A coordination-based approach to elasticity of floppy and stiff random networks

We study the role of connectivity on the linear and nonlinear elastic behavior of amorphous systems using a two-dimensional random network of harmonic springs as a model system. A natural characterization of these systems arises in terms of the network coordination relative to that of an isostatic network $\delta z$; a floppy network has $\delta z<0$, while a stiff network has $\delta z>0$. Under the influence of an externally applied load we observe that the response of both floppy and rigid network are controlled by the same critical point, corresponding to the onset of rigidity. We use numerical simulations to compute the exponents which characterize the shear modulus, the amplitude of non-affine displacements, and the network stiffening as a function of $\delta z$, derive these theoretically and make predictions for the mechanical response of glasses and fibrous networks.

Non-reflective boundary conditions for non-uniform mean velocity inlet and outlet flows

The numerical solution of problems in unbounded physical space requires a truncation of the computational domain to a reasonable size. As a result, the conditions on the artificial boundaries are generally unknown. Assumptions like constant pressure or velocities are only valid in the far field and lead to spurious reflections if applied on the boundaries of the truncated domain. A number of attempts have been made over the past decades to design conditions that prevent such reflections. One approach is based on characteristics. The standard analysis assumes a spatially uniform mean flow field but this is often impractical. In the present paper we show how to extend the formulation to the more general case of a non-uniform mean velocity field. A number of test cases are provided and our results compare favourably with other boundary conditions. In principle the present approach can be extended to include non-uniformities in all variables.

Sufficient conditions for zeno behavior in lagrangian hybrid systems

This paper presents easily verifiable sufficient conditions for the existence of Zenobehavior in Lagrangian hybrid systems, i.e., hybrid systems modeling mechanical systemsundergoing impacts. © 2008 Springer-Verlag Berlin Heidelberg.

Lyapunov-like conditions for the existence of zeno behavior in hybrid and lagrangian hybrid systems

Lyapunov-like conditions that utilize generalizations of energy and barrier functions certifying Zeno behavior near Zeno equilibria are presented. To better illustrate these conditions, we will study them in the context of Lagrangian hybrid systems. Through the observation that Lagrangian hybrid systems with isolated Zeno equilibria must have a onedimensional configuration space, we utilize our Lyapunov-like conditions to obtain easily verifiable necessary and sufficient conditions for the existence of Zeno behavior in systems of this form. © 2007 IEEE.

Effect of soil conditions on uplift of underground structures in liquefied soil

In an earthquake, underground structures located in liquefiable soil deposits are susceptible to floatation following an earthquake event due to their lower unit weight relative to the surrounding saturated soil. Such uplift response of the buoyant structure is influenced by the soil it is buried in. In the case of a liquefiable soil deposit, the soil can lose its shear strength significantly in the event of an earthquake. If the soil liquefies fully, the buoyant structure can float towards the soil surface. However, a partly liquefied soil deposit retains some of its initial shear strength and resists the uplift. This paper discusses the different soil conditions and their influence on the uplift response of buoyant structures. © 2012 World Scientific Publishing Company.

Dynamical structure function identifiability conditions enabling signal structure reconstruction

Networks of controlled dynamical systems exhibit a variety of interconnection patterns that could be interpreted as the structure of the system. One such interpretation of system structure is a system's signal structure, characterized as the open-loop causal dependencies among manifest variables and represented by its dynamical structure function. Although this notion of structure is among the weakest available, previous work has shown that if no a priori structural information is known about the system, not even the Boolean structure of the dynamical structure function is identifiable. Consequently, one method previously suggested for obtaining the necessary a priori structural information is to leverage knowledge about target specificity of the controlled inputs. This work extends these results to demonstrate precisely the a priori structural information that is both necessary and sufficient to reconstruct the network from input-output data. This extension is important because it significantly broadens the applicability of the identifiability conditions, enabling the design of network reconstruction experiments that were previously impossible due to practical constraints on the types of actuation mechanisms available to the engineer or scientist. The work is motivated by the proteomics problem of reconstructing the Per-Arnt-Sim Kinase pathway used in the metabolism of sugars. © 2012 IEEE.

Complex chemistry DNS of n-heptane spray autoignition at high pressure and intermediate temperature conditions

Direct Numerical Simulations (DNS) of turbulent n-heptane sprays autoigniting at high pressure (P=24bar) and intermediate air temperature (Tair=1000K) have been performed to investigate the physical mechanisms present under conditions where low-temperature chemistry is expected to be important. The initial turbulence in the carrier gas, the global equivalence ratio in the spray region, and the initial droplet size distribution of the spray were varied. Results show that spray ignition exhibits a spotty nature, with several kernels developing independently in those regions where the mixture fraction is close to its most reactive value ξMR (as determined from homogeneous reactor calculations) and the scalar dissipation rate is low. Turbulence reduces the ignition delay time as it promotes mixing between air and the fuel vapor, eventually resulting in lower values of scalar dissipation. High values of the global equivalence ratio are responsible for a larger number of ignition kernels, due to the higher probability of finding regions where ξ=ξMR. Spray polydispersity results in the occurrence of ignition over a wider range of mixture fraction values. This is a consequence of the inhomogeneities in the mixing field that characterize these sprays, where poorly mixed rich spots are seen to alternate with leaner ones which are well-mixed. The DNS simulations presented in this work have also been used to assess the applicability of the Conditional Moment Closure (CMC) method to the simulation of spray combustion. CMC is found to be a valid method for capturing spray autoignition, although care should be taken in the modelling of the unclosed terms appearing in the CMC equations. © 2013 The Combustion Institute.

Effect of operating conditions and fuel type on crevice hc emissions: Model results and comparison with experiments

A one-dimensional model for crevice HC post-flame oxidation is used to calculate and understand the effect of operating parameters and fuel type (propane and isooctane) on the extent of crevice hydrocarbon and the product distribution in the post flame environment. The calculations show that the main parameters controlling oxidation are: bulk burned gas temperatures, wall temperatures, turbulent diffusivity, and fuel oxidation rates. Calculated extents of oxidation agree well with experimental values, and the sensitivities to operating conditions (wall temperatures, equivalence ratio, fuel type) are reasonably well captured. Whereas the bulk gas temperatures largely determine the extent of oxidation, the hydrocarbon product distribution is not very much affected by the burned gas temperatures, but mostly by diffusion rates. Uncertainties in both turbulent diffusion rates as well as in mechanisms are an important factor limiting the predictive capabilities of the model. However, it seems well suited to sensitivity calculations about a baseline. Copyright © 1999 Society of Automotive Engineers, Inc.

Coordinated motion design on lie groups

The present paper proposes a unified geometric framework for coordinated motion on Lie groups. It first gives a general problem formulation and analyzes ensuing conditions for coordinated motion. Then, it introduces a precise method to design control laws in fully actuated and underactuated settings with simple integrator dynamics. It thereby shows that coordination can be studied in a systematic way once the Lie group geometry of the configuration space is well characterized. Applying the proposed general methodology to particular examples allows to retrieve control laws that have been proposed in the literature on intuitive grounds. A link with Brockett's double bracket flows is also made. The concepts are illustrated on SO(3), SE(2) and SE(3). © 2010 IEEE.

A PDE viewpoint on basic properties of coordination algorithms with symmetries

Several recent control applications consider the coordination of subsystems through local interaction. Often the interaction has a symmetry in state space, e.g. invariance with respect to a uniform translation of all subsystem values. The present paper shows that in presence of such symmetry, fundamental properties can be highlighted by viewing the distributed system as the discrete approximation of a partial differential equation. An important fact is that the symmetry on the state space differs from the popular spatial invariance property, which is not necessary for the present results. The relevance of the viewpoint is illustrated on two examples: (i) ill-conditioning of interaction matrices in coordination/consensus problems and (ii) the string instability issue. ©2009 IEEE.

Group coordination and cooperative control of steered particles in the plane

The paper overviews recent and ongoing efforts by the authors to develop a design methodology to stabilize isolated relative equilibria in a kinematic model of identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or to circular motion of all particles about the same center with fixed relative headings. © Springer-Verlag Berlin Heidelberg 2006.