Related papers: Depinning of elastic manifolds
We present a method to derive an analytical expression for the roughness of an eroded surface whose dynamics are ruled by cellular automaton. Starting from the automaton, we obtain the time evolution of the height average and height…
Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a…
The statistical correlations of two copies of a d-dimensional elastic manifold embedded in slightly different frozen disorder are studied using the Functional Renormalization Group to one-loop accuracy, order O(eps = 4-d). Determining the…
We consider the system of elastic waves with critical space dependent damping $V(x)$. We study the Cauchy problem for this model in the $2$-dimensional Euclidean space ${\bf R}^{2}$, and we obtain faster decay rates of the total energy as…
The pinning of flux lattices by weak impurity disorder is studied in the absence of free dislocations using both the gaussian variational method and, to $O(\epsilon=4-d)$, the functional renormalization group. We find universal logarithmic…
In order to estimate roughness exponents of interface growth models, we propose the calculation of effective exponents from the roughness fluctuation (sigma) in the steady state. We compare the finite-size behavior of these exponents and…
In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space, $\mathbb{R}^k$. We prove the $\Gamma$-convergence of elastic energies for configurations of a converging…
The depinning of a contact line is studied as a dynamical critical phenomenon by a functional renormalization group technique. In $D=2-\epsilon$ interface dimensions, the roughness exponent is $\zeta=\epsilon/3$ to all orders in…
In this work we generalize the etching model (Mello et al 2001 Phys. Rev. E 63 041113) to d + 1 dimensions. The dynamic exponents of this model are compatible with those of the Kardar-Parisi-Zhang universality class. We investigate the…
Criticality in the class of disordered systems comprising the random-field Ising model (RFIM) and elastic manifolds in a random environment is controlled by zero-temperature fixed points that must be treated through a functional…
The simultaneous effect of both disorder and crystal-lattice pinning on the equilibrium behavior of oriented elastic objects is studied using scaling arguments and a functional renormalization group technique. Our analysis applies to…
We perform Transition matrix Monte Carlo simulations to evaluate the entropy of rhombus tilings with fixed polygonal boundaries and 2D-fold rotational symmetry. We estimate the large-size limit of this entropy for D=4 to 10. We confirm…
Predicting the future behaviour of complex systems exhibiting critical-like dynamics is often considered to be an intrinsically hard task. Here, we study the predictability of the depinning dynamics of elastic interfaces in random media…
An energy-minimal simulation is proposed to study the patterns and mechanical properties of elastically crumpled wires in two dimensions. We varied the bending rigidity and stretching modulus to measure the energy allocation, size-mass…
Driven elastic manifolds in random media exhibit a depinning transition to a state with non-vanishing velocity at a critical driving force. We study the depinning of stiff directed lines, which are governed by a bending rigidity rather than…
We investigate the effective elastic properties of periodic dilute two-phase composites consisting of an homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply…
A method for the calculation of elastic constants in the NVT ensamble, using molecular dynamics (MD) simulation with a realistic many-body embedded-atom-model (EAM) potential, is studied in detail. It is shown that in such NVT MD…
We study the rescaled probability distribution of the critical depinning force of an elastic system in a random medium. We put in evidence the underlying connection between the critical properties of the depinning transition and the extreme…
Under suitable regularity assumptions the $p$-elastic energy of a planar set $E\subset\mathbb{R}^2$ is defined to be $\int_{\partial E} 1 + |k_{\partial E}|^p \,\, d\mathcal{H}^1,$ where $k_{\partial E}$ is the curvature of the boundary…
The properties of a hinged floating elastic sheet of finite length under compression are considered. Numerical continuation is used to compute spatially localized buckled states with many spatially localized folds. Both symmetric and…