108 citations · 419 across the 35 of their papers we have counts for
20 papers · 1 filter
Reaction-diffusion kinetics in growing domains
C. Escudero, S. B. Yuste, E. Abad +1
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated st…
Diffusion in an expanding medium: Fokker-Planck equation, Green's function and first-passage properties
S. B. Yuste, E. Abad, C. Escudero
We present a classical, mesoscopic derivation of the Fokker-Planck equation for diffusion in an expanding medium. To this end, we take a conveniently generalized Chapman-Kolmogorov…
Invited review: KPZ. Recent developments via a variational formulation
Horacio S. Wio, Roberto R. Deza, Carlos Escudero +1
Recently, a variational approach has been introduced for the paradigmatic Kardar--Parisi--Zhang (KPZ) equation. Here we review that approach, together with the functional Taylor ex…
Nonlinear field theories during homogeneous spatial dilation
Carlos Escudero
The effect of a uniform dilation of space on stochastically driven nonlinear field theories is examined. This theoretical question serves as a model problem for examining the prope…
Two species coagulation approach to consensus by group level interactions
Carlos Escudero, Fabricio Macia, Juan J. L. Velazquez
We explore the self-organization dynamics of a set of entities by considering the interactions that affect the different subgroups conforming the whole. To this end, we employ the…
Origins of scaling relations in nonequilibrium growth
Carlos Escudero, Elka Korutcheva
Scaling and hyperscaling laws provide exact relations among critical exponents describing the behavior of a system at criticality. For nonequilibrium growth models with a conserved…
Chemical Oscillations out of Chemical Noise
Carlos Escudero, Andres M. Rivera, Pedro J. Torres
The dynamics of one species chemical kinetics is studied. Chemical reactions are modelled by means of continuous time Markov processes whose probability distribution obeys a suitab…
Discretization-related issues in the KPZ equation: Consistency, Galilean-invariance violation, and fluctuation--dissipation relation
H. S. Wio, J. A. Revelli, R. R. Deza +2
In order to perform numerical simulations of the KPZ equation, in any dimensionality, a spatial discretization scheme must be prescribed. The known fact that the KPZ equation can b…
Stochastic growth of radial clusters: weak convergence to the asymptotic profile and implications for morphogenesis
Carlos Escudero
The asymptotic shape of randomly growing radial clusters is studied. We pose the problem in terms of the dynamics of stochastic partial differential equations. We concentrate on th…
Some open questions concerning biological growth
Carlos Escudero
We briefly review the properties of radially growing interfaces and their connection to biological growth. We focus on simplified models which result from the abstraction of only c…
Dynamics of Generalized Hydrodynamics: Hyperbolic and Pseudohyperbolic Burgers Equations
Carlos Escudero
The equations of continuum hydrodynamics can be derived from the Boltzmann equation, which describes rarefied gas dynamics at the kinetic level, by means of the Chapman-Enskog expa…
Statistics of interfacial fluctuations of radially growing clusters
Carlos Escudero
The dynamics of fluctuating radially growing interfaces is approached using the formalism of stochastic growth equations on growing domains. This framework reveals a number of dyna…
Addendum to the Reply Comment [Phys. Rev. Lett. 102, 139602 (2009), arXiv:0811.0518] on ''Dynamic Scaling of Non-Euclidean Interfaces''
Carlos Escudero
This is an addendum to the Reply Comment [Phys. Rev. Lett. 102, 139602 (2009), arXiv:0811.0518] to Comment [Phys. Rev. Lett. 102, 139601 (2009), arXiv:0810.4791] on Letter [Phys. R…
Stochastic growth equations on growing domains
Carlos Escudero
The dynamics of linear stochastic growth equations on growing substrates is studied. The substrate is assumed to grow in time following the power law , where the growth index…
On the Geometric Principles of Surface Growth
Carlos Escudero
We introduce a new equation describing epitaxial growth processes. This equation is derived from a simple variational geometric principle and it has a straightforward interpretatio…
Reply to the revised Comment [PRL 102, 139601; arXiv:0810.4791] on ''Dynamic Scaling of Non-Euclidean Interfaces''
Carlos Escudero
This is the Reply to the revised Comment [Phys. Rev. Lett. 102, 139601; arXiv:0810.4791] by Joachim Krug on our paper: C. Escudero, Phys. Rev. Lett. 100, 116101 (2008); arXiv:0804.…
Dynamics of curved interfaces
Carlos Escudero
Stochastic growth phenomena on curved interfaces are studied by means of stochastic partial differential equations. These are derived as counterparts of linear planar equations on…
Dynamic Scaling of Non-Euclidean Interfaces
Carlos Escudero
The dynamic scaling of curved interfaces presents features that are strikingly different from those of the planar ones. Spherical surfaces above one dimension are flat because the…
Persistence of instanton connections in chemical reactions with time dependent rates
Carlos Escudero, Jose Angel Rodriguez
The evolution of a system of chemical reactions can be studied, in the eikonal approximation, by means of a Hamiltonian dynamical system. The fixed points of this dynamical system…
Stochastic resonance due to internal noise in reaction kinetics
Carlos Escudero
We study a reaction model that presents stochastic resonance purely due to internal noise. This means that the only source of fluctuations comes from the discrete character of the…