TY - JOUR
A1 - Palyulin, Vladimir V
A1 - Blackburn, George
A1 - Lomholt, Michael A
A1 - Watkins, Nicholas W
A1 - Metzler, Ralf
A1 - Klages, Rainer
A1 - Chechkin, Aleksei V
T1 - First passage and first hitting times of Lévy flights and Lévy walks
JF - New Journal of Physics
N2 - For both Lévy flight and Lévy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For Lévy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it ('leapovers'), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the Lévy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms.
KW - Lévy flights
KW - Lévy walks
KW - first-passage time
KW - first-hitting time
Y1 - 2019
U6 - http://dx.doi.org/10.1088/1367-2630/ab41bb
SN - 1367-2630
VL - 21
PB - Dt. Physikalische Ges.
CY - Bad Honnef
ER -
TY - GEN
A1 - Palyulin, Vladimir V
A1 - Blackburn, George
A1 - Lomholt, Michael A
A1 - Watkins, Nicholas W
A1 - Metzler, Ralf
A1 - Klages, Rainer
A1 - Chechkin, Aleksei V
T1 - First passage and first hitting times of Lévy flights and Lévy walks
T2 - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe
N2 - For both Lévy flight and Lévy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For Lévy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it ('leapovers'), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the Lévy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 785
KW - Lévy flights
KW - Lévy walks
KW - first-passage time
KW - first-hitting time
Y1 - 2019
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-439832
SN - 1866-8372
IS - 785
ER -
TY - GEN
A1 - Kindler, Oliver
A1 - Pulkkinen, Otto
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Burst Statistics in an Early Biofilm Quorum Sensing Mode
BT - The Role of Spatial Colony-Growth Heterogeneity
T2 - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe
N2 - Quorum-sensing bacteria in a growing colony of cells send out signalling molecules (so-called “autoinducers”) and themselves sense the autoinducer concentration in their vicinity. Once—due to increased local cell density inside a “cluster” of the growing colony—the concentration of autoinducers exceeds a threshold value, cells in this clusters get “induced” into a communal, multi-cell biofilm-forming mode in a cluster-wide burst event. We analyse quantitatively the influence of spatial disorder, the local heterogeneity of the spatial distribution of cells in the colony, and additional physical parameters such as the autoinducer signal range on the induction dynamics of the cell colony. Spatial inhomogeneity with higher local cell concentrations in clusters leads to earlier but more localised induction events, while homogeneous distributions lead to comparatively delayed but more concerted induction of the cell colony, and, thus, a behaviour close to the mean-field dynamics. We quantify the induction dynamics with quantifiers such as the time series of induction events and burst sizes, the grouping into induction families, and the mean autoinducer concentration levels. Consequences for different scenarios of biofilm growth are discussed, providing possible cues for biofilm control in both health care and biotechnology.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 777
Y1 - 2019
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-439099
SN - 1866-8372
IS - 777
ER -
TY - JOUR
A1 - Kindler, Oliver
A1 - Pulkkinen, Otto
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Burst Statistics in an Early Biofilm Quorum Sensing Mode
BT - The Role of Spatial Colony-Growth Heterogeneity
JF - Scientific Reports
N2 - Quorum-sensing bacteria in a growing colony of cells send out signalling molecules (so-called “autoinducers”) and themselves sense the autoinducer concentration in their vicinity. Once—due to increased local cell density inside a “cluster” of the growing colony—the concentration of autoinducers exceeds a threshold value, cells in this clusters get “induced” into a communal, multi-cell biofilm-forming mode in a cluster-wide burst event. We analyse quantitatively the influence of spatial disorder, the local heterogeneity of the spatial distribution of cells in the colony, and additional physical parameters such as the autoinducer signal range on the induction dynamics of the cell colony. Spatial inhomogeneity with higher local cell concentrations in clusters leads to earlier but more localised induction events, while homogeneous distributions lead to comparatively delayed but more concerted induction of the cell colony, and, thus, a behaviour close to the mean-field dynamics. We quantify the induction dynamics with quantifiers such as the time series of induction events and burst sizes, the grouping into induction families, and the mean autoinducer concentration levels. Consequences for different scenarios of biofilm growth are discussed, providing possible cues for biofilm control in both health care and biotechnology.
Y1 - 2019
U6 - http://dx.doi.org/10.1038/s41598-019-48525-2
SN - 2045-2322
VL - 9
PB - Macmillan Publishers Limited part of Springer Nature
CY - London
ER -
TY - GEN
A1 - Ślęzak, Jakub
A1 - Burnecki, Krzysztof
A1 - Metzler, Ralf
T1 - Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems
T2 - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe
N2 - Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as ‘superstatistics’ or ‘diffusing diffusivity’. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 765
KW - diffusion
KW - Langevin equation
KW - Brownian yet non-Gaussian diffusion
KW - diffusing diffusivity
KW - superstatistics
KW - autoregressive models
KW - time series analysis
KW - codifference
Y1 - 2019
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-437923
SN - 1866-8372
IS - 765
ER -
TY - JOUR
A1 - Ślęzak, Jakub
A1 - Burnecki, Krzysztof
A1 - Metzler, Ralf
T1 - Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems
JF - New Journal of Physics
N2 - Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as ‘superstatistics’ or ‘diffusing diffusivity’. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion.
KW - diffusion
KW - Langevin equation
KW - Brownian yet non-Gaussian diffusion
KW - diffusing diffusivity
KW - superstatistics
KW - autoregressive models
KW - time series analysis
KW - codifference
Y1 - 2019
U6 - http://dx.doi.org/10.1088/1367-2630/ab3366
SN - 1367-2630
VL - 21
PB - Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics
CY - Bad Honnef und London
ER -
TY - THES
A1 - Thater, Sabine
T1 - The interplay between supermassive black holes and their host galaxies
T1 - Das Zusammenspiel zwischen supermassereichen Schwarzen Löchern und ihren Muttergalaxien
N2 - Supermassive black holes reside in the hearts of almost all massive galaxies. Their evolutionary path seems to be strongly linked to the evolution of their host galaxies, as implied by several empirical relations between the black hole mass (M BH ) and different host galaxy properties. The physical driver of this co-evolution is, however, still not understood. More mass measurements over homogeneous samples and a detailed understanding of systematic uncertainties are required to fathom the origin of the scaling relations.
In this thesis, I present the mass estimations of supermassive black holes in the nuclei of one late-type and thirteen early-type galaxies. Our SMASHING sample extends from the intermediate to the massive galaxy mass regime and was selected to fill in gaps in number of galaxies along the scaling relations. All galaxies were observed at high spatial resolution, making use of the adaptive-optics mode of integral field unit (IFU) instruments on state-of-the-art telescopes (SINFONI, NIFS, MUSE). I extracted the stellar kinematics from these observations and constructed dynamical Jeans and Schwarzschild models to estimate the mass of the central black holes robustly. My new mass estimates increase the number of early-type galaxies with measured black hole masses by 15%. The seven measured galaxies with nuclear light deficits (’cores’) augment the sample of cored galaxies with measured black holes by 40%. Next to determining massive black hole masses, evaluating the accuracy of black hole masses is crucial for understanding the intrinsic scatter of the black hole- host galaxy scaling relations. I tested various sources of systematic uncertainty on my derived mass estimates.
The M BH estimate of the single late-type galaxy of the sample yielded an upper limit, which I could constrain very robustly. I tested the effects of dust, mass-to-light ratio (M/L) variation, and dark matter on my measured M BH . Based on these tests, the typically assumed constant M/L ratio can be an adequate assumption to account for the small amounts of dark matter in the center of that galaxy. I also tested the effect of a variable M/L variation on the M BH measurement on a second galaxy. By considering stellar M/L variations in the dynamical modeling, the measured M BH decreased by 30%. In the future, this test should be performed on additional galaxies to learn how an as constant assumed M/L flaws the estimated black hole masses.
Based on our upper limit mass measurement, I confirm previous suggestions that resolving the predicted BH sphere-of-influence is not a strict condition to measure black hole masses. Instead, it is only a rough guide for the detection of the black hole if high-quality, and high signal-to-noise IFU data are used for the measurement. About half of our sample consists of massive early-type galaxies which show nuclear surface brightness cores and signs of triaxiality. While these types of galaxies are typically modeled with axisymmetric modeling methods, the effects on M BH are not well studied yet. The massive galaxies of our presented galaxy sample are well suited to test the effect of different stellar dynamical models on the measured black hole mass in evidently triaxial galaxies. I have compared spherical Jeans and axisymmetric Schwarzschild models and will add triaxial Schwarzschild models to this comparison in the future. The constructed Jeans and Schwarzschild models mostly disagree with each other and cannot reproduce many of the triaxial features of the galaxies (e.g., nuclear sub-components, prolate rotation). The consequence of the axisymmetric-triaxial assumption on the accuracy of M BH and its impact on the black hole - host galaxy relation needs to be carefully examined in the future.
In the sample of galaxies with published M BH , we find measurements based on different dynamical tracers, requiring different observations, assumptions, and methods. Crucially, different tracers do not always give consistent results. I have used two independent tracers (cold molecular gas and stars) to estimate M BH in a regular galaxy of our sample. While the two estimates are consistent within their errors, the stellar-based measurement is twice as high as the gas-based. Similar trends have also been found in the literature. Therefore, a rigorous test of the systematics associated with the different modeling methods is required in the future. I caution to take the effects of different tracers (and methods) into account when discussing the scaling relations.
I conclude this thesis by comparing my galaxy sample with the compilation of galaxies with measured black holes from the literature, also adding six SMASHING galaxies, which were published outside of this thesis. None of the SMASHING galaxies deviates significantly from the literature measurements. Their inclusion to the published early-type galaxies causes a change towards a shallower slope for the M BH - effective velocity dispersion relation, which is mainly driven by the massive galaxies of our sample. More unbiased and homogenous measurements are needed in the future to determine the shape of the relation and understand its physical origin.
N2 - Supermassereiche schwarze Löcher befinden sich in den Herzen von fast allen massiven Galaxien. Ihr evolutionärer Werdegang scheint stark mit dem Wachstum ihrer Muttergalaxien in Verbindung zu stehen, wie mehrere empirische Beziehungen zwischen der Masse der schwarzen Löcher (M BH ) und verschiedenen Eigenschaften der Muttergalaxien andeuten. Der physikalische Ursprung dieser Koevolution ist jedoch immer noch nicht verstanden. Weitere Massenmessungen über homogene Galaxienproben und ein detailliertes Verständnis der systematischen Unsicherheiten sind erforderlich, um den Ursprung dieser Skalierungsbeziehungen zu ergründen.
In dieser Arbeit präsentiere ich die Massenabschätzungen von Supermassereichen Schwarzen Löchern der Zentren einer Spiral- und dreizehn elliptischer und linsenförmiger Galaxien. Meine SMASHING-Probe erstreckt sich vom mittleren bis zum hohen Galaxienmassenbereich und wurde ausgewählt, um Lücken entlang der Skalierungsbeziehungen zu schließen. Alle Galaxien wurden mit hoher räumlicher Auflösung beobachtet, wobei der adaptivoptische Modus von Integralfeldspektrographen (IFU) modernster Teleskope (SINFONI, NIFS, MUSE) verwendet wurde. Aus diesen Beobachtungen habe ich die Sternenkinematik extrahiert und dynamische Jeans- und Schwarzschildmodelle konstruiert, um die Masse der zentralen Schwarzen Löcher robust zu bestimmen. Meine neuen Massenschätzungen erhöhen die Anzahl elliptischer Galaxien mit vermessenen Schwarzen Löchern um 15%. Die sieben vermessenen Galaxien mit inneren Lichtdefiziten ("Cores") ergänzen die Probe der Core-Galaxien mit gemessenen schwarzen Löchern um 40%. Neben der Bestimmung ist die Beurteilung der Genauigkeit von Schwarzlochmassen entscheidend für das Verständnis der intrinsischen Streuung der Beziehungen zwischen schwarzem Loch und Muttergalaxie. Ich habe meine abgeleiteten Massenabschätzungen auf verschiedene systematische Fehlerquellen getestet. Dabei habe ich Bezug genommen auf die Auswirkungen von Staub, Variation des Masse-Licht-Verhältnisses (M/L), Dunkler Materie, verschiedener dynamischer Modelle und verschiedener dynamischer Tracer. Die Ergebnisse präsentiere ich in dieser Arbeit.
Ich schließe diese Arbeit, indem ich meine Galaxienprobe mit der den in der Forschungsliteratur zusammengestellten Galaxien mit bereits vermessenen Schwarzen Löchern vergleiche und auch sechs SMASHING-Galaxien hinzufüge, die außerhalb dieser Arbeit veröffentlicht wurden. Keine der SMASHING-Galaxien weicht signifikant von den veröffentlichten Messungen ab. Eine gemeinsame Analyse meiner Messungen und der veröffentlichten elliptischen Galaxien ergibt eine Abflachung der Steigung für die M BH - effektive Geschwindigkeitsdispersionsbeziehung, die hauptsächlich von den massiven Galaxien meiner Probe bewirkt wird. In Zukunft sind unvoreingenommene und homogenere Messungen erforderlich, um die Form der Skalierungsbeziehung zu bestimmen und ihren physikalischen Ursprung zu verstehen.
KW - supermassive black holes
KW - galaxy evolution
KW - stellar kinematics
KW - galaxy dynamics
KW - integral field spectroscopy
KW - supermassereiche Schwarze Löcher
KW - Galaxienentwicklung
KW - stellare Kinematik
KW - Galaxiendynamik
KW - Integralfieldspektroskopie
Y1 - 2019
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-437570
ER -
TY - THES
A1 - Wagle, Swapnil
T1 - Multi scale modeling of SNARE-mimetic peptides for their applications in membrane fusion
Y1 - 2019
ER -
TY - GEN
A1 - Guggenberger, Tobias
A1 - Pagnini, Gianni
A1 - Vojta, Thomas
A1 - Metzler, Ralf
T1 - Fractional Brownian motion in a finite interval
BT - correlations effect depletion or accretion zones of particles near boundaries
T2 - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe
N2 - Fractional Brownian motion (FBM) is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically FBM confined to a finite interval with reflecting boundary conditions. The probability density function of this reflected FBM at long times converges to a stationary distribution showing distinct deviations from the fully flat distribution of amplitude 1/L in an interval of length L found for reflected normal Brownian motion. While for superdiffusion, corresponding to a mean squared displacement (MSD) 〈X² (t)〉 ⋍ tᵅ with 1 < α < 2, the probability density function is lowered in the centre of the interval and rises towards the boundaries, for subdiffusion (0 < α < 1) this behaviour is reversed and the particle density is depleted close to the boundaries. The MSD in these cases at long times converges to a stationary value, which is, remarkably, monotonically increasing with the anomalous diffusion exponent α. Our a priori surprising results may have interesting consequences for the application of FBM for processes such as molecule or tracer diffusion in the confines of living biological cells or organelles, or other viscoelastic environments such as dense liquids in microfluidic chambers.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 755
KW - anomalous diffusion
KW - fractional Brownian motion
KW - reflecting boundary conditions
Y1 - 2019
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-436665
SN - 1866-8372
IS - 755
ER -
TY - JOUR
A1 - Guggenberger, Tobias
A1 - Pagnini, Gianni
A1 - Vojta, Thomas
A1 - Metzler, Ralf
T1 - Fractional Brownian motion in a finite interval
BT - correlations effect depletion or accretion zones of particles near boundaries
JF - New Journal of Physics
N2 - Fractional Brownian motion (FBM) is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically FBM confined to a finite interval with reflecting boundary conditions. The probability density function of this reflected FBM at long times converges to a stationary distribution showing distinct deviations from the fully flat distribution of amplitude 1/L in an interval of length L found for reflected normal Brownian motion. While for superdiffusion, corresponding to a mean squared displacement (MSD) 〈X² (t)〉 ⋍ tᵅ with 1 < α < 2, the probability density function is lowered in the centre of the interval and rises towards the boundaries, for subdiffusion (0 < α < 1) this behaviour is reversed and the particle density is depleted close to the boundaries. The MSD in these cases at long times converges to a stationary value, which is, remarkably, monotonically increasing with the anomalous diffusion exponent α. Our a priori surprising results may have interesting consequences for the application of FBM for processes such as molecule or tracer diffusion in the confines of living biological cells or organelles, or other viscoelastic environments such as dense liquids in microfluidic chambers.
KW - anomalous diffusion
KW - fractional Brownian motion
KW - reflecting boundary conditions
Y1 - 2019
U6 - http://dx.doi.org/10.1088/1367-2630/ab075f
SN - 1367-2630
VL - 21
PB - Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics
CY - Bad Honnef und London
ER -