in pre-stressed fibre-reinforced composites

A theoretical investigation of the effect of pre-stress on wave propagation in a fibre-reinforced plate is carried out using a continuum material model. In the case of both extensional and flexural waves the high wave number phase speed limit of the fundamental mode of the dispersion relation is found to be the corresponding surface wave speed. Whenever such a wave exists it is shown to be unique. The existence of such waves is dependent on the underlying primary deformation; necessary and sufficient conditions for existence are established. For the harmonics, numerical calculations indicate the possibility of two distinct classes of material response. One of these is similar to classical linear isotropic theory. The other is quite different, with a shear wave front arising from the cumulative effect of the harmonics, the contribution of successive harmonics arising in adjacent wave number regimes, and flexural and extensional modes intersecting in both the moderate and high wave number regimes. This shear wave front is further illuminated through examination of the associated group velocity curves, in which corresponding distinct flat maxima are observed. High and low wave number representations of the dispersion relations are derived for each harmonic, giving phase speed as a function of wave number, pre-stress and the arbitrary tension and provide excellent agreement with some illustrative numerical solutions. The paper is concluded with a brief discussion of stability and bifurcation.

Reconstruction of scar hernias--intraoperative tensiometry for objective determination of procedure of choice

The reappearance of incisional hernias after reconstruction depends on the size and tension of the hernia. An additional risk factor is the number of operations that have been performed before. There are two decisive factors that influence the rate of recurrence: the operation technique and the tension applied. To reach a functional reconstruction the incisional hernia must be closed and the abdominal wall must be joined together in an anatomical way. The technique used must be able to tolerate the tension which is necessary to close the abdominal wall. Application of arbitrary tension produces a high rate of recurrence, irrespective of the kind of reconstruction used. Through the intraoperative measurement of the tension applied one can match each hernia (according to size, value and tension) to the most suitable technique. Here the inlay/onlay technique tolerates the highest tension, up to 3.5 kp. With this method and a maximum tension of 3.5 kp we achieved a complete functional reconstruction in 65% of cases and our rate of recurrence amounted to 2.3%.

Numerical analysis of stresses and deformations in composite materials sheet forming: central indentation of a circular sheet

A finite element model is presented for the analysis of predominantly planar composite sheet-forming problems and the numerical results compared with experimental observations. The problem of diaphragm forming a small indentation in the centre of a large composite sheet is treated in detail, by considering uniform radial velocity or pressure boundary conditions at the inner radius. The analysis is carried out for a single ply, which is assumed to behave as a transversely isotropic, incompressible Newtonian fluid at forming temperature. The presence of high volume fractions of continuous elastic reinforcing fibres in the molten polymer leads to the kinematic constraint of inextensibility in the fibre direction, and associated arbitrary tension stresses. A mixed penalty numerical formulation is constructed by discretizing the weak forms of the constraint and governing equations for creeping flow, using independent interpolation of the velocity and tension stress fields. Deformation fields are depicted at each step in the forming process and are shown to be kinematically dominated by the inextensibility of the fibres. Two modes of instability are predicted in the composite laminates: shear-buckling due to the presence of tangential compressive stresses at 45° to the fibre directions; and columnar buckling due to compressive axial stresses in the fibre direction. These compressive stresses are shown to depend on the forming rate, material viscosities, composite sheet dimensions and diaphragm stiffness. Comparisons with relevant experimental observations are included throughout.

A finite element formulation for highly anisotropic incompressible elastic solids

AbstractA numerical approach is developed for the solution of problems of materials with extremely strong directions. Small deformations of a transversely isotropic linear elastic solid, reinforced by a single family of inextensible fibres, are considered. The kinematic constraint equations of incompressibility and inextensibility in the fibre direction lead to the appearance of an arbitrary hydrostatic pressure and an arbitrary tension stress in the constitutive equations. A Galerkin approach is used to discretize the virtual work and weak form of the constraint equations. Independent interpolation of the displacement, pressure and tension fields leads to a mixed system of equations, with characteristic zero‐diagonal terms. The assumption of plane stress conditions in the plane of the fibres results in a simplified displacement‐tension formulation, analogous to the primitive‐variable formulation of Stokes flow. A mixed penalty approximation is then employed to solve for displacement and tension stress fields. Computations are carried out using a biquadratic displacement element with discontinuous bilinear tension stress interpolation. The formulation is used to solve a number of simple beam problems and the results compared to closed‐form solutions.

Prediction of Mechanical States in Wound Capacitors

The problem of determining the mechanical states inside wound capacitor rolls is addressed through the application of two dimensional, linear elasticity. Allowances are made for heterogeneous wound construction of the capacitor, orthotropic material behavior of the capacitor constitutents, and arbitrary winding tension. A key element in the formulation is the derivation of material properties for a wound, orthotropic layer which is equivalent in behavior to a stack of dissimilar piles such as are actually wound on the capacitor simultaneously during one turn of the mandrel. The dissimilar plies are necessary by virtue of the conductor and dielectric materials which must be present in a capacitor. The derivation of predictive equations is based on winding the equivalent layer on an appropriate mandrel, followed by a recovery of the individual ply responses. The capability to explicitly calculate the winding tensions which would be necessary to produce a required wound tension dependence upon capacitor radius is also developed. Numerical results for typical capacitor design and construction are presented, and justification for the application of optimization theory in capacitor development is demonstrated.