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Experimental studies of the diffusion of biomolecules within biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule trajectories quite intricate. Here, we consider subdiffusive continuous time random walks that represent a seminal model for the anomalous diffusion of tracer particles in complex environments. This motion is characterized by multiple trapping events with infinite mean sojourn time. In real physical situations, however, instead of the full immobilization predicted by the continuous time random walk model, the motion of the tracer particle shows additional jiggling, for instance, due to thermal agitation of the environment. We here present and analyze in detail an extension of the continuous time random walk model. Superimposing the multiple trapping behavior with additive Gaussian noise of variable strength, we demonstrate that the resulting process exhibits a rich variety of apparent dynamic regimes. In particular, such noisy continuous time random walks may appear ergodic, while the bare continuous time random walk exhibits weak ergodicity breaking. Detailed knowledge of this behavior will be useful for the truthful physical analysis of experimentally observed subdiffusion.
We present a generic analytical scheme for the quantification of fluctuations due to bifunctionality-induced signal transduction within the members of a bacterial two-component system. The proposed model takes into account post-translational modifications in terms of elementary phosphotransfer kinetics. Sources of fluctuations due to autophosphorylation, kinase, and phosphatase activity of the sensor kinase have been considered in the model via Langevin equations, which are then solved within the framework of linear noise approximation. The resultant analytical expression of phosphorylated response regulators are then used to quantify the noise profile of biologically motivated single and branched pathways. Enhancement and reduction of noise in terms of extra phosphate outflux and influx, respectively, have been analyzed for the branched system. Furthermore, the role of fluctuations of the network output in the regulation of a promoter with random activation-deactivation dynamics has been analyzed.
As the oldest known magnetic material, magnetite (Fe3O4) has fascinated mankind for millennia. As the first oxide in which a relationship between electrical conductivity and fluctuating/localized electronic order was shown(1), magnetite represents a model system for understanding correlated oxides in general. Nevertheless, the exact mechanism of the insulator-metal, or Verwey, transition has long remained inaccessible(2-8). Recently, three- Fe- site lattice distortions called trimeronswere identified as the characteristic building blocks of the low-temperature insulating electronically ordered phase(9). Here we investigate the Verwey transition with pump- probe X- ray diffraction and optical reflectivity techniques, and show how trimerons become mobile across the insulator-metal transition. We find this to be a two- step process. After an initial 300 fs destruction of individual trimerons, phase separation occurs on a 1.5 +/- 0.2 ps timescale to yield residual insulating and metallic regions. This work establishes the speed limit for switching in future oxide electronics(10).
We present an accurate analysis of the H-2 absorption lines from the z(abs) similar to 2.4018 damped Ly alpha system towards HE 0027-1836 observed with the Very Large Telescope Ultraviolet and Visual Echelle Spectrograph (VLT/UVES) as a part of the European Southern Observatory Large Programme 'The UVES large programme for testing fundamental physics' to constrain the variation of proton-to-electron mass ratio, mu m(p)/m(e). We perform cross-correlation analysis between 19 individual exposures taken over three years and the combined spectrum to check the wavelength calibration stability. We notice the presence of a possible wavelength-dependent velocity drift especially in the data taken in 2012. We use available asteroids spectra taken with UVES close to our observations to confirm and quantify this effect. We consider single-and two-component Voigt profiles to model the observed H-2 absorption profiles. We use both linear regression analysis and Voigt profile fitting where Delta mu/mu is explicitly considered as an additional fitting parameter. The two-component model is marginally favoured by the statistical indicators and we get Delta mu/mu = -2.5 +/- 8.1(stat) +/- 6.2(sys) ppm. When we apply the correction to the wavelength-dependent velocity drift, we find Delta mu/mu = -7.6 +/- 8.1(stat) +/- 6.3(sys) ppm. It will be important to check the extent to which the velocity drift we notice in this study is present in UVES data used for previous Delta mu/mu measurements.
In most cases tendency to synchrony in networks of oscillatory units increases with the coupling strength. Using the popular Hindmarsh-Rose neuronal model, we demonstrate that even for identical neurons and simple coupling the dynamics can be more complicated. Our numerical analysis for globally coupled systems and oscillator lattices reveals a new scenario of synchrony breaking with the increase of coupling, resulting in a quasiperiodic, modulated synchronous state.
The formation of unmagnetized electrostatic shock-like structures with a high Mach number is examined with one-and two-dimensional particle-in-cell (PIC) simulations. The structures are generated through the collision of two identical plasma clouds, which consist of equally hot electrons and ions with a mass ratio of 250. The Mach number of the collision speed with respect to the initial ion acoustic speed of the plasma is set to 4.6. This high Mach number delays the formation of such structures by tens of inverse ion plasma frequencies. A pair of stable shock-like structures is observed after this time in the 1D simulation, which gradually evolves into electrostatic shocks. The ion acoustic instability, which can develop in the 2D simulation but not in the 1D one, competes with the nonlinear process that gives rise to these structures. The oblique ion acoustic waves fragment their electric field. The transition layer, across which the bulk of the ions change their speed, widens and their speed change is reduced. Double layer-shock hybrid structures develop.
Background: The linear noise approximation (LNA) is commonly used to predict how noise is regulated and exploited at the cellular level. These predictions are exact for reaction networks composed exclusively of first order reactions or for networks involving bimolecular reactions and large numbers of molecules. It is however well known that gene regulation involves bimolecular interactions with molecule numbers as small as a single copy of a particular gene. It is therefore questionable how reliable are the LNA predictions for these systems.
Results: We implement in the software package intrinsic Noise Analyzer (iNA), a system size expansion based method which calculates the mean concentrations and the variances of the fluctuations to an order of accuracy higher than the LNA. We then use iNA to explore the parametric dependence of the Fano factors and of the coefficients of variation of the mRNA and protein fluctuations in models of genetic networks involving nonlinear protein degradation, post-transcriptional, post-translational and negative feedback regulation. We find that the LNA can significantly underestimate the amplitude and period of noise-induced oscillations in genetic oscillators. We also identify cases where the LNA predicts that noise levels can be optimized by tuning a bimolecular rate constant whereas our method shows that no such regulation is possible. All our results are confirmed by stochastic simulations.
Conclusion: The software iNA allows the investigation of parameter regimes where the LNA fares well and where it does not. We have shown that the parametric dependence of the coefficients of variation and Fano factors for common gene regulatory networks is better described by including terms of higher order than LNA in the system size expansion. This analysis is considerably faster than stochastic simulations due to the extensive ensemble averaging needed to obtain statistically meaningful results. Hence iNA is well suited for performing computationally efficient and quantitative studies of intrinsic noise in gene regulatory networks.
In this paper, we introduce and study systematically, in terms of phase response curves, the effect of dual-pulse excitation on the dynamics of an autonomous oscillator. Specifically, we test the deviations from linear summation of phase advances resulting from two small perturbations. We analytically derive a correction term, which generally appears for oscillators whose intrinsic dimensionality is >1. The nonlinear correction term is found to be proportional to the square of the perturbation. We demonstrate this effect in the Stuart-Landau model and in various higher dimensional neuronal models. This deviation from the superposition principle needs to be taken into account in studies of networks of pulse-coupled oscillators. Further, this deviation could be used in the verification of oscillator models via a dual-pulse excitation.
We recorded large data sets of swimming trajectories of the soil bacterium Pseudomonas putida. Like other prokaryotic swimmers, P. putida exhibits a motion pattern dominated by persistent runs that are interrupted by turning events. An in-depth analysis of their swimming trajectories revealed that the majority of the turning events is characterized by an angle of phi(1) = 180 degrees (reversals). To a lesser extent, turning angles of phi(2 Sigma Sigma Sigma Sigma) = 00 are also found. Remarkably, we observed that, upon a reversal, the swimming speed changes by a factor of two on average a prominent feature of the motion pattern that, to our knowledge, has not been reported before. A theoretical model, based on the experimental values for the average run time and the rotational diffusion, recovers the mean-square displacement of P. putida if the two distinct swimming speeds are taken into account. Compared to a swimmer that moves with a constant intermediate speed, the mean-square displacement is strongly enhanced. We furthermore observed a negative dip in the directional autocorrelation at intermediate times, a feature that is only recovered in an extended model, where the nonexponential shape of the run-time distribution is taken into account.
Standing waves are studied as solutions of a complex Ginzburg-Landau equation subjected to local and global time-delay feedback terms. The onset is described as an instability of the uniform oscillations with respect to spatially periodic perturbations. The solution of the standing wave pattern is given analytically and studied through simulations.
We report the detection of a new TeV gamma-ray source, VER J0521+211, based on observations made with the VERITAS imaging atmospheric Cherenkov Telescope Array. These observations were motivated by the discovery of a cluster of >30 GeV photons in the first year of Fermi Large Area Telescope observations. VER J0521+211 is relatively bright at TeV energies, with a mean photon flux of (1.93 +/- 0.13(stat) +/- 0.78(sys)) x 10(-11) cm(-2) s(-1) above 0.2 TeV during the period of the VERITAS observations. The source is strongly variable on a daily timescale across all wavebands, from optical to TeV, with a peak flux corresponding to similar to 0.3 times the steady Crab Nebula flux at TeV energies. Follow-up observations in the optical and X-ray bands classify the newly discovered TeV source as a BL Lac-type blazar with uncertain redshift, although recent measurements suggest z = 0.108. VER J0521+211 exhibits all the defining properties of blazars in radio, optical, X-ray, and gamma-ray wavelengths.
The heat transport mediated by near-field interactions in networks of plasmonic nanostructures is shown to be analogous to a generalized random walk process. The existence of superdiffusive regimes is demonstrated both in linear ordered chains and in three-dimensional random networks by analyzing the asymptotic behavior of the corresponding probability distribution function. We show that the spread of heat in these networks is described by a type of Levy flight. The presence of such anomalous heat-transport regimes in plasmonic networks opens the way to the design of a new generation of composite materials able to transport heat faster than the normal diffusion process in solids.
In this paper, we report on in-situ atomic force microscopy (AFM) studies of topographical changes in azobenzene-containing photosensitive polymer films that are irradiated with light interference patterns. We have developed an experimental setup consisting of an AFM combined with two-beam interferometry that permits us to switch between different polarization states of the two interfering beams while scanning the illuminated area of the polymer film, acquiring corresponding changes in topography in-situ. This way, we are able to analyze how the change in topography is related to the variation of the electrical field vector within the interference pattern. It is for the first time that with a rather simple experimental approach a rigorous assignment can be achieved. By performing in-situ measurements we found that for a certain polarization combination of two interfering beams [namely for the SP (a dagger center dot, a dagger") polarization pattern] the topography forms surface relief grating with only half the period of the interference patterns. Exploiting this phenomenon we are able to fabricate surface relief structures with characteristic features measuring only 140 nm, by using far field optics with a wavelength of 491 nm. We believe that this relatively simple method could be extremely valuable to, for instance, produce structural features below the diffraction limit at high-throughput, and this could significantly contribute to the search of new fabrication strategies in electronics and photonics industry.
Mode structure and polaritonic contributions to the Casimir effect in a magnetodielectric cavity
(2013)
We present a full analysis of the mode spectrum in a cavity formed by two parallel plates, one of which is magnetodielectric (metamaterial) while the other one is metallic, and obtain dispersion relations in closed form. The optical properties of the cavity walls are described in terms of realistic models for effective permittivity and permeability. Surface polaritons, i.e., electromagnetic modes that have at least partly an evanescent character, are shown to dominate the Casimir interaction at small separations. We analyze in detail the s-polarized polaritons, which are a characteristic feature of a magnetodielectric configuration, and discuss their role in the repulsive Casimir force.
In this paper we report on an opto-mechanical scission of polymer chains within photosensitive diblock-copolymer brushes grafted to flat solid substrates. We employ surface-initiated polymerization of methylmethacrylate (MMA) and t-butyl methacrylate (tBMA) to grow diblock-copolymer brushes of poly(methylmethacrylate-b-t-butyl methacrylate) following the atom transfer polymerization (ATRP) scheme. After the synthesis, deprotection of the PtBMA block yields poly(methacrylic acid) (PMAA). To render PMMA-b-PMAA copolymers photosensitive, cationic azobenzene containing surfactants are attached to the negatively charged outer PMAA block. During irradiation with an ultraviolet (UV) interference pattern, the extent of photoisomerization of the azobenzene groups varies spatially and results in a topography change of the brush, i.e., formation of surface relief gratings (SRG). The SRG formation is accompanied by local rupturing of the polymer chains in areas from which the polymer material recedes. This opto-mechanically induced scission of the polymer chains takes place at the interfaces of the two blocks and depends strongly on the UV irradiation intensity. Our results indicate that this process may be explained by employing classical continuum fracture mechanics, which might be important for tailoring the phenomenon for applying it to poststructuring of polymer brushes.
We study the Kuramoto model of globally coupled oscillators with a biharmonic coupling function. We develop an analytic self-consistency approach to find stationary synchronous states in the thermodynamic limit and demonstrate that there is a huge multiplicity of such states, which differ microscopically in the distributions of locked phases. These synchronous regimes already exist prior to the linear instability transition of the fully asynchronous state. In the presence of white Gaussian noise, the multiplicity is lifted, but the dependence of the order parameters on coupling constants remains nontrivial.
Axionlike particles (ALPs) are hypothetical light (sub-eV) bosons predicted in some extensions of the Standard Model of particle physics. In astrophysical environments comprising high-energy gamma rays and turbulent magnetic fields, the existence of ALPs can modify the energy spectrum of the gamma rays for a sufficiently large coupling between ALPs and photons. This modification would take the form of an irregular behavior of the energy spectrum in a limited energy range. Data from the H. E. S. S. observations of the distant BL Lac object PKS 2155 - 304 (z = 0.116) are used to derive upper limits at the 95% C. L. on the strength of the ALP coupling to photons, g(gamma a) < 2.1 x 10(-11) GeV-1 for an ALP mass between 15 and 60 neV. The results depend on assumptions on the magnetic field around the source, which are chosen conservatively. The derived constraints apply to both light pseudoscalar and scalar bosons that couple to the electromagnetic field.
A detailed investigation of the open circuit voltage (V-OC) of organic bulk heterojunction solar cells comprising three different donor polymers and two different fullerene-based acceptors is presented. Bias amplified charge extraction (BACE) is combined with Kelvin Probe measurements to derive information on the relevant energetics in the blend. On the example of P3HT:PC70BM the influence of composition and preparation conditions on the relevant transport levels will be shown. Moderate upward shifts of the P3HT HOMO depending on crystallinity are observed, but contrarily to common believe, the dependence of V-OC on blend composition and thermal history is found to be largely determined by the change in the PCBM LUMO energy. Following this approach, we quantified the energetic contribution to the V-OC in blends with fluorinated polymers or higher adduct fullerenes.
Aqueous mixtures of a dye-labeled non-ionic thermoresponsive copolymer and a conjugated cationic polyelectrolyte are shown to exhibit characteristic changes in fluorescence properties in response to temperature and to the presence of salts, enabling a double-stimuli responsiveness. In such mixtures at room temperature, i.e., well below the lower critical solution temperature (LCST), the emission of the dye is strongly quenched due to energy transfer to the polycation, pointing to supramolecular interactions between the two macromolecules. Increasing the concentration of salts weakens the interpolymer interactions, the extent of which is simultaneously monitored from the change in the relative emission intensity of the components. When the mixture is heated above its LCST, the transfer efficiency is significantly reduced, signaling a structural reorganization process, however, surprisingly only if the mixture contains salt ions. To elucidate the reasons behind such thermo- and ion-sensitive fluorescence characteristics, we investigate the effect of salts of alkali chlorides, in particular of NaCl, on the association behavior of these macromolecules before and after the polymer phase transition by a combination of UV-vis, fluorescence, and H-1 NMR spectroscopy with light scattering and small-angle neutron scattering measurements.
Standard continuous time random walk (CTRW) models are renewal processes in the sense that at each jump a new, independent pair of jump length and waiting time are chosen. Globally, anomalous diffusion emerges through scale-free forms of the jump length and/or waiting time distributions by virtue of the generalized central limit theorem. Here we present a modified version of recently proposed correlated CTRW processes, where we incorporate a power-law correlated noise on the level of both jump length and waiting time dynamics. We obtain a very general stochastic model, that encompasses key features of several paradigmatic models of anomalous diffusion: discontinuous, scale-free displacements as in Levy flights, scale-free waiting times as in subdiffusive CTRWs, and the long-range temporal correlations of fractional Brownian motion (FBM). We derive the exact solutions for the single-time probability density functions and extract the scaling behaviours. Interestingly, we find that different combinations of the model parameters lead to indistinguishable shapes of the emerging probability density functions and identical scaling laws. Our model will be useful for describing recent experimental single particle tracking data that feature a combination of CTRW and FBM properties.