相关论文: Autonomy and Singularity in Dynamic Fracture

This study presents the formulation, the numerical solution, and the validation of a theoretical framework based on the concept of variable-order mechanics and capable of modeling dynamic fracture in brittle and quasi-brittle solids. More…

The concept of cracking refers to the tendency of a fluid distribution to "split'', once it abandons the equilibrium. In this manuscript we develop a general formalism to describe the occurrence of cracking within a dissipative fluid…

We investigate spontaneous symmetry breaking in a conformally invariant gravitational model. In particular, we use a conformally invariant scalar tensor theory as the vacuum sector of a gravitational model to examine the idea that…

Models of faults incorporating slip rate- and state-dependent friction have reproduced phenomena from spontaneous slow, aseismic slip to earthquake-generating dynamic rupture. Numerical explorations of model parameter space regularly show…

We propose a phase-field model of dynamic fracture based on the Ambrosio--Tortorelli's approximation, which takes into account dissipative effects due to the speed of the crack tips. By adapting the time discretization scheme contained in…

Optimal paths play a fundamental role in numerous physical applications ranging from random polymers to brittle fracture, from the flow through porous media to information propagation. Here for the first time we explore the path that is…

Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…

A dry frictional interface loaded in shear often displays stick-slip. The amplitude of this cycle depends on the probability that a microscopic event nucleates a rupture and on the rate at which microscopic events are triggered. The latter…

We examine in a generic context how the $\mu$ problem can be resolved by means of a spontaneously broken gauge symmetry. We then focus on the new scheme based on a discrete gauge R symmetry which is spontaneously broken by nonperturbative…

This paper has been withdrawn. Consider an isolated complex hypersurface singularity, f(x_1,..,x_n)=0. For Newton-non-degenerate singularities the local topology is completely determined by an associated polyhedral object, the Newton…

We report numerical results on the velocity statistics of topological defects during the dynamics of phase ordering and non-relaxational evolution assisted by an external shear ow. We propose a numerically efficient tracking method for…

The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is strong evidence that all integrable…

To model rupture dynamics, a friction law must be assumed. Commonly used constitutive laws for modeling friction include slip-weakening laws which are characterized by a drop from static to dynamic frictional stress. Within this framework,…

In this paper, we give a singular function on a unit interval derived from the dynamic of the one-dimensional elementary cellular automaton Rule 150. We describe properties of the resulting function, that is strictly increasing, uniformly…

The frictional instability associated with earthquake initiation and earthquake dynamics is believed to be mainly controlled by the dynamics of fragmented rocks within the fault gauge. Principal features of the emerging seismicity (e.g.…

In linearised continuum elasticity, the elastic strain due to a straight dislocation line decays as $O(r^{-1})$, where $r$ denotes the distance to the defect core. It is shown in Ehrlacher, Ortner, Shapeev (2016) that the core correction…

The extent to which time-dependent fracture criteria affect the dynamic behavior of fracture in a discrete structure is discussed in this work. The simplest case of a semi-infinite isotropic chain of oscillators has been studied. Two…

We study the Cauchy problem for the $3D$ compressible Euler equations under an arbitrary equation of state with positive speed of sound, aside from that of a Chaplygin gas. For open sets of smooth initial data with non-trivial vorticity and…

We study, both analytically and numerically, the dynamics of elastic boundaries such as crack fronts in fracture and surfaces of contact in solid on solid friction. The elastic waves in the solid give rise to kinks that move with a…

The damped and parametrically driven nonlinear Dirac equation with arbitrary nonlinearity parameter $\kappa$ is analyzed, when the external force is periodic in space and given by $f(x) =r\cos(K x)$, both numerically and in a variational…