Related papers: Conformal Invariance of Iso-height Lines in two-di…
We study a generalized Kardar-Parisi-Zhang (KPZ) equation [Jana et al., Phys. Rev. E 109, L032104 (2024)] that sets the paradigm for universality in roughening of growing nonequilibrium surfaces without any conservation laws but with…
A modified Kardar-Parisi-Zhang (KPZ) equation is introduced, and solved exactly in the infinite-range limit. In the low-noise limit the system exhibits a weak-to-strong coupling transition, rounded for non-zero noise, as a function of the…
We argue that conformal invariance is a common thread linking several scalar effective field theories that appear in the double copy and scattering equations. For a derivatively coupled scalar with a quartic ${\cal O}(p^4)$ vertex,…
Amorphous solids may resist external deformation such as shear or compression while they do not present any long-range translational order or symmetry at the microscopic scale. Yet, it was recently discovered that, when they become rigid,…
The following question is the subject of our work: could a two-dimensional random path pushed by some constraints to an improbable "large deviation regime", possess extreme statistics with one-dimensional Kardar-Parisi-Zhang (KPZ)…
A novel discrete growth model in 2+1 dimensions is presented in three equivalent formulations: i) directed motion of zigzags on a cylinder, ii) interacting interlaced TASEP layers, and iii) growing heap over 2D substrate with a restricted…
In this paper I study a model for a growing surface in the presence of anomalous diffusion, also known as the Fractal Kardar-Parisi-Zhang equation (FKPZ). This equation includes a fractional Laplacian that accounts for the possibility that…
To investigate universal behavior and effects of long-range temporal correlations in kinetic roughening, we perform extensive simulations on the Kardar-Parisi-Zhang (KPZ) equation with temporally correlated noise based on pseudospectral…
We have simulated an automaton version of the quenched Kardar-Parisi-Zhang (qKPZ) equation in one and two dimensions in order to study the scaling properties of the interface at the depinning transition. Specifically, the $\alpha$, $\beta$,…
We investigate the origin of the scaling corrections in ballistic deposition models in high dimensions using the method proposed by Alves \textit{et al}. [Phys Rev. E \textbf{90}, 052405 (20014)] in $d=2+1$ dimensions, where the intrinsic…
We show that in the continuum limit watersheds dividing drainage basins are Schramm-Loewner Evolution (SLE) curves, being described by one single parameter $\kappa$. Several numerical evaluations are applied to ascertain this. All…
We study the solution of the Kardar-Parisi-Zhang (KPZ) equation for the stochastic growth of an interface of height $h(x,t)$ on the positive half line, equivalently the free energy of the continuum directed polymer in a half space with a…
Tracy-Widom and Baik-Rains distributions appear as universal limit distributions for height fluctuations in the one-dimensional Kardar-Parisi-Zhang (KPZ) \textit{stochastic} partial differential equation (PDE). We obtain the same universal…
We analyze the shapes of roughness distributions of discrete models in the Kardar, Parisi and Zhang (KPZ) and in the Villain, Lai and Das Sarma (VLDS) classes of interface growth, in one and two dimensions. Three KPZ models in d=2 confirm…
We show that two semi-infinite positive temperature polymers coalesce on the scale predicted by KPZ (Kardar-Parisi-Zhang) universality. The two polymer paths have the same asymptotic direction and evolve in the same environment,…
It is widely believed that the scaling limit of self-avoiding walks (SAWs) at the critical temperature is (i) conformally invariant, and (ii) describable by Schramm-Loewner Evolution (SLE) with parameter $\kappa = 8/3.$ We consider SAWs in…
A recent exponent inequality is applied to a number of dynamical growth models. Many of the known exponents for models such as the Kardar-Parisi-Zhang (KPZ) equation are shown to be consistent with the inequality. In some cases, such as the…
Stochastic partial differential equations can be used to model second order thermodynamical phase transitions, as well as a number of critical out-of-equilibrium phenomena. In (2+1) dimensions, many of these systems are conjectured (and…
We study the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) interfaces growing inward from ring-shaped initial conditions, experimentally and numerically, using growth of a turbulent state in liquid-crystal electroconvection and an…
One of the main difficulties in proving convergence of discrete models of surface growth to the Kardar-Parisi-Zhang (KPZ) equation in dimensions higher than one is that the correct way to take a scaling limit, so that the limit is…