arXiv subjects

G. Schmid

Publications and source records attributed to G. Schmid.

At least 19 recordsLinked to original sources

arXiv2014

Giant enhancement of hydrodynamically enforced entropic trapping in thin channels

Using our generalized Fick-Jacobs approach [Martens et al., PRL 110, 010601 (2013); Martens et al., Eur. Phys. J. Spec. Topics 222, 2453-2463 (2013)] and extensive Brownian dynamics simulations, we study particle transport through three-dimensional periodic channels of different height. Directed motion is caused by the interplay of constant bias acting along the channel axis and a pressure-driven flow. The tremendous change of the flow profile shape in channel direction with the channel height is reflected in a crucial dependence of the mean particle velocity and the effective diffusion coefficient on the channel height. In particular, we observe a giant suppression of the effective diffusivity in thin channels; four orders of magnitude compared to the bulk value.

cond-mat.stat-mech↗

arXiv2013

Time-Resolved Measurement of Interatomic Coulombic Decay in Ne_2

The lifetime of interatomic Coulombic decay (ICD) [L. S. Cederbaum et al., Phys. Rev. Lett. 79, 4778 (1997)] in Ne_2 is determined via an extreme ultraviolet pump-probe experiment at the Free-Electron Laser in Hamburg. The pump pulse creates a 2s inner-shell vacancy in one of the two Ne atoms, whereupon the ionized dimer undergoes ICD resulting in a repulsive Ne^{+}(2p^{-1}) - Ne^{+}(2p^{-1}) state, which is probed with a second pulse, removing a further electron. The yield of coincident Ne^{+} - Ne^{2+} pairs is recorded as a function of the pump-probe delay, allowing us to deduce the ICD lifetime of the Ne_{2}^{+}(2s^{-1}) state to be (150 +/- 50) fs in agreement with quantum calculations.

physics.atm-clus↗

arXiv2013

How entropy and hydrodynamics cooperate in rectifying particle transport

Using the analytical Fick-Jacobs approximation formalism and extensive Brownian dynamics simulations we study particle transport through two-dimensional periodic channels with triangularly shaped walls. Directed motion is caused by the interplay of constant bias acting along the channel axis and a pressure-driven flow. In particular, we analyze the particle mobility and the effective diffusion coefficient. The mechanisms of entropic rectification is revealed in channels with a broken spatial reflection symmetry in presence of hydrodynamically enforced entropic trapping. Due to the combined action of the forcing and the pressure-driven flow field, efficient rectification with a drastically reduced diffusivity is achieved.

cond-mat.stat-mech↗

arXiv2012

Hydrodynamically enforced entropic trapping of Brownian particles

We study the transport of Brownian particles through a corrugated channel caused by a force field containing curl-free (scalar potential) and divergence-free (vector potential) parts. We develop a generalized Fick-Jacobs approach leading to an effective one-dimensional description involving the potential of mean force. As an application, the interplay of a pressure-driven flow and an oppositely oriented constant bias is considered. We show that for certain parameters, the particle diffusion is significantly suppressed via the property of hyrodynamically enforced entropic particle trapping.

cond-mat.stat-mech↗

arXiv2012

Brownian transport in corrugated channels with inertia

The transport of suspended Brownian particles dc-driven along corrugated narrow channels is numerically investigated in the regime of finite damping. We show that inertial corrections cannot be neglected as long as the width of the channel bottlenecks is smaller than an appropriate particle diffusion length, which depends on the the channel corrugation and the drive intensity. Being such a diffusion length inversely proportional to the damping constant, transport through sufficiently narrow obstructions turns out to be always sensitive to the viscosity of the suspension fluid. The inertia corrections to the transport quantifiers, mobility and diffusivity, markedly differ for smoothly and sharply corrugated channels.

physics.chem-ph↗

arXiv2012

Detectable inertial effects on Brownian transport through narrow pores

We investigate the transport of suspended Brownian particles dc driven along corrugated narrow channels in a regime of finite damping. We demonstrate that inertial corrections cannot be neglected as long as the width of the channel bottlenecks is smaller than an appropriate particle diffusion length, which depends on both, the temperature and the strength of the dc drive. Therefore, transport through sufficiently narrow constrictions turns out to be sensitive to the viscosity of the suspension fluid. Applications to colloidal systems are discussed.

cond-mat.stat-mech↗

arXiv2011

Driven Brownian transport through arrays of symmetric obstacles

We numerically investigate the transport of a suspended overdamped Brownian particle which is driven through a two-dimensional rectangular array of circular obstacles with finite radius. Two limiting cases are considered in detail, namely, when the constant drive is parallel to the principal or the diagonal array axes. This corresponds to studying the Brownian transport in periodic channels with reflecting walls of different topologies. The mobility and diffusivity of the transported particles in such channels are determined as functions of the drive and the array geometric parameters. Prominent transport features, like negative differential mobilities, excess diffusion peaks, and unconventional asymptotic behaviors, are explained in terms of two distinct lengths, the size of single obstacles (trapping length) and the lattice constant of the array (local correlation length). Local correlation effects are further analyzed by continuously rotating the drive between the two limiting orientations.

physics.chem-ph↗

arXiv2011

Entropic Splitter for Particle Separation

We present a particle separation mechanism which induces motion of particles of different sizes in opposite directions. The mechanism is based on the combined action of a driving force and an entropic rectification of the Brownian fluctuations caused by the asymmetric form of the channel along which particles proceed. The entropic splitting effect shown could be controlled upon variation of the geometrical parameters of the channel and could be implemented in narrow channels and microfluidic devices.

cond-mat.stat-mech↗

arXiv2010

Steering the potential barriers: entropic to energetic

We propose a new mechanism to alter the nature of the potential barriers when a biased Brownian particle under goes a constrained motion in narrow, periodic channel. By changing the angle of the external bias, the nature of the potential barriers changes from purely entropic to energetic which in turn effects the diffusion process in the system. At an optimum angle of the bias, the nonlinear mobility exhibits a striking bell-shaped behavior. Moreover, the enhancement of the scaled effective diffusion coefficient can be efficiently controlled by the angle of the bias. This mechanism enables the proper design of channel structures for transport of molecules and small particles. The approximative analytical predictions have been verified by precise Brownian dynamic simulations.

cond-mat.stat-mech↗

arXiv2010

Controlling diffusive transport in confined geometries

We analyze the diffusive transport of Brownian particles in narrow channels with periodically varying cross-section. The geometrical confinements lead to entropic barriers, the particle has to overcome in order to proceed in transport direction. The transport characteristics exhibit peculiar behaviors which are in contrast to what is observed for the transport in potentials with purely energetic barriers. By adjusting the geometric parameters of the channel one can effectively tune the transport and diffusion properties. A prominent example is the maximized enhancement of diffusion for particular channel parameters. The understanding of the role of channel-shape provides the possibility for a design of stylized channels wherein the quality of the transport can be efficiently optimized.

cond-mat.stat-mech↗

arXiv2009

Double Entropic Stochastic Resonance

We demonstrate the appearance of a purely entropic stochastic resonance (ESR) occurring in a geometrically confined system, where the irregular boundaries cause entropic barriers. The interplay between a periodic input signal, a constant bias and intrinsic thermal noise leads to a resonant ESR-phenomenon in which feeble signals become amplified. This new phenomenon is characterized by the presence of two peaks in the spectral amplification at corresponding optimal values of the noise strength. The main peak is associated with the manifest stochastic resonance synchronization mechanism involving the inter-well noise-activated dynamics while a second peak relates to a regime of optimal sensitivity for intra-well dynamics. The nature of ESR, occurring when the origin of the barrier is entropic rather than energetic, offers new perspectives for novel investigations and potential applications. ESR by itself presents yet another case where one constructively can harvest noise in driven nonequilibrium systems.

cond-mat.stat-mech↗

arXiv2009

Entropic stochastic resonance: the constructive role of the unevenness

We demonstrate the existence of stochastic resonance (SR) in confined systems arising from entropy variations associated to the presence of irregular boundaries. When the motion of a Brownian particle is constrained to a region with uneven boundaries, the presence of a periodic input may give rise to a peak in the spectral amplification factor and therefore to the appearance of the SR phenomenon. We have proved that the amplification factor depends on the shape of the region through which the particle moves and that by adjusting its characteristic geometric parameters one may optimize the response of the system. The situation in which the appearance of such entropic stochastic resonance (ESR) occurs is common for small-scale systems in which confinement and noise play an prominent role. The novel mechanism found could thus constitute an important tool for the characterization of these systems and can put to use for controlling their basic properties.

cond-mat.stat-mech↗

arXiv2008

A singular perturbation approach to the steady-state 1D Poisson-Nernst-Planck modeling

The reduced 1D Poisson-Nernst-Planck (PNP) model of artificial nanopores in the presence of a permanent charge on the channel wall is studied. More specifically, we consider the limit where the channel length exceed much the Debye screening length and channel's charge is sufficiently small. Ion transport is described by the nonequillibrium steady-state solution of the PNP system within a singular perturbation treatment. The quantities, 1/lambda -- the ratio of the Debye length to a characteristic length scale and epsilon -- the scaled intrinsic charge density, serve as the singular and the regular perturbation parameters, respectively. The role of the boundary conditions is discussed. A comparison between numerics and the analytical results of the singular perturbation theory is presented.

physics.chem-ph↗

arXiv2008

Entropic Stochastic Resonance

We present a novel scheme for the appearance of Stochastic Resonance when the dynamics of a Brownian particle takes place in a confined medium. The presence of uneven boundaries, giving rise to an entropic contribution to the potential, may upon application of a periodic driving force result in an increase of the spectral amplification at an optimum value of the ambient noise level. This Entropic Stochastic Resonance (ESR), characteristic of small-scale systems, may constitute a useful mechanism for the manipulation and control of single-molecules and nano-devices.

cond-mat.stat-mech↗

arXiv2008

Entropic particle transport in periodic channels

The dynamics of Brownian motion has widespread applications extending from transport in designed micro-channels up to its prominent role for inducing transport in molecular motors and Brownian motors. Here, Brownian transport is studied in micro-sized, two dimensional periodic channels, exhibiting periodically varying cross sections. The particles in addition are subjected to an external force acting alongside the direction of the longitudinal channel axis. For a fixed channel geometry, the dynamics of the two dimensional problem is characterized by a single dimensionless parameter which is proportional to the ratio of the applied force and the temperature of the particle environment. In such structures entropic effects may play a dominant role. Under certain conditions the two dimensional dynamics can be approximated by an effective one dimensional motion of the particle in the longitudinal direction. The Langevin equation describing this reduced, one dimensional process is of the type of the Fick-Jacobs equation. It contains an entropic potential determined by the varying extension of the eliminated channel direction, and a correction to the diffusion constant that introduces a space dependent diffusion. Different forms of this correction term have been suggested before, which we here compare for a particular class of models. We analyze the regime of validity of the Fick-Jacobs equation, both by means of analytical estimates and the comparisons with numerical results for the full two dimensional stochastic dynamics. For the nonlinear mobility we find a temperature dependence which is opposite to that known for particle transport in periodic potentials. The influence of entropic effects is discussed for both, the nonlinear mobility and the effective diffusion constant.

cond-mat.stat-mech↗

arXiv2008

Rectification in synthetic conical nanopores: a one-dimensional Poisson-Nernst-Planck modeling

Ion transport in biological and synthetic nanochannels is characterized by phenomena such as ion current fluctuations and rectification. Recently, it has been demonstrated that nanofabricated synthetic pores can mimic transport properties of biological ion channels [P. Yu. Apel, {\it et al.}, Nucl. Instr. Meth. B {\bf 184}, 337 (2001); Z. Siwy, {\it et al.}, Europhys. Lett. {\bf 60}, 349 (2002)]. Here, the ion current rectification is studied within a reduced 1D Poisson-Nernst-Planck (PNP) model of synthetic nanopores. A conical channel of a few $\mathrm{nm}$ to a few hundred of nm in diameter, and of few $μ$m long is considered in the limit where the channel length considerably exceeds the Debye screening length. The rigid channel wall is assumed to be weakly charged. A one-dimensional reduction of the three-dimensional problem in terms of corresponding entropic effects is put forward. The ion transport is described by the non-equilibrium steady-state solution of the 1D Poisson-Nernst-Planck system within a singular perturbation treatment. An analytic formula for the approximate rectification current in the lowest order perturbation theory is derived. A detailed comparison between numerical results and the singular perturbation theory is presented. The crucial importance of the asymmetry in the potential jumps at the pore ends on the rectification effect is demonstrated. This so constructed 1D theory is shown to describe well the experimental data in the regime of small-to-moderate electric currents.

physics.class-ph↗

arXiv2007

Biased diffusion in confined media: Test of the Fick-Jacobs approximation and validity criteria

We study biased, diffusive transport of Brownian particles through narrow, spatially periodic structures in which the motion is constrained in lateral directions. The problem is analyzed under the perspective of the Fick-Jacobs equation which accounts for the effect of the lateral confinement by introducing an entropic barrier in a one dimensional diffusion. The validity of this approximation, being based on the assumption of an instantaneous equilibration of the particle distribution in the cross-section of the structure, is analyzed by comparing the different time scales that characterize the problem. A validity criterion is established in terms of the shape of the structure and of the applied force. It is analytically corroborated and verified by numerical simulations that the critical value of the force up to which this description holds true scales as the square of the periodicity of the structure. The criterion can be visualized by means of a diagram representing the regions where the Fick-Jacobs description becomes inaccurate in terms of the scaled force versus the periodicity of the structure.

cond-mat.stat-mech↗

arXiv2006

Capacitance fluctuations causing channel noise reduction in stochastic Hodgkin-Huxley systems

Voltage-dependent ion channels determine the electric properties of axonal cell membranes. They not only allow the passage of ions through the cell membrane but also contribute to an additional charging of the cell membrane resulting in the so-called capacitance loading. The switching of the channel gates between an open and a closed configuration is intrinsically related to the movement of gating charge within the cell membrane. At the beginning of an action potential the transient gating current is opposite to the direction of the current of sodium ions through the membrane. Therefore, the excitability is expected to become reduced due to the influence of a gating current. Our stochastic Hodgkin-Huxley like modeling takes into account both the channel noise -- i.e. the fluctuations of the number of open ion channels -- and the capacitance fluctuations that result from the dynamics of the gating charge. We investigate the spiking dynamics of membrane patches of variable size and analyze the statistics of the spontaneous spiking. As a main result, we find that the gating currents yield a drastic reduction of the spontaneous spiking rate for sufficiently large ion channel clusters. Consequently, this demonstrates a prominent mechanism for channel noise reduction.

q-bio.NC↗