Moment Closure - A Brief Review

Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation describes the evolution of one "moment", a suitable coarse-grained quantity computable from the full state space. If the system is too large for analytical and/or numerical methods, then one aims to reduce it by finding a moment closure relation expressing "higher-order moments" in terms of "lower-order moments". In this brief review, we focus on highlighting how moment closure methods occur in different contexts. We also conjecture via a geometric explanation why it has been difficult to rigorously justify many moment closure approximations although they work very well in practice.Comment: short survey paper (max 20 pages) for a broad audience in mathematics, physics, chemistry and quantitative biolog

Influence of variability of material mechanical properties on seismic performance of steel and steel-concrete composite structures

Modern standards for constructions in seismic zones allow the construction of buildings able to dissipate the energy of the seismic input through an appropriate location of cyclic plastic deformations involving the largest possible number of structural elements, forming thus a global collapse mechanisms without failure and instability phenomena both at local and global level. The key instrument for this purpose is the capacity design approach, which requires an appropriate selection of the design forces and an accurate definition of structural details within the plastic hinges zones, prescribing at the same time the oversizing of non-dissipative elements that shall remain in the elastic field during the earthquake. However, the localization of plastic hinges and the development of the global collapse mechanism is strongly influenced by the mechanical properties of materials, which are characterized by an inherent randomness. This variability can alter the final structural behaviour not matching the expected performance. In the present paper, the influence of the variability of material mechanical properties on the structural behaviour of steel and steel/concrete composite buildings is analyzed, evaluating the efficiency of the capacity design approach as proposed by Eurocode 8 and the possibility of introducing an upper limitation to the nominal yielding strength adopted in the design

The J-value and its role in evaluating investments in fire safety schemes

Fire safety engineers endeavour to ensure that a design achieves an adequate level of fire safety. For uncommon buildings, adequate safety cannot be based on precedent and an explicit evaluation of the adequacy of proposed safety features may be required. Commonly, this requires demonstration that the residual risk associated with the design is as low as is reasonably practicable. In those situations, a measure for a safety scheme’s benefit relative to its cost is required, as more efficient safety schemes should be preferred over less efficient ones to maximize the number of lives saved under societal resource constraints. To this end, the J-value has been introduced in other engineering fields as a decision support indicator for assessing the efficacy of safety features. The J-value has been derived from societal welfare considerations (the Life Quality Index) and is adopted in the current paper for applications in fire safety engineering. It is demonstrated herein how the J-value can inform decisions on fire safety, and how it can provide a basis for assessing whether or not a proposed fire safety scheme should be implemented. Future work will focus on its implementation as a tool for assessing the benefit of real life fire safety scheme implementations, such as sprinkler installations