Symmetry and order parameter dynamics of the human odometer

Bipedal gaits have been classified on the basis of the group symmetry of the minimal network of identical differential equations (alias cells) required to model them. Primary bipedal gaits (e.g., walk, run) are characterized by dihedral symmetry, whereas secondary bipedal gaits (e.g., gallop-walk, gallop- run) are characterized by a lower, cyclic symmetry. This fact has been used in tests of human odometry (e.g., Turvey et al. in P Roy Soc Lond B Biol 276:4309–4314, 2009, J Exp Psychol Hum Percept Perform 38:1014–1025, 2012). Results suggest that when distance is measured and reported by gaits from the same symmetry class, primary and secondary gaits are comparable. Switching symmetry classes at report compresses (primary to secondary) or inflates (secondary to primary) measured distance, with the compression and inflation equal in magnitude. The present research (a) extends these findings from overground locomotion to treadmill locomotion and (b) assesses a dynamics of sequentially coupled measure and report phases, with relative velocity as an order parameter, or equilibrium state, and difference in symmetry class as an imperfection parameter, or detuning, of those dynamics. The results suggest that the symmetries and dynamics of distance measurement by the human odometer are the same whether the odometer is in motion relative to a stationary ground or stationary relative to a moving ground.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Evaluating vehicle painting plans in an automobile assembly plant using an integrated AHP-PROMETHEE approach

The painting activity is one of the most complex and important activities in automobile manufacturing. The inherent complexity of the painting activity and the frequent need for repainting usually turn the painting process into a bottleneck in automobile assembly plants, which is reflected in higher operating costs and longer overall cycle times. One possible approach for optimizing the performance of the paint shop is to improve the efficiency of the color planning. This can be accomplished by evaluating the relative merits of a set of vehicle painting plans. Since this problem has a multicriteria nature, we resort to the multicriteria decision analysis (MCDA) methodology to tackle it. A recent trend in the MCDA field is the development of hybrid approaches that are used to achieve operational synergies between different methods. Here we apply, for the first time, an integrated approach that combines the strengths of the analytic hierarchy process (AHP) and the Preference Ranking Organization METHod for Enrichment Evaluations (PROMETHEE), aided by Geometrical Analysis for Interactive Aid (GAIA), to the problem of assessing alternative vehicle painting plans. The management of the assembly plant found the results of value and is currently using them in order to schedule the painting activities such that an enhancement of the operational efficiency of the paint shop is obtained. This efficiency gain has allowed the management to bid for a new automobile model to be assembled at this specific plant.

Simulation of masonry out-of-plane failure modes by multi-body dynamics

The seismic assessment of the local failure modes in existing masonry buildings is currently based on the identification of the so-called local mechanisms, often associated with the out-of-plane wall behavior, whose stability is evaluated by static force-based approaches and, more recently, by some displacement-based proposals. Local mechanisms consist of kinematic chains of masonry portions, often regarded as rigid bodies, with geometric nonlinearity and concentrated nonlinearity in predefined contact regions (unilateral no-tension behavior, possible sliding with friction). In this work, the dynamic behavior of local mechanisms is simulated through multi-body dynamics, to obtain the nonlinear response with efficient time history analyses that directly take into account the characteristics of the ground motion. The amplification/filtering effects of the structure are considered within the input motion. The proposed approach is validated with experimental results of two full-scale shaking-table tests on stone masonry buildings: a sacco-stone masonry façade tested at Laboratório Nacional de Engenharia Civil and a two-storey double-leaf masonry building tested at European Centre for Training and Research in Earthquake Engineering (EUCENTRE).