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We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of dependence that was previously studied mainly in the context of stable processes, we here extend its range of applicability to random-parameter and diffusing-diffusivity models which are important in contemporary physics, biology and financial engineering. We prove that the codifference detects forms of dependence and ergodicity breaking which are not visible from analysing the covariance and correlation functions. We also discuss a related measure of dispersion, which is a nonlinear analogue of the mean squared displacement.
We combine ultrafast X-ray diffraction (UXRD) and time-resolved Magneto-Optical Kerr Effect (MOKE) measurements to monitor the strain pulses in laser-excited TbFe2/Nb heterostructures. Spatial separation of the Nb detection layer from the laser excitation region allows for a background-free characterization of the laser-generated strain pulses. We clearly observe symmetric bipolar strain pulses if the excited TbFe2 surface terminates the sample and a decomposition of the strain wavepacket into an asymmetric bipolar and a unipolar pulse, if a SiO2 glass capping layer covers the excited TbFe2 layer. The inverse magnetostriction of the temporally separated unipolar strain pulses in this sample leads to a MOKE signal that linearly depends on the strain pulse amplitude measured through UXRD. Linear chain model simulations accurately predict the timing and shape of UXRD and MOKE signals that are caused by the strain reflections from multiple interfaces in the heterostructure.
Optical excitation of spin-ordered rare earth metals triggers a complex response of the crystal lattice since expansive stresses from electron and phonon excitations compete with a contractive stress induced by spin disorder. Using ultrafast x-ray diffraction experiments, we study the layer specific strain response of a dysprosium film within a metallic heterostructure upon femtosecond laser-excitation. The elastic and diffusive transport of energy to an adjacent, non-excited detection layer clearly separates the contributions of strain pulses and thermal excitations in the time domain. We find that energy transfer processes to magnetic excitations significantly modify the observed conventional bipolar strain wave into a unipolar pulse. By modeling the spin system as a saturable energy reservoir that generates substantial contractive stress on ultrafast timescales, we can reproduce the observed strain response and estimate the time- and space dependent magnetic stress. The saturation of the magnetic stress contribution yields a non-monotonous total stress within the nanolayer, which leads to unconventional picosecond strain pulses.
Polysulfobetaines in aqueous solution show upper critical solution temperature (UCST) behavior. We investigate here the representative of this class of materials, poly (N,N-dimethyl-N-(3-methacrylamidopropyl) ammonio propane sulfonate) (PSPP), with respect to: (i) the dynamics in aqueous solution above the cloud point as function of NaBr concentration; and (ii) the swelling behavior of thin films in water vapor as function of the initial film thickness. For PSPP solutions with a concentration of 5 wt.%, the temperature dependence of the intensity autocorrelation functions is measured with dynamic light scattering as function of molar mass and NaBr concentration (0-8 mM). We found a scaling of behavior for the scattered intensity and dynamic correlation length. The resulting spinodal temperatures showed a maximum at a certain (small) NaBr concentration, which is similar to the behavior of the cloud points measured previously by turbidimetry. The critical exponent of susceptibility depends on NaBr concentration, with a minimum value where the spinodal temperature is maximum and a trend towards the mean-field value of unity with increasing NaBr concentration. In contrast, the critical exponent of the correlation length does not depend on NaBr concentration and is lower than the value of 0.5 predicted by mean-field theory. For PSPP thin films, the swelling behavior was found to depend on film thickness. A film thickness of about 100 nm turns out to be the optimum thickness needed to obtain fast hydration with H2O.
Abstract
The emerging diffusive dynamics in many complex systems show a characteristic crossover behaviour from anomalous to normal diffusion which is otherwise fitted by two independent power-laws. A prominent example for a subdiffusive–diffusive crossover are viscoelastic systems such as lipid bilayer membranes, while superdiffusive–diffusive crossovers occur in systems of actively moving biological cells. We here consider the general dynamics of a stochastic particle driven by so-called tempered fractional Gaussian noise, that is noise with Gaussian amplitude and power-law correlations, which are cut off at some mesoscopic time scale. Concretely we consider such noise with built-in exponential or power-law tempering, driving an overdamped Langevin equation (fractional Brownian motion) and fractional Langevin equation motion. We derive explicit expressions for the mean squared displacement and correlation functions, including different shapes of the crossover behaviour depending on the concrete tempering, and discuss the physical meaning of the tempering. In the case of power-law tempering we also find a crossover behaviour from faster to slower superdiffusion and slower to faster subdiffusion. As a direct application of our model we demonstrate that the obtained dynamics quantitatively describes the subdiffusion–diffusion and subdiffusion–subdiffusion crossover in lipid bilayer systems. We also show that a model of tempered fractional Brownian motion recently proposed by Sabzikar and Meerschaert leads to physically very different behaviour with a seemingly paradoxical ballistic long time scaling.