Stochastic gravitational background from inflationary phase transitions

We consider true vacuum bubbles generated in a first order phase transition occurring during the slow rolling era of a two field inflation: it is known that gravitational waves are produced by the collision of such bubbles. We find that the epoch of the phase transition strongly affects the characteristic peak frequency of the gravitational waves, causing an observationally interesting redshift in addition to the post-inflationary expansion. In particular it is found that a phase transition occurring typically 10$\div$20 $e-$foldings before the reheating at $kT\simeq 10^{15}$ GeV may be detected by the next Ligo gravity waves interferometers. Moreover, for recently proposed models capable of generating the observed large scale voids as remnants of the primordial bubbles (for which the characteristic wave lengths are several tens of Mpc), it is found that the level of anisotropy of the cosmic microwave background provides a deep insight upon the physical parameters of the effective Lagrangian.Comment: 12 pages, 3 figures. Phys.Rev.D in pres

Collision avoidance maneuver design based on multi-objective optimization

The possibility of having collision between a satellite and a space debris or another satellite is becoming frequent. The amount of propellant is directly related to a satellite’s operational lifetime and revenue. Thus, collision avoidance maneuvers should be performed in the most efficient and effective manner possible. In this work the problem is formulated as a multi-objective optimization. The first objective is the Δv, whereas the second and third one are the collision probability and relative distance between the satellite and the threatening object in a given time window after the maneuver. This is to take into account that multiple conjunctions might occur in the short-term. This is particularly true for the GEO regime, where close conjunction between a pair of object can occur approximately every 12h for a few days. Thus, a CAM can in principle reduce the collision probability for one event, but significantly increase it for others. Another objective function is then added to manage mission constraint. To evaluate the objective function, the TLE are propagated with SGP4/SDP4 to the current time of the maneuver, then the Δv is applied. This allow to compute the corresponding “modified” TLE after the maneuver and identify (in a given time window after the CAM) all the relative minima of the squared distance between the spacecraft and the approaching object, by solving a global optimization problem rigorously by means of the verified global optimizer COSY-GO. Finally the collision probability for the sieved encounters can be computed. A Multi-Objective Particle Swarm Optimizer is used to compute the set of Pareto optimal solutions.The method has been applied to two test cases, one that considers a conjunction in GEO and another in LEO. Results show that, in particular for the GEO case, considering all the possible conjunctions after one week of the execution of a CAM can prevent the occurrence of new close encounters in the short-term

Discretization schemes for constraint stabilization in nonlinear differential-algebraic systems

In this paper the problem of simulation of differential-algebraic systems is addressed. In modelling mechanical systems the use of redundant coordinates and constraints results in differential-algebraic equations, the integration of which can lead to numerical instabilities, such as the so-called drift phenomenon. In [1] the authors have proposed a globally convergent conceptual continuous-time algorithm for the integration of constrained mechanical systems which ensures the existence of solutions and global attractivity of the solution manifold. The objective of this paper is to study the numerical implementation of the algorithm presented in [1]. In addition, the stability properties of the constrained system in the manifold are studied in both the continuous and discrete time cases. The proposed technique is illustrated by means of a simple example

Long term nonlinear propagation of uncertainties in perturbed geocentric dynamics using automatic domain splitting

Current approaches to uncertainty propagation in astrodynamics mainly refer tolinearized models or Monte Carlo simulations. Naive linear methods fail in nonlinear dynamics, whereas Monte Carlo simulations tend to be computationallyintensive. Differential algebra has already proven to be an efficient compromiseby replacing thousands of pointwise integrations of Monte Carlo runs with thefast evaluation of the arbitrary order Taylor expansion of the flow of the dynamics. However, the current implementation of the DA-based high-order uncertainty propagator fails in highly nonlinear dynamics or long term propagation. We solve this issue by introducing automatic domain splitting. During propagation, the polynomial of the current state is split in two polynomials when its accuracy reaches a given threshold. The resulting polynomials accurately track uncertainties, even in highly nonlinear dynamics and long term propagations. Furthermore, valuable additional information about the dynamical system is available from the pattern in which those automatic splits occur. From this pattern it is immediately visible where the system behaves chaotically and where its evolution is smooth. Furthermore, it is possible to deduce the behavior of the system for each region, yielding further insight into the dynamics. In this work, the method is applied to the analysis of an end-of-life disposal trajectory of the INTEGRAL spacecraft

Ultimate capacity of diagrid systems for tall buildings in nominal configuration and damaged state

One of the evocative structural design solutions for tall buildings is recently embraced by the diagrid (diagonal grid) structural system. Diagrid, with a perimeter structural configuration characterized by a narrow grid of diagonal members involved both in gravity and in lateral load resistance, requires less structural steel than a conventional steel frame, provides for a more sustainable structure and has emerged as a new design trend for tall-shaped complex structures due to aesthetics and structural performance. The purpose of this study is twofold. First, to assess the optimal structural design of a diagrid tall-building, also compared to a typical outrigger building, focusing on the sustainability (the use of structural steel) and the structural safety and serviceability. To this aim, dierent diagrid geometries are tested and compared. Second, to provide some insight on the residual strength of diagrid structures, also in the damaged state (modelled by the elimination of diagonal grids). Both goals are accomplished using FEM nonlinear analyses

Simplified FEM modelling for the collapse assessment of a masonry vault

This study is motivated from the collapse of an old masonry building in the Southern Italy. FEM analyses are carried out focusing on the influence of the contrasting wall on the stability of the vault. In the analyses, the structure is subjected to a damage scenario on the contrasting wall due to a demolition project, and the consequence of the damage is evaluated using the explicit dynamic simulation made by Ls-Dyna®. A micro modelling technique (discrete FEM model) is adopted to model the masonry: the mortar is modelled by contact surfaces between the masonry units, which are explicitly modelled by blocks of meshes. This modelling technique is proven to be effective to predict the collapse behavior of the structure

Simplified FEM modelling for the collapse assessment of a masonry vault

This study is motivated from the collapse of an old masonry building in the Southern Italy. FEM analyses are carried out focusing on the influence of the contrasting wall on the stability of the vault. In the analyses, the structure is subjected to a damage scenario on the contrasting wall due to a demolition project, and the consequence of the damage is evaluated using the explicit dynamic simulation made by Ls-Dyna�. A micro modelling technique (discrete FEM model) is adopted to model the masonry: the mortar is modelled by contact surfaces between the masonry units, which are explicitly modelled by blocks of meshes. This modelling technique is proven to be effective to predict the collapse behavior of the structure

An automatic domain splitting technique to propagate uncertainties in highly nonlinear orbital dynamics

Current approaches to uncertainty propagation in astrodynamics mainly refer to linearized models or Monte Carlo simulations. Naive linear methods fail in nonlinear dynamics, whereas Monte Carlo simulations tend to be computationally intensive. Differential algebra has already proven to be an efficient compromise by replacing thousands of pointwise integrations of Monte Carlo runs with the fast evaluation of the arbitrary order Taylor expansion of the flow of the dynamics. However, the current implementation of the DA-based high-order uncertainty propagator fails in highly nonlinear dynamics or long term propagation. We solve this issue by introducing automatic domain splitting. During propagation, the polynomial of the current state is split in two polynomials when its accuracy reaches a given threshold. The resulting polynomials accurately track uncertainties, even in highly nonlinear dynamics. The method is tested on the propagation of (99942) Apophis post-encounter motion