Related papers: Autonomy and Singularity in Dynamic Fracture
We study how the loading rate, specimen geometry and microstructural texture select the dynamics of a crack moving through an heterogeneous elastic material in the quasi-static approximation. We find a transition, fully controlled by two…
Some exact, nonlinear, vacuum gravitational wave solutions are derived for certain polynomial $f(R)$ gravities. We show that the boundaries of the gravitational domain of dependence, associated with events in polynomial $f(R)$ gravity, are…
The equations of stress equilibrium and strain compatibility/incompatibility are discussed for fields with point singularities in a planar domain. The sufficiency (or insufficiency) of the smooth maps, obtained by restricting the singular…
The possibility to avoid the cosmic initial singularity as a consequence of nonlinear effects on the Maxwell eletromagnetic theory is discussed. For a flat FRW geometry we derive the general nonsingular solution supported by a magnetic…
We offer a fractonic perspective on a familiar observation -- a flat sheet of paper can be folded only along a straight line if one wants to avoid the creation of additional creases or tears. Our core underlying technical result is the…
Spontaneous symmetry breaking in statistical mechanics primarily occurs during phase transitions at the thermodynamic limit where the Hamiltonian preserves inversion symmetry, yet the low-temperature free energy exhibits reduced symmetry.…
The lifetime and performance of any engineering component, from nanoscale sensors to macroscopic structures, are strongly influenced by fracture processes. Fracture itself is a highly localized event; originating at the atomic scale by bond…
A nonlocal field theory of peridynamic type is applied to model the brittle fracture problem. The elastic fields obtained from the nonlocal model are shown to converge in the limit of vanishing non-locality to solutions of classic plane…
In this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the…
A recent purely theoretical prediction stated that in frictional granular packings, mechanical balance and material isotropy constrain the stress auto-correlation matrix to be fully determined by two spatially isotropic functions: the…
It is well known from the quantum theory of strongly correlated systems that poles (or more subtle singularities) of dynamic correlation functions in complex plane usually correspond to the collective or localized modes. Here we address…
We present a new data-driven paradigm for variational brittle fracture mechanics. The fracture-related material modeling assumptions are removed and the governing equations stemming from variational principles are combined with a set of…
Flutter stability is a dominant design constraint of modern gas and steam turbines. To further increase the feasible design space, flutter-tolerant designs are currently explored, which may undergo Limit Cycle Oscillations (LCOs) of…
In the present work, we introduce a discrete formulation of the nonlinear Dirac equation in the form of a discretization of the Gross-Neveu model. The motivation for this discrete model proposal is both computational (near the continuum…
We report exact black hole solutions in asymptotically flat or (A)dS four-dimensional spacetime with a conformally coupled self-interacting scalar field in $f(R)$ gravity. We first consider the asymptotically flat model $f(R) = R -2\alpha…
The linear response of two-dimensional amorphous elastic bodies to an external delta force is determined in analogy with recent experiments on granular aggregates. For the generated forces, stress and displacement fields, we find strong…
We consider a simple model of particle transport on the line defined by a dynamical map F satisfying F(x+1) = 1 + F(x) for all x in R and F(x) = ax + b for |x| < 0.5. Its two parameters a (`slope') and b (`bias') are respectively symmetric…
Rayleigh-Taylor instability (RTI) occurs in a range of industrial and natural processes. Whereas the vast majority of existing studies have considered constant acceleration, RTI is in most instances driven by variable acceleration. Here we…
Using an elastostatic description of crack growth based on the Griffith criterion and the principle of local symmetry, we present a stochastic model describing the propagation of a crack tip in a 2D heterogeneous brittle material. The model…
We show that nonlinear tight-binding lattices of different geometries and dimensionalities, display an universal selftrapping behavior. First, we consider the single nonlinear impurity problem in various tight-binding lattices, and use the…