arXiv subjects

Philipp Maass

Publications and source records attributed to Philipp Maass.

At least 73 records · Page 4Linked to original sources

arXiv2010

Attempt-time Monte Carlo: an alternative for simulation of stochastic jump processes with time-dependent transition rates

We present a new method for simulating Markovian jump processes with time-dependent transitions rates, which avoids the transformation of random numbers by inverting time integrals over the rates. It relies on constructing a sequence of random time points from a homogeneous Poisson process, where the system under investigation attempts to change its state with certain probabilities. With respect to the underlying master equation the method corresponds to an exact formal solution in terms of a Dyson series. Different algorithms can be derived from the method and their power is demonstrated for a set of interacting two-level systems that are periodically driven by an external field.

cond-mat.stat-mech↗

arXiv2010

Time-Dependent Density Functional Theory for Driven Lattice Gas Systems with Interactions

We present a new method to describe the kinetics of driven lattice gases with particle-particle interactions beyond hard-core exclusions. The method is based on the time-dependent density functional theory for lattice systems and allows one to set up closed evolution equations for mean site occupation numbers in a systematic manner. Application of the method to a totally asymmetric site exclusion process with nearest-neighbor interactions yields predictions for the current-density relation in the bulk, the phase diagram of non-equilibrium steady states and the time evolution of density profiles that are in good agreement with results from kinetic Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2010

Glass former units and transport in ion-conducting network glasses

A new theoretical approach is presented for relating structural information to transport properties in ion conducting network glasses. It relies on the consideration of the different types of glass forming units and the charges associated with them. Changes in the compositions of these units lead to a re-distribution of Coulomb traps for the mobile ions and to a subsequent change in long-range ionic mobilities. It is furthermore shown how measured changes of the unit compositions can be explained by thermodynamic modeling. The theories are tested against experiments on borophosphate glasses and yield good agreement with the measured data both for the compositional changes of the units and the variation of the activation energy.

cond-mat.mtrl-sci↗

arXiv2010

Island size distributions in submonolayer growth: successful prediction by mean field theory with coverage dependent capture numbers

We show that mean-field rate equations for submonolayer growth can successfully predict island size distributions in the pre-coalescence regime if the full dependence of capture numbers on both the island size and the coverage is taken into account. This is demonstrated by extensive Kinetic Monte Carlo simulations for a growth kinetics with hit and stick aggregation. A detailed analysis of the capture numbers reveals a nonlinear dependence on the island size for small islands. This nonlinearity turns out to be crucial for the successful prediction of the island size distribution and renders an analytical treatment based on a continuum limit of the mean-field rate equations difficult.

cond-mat.stat-mech↗

arXiv2010

Influence of spatially modified tissue on atrial fibrillation patterns: Insight from solutions of the FitzHugh-Nagumo equations

We study the interplay between traveling action potentials and spatial inhomogeneities in the FitzHugh-Nagumo model to investigate possible mechanisms for the occurrence of fibrillatory states in the atria of the heart. Different dynamical patterns such as ectopic foci, localized and meandering spiral waves are found depending on the characteristics of the inhomogeneities. Their appearance in dependence of the size and strength of the inhomogeneities is quantified by phase diagrams. Furthermore it is shown that regularly paced waves in a region R, that is connected by a small bridge connection to another region L with perturbing waves emanating from an additional pacemaker, can be strongly disturbed, so that a fibrillatory state emerges in region R after a transient time interval. This finding supports conjectures that fibrillatory states in the right atrium can be induced by self-excitatory pacemakers in the left atrium.

physics.bio-ph↗

arXiv2009

Energetics and performance of a microscopic heat engine based on exact calculations of work and heat distributions

We investigate a microscopic motor based on an externally controlled two-level system. One cycle of the motor operation consists of two strokes. Within each stroke, the two-level system is in contact with a given thermal bath and its energy levels are driven with a constant rate. The time evolution of the occupation probabilities of the two states are controlled by one rate equation and represent the system's response with respect to the external driving. We give the exact solution of the rate equation for the limit cycle and discuss the emerging thermodynamics: the work done on the environment, the heat exchanged with the baths, the entropy production, the motor's efficiency, and the power output. Furthermore we introduce an augmented stochastic process which reflects, at a given time, both the occupation probabilities for the two states and the time spent in the individual states during the previous evolution. The exact calculation of the evolution operator for the augmented process allows us to discuss in detail the probability density for the performed work during the limit cycle. In the strongly irreversible regime, the density exhibits important qualitative differences with respect to the more common Gaussian shape in the regime of weak irreversibility.

cond-mat.stat-mech↗

arXiv2009

Evaluation of Reverse Monte Carlo Models based on Molecular Dynamics Simulations: A Case Study of Ion Conducting Network Glasses

We investigate the quality of structural models generated by the Reverse Monte Carlo (RMC) method in a typical application to amorphous systems. To this end we calculate surrogate diffraction data from a Li2O-SiO2 molecular dynamics (MD) simulation and use the total scattering function, in addition to minimal pair distances and coordination numbers of silicon (oxygen) to oxygen (silicon) ions, as input for the RMC modeling. Then we compare partial radial distribution functions, coordination numbers, bond angles, and ring sizes predicted by the RMC models with those of the MD system. It is found that partial distributions functions and properties on small lengths scales, as distributions of coordination numbers and bond angles, are well reproduced by the RMC modeling. Properties in the medium-range order regime are, however, not well captured, as is demonstrated by comparison of ring size distributions. Due care therefore has to be exercised when extracting structural features from RMC models in this medium-range order regime. In particular we show that the occurrence of such features can be a mere consequence of the chosen starting configuration.

cond-mat.mtrl-sci↗

arXiv2009

Nonlinear hopping transport in ring systems and open channels

We study the nonlinear hopping transport in one-dimensional rings and open channels. Analytical results are derived for the stationary current response to a constant bias without assuming any specific coupling to the external fields. It is shown that anomalous large effective jump lengths, as observed in recent experiments by taking the ratio of the third order nonlinear and the linear conductivity, can occur already in ordered systems. Rectification effects due to site energy disorder in ring systems are expected to become irrelevant for large system sizes. In open channels in contrast, rectification effects occur already for disorder in the jump barriers and do not vanish in the thermodynamic limit. Numerical solutions for a sinusoidal bias show that the ring system provides a good description for the transport behavior in the open channel for intermediate and high frequencies. For low frequencies temporal variations in the mean particle number have to be taken into account in the open channel, which cannot be captured in the more simple ring model.

cond-mat.stat-mech↗

arXiv2009

Fundamental questions relating to ion conduction in disordered solids

A number of basic scientific questions relating to ion conduction in homogeneously disordered solids are discussed. The questions deal with how to define the mobile ion density, what can be learned from electrode effects, what is the ion transport mechanism, the role of dimensionality, and what are the origins of the mixed-alkali effect, of time-temperature superposition, and of the nearly-constant loss. Answers are suggested to some of these questions, but the main purpose of the paper is to draw attention to the fact that this field of research still presents several fundamental challenges.

cond-mat.dis-nn↗

arXiv2007

Structure of glassy lithium sulfate films sputtered in nitrogen (LISON): Insight from Raman spectroscopy and ab initio calculations

Raman spectra of thin solid electrolyte films obtained by sputtering a lithium sulfate target in nitrogen plasma are measured and compared to ab initio electronic structure calculations for clusters composed of 28 atoms. Agreement between measured and calculated spectra is obtained when oxygen atoms are replaced by nitrogen atoms and when the nitrogen atoms form bonds with each other. This suggests that the incorporation of nitrogen during the sputtering process leads to structures in the film, which prevent crystallization of these thin film salt glasses.

cond-mat.mtrl-sci↗

arXiv2006

Influence of external magnetic fields on growth of alloy nanoclusters

Kinetic Monte Carlo simulations are performed to study the influence of external magnetic fields on the growth of magnetic fcc binary alloy nanoclusters with perpendicular magnetic anisotropy. The underlying kinetic model is designed to describe essential structural and magnetic properties of CoPt_3-type clusters grown on a weakly interacting substrate through molecular beam epitaxy. The results suggest that perpendicular magnetic anisotropy can be enhanced when the field is applied during growth. For equilibrium bulk systems a significant shift of the onset temperature for L1_2 ordering is found, in agreement with predictions from Landau theory. Stronger field induced effects can be expected for magnetic fcc-alloys undergoing L1_0 ordering.

cond-mat.mtrl-sci↗

arXiv2006

Comparison of ion sites and diffusion paths in glasses obtained by molecular dynamics simulations and bond valence analysis

Based on molecular dynamics simulations of a lithium metasilicate glass we study the potential of bond valence sum calculations to identify sites and diffusion pathways of mobile Li ions in a glassy silicate network. We find that the bond valence method is not well suitable to locate the sites, but allows one to estimate the number of sites. Spatial regions of the glass determined as accessible for the Li ions by the bond valence method can capture up to 90% of the diffusion path. These regions however entail a significant fraction that does not belong to the diffusion path. Because of this low specificity, care must be taken to determine the diffusive motion of particles in amorphous systems based on the bond valence method. The best identification of the diffusion path is achieved by using a modified valence mismatch in the BV analysis that takes into account that a Li ion favors equal partial valences to the neighboring oxygen ions. Using this modified valence mismatch it is possible to replace hard geometric constraints formerly applied in the BV method. Further investigations are necessary to better understand the relation between the complex structure of the host network and the ionic diffusion paths.

cond-mat.mtrl-sci↗

arXiv2006

Exponential distribution of long heart beat intervals during atrial fibrillation and their relevance for white noise behaviour in power spectrum

The statistical properties of heart beat intervals of 130 long-term surface electrocardiogram recordings during atrial fibrillation (AF) are investigated. We find that the distribution of interbeat intervals exhibits a characteristic exponential tail, which is absent during sinus rhythm, as tested in a corresponding control study with 72 healthy persons. The rate of the exponential decay lies in the range 3-12 Hz and shows diurnal variations. It equals, up to statistical uncertainties, the level of the previously uncovered white noise part in the power spectrum, which is also characteristic for AF. The overall statistical features can be described by decomposing the intervals into two statistically independent times, where the first one is associated with a correlated process with 1/f noise characteristics, while the second one belongs to an uncorrelated process and is responsible for the exponential tail. It is suggested to use the rate of the exponential decay as a further parameter for a better classification of AF and for the medical diagnosis. The relevance of the findings with respect to a general understanding of AF is pointed out.

cond-mat.other↗

arXiv2005

Perpendicular magnetic anisotropy in nanoclusters caused by surface segregation and shape

The growth of binary alloy clusters on a weakly interacting substrate through codeposition of two atomic species is studied by kinetic Monte Carlo simulation. Our model describes salient features of CoPt$_3$-nanoclusters, as obtained recently by the molecular-beam epitaxy technique. The clusters display perpendicular magnetic anisotropy (PMA) in a temperature window of growth favorable for applications. This temperature window is found to arise from the interplay of Pt surface segregation and aspect ratio for cluster shapes. Conclusions are drawn how to optimize growth parameters with respect to PMA.

cond-mat.stat-mech↗

arXiv2005

Internal Friction and Vulnerability of Mixed Alkali Glasses

Based on a hopping model we show how the mixed alkali effect in glasses can be understood if only a small fraction c_V ofthe available sites for the mobile ions is vacant. In particular, we reproduce the peculiar behavior of the internal friction and the steep fall (''vulnerability'') of the mobility of the majority ion upon small replacements by the minority ion. The single and mixed alkali internal friction peaks are caused by ion-vacancy and ion-ion exchange processes. If c_V is small, they can become comparable in height even at small mixing ratios. The large vulnerability is explained by a trapping of vacancies induced by the minority ions. Reasonable choices of model parameters yield typical behaviors found in experiments.

cond-mat.mtrl-sci↗

arXiv2004

Quasicrystalline Order in Binary Dipolar Systems

Motivated by recent experimental findings, we investigate the possible occurrence and characteristics of quasicrystalline order in two-dimensional mixtures of point dipoles with two sorts of dipole moments. Despite the fact that the dipolar interaction potential does not exhibit an intrinsic length scale and cannot be tuned a priori to support the formation of quasicrystalline order, we find that configurations with long--range quasicrystallinity yield minima in the potential energy surface of the many particle system. These configurations emanate from an ideal or perturbed ideal decoration of a binary tiling by steepest descent relaxation. Ground state energy calculations of alternative ordered states and parallel tempering Monte-Carlo simulations reveal that the quasicrystalline configurations do not correspond to a thermodynamically stable state. On the other hand, steepest descent relaxations and conventional Monte-Carlo simulations suggest that they are rather robust against fluctuations. Local quasicrystalline order in the disordered equilibrium states can be strong.

cond-mat.other↗

arXiv2003

A real space renormalization group approach to spin glass dynamics

The slow non-equilibrium dynamics of the Edwards-Anderson spin glass model on a hierarchical lattice is studied by means of a coarse-grained description based on renormalization concepts. We evaluate the isothermal aging properties and show how the occurrence of temperature chaos is connected to a gradual loss of memory when approaching the overlap length. This leads to rejuvenation effects in temperature shift protocols and to rejuvenation--memory effects in temperature cycling procedures with a pattern of behavior parallel to experimental observations.

cond-mat.dis-nn↗

arXiv2001

Spin precession in disordered systems: Anomalous relaxation due to heavy tailed field distributions

We investigate spin precession in the presence of randomly distributed field sources. Their fields h_i reorient by thermally activated transitions and decrease as r^{-mu} with the distance from the spin probe. Based on analytical calculations and scaling arguments we find that the polarization decay of a spin ensemble exhibits a rich behavior characterized by stretched exponenentials and power laws with exponents depending on mu and the dimension d. The anomalous relaxation laws result from heavy tailed local field distributions and are verified by computer simulations. Implications for experiments are pointed out.

cond-mat↗