Bulk-Surface Electrothermodynamics and Applications to Electrochemistry.

We propose a modeling framework for magnetizable, polarizable, elastic, viscous, heat conducting, reactive mixtures in contact with interfaces. To this end, we first introduce bulk and surface balance equations that contain several constitutive quantities. For further modeling of the constitutive quantities, we formulate constitutive principles.

Impact of Shell Growth on Recombination Dynamics and Exciton-Phonon Interaction in CdSe-CdS Core-Shell Nanoplatelets.

We investigate the impact of shell growth on the carrier dynamics and exciton-phonon coupling in CdSe-CdS core-shell nanoplatelets with varying shell thickness. We observe that the recombination dynamics can be prolonged by more than one order of magnitude, and analyze the results in a global rate model as well as with simulations including strain and excitonic effects. We reveal that type I band alignment in the hetero platelets is maintained at least up to three monolayers of CdS, resulting in approximately constant radiative rates.

Impact of energy dissipation on interface shapes and on rates for dewetting from liquid substrates.

We revisit the fundamental problem of liquid-liquid dewetting and perform a detailed comparison of theoretical predictions based on thin-film models with experimental measurements obtained by atomic force microscopy. Specifically, we consider the dewetting of a liquid polystyrene layer from a liquid polymethyl methacrylate layer, where the thicknesses and the viscosities of both layers are similar. Using experimentally determined system parameters like viscosity and surface tension, an excellent agreement of experimentally and theoretically obtained rim profile shapes are obtained including the liquid-liquid interface and even dewetting rates.

Lead-DBS v2: Towards a comprehensive pipeline for deep brain stimulation imaging.

Deep brain stimulation (DBS) is a highly efficacious treatment option for movement disorders and a growing number of other indications are investigated in clinical trials. To ensure optimal treatment outcome, exact electrode placement is required. Moreover, to analyze the relationship between electrode location and clinical results, a precise reconstruction of electrode placement is required, posing specific challenges to the field of neuroimaging.

Gradient and GENERIC Systems in the Space of Fluxes, Applied to Reacting Particle Systems.

In a previous work we devised a framework to derive generalised gradient systems for an evolution equation from the large deviations of an underlying microscopic system, in the spirit of the Onsager-Machlup relations. Of particular interest is the case where the microscopic system consists of random particles, and the macroscopic quantity is the empirical measure or concentration. In this work we take the particle flux as the macroscopic quantity, which is related to the concentration via a continuity equation.

Phase-sensitive excitability of a limit cycle.

The classical notion of excitability refers to an equilibrium state that shows under the influence of perturbations a nonlinear threshold-like behavior. Here, we extend this concept by demonstrating how periodic orbits can exhibit a specific form of excitable behavior where the nonlinear threshold-like response appears only after perturbations applied within a certain part of the periodic orbit, i.e.

Universal relations of local order parameters for partially synchronized oscillators.

Interactions among discrete oscillatory units (e.g., cells) can result in partially synchronized states when some of the units exhibit phase locking and others phase slipping.

Light bullets in a time-delay model of a wide-aperture mode-locked semiconductor laser.

Recently, a mechanism of formation of light bullets (LBs) in wide-aperture passively mode-locked lasers was proposed. The conditions for existence and stability of these bullets, found in the long cavity limit, were studied theoretically under the mean field (MF) approximation using a Haus-type model equation. In this paper, we relax the MF approximation and study LB formation in a model of a wide-aperture three section laser with a long diffractive section and short absorber and gain sections.

Sasa-Satsuma hierarchy of integrable evolution equations.

We present the infinite hierarchy of Sasa-Satsuma evolution equations. The corresponding Lax pairs are given, thus proving its integrability. The lowest order member of this hierarchy is the nonlinear Schrödinger equation, while the next one is the Sasa-Satsuma equation that includes third-order terms.

Optimal design of tweezer control for chimera states.

Chimera states are complex spatio-temporal patterns which consist of coexisting domains of spatially coherent and incoherent dynamics in systems of coupled oscillators. In small networks, chimera states usually exhibit short lifetimes and erratic drifting of the spatial position of the incoherent domain. A tweezer feedback control scheme can stabilize and fix the position of chimera states.

Localized instabilities and spinodal decomposition in driven systems in the presence of elasticity.

We study numerically and analytically the instabilities associated with phase separation in a solid layer on which an external material flux is imposed. The first instability is localized within a boundary layer at the exposed free surface by a process akin to spinodal decomposition. In the limiting static case, when there is no material flux, the coherent spinodal decomposition is recovered.

Mode locking in systems of globally coupled phase oscillators.

We investigate the dynamics of a Kuramoto-type system of globally coupled phase oscillators with equidistant natural frequencies and a coupling strength below the synchronization threshold. It turns out that in such cases one can observe a stable regime of sharp pulses in the mean field amplitude with a pulsation frequency given by spacing of the natural frequencies. This resembles a process known as mode locking in lasers and relies on the emergence of a phase relation induced by the nonlinear coupling.

Embedding the dynamics of a single delay system into a feed-forward ring.

We investigate the relation between the dynamics of a single oscillator with delayed self-feedback and a feed-forward ring of such oscillators, where each unit is coupled to its next neighbor in the same way as in the self-feedback case. We show that periodic solutions of the delayed oscillator give rise to families of rotating waves with different wave numbers in the corresponding ring. In particular, if for the single oscillator the periodic solution is resonant to the delay, it can be embedded into a ring with instantaneous couplings.

Role of Intrapulse Coherence in Carrier-Envelope Phase Stabilization.

The concept of coherence is of fundamental importance for describing the physical characteristics of light and for evaluating the suitability for experimental application. In the case of pulsed laser sources, the pulse-to-pulse coherence is usually considered for a judgment of the compressibility of the pulse train. This type of coherence is often lost during propagation through a highly nonlinear medium, and pulses prove incompressible despite multioctave spectral coverage.

Symmetry Breaking and Strong Persistent Plasma Currents via Resonant Destabilization of Atoms.

The ionization rate of an atom in a strong optical field can be resonantly enhanced by the presence of long-living atomic levels (so-called Freeman resonances). This process is most prominent in the multiphoton ionization regime, meaning that the ionization event takes many optical cycles. Nevertheless, here, we show that these resonances can lead to rapid subcycle-scale plasma buildup at the resonant values of the intensity in the pump pulse.

Delayed feedback control of self-mobile cavity solitons in a wide-aperture laser with a saturable absorber.

We investigate the spatiotemporal dynamics of cavity solitons in a broad area vertical-cavity surface-emitting laser with saturable absorption subjected to time-delayed optical feedback. Using a combination of analytical, numerical, and path continuation methods, we analyze the bifurcation structure of stationary and moving cavity solitons and identify two different types of traveling localized solutions, corresponding to slow and fast motion. We show that the delay impacts both stationary and moving solutions either causing drifting and wiggling dynamics of initially stationary cavity solitons or leading to stabilization of intrinsically moving solutions.

Introduction to Focus Issue: Time-delay dynamics.

The field of dynamical systems with time delay is an active research area that connects practically all scientific disciplines including mathematics, physics, engineering, biology, neuroscience, physiology, economics, and many others. This Focus Issue brings together contributions from both experimental and theoretical groups and emphasizes a large variety of applications. In particular, lasers and optoelectronic oscillators subject to time-delayed feedbacks have been explored by several authors for their specific dynamical output, but also because they are ideal test-beds for experimental studies of delay induced phenomena.

Bound Pulse Trains in Arrays of Coupled Spatially Extended Dynamical Systems.

We study the dynamics of an array of nearest-neighbor coupled spatially distributed systems each generating a periodic sequence of short pulses. We demonstrate that, unlike a solitary system generating a train of equidistant pulses, an array of such systems can produce a sequence of clusters of closely packed pulses, with the distance between individual pulses depending on the coupling phase. This regime associated with the formation of locally coupled pulse trains bounded due to a balance of attraction and repulsion between them is different from the pulse bound states reported earlier in different laser, plasma, chemical, and biological systems.

Density of convex intersections and applications.

In this paper, we address density properties of intersections of convex sets in several function spaces. Using the concept of -convergence, it is shown in a general framework, how these density issues naturally arise from the regularization, discretization or dualization of constrained optimization problems and from perturbed variational inequalities. A variety of density results (and counterexamples) for pointwise constraints in Sobolev spaces are presented and the corresponding regularity requirements on the upper bound are identified.

Benchmark problems for numerical treatment of backflow at open boundaries.

In computational fluid dynamics, incoming velocity at open boundaries, or backflow, often yields unphysical instabilities already for moderate Reynolds numbers. Several treatments to overcome these backflow instabilities have been proposed in the literature. However, these approaches have not yet been compared in detail in terms of accuracy in different physiological regimes, in particular because of the difficulty to generate stable reference solutions apart from analytical forms.

Dispersive Time-Delay Dynamical Systems.

We present a theoretical approach to investigate the effect of dispersion in dynamical systems commonly described by time-delay models. The introduction of a polarization equation provides a means to introduce dispersion as a distributed delay term. The expansion of this term in power series, as usually performed to study the propagation of waves in spatially extended systems, can lead to the appearance of spurious instabilities.

Exact firing time statistics of neurons driven by discrete inhibitory noise.

Neurons in the intact brain receive a continuous and irregular synaptic bombardment from excitatory and inhibitory pre- synaptic neurons, which determines the firing activity of the stimulated neuron. In order to investigate the influence of inhibitory stimulation on the firing time statistics, we consider Leaky Integrate-and-Fire neurons subject to inhibitory instantaneous post- synaptic potentials. In particular, we report exact results for the firing rate, the coefficient of variation and the spike train spectrum for various synaptic weight distributions.

Regularizing Aperiodic Cycles of Resonant Radiation in Filament Light Bullets.

We demonstrate an up to now unrecognized and very effective mechanism which prevents filament collapse and allows persistent self-guiding propagation retaining a large portion of the optical energy on axis over unexpected long distances. The key ingredient is the possibility of continuously leaking energy into the normal dispersion regime via the emission of resonant radiation. The frequency of the radiation is determined by the dispersion dynamically modified by photogenerated plasma, thus allowing us to excite new frequencies in spectral ranges which are otherwise difficult to access.

Is there an impact of small phase lags in the Kuramoto model?

We discuss the influence of small phase lags on the synchronization transitions in the Kuramoto model for a large inhomogeneous population of globally coupled phase oscillators. Without a phase lag, all unimodal distributions of the natural frequencies give rise to a classical synchronization scenario, where above the onset of synchrony at the Kuramoto threshold, there is an increasing synchrony for increasing coupling strength. We show that already for arbitrarily small phase lags, there are certain unimodal distributions of natural frequencies such that for increasing coupling strength synchrony may decrease and even complete incoherence may regain stability.

Assessment of reduced-order unscented Kalman filter for parameter identification in 1-dimensional blood flow models using experimental data.

This work presents a detailed investigation of a parameter estimation approach on the basis of the reduced-order unscented Kalman filter (ROUKF) in the context of 1-dimensional blood flow models. In particular, the main aims of this study are (1) to investigate the effects of using real measurements versus synthetic data for the estimation procedure (i.e.