TY - JOUR A1 - Berenstein, Igal T1 - Pattern formation in a reaction-diffusion-advection system with wave instability JF - Chaos : an interdisciplinary journal of nonlinear science N2 - In this paper, we show by means of numerical simulations how new patterns can emerge in a system with wave instability when a unidirectional advective flow (plug flow) is added to the system. First, we introduce a three variable model with one activator and two inhibitors with similar kinetics to those of the Oregonator model of the Belousov-Zhabotinsky reaction. For this model, we explore the type of patterns that can be obtained without advection, and then explore the effect of different velocities of the advective flow for different patterns. We observe standing waves, and with flow there is a transition from out of phase oscillations between neighboring units to in-phase oscillations with a doubling in frequency. Also mixed and clustered states are generated at higher velocities of the advective flow. There is also a regime of "waving Turing patterns" (quasi-stationary structures that come close and separate periodically), where low advective flow is able to stabilize the stationary Turing pattern. At higher velocities, superposition and interaction of patterns are observed. For both types of patterns, at high velocities of the advective field, the known flow distributed oscillations are observed. Y1 - 2012 U6 - https://doi.org/10.1063/1.4704809 SN - 1054-1500 VL - 22 IS - 2 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Berenstein, Igal A1 - Beta, Carsten T1 - Flow-induced transitions in bistable systems JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We studied transitions between spatiotemporal patterns that can be induced in a spatially extended nonlinear chemical system by a unidirectional flow in combination with constant inflow concentrations. Three different scenarios were investigated. (i) Under conditions where the system exhibited two stable fixed points, the propagation direction of trigger fronts could be reversed, so that domains of the less stable fixed point invaded the system. (ii) For bistability between a stable fixed point and a limit cycle we observed that above a critical flow velocity, the unstable focus at the center of the limit cycle could be stabilized. Increasing the flow speed further, a regime of damped flow-distributed oscillations was found and, depending on the boundary values at the inflow, finally the stable fixed point dominated. Similarly, also in the case of spatiotemporal chaos (iii), the unstable steady state could be stabilized and was replaced by the stable fixed point with increasing flow velocity. We finally outline a linear stability analysis that can explain part of our findings. Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevE.86.056205 SN - 1539-3755 VL - 86 IS - 5 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Berenstein, Igal A1 - Beta, Carsten T1 - Spatiotemporal chaos arising from standing waves in a reaction-diffusion system with cross-diffusion JF - The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr N2 - We show that quasi-standing wave patterns appear in the two-variable Oregonator model of the Belousov-Zhabotinsky reaction when a cross-diffusion term is added, no wave instability is required in this case. These standing waves have a frequency that is half the frequency of bulk oscillations displayed in the absence of diffusive coupling. The standing wave patterns show a dependence on the systems size. Regular standing waves can be observed for small systems, when the system size is an integer multiple of half the wavelength. For intermediate sizes, irregular patterns are observed. For large sizes, the system shows an irregular state of spatiotemporal chaos, where standing waves drift, merge, and split, and also phase slips may occur. Y1 - 2012 U6 - https://doi.org/10.1063/1.3676577 SN - 0021-9606 VL - 136 IS - 3 PB - American Institute of Physics CY - Melville ER - TY - THES A1 - Berger, Florian T1 - Different modes of cooperative transport by molecular motors T1 - Verschiedene Arten kooperativen Transportes mittels molekularer Motoren N2 - Cargo transport by molecular motors is ubiquitous in all eukaryotic cells and is typically driven cooperatively by several molecular motors, which may belong to one or several motor species like kinesin, dynein or myosin. These motor proteins transport cargos such as RNAs, protein complexes or organelles along filaments, from which they unbind after a finite run length. Understanding how these motors interact and how their movements are coordinated and regulated is a central and challenging problem in studies of intracellular transport. In this thesis, we describe a general theoretical framework for the analysis of such transport processes, which enables us to explain the behavior of intracellular cargos based on the transport properties of individual motors and their interactions. Motivated by recent in vitro experiments, we address two different modes of transport: unidirectional transport by two identical motors and cooperative transport by actively walking and passively diffusing motors. The case of cargo transport by two identical motors involves an elastic coupling between the motors that can reduce the motors’ velocity and/or the binding time to the filament. We show that this elastic coupling leads, in general, to four distinct transport regimes. In addition to a weak coupling regime, kinesin and dynein motors are found to exhibit a strong coupling and an enhanced unbinding regime, whereas myosin motors are predicted to attain a reduced velocity regime. All of these regimes, which we derive both by analytical calculations and by general time scale arguments, can be explored experimentally by varying the elastic coupling strength. In addition, using the time scale arguments, we explain why previous studies came to different conclusions about the effect and relevance of motor-motor interference. In this way, our theory provides a general and unifying framework for understanding the dynamical behavior of two elastically coupled molecular motors. The second mode of transport studied in this thesis is cargo transport by actively pulling and passively diffusing motors. Although these passive motors do not participate in active transport, they strongly enhance the overall cargo run length. When an active motor unbinds, the cargo is still tethered to the filament by the passive motors, giving the unbound motor the chance to rebind and continue its active walk. We develop a stochastic description for such cooperative behavior and explicitly derive the enhanced run length for a cargo transported by one actively pulling and one passively diffusing motor. We generalize our description to the case of several pulling and diffusing motors and find an exponential increase of the run length with the number of involved motors. N2 - Lastentransport mittels Motorproteinen ist ein grundlegender Mechanismus aller eukaryotischen Zellen und wird üblicherweise von mehreren Motoren kooperativ durchgeführt, die zu einer oder zu verschiedenen Motorarten wie Kinesin, Dynein oder Myosin gehören. Diese Motoren befördern Lasten wie zum Beispiel RNAs, Proteinkomplexe oder Organellen entlang Filamenten, von denen sie nach einer endlichen zurückgelegten Strecke abbinden. Es ist ein zentrales und herausforderndes Problem zu verstehen, wie diese Motoren wechselwirken und wie ihre Bewegungen koordiniert und reguliert werden. In der vorliegenden Arbeit wird eine allgemeine theoretische Herangehensweise zur Untersuchung solcher Transportprozesse beschrieben, die es uns ermöglicht, das Verhalten von intrazellularem Transport, ausgehend von den Transporteigenschaften einzelner Motoren und ihren Wechselwirkungen, zu verstehen. Wir befassen uns mit zwei Arten kooperativen Transports, die auch kürzlich in verschiedenen in vitro-Experimenten untersucht wurden: (i) gleichgerichteter Transport mit zwei identischen Motorproteinen und (ii) kooperativer Transport mit aktiv schreitenden und passiv diffundierenden Motoren. Beim Lastentransport mit zwei identischen Motoren sind die Motoren elastisch gekoppelt, was eine Verminderung ihrer Geschwindigkeit und/oder ihrer Bindezeit am Filament hervorrufen kann. Wir zeigen, dass solch eine elastische Kopplung im Allgemeinen zu vier verschiedenen Transportcharakteristiken führt. Zusätzlich zu einer schwachen Kopplung, können bei Kinesinen und Dyneinen eine starke Kopplung und ein verstärktes Abbinden auftreten, wohingegen bei Myosin Motoren eine verminderte Geschwindigkeit vorhergesagt wird. All diese Transportcharakteristiken, die wir mit Hilfe analytischer Rechnungen und Zeitskalenargumenten herleiten, können durch Änderung der elastischen Kopplung experimentell untersucht werden. Zusätzlich erklären wir anhand der Zeitskalenargumente, warum frühere Untersuchungen zu unterschiedlichen Erkenntnissen über die Auswirkung und die Wichtigkeit der gegenseitigen Beeinflussung der Motoren gelangt sind. Auf diese Art und Weise liefert unsere Theorie eine allgemeine und vereinheitlichende Beschreibung des dynamischen Verhaltens von zwei elastisch gekoppelten Motorproteinen. Die zweite Art von Transport, die in dieser Arbeit untersucht wird ist der Lastentransport durch aktiv ziehende und passiv diffundierende Motoren. Obwohl die passiven Motoren nicht zum aktiven Transport beitragen, verlängern sie stark die zurückgelegte Strecke auf dem Filament. Denn wenn ein aktiver Motor abbindet, wird das Lastteilchen immer noch am Filament durch den passiven Motor festgehalten, was dem abgebundenen Motor die Möglichkeit gibt, wieder an das Filament anzubinden und den aktiven Transport fortzusetzen. Für dieses kooperative Verhalten entwickeln wir eine stochastische Beschreibung und leiten explizit die verlängerte Transportstrecke für einen aktiv ziehenden und einen passiv diffundierenden Motor her. Wir verallgemeinern unsere Beschreibung für den Fall von mehreren ziehenden und diffundierenden Motoren und finden ein exponentielles Anwachsen der zurückgelegten Strecke in Abhängigkeit von der Anzahl der beteiligten Motoren. KW - molekulare Motoren KW - kooperativer Transport KW - intrazellulärer Transport KW - elastische Kopplung KW - stochastische Prozesse KW - molecular motors KW - cooperative transport KW - intracellular transport KW - elastic coupling KW - stochastic processes Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-60319 ER - TY - JOUR A1 - Bergner, Andre A1 - Frasca, M. A1 - Sciuto, G. A1 - Buscarino, A. A1 - Ngamga, Eulalie Joelle A1 - Fortuna, L. A1 - Kurths, Jürgen T1 - Remote synchronization in star networks JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We study phase synchronization in a network motif with a starlike structure in which the central node's (the hub's) frequency is strongly detuned against the other peripheral nodes. We find numerically and experimentally a regime of remote synchronization (RS), where the peripheral nodes form a phase synchronized cluster, while the hub remains free with its own dynamics and serves just as a transmitter for the other nodes. We explain the mechanism for this RS by the existence of a free amplitude and also show that systems with a fixed or constant amplitude, such as the classic Kuramoto phase oscillator, are not able to generate this phenomenon. Further, we derive an analytic expression which supports our explanation of the mechanism. Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevE.85.026208 SN - 1539-3755 VL - 85 IS - 2 PB - American Physical Society CY - College Park ER - TY - THES A1 - Bidan, Cecile T1 - Geometric control of tissue growth and organisation Y1 - 2012 CY - Potsdam ER - TY - JOUR A1 - Bodrova, Anna A1 - Schmidt, Jürgen A1 - Spahn, Frank A1 - Brilliantov, Nikolai V. T1 - Adhesion and collisional release of particles in dense planetary rings JF - Icarus : international journal of solar system studies N2 - We propose a simple theoretical model for aggregative and fragmentative collisions in Saturn's dense rings. In this model the ring matter consists of a bimodal size distribution: large (meter sized) boulders and a population of smaller particles (tens of centimeters down to dust). The small particles can adhesively stick to the boulders and can be released as debris in binary collisions of their carriers. To quantify the adhesion force we use the JKR theory (Johnson, K., Kendall, K., Roberts, A. [1971]. Proc. R. Soc. Lond. A 324, 301-313). The rates of release and adsorption of particles are calculated, depending on material parameters, sizes, and plausible velocity dispersions of carriers and debris particles. In steady state we obtain an expression for the amount of free debris relative to the fraction still attached to the carriers. In terms of this conceptually simple model a paucity of subcentimeter particles in Saturn's rings (French, R.G., Nicholson, P.D. [2000]. Icarus 145, 502-523; Marouf, E. et al. [2008]. Abstracts for "Saturn after Cassini-Huygens" Symposium, Imperial College London, UK, July 28 to August 1, p. 113) can be understood as a consequence of the increasing strength of adhesion (relative to inertial forces) for decreasing particle size. In this case particles smaller than a certain critical radius remain tightly attached to the surfaces of larger boulders, even when the boulders collide at their typical speed. Furthermore, we find that already a mildly increased velocity dispersion of the carrier-particles may significantly enhance the fraction of free debris particles, in this way increasing the optical depth of the system. KW - Planetary rings KW - Saturn, Rings KW - Collisional physics Y1 - 2012 U6 - https://doi.org/10.1016/j.icarus.2011.11.011 SN - 0019-1035 SN - 1090-2643 VL - 218 IS - 1 SP - 60 EP - 68 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Bojahr, Andre A1 - Herzog, Marc A1 - Schick, Daniel A1 - Vrejoiu, Ionela A1 - Bargheer, Matias T1 - Calibrated real-time detection of nonlinearly propagating strain waves JF - Physical review : B, Condensed matter and materials physics N2 - Epitaxially grown metallic oxide transducers support the generation of ultrashort strain pulses in SrTiO3 (STO) with high amplitudes up to 0.5%. The strain amplitudes are calibrated by real-time measurements of the lattice deformation using ultrafast x-ray diffraction. We determine the speed at which the strain fronts propagate by broadband picosecond ultrasonics and conclude that, above a strain level of approx. 0.2%, the compressive and tensile strain components travel at considerably different sound velocities, indicating nonlinear wave behavior. Simulations based on an anharmonic linear-chain model are in excellent accord with the experimental findings and show how the spectrum of coherent phonon modes changes with time. Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevB.86.144306 SN - 1098-0121 VL - 86 IS - 14 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Bojahr, Andre A1 - Schick, Daniel A1 - Märten, Lena A1 - Herzog, Marc A1 - Vrejoiu, Ionela A1 - von Korff Schmising, Clemens A1 - Milne, Chris A1 - Johnson, Steven Lee A1 - Bargheer, Matias T1 - Comparing the oscillation phase in optical pump-probe spectra to ultrafast x-ray diffraction in the metal-dielectric SrRuO3/SrTiO3 superlattice JF - Physical review : B, Condensed matter and materials physics N2 - We measured the ultrafast optical response of metal-dielectric superlattices by broadband all-optical pump-probe spectroscopy. The observed phase of the superlattice mode depends on the probe wavelength, making assignments of the excitation mechanism difficult. Ultrafast x-ray diffraction data reveal the true oscillation phase of the lattice which changes as a function of the excitation fluence. This result is confirmed by the fluence dependence of optical transients. We set up a linear chain model of the lattice dynamics and successfully simulated the broadband optical reflection by unit-cell resolved calculation of the strain-dependent dielectric functions of the constituting materials. Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevB.85.224302 SN - 1098-0121 VL - 85 IS - 22 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Braun, W. A1 - Pikovskij, Arkadij A1 - Matias, M. A. A1 - Colet, P. T1 - Global dynamics of oscillator populations under common noise JF - epl : a letters journal exploring the frontiers of physics N2 - Common noise acting on a population of identical oscillators can synchronize them. We develop a description of this process which is not limited to the states close to synchrony, but provides a global picture of the evolution of the ensembles. The theory is based on the Watanabe-Strogatz transformation, allowing us to obtain closed stochastic equations for the global variables. We show that at the initial stage, the order parameter grows linearly in time, while at the later stages the convergence to synchrony is exponentially fast. Furthermore, we extend the theory to nonidentical ensembles with the Lorentzian distribution of natural frequencies and determine the stationary values of the order parameter in dependence on driving noise and mismatch. Y1 - 2012 U6 - https://doi.org/10.1209/0295-5075/99/20006 SN - 0295-5075 VL - 99 IS - 2 PB - EDP Sciences CY - Mulhouse ER - TY - JOUR A1 - Burnecki, Krzysztof A1 - Wylomanska, Agnieszka A1 - Beletskii, Aleksei A1 - Gonchar, Vsevolod A1 - Chechkin, Aleksei V. T1 - Recognition of stable distribution with levy index alpha close to 2 JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We address the problem of recognizing alpha-stable Levy distribution with Levy index close to 2 from experimental data. We are interested in the case when the sample size of available data is not large, thus the power law asymptotics of the distribution is not clearly detectable, and the shape of the empirical probability density function is close to a Gaussian. We propose a testing procedure combining a simple visual test based on empirical fourth moment with the Anderson-Darling and Jarque-Bera statistical tests and we check the efficiency of the method on simulated data. Furthermore, we apply our method to the analysis of turbulent plasma density and potential fluctuations measured in the stellarator-type fusion device and demonstrate that the phenomenon of the L-H transition from low confinement, L mode, to a high confinement, H mode, which occurs in this device is accompanied by the transition from Levy to Gaussian fluctuation statistics. Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevE.85.056711 SN - 1539-3755 VL - 85 IS - 5 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Bykov, Andrei A1 - Gehrels, Neil A1 - Krawczynski, Henric A1 - Lemoine, Martin A1 - Pelletier, Guy A1 - Pohl, Martin T1 - Particle acceleration in relativistic outflows JF - Space science reviews N2 - In this review we confront the current theoretical understanding of particle acceleration at relativistic outflows with recent observational results on various source classes thought to involve such outflows, e.g. gamma-ray bursts, active galactic nuclei, and pulsar wind nebulae. We highlight the possible contributions of these sources to ultra-high-energy cosmic rays. KW - Cosmic rays KW - Particle acceleration KW - Shocks Y1 - 2012 U6 - https://doi.org/10.1007/s11214-012-9896-y SN - 0038-6308 VL - 173 IS - 1-4 SP - 309 EP - 339 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Bödecker, Geesche A1 - Henkel, Carsten T1 - Validity of the quantum regression theorem for resonance fluorescence in a photonic crystal JF - Annalen der Physik N2 - Correlation functions of a driven two-level system embedded in a photonic crystal are analyzed. The spectral density of the photonic bands near a gap makes this system non-Markovian. The equations of motion for two-time correlations are derived by two different methods, the quantum regression theorem and the fluctuation dissipation theorem, and found to be the same. KW - Resonance fluorescence KW - fluctuation dissipation theorem KW - quantum regression theorem KW - non-Markovian dynamics KW - open quantum system KW - photonic bandgap Y1 - 2012 U6 - https://doi.org/10.1002/andp.201200135 SN - 0003-3804 VL - 524 IS - 12 SP - 805 EP - 813 PB - Wiley-VCH CY - Weinheim ER - TY - JOUR A1 - Campbell, Earl T. A1 - Eisert, Jens T1 - Gaussification and entanglement distillation of continuous-variable systems a unifying picture JF - Physical review letters N2 - Distillation of entanglement using only Gaussian operations is an important primitive in quantum communication, quantum repeater architectures, and distributed quantum computing. Existing distillation protocols for continuous degrees of freedom are only known to converge to a Gaussian state when measurements yield precisely the vacuum outcome. In sharp contrast, non-Gaussian states can be deterministically converted into Gaussian states while preserving their second moments, albeit by usually reducing their degree of entanglement. In this work-based on a novel instance of a noncommutative central limit theorem-we introduce a picture general enough to encompass the known protocols leading to Gaussian states, and new classes of protocols including multipartite distillation. This gives the experimental option of balancing the merits of success probability against entanglement produced. Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevLett.108.020501 SN - 0031-9007 VL - 108 IS - 2 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Caravelli, Francesco A1 - Hamma, Alioscia A1 - Markopoulou, Fotini A1 - Riera, Arnau T1 - Trapped surfaces and emergent curved space in the Bose-Hubbard model JF - Physical review : D, Particles, fields, gravitation, and cosmology N2 - A Bose-Hubbard model on a dynamical lattice was introduced in previous work as a spin system analogue of emergent geometry and gravity. Graphs with regions of high connectivity in the lattice were identified as candidate analogues of spacetime geometries that contain trapped surfaces. We carry out a detailed study of these systems and show explicitly that the highly connected subgraphs trap matter. We do this by solving the model in the limit of no back-reaction of the matter on the lattice, and for states with certain symmetries that are natural for our problem. We find that in this case the problem reduces to a one-dimensional Hubbard model on a lattice with variable vertex degree and multiple edges between the same two vertices. In addition, we obtain a (discrete) differential equation for the evolution of the probability density of particles which is closed in the classical regime. This is a wave equation in which the vertex degree is related to the local speed of propagation of probability. This allows an interpretation of the probability density of particles similar to that in analogue gravity systems: matter inside this analogue system sees a curved spacetime. We verify our analytic results by numerical simulations. Finally, we analyze the dependence of localization on a gradual, rather than abrupt, falloff of the vertex degree on the boundary of the highly connected region and find that matter is localized in and around that region. Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevD.85.044046 SN - 1550-7998 VL - 85 IS - 4 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Chechkin, Aleksei V. A1 - Lenz, F. A1 - Klages, Rainer T1 - Normal and anomalous fluctuation relations for gaussian stochastic dynamics JF - Journal of statistical mechanics: theory and experiment N2 - We study transient work fluctuation relations (FRs) for Gaussian stochastic systems generating anomalous diffusion. For this purpose we use a Langevin approach by employing two different types of additive noise: (i) internal noise where the fluctuation dissipation relation of the second kind (FDR II) holds, and (ii) external noise without FDR II. For internal noise we demonstrate that the existence of FDR II implies the existence of the fluctuation dissipation relation of the first kind (FDR I), which in turn leads to conventional (normal) forms of transient work FRs. For systems driven by external noise we obtain violations of normal FRs, which we call anomalous FRs. We derive them in the long-time limit and demonstrate the existence of logarithmic factors in FRs for intermediate times. We also outline possible experimental verifications. KW - stochastic particle dynamics (theory) KW - fluctuations (theory) KW - stochastic processes (theory) KW - diffusion Y1 - 2012 U6 - https://doi.org/10.1088/1742-5468/2012/11/L11001 SN - 1742-5468 IS - 4 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Chechkin, Aleksei V. A1 - Zaid, Irwin M. A1 - Lomholt, Michael A. A1 - Sokolov, Igor M. A1 - Metzler, Ralf T1 - Bulk-mediated diffusion on a planar surface full solution JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We consider the effective surface motion of a particle that intermittently unbinds from a planar surface and performs bulk excursions. Based on a random-walk approach, we derive the diffusion equations for surface and bulk diffusion including the surface-bulk coupling. From these exact dynamic equations, we analytically obtain the propagator of the effective surface motion. This approach allows us to deduce a superdiffusive, Cauchy-type behavior on the surface, together with exact cutoffs limiting the Cauchy form. Moreover, we study the long-time dynamics for the surface motion. Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevE.86.041101 SN - 1539-3755 VL - 86 IS - 4 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Cherstvy, Andrey G. T1 - Critical polyelectrolyte adsorption under confinement Planar slit, cylindrical pore, and spherical cavity JF - Biopolymers N2 - We explore the properties of adsorption of flexible polyelectrolyte chains in confined spaces between the oppositely charged surfaces in three basic geometries. A method of approximate uniformly valid solutions for the Green function equation for the eigenfunctions of polymer density distributions is developed to rationalize the critical adsorption conditions. The same approach was implemented in our recent study for the inverse problem of polyelectrolyte adsorption onto a planar surface, and on the outer surface of rod-like and spherical obstacles. For the three adsorption geometries investigated, the theory yields simple scaling relations for the minimal surface charge density that triggers the chain adsorption, as a function of the Debye screening length and surface curvature. The encapsulation of polyelectrolytes is governed by interplay of the electrostatic attraction energy toward the adsorbing surface and entropic repulsion of the chain squeezed into a thin slit or small cavities. Under the conditions of surface-mediated confinement, substantially larger polymer linear charge densities are required to adsorb a polyelectrolyte inside a charged spherical cavity, relative to a cylindrical pore and to a planar slit (at the same interfacial surface charge density). Possible biological implications are discussed briefly in the end. KW - polymers KW - adsorption KW - electrostatics KW - confinement Y1 - 2012 U6 - https://doi.org/10.1002/bip.22023 SN - 0006-3525 VL - 97 IS - 5 SP - 311 EP - 317 PB - Wiley-Blackwell CY - Hoboken ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Winkler, R. G. T1 - Polyelectrolyte adsorption onto oppositely charged interfaces image-charge repulsion and surface curvature JF - The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces & biophysical chemistry N2 - We analyze theoretically the influence of low-dielectric boundaries on the adsorption of flexible polyelectrolytes onto planar and spherical oppositely charged surfaces in electrolyte solutions. We rationalize to what extent polymer chains are depleted from adsorbing interfaces by repulsive image forces. We employ the WKB (Wentzel-Kramers-Brillouin) quantum mechanical method for the Green function of the Edwards equation to determine the adsorption equilibrium. Scaling relations are determined for the critical adsorption strength required to initiate polymer adsorption onto these low-dielectric supports. Image-force repulsion shifts the equilibrium toward the desorbed state, demanding larger surface charge densities and polyelectrolyte linear charge densities for the adsorption to take place. The effect is particularly pronounced for a planar interface in a low-salt regime, where a dramatic change in the scaling behavior for the adsorption-desorption transition is predicted. For the adsorbed state, polymers with higher charge densities are displaced further from the interface by image-charge repulsions. We discuss relevant experimental evidence and argue about possible biological applications of the results. Y1 - 2012 U6 - https://doi.org/10.1021/jp304980e SN - 1520-6106 VL - 116 IS - 32 SP - 9838 EP - 9845 PB - American Chemical Society CY - Washington ER - TY - JOUR A1 - Cubitt, Toby S. A1 - Eisert, Jens A1 - Wolf, Michael M. T1 - The complexity of relating quantum channels to master equations JF - Communications in mathematical physics N2 - Completely positive, trace preserving (CPT) maps and Lindblad master equations are both widely used to describe the dynamics of open quantum systems. The connection between these two descriptions is a classic topic in mathematical physics. One direction was solved by the now famous result due to Lindblad, Kossakowski, Gorini and Sudarshan, who gave a complete characterisation of the master equations that generate completely positive semi-groups. However, the other direction has remained open: given a CPT map, is there a Lindblad master equation that generates it (and if so, can we find its form)? This is sometimes known as the Markovianity problem. Physically, it is asking how one can deduce underlying physical processes from experimental observations. We give a complexity theoretic answer to this problem: it is NP-hard. We also give an explicit algorithm that reduces the problem to integer semi-definite programming, a well-known NP problem. Together, these results imply that resolving the question of which CPT maps can be generated by master equations is tantamount to solving P = NP: any efficiently computable criterion for Markovianity would imply P = NP; whereas a proof that P = NP would imply that our algorithm already gives an efficiently computable criterion. Thus, unless P does equal NP, there cannot exist any simple criterion for determining when a CPT map has a master equation description. However, we also show that if the system dimension is fixed (relevant for current quantum process tomography experiments), then our algorithm scales efficiently in the required precision, allowing an underlying Lindblad master equation to be determined efficiently from even a single snapshot in this case. Our work also leads to similar complexity-theoretic answers to a related long-standing open problem in probability theory. Y1 - 2012 U6 - https://doi.org/10.1007/s00220-011-1402-y SN - 0010-3616 VL - 310 IS - 2 SP - 383 EP - 418 PB - Springer CY - New York ER -