Temperature dependence of thermal conductivities of coupled rotator lattice and the momentum diffusion in standard map

In contrary to other 1D momentum-conserving lattices such as the Fermi-Pasta-Ulam $\beta$ (FPU-$\beta$) lattice, the 1D coupled rotator lattice is a notable exception which conserves total momentum while exhibits normal heat conduction behavior. The temperature behavior of the thermal conductivities of 1D coupled rotator lattice had been studied in previous works trying to reveal the underlying physical mechanism for normal heat conduction. However, two different temperature behaviors of thermal conductivities have been claimed for the same coupled rotator lattice. These different temperature behaviors also intrigue the debate whether there is a phase transition of thermal conductivities as the function of temperature. In this work, we will revisit the temperature dependent thermal conductivities for the 1D coupled rotator lattice. We find that the temperature dependence follows a power law behavior which is different with the previously found temperature behaviors. Our results also support the claim that there is no phase transition for 1D coupled rotator lattice. We also give some discussion about the similarity of diffusion behaviors between the 1D coupled rotator lattice and the single kicked rotator also called the Chirikov standard map.Comment: 6 pages, 5 figure

Noisy saltatory spike propagation: The breakdown of signal transmission due to channel noise

Noisy saltatory spike propagation along myelinated axons is studied within a stochastic Hodgkin-Huxley model. The intrinsic noise (whose strength is inverse proportional to the nodal membrane size) arising from fluctuations of the number of open ion channels influences the dynamics of the membrane potential in a node of Ranvier where the sodium ion channels are predominantly localized. The nodes of Ranvier are linearly coupled. As the measure for the signal propagation reliability we focus on the ratio between the number of initiated spikes and the transmitted spikes. This work supplements our earlier study [A. Ochab-Marcinek, G. Schmid, I. Goychuk and P. H\"anggi, Phys. Rev E 79, 011904 (2009)] towards stronger channel noise intensity and supra-threshold coupling. For strong supra-threshold coupling the transmission reliability decreases with increasing channel noise level until the causal relationship is completely lost and a breakdown of the spike propagation due to the intrinsic noise is observed.Comment: To appear in EPJS

Thermal conductance of the coupled-rotator chain: Influence of temperature and size

Thermal conductance of a homogeneous 1D nonlinear lattice system with neareast neighbor interactions has recently been computationally studied in detail by Li et al [Eur. Phys. J. B {\bf 88}, 182 (2015)], where its power-law dependence on temperature $T$ for high temperatures is shown. Here, we address its entire temperature dependence, in addition to its dependence on the size $N$ of the system. We obtain a neat data collapse for arbitrary temperatures and system sizes, and numerically show that the thermal conductance curve is quite satisfactorily described by a fat-tailed $q$-Gaussian dependence on $TN^{1/3}$ with $q \simeq 1.55$. Consequently, its $T \to\infty$ asymptotic behavior is given by $T^{-\alpha}$ with $\alpha=2/(q-1) \simeq 3.64$.Comment: 5 pages including 2 figure

Hydrodynamic and entropic effects on colloidal diffusion in corrugated channels

In the absence of advection, confined diffusion characterizes transport in many natural and artificial devices, such as ionic channels, zeolites, and nanopores. While extensive theoretical and numerical studies on this subject have produced many important predictions, experimental verifications of the predictions are rare. Here, we experimentally measure colloidal diffusion times in microchannels with periodically varying width and contrast results with predictions from the Fick-Jacobs theory and Brownian dynamics simulation. While the theory and simulation correctly predict the entropic effect of the varying channel width, they fail to account for hydrodynamic effects, which include both an overall decrease and a spatial variation of diffusivity in channels. Neglecting such hydrodynamic effects, the theory and simulation underestimate the mean and standard deviation of first passage times by 40\% in channels with a neck width twice the particle diameter. We further show that the validity of the Fick-Jakobs theory can be restored by reformulating it in terms of the experimentally measured diffusivity. Our work thus demonstrates that hydrodynamic effects play a key role in diffusive transport through narrow channels and should be included in theoretical and numerical models.Comment: 7 pages, 4 figure

Active Brownian motion in a narrow channel

We review recent advances in rectification control of artificial microswimmers, also known as Janus particles, diffusing along narrow, periodically corrugated channels. The swimmer self-propulsion mechanism is modeled so as to incorporate a nonzero torque (propulsion chirality). We first summarize the effects of chirality on the autonomous current of microswimmers freely diffusing in channels of different geometries. In particular, left-right and upside-down asymmetric channels are shown to exhibit different transport properties. We then report new results on the dependence of the diffusivity of chiral microswimmers on the channel geometry and their own self-propulsion mechanism. The self-propulsion torque turns out to play a key role as a transport control parameter.Comment: to be published in Eur. Phys. J Special Topic

Diffusion of Colloidal Rods in Corrugated Channels

In many natural and artificial devices diffusive transport takes place in confined geometries with corrugated boundaries. Such boundaries cause both entropic and hydrodynamic effects, which have been studied only for the case of spherical particles. Here we experimentally investigate diffusion of particles of elongated shape confined into a corrugated quasi-two-dimensional channel. Elongated shape causes complex excluded-volume interactions between particle and channel walls which reduce the accessible configuration space and lead to novel entropic free energy effects. The extra rotational degree of freedom also gives rise to a complex diffusivity matrix that depends on both the particle location and its orientation. We further show how to extend the standard Fick-Jacobs theory to incorporate combined hydrodynamic and entropic effects, so as, for instance, to accurately predict experimentally measured mean first passage times along the channel. Our approach can be used as a generic method to describe translational diffusion of anisotropic particles in corrugated channels.Comment: 12 pages and 4 figure

Spontaneous spiking in an autaptic Hodgkin-Huxley set up

The effect of intrinsic channel noise is investigated for the dynamic response of a neuronal cell with a delayed feedback loop. The loop is based on the so-called autapse phenomenon in which dendrites establish not only connections to neighboring cells but as well to its own axon. The biophysical modeling is achieved in terms of a stochastic Hodgkin-Huxley model containing such a built in delayed feedback. The fluctuations stem from intrinsic channel noise, being caused by the stochastic nature of the gating dynamics of ion channels. The influence of the delayed stimulus is systematically analyzed with respect to the coupling parameter and the delay time in terms of the interspike interval histograms and the average interspike interval. The delayed feedback manifests itself in the occurrence of bursting and a rich multimodal interspike interval distribution, exhibiting a delay-induced reduction of the spontaneous spiking activity at characteristic frequencies. Moreover, a specific frequency-locking mechanism is detected for the mean interspike interval.Comment: 8 pages, 10 figure