20 research outputs found
Nonlinear dynamics of hysteretic oscillators
The dynamic response and bifurcations of a harmonic oscillator with a hysteretic
restoring force and sinusoidal excitation are investigated. A multilinear model
of hysteresis is presented. A hybrid system approach is used to formulate and study
the problem. A novel method for obtaining exact transient and steady state response
of the system is discussed. Simple periodic orbits of the system are analyzed using
the KBM method and an analytic criterion for existence of bound and unbound
resonance is derived. Results of KBM analysis are compared with those from numerical
simulations. Stability and bifurcations of higher period orbits are studied using
Poincar´e maps. The Poincar´e map for the system is constructed by composing the
corresponding maps for the individual subsystems of the hybrid system. The novelty
of this work lies in a.) the study of a multilinear model of hysteresis, and, b.) developing
a methodology for obtaining the exact transient and steady state response of
the system
Fracture strength: Stress concentration, extreme value statistics and the fate of the Weibull distribution
The fracture strength distribution of materials is often described in terms
of the Weibull law which can be derived by using extreme value statistics if
elastic interactions are ignored. Here, we consider explicitly the interplay
between elasticity and disorder and test the asymptotic validity of the Weibull
distribution through numerical simulations of the two-dimensional random fuse
model. Even when the local fracture strength follows the Weibull distribution,
the global failure distribution is dictated by stress enhancement at the tip of
the cracks and sometimes deviates from the Weibull law. Only in the case of a
pre-existing power law distribution of crack widths do we find that the failure
strength is Weibull distributed. Contrary to conventional assumptions, even in
this case, the Weibull exponent can not be simply inferred from the exponent of
the initial crack width distribution. Our results thus raise some concerns on
the applicability of the Weibull distribution in most practical cases
Toughness and Strength of Nanocrystalline Graphene
Pristine monocrystalline graphene is claimed to be the strongest material
known with remarkable mechanical and electrical properties. However, graphene
made with scalable fabrication techniques is polycrystalline and contains
inherent nano-scale line and point defects - grain boundaries and
grain-boundary triple junctions - that lead to significant statistical
fluctuations in toughness and strength. These fluctuations become particularly
pronounced for nanocrystalline graphene where the density of defects is high.
Here we use large-scale simulation and continuum modeling to show that the
statistical variation in toughness and strength can be understood with
'weakest-link' statistics. We develop the first statistical theory of toughness
in polycrystalline graphene, and elucidate the nano-scale origins of the
grain-size dependence of its strength and toughness. Our results should lead to
more reliable graphene device design, and provide a framework to interpret
experimental results in a broad class of 2D materials.Comment: 6 pages, 5 figures, 50 Reference
Dielectric breakdown and avalanches at non-equilibrium metal-insulator transitions
Motivated by recent experiments on the finite temperature Mott transition in
VO2 films, we propose a classical coarse-grained dielectric breakdown model
where each degree of freedom represents a nanograin which transitions from
insulator to metal with increasing temperature and voltage at random thresholds
due to quenched disorder. We describe the properties of the resulting
non-equilibrium metal-insulator transition and explain the universal
characteristics of the resistance jump distribution. We predict that by tuning
voltage, another critical point is approached, which separates a phase of
"bolt"-like avalanches from percolation-like ones.Comment: 4 pages, 3 figure
Fracture Strength of Disordered Media: Universality, Interactions, and Tail Asymptotics
We study the asymptotic properties of fracture strength distributions of disordered elastic media by a combination of renormalization group, extreme value theory, and numerical simulation. We investigate the validity of the “weakest-link hypothesis” in the presence of realistic long-ranged interactions in the random fuse model. Numerical simulations indicate that the fracture strength is well-described by the Duxbury-Leath-Beale (DLB) distribution which is shown to flow asymptotically to the Gumbel distribution. We explore the relation between the extreme value distributions and the DLB-type asymptotic distributions and show that the universal extreme value forms may not be appropriate to describe the nonuniversal low-strength tail.Peer reviewe
Deformation of Crystals: Connections with Statistical Physics
We give a bird's-eye view of the plastic deformation of crystals aimed at the statistical physics community, as well as a broad introduction to the statistical theories of forced rigid systems aimed at the plasticity community. Memory effects in magnets, spin glasses, charge density waves, and dilute colloidal suspensions are discussed in relation to the onset of plastic yielding in crystals. Dislocation avalanches and complex dislocation tangles are discussed via a brief introduction to the renormalization group and scaling. Analogies to emergent scale invariance in fracture, jamming, coarsening, and a variety of depinning transitions are explored. Dislocation dynamics in crystals challenge nonequilibrium statistical physics. Statistical physics provides both cautionary tales of subtle memory effects in nonequilibrium systems and systematic tools designed to address complex scale-invariant behavior on multiple length scales and timescales
Deformation of Crystals: Connections with Statistical Physics
We give a bird's-eye view of the plastic deformation of crystals aimed at the statistical physics community, as well as a broad introduction to the statistical theories of forced rigid systems aimed at the plasticity community. Memory effects in magnets, spin glasses, charge density waves, and dilute colloidal suspensions are discussed in relation to the onset of plastic yielding in crystals. Dislocation avalanches and complex dislocation tangles are discussed via a brief introduction to the renormalization group and scaling. Analogies to emergent scale invariance in fracture, jamming, coarsening, and a variety of depinning transitions are explored. Dislocation dynamics in crystals challenge nonequilibrium statistical physics. Statistical physics provides both cautionary tales of subtle memory effects in nonequilibrium systems and systematic tools designed to address complex scale-invariant behavior on multiple length scales and timescales