arXiv subjects

Philipp Maass

Publications and source records attributed to Philipp Maass.

At least 37 records · Page 2Linked to original sources

arXiv2022

Brownian dynamics simulations of hard rods in external fields and with contact interactions

We propose a simulation method for Brownian dynamics of hard rods in one dimension for arbitrary continuous external force fields. It is an event-driven procedure based on the fragmentation and mergers of clusters formed by particles in contact. It allows one to treat particle interactions in addition to the hard-sphere exclusion as long as the corresponding interaction forces are continuous functions of the particle coordinates. We furthermore develop a treatment of sticky hard spheres as described by Baxter's contact interaction potential.

cond-mat.stat-mech↗

arXiv2022

On the possibility of exploring tip-molecule interactions with STM experiments

We present a theory for analyzing residence times of single molecules in a fixed detection area of a scanning tunneling microscope (STM). The approach is developed for one-dimensional molecule diffusion and can be extended to two dimensions by using the same methodology. Explicit results are derived for an harmonic attractive and repulsive tip-molecule interaction. Applications of the theory allows one to estimate the type and strength of interactions between the STM tip and the molecule. This includes the possibility of an estimation of molecule-molecule interaction when the tip is decorated by a molecule. Despite our focus on STM, this theory can analogously be applied to other experimental probes that monitor single molecules.

cond-mat.mes-hall↗

arXiv2022

Solitons in overdamped Brownian dynamics

Solitons are commonly known as waves that propagate without dispersion. Here we show that they can occur for driven overdamped Brownian dynamics of hard spheres in periodic potentials at high densities. The solitons manifest themselves as periodic sequences of different assemblies of particles moving in the limit of zero noise, where transport of single particles is not possible. They give rise to particle currents at even low temperature that appear in band-like structures around certain hard-sphere diameters. At high temperatures, the band-like structures are washed out by the noise, but the particle transport is still dominated by the solitons. All these predicted features should occur in a broad class of periodic systems and are amenable to experimental tests.

cond-mat.stat-mech↗

arXiv2021

Driven transport of soft Brownian particles through pore-like structures: Effective size method

Single-file transport in pore-like structures constitute an important topic for both theory and experiment. For hardcore interacting particles, a good understanding of the collective dynamics has been achieved recently. Here we study how softness in the particle interaction affects the emergent transport behavior. To this end, we investigate the driven Brownian motion of particles in a periodic potential. The particles interact via a repulsive softcore potential with a shape corresponding to a smoothed rectangular barrier. This shape allows us to elucidate effects of mutual particle penetration and particle crossing in a controlled manner. We find that even weak deviations from the hardcore case can have a strong impact on the particle current. Despite this fact, the knowledge about the transport in a corresponding hardcore system is shown to be useful to describe and interpret our findings for the softcore case. This is achieved by assigning a thermodynamic effective size to the particles based on the equilibrium density functional of hard spheres.

cond-mat.stat-mech↗

arXiv2021

Predicting conductivities of alkali borophosphate glasses based on site energy distributions derived from network former unit concentrations

For ion transport in network glasses, it is a great challenge to predict conductivities specifically based on structural properties. To this end it is necessary to gain an understanding of the energy landscape where the thermally activated hopping motion of the ions takes place. For alkali borophosphate glasses, a statistical mechanical approach was suggested to predict essential characteristics of the distribution of energies at the residence sites of the mobile alkali ions. The corresponding distribution of site energies was derived from the chemical units forming the glassy network. A hopping model based on the site energy landscape allowed to model the change of conductivity activation energies with the borate to phosphate mixing ratio. Here we refine and extend this general approach to cope with minimal local activation barriers and to calculate dc-conductivities without the need of performing extensive Monte-Carlo simulations. This calculation relies on the mapping of the many-body ion dynamics onto a network of local conductances derived from the elementary jump rates of the mobile ions. Application of the theoretical modelling to three series of alkali borophosphate glasses with the compositions $0.33$Li$_2$O$-0.67$[$x$B$_2$O$_3$-$(1\!-\!x)$P$_2$O$_5$], $0.35$Na$_2$O$-0.65$[$x$B$_2$O$_3$-$(1\!-\!x)$P$_2$O$_5$] and $0.4$Na$_2$O$-0.6$[$x$B$_2$O$_3$-$(1\!-\!x)$P$_2$O$_5$] shows good agreement with experimental data.

cond-mat.mtrl-sci↗

arXiv2021

Network-forming units, energy landscapes and conductivity activation energies in alkali borophosphate glasses: analytical approaches

A major challenge in the modeling of ionically conducting glasses is to understand how the large variety of possible chemical compositions and specific structural properties influence ionic transport quantities. Here we revisit and extend a theoretical approach for alkali borophosphate glasses, where changes of conductivity activation energies with the borate to phosphate mixing ratio are related to modifications of the ionic site energy landscape. The landscape modifications are caused by varying amounts of different units forming the glassy network, which lead to spatial redistributions of the counter-charges of the mobile alkali ions. Theoretical approaches are presented to calculate variations of both network former unit concentrations and activation energies with the glass composition. Applications to several alkali borophosphate glasses show good agreement with experimental data.

cond-mat.mtrl-sci↗

arXiv2021

Hydrodynamic interactions can induce jamming in flow-driven systems

Hydrodynamic interactions between fluid-dispersed particles are ubiquitous in soft matter and biological systems and they give rise to intriguing collective phenomena. While it was reported that these interactions can facilitate force-driven particle motion over energetic barriers, here we show the opposite effect in a flow-driven system, i.e. that hydrodynamic interactions hinder transport across barriers. We demonstrate this result by combining experiments and theory. In the experiments, we drive colloidal particles using rotating optical traps, thus creating a vortex flow in the corotating reference frame. We observe a jamming-like decrease of particle currents with density for large barriers between traps. The theoretical model shows that this jamming arises from hydrodynamic interactions between the particles. The impact of hydrodynamic interactions is reversed compared to force-driven motion, suggesting that our findings are a generic feature of flow-driven transport.

cond-mat.soft↗

arXiv2020

Molecular self-assembly: Quantifying the balance between intermolecular attraction and repulsion from distance and length distributions

Molecular self-assembly on surfaces constitutes a powerful method for creating tailor-made surface structures with dedicated functionalities. Varying the intermolecular interactions allows for tuning the resulting molecular structures in a rational fashion. So far, however, the discussion of the involved intermolecular interactions is often limited to attractive forces only. In real systems, the intermolecular interaction can be composed of both, attractive and repulsive forces. Adjusting the balance between these interactions provides a promising strategy for extending the structural variety in molecular self-assembly on surfaces. This strategy, however, relies on a method to quantify the involved interactions. Here, we investigate a molecular model system of 3-hydroxybenzoic acid molecules on calcite (10.4) in ultrahigh vacuum. This system offers both anisotropic short-range attraction and long-range repulsion between the molecules, resulting in the self-assembly of molecular stripes. We analyze the stripe-to-stripe distance distribution and the stripe length distribution and compare these distributions with analytical expressions from an anisotropic Ising model with additional repulsive interaction. We show that this approach allows to extract quantitative information about the strength of the attractive and repulsive interactions. Our work demonstrates how the detailed analysis of the self-assembled structures can be used to obtain quantitative insight into the molecule-molecule interactions.

cond-mat.mes-hall↗

arXiv2020

Cycle completion times probe interactions with environment

Recent measurements of durations of non-equilibrium processes provide valuable information on microscopic mechanisms and energetics. Comprehensive theory for corresponding experiments so far is well developed for single-particle systems only. Little is known for interacting systems in non-equilibrium environments. Here, we introduce and study a basic model for cycle processes interacting with an environment that can exhibit a net particle flow. We find a surprising richness of cycle time variations with environmental conditions. This manifests itself in unequal cycle times $τ^+$ and $τ^-$ in forward and backward cycle direction with both asymmetries $τ^-<τ^+$ and $τ^->τ^+$, speeding up of backward cycles by interactions, and dynamical phase transitions, where cycle times become multimodal functions of the bias. The model allows us to relate these effects to specific microscopic mechanisms, which can be helpful for interpreting experiments.

cond-mat.stat-mech↗

arXiv2020

Statistics of work performed by optical tweezers with general time-variation of their stiffness

We derive an exact expression for the probability density of work done on a particle that diffuses in a parabolic potential with a stiffness varying by an arbitrary piecewise constant protocol. Based on this result, the work distribution for time-continuous protocols of the stiffness can be determined up to any degree of accuracy. This is achieved by replacing the continuous driving by a piecewise constant one with a number $n$ of positive or negative steps of increasing or decreasing stiffness. With increasing $n$, the work distributions for the piecewise protocols approach that for the continuous protocol. The moment generating function of the work is given by the inverse square root of a polynomial of degree $n$, whose coefficients are efficiently calculated from a recurrence relation. The roots of the polynomials are real and positive (negative) steps of the protocol are associated with negative (positive) roots. Using these properties the inverse Laplace transform of the moment generating function is carried out explicitly. Fluctuation theorems are used to derive further properties of the polynomials and their roots.

cond-mat.stat-mech↗

arXiv2020

Nonequilibrium transport and phase transitions in driven diffusion of interacting particles

Driven diffusive systems constitute paradigmatic models of nonequilibrium physics. Among them, a driven lattice gas known as the asymmetric simple exclusion process (ASEP) is the most prominent example for which many intriguing exact results have been obtained. After summarizing key findings, including the mapping of the ASEP to quantum spin chains, we discuss the recently introduced Brownian asymmetric simple exclusion process (BASEP) as a related class of driven diffusive system with continuous space dynamics. In the BASEP, driven Brownian motion of hardcore-interacting particles through one-dimensional periodic potentials is considered. We study whether current-density relations of the BASEP can be considered as generic for arbitrary periodic potentials and whether repulsive particle interactions other than hardcore lead to similar results. Our findings suggest that shapes of current-density relations are generic for single-well periodic potentials and can always be attributed to the interplay of a barrier reduction, blocking and exchange symmetry effect. This implies that in general up to five different phases of nonequilibrium steady states are possible for such potentials. The phases can occur in systems coupled to particle reservoirs, where the bulk density is the order parameter. For multiple-well periodic potentials, more complex current-density relations are possible and more phases can appear. Taking a repulsive Yukawa potential as an example, we show that the effects of barrier reduction and blocking on the current are also present. The exchange symmetry effect requires hardcore interactions and we demonstrate that it can still be identified when hardcore interactions are combined with weak Yukawa interactions.

cond-mat.stat-mech↗

arXiv2019

Single-file transport in periodic potentials: The Brownian asymmetric exclusion process

Single-file Brownian motion in periodic structures is an important process in nature and technology, which becomes increasingly amenable for experimental investigation under controlled conditions. To explore and understand generic features of this motion, the Brownian asymmetric simple exclusion process (BASEP) was recently introduced. The BASEP refers to diffusion models, where hard spheres are driven by a constant drag force through a periodic potential. Here, we derive general properties of the rich collective dynamics in the BASEP. Average currents in the steady state change dramatically with the particle size and density. For an open system coupled to particle reservoirs, extremal current principles predict various nonequilibrium phases, which we verify by Brownian dynamics simulations. For general pair interactions we discuss connections to single-file transport by traveling-wave potentials and prove the impossibility of current reversals in systems driven by a constant drag and by traveling waves.

cond-mat.stat-mech↗

arXiv2019

Heterogeneities in electricity grids strongly enhance non-Gaussian features of frequency fluctuations under stochastic power input

Stochastic feed-in of fluctuating renewable energies is steadily increasing in modern electricity grids and this becomes an important risk factor for maintaining power grid stability. Here we study the impact of wind power feed-in on the short-term frequency fluctuations in power grids based on an IEEE test grid structure, the swing equation for the dynamics of voltage phase angles, and a series of measured wind speed data. External control measures are accounted for by adjusting the grid state to the average power feed-in on a time scale of one minute. The wind power is injected at a single node by replacing one of the conventional generator nodes in the test grid by a wind farm. We determine histograms of local frequencies for a large number of one-minute wind speed sequences taken from the measured data and for different injection nodes. These histograms exhibit a common type of shape, which can be described by a Gaussian distribution for small frequencies and a nearly exponentially decaying tail part. Non-Gaussian features become particularly pronounced for wind power injection at locations, which are weakly connected to the main grid structure. This effect is only present when taking into account the heterogeneities in transmission line and node properties of the grid, while it disappears upon homogenizing of these features. The standard deviation of the frequency fluctuations increases linearly with the average injected wind power.

nlin.AO↗

arXiv2018

Bridging between Load-Flow and Kuramoto-like Power Grid Models: A Flexible Approach to Integrating Electrical Storage Units

In future power systems, electrical storage will be the key technology for balancing feed-in fluctuations. With increasing share of renewables and reduction of system inertia, the focus of research expands towards short-term grid dynamics and collective phenomena. Against this backdrop, Kuramoto-like power grids have been established as a sound mathematical modeling framework bridging between the simplified models from nonlinear dynamics and the more detailed models used in electrical engineering. However, they have a blind spot concerning grid components, which cannot be modeled by oscillator equations, and hence do not allow to investigate storage-related issues from scratch. We remove this shortcoming by bringing together Kuramoto-like and algebraic load-flow equations. This is a substantial extension of the current Kuramoto framework with arbitrary grid components. Based on this concept, we provide a solid starting point for the integration of flexible storage units enabling to address current problems like smart storage control, optimal siting and rough cost estimations. For demonstration purpose, we here consider a wind power application with realistic feed-in conditions. We show how to implement basic control strategies from electrical engineering, give insights into their potential with respect to frequency quality improvement and point out their limitations by maximum capacity and finite-time response.

nlin.AO↗

arXiv2018

Brownian asymmetric simple exclusion process

We study the driven Brownian motion of hard rods in a one-dimensional cosine potential with an amplitude large compared to the thermal energy. In a closed system, we find surprising features of the steady-state current in dependence of the particle density. The form of the current-density relation changes greatly with the particle size and can exhibit both a local maximum and minimum. The changes are caused by an interplay of a barrier reduction, blocking and exchange symmetry effect. The latter leads to a current equal to that of non-interacting particles for a particle size commensurate with the period length of the cosine potential. For an open system coupled to particle reservoirs, we predict five different phases of non-equilibrium steady states to occur. Our results show that the particle size can be of crucial importance for non-equilibrium phase transitions in driven systems. Possible experiments for demonstrating our findings are pointed out.

cond-mat.stat-mech↗

arXiv2018

Stress-stress fluctuation formula for elastic constants in the NPT ensemble

Several fluctuation formulas are available for calculating elastic constants from equilibrium correlation functions in computer simulations, but the ones available for simulations at constant pressure exhibit slow convergence properties and cannot be used for the determination of local elastic constants. To overcome these drawbacks, we derive a stress-stress fluctuation formula in the $NPT$ ensemble based on known expressions in the $NVT$ ensemble. We validate the formula in the $NPT$ ensemble by calculating elastic constants for the simple nearest-neighbor Lennard-Jones crystal and by comparing the results with those obtained in the $NVT$ ensemble. For both local and bulk elastic constants we find an excellent agreement between the simulated data in the two ensembles. To demonstrate the usefulness of the new formula, we apply it to determine the elastic constants of a simulated lipid bilayer.

physics.comp-ph↗

arXiv2018

Power grid stability under perturbation of single nodes: Effects of heterogeneity and internal nodes

Non-linear equations describing the time evolution of frequencies and voltages in power grids exhibit fixed points of stable grid operation. The dynamical behaviour after perturbations around these fixed points can be used to characterise the stability of the grid. We investigate both probabilities of return to a fixed point and times needed for this return after perturbation of single nodes. Our analysis is based on an IEEE test grid and the second-order swing equations for voltage phase angles $θ_j$ at nodes $j$ in the synchronous machine model. The perturbations cover all possible changes $Δθ$ of voltage angles and a wide range of frequency deviations in a range $Δf=\pm1$~Hz around the common frequency $ω=2πf=\dotθ_j$ in a synchronous fixed point state. Extensive numerical calculations are carried out to determine, for all node pairs $(j,k)$, the return times $t_{jk}(Δθ,Δω)$ of node $k$ after a perturbation of node $j$. We find that for strong perturbations of some nodes, the grid does not return to its synchronous state. If returning to the fixed point, the times needed for the return are strongly different for different disturbed nodes and can reach values up to 20 seconds and more. When homogenising transmission line and node properties, the grid always returns to a synchronous state for the considered perturbations, and the longest return times have a value of about 4 seconds for all nodes. The neglect of reactances between points of power generation (internal nodes) and injection (terminal nodes) leads to an underestimation of return probabilities.

nlin.AO↗

arXiv2018

Density profiles of a self-gravitating lattice gas in one, two, and three dimensions

We consider a lattice gas in spaces of dimensionality $\mathcal{D}=1,2,3$. The particles are subject to a hardcore exclusion interaction and an attractive pair interaction that satisfies Gauss' law as do Newtonian gravity in $\mathcal{D}=3$, a logarithmic potential in $\mathcal{D}=2$, and a distance-independent force in $\mathcal{D}=1$. Under mild additional assumptions regarding symmetry and fluctuations we investigate equilibrium states of self-gravitating material clusters, in particular radial density profiles for closed and open systems. We present exact analytic results in several instances and high-precision numerical data in others. The density profile of a cluster with finite mass is found to exhibit exponential decay in $\mathcal{D}=1$ and power-law decay in $\mathcal{D}=2$ with temperature-dependent exponents in both cases. In $\mathcal{D}=2$ the gas evaporates in a continuous transition at a nonzero critical temperature. We describe clusters of infinite mass in $\mathcal{D}=3$ with a density profile consisting of three layers (core, shell, halo) and an algebraic large-distance asymptotic decay. In $\mathcal{D}=3$ a cluster of finite mass can be stabilized at $T>0$ via confinement to a sphere of finite radius. In some parameter regime, the gas thus enclosed undergoes a discontinuous transition between distinct density profiles. For the free energy needed to identify the equilibrium state we introduce a construction of gravitational self-energy that works in all $\mathcal{D}$ for the lattice gas. The decay rate of the density profile of an open cluster is shown to transform via a stretched exponential for $1<\mathcal{D}<2$ whereas it crosses over from one power-law at intermediate distances to a different power-law at larger distances for $2<\mathcal{D}<3$.

cond-mat.stat-mech↗