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We present a Bayesian inference scheme for scaled Brownian motion, and investigate its performance on synthetic data for parameter estimation and model selection in a combined inference with fractional Brownian motion. We include the possibility of measurement noise in both models. We find that for trajectories of a few hundred time points the procedure is able to resolve well the true model and parameters. Using the prior of the synthetic data generation process also for the inference, the approach is optimal based on decision theory. We include a comparison with inference using a prior different from the data generating one.
Recently, glasses, a subset of amorphous solids, have gained attention in various fields, such as polymer chemistry, optical fibers, and pharmaceuticals. One of their characteristic features, the glass transition temperature (T-g) which is absent in 100% crystalline materials, influences several material properties, such as free volume, enthalpy, viscosity, thermodynamic transitions, molecular motions, physical stability, mechanical properties, etc. In addition to T-g, there may be several other temperaturedependent transitions known as sub-T-g transitions (or beta-, gamma-, and delta-relaxations) which are identified by specific analytical techniques. The study of T-g and sub-T-g transitions occurring in amorphous solids has gained much attention because of its importance in understanding molecular kinetics, and it requires the combination of conventional and novel characterization techniques. In the present study, three different analytical techniques [modulated differential scanning calorimetry (mDSC), dynamic mechanical analysis (DMA), and dielectric relaxation spectroscopy (DRS)] were used to perform comprehensive qualitative/quantitative characterization of molecular relaxations, miscibility, and molecular interactions present in an amorphous polymer (PVPVA), a model drug (indomethacin, IND), and IND/PVPVA-based amorphous solid dispersions (ASDs). This is the first ever reported DMA study on PVPVA in its powder form, which avoids the contribution of solvent to the mechanical properties when a selfstanding polymer film is used. A good correlation between the techniques in determining the T-g value of PVPVA, IND, and IND/ PVPVA-based ASDs is established, and the negligible difference (within 10 degrees C) is attributed to the different material properties assessed in each technique. However, the overall T-g behavior, the decrease in T-g with increase in drug loading in ASDs, is universally observed in all the above-mentioned techniques, which reveals their complementarity. DMA and DRS techniques are used to study the different sub-T-g transitions present in PVPVA, amorphous IND, and IND/PVPVA-based ASDs because these transitions are normally too weak or too broad for mDSC to detect. For IND/PVPVA-based ASDs, both techniques show a shift of sub-T-g transitions (or secondary relaxation peaks) toward the high-temperature region from -140 to -45 degrees C. Thus, this paper outlines the usage of different solid-state characterization techniques in understanding the different molecular dynamics present in the polymer, drug, and their interactions in ASDs with the integrated information obtained from individual techniques.
Cosmic rays (CRs) are a ubiquitous and an important component of astrophysical environments such as the interstellar medium (ISM) and intracluster medium (ICM). Their plasma physical interactions with electromagnetic fields strongly influence their transport properties. Effective models which incorporate the microphysics of CR transport are needed to study the effects of CRs on their surrounding macrophysical media. Developing such models is challenging because of the conceptional, length-scale, and time-scale separation between the microscales of plasma physics and the macroscales of the environment. Hydrodynamical theories of CR transport achieve this by capturing the evolution of CR population in terms of statistical moments. In the well-established one-moment hydrodynamical model for CR transport, the dynamics of the entire CR population are described by a single statistical quantity such as the commonly used CR energy density. In this work, I develop a new hydrodynamical two-moment theory for CR transport that expands the well-established hydrodynamical model by including the CR energy flux as a second independent hydrodynamical quantity. I detail how this model accounts for the interaction between CRs and gyroresonant Alfvén waves. The small-scale magnetic fields associated with these Alfvén waves scatter CRs which fundamentally alters CR transport along large-scale magnetic field lines. This leads to the effects of CR streaming and diffusion which are both captured within the presented hydrodynamical theory. I use an Eddington-like approximation to close the hydrodynamical equations and investigate the accuracy of this closure-relation by comparing it to high-order approximations of CR transport. In addition, I develop a finite-volume scheme for the new hydrodynamical model and adapt it to the moving-mesh code Arepo. This scheme is applied using a simulation of a CR-driven galactic wind. I investigate how CRs launch the wind and perform a statistical analysis of CR transport properties inside the simulated circumgalactic medium (CGM). I show that the new hydrodynamical model can be used to explain the morphological appearance of a particular type of radio filamentary structures found inside the central molecular zone (CMZ). I argue that these harp-like features are synchrotron-radiating CRs which are injected into braided magnetic field lines by a point-like source such as a stellar wind of a massive star or a pulsar. Lastly, I present the finite-volume code Blinc that uses adaptive mesh refinement (AMR) techniques to perform simulations of radiation and magnetohydrodynamics (MHD). The mesh of Blinc is block-structured and represented in computer memory using a graph-based approach. I describe the implementation of the mesh graph and how a diffusion process is employed to achieve load balancing in parallel computing environments. Various test problems are used to verify the accuracy and robustness of the employed numerical algorithms.
We present the analysis of the optical variability of the early, nitrogen-rich Wolf-Rayet (WR) star WR 7. The analysis of multisector Transiting Exoplanet Survey Satellite (TESS) light curves and high-resolution spectroscopic observations confirm multiperiodic variability that is modulated on time-scales of years. We detect a dominant period of 2.6433 +/- 0.0005 d in the TESS sectors 33 and 34 light curves in addition to the previously reported high-frequency features from sector 7. We discuss the plausible mechanisms that may be responsible for such variability in WR 7, including pulsations, binarity, co-rotating interaction regions (CIRs), and clumpy winds. Given the lack of strong evidence for the presence of a stellar or compact companion, we suggest that WR 7 may pulsate in quasi-coherent modes in addition to wind variability likely caused by CIRs on top of stochastic low-frequency variability. WR 7 is certainly a worthy target for future monitoring in both spectroscopy and photometry to sample both the short (less than or similar to 1 d) and long (greater than or similar to 1000 d) variability time-scales.
Designing gentle sinusoidal nanotextures enables the realization of high-efficiency perovskite-silicon solar cells <br /> Perovskite-silicon tandem solar cells offer the possibility of overcoming the power conversion efficiency limit of conventional silicon solar cells. Various textured tandem devices have been presented aiming at improved optical performance, but optimizing film growth on surface-textured wafers remains challenging. Here we present perovskite-silicon tandem solar cells with periodic nanotextures that offer various advantages without compromising the material quality of solution-processed perovskite layers. We show a reduction in reflection losses in comparison to planar tandems, with the new devices being less sensitive to deviations from optimum layer thicknesses. The nanotextures also enable a greatly increased fabrication yield from 50% to 95%. Moreover, the open-circuit voltage is improved by 15 mV due to the enhanced optoelectronic properties of the perovskite top cell. Our optically advanced rear reflector with a dielectric buffer layer results in reduced parasitic absorption at near-infrared wavelengths. As a result, we demonstrate a certified power conversion efficiency of 29.80%.
In this paper we introduce a fractional variant of the characteristic function of a random variable. It exists on the whole real line, and is uniformly continuous. We show that fractional moments can be expressed in terms of Riemann-Liouville integrals and derivatives of the fractional characteristic function. The fractional moments are of interest in particular for distributions whose integer moments do not exist. Some illustrative examples for particular distributions are also presented.
We formulate a linear phase and frequency response theory for hyperbolic flows, which generalizes phase response theory for autonomous limit cycle oscillators to hyperbolic chaotic dynamics. The theory is based on a shadowing conjecture, stating the existence of a perturbed trajectory shadowing every unperturbed trajectory on the system attractor for any small enough perturbation of arbitrary duration and a corresponding unique time isomorphism, which we identify as phase such that phase shifts between the unperturbed trajectory and its perturbed shadow are well defined. The phase sensitivity function is the solution of an adjoint linear equation and can be used to estimate the average change of phase velocity to small time dependent or independent perturbations. These changes in frequency are experimentally accessible, giving a convenient way to define and measure phase response curves for chaotic oscillators. The shadowing trajectory and the phase can be constructed explicitly in the tangent space of an unperturbed trajectory using co-variant Lyapunov vectors. It can also be used to identify the limits of the regime of linear response.
The subsequent observing runs of the advanced gravitational-wave detector network will likely provide us with various gravitational-wave observations of binary neutron star systems. For an accurate interpretation of these detections, we need reliable gravitational-wave models. To test and to point out how existing models could be improved, we perform a set of high-resolution numerical relativity simulations for four different physical setups with mass ratios q = 1.25, 1.50, 1.75, 2.00, and total gravitational mass M = 2.7 M???. Each configuration is simulated with five different resolutions to allow a proper error assessment. Overall, we find approximately second-order converging results for the dominant (2,2) mode, but also the subdominant (2,1), (3,3), and (4,4) modes, while generally, the convergence order reduces slightly for an increasing mass ratio. Our simulations allow us to validate waveform models, where we find generally good agreement between state-of-the-art models and our data, and to prove that scaling relations for higher modes currently employed for binary black hole waveform modeling also apply for the tidal contribution. Finally, we also test if the current NRTidal model used to describe tidal effects is a valid description for high-mass-ratio systems. We hope that our simulation results can be used to further improve and test waveform models in preparation for the next observing runs.
The current paradigm of cosmic-ray (CR) origin states that the greater part of galactic CRs is produced by supernova remnants. The interaction of supernova ejecta with the interstellar medium after a supernova's explosions results in shocks responsible for CR acceleration via diffusive shock acceleration (DSA). We use particle-in-cell (PIC) simulations and a combined PIC-magnetohydrodynamic (PIC-MHD) technique to investigate whether DSA can occur in oblique high Mach number shocks. Using the PIC method, we follow the formation of the shock and determine the fraction of the particles that gets involved in DSA. With this result, we use PIC-MHD simulations to model the large-scale structure of the plasma and the magnetic field surrounding the shock and find out whether or not the reflected particles can generate upstream turbulence and trigger DSA. We find that the feasibility of this process in oblique shocks depends strongly on the Alfvenic Mach number, and the DSA process is more likely to be triggered at high Mach number shocks.
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.
Anomalous diffusion or, more generally, anomalous transport, with nonlinear dependence of the mean-squared displacement on the measurement time, is ubiquitous in nature. It has been observed in processes ranging from microscopic movement of molecules to macroscopic, large-scale paths of migrating birds. Using data from multiple empirical systems, spanning 12 orders of magnitude in length and 8 orders of magnitude in time, we employ a method to detect the individual underlying origins of anomalous diffusion and transport in the data. This method decomposes anomalous transport into three primary effects: long-range correlations (“Joseph effect”), fat-tailed probability density of increments (“Noah effect”), and nonstationarity (“Moses effect”). We show that such a decomposition of real-life data allows us to infer nontrivial behavioral predictions and to resolve open questions in the fields of single-particle tracking in living cells and movement ecology.
Anomalous diffusion or, more generally, anomalous transport, with nonlinear dependence of the mean-squared displacement on the measurement time, is ubiquitous in nature. It has been observed in processes ranging from microscopic movement of molecules to macroscopic, large-scale paths of migrating birds. Using data from multiple empirical systems, spanning 12 orders of magnitude in length and 8 orders of magnitude in time, we employ a method to detect the individual underlying origins of anomalous diffusion and transport in the data. This method decomposes anomalous transport into three primary effects: long-range correlations (“Joseph effect”), fat-tailed probability density of increments (“Noah effect”), and nonstationarity (“Moses effect”). We show that such a decomposition of real-life data allows us to infer nontrivial behavioral predictions and to resolve open questions in the fields of single-particle tracking in living cells and movement ecology.
The field of movement ecology has seen a rapid increase in high-resolution data in recent years, leading to the development of numerous statistical and numerical methods to analyse relocation trajectories. Data are often collected at the level of the individual and for long periods that may encompass a range of behaviours.
Here, we use the power spectral density (PSD) to characterise the random movement patterns of a black-winged kite (Elanus caeruleus) and a white stork (Ciconia ciconia). The tracks are first segmented and clustered into different behaviours (movement modes), and for each mode we measure the PSD and the ageing properties of the process.
For the foraging kite we find 1/f noise, previously reported in ecological systems mainly in the context of population dynamics, but not for movement data. We further suggest plausible models for each of the behavioural modes by comparing both the measured PSD exponents and the distribution of the single-trajectory PSD to known theoretical results and simulations.
We study a non-Markovian and nonstationary model of animal mobility incorporating both exploration and memory in the form of preferential returns. Exact results for the probability of visiting a given number of sites are derived and a practical WKB approximation to treat the nonstationary problem is developed. A mean-field version of this model, first suggested by Song et al., [Modelling the scaling properties of human mobility, Nat. Phys. 6, 818 (2010)] was shown to well describe human movement data. We show that our generalized model adequately describes empirical movement data of Egyptian fruit bats (Rousettus aegyptiacus) when accounting for interindividual variation in the population. We also study the probability of visiting any site a given number of times and derive a mean-field equation. Our analysis yields a remarkable phase transition occurring at preferential returns which scale linearly with past visits. Following empirical evidence, we suggest that this phase transition reflects a trade-off between extensive and intensive foraging modes.
How do near-bankruptcy events in the past affect the dynamics of stock-market prices in the future? Specifically, what are the long-time properties of a time-local exponential growth of stock-market prices under the influence of stochastically occurring economic crashes? Here, we derive the ensemble- and time-averaged properties of the respective "economic" or geometric Brownian motion (GBM) with a nonzero drift exposed to a Poissonian constant-rate price-restarting process of "resetting." We examine-based both on thorough analytical calculations and on findings from systematic stochastic computer simulations-the general situation of reset GBM with a nonzero [positive] drift and for all special cases emerging for varying parameters of drift, volatility, and reset rate in the model. We derive and summarize all short- and long-time dependencies for the mean-squared displacement (MSD), the variance, and the mean time-averaged MSD (TAMSD) of the process of Poisson-reset GBM under the conditions of both rare and frequent resetting. We consider three main regions of model parameters and categorize the crossovers between different functional behaviors of the statistical quantifiers of this process. The analytical relations are fully supported by the results of computer simulations. In particular, we obtain that Poisson-reset GBM is a nonergodic stochastic process, with generally MSD(Delta) not equal TAMSD(Delta) and Variance(Delta) not equal TAMSD(Delta) at short lag times Delta and for long trajectory lengths T. We investigate the behavior of the ergodicity-breaking parameter in each of the three regions of parameters and examine its dependence on the rate of reset at Delta/T << 1. Applications of these theoretical results to the analysis of prices of reset-containing options are pertinent.
We derive. the ensemble-and time-averaged mean-squared displacements (MSD, TAMSD) for Poisson-reset geometric Brownian motion (GBM), in agreement with simulations. We find MSD and TAMSD saturation for frequent resetting, quantify the spread of TAMSDs via the ergodicity-breaking parameter and compute distributions of prices. General MSD-TAMSD nonequivalence proves reset GBM nonergodic.
The increase in the performance of organic solar cells observed over the past few years has reinvigorated the search for a deeper understanding of the loss and extraction processes in this class of device. A detailed knowledge of the density of free charge carriers under different operating conditions and illumination intensities is a prerequisite to quantify the recombination and extraction dynamics. Differential charging techniques are a promising approach to experimentally obtain the charge carrier density under the aforementioned conditions. In particular, the combination of transient photovoltage and photocurrent as well as impedance and capacitance spectroscopy have been successfully used in past studies to determine the charge carrier density of organic solar cells. In this Tutorial, these experimental techniques will be discussed in detail, highlighting fundamental principles, practical considerations, necessary corrections, advantages, drawbacks, and ultimately their limitations. Relevant references introducing more advanced concepts will be provided as well. Therefore, the present Tutorial might act as an introduction and guideline aimed at new prospective users of these techniques as well as a point of reference for more experienced researchers. Published under an exclusive license by AIP Publishing.
A magnetic field modifies optical properties and provides valley splitting in a molybdenum disulfide (MoS2) monolayer.
Here we demonstrate a scalable approach to the epitaxial synthesis of MoS2 monolayer on a magnetic graphene/Co system.
Using spin- and angle-resolved photoemission spectroscopy we observe a magnetic proximity effect that causes a 20 meV spin-splitting at the (Gamma) over bar point and canting of spins at the (K) over bar point in the valence band toward the in-plane direction of cobalt magnetization.
Our density functional theory calculations reveal that the in-plane spin component at (K) over bar is localized on Co atoms in the valence band, while in the conduction band it is localized on the MoS2 layer.
The calculations also predict a 16 meV spin-splitting at the (Gamma) over bar point and 8 meV (K) over bar-(K) over bar' valley asymmetry for an out-of-plane magnetization. These findings suggest control over optical transitions in MoS2 via Co magnetization. Our estimations show that the magnetic proximity effect is equivalent to the action of the magnetic field as large as 100 T.
A task-based parallel elliptic solver for numerical relativity with discontinuous Galerkin methods
(2022)
Elliptic partial differential equations are ubiquitous in physics. In numerical relativity---the study of computational solutions to the Einstein field equations of general relativity---elliptic equations govern the initial data that seed every simulation of merging black holes and neutron stars. In the quest to produce detailed numerical simulations of these most cataclysmic astrophysical events in our Universe, numerical relativists resort to the vast computing power offered by current and future supercomputers. To leverage these computational resources, numerical codes for the time evolution of general-relativistic initial value problems are being developed with a renewed focus on parallelization and computational efficiency. Their capability to solve elliptic problems for accurate initial data must keep pace with the increasing detail of the simulations, but elliptic problems are traditionally hard to parallelize effectively.
In this thesis, I develop new numerical methods to solve elliptic partial differential equations on computing clusters, with a focus on initial data for orbiting black holes and neutron stars. I develop a discontinuous Galerkin scheme for a wide range of elliptic equations, and a stack of task-based parallel algorithms for their iterative solution. The resulting multigrid-Schwarz preconditioned Newton-Krylov elliptic solver proves capable of parallelizing over 200 million degrees of freedom to at least a few thousand cores, and already solves initial data for a black hole binary about ten times faster than the numerical relativity code SpEC. I also demonstrate the applicability of the new elliptic solver across physical disciplines, simulating the thermal noise in thin mirror coatings of interferometric gravitational-wave detectors to unprecedented accuracy. The elliptic solver is implemented in the new open-source SpECTRE numerical relativity code, and set up to support simulations of astrophysical scenarios for the emerging era of gravitational-wave and multimessenger astronomy.