arXiv subjects

Lutz Schimansky-Geier

Publications and source records attributed to Lutz Schimansky-Geier.

At least 19 recordsLinked to original sources

arXiv2020

Demixing of two species via reciprocally concentration-dependent diffusivity

We propose a model for demixing of two species by assuming a density-dependent effective diffusion coefficient of the particles. Both sorts of microswimmers diffuse as active overdamped Brownian particles with a noise intensity that is determined by the surrounding density of the respective other species within a sensing radius $r_s$. A higher concentration of the first (second) sort will enlarge the diffusion and, in consequence, the intensity of the noise experienced by the second (first) sort. Numerical and analytical investigations of steady states of the macroscopic equations prove the demixing of particles due to this reciprocally concentration-dependent diffusivity. An ambiguity of the numerical integration scheme for the purely local model ($r_s\to 0$) is resolved by considering nonvanishing sensing radii in a nonlocal model with $r_s > 0$.

physics.bio-ph↗

arXiv2018

Variability of collective dynamics in random tree networks of strongly-coupled stochastic excitable elements

We study the collective dynamics of strongly diffusively coupled excitable elements on small random tree networks. Stochastic external inputs are applied to the leaves causing large spiking events. Those events propagate along the tree branches and, eventually, exciting the root node. Using Hodgkin-Huxley type nodal elements, such a setup serves as a model for sensory neurons with branched myelinated distal terminals. We focus on the influence of the variability of tree structures on the spike train statistics of the root node. We present a statistical description of random tree network and show how the structural variability translates into the collective network dynamics. In particular, we show that in the physiologically relevant case of strong coupling the variability of collective response is determined by the joint probability distribution of the total number of leaves and nodes. We further present analytical results for the strong coupling limit in which the entire tree network can be represented by an effective single element.

physics.bio-ph↗

arXiv2017

Adiabatic elimination of inertia of the stochastic microswimmer driven by $α-$stable noise

We consider a microswimmer that moves in two dimensions at a constant speed and changes the direction of its motion due to a torque consisting of a constant and a fluctuating component. The latter will be modeled by a symmetric Lévy-stable ($α$-stable) noise. The purpose is to develop a kinetic approach to eliminate the angular component of the dynamics in order to find a coarse grained description in the coordinate space. By defining the joint probability density function of the position and of the orientation of the particle through the Fokker-Planck equation, we derive transport equations for the position-dependent marginal density, the particle's mean velocity and the velocity's variance. At time scales larger than the relaxation time of the torque $τ_ϕ$ the two higher moments follow the marginal density, and can be adiabatically eliminated. As a result, a closed equation for the marginal density follows. This equation which gives a coarse-grained description of the microswimmer's positions at time scales $t\gg τ_ϕ$, is a diffusion equation with a constant diffusion coefficient depending on the properties of the noise. Hence, the long time dynamics of a microswimmer can be described as a normal, diffusive, Brownian motion with Gaussian increments.

cond-mat.stat-mech↗

arXiv2017

Stochastic Dynamics of Resistive Switching: Fluctuations Lead to Optimal Particle Number

Resistive switching is one of the foremost candidates for building novel types of non-volatile random access memories. Any practical implementation of such a memory cell calls for a strong miniaturization, at which point fluctuations start playing a role that cannot be neglected. A detailed understanding of switching mechanisms and reliability is essential. For this reason, we formulate a particle model based on the stochastic motion of oxygen vacancies. It allows us to investigate fluctuations in the resistance states of a switch with two active zones. The vacancies' dynamics is governed by a master equation. Upon the application of a voltage pulse, the vacancies travel collectively through the switch. By deriving a generalized Burgers equation we can interpret this collective motion as nonlinear traveling waves, and numerically verify this result. Further, we define binary logical states by means of the underlying vacancy distributions, and establish a framework of writing and reading such memory element with voltage pulses. Considerations about the dis- criminability of these operations under fluctuations together with the markedness of the resistive switching effect itself lead to the conclusion, that an intermediate vacancy number is optimal for performance.

cond-mat.mtrl-sci↗

arXiv2017

Anomalous diffusion in run-and-tumble motion

A random walk scheme, consisting of alternating phases of regular Brownian motion and Lévy walks, is proposed as a model for run-and-tumble bacterial motion. Within the continuous-time random walk approach we obtain the long-time and short-time behavior of the mean squared displacement of the walker as depending on the properties of dwelling time distribution in each phase. Depending on these distributions, normal diffusion, superdiffusion and ballistic spreading may arise.

physics.bio-ph↗

arXiv2017

Emergent stochastic oscillations and signal detection in tree networks of excitable elements

We study the stochastic dynamics of strongly-coupled excitable elements on a tree network. The peripheral nodes receive independent random inputs which may induce large spiking events propagating through the branches of the tree and leading to global coherent oscillations in the network. This scenario may be relevant to action potential generation in certain sensory neurons, which possess myelinated distal dendritic tree-like arbors with excitable nodes of Ranvier at peripheral and branching nodes and exhibit noisy periodic sequences of action potentials. We focus on the spiking statistics of the central node, which fires in response to a noisy input at peripheral nodes. We show that, in the strong coupling regime, relevant to myelinated dendritic trees, the spike train statistics can be predicted from an isolated excitable element with rescaled parameters according to the network topology. Furthermore, we show that by varying the network topology the spike train statistics of the central node can be tuned to have a certain firing rate and variability, or to allow for an optimal discrimination of inputs applied at the peripheral nodes.

physics.bio-ph↗

arXiv2016

Tristable and multiple bistable activity in complex random binary networks of two-state units

We study complex networks of stochastic two-state units. Our aim is to model discrete stochastic excitable dynamics with a rest and an excited state. Both states are assumed to possess different waiting time distributions. The rest state is treated as an activation process with an exponentially distributed life time, whereas the latter in the excited state shall have a constant mean which may originate from any distribution. The activation rate of any single unit is determined by its neighbors according to a random complex network structure. In order to treat this problem in an analytical way, we use a heterogeneous mean-field approximation yielding a set of equations general valid for uncorrelated random networks. Based on this derivation we focus on random binary networks where the network is solely comprised of nodes with either of two degrees. The ratio between the two degrees is shown to be a crucial parameter. Dependent on the composition of the network the steady states show the usual transition from disorder to homogeneous ordered bistability as well as new scenarios that include inhomogeneous ordered and disordered bistability as well as tristability. The various steady states differ in their spiking activity expressed by a state dependent spiking rate. Numerical simulations agree with analytic results of the heterogeneous mean-field approximation.

physics.soc-ph↗

arXiv2016

Gaussian theory for spatially distributed self-propelled particles

Obtaining a reduced description with particle and momentum flux densities outgoing from the microscopic equations of motion of the particles requires approximations. The usual method, we refer to as truncation method, is to zero Fourier modes of the orientation distribution starting from a given number. Here we propose another method to derive continuum equations for interacting self-propelled particles. The derivation is based on a Gaussian approximation (GA) of the distribution of the direction of particles. First, by means of simulation of the microscopic model we justify that the distribution of individual directions fits well to a wrapped Gaussian distribution. Second, we numerically integrate the continuum equations derived in the GA in order to compare with results of simulations. We obtain that the global polarization in the GA exhibits a hysteresis in dependence on the noise intensity. It shows qualitatively the same behavior as we find in particles simulations. Moreover, both global polarizations agree perfectly for low noise intensities. The spatio-temporal structures of the GA are also in agreement with simulations. We conclude that the GA shows qualitative agreement for a wide range of noise intensities. In particular, for low noise intensities the agreement with simulations is better as other approximations, making the GA to an acceptable candidates of describing spatially distributed self-propelled particles.

cond-mat.stat-mech↗

arXiv2016

Diffusion of Active Particles With Stochastic Torques Modeled as $α$-Stable Noise

We investigate the stochastic dynamics of an active particle moving at a constant speed under the influence of a fluctuating torque. In our model the angular velocity is generated by a constant torque and random fluctuations described as a Lévy-stable noise. Two situations are investigated. First, we study white Lévy noise where the constant speed and the angular noise generate a persistent motion characterized by the persistence time $τ_D$. At this time scale the crossover from ballistic to normal diffusive behavior is observed. The corresponding diffusion coefficient can be obtained analytically for the whole class of symmetric $α$-stable noises. As typical for models with noise-driven angular dynamics, the diffusion coefficient depends non-monotonously on the angular noise intensity. As second example, we study angular noise as described by an Ornstein-Uhlenbeck process with correlation time $τ_c$ driven by the Cauchy white noise. We discuss the asymptotic diffusive properties of this model and obtain the same analytical expression for the diffusion coefficient as in the first case which is thus independent on $τ_c$. Remarkably, for $τ_c>τ_D$ the crossover from a non-Gaussian to a Gaussian distribution of displacements takes place at a time $τ_G$ which can be considerably larger than the persistence time $τ_D$.

cond-mat.stat-mech↗

arXiv2016

Traveling phase waves in asymmetric networks of noisy chaotic attractors

We explore identical Rössler systems organized into two equally-sized groups, among which differing positive and negative in- and out-coupling strengths are allowed. Patterns of distinctly synchronized phase dynamics are observed, which coexist with chaotically evolving amplitudes. In particular, we report the emergence of traveling phase waves, i.e. states in which the oscillators settle on a new rhythm different from their own. We further elucidate our findings through phase-coupled Rössler systems, establishing a connection with the Kuramoto model. Together with the study of noise effects, our results suggest a promising new avenue towards the coexistence of chaotic, noisy and regular collective dynamics.

nlin.CD↗

arXiv2015

Emergence and coherence of oscillations in star networks of stochastic excitable elements

We study the emergence and coherence of stochastic oscillations in star networks of excitable elements in which peripheral nodes receive independent random inputs. A biophysical model of a distal branch of sensory neuron in which peripheral nodes of Ranvier are coupled to a central node by myelinated cable segments is used along with a generic model of networked stochastic active rotators. We show that coherent oscillations can emerge due to stochastic synchronization of peripheral nodes and that the degree of coherence can be maximized by tuning the coupling strength and the size of the network. Analytical results are obtained for the strong coupling regime of the active rotator network. In particular, we show that in the strong coupling regime the network dynamics can be described by an effective single active rotator with rescaled parameters and noise.

physics.bio-ph↗

arXiv2015

A Nonlinear HP-Type Complementary Resistive Switch

Resistive Switching (RS) is the change in resistance of a dielectric under the influence of an external current or electric field. This change is non-volatile, and the basis of both the memristor and resistive random access memory. In the latter, high integration densities favor the anti-serial combination of two RS-elements to a single cell, termed the complementary resistive switch (CRS). Motivated by the irregular shape of the filament protruding into the device, we suggest a nonlinearity in the resistance-interpolation function, and thereby expand the original HP-memristor. We numerically simulate and analytically solve this model. Further, the nonlinearity allows for its application to the CRS.

cond-mat.mes-hall↗

arXiv2015

Collective dynamics in two populations of noisy oscillators with asymmetric interactions

We study two intertwined globally coupled networks of noisy Kuramoto phase oscillators that have the same natural frequency, but differ in their perception of the mean field and their contribution to it. Such a give-and-take mechanism is given by asymmetric in- and out-coupling strengths which can be both positive and negative. We uncover in this minimal network of networks intriguing patterns of discordance, where the ensemble splits into two clusters separated by a constant phase lag. If it differs from $π$, then traveling wave solutions emerge. We observe a second route to traveling waves via traditional one-cluster states. Bistability is found between the various collective states. Analytical results and bifurcation diagrams are derived with a reduced system.

nlin.AO↗

arXiv2015

Motion of Euglena Gracilis: Active Fluctuations and Velocity Distribution

We study the velocity distribution of unicellular swimming algae Euglena gracilis using optical microscopy and theory. To characterize a peculiar feature of the experimentally observed distribution at small velocities we use the concept of active fluctuations, which was recently proposed for the description of stochastically self-propelled particles [Romanczuk, P. and Schimansky-Geier, L., Phys. Rev. Lett. 106, 230601 (2011)]. In this concept, the fluctuating forces arise due to internal random performance of the propulsive motor. The fluctuating forces are directed in parallel to the heading direction, in which the propulsion acts. In the theory, we introduce the active motion via the depot model [Schweitzer et al., Phys. Rev. Lett. 80, 23, 5044 (1998)]. We demonstrate that the theoretical predictions based on the depot model with active fluctuations are consistent with the experimentally observed velocity distributions. In addition to the model with additive active noise, we obtain theoretical results for a constant propulsion with multiplicative noise.

physics.bio-ph↗

arXiv2015

Pattern formation in active particle systems due to competing alignment interactions

Recently, we proposed a self-propelled particle model with competing alignment interactions: nearby particles tend to align their velocities whereas they anti-align their direction of motion with particles which are further away [R. Grossmann et al., Phys. Rev. Lett. 113, 258104 (2014)]. Here, we extend our previous numerical analysis of the high density regime considering low particle densities too. We report on the emergence of various macroscopic patterns such as vortex arrays, mesoscale turbulence as well as the formation of polar clusters, polar bands and nematically ordered states. Furthermore, we study analytically the instabilities leading to pattern formation in mean-field approximation. We argue that these instabilities are well described by a reduced set of hydrodynamic equations in the limit of high density.

cond-mat.soft↗

arXiv2014

Noise-controlled bistability in an excitable system with positive feedback

We study the interplay between noise and a positive feedback mechanism in an excitable system that generates events. We show that such a system can exhibit a bistability in the dynamics of the event generation (states of low and high activity). The stability of the two states is determined by the strength of the noise such that a change of noise intensity permits complete control over the probabilities with which the two states are occupied. The bistability also has strong implications for the regularity of the event generation. While the irregularity of the interevent interval (short-time variability) and of the asymptotic Fano factor of the event count (long-time variability) is limited if the system is only in one of the two states, we show that both measures of variability display giant values if both states are equally likely. The long-time variability is additionally amplified by long-range positive correlations of the interevent intervals.

cond-mat.stat-mech↗

arXiv2014

Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations

We study the collective dynamics of noise-driven excitable elements, so-called active rotators. Crucially here, the natural frequencies and the individual coupling strengths are drawn from some joint probability distribution. Combining a mean-field treatment with a Gaussian approximation allows us to find examples where the infinite-dimensional system is reduced to a few ordinary differential equations. Our focus lies in the cooperative behavior in a population consisting of two parts, where one is composed of excitable elements, while the other one contains only self-oscillatory units. Surprisingly, excitable behavior in the whole system sets in only if the excitable elements have a smaller coupling strength than the self-oscillating units. In this way positive local correlations between natural frequencies and couplings shape the global behavior of mixed populations of excitable and oscillatory elements.

cond-mat.dis-nn↗

arXiv2014

Modulational instability and resonant wave modes act on the metastability of oscillator chains

We describe the emergence and interactions of breather modes and resonant wave modes within a two-dimensional ring-like oscillator chain in a microcanonical situation. Our analytical results identify different dynamical regimes characterized by the potential dominance of either type of mode. The chain is initially placed in a meta-stable state which it can leave by passing over the brim of the applied Mexican-hat-like potential. We elucidate the influence of the different wave modes on the mean-first passage time. A central finding is that also in this complex potential landscape a fast noise-free escape scenario solely relying on nonlinear cooperative effects is accomplishable even in a low energy setting.

nlin.CD↗