Related papers: Transient localized wave patterns and their applic…
MicroRNAs are extensively known for post-transcriptional gene regulation and pattern formation in the embryonic developmental stage. We explore the origin of these spatio-temporal patterns mathematically, considering three different motifs…
Cortical slow oscillations are an emergent property of the cortical network, a hallmark of low complexity brain states like sleep, and represent a default activity pattern. Here, we present a methodological approach for quantifying the…
We propose a generic uncertainty relationship for cross-diffusion (quasi-soliton) waves triggered by local instabilities through Thermo-Hydro-Mechano-Chemical (THMC) coupling and cross-scale feedbacks. Cross-diffusion waves nucleate when…
Migraine (MGR) ranks first among diseases in terms of years of lost healthy life in young adult and adult women. Currently, there is no theory of MGR. This paper presents a complete theory of migraine that explains its etiology, symptoms,…
Subdiffusion is a hallmark of complex systems, ranging from protein folding to transport in viscoelastic media. However, despite its pervasiveness, the mechanistic origins of subdiffusion remain contested. Here, we analyze both Markovian…
Differential equation-based physiological models of sleep-wake networks describe sleep-wake regulation by simulating the activity of wake- and sleep-promoting neuronal populations and the modulation of these populations by homeostatic and…
Little is currently known about the coordination of neural activity over longitudinal time-scales and how these changes relate to behavior. To investigate this issue, we used resting-state fMRI data from a single individual to identify the…
We investigate the stability and nonlinear local dynamics of spectrally stable wave trains in reaction-diffusion systems. For each $N\in\mathbb{N}$, such $T$-periodic traveling waves are easily seen to be nonlinearly asymptotically stable…
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…
In the mean-field theory of magnetic fields, turbulent transport, i.e. the turbulent electromotive force, is described by a combination of the alpha effect and turbulent magnetic diffusion, which are usually assumed to be proportional…
Formation of diverse patterns in spatially extended reaction-diffusion systems is an important aspect of study which is pertinent to many chemical and biological processes. Of special interest is the peculiar phenomenon of chimera state…
We study a model for the depinning and driven steady state phases of a solid tuned across a polymorphic phase transition between ground states of triangular and square symmetry. These include pinned states which may have dominantly…
The appearence of long-range correlations near the Dirac point of a Dirac-like spinor model with random vector potential is studied. These correlations originate from a spontaneously broken symmetry and their corresponding Goldstone modes.…
The brain encodes external stimuli through patterns of neural activity, forming internal representations of the world. Recent experiments show that neural representations for a given stimulus change over time. However, the mechanistic…
We investigate electronic transport across a magnetic domain wall (DW) in a three-dimensional (3D) second-order topological insulator subject to Anderson disorder. In the clean limit, the DW hosts two co-propagating one-dimensional (1D)…
Strong effects of the Faraday instability on suspensions of rodlike colloidal particles are reported through measurements of the critical acceleration and of the surface wave amplitude. We show that the transition to parametrically excited…
When the steady states at infinity become unstable through a pattern forming bifurcation, a travelling wave may bifurcate into a modulated front which is time-periodic in a moving frame. This scenario has been studied by B.Sandstede and…
We examine the effects of a periodically varying flow velocity on the standing and travelling wave patterns formed by the flow-distributed oscillation (FDO) mechanism. In the kinematic (or diffusionless) limit, the phase fronts undergo a…
We present fully three-dimensional local MRI simulations with the object of studying the excitation of non-axisymmetric spiral density waves that are observed to always be present in such simulations. They are potentially important for…
The motility of eukaryotic cells is strongly influenced by their environment, with confined cells often developing qualitatively different motility patterns from those migrating on simple two-dimensional substrates. Recent experiments,…