Related papers: Catastrophe in Elastic Tensegrity Frameworks
We discuss the equilibrium of a single collective variable characterizing a finite set of coupled, noisy, bistable systems as the noise strength, the size and the coupling parameter are varied. We identify distinct regions in parameter…
Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant…
For a bar-joint framework $(G,p)$, a subgroup $\Gamma$ of the automorphism group of $G$, and a subgroup of the orthogonal group isomorphic to $\Gamma$, we introduce a symmetric averaging map which produces a bar-joint framework on $G$ with…
During a financial crisis, the capital markets network frequently exhibits a high correlation between returns. We developed a network analysis framework based on daily returns from 42 countries to determine systemic stability. Our network…
We examine the issue of stability of probability in reasoning about complex systems with uncertainty in structure. Normally, propositions are viewed as probability functions on an abstract random graph where it is implicitly assumed that…
Representing and quantifying uncertainty in physical parameterisations is a central challenge in weather and climate modelling, and approaches are often developed separately for different timescales. Here, we introduce a unified framework…
A re-investigation of the gravothermal catastrophe is presented. By means of a linear perturbation analysis, we study the dynamical stability of a spherical self-gravitating isothermal fluid of finite volume and find that the conditions for…
The failure of mechanical metamaterials is a function of the interplay between the properties of the base material and the microstructural geometry. Stochastic failure properties of the base material and disordered microstructural…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
Hysteresis is a nonlinear phenomenon with memory effects, where a system's output depends on both its current state and past states. It is prevalent in various physical and mechanical systems, such as yielding structures under seismic…
An economy-wide production network, manifested through monetary input-output coefficients, inherently destabilizes during the general equilibrium propagation of sectoral productivity shocks when substitution elasticities are non-neutral.…
We present a computational framework for analyzing and quantifying system flexibility. Our framework incorporates new features that include: general uncertainty characterizations that are constructed using composition of sets, procedures…
A central problem in uncertainty quantification is how to characterize the impact that our incomplete knowledge about models has on the predictions we make from them. This question naturally lends itself to a probabilistic formulation, by…
We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on…
Linear stability analysis of speckle pattern resulting from multiple, diffuse scattering of coherent light waves in random media with intensity-dependent refractive index (noninstantaneous Kerr nonlinearity) is performed. The speckle…
The stability analysis of elastic rings subjected to various loading conditions is examined, focusing on stable and unstable configurations. The harmonic balance method is employed to investigate the stability range under different loading…
Kinetic traps are a notorious problem in equilibrium statistical mechanics, where temperature quenches ultimately fail to bring the system to low energy configurations. Using multifarious self-assembly as a model system, we introduce a…
This paper presents the formulations of nonlinear and linearized statics, dynamics, and control for any clustered tensegrity system (CTS). Based on the Lagrangian method and FEM assumptions, the nonlinear clustered tensegrity dynamics with…
The Numerical Assembly Technique is extended to investigate arbitrary planar frame structures with the focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial…