José Luis Aragón

Universidad Nacional Autónoma de México | UNAM · Centro de Física Aplicada y Tecnología Avanzada

A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the calculations of geometric, outer and inner products, as well as many other calculations related with geometric trans...

Here we discuss the formation of phyllotactic patterns in the shoot apical meristem (SAM) of plants, where the spatial distribution of the phytohormone auxin determines phyllotaxis in a domain that is growing and changing in time. We assume that the concentration of auxin modifies the mechanical properties of the domain and that the mechanical stre...

In this study, we propose a mathematical model based on parametric surfaces for the shell morphology of the phylum Mollusca. Since David Raup’s pioneering works, many mathematical models have been proposed for different contexts to describe general shell morphology; however, there has been a gap in the practicality of models that allow the estimati...

In this work, we study reaction–diffusion equations with space-dependent, differentiable, and ɛ -periodic diffusion coefficients, using the asymptotic homogenization technique. The importance of this problem is that experimental evidence suggests that in some biological systems, spatial inhomogeneities are important to regulate spatial patterns, an...

This work provides a comprehensive characterization of coincidence site lattices that arise from the compositions of the reflections of cubic lattices. For this purpose, we apply Cartan's theorem and use reflections as basic isometries, which allows the use of Clifford algebra as a powerful tool to handle reflections and products of reflections, le...

Although healthcare and medical technology have advanced significantly over the past few decades, heart disease continues to be a major cause of mortality globally. Electrocardiography (ECG) is one of the most widely used tools for the detection of heart diseases. This study presents a mathematical model based on transfer functions that allows for...

We experimentally study the infinite-size limit of the Dicke model of quantum optics with a parity-breaking deformation strength that couples the system to an external bosonic reservoir. We focus on the dynamical consequences of such symmetry breaking, which makes the classical phase space asymmetric with non-equivalent energy wells. We present an...

The interaction of a laser with a liquid can cause temperature changes in the liquid from which some properties of the latter can be indirectly obtained. However, from just temperature changes, a sample cannot be identified. Here, we report on the interaction of tightly focused femtosecond infrared light into secondary hydrogen-bonded liquids like...

Arrhythmias are conditions characterized by a faster, slower, or irregular heart rhythm. Some of them may be harmless and brief, but others can lead to sudden cardiac arrest. Thus, procedures that safely restore a normal heartbeat are a matter of interest. Laboratory experiments have evidenced that some arrhythmia exhibit nonlinear deterministic be...

In the past, laser propagation in a fluid with heat transfer has been modeled using simplistic conduction and convection conditions yielding inaccurate predictions. Here we present a detailed numerical study describing the thermal profile of the fluid and its interaction with the laser. Furthermore, we evaluate the diffraction field in the far fiel...

The problem of pattern formation in reaction–diffusion systems with space varying diffusion is studied. On this regard, it has already been shown that the necessary conditions for Turing instability are the same as for the case of homogeneous diffusion, but the sufficient conditions depend on the specific space dependence of the diffusion coefficie...

What is the fate of an oscillator when its inductance and capacitance are varied while its frequency is kept constant? Inspired by this question, we propose a protocol to implement parity-time (PT) symmetry in a lone oscillator. Different forms of constrained variations lead to static, periodic, or arbitrary balanced gain and loss profiles, that ca...

Coincidence site lattices of oblique planar lattices are algebraically characterized using as basic tool the Cartan-Dieudonn\'e theorem, that is, the decomposition of an orthogonal transformation as a product of reflections. The case of rectangular lattices is worked out in detail. We use the rectangular lattices for obtain the characterization of...

p>Arrhythmias are conditions characterized by a faster, slower, or irregular heart rhythm. Some of them may be harmless and brief, but others can lead to a sudden cardiac arrest. Thus, procedures that safely restore the normal heartbeat are a matter of interest. Experimental evidence shows that some arrhythmia may have an origin in chaotic dynamics...

In the past, laser propagation in a fluid with heat transfer has been modeled using simplistic conduction and convection conditions yielding inaccurate predictions. Here we present a detailed numerical study describing the thermal profile of the fluid and its interaction with the laser. Furthermore, we evaluate the diffraction field in the far fiel...

In this work, we propose a versatile, low-cost, and tunable electronic device to generate realistic electrocardiogram (ECG) waveforms, capable of simulating ECG of patients within a wide range of possibilities. A visual analysis of the clinical ECG register provides the cardiologist with vital physiological information to determine the patient’s he...

Parity-Time (PT) symmetric systems have been widely recognized as fundamental building blocks for the development of novel, ultra-sensitive opto-electronic devices. However, arguably one of their major drawbacks is that they rely on non-linear amplification processes that could limit their potential applications, particularly in the quantum realm....

In this work, we propose a strategy based on an analog active network to detect Hopf bifurcations in two–dimensional dynamical systems described by ordinary differential equations. With the proposed strategy, two parameters of the nonlinear system are established in the analog active network by using external controllable voltage levels in order to...

In this article, we show an alternative low-cost fabrication method to obtain poly(dimethyl siloxane) (PDMS) microfluidic devices. The proposed method allows the inscription of micron resolution channels on polystyrene (PS) surfaces, used as a mold for the wanted microchip’s production, by applying a high absorption coating film on the PS surface t...

Motivated by questions on orthogonality of isometries, we present a new construction of the conformal model of the 3D space using just elementary linear algebra. In addition to pictures that can help the readers to understand the conformal model, our approach allows to obtain matrix representation of isometries that can be useful, for example, in a...

We put forward a versatile, highly scalable, tunable electronic platform for the simulation of single-excitation quantum transport phenomena. Our system, comprising 10 state-of-the-art, fully reconfigurable electronic oscillators, is implemented by making use of functional blocks synthesized with operational amplifiers and passive linear electrical...

In this letter, we show an alternative low-cost fabrication method to obtain poly(dimethyl siloxane) (PDMS) microfluidic devices. The proposed method allows the inscription of micron resolution channels on polystyrene (PS) surfaces, used as a mold for the wanted microchip’s production, by applying a high absorption coating film on the PS surface to...

In this work, we show theoretically and numerically that a one-dimensional reaction-diffusion system, near the Turing bifurcation, produce different number of stripes when, in addition to random noise, the Fourier mode of a prepattern used to initialize the system changes. We lso show that the Fourier modes that persist are inside the Eckhaus stabi...

Nuclear Magnetic Resonance (NMR) experiments can be used to calculate 3D protein structures and geometric properties of protein molecules allow us to solve the problem iteratively using a combinatorial method, called Branch-and-Prune (BP). The main step of BP algorithm is to intersect three spheres centered at the positions for atoms i − 3, i − 2,...

In 1981, Richard Feynman discussed the possibility of performing quantum mechanical simulations of nature. Ever since, there has been an enormous interest in using quantum mechanical systems, known as quantum simulators, to mimic specific physical systems. Hitherto, these controllable systems have been implemented on different platforms that rely o...

We report the experimental implementation of the classical description of the Dicke model whose quantum version describes a large number of two-level atoms interacting with a single-mode electromagnetic field in a perfectly reflecting cavity. This is performed by employing two nonlinearly coupled active, synthetic LC circuits, implemented by means...

We report the experimental implementation of the Dicke model in the semiclassical approximation, which describes a large number of two-level atoms interacting with a single-mode electromagnetic field in a perfectly reflecting cavity. This is managed by making use of two non-linearly coupled active, synthetic LC circuits, implemented by means of ana...

We propose a model to generate electrocardiogram signals based on a discretized reaction-diffusion system to produce a set of three nonlinear oscillators that simulate the main pacemakers in the heart. The model reproduces electrocardiograms from healthy hearts and from patients suffering various well-known rhythm disorders. In particular, it is sh...

In this paper, the solutions of the coupled Ginzburg-Landau equations are numerically studied with the aim to describe the dynamics of systems close to the Turing-Hopf bifur- cation. We found that the spatial modulations of the Turing and Hopf amplitudes increase with the domain size due to inhomogeneous perturbations. By measuring the growth of sp...

In this work, a modified version of the cut and projection approach is proposed to describe the structure of graphene bilayers with twist angles. With this method, the rotation between two graphene layers is viewed as a rotation of the projection space and the resulting projected structure is interpreted as the set of points of best fit between the...

In this work, we provide a framework to understand and quantify the spatiotemporal structures near the codimension-two Turing-Hopf point, resulting from secondary instabilities of Mixed Mode solutions of the Turing-Hopf amplitude equations. These instabilities are responsible for solutions such as (1) patterns which change their effective wavenumbe...

The aim of this work is to carry a performance analysis based on first and second law of thermodynamics for some operational configurations of feasible gasketed-plate heat exchangers. To achieve this, 40 simulations were done solving the distributed-U differential model proposed by Pinto and Gut, using an adaptive damped secant shooting method. Hea...

Space-time structures near the codimension-two Turing-Hopf point (CTHP) that combine a spatial pattern with temporal oscillations are studied for a particular reaction diffusion (RD) system, which has been useful to model many different biological processes. We show that in this sytem, these Mixed mode solutions arise in regions of the parameter sp...

A three-species population system under a facultative mutualistic relationship of one of the species is studied. The considered interactions are as follows: facultative between the first species and the second species, obligatory mutualism between the second species and the first one, and the third species is a predator of the first species. For th...

Abstrct Passive parity-time symmetry breaking transitions, where long-lived eigenmodes emerge in a locally dissipative system, have been extensively studied in recent years. Conventional wisdom says that they occur at exceptional points. Here we report the observation of multiple transitions showing the emergence of slowly decaying eigenmodes in a...

We propose a simple model of the electrical activity of the heart that reproduces realistic healthy electrocardiogram (ECG) signals. The model consists of two RLC linear oscillators periodically kicked by impulses of the main pacemaker with the frequency rate of a real heart. In the proposed model, one oscillator represents the atria, another repre...

We present the algorithm for the extended heterogeneous oscillator model of cardiac conduction system published in "Cardiac conduction model for generating 12 lead ECG signals with realistic heart rate dynamics". This code includes the generation of an artificial RR-tachogram with specific statistics of heart rate. The frequency-domain characterist...

We present the code to fit the parameters of the extended heterogeneous oscillator model of cardiac conduction system and to reconstruct real ECG records. With the code presented here, we can fit it individual characteristics of a subject considering weighted linear combination of the depolarization and repolarization responses provide for the exte...

System and device for generating random waveforms that comprises a SD-BVAM mathematical model with four non-linear ordinary differential equations from the simplification of the spatial discretization from the reaction-diffusion model proposed by Barrio (1999), which has been used to describe pattern formation in the biological pigmentation of fish...

We present extended heterogeneous oscillator model of cardiac conduction system for generation of realistic 12 lead ECG waveforms. The model consists of main natural pacemakers represented by modified van der Pol equations, and atrial and ventricular muscles, in which the depolarization and repolarization processes are described by modified FitzHug...

A basic pattern in the body plan architecture of many animals, plants and some molecular and cellular systems is five-part units. This pattern has been understood as a result of genetic blueprints in development and as a widely conserved evolutionary character. Despite some efforts, a definitive explanation of the abundance of pentagonal symmetry a...

Emergence of primordia with 4-fold symmetry. Corresponding to Fig 2A and 2D of the main text. (MP4)

Emergence of ribs with 6-fold symmetry. Corresponding to Fig 7B of the main text. (MP4)

Emergence of primordia into whorled phyllotactic pattern with 2-fold symmetry. Parameter values are β = 0.5, γ = 0.2, G[u] (width of R/2), κ = 2, c = 0.57, η = 0.2014. The remaining parameters are indicated in the main text. (MP4)

Curvature tensor, dynamical equations and stability of Turing patterns. (PDF)

Emergence of primordia with 5-fold symmetry. Corresponding to Fig 7C of the main text. (MP4)

Emergence of ribs with 6-fold symmetry. Corresponding to Fig 7A of the main text. (MP4)

Emergence of primordia into whorled phyllotactic pattern with 6-fold symmetry. Parameter values are β = 0.5, γ = 0.2, G[u] (width of R/2), κ = 2, c = 0.33, η = 0.8919 and the rest of parameters as indicated in the main text. (MP4)

Emergence of primordia with 3-fold symmetry. Corresponding to Fig 2B and 2E of the main text. (MP4)

Emergence of primordia into whorled phyllotactic pattern with 5-fold symmetry. Parameter values are β = 0.5, γ = 0.2, G[u] (width of R/2), κ = 2, c = 0.33, η = 0.6504 and the rest of parameters as indicated in the main text. (MP4)

Principal directions of stress tensor in whorled phyllotactic patterning with 3-fold symmetry. In the top we plotted front and top views of the principal directions of the stress tensor (black arrows) in the volume. In the bottom, the principal directions of stress (black arrows) are plotted only in the surface. The domain was plotted in diffused c...

We report the first experimental observation of multiple transitions showing the emergence and disappearance of slowly decaying eigenmodes in a dissipative, Floquet electronic system with synthetic components. Conventional wisdom has it that such transitions occur at exceptional points, and avoided-level-crossing driven phenomena in purely dissipat...

It was recently proposed that the lateral resonances around the working resonance band of ultrasonic piezoelectric sandwich transducers can be stopped by a periodic array of circular holes drilled along the main propagation direction (a phononic crystal). In this work, the performance of different transducer designs made with this procedure is test...

In this work, we present a short review on generalized reciprocal vectors, a field created by Alan L. Mackay. In particular , we discuss the concept of generalized reciprocal vectors, its relation with eutactic stars used in quasicrystallography and their calculation using Moore–Penrose pseudoinverses. Additionally, we propose a plain Gaussian algo...

We report on the experimental observation of an emerging negative resistance in a system of coupled linear electronic RLC harmonic oscillators under the influence of multiplicative noise with long correlation time. When two oscillators are coupled by a noisy inductor, an analysis in the Fourier space of the electrical variables unveils the presence...

By using the principles behind phononic crystals, a periodic array of circular holes made along the polarization thickness direction of piezoceramic resonators are used to stop the planar resonances around the thickness mode band. In this way, a piezoceramic resonator adequate for operation in the thickness mode with an in phase vibration surface i...

It has been suggested that cardiac arrhythmias are instances of chaos. In particular that the ventricular fibrillation is a form of spatio-temporal chaos that arises from normal rhythm through a quasi-periodicity or Ruelle-Takens-Newhouse route to chaos. In this work, we modify the heterogeneous oscillator model of cardiac conduction system propose...

A method for generating all rational generalized matrices on indefinite real inner product spaces isomorphic to $R^{p,q}$ is presented. The proposed method is based on the proof of a weak version of the Cartan–Dieudonné theorem, handled using Clifford algebras. It is shown that all rational B-orthogonal matrices in an indefinite inner product space...

The Clifford algebra of a n-dimensional Euclidean vector space provides a general language comprising vectors, complex numbers, quaternions, Grassman algebra, Pauli and Dirac matrices. In this work, we present an introduction to the main ideas of Clifford algebra, with the main goal to develop a package for Clifford algebra calculations for the com...

Noise is generally thought as detrimental for energy transport in coupled oscillator networks. However, it has been shown that for certain coherently evolving systems, the presence of noise can enhance, somehow unexpectedly, their transport efficiency; a phenomenon called environment-assisted quantum transport (ENAQT) or dephasing assisted transpor...

Background: The quantification of the spatial order of biological patterns or mosaics provides useful information as many properties are determined by the spatial distribution of their constituent elements. These are usually characterised by methods based on nearest neighbours distances, by the number of sides of cells, or by angles defined by the...

En este trabajo se presenta un circuito electrónico digital que genera señales sintéticas de electrocardiograma (ECG) utilizando una modificación del modelo matemático propuesto Gois et. al. (2009). Con el circuito electrónico propuesto se pueden generar ritmos cardiacos normales y patológicos representados por señales ECG. Los ritmos patológicos s...

Biodiesel is a renewable alternative to petroleum-based diesel fuel that could potentially still prove to be substantially more environmentally friendly than their fossil alternatives. It is obtained by a transesterification reaction from any triglyceride material (edible and non-edible oils, animal fats, lipid algae, etc.) being a potential tool f...

A modularity approach is used to study disparity rates and evolvability of sea urchins belonging to the Atelostomata superorder. For this purpose, the pentameric sea urchin architecture is partitioned into modular spatial components and the interference between modules is quantified using areas and a measurement of the regularity of the spatial par...

The problem of characterizing the coincidence site lattices obtained by superimposing a planar hexagonal lattice with its rotated version is solved using simple reflections handled with Clifford algebras. For any possible coincidence rotation, analytical expressions for the coincidence index and for a basis of the coincidence site lattices are deduce...

Alan Turing’s seminal 1952 work on morphogenesis [1] is widely known and recognised in the field of mathematical biology. Less known is his work on the problem of phyllotaxis, which was never published at his time but is included in Turing’s collected works [2]. It consists on three parts: the first is a detailed mathematical description of the arr...

In cardiac electrical activity, different types of waves meander through the heart. We present a model of the electrical activity of the heart that proposes that the homogeneous wave fronts propagating through the heart are in fact solitons. We use a general set of reaction-diffusion equations known as the Barrio-Varea-Aragón-Maini (BVAM) model[1]...

We have shown that the expression theta=2tan-1/ derived by Ranganathan to calculate the angles at which there exists a CSL for rotational interfaces in the cubic system can also be applied to general (oblique) two-dimensional lattices provided that the quantities 2 and /cos() are rational numbers, with =|b|/|a| and is the angle between the basis ve...

This paper shows a digital noise generator designed in FPGA, based on a variant of the one-dimensional (1D) chaotic tent map (T-1D). The T-1D map is a piecewise linear 1D chaotic map that defines the statistical behavior of the generated sequences using its control parameter. In this way, the proposed noise generator is a highly competitive alterna...

We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads...

We address the problem of teaching the mathematics of entanglement using only elementary linear algebra. For this goal, we first discuss tensor products using only matrix multiplication and with this we discuss entanglement for pure bipartite systems of arbitrary dimensions. We show how to assess entanglement using only Gaussian methods, i.e. the r...

In this work simple reflections or rotations of canonical vectors are used to generate all Pythagorean vectors, i.e. vectors in \mathbbQn{\mathbb{Q}^{n}} that satisfy the Pythagoras generalized equation. By using Clifford algebra we develop a constructive method that explicitly provides an algorithm to generate generalized Pythagorean numbers. M...

In this work, the equivalence class representatives of integer solutions of the Diophantine equation of the type \({{a_1x_1^2+ .\,.\,. + a_px_p^2 = a_{p+1}x^2_{p+1} + .\,.\,. +a_{p+q}x^2_{p+q} +a_1x^2_{n+1} (a_i > 0,i=1, .\,.\,.\,,p+q,x_{n+1}\neq0)}}\) are found using simple reflections of orthogonal vectors, manipulated using the Clifford algebra...

The problem of coincidences of lattices in the space R(p,q), with p + q = 2, is analyzed using Clifford algebra. We show that, as in R(n), any coincidence isometry can be decomposed as a product of at most two reflections by vectors of the lattice. Bases and coincidence indices are constructed explicitly for several interesting lattices. Our proced...

Fivefold symmetry is important in many scientific areas. In particular, five-part units or pentamerism is a basic pattern in the design of many animals and plants. Despite some efforts, a definite explanation of the abundance of this pentamerism is still missing. In this note we use sea urchins as working examples to propose some ideas, based on sp...

We present an algorithmic proof of the Cartan-Dieudonn\'e theorem on generalized real scalar product spaces with arbitrary signature. We use Clifford algebras to compute the factorization of a given orthogonal transformation as a product of reflections with respect to hyperplanes. The relationship with the Cartan-Dieudonn\'e-Scherk theorem is also...

Solitonlike structures called "droplets" are found to exist within a paradigm reaction-diffusion model that can be used to describe patterning in a number of biological systems, for example, on the skin of various fish species. They have also been found in many other systems that can be modeled with a complex Ginzburg-Landau system. These droplets...

In this article, simple reflections, rotations and the Cartan theorem are handled using Clifford algebras. With this tool we provide a constructive proof of the Cartan theorem and the relationship with Pythagorean numbers is discussed.

The Clifford algebra of a n-dimensional Euclidean vector space provides a general language comprising vectors, complex numbers, quaternions, Grassman algebra, Pauli and Dirac matrices. In this work, a package for Clifford algebra calculations for the computer algebra program Mathematica is introduced through a presentation of the main ideas of Clif...

One of the few examples in which the physical properties of an incommensurable system reflect an underlying higher dimensionality is presented. Specifically, we show that the reflectivity distribution of an incommensurable one-dimensional cavity is given by the density of states of a tight-binding Hamiltonian in a two-dimensional triangular lattice...

An eutactic star, in a n-dimensional space, is a set of N vectors which can be viewed as the projection of N orthogonal vectors in a N-dimensional space. By adequately associating a star of vectors to a particular sea urchin, we propose that a measure of the eutacticity of the star constitutes a measure of the regularity of the sea urchin. Then, we...

Recibido el 6 de junio de 2006; aceptado el 9 de marzo de 2007 El presente trabajo ofrece una introducción didáctica al problema de la sincronización y simpatía entre sistemas dinámicos, que es abundante en diferentes ramas de la física, la biología, la ingeniería y los sistemas sociales. Sistemas tan diversos como la sincronización de relojes, el...

A eutactic star is a set of M vectors in n (M>n) that are projections of M orthogonal vectors in M. Eutactic stars have remarkable properties that have been exploited in several fields such as crystallography, graph theory, wavelets, and quantum measurement theory. In this work we show that given an arbitrary star of vectors, there exists a closest...

Conformal mapping of a slab of a two-dimensional ultrasonic crystal generates a closed geometrical arrangement of ultrasonic scatterers with appealing acoustic properties. This acoustic shell is able to confine ultrasonic modes. Some of these internal resonances can be induced from an external wave source. The mapping of a linear defect produces a...

By considering the structure of holococcoliths (calcite plates that cover holococcolithophores, a haploid phase of the coccolithophore life cycle) as a photonic structure, we apply a discrete dipolar approximation to study the light backscattering properties of these algae. We show that some holococcolith structures have the ability to scatter the...

The eigenfunctions of nested wells with an incommensurate boundary geometry, in both the hydrodynamic shallow water regime and quantum cases, are systematically and exhaustively studied in this Letter. The boundary arrangement of the nested wells consists of polygonal ones, square or hexagonal, with a concentric immersed, similar but rotated, well...

Everything in the last period of Vincent van Gogh paintings seems to be moving; this dynamical style served to transmit his own feelings about a figure or a landscape. Since the early impressionism, artists emprically discovered that an adequate use of luminance could generate the sensation of motion. This sentation was more complex in the case of...

A subtle procedure to confine quasiperiodic hydrodynamic modes within an isolated region on the free surface of a fluid is presented. The experiment consists of a square vessel with an immersed concentric square well vibrating vertically, so that the surface waves generated by the meniscus at the vessel boundary interfere with the bound wave states...

The scaling limit of the energy correlations in non-integrable Ising models In this work, an algorithm to decompose a given orthogonal transformation as a product of reflections through hyperplanes is presented. This in fact constitutes a constructive proof of a Cartan theorem, valid over any field K = Q, R or C. Clifford algebras are used to expli...

Inspired by the locomotion mechanism of sea urchins, we study the locomotion of an irregular echinoid by means of a simplified dynamical model. We prove that if two conjectures are assumed, the geometrical arrangement of the five ambulacral petals of irregular echinoids should form a eutactic star in order to optimize motility. We firstly propose a...

The problem of coincidences of planar lattices is analyzed using Clifford algebra. It is shown that an arbitrary coincidence isometry can be decomposed as a product of coincidence reflections and this allows planar coincidence lattices to be characterized algebraically. The cases of square, rectangular and rhombic lattices are worked out in detail....

A subtle procedure to confine hydrodynamic modes on the free surface of a fluid is presented here. The experiment consists of a square vessel with an immersed square central well vibrating vertically so that the surface waves generated by the meniscus at the vessel boundary interfere with the bound states of the well. This is a classical analogy of...

It is shown that a star of M vectors in ℝ n (M>n) is self-reciprocal, in the sense that it coincides with its Mackay generalized reciprocal star, if and only if it forms a eutactic star. We also show that eutactic stars behave in ways that resemble the behavior of orthonormal sets. A characterization of eutactic stars based on the Moore-Penrose pse...

An eutactic star is a set of N vectors in Rn (N > n) that are projections of N orthogonal vectors in RN. First introduced in the context of regular polytopes, eutactic stars are particularly useful in the field of quasicrystals where a method to generate quasiperiodic tilings is by projecting higher-dimensional lattices. Here are defined the concep...

By considering fluctuations of a random phason field, we show that phasons defects are correlated in real space. This produces regions of the quasicrystal that are more stable than others against phason disorder. Analytical formulae for the stable and unstable parts of a quasilattice are provided, and a discussion about the physical consequences of...