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Anomalous diffusion with a power-law time dependence vertical bar R vertical bar(2)(t) similar or equal to t(alpha i) of the mean squared displacement occurs quite ubiquitously in numerous complex systems. Often, this anomalous diffusion is characterised by crossovers between regimes with different anomalous diffusion exponents alpha(i). Here we consider the case when such a crossover occurs from a first regime with alpha(1) to a second regime with alpha(2) such that alpha(2) > alpha(1), i.e., accelerating anomalous diffusion. A widely used framework to describe such crossovers in a one-dimensional setting is the bi-fractional diffusion equation of the so-called modified type, involving two time-fractional derivatives defined in the Riemann-Liouville sense. We here generalise this bi-fractional diffusion equation to higher dimensions and derive its multidimensional propagator (Green's function) for the general case when also a space fractional derivative is present, taking into consideration long-ranged jumps (Levy flights). We derive the asymptotic behaviours for this propagator in both the short- and long-time as well the short- and long-distance regimes. Finally, we also calculate the mean squared displacement, skewness and kurtosis in all dimensions, demonstrating that in the general case the non-Gaussian shape of the probability density function changes.
In recent years, gravitational-wave astronomy has motivated increasingly accurate perturbative studies of gravitational dynamics in compact binaries. This in turn has enabled more detailed analyses of the dynamical black holes in these systems. For example, Pound et al. [Phys. Rev. Lett. 124, 021101 (2020)] recently computed the surface area of a Schwarzschild black hole's apparent horizon, perturbed by an orbiting body, to second order in the binary's mass ratio. In this paper, we take that as the starting point for a comprehensive study of a perturbed Schwarzschild black hole's apparent and event horizon at second perturbative order, deriving generic formulas for the first- and second-order corrections to the horizons' radial profiles, surface areas, Hawking masses, and intrinsic curvatures. We find that the two horizons are remarkably similar, and that any teleological behavior of the event horizon is suppressed in several ways. Critically, we establish that at all orders, the perturbed event horizon in a small-mass-ratio binary is effectively localized in time. Even more pointedly, the event horizon is identical to the apparent horizon at linear order regardless of the source of perturbation, implying that the seemingly teleological "tidal lead," previously observed in linearly perturbed event horizons, is not genuinely teleological in origin. The two horizons do generically differ at second order, but their Hawking masses remain identical, implying that the event horizon obeys the same energy-flux balance law as the apparent horizon. At least in the case of a binary system, the difference between their surface areas remains extremely small even in the late stages of inspiral. In the course of our analysis, we also numerically illustrate puzzling behavior in the black hole's motion around the binary's center of mass.
The stratosphere is one of the main potential sources for subseasonal to seasonal predictability in midlatitudes in winter. The ability of an atmospheric model to realistically simulate the stratospheric dynamics is essential in order to move forward in the field of seasonal predictions in midlatitudes. Earlier studies with the ICOsahedral Nonhydrostatic atmospheric model (ICON) point out that stratospheric westerlies in ICON are underestimated. This is the first extensive study on the evaluation of Northern Hemisphere stratospheric winter circulation with ICON in numerical weather prediction (NWP) mode. Seasonal experiments with the default setup are able to reproduce the basic climatology of the stratospheric polar vortex. However, westerlies are too weak and major stratospheric warmings too frequent in ICON. Both a reduction of the nonorographic, and a reduction of the orographic gravity wave and wake drag lead to a strengthening of the stratospheric vortex and a bias reduction, in particular in January. However, the effect of the nonorographic gravity wave drag scheme on the stratosphere is stronger. Stratosphere-troposphere coupling is intensified and more realistic due to a reduced gravity wave drag. Furthermore, an adjustment of the subgrid-scale orographic drag parameterization leads to a significant error reduction in the mean sea level pressure. As a result of these findings, we present our current suggested improved setup for seasonal experiments with ICON-NWP. <br /> Plain Language Summary Although seasonal forecasts for midlatitudes have the potential to be highly beneficial to the public sector, they are still characterized by a large amount of uncertainty. Exact simulations of the circulation in the stratosphere can help to improve tropospheric predictability on seasonal time scales. For this reason, we investigate how well the new German atmospheric model is able to simulate the stratospheric circulation. The model reproduces the basic behavior of the Northern Hemisphere stratospheric polar vortex, but the westerly circulation in winter is underestimated. The stratospheric circulation is influenced by gravity waves that exert drag on the flow. These processes are only partly physically represented in the model, but are very important and are hence parameterized. By adjusting the parameterizations for the gravity wave drag, the stratospheric polar vortex is strengthened, thereby yielding a more realistic stratospheric circulation. In addition, the altered parameterizations improve the simulated surface pressure pattern. Based upon this, we present our current suggested improved model setup for seasonal experiments.
The Dirac point of a topological surface state (TSS) is protected against gapping by time-reversal symmetry. Conventional wisdom stipulates, therefore, that only through magnetisation may a TSS become gapped. However, non-magnetic gaps have now been demonstrated in Bi2Se3 systems doped with Mn or In, explained by hybridisation of the Dirac cone with induced impurity resonances. Recent photoemission experiments suggest that an analogous mechanism applies even when Bi2Se3 is surface dosed with Au. Here, we perform a systematic spin- and angle-resolved photoemission study of Au-dosed Bi2Se3. Although there are experimental conditions wherein the TSS appears gapped due to unfavourable photoemission matrix elements, our photon-energy-dependent spectra unambiguously demonstrate the robustness of the Dirac cone against high Au coverage. We further show how the spin textures of the TSS and its accompanying surface resonances remain qualitatively unchanged following Au deposition, and discuss the mechanism underlying the suppression of the spectral weight.
Tautomerism is one of the most important forms of isomerism, owing to the facile interconversion between species and the large differences in chemical properties introduced by the proton transfer connecting the tautomers. Spectroscopic techniques are often used for the characterization of tautomers. In this context, separating the overlapping spectral response of coexisting tautomers is a long-standing challenge in chemistry. Here, we demonstrate that by using resonant inelastic X-ray scattering tuned to the core excited states at the site of proton exchange between tautomers one is able to experimentally disentangle the manifold of valence excited states of each tautomer in a mixture. The technique is applied to the prototypical keto-enol equilibrium of 3-hydroxypyridine in aqueous solution. We detect transitions from the occupied orbitals into the LUMO for each tautomer in solution, which report on intrinsic and hydrogen-bond-induced orbital polarization within the pi and sigma manifolds at the proton-transfer site.
As the use of free electron laser (FEL) sources increases, so do the findings mentioning non-linear phenomena occurring at these experiments, such as saturable absorption, induced transparency and scattering breakdowns. These are well known among the laser community, but are still rarely understood and expected among the X-ray community and to date lack tools and theories to accurately predict the respective experimental parameters and results. We present a simple theoretical framework to access short X-ray pulse induced light- matter interactions which occur at intense short X-ray pulses as available at FEL sources. Our approach allows to investigate effects such as saturable absorption, induced transparency and scattering suppression, stimulated emission, and transmission spectra, while including the density of state influence relevant to soft X-ray spectroscopy in, for example, transition metal complexes or functional materials. This computationally efficient rate model based approach is intuitively adaptable to most solid state sample systems in the soft X-ray spectrum with the potential to be extended for liquid and gas sample systems as well. The feasibility of the model to estimate the named effects and the influence of the density of state is demonstrated using the example of CoPd transition metal systems at the Co edge. We believe this work is an important contribution for the preparation, performance, and understanding of FEL based high intensity and short pulse experiments, especially on functional materials in the soft X-ray spectrum.
Suppression of the TeV Pair-beam-Plasma Instability by a Tangled Weak Intergalactic Magnetic Field
(2022)
We study the effect of a tangled sub-fG level intergalactic magnetic field (IGMF) on the electrostatic instability of a blazar-induced pair beam. Sufficiently strong IGMF may significantly deflect the TeV pair beams, which would reduce the flux of secondary cascade emission below the observational limits. A similar flux reduction may result from the electrostatic beam-plasma instability, which operates the best in the absence of IGMF. Considering IGMF with correlation lengths smaller than a kiloparsec, we find that weak magnetic fields increase the transverse momentum of the pair-beam particles, which dramatically reduces the linear growth rate of the electrostatic instability and hence the energy-loss rate of the pair beam. We show that the beam-plasma instability is eliminated as an effective energy-loss agent at a field strength three orders of magnitude below that needed to suppress the secondary cascade emission by magnetic deflection. For intermediate-strength IGMF, we do not know a viable process to explain the observed absence of GeV-scale cascade emission.
Nanostructured silicon and silicon-aluminum compounds are synthesized by a novel synthesis strategy based on spark plasma sintering (SPS) of silicon nanopowder, mesoporous silicon (pSi), and aluminum nanopowder. The interplay of metal-assisted crystallization and inherent porosity is exploited to largely suppress thermal conductivity. Morphology and temperature-dependent thermal conductivity studies allow us to elucidate the impact of porosity and nanostructure on the macroscopic heat transport. Analytic electron microscopy along with quantitative image analysis is applied to characterize the sample morphology in terms of domain size and interpore distance distributions. We demonstrate that nanostructured domains and high porosity can be maintained in densified mesoporous silicon samples. In contrast, strong grain growth is observed for sintered nanopowders under similar sintering conditions. We observe that aluminum agglomerations induce local grain growth, while aluminum diffusion is observed in porous silicon and dispersed nanoparticles. A detailed analysis of the measured thermal conductivity between 300 and 773 K allows us to distinguish the effect of reduced thermal conductivity caused by porosity from the reduction induced by phonon scattering at nanosized domains. With a modified Landauer/Lundstrom approach the relative thermal conductivity and the scattering length are extracted. The relative thermal conductivity confirms the applicability of Kirkpatrick's effective medium theory. The extracted scattering lengths are in excellent agreement with the harmonic mean of log-normal distributed domain sizes and the interpore distances combined by Matthiessen's rule.
In this work, it is revealed how the photoinduced deformation of azobenzene containing polymers relates to the local direction of optomechanical stresses generated during irradiation with interference patterns (IPs). It can be substantiated by the modeling approach proposed by Saphiannikova et al., which describes the directional photodeformations in glassy side-chain azobenzene polymers, and proves that these deformations arise from the reorientation of rigid backbone segments along the light polarization direction. In experiments and modeling, surface relief gratings in pre-elongated photosensitive colloids of few micrometers length are inscribed using different IPs such as SS, PP, +/- 45, SP, RL, and LR. The deformation of colloidal particles is studied in situ, whereby the local variation of polymer topography is assigned to the local distribution of the electrical field vector for all IPs. Experimentally observed shapes are reproduced exactly with modeling azopolymer samples as visco-plastic bodies in the finite element software ANSYS. Orientation approach correctly predicts local variations of the main axis of light-induced stress in each interference pattern for both initially isotropic and highly oriented materials. With this work, it is suggested that the orientation approach implements a self-sufficient and convincing mechanism to describe photoinduced deformation in azopolymer films that in principle does not require auxiliary assumptions.
In this work, the fabrication and characterization of a simple, inexpensive, and effective microfluidic paper analytic device (mu PAD) for monitoring DNA samples is reported. The glass microfiber-based chip has been fabricated by a new wax-based transfer-printing technique and an electrode printing process. It is capable of moving DNA effectively in a time-dependent fashion. The nucleic acid sample is not damaged by this process and is accumulated in front of the anode, but not directly on the electrode. Thus, further DNA processing is feasible. The system allows the DNA to be purified by separating it from other components in sample mixtures such as proteins. Furthermore, it is demonstrated that DNA can be moved through several layers of the glass fiber material. This proof of concept will provide the basis for the development of rapid test systems, e.g., for the detection of pathogens in water samples.