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Starting with the relative entropy for two close statistical states we define the metric and calculate the scalar curvature $R$ for systems with classical, boson and fermion fractal distribution functions with moment order parameter $q$. In…
The structure of spiral waves is investigated in super-excitable reaction-diffusion systems where the local dynamics exhibits multi-looped phase space trajectories. It is shown that such systems support stable spiral waves with broken…
The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the $q$-deformed algebra of coherent states. Self-similar structures are related to dissipation and to noncommutative…
We study one-dimensional wave equations defined by a class of fractal Laplacians. These Laplacians are defined by fractal measures generated by iterated function systems with overlaps, such as the well-known infinite Bernoulli convolution…
Three-dimensional excitable systems can create nonlinear scroll waves that rotate around one-dimensional phase singularities. Recent theoretical work predicts that these filaments drift along step-like height variations. Here we test this…
When a solid body floats at the interface of a vibrating liquid bath, the relative motion between the object and interface generates outwardly propagating surface waves. It has recently been demonstrated that millimetric objects with…
We show that a class of $L$-loop conformal ladder graphs correspond to twisted partition functions of free massive complex scalars in $d=2L+1$ dimensions. The graphs arise as four-point functions in certain two- and four-dimensional…
We present a theoretical framework for understanding the wavefunctions and spectrum of an extensively studied paradigm for quasiperiodic systems, namely the Fibonacci chain. Our analytical results, which are obtained in the limit of strong…
Spiral waves in active media react to small perturbations as particle-like objects. Here we apply the asymptotic theory to the interaction of spiral waves with a localized inhomogeneity, which leads to a novel prediction: drift of the…
In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic up in a moving frame of reference. Examples include traveling waves or spiral waves in chemical systems or cardiac tissue. We present a…
When propagated action potentials in cardiac tissue interact with local heterogeneities, reflected waves can sometimes be induced. These reflected waves have been associated with the onset of cardiac arrhythmias, and while their generation…
Rotating spiral waves are a form of self-organization observed in spatially extended systems of physical, chemical, and biological nature. A small perturbation causes gradual change in spatial location of spiral's rotation center and…
This thesis investigates in the time domain a particular class of second order perturbations of a perfect fluid non-rotating compact star: those arising from the coupling between first order radial and non-radial perturbations. This problem…
Using numerical analysis of fundamental frequencies we study the orbital structure of a tidally induced bar formed in a simulated dwarf galaxy orbiting a Milky Way-like host. We find that only about 10% of stars have frequencies compatible…
Spirals in protoplanetary discs have been used to locate the potential planet in discs. Since only the spiral shape from a circularly orbiting perturber is known, most previous works assume that the planet is in a circular orbit. We develop…
Following [14] and [12], we formalize the notion of an oscillatory integral interpreted as a functional on the amplitudes supported near a fixed critical point $x_0$ of the phase function with zero critical value. We relate to an…
For fixed natural numbers $r$ and $s$, where $2\leq s \leq r$, we consider a representation of numbers from the interval $[0;\frac{r}{s-1}]$ obtained by encoding numbers by means of the alphabet $A=\{0,1,...,r\}$ via the expansion…
I present the numerical computation of speed and direction of the drift of a spiral wave in an excitable medium in the presence of an electric field. In contrast to earlier results, the drift speed presents a strong variation close to the…
Motivated by the recent results of \citet{Lesur_Ogilvie10} on the transport properties of incompressible convection in protoplanetary discs, in this paper we study the role of compressibility and hence of another basic mode -- spiral…
We show that rocky shorelines with fractal dimension 4/3 are conformally invariant curves by measuring the statistics of their winding angles from global high-resolution data. Such coastlines are thus statistically equivalent to the outer…