Vladimir García-Morales

Coexistence of synchrony and incoherence in oscillatory media under nonlinear global coupling

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 identical oscillators. Considering Stuart-Landau oscillators, we demonstrate that a nonlinear global coupling can induce this symmetry breaking. We find chimera states also in a spatially extended system, a modified complex Ginzburg-Landau equation. This theoretical prediction is validated with an oscillatory electrochemical system, the electro-oxidation of silicon, where the spontaneous formation of chimeras is observed without any external feedback control.

On the demonstration of the Young-Laplace equation in introductory physics courses

The Young-Laplace equation is usually introduced using mechanical rather than thermodynamic arguments when teaching surface phenomena at an elementary level. We discuss here three mechanical methods to deduce this equation, with the intention of avoiding certain misunderstandings that are found in these derivations, thus providing the correct demonstrations of the equation.

Microcanonical foundation of nonextensivity and generalized thermostatistics based on the fractality of the phase space

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 approach leads naturally to Boltzmann–Gibbs standard thermostatistics while, in the latter, Tsallis thermostatistics is straightforwardly obtained as the most appropriate formalism. We first focus on the microcanonical ensemble stressing the importance of the limit t→∞ on the form of the microcanonical measure. Interestingly, this approach leads to interpret the entropic index q as the box-counting dimension of the (microcanonical) phase space when fractality is considered.

Fluctuation enhanced electrochemical reaction rates at the nanoscale

The electrode potential constitutes a dynamical variable whenever an electrode is resistively coupled to the electric circuit. We show that at the nanoscale, the discreteness and stochasticity of an electron transfer event causes fluctuations of the electrode potential that render all elementary electrochemical reactions to be faster on a nanoelectrode than predicted by the macroscopic (Butler–Volmer) electrochemical kinetics. This phenomenon is substantiated by means of a generalized (electro)chemical master equation.

The complex Ginzburg–Landau equation: an introduction

The complex Ginzburg–Landau equation (CGLE), probably the most celebrated nonlinear equation in physics, describes generically the dynamics of oscillating, spatially extended systems close to the onset of oscillations. Using symmetry arguments, this article gives an easy access to this equation and an introduction into the rich spatio-temporal behaviour it describes. Starting out from the familiar linear oscillator, we first show how the generic model for an individual nonlinear oscillator, the so-called Stuart–Landau equation, can be derived from symmetry arguments. Then, we extend our symmetry considerations to spatially extended systems, arriving at the CGLE. A comparison of diffusively coupled linear and nonlinear oscillators makes apparent the source of instability in the latter systems. A concise survey of the most typical patterns in 1D and 2D is given. Finally, more recent extensions of the CGLE are discussed that comprise external, time-periodic forcing as well as nonlocal and global spatial coupling.

On the experimental values of the water surface tension used in some textbooks

A thermodynamic study of one component liquid–vapor planar interfaces and the temperature dependence of some relevant thermodynamic quantities is presented. A critical review of data for the surface tension of water found in some textbooks is given. More accurate measurements show a qualitative change in the temperature dependence of the surface tension, from the almost linear dependence of the old data to nonlinear behavior and the occurrence of an inflection point in the more accurate, more recent data.

Electrochemical Properties of Phospholipid Monolayers at Liquid–Liquid Interfaces

Biomembrane models built at the interface between two immiscible electrolytes (ITIES) are useful systems to study phenomena of biological relevance by means of their electrochemical processes. The unique properties of ITIES allow one either to control or measure the potential difference across the biomimetic membranes. Herein we focus on phospholipid monolayers adsorbed at liquid-liquid interfaces, and besides discussing recent developments on the subject, we describe electrochemical techniques that can be used to get insight on the interfacial processes and electrostatic properties of phospholipid membranes at the ITIES. In particular, we examine the electrochemical and physicochemical properties of (modified) phospholipid monolayers and their interaction with other biologically relevant compounds. The use of liquid-liquid electrochemistry as a powerful tool to characterize drug properties is outlined. Although this review is not a survey of all the work in the field, it provides a comprehensive referencing to current research.

Correct thermodynamic forces in Tsallis thermodynamics: connection with Hill nanothermodynamics

The equivalence between Tsallis thermodynamics and Hills nanothermodynamics is established. The correct thermodynamic forces in Tsallis thermodynamics are pointed out. Through this connection we also find a general expression for the entropic index q which we illustrate with two physical examples, allowing in both cases to relate q to the underlying dynamics of the Hamiltonian systems.

Superstatistics in nanoscale electrochemical systems

Stochastic electrochemical reaction steps on nanosized electrodes are non-Markovian when externally driven by an applied voltage. We show that, compared to the Markovian case (when external driving is absent), nanoscale electrochemical systems obey a superstatistics characterized by a superposition of Tsallis’ q indices. The distribution of Tsallis’ q indices along stochastic trajectories can be calculated from the electrochemical master equation and normal distributions from Boltzmann–Gibbs thermostatistics are recovered in the thermodynamic limit (the infinite electrode size limit). Although on the nanoscale the external control makes intricate correlations between the microstates, in the superstatistical frame one can still address the microstates as if they were uncorrelated. The resulting superstatistical entropic form is additive in this frame and Tsallis’ indices have on the time-average values , which is, indeed, an example of a superstatistical system where no ad hoc distribution has to be assumed for the fluctuations; rather, the distribution is directly calculated from a mesoscopic master equation without freely adjustable parameters.

Quantum Mechanics and the Principle of Least Radix Economy

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 established, showing how physical laws can be derived from this concept in a unified way. The principle reinterprets and generalizes the principle of least action yielding two classes of physical solutions: least action paths and quantum wavefunctions. A new physical foundation of the Hilbert space of quantum mechanics is then accomplished and it is used to derive the Schrödinger and Dirac equations and the breaking of the commutativity of spacetime geometry. The formulation provides an explanation of how determinism and random statistical behavior coexist in spacetime and a framework is developed that allows dynamical processes to be formulated in terms of chains of digits. These methods lead to a new (pre-geometrical) foundation for Lorentz transformations and special relativity. The Parker-Rhodes combinatorial hierarchy is encompassed within our approach and this leads to an estimate of the interaction strength of the electromagnetic and gravitational forces that agrees with the experimental values to an error of less than one thousandth. Finally, it is shown how the principle of least-radix economy naturally gives rise to Boltzmann’s principle of classical statistical thermodynamics. A new expression for a general (path-dependent) nonequilibrium entropy is proposed satisfying the Second Law of Thermodynamics.