Low-energy effective theory for a Randall-Sundrum scenario with a moving bulk brane

We derive the low-energy effective theory of gravity for a generalized Randall-Sundrum scenario, allowing for a third self-gravitating brane to live in the 5D bulk spacetime. At zero order the 5D spacetime is composed of two slices of anti-de Sitter spacetime, each with a different curvature scale, and the 5D Weyl tensor vanishes. Two boundary branes are at the fixed points of the orbifold whereas the third brane is free to move in the bulk. At first order, the third brane breaks the otherwise continuous evolution of the projection of the Weyl tensor normal to the branes. We derive a junction condition for the projected Weyl tensor across the bulk brane, and combining this constraint with the junction condition for the extrinsic curvature tensor, allows us to derive the first-order field equations on the middle brane. The effective theory is a generalized Brans-Dicke theory with two scalar fields. This is conformally equivalent to Einstein gravity and two scalar fields, minimally coupled to the geometry, but nonminimally coupled to matter on the three branes.Comment: 16 pages, 1 figure, typos correcte

Finite Element Analysis of G-10 Flange/Board for the CC Feedthrough Box

The assembly of the stainless steel feedthrough box for the CC cryostat resulted in distortion of the slotted plates through which the circuit boards must be installed. Due to the o-ring grooves in the plates and the presence of small pump out passages it is difficult to machine the surface flat after installation. Installing the boards on the distorted surface requires distorting the g-10 flange and the board which is glued to it to match the surface distortion and achieve a seal. This results in stresses for which the epoxy bond may not be adequate. The purpose of this work is to estimate the shear and normal stresses in the two critical planes between the board and flange and evaluate epoxy joint performance

Summary of Deflections from Fully Assembled EC Structure Finite Element Model

The purpose of this note is to summarize the deflections in the fully assembled EC OH and MH module arrays as calculated by a superelement finite element model. These results are for the case where the OH modules are fully connected at four locations on the inner radius and four locations on the outer radius. Both the OH and MH modules are modeled as skins and endplates (and in the case of OH, internal structural plates) only. The OH module has a skin thickness of 1/16-in. Fig. 1 shows the fully assembled model and the coordinate system used to express deflections. The deflections at the inner and outer radius at both the front (nearest the collision center) and the back of the module assemblies are given in Tables I-IV. A summary of the deflections is given

Finite Element Analysis of EC Insert Plug

The proposed EC calorimeter insert plug was modeled with ANSYS to verify that the shell thickness calculated with beam formulas are adequate. The finite element model and dimensions is shown in Fig. 1. The geometry and shell thicknesses used were the best numbers available as of 3/28/86. The model includes only the inner and outer shells and intermediate structural discs. The total weight of the plug is calculated to be 75000 lbs. The plug is supported against this weight at the four nodes indicated in Fig. 1. A vertical constraint was used. The calorimeter plates are not explicitly modeled. Their weight is placed on the inner shell by giving the shell material an appropriate density and applying a global acceleration. In addition to the weight loading, there will also be a pressure loading applied to both end plates as a result of preloading the calorimeter plates compressively. This pressure is estimated to be 20 pSi, and was represented in the model as a uniform pressure applied across each end plate. The large axial force produced by this pressure precludes the possibility of attaching the inner shell to both end plates. Such attachments would be under unreasonably high stress as the plates were preloaded, and the inner shell would be under a state of tension in trying to resist the axial force. In the real structure, the inner shell will be attached to at most one of the end plates. The axial force is then developed solely in the outer shell, which has a considerable area of attachment. To emulate this in the finite model, nodal coupling was used to couple the shell laterally to both end plates and all intermediate discs to ensure weight transfer, but axially the shell was only coupled to one of the end plates. The materials used were assumed to be SS 3011 with a Young's modulus of 28.3 (10{sup 6}) psi. Stresses were evaluated according to the limits and claSSifications of the ASME Boiler and Pressure Vessel Code, Section VIII, Division 2, Appendix 11 assuming a maximum allowable stress intensity of 20000 psi for primary membrane stress

Summary of Stress Analysis of CC Cryostat w/o Stiffening Rings

A finite element model of the CC cryostat was used to investigate the stresses resulting in this structure under internal pressure (30 psi at the top of the vessel increasing linearly to 40 psi at the bottom) and weight loadings. Figures 1 and 2 show the model and relevant physical dimensions. The results are given in Table I. The stresses were extracted. from the nodal stress output for individual elements. The variation of stress over the element is some indication of mesh adequacy in the absence of additional results from a finer mesh. Based on this variation, the stresses output for the central cylinder and head appear to be quite good. The nodal stresses vary about 15% within the most highly stressed elements. The maximum stresses in the outer cylinder occur in the element defined by the four nodes used for support. Stresses within this element vary by a factor of {approx}2. It is fair to say that no detailed information on stresses in the shell at the support is available with this mesh. However, outer shell stresses away from the supports are well within the limits for SS 304 as given by Section VIII, Division 2, Appendix 4. A basic node map of the axisymmetric node pattern is shown in Fig. 3 as an aid in interpreting output. This pattern is repeated 25 times about the Y-axis, with an increment of 70 in node number, and an angular increment of 7.5{sup o}. It can be concluded from the stress results that stiffening rings are not necessary in the assembled central calorimeter cryostat due to the relatively short length of the vessel and the stiffening effects of the heads. Detailed stress results in the region of the supports will be investigated in the future with a refined local mesh

Primordial non-Gaussianity from two curvaton decays

We study a model where two scalar fields, that are subdominant during inflation, decay into radiation some time after inflation has ended but before primordial nucleosynthesis. Perturbations of these two curvaton fields can be responsible for the primordial curvature perturbation. We write down the full non-linear equations that relate the primordial perturbation to the curvaton perturbations on large scales, calculate the power spectrum of the primordial perturbation, and finally go to second order to find the non-linearity parameter, fNL. We find large positive values of fNL if the energy densities of the curvatons are sub-dominant when they decay, as in the single curvaton case. But we also find a large fNL even if the curvatons dominate the total energy density in the case when the inhomogeneous radiation produced by the first curvaton decay is diluted by the decay of a second nearly homogeneous curvaton. The minimum value min(fNL)=-5/4 which we find is the same as in the single-curvaton case.Comment: 20 pages, 5 figure

Coupled boundary and bulk fields in anti-de Sitter

We investigate the dynamics of a boundary field coupled to a bulk field with a linear coupling in an anti-de Sitter bulk spacetime bounded by a Minkowski (Randall-Sundrum) brane. An instability criterion for the coupled boundary and bulk system is found. There exists a tachyonic bound state when the coupling is above a critical value, determined by the masses of the brane and bulk fields and AdS curvature scale. This bound state is normalizable and localised near the brane, and leads to a tachonic instability of the system on large scales. Below the critical coupling, there is no tachyonic state and no bound state. Instead, we find quasi-normal modes which describe stable oscillations, but with a finite decay time. Only if the coupling is tuned to the critical value does there exist a massless stable bound state, as in the case of zero coupling for massless fields. We discuss the relation to gravitational perturbations in the Randall-Sundrum brane-world.Comment: 12 pages, 4 figures, revtex

Brane-world inflation: slow-roll corrections to the spectral index

We quantify the slow-roll corrections to primordial density perturbations arising from inflation driven by a four-dimensional scalar field with a monomial potential in a five-dimensional non-compact bulk spacetime. Although the difference between the classical brane-world solutions and standard four-dimensional solutions is large at early times, the change to the amplitude at late times of perturbations generated from quantum fluctuations is first-order in slow-roll parameters, leading to second-order slow-roll corrections to the spectral index. This confirms that the leading-order effects are correctly given by previous work in the literature.Comment: 6 pages, 1 figur