285 citations · 412 across the 16 of their papers we have counts for
17 papers
On the nontrivial zeros of the Dirichlet eta function
Vladimir García-Morales
We construct a two-parameter complex function , , that we call a holomorphic nonlinear embedding and that is gi…
Unifying vectors and matrices of different dimensions through nonlinear embeddings
Vladimir García-Morales
Complex systems may morph between structures with different dimensionality and degrees of freedom. As a tool for their modelling, nonlinear embeddings are introduced that encompass…
Weakly coupled map lattice models for multicellular patterning and collective normalization of abnormal single-cell states
Vladimir García-Morales, José A. Manzanares, Salvador Mafe
We present a weakly coupled map lattice model for patterning that explores the effects exerted by weakening the local dynamic rules on model biological and artificial networks comp…
Digit replacement: A generic map for nonlinear dynamical systems
Vladimir García-Morales
A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the m…
Fractal surfaces from simple arithmetic operations
Vladimir Garcia-Morales
Fractal surfaces ('patchwork quilts') are shown to arise under most general circumstances involving simple bitwise operations between real numbers. A theory is presented for all de…
Digital calculus and finite groups in quantum mechanics
Vladimir Garcia-Morales
By means of a digit function that has been introduced in a recent formulation of classical and quantum mechanics, we provide a new construction of some infinite families of finite…
The fractal decomposition: Nontrivial partitions of conserved physical quantities
Vladimir Garcia-Morales
A mathematical method for constructing fractal curves and surfaces, termed the fractal decomposition, is presented. It allows any function to be split into a finite set of fr…
Digital calculus: Cellular automata dynamics in closed form
Vladimir Garcia-Morales
A simple mathematical expression for the universal map for cellular automata is found in closed form with the help of a digit function, whose most basic properties are established.…
Quantum Mechanics and the Principle of Least Radix Economy
Vladimir Garcia-Morales
A new variational method, the principle of least radix economy, is formulated. The mathematical and physical relevance of the radix economy, also called digit capacity, is establis…
Coexistence of synchrony and incoherence in oscillatory media under nonlinear global coupling
Lennart Schmidt, Konrad Schönleber, Katharina Krischer +1
We report a novel mechanism for the formation of chimera states, a peculiar spatiotemporal pattern with coexisting synchronized and incoherent domains found in ensembles of identic…
Nonlocal and global dynamics of cellular automata: A theoretical computer arithmetic for real continuous maps
Vladimir Garcia-Morales
A digit function is presented which provides the th-digit in base of any real number . By means of this function, formulated within -calculus, the local, non…
Origin of Complexity and Conditional Predictability in Cellular Automata
Vladimir Garcia-Morales
A simple mechanism for the emergence of complexity in cellular automata out of predictable dynamics is described. This leads to unfold the concept of conditional predictability for…
Substitution Systems and Nonextensive Statistics
Vladimir Garcia-Morales
Substitution systems evolve in time by generating sequences of symbols from a finite alphabet: At a certain iteration step, the existing symbols are systematically replaced by bloc…
Mathematical Physics of Cellular Automata
Vladimir Garcia-Morales
A universal map is derived for all deterministic 1D cellular automata (CA) containing no freely adjustable parameters. The map can be extended to an arbitrary number of dimensions…
Microcanonical foundation of nonextensivity and generalized thermostatistics based on the fractality of the phase space
V. Garcia-Morales, J. Pellicer
We develop a generalized theory of (meta)equilibrium statistical mechanics in the thermodynamic limit valid for both smooth and fractal phase spaces. In the former case, our approa…
Coupling theory for counterion distributions based in Tsallis statistics
V. Garcia-Morales, J. Cervera, J. Pellicer
It is well known that the Poisson-Boltzmann (PB) equation yields the exact counterion density around charged objects in the weak coupling limit. In this paper we generalize the PB…
Statistical mechanics and thermodynamics of complex systems
V. Garcia-Morales, J. Pellicer
An unified thermodynamical framework based in the use of a generalized Massieu-Planck thermodynamic potential is proposed and a new formulation of Boltzmann-Gibbs Statistical Mecha…