arXiv subjects

Lukas P. Fischer

Publications and source records attributed to Lukas P. Fischer.

5 recordsLinked to original sources

arXiv2019

Free diffusion bounds the precision of currents in underdamped dynamics

The putative generalization of the thermodynamic uncertainty relation (TUR) to underdamped dynamics is still an open problem. So far, bounds that have been derived for such a dynamics are not particularly transparent and they do not converge to the known TUR in the overdamped limit. Furthermore, it was found that there are restrictions for a TUR to hold such as the absence of a magnetic field. In this article we first analyze the properties of driven free diffusion in the underdamped regime and show that it inherently violates the overdamped TUR for finite times. Based on numerical evidence, we then conjecture a bound for one-dimensional driven diffusion in a potential which is based on the result for free diffusion. This bound converges to the known overdamped TUR in the corresponding limit. Moreover, the conjectured bound holds for observables that involve higher powers of the velocity as long as the observable is odd under time-reversal. Finally, we address the applicability of this bound to underdamped dynamics in higher dimensions.

cond-mat.stat-mech↗

arXiv2019

Effect of a magnetic field on the thermodynamic uncertainty relation

The thermodynamic uncertainty relation provides a universal lower bound on the product of entropy production and the fluctuations of any current. While proven for Markov dynamics on a discrete set of states and for overdamped Langevin dynamics, its status for underdamped dynamics is still open. We consider a two-dimensional harmonically confined charged particle in a magnetic field under the action of an external torque. We show analytically that, depending on the sign of the magnetic field, the thermodynamic uncertainty relation does not hold for the currents associated with work and heat. A strong magnetic field can effectively localize the particle with concomitant bounded fluctuations and low dissipation. Numerical results for a three-dimensional variant and for further currents suggest that the existence of such a bound depends crucially on the specific current.

cond-mat.stat-mech↗

arXiv2018

Large Deviation Function for a Driven Underdamped Particle in a Periodic Potential

Employing large deviation theory, we explore current fluctuations of underdamped Brownian motion for the paradigmatic example of a single particle in a one dimensional periodic potential. Two different approaches to the large deviation function of the particle current are presented. First, we derive an explicit expression for the large deviation functional of the empirical phase space density, which replaces the level 2.5 functional used for overdamped dynamics. Using this approach, we obtain several bounds on the large deviation function of the particle current. We compare these to bounds for overdamped dynamics that have recently been derived motivated by the thermodynamic uncertainty relation. Second, we provide a method to calculate the large deviation function via the cumulant generating function. We use this method to assess the tightness of the bounds in a numerical case study for a cosine potential.

cond-mat.stat-mech↗

arXiv2016

The Raspberry Model for Hydrodynamic Interactions Revisited. II. The Effect of Confinement

The so-called 'raspberry' model refers to the hybrid lattice-Boltzmann (LB) and Langevin molecular dynamics scheme for simulating the dynamics of suspensions of colloidal particles, originally developed by [V. Lobaskin and B. Dünweg, New J. Phys. 6, 54 (2004)], wherein discrete surface points are used to achieve fluid-particle coupling. In this paper, we present a follow up to our study of the effectiveness of the raspberry model in reproducing hydrodynamic interactions in the Stokes regime for spheres arranged in a simple-cubic crystal [L. Fischer, et al., J. Chem. Phys. 143, 084108 (2015)]. Here, we consider the accuracy with which the raspberry model is able to reproduce such interactions for particles confined between two parallel plates. To this end, we compare our LB simulation results to established theoretical expressions and finite-element calculations. We show that there is a discrepancy between the translational and rotational mobility when only surface coupling points are used, as also found in Part I of our joint publication. We demonstrate that adding internal coupling points to the raspberry, can be used to correct said discrepancy in confining geometries as well. Finally, we show that the raspberry model accurately reproduces hydrodynamic interactions between a spherical colloid and planar walls up to roughly one LB lattice spacing.

cond-mat.soft↗

arXiv2015

The Raspberry Model for Hydrodynamic Interactions Revisited. I. Periodic Arrays of Spheres and Dumbbells

The so-called 'raspberry' model refers to the hybrid lattice-Boltzmann and Langevin molecular dynamics scheme for simulating the dynamics of suspensions of colloidal particles, originally developed by [V. Lobaskin and B. Dünweg, New J. Phys. 6, 54 (2004)], wherein discrete surface points are used to achieve fluid-particle coupling. This technique has been used in many simulation studies on the behavior of colloids. However, there are fundamental questions with regards to the use of this model. In this paper, we examine the accuracy with which the raspberry method is able to reproduce Stokes-level hydrodynamic interactions when compared to analytic expressions for solid spheres in simple-cubic crystals. To this end, we consider the quality of numerical experiments that are traditionally used to establish these properties and we discuss their shortcomings. We show that there is a discrepancy between the translational and rotational mobility reproduced by the simple raspberry model and present a way to numerically remedy the problem by adding internal coupling points. Finally, we examine a non-convex shape, namely a colloidal dumbbell, and show that the filled raspberry model replicates the desired hydrodynamic behavior in bulk for this more complicated shape. Our investigation is continued in [J. de Graaf, et al., J. Chem. Phys. 143, 084107 (2015)], wherein we consider the raspberry model in the confining geometry of two parallel plates.

cond-mat.soft↗