arXiv subjects

Philipp Maass

Publications and source records attributed to Philipp Maass.

At least 55 records · Page 3Linked to original sources

arXiv2017

Modeling specific action potentials in the human atria based on a minimal reaction-diffusion model

We present an effective method to model empirical action potentials of specific patients in the human atria based on the minimal model of Bueno-Orovio, Cherry and Fenton adapted to atrial electrophysiology. In this model, three ionic are currents introduced, where each of it is governed by a characteristic time scale. By applying a nonlinear optimization procedure, a best combination of the respective time scales is determined, which allows one to reproduce specific action potentials with a given amplitude, width and shape. Possible applications for supporting clinical diagnosis are pointed out.

physics.med-ph↗

arXiv2015

On asymptotic behavior of work distributions for driven Brownian motion

We propose a simple conjecture for the functional form of the asymptotic behavior of work distributions for driven overdamped Brownian motion of a particle in confining potentials. This conjecture is motivated by the fact that these functional forms are independent of the velocity of the driving for all potentials and protocols, where explicit analytical solutions for the work distributions have been derived in the literature. To test the conjecture, we use Brownian dynamics simulations and a recent theory developed by Engel and Nickelsen (EN theory), which is based on the contraction principle of large deviation theory. Our tests suggest that the conjecture is valid for potentials with a confinement equal to or weaker than the parabolic one, both for equilibrium and for nonequilibrium distributions of the initial particle position. In addition we obtain a new analytical solution for the asymptotic behavior of the work distribution for the V-potential by application of the EN theory, and we extend this theory to nonequilibrated initial particle positions.

cond-mat.stat-mech↗

arXiv2015

Monodisperse hard rods in external potentials

We consider linear arrays of cells of volume $V_\mathrm{c}$ populated by monodisperse rods of size $σV_\mathrm{c}$, $σ=1,2,\ldots$, subject to hardcore exclusion interaction. Each rod experiences a position-dependent external potential. In one application we also examine effects of contact forces between rods. We employ two distinct methods of exact analysis with complementary strengths and different limits of spatial resolution to calculate profiles of pressure and density on mesoscopic and microscopic length scales at thermal equilibrium. One method uses density functionals and the other statistically interacting vacancy particles. The applications worked out include gravity, power-law traps, and hard walls. We identify oscillations in the profiles on a microscopic length scale and show how they are systematically averaged out on a well-defined mesoscopic length scale to establish full consistency between the two approaches. The continuum limit, realized as $V_\mathrm{c}\to0$, $σ\to\infty$ at nonzero and finite $σV_\mathrm{c}$, connects our highest-resolution results with known exact results for monodisperse rods in a continuum. We also compare the pressure profiles obtained from density functionals with the average microscopic pressure profiles derived from the pair distribution function.

cond-mat.stat-mech↗

arXiv2014

Self-consistent rate theory for submonolayer surface growth of multi-component systems

The self-consistent rate theory for surface growth in the submonolayer regime is generalized from mono- to multi-component systems, which are formed by codeposition of different types of atoms or molecules. As a new feature, the theory requires the introduction of pair density distributions to enable a symmetric treatment of reactions among different species. The approach is explicitly developed for binary systems and tested against kinetic Monte Carlo simulations. Using a reduced set of rate equations, only a few differential equations need to be solved to obtain good quantitative predictions for island and adatom densities, as well as densities of unstable clusters.

cond-mat.mtrl-sci↗

arXiv2014

Colloquium: Cluster growth on surfaces - densities, size distributions and morphologies

Understanding and control of cluster and thin film growth on solid surfaces is a subject of intensive research to develop nanomaterials with new physical properties. In this Colloquium we review basic theoretical concepts to describe submonolayer growth kinetics under non-equilibrium conditions. It is shown how these concepts can be extended and further developed to treat self-organized cluster formation in material systems of current interest, such as nanoalloys and molecular clusters in organic thin film growth. The presentation is focused on ideal flat surfaces to limit the scope and to discuss key ideas in a transparent way. Open experimental and theoretical challenges are pointed out.

cond-mat.mtrl-sci↗

arXiv2014

Phase Transitions in Brownian Pumps

We study stochastic particle transport between two reservoirs along a channel, where the particles are pumped against a bias by a traveling wave potential. It is shown that phase transitions of period-averaged densities or currents occur inside the channel when exclusion interactions between the particles are taken into account. These transitions reflect those known for the asymmetric simple exclusion process (ASEP). We argue that their occurrence is a generic feature of Brownian motors operating in open systems.

cond-mat.stat-mech↗

arXiv2014

Statistically interacting vacancy particles

The equilibrium statistical mechanics of one-dimensional lattice gases with interactions of arbitrary range and shape between first-neighbor atoms is solved exactly on the basis of statistically interacting vacancy particles. Two sets of vacancy particles are considered. In one set all vacancies are of one-cell size. In the other set the sizes of vacancy particles match the separation between atoms. Explicit expressions are obtained for the Gibbs free energy and the distribution of spaces between atoms at thermal equilibrium. Applications to various types of interaction potentials are discussed, including long-range potentials that give rise to phase transitions. Extensions to hard rod systems are straightforward and are shown to agree with existing results for lattice models and their continuum limits.

cond-mat.stat-mech↗

arXiv2013

Unfolding kinetics of periodic DNA hairpins

DNA hairpin molecules with periodic base sequences can be expected to exhibit a regular coarse-grained free energy landscape (FEL) as function of the number of open base pairs and applied mechanical force. Using a commonly employed model, we first analyse for which types of sequences a particularly simple landscape structure is predicted, where forward and backward energy barriers between partly unfolded states are decreasing linearly with force. Stochastic unfolding trajectories for such molecules with simple FEL are subsequently generated by kinetic Monte Carlo simulations. Introducing probabilities that can be sampled from these trajectories, it is shown how the parameters characterising the FEL can be estimated. Already 300 trajectories, as typically generated in experiments, provide faithful results for the FEL parameters.

physics.bio-ph↗

arXiv2013

Interacting hard rods on a lattice: Distribution of microstates and density functionals

We derive exact density functionals for systems of hard rods with first-neighbor interactions of arbitrary shape but limited range on a one-dimensional lattice. The size of all rods is the same integer unit of the lattice constant. The derivation, constructed from conditional probabilities in a Markov chain approach, yields the exact joint probability distribution for the positions of the rods as a functional of their density profile. For contact interaction ("sticky core model") between rods we give a lattice fundamental measure form of the density functional and present explicit results for contact correlators, entropy, free energy, and chemical potential. Our treatment includes inhomogeneous couplings and external potentials.

cond-mat.stat-mech↗

arXiv2013

Diffusion coefficients from signal fluctuations: Influence of molecular shape and rotational diffusion

Analysis of signal fluctuations of a locally fixed probe, caused by molecules diffusing under the probe, can be used to determine diffusion coefficients. Theoretical treatments so far have been limited to point-like particles or to molecules with circle-like shapes. Here we extend these treatments to molecules with rectangle-like shapes, for which also rotational diffusion needs to be taken into account. Focusing on the distribution of peak widths in the signal, we show how translational as well as rotational diffusion coefficients can be determined. We address also the question, how the distribution of interpeak time intervals and autocorrelation function can be employed for determining diffusion coefficients. Our approach is validated against kinetic Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2013

One-dimensional transport of interacting particles: Currents, density profiles, phase diagrams and symmetries

Driven lattice gases serve as canonical models for investigating collective transport phenomena and properties of non-equilibrium steady states (NESS). Here we study one-dimensional transport with nearest-neighbor interactions both in closed bulk systems and in open channels coupled to two particle reservoirs at the ends of the channel. For the widely employed Glauber rates we derive an exact current-density relation in the bulk for unidirectional hopping. An approach based on time-dependent density functional theory provides a good description of the kinetics. For open systems, the system-reservoir couplings are shown to have a striking influence on boundary-induced phase diagrams. The role of particle-hole symmetry is discussed and its consequence on the topology of the phase diagrams. It is furthermore demonstrated that systems with weak bias can be mapped onto systems with unidirectional hopping.

cond-mat.stat-mech↗

arXiv2013

Work distribution in time-dependent logarithmic-harmonic potential: exact results and asymptotic analysis

We investigate the distribution of work performed on a Brownian particle in a time-dependent asymmetric potential well. The potential has a harmonic component with time-dependent force constant and a time-independent logarithmic barrier at the origin. For arbitrary driving protocol, the problem of solving the Fokker-Planck equation for the joint probability density of work and particle position is reduced to the solution of the Riccati differential equation. For a particular choice of the driving protocol, an exact solution of the Riccati equation is presented. Asymptotic analysis of the resulting expression yields the tail behavior of the work distribution for small and large work values. In the limit of vanishing logarithmic barrier, the work distribution for the breathing parabola model is obtained.

cond-mat.stat-mech↗

arXiv2012

Determining molecule diffusion coefficients on surfaces from a locally fixed probe: On the analysis of signal fluctuations

Methods of determining surface diffusion coefficients of molecules from signal fluctuations of a locally fixed probe are revisited and refined. Particular emphasis is put on the influence of the molecule's extent. In addition to the formerly introduced autocorrelation method and residence time method, we develop a further method based on the distribution of intervals between successive peaks in the signal. The theoretical findings are applied to STM measurements of copper phthalocyanine (CuPc) molecules on the Ag(100) surface. We discuss advantages and disadvantages of each method and suggest a combination to obtain accurate results for diffusion coefficients.

cond-mat.mes-hall↗

arXiv2012

Dynamics and energetics of a molecular zipper under external driving

We investigate the dynamics of a single-ended N-state molecular zipper based on a model originally proposed by Kittel. The molecule is driven unidirectionally towards the completely unzipped state with increasing time t, where the driving lowers the energies of states with k unzipped links by an amount proportional to kt. We solve the Pauli rate equation for the state probabilities and the partial differential equations, which yield the probability distributions for the work performed on the zipper and for the heat exchanged with the thermal reservoir. Similarly to the related equilibrium model, two different regimes can be identified at a given temperature with respect to the released molecular degrees of freedom per broken bond. In these two regimes the time evolution of the state probabilities as well as of the work and heat distributions show a qualitatively different behavior.

cond-mat.stat-mech↗

arXiv2012

Capture numbers and islands size distributions in models of submonolayer surface growth

The capture numbers entering the rate equations (RE) for submonolayer film growth are determined from extensive kinetic Monte Carlo (KMC) simulations for simple representative growth models yielding point, compact, and fractal island morphologies. The full dependence of the capture numbers on island size, and on both the coverage and the D/F ratio between the adatom diffusion coefficient D and deposition rate F is determined. Based on this information, the RE are solved to give the RE island size distribution (RE-ISD). The RE-ISDs are shown to agree well with the corresponding KMC-ISDs for all island morphologies. For compact morphologies, however, this agreement is only present for coverages smaller than about 5% due to a significantly increased coalescence rate compared to fractal morphologies. As found earlier, the scaled KMC-ISDs as a function of scaled island size approach, for fixed coverage, a limiting curve for D/F going to infinity. Our findings provide evidence that the limiting curve is independent of the coverage for point islands, while the results for compact and fractal island morphologies indicate a dependence on the coverage.

cond-mat.stat-mech↗

arXiv2012

Exact density functional for hard rod mixtures derived from Markov chain approach

Using a Markov chain approach we rederive the exact density functional for hard rod mixtures on a one-dimensional lattice, which forms the basis of the lattice fundamental measure theory. The transition probability in the Markov chain depends on a set of occupation numbers, which reflects the property of a zero-dimensional cavity to hold at most one particle. For given mean occupation numbers (density profile), an exact expression for the equilibrium distribution of microstates is obtained, that means an expression for the unique external potential that generates the density profile in equilibrium. By considering the rod ends to fall onto lattice sites, the mixture is always additive.

cond-mat.stat-mech↗

arXiv2011

Classical Driven Transport in Open Systems with Particle Interactions and General Couplings to Reservoirs

We study nonequilibrium steady states of lattice gases with nearest-neighbor interactions that are driven between two reservoirs. Density profiles in these systems exhibit oscillations close to the reservoirs. We demonstrate that an approach based on time-dependent density functional theory copes with these oscillations and predicts phase diagrams of bulk densities to a good approximation under arbitrary boundary-reservoir couplings. The minimum or maximum current principles can be applied only for specific bulk-adapted couplings. We show that they generally fail to give the correct topology of phase diagrams but can still be useful for getting insight into the mutual arrangement of different phases.

cond-mat.stat-mech↗

arXiv2011

Folding and unfolding of a triple-branch DNA molecule with four conformational states

Single-molecule experiments provide new insights into biological processes hitherto not accessible by measurements performed on bulk systems. We report on a study of the kinetics of a triple-branch DNA molecule with four conformational states by pulling experiments with optical tweezers and theoretical modelling. Three distinct force rips associated with different transitions between the conformational states are observed in the folding and unfolding trajectories. By applying transition rate theory to a free energy model of the molecule, probability distributions for the first rupture forces of the different transitions are calculated. Good agreement of the theoretical predictions with the experimental findings is achieved. Furthermore, due to our specific design of the molecule, we found a useful method to identify permanently frayed molecules by estimating the number of opened basepairs from the measured force jump values.

physics.bio-ph↗