Physik - Open Access LMU - Teil 01/02
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Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. Here, we study a broad class of bistable models subject to self-activation, degradation, and spatially inhomogeneous activating agents. We determine the conditions under which wave-front localization is possible and analyze the stability thereof with respect to extrinsic perturbations and internal noise. It is found that stability is enhanced upon regulating a positional signal and, surprisingly, also for a low degree of binding cooperativity. We further show a contrasting impact of self-activation to the stability of these two sources of destabilization. DOI: 10.1103/PhysRevLett.110.038102
Eine naturphilosophische Leitwährung für die Beschreibung der Wirlichkeit ist bereits bei Aristoteles die Form. Sie informiert die Materie und vermittelt dadurch das Sein. Der Informationsbegriff jedoch ist multivalent: man kann zwischen potentieller Information (QuBits), basaler einfacher Information (Bits) und komplexer Information (Systemordner-Information) unterscheiden. Die komplexe Information wird im Bit kodiert, indem es das QuBit disponiert. Die Kodierung erfolgt holografisch und somit analog. Letztlich inkarnieren sich Systeme in der physikalischen Wirklichkeit, indem sie sie komplex informieren (ordnen, ermöglichen, steuern, formieren). Das Universum würde dann der Materialisierung und Dekodierung von autopoetischen Systemen dienen.
Actively propelled particles undergoing dissipative collisions are known to develop a state of spatially distributed coherently moving clusters. For densities larger than a characteristic value, clusters grow in time and form a stationary well-ordered state of coherent macroscopic motion. In this work we address two questions. (i) What is the role of the particles’ aspect ratio in the context of cluster formation, and does the particle shape affect the system’s behavior on hydrodynamic scales? (ii) To what extent does particle conservation influence pattern formation? To answer these questions we suggest a simple kinetic model permitting us to depict some of the interaction properties between freely moving particles and particles integrated in clusters. To this end, we introduce two particle species: single and cluster particles. Specifically, we account for coalescence of clusters from single particles, assembly of single particles on existing clusters, collisions between clusters and cluster disassembly. Coarse graining our kinetic model, (i) we demonstrate that particle shape (i.e. aspect ratio) shifts the scale of the transition density, but does not impact the instabilities at the ordering threshold and (ii) we show that the validity of particle conservation determines the existence of a longitudinal instability, which tends to amplify density heterogeneities locally, and in turn triggers a wave pattern with wave vectors parallel to the axis of macroscopic order. If the system is in contact with a particle reservoir, this instability vanishes due to a compensation of density heterogeneities.
We demonstrate how organic solar cell efficiency can be increased by introducing a pure polymer interlayer between the PEDOT:PSS layer and the polymer: fullerene blend. We observe an increase in device efficiency with three different material systems over a number of devices. Using both electrical characterization and numerical modeling we show that the increase in efficiency is caused by optical absorption in the pure polymer layer and hence efficient charge separation at the polymer bulkheterojunction interface.
While the existence of polar ordered states in active systems is well established, the dynamics of the self-assembly processes are still elusive. We study a lattice gas model of self-propelled elongated particles interacting through excluded volume and alignment interactions, which shows a phase transition from an isotropic to a polar ordered state. By analyzing the ordering process we find that the transition is driven by the formation of a critical nucleation cluster and a subsequent coarsening process. Moreover, the time to establish a polar ordered state shows a power-law divergence.
Length regulation of microtubules (MTs) is essential for many cellular processes. Molecular motors like kinesin-8, which move along MTs and also act as depolymerases, are known as key players in MT dynamics. However, the regulatory mechanisms of length control remain elusive. Here, we investigate a stochastic model accounting for the interplay between polymerization kinetics and motor-induced depolymerization. We determine the dependence of MT length and variance on rate constants and motor concentration. Moreover, our analyses reveal how collective phenomena lead to a well-defined MT length.
Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes leading to extinction of species, whose understanding is a key component in the study of evolution and biodiversity, are influenced by both of these factors. Here, we investigate a class of stochastic population dynamics models based on generalized Lotka-Volterra systems. In the case of neutral stability of the underlying deterministic model, the impact of intrinsic noise on the survival of species is dramatic: It destroys coexistence of interacting species on a time scale proportional to the population size. We introduce a new method based on stochastic averaging which allows one to understand this extinction process quantitatively by reduction to a lower-dimensional effective dynamics. This is performed analytically for two highly symmetrical models and can be generalized numerically to more complex situations. The extinction probability distributions and other quantities of interest we obtain show excellent agreement with simulations.
Diffusion-limited reactions are studied in detail on the classical coalescing process. We demonstrate how, with the aid of a recent renormalization group approach, fluctuations can be integrated systematically. We thereby obtain an exact relation between the microscopic physics (lattice structure and particle shape and size) and the macroscopic decay rate in the law of mass action. Moreover, we find a strong violation of the law of mass action. The corresponding term in the kinetic equations originates in longwavelength fluctuations and is a universal function of the macroscopic decay rate.
Microbes providing public goods are widespread in nature despite running the risk of being exploited by free-riders. However, the precise ecological factors supporting cooperation are still puzzling. Following recent experiments, we consider the role of population growth and the repetitive fragmentation of populations into new colonies mimicking simple microbial life-cycles. Individual-based modeling reveals that demographic fluctuations, which lead to a large variance in the composition of colonies, promote cooperation. Biased by population dynamics these fluctuations result in two qualitatively distinct regimes of robust cooperation under repetitive fragmentation into groups. First, if the level of cooperation exceeds a threshold, cooperators will take over the whole population. Second, cooperators can also emerge from a single mutant leading to a robust coexistence between cooperators and free-riders. We find frequency and size of population bottlenecks, and growth dynamics to be the major ecological factors determining the regimes and thereby the evolutionary pathway towards cooperation.
Studies have suggested that there is a strong correlation between the masses of nuclear star clusters (NSCs) and their host galaxies, a correlation which is said to be an extension of the well-known correlations between supermassive black holes (SMBHs) and their host galaxies. But careful analysis of disk galaxies-including 2D bulge/disk/bar decompositions-shows that while SMBHs correlate with the stellar mass of the bulge component of galaxies, the masses of NSCs correlate much better with the total galaxy stellar mass. In addition, the mass ratio M-NSC/M-star,M- tot for NSCs in spirals (at least those with Hubble types Sc and later) is typically an order of magnitude smaller than the mass ratio M-BH/M-star,M- bul of SMBHs. The absence of a universal ``central massive object'' correlation argues against common formation and growth mechanisms for both SMBHs and NSCs. We also discuss evidence for a break in the NSC-host galaxy correlation, galaxies with Hubble types earlier than Sbc appear to host systematically more massive NSCs than do types Sc and later.
Die Aufgaben und Übungen beziehen sich auf das Buch: , das im Hochschulnetz der LMU abrufbar ist unter der URL: http://dx.doi.org/10.1007/978-3-642-05098-5
Observational constraints on the average radial distribution profile of AGN in distant galaxy clusters can provide important clues on the triggering mechanisms of AGN activity in dense environments and are essential for a completeness evaluation of cluster selection techniques in the X-ray and mm wavebands. The aim of this work is a statistical study with XMM-Newton of the presence and distribution of X-ray AGN in the large-scale structure environments of 22 X-ray luminous galaxy clusters in the redshift range 0.9 < z less than or similar to 1.6 compiled by the XMM-Newton Distant Cluster Project (XDCP). To this end, the X-ray point source lists from detections in the soft band (0.35-2.4 keV) and full band (0.3-7.5 keV) were stacked in cluster-centric coordinates and compared to average background number counts extracted from three independent control fields in the same observations. A significant full-band (soft-band) excess of similar to 78 (67) X-ray point sources is found in the cluster fields within an angular distance of 8' (4 Mpc) at a statistical confidence level of 4.0 sigma (4.2 sigma), corresponding to an average number of detected excess AGN per cluster environment of 3.5 +/- 0.9 (3.0 +/- 0.7). The data point towards a rising radial profile in the cluster region (r < 1Mpc) of predominantly low-luminosity AGN with an average detected excess of about one point source per system, with a tentative preferred occurrence along the main cluster elongation axis. A second statistically significant overdensity of brighter soft-band-detected AGN is found at cluster-centric distances of 4'-6' (2-3 Mpc), corresponding to about three times the average cluster radius R-200 of the systems. If confirmed, these results would support the idea of two different physical triggering mechanisms of X-ray AGN activity in dependence of the radially changing large-scale structure environment of the distant clusters. For high-z cluster studies at lower spatial resolution with the upcoming eROSITA all-sky X-ray survey, the results suggest that cluster-associated X-ray AGN may impose a bias in the spectral analysis of high-z systems, while their detection and flux measurements in the soft band may not be significantly affected.
We study the mechanical relaxation behavior of human red blood cells by observing the time evolution of shape change of cells flowing through microchannels with abrupt constrictions. We observe two types of relaxation processes. In the first fast process (tau(1) similar to 200 ms) the initially parachute shaped cells relax into cup-shaped cells (stomatocytes). These cells relax and reorient in a second relaxation process with a response time of tau(1/2) similar to 10 s into the equilibrium discoid shapes. The values for the relaxation times of single red blood cells in the population scatter significantly within the cell population between 0.11 s < tau(1) < 0.52 s and 9 s < tau(1/2) < 49 s, respectively. However, when plotting tau(1/2) against tau(1), we find a linear relationship between the two timescales and are able to relate both to the elastic properties of the spectrin cytoskeleton underlying the red cell's plasma membrane. Adenosine Triphosphate (ATP) enhances dissociation of spectrin filaments resulting in a reduced shear modulus. We modify the cytoskeleton connectivity by depletion and repletion of ATP and study the effect on relaxation. Both the linear relationship of timescales as well as the ATP dependence can be understood by theoretical models.
Min-protein oscillations in Escherichia coli are characterized by the remarkable robustness with which spatial patterns dynamically adapt to variations of cell geometry. Moreover, adaption, and therefore proper cell division, is independent of temperature. These observations raise fundamental questions about the mechanisms establishing robust Min oscillations, and about the role of spatial cues, as they are at odds with present models. Here, we introduce a robust model based on experimental data, consistently explaining the mechanisms underlying pole-to-pole, striped, and circular patterns, as well as the observed temperature dependence of the oscillation period. Contrary to prior conjectures, the model predicts that MinD and cardiolipin domains are not colocalized. The transient sequestration of MinE and highly canalized transfer of MinD between polar zones are the key mechanisms underlying oscillations. MinD channeling enhances midcell localization and facilitates stripe formation, revealing the potential optimization process from which robust Min-oscillations originally arose.
Solution-based self-assembly of quasi-one-dimensional semiconductor nanostructures (nanowires) from quasi-zero-dimensional (quantum dots) colloidal nanocrystal building blocks has proven itself as a powerful and flexible preparation technique. Polycrystalline CdTe nanowires self-assembled from light-emitting thiol-capped CdTe nanocrystals are the focus of this Feature Article. These nanowires represent an interesting model system for quantum dot solids, where electronic coupling between the individual nanocrystals can be optically accessed and controlled. We provide a literature-based summary of the formation mechanism and the morphology-related aspects of self-assembled CdTe nanowires, and highlight several fundamental and application-related optical properties of these nanostructures. These include fundamental aspects of polarization anisotropies in photoluminescence excitation and emission, the electronic coupling between individual semiconductor nanocrystals constituting the nanowires, and more applied, waveguiding properties of CdTe nanowire bundles and anti-Stokes photoluminescence in a prototypical structure of co-axial nanowires. The optical properties of self-assembled CdTe nanowires considered here render them potential candidates for photonic nanoscale devices.
The light-driven disassembly process of amyloid-like structures formed by azobenzene model peptides is studied by time-resolved mid-IR spectroscopy from nanoseconds to minutes. The investigated peptide consists of two amino acid strands connected by the azobenzene switch. The peptides aggregate to amyloid-like structures when the azobenzene chromophore is in the trans-conformation. Illumination, resulting in a trans-to cis-isomerization of the azobenzene, leads to disaggregation of the aggregated structures. After optical excitation and isomerization of the azobenzene, one finds absorption changes which recover to a large extent on the time scale of few nanoseconds. These early absorption transients are assigned to the relaxation of vibrational excess energy (heat) or to structural rearrangements of isomerized azobenzene and the aggregated surroundings. It is only on the time scale of minutes that spectral signatures appear which are characteristic for the disassembly of the aggregated structure.
We study the interplay of population growth and evolutionary dynamics using a stochastic model based on birth and death events. In contrast to the common assumption of an independent population size, evolution can be strongly affected by population dynamics in general. Especially for fast reproducing microbes which are subject to selection, both types of dynamics are often closely intertwined. We illustrate this by considering different growth scenarios. Depending on whether microbes die or stop to reproduce (dormancy), qualitatively different behaviors emerge. For cooperating bacteria, a permanent increase of costly cooperation can occur. Even if not permanent, cooperation can still increase transiently due to demographic fluctuations. We validate our analysis via stochastic simulations and analytic calculations. In particular, we derive a condition for an increase in the level of cooperation.
The colonization of unoccupied territory by invading species, known as range expansion, is a spatially heterogeneous non-equilibrium growth process. We introduce a two-species Eden growth model to analyze the interplay between uni-directional (irreversible) mutations and selection at the expanding front. While the evolutionary dynamics leads to coalescence of both wild-type and mutant clusters, the non-homogeneous advance of the colony results in a rough front. We show that roughening and domain dynamics are strongly coupled, resulting in qualitatively altered bulk and front properties. For beneficial mutations the front is quickly taken over by mutants and growth proceeds Eden-like. In contrast, if mutants grow slower than wild-types, there is an antagonism between selection pressure against mutants and growth by the merging of mutant domains with an ensuing absorbing state phase transition to an all-mutant front. We find that surface roughening has a marked effect on the critical properties of the absorbing state phase transition. While reference models, which keep the expanding front flat, exhibit directed percolation critical behavior, the exponents of the two-species Eden model strongly deviate from it. In turn, the mutation-selection process induces an increased surface roughness with exponents distinct from that of the classical Eden model.
A punctured Riemann surface is a compact Riemann surface with finitely many points removed. We will discuss an equivalence by [Sim90] between tame harmonic bundles, regular filtered stable Higgs bundles resp. D-modules and regular filtered local systems over these surfaces.
We investigate a driven two-channel system where particles on different lanes mutually obstruct each other's motion, extending an earlier model by Popkov and Peschel Phys. Rev. E 64, 026126 (2001)]. This obstruction may occur in biological contexts due to steric hinderance where motor proteins carry cargos by "walking" on microtubules. Similarly, the model serves as a description for classical spin transport where charged particles with internal states move unidirectionally on a lattice. Three regimes of qualitatively different behavior are identified, depending on the strength of coupling between the lanes. For small and large coupling strengths the model can be mapped to a one-channel problem, whereas a rich phase behavior emerges for intermediate ones. We derive an approximate but quantitatively accurate theoretical description in terms of a one-site cluster approximation, and obtain insight into the phase behavior through the current-density relations combined with an extremal-current principle. Our results are confirmed by stochastic simulations.
The longitudinal response of single semiflexible polymers to sudden changes in externally applied forces is known to be controlled by the propagation and relaxation of backbone tension. Under many experimental circumstances, realized, for example, in nanofluidic devices or in polymeric networks or solutions, these polymers are effectively confined in a channel-or tubelike geometry. By means of heuristic scaling laws and rigorous analytical theory, we analyze the tension dynamics of confined semiflexible polymers for various generic experimental setups. It turns out that in contrast to the well-known linear response, the influence of confinement on the nonlinear dynamics can largely be described as that of an effective prestress. We also study the free relaxation of an initially confined chain, finding a surprising superlinear similar to t(9/8) growth law for the change in end-to-end distance at short times.
