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Diffusion with stochastic resetting is a paradigm of resetting processes. Standard renewal or master equation approach are typically used to study steady state and other transport properties such as average, mean squared displacement etc.
What remains less explored is the two time point correlation functions whose evaluation is often daunting since it requires the implementation of the exact time dependent probability density functions of the resetting processes which are unknown for most of the problems.
We adopt a different approach that allows us to write a stochastic solution for a single trajectory undergoing resetting.
Moments and the autocorrelation functions between any two times along the trajectory can then be computed directly using the laws of total expectation. Estimation of autocorrelation functions turns out to be pivotal for investigating the ergodic properties of various observables for this canonical model.
In particular, we investigate two observables (i) sample mean which is widely used in economics and (ii) time-averaged-mean-squared-displacement (TAMSD) which is of acute interest in physics.
We find that both diffusion and drift-diffusion processes with resetting are ergodic at the mean level unlike their reset-free counterparts. In contrast, resetting renders ergodicity breaking in the TAMSD while both the stochastic processes are ergodic when resetting is absent. We quantify these behaviors with detailed analytical study and corroborate with extensive numerical simulations.
Our results can be verified in experimental set-ups that can track single particle trajectories and thus have strong implications in understanding the physics of resetting.
Losses of radiation belt energetic particles by encounters with four of the inner Moons of Jupiter
(2022)
Based on an improved model of the moon absorption of Jovian radiation belt particles, we investigate quantitatively and comprehensively the absorption probabilities and particle lifetimes due to encounters with four of the inner moons of Jupiter (Amalthea, Thebe, Io, and Europa) inside L < 10. Our results demonstrate that the resultant average lifetimes of energetic protons and electrons vary dramatically between similar to 0.1 days and well above 1,000 days, showing a strong dependence on the particle equatorial pitch angle, kinetic energy and moon orbit. The average lifetimes of energetic protons and electrons against moon absorption are shortest for Io (i.e., similar to 0.1-10 days) and longest for Thebe (i.e., up to thousands of days), with the lifetimes in between for Europa and Amalthea. Due to the diploe tilt angle absorption effect, the average lifetimes of energetic protons and electrons vary markedly below and above alpha eq ${\alpha }_{\mathrm{e}\mathrm{q}}$ = 67 degrees. Overall, the average electron lifetimes exhibit weak pitch angle dependence, but the average proton lifetimes are strongly dependent on equatorial pitch angle. The average lifetimes of energetic protons decrease monotonically and substantially with the kinetic energy, but the average lifetimes of energetic electrons are roughly constant at energies <similar to 10 MeV, increase substantially around the Kepler velocities of the moons (similar to 10-50 MeV), and decrease quickly at even higher energies. Compared with the averaged electron lifetimes, the average proton lifetimes are longer at energies below a few MeV and shorter at energies above tens of MeV.
Context. The Large Magellanic Cloud (LMC) is the most luminous satellite galaxy of the Milky Way and, owing to its companion, the Small Magellanic Cloud (SMC), represents an excellent laboratory to study the interaction of dwarf galaxies. Aims. The aim of this study is to investigate the kinematics of the outer regions of the LMC by using stellar proper motions to understand the impact of interactions, for example with the SMC about 250 Myr ago. Methods. We calculate proper motions using multi-epoch K s -band images from the VISTA survey of the Magellanic Cloud system (VMC). Observations span a time baseline of 2-5 yr. We combine the VMC data with data from the Gaia Early Data Release 3 and introduce a new method to distinguish between Magellanic and Milky Way stars based on a machine learning algorithm. This new technique enables a larger and cleaner sample selection of fainter sources as it reaches below the red clump of the LMC. Results. We investigate the impact of the SMC on the rotational field of the LMC and find hints of stripped SMC debris. The southeastern region of the LMC shows a slow rotational speed compared to the overall rotation. N-body simulations suggest that this could be caused by a fraction of stripped SMC stars located in that particular region that move opposite to the expected rotation.
With the increasing sensitivity of gravitational-wave detectors, we expect to observe multiple binary neutron-star systems through gravitational waves in the near future. The combined analysis of these gravitational-wave signals offers the possibility to constrain the neutron-star radius and the equation of state of dense nuclear matter with unprecedented accuracy. However, it is crucial to ensure that uncertainties inherent in the gravitational-wave models will not lead to systematic biases when information from multiple detections is combined. To quantify waveform systematics, we perform an extensive simulation campaign of binary neutron-star sources and analyze them with a set of four different waveform models. For our analysis with 38 simulations, we find that statistical uncertainties in the neutron-star radius decrease to 1250 m (2% at 90% credible interval) but that systematic differences between currently employed waveform models can be twice as large. Hence, it will be essential to ensure that systematic biases will not become dominant in inferences of the neutron-star equation of state when capitalizing on future developments.
Numerical studies of the dynamics of gravitational systems, e.g., black hole-neutron star systems, require physical and constraint-satisfying initial data. In this article, we present the newly developed pseudospectral code ELLIPTICA, an infrastructure for construction of initial data for various binary and single gravitational systems of all kinds. The elliptic equations under consideration are solved on a single spatial hypersurface of the spacetime manifold. Using coordinate maps, the hypersurface is covered by patches whose boundaries can adapt to the surface of the compact objects. To solve elliptic equations with arbitrary boundary condition, ELLIPTICA deploys a Schur complement domain decomposition method with a direct solver. In this version, we use cubed sphere coordinate maps and the fields are expanded using Chebyshev polynomials of the first kind. Here, we explain the building blocks of ELLIPTICA and the initial data construction algorithm for a black hole-neutron star binary system. We perform convergence tests and evolve the data to validate our results. Within our framework, the neutron star can reach spin values close to breakup with arbitrary direction, while the black hole can have arbitrary spin with dimensionless spin magnitude ∼0.8.
The geomagnetic activity index Kp is widely used but is restricted by low time resolution (3-hourly) and an upper limit. To address this, new geomagnetic activity indices, Hpo, are introduced. Similar to Kp, Hpo expresses the level of planetary geomagnetic activity in units of thirds (0o, 0+, 1-, 1o, 1+, 2-, horizontal ellipsis ) based on the magnitude of geomagnetic disturbances observed at subauroral observatories. Hpo has a higher time resolution than Kp. 30-min (Hp30) and 60-min (Hp60) indices are produced. The frequency distribution of Hpo is designed to be similar to that of Kp so that Hpo may be used as a higher time-resolution alternative to Kp. Unlike Kp, which is capped at 9o, Hpo is an open-ended index and thus can characterize severe geomagnetic storms more accurately. Hp30, Hp60 and corresponding linearly scaled ap30 and ap60 are available, in near real time, at the GFZ website (https://www.gfz-potsdam.de/en/hpo-index).
We perform numerical studies of a thermally driven, overdamped particle in a random quenched force field, known as the Sinai model. We compare the unbounded motion on an infinite 1-dimensional domain to the motion in bounded domains with reflecting boundaries and show that the unbounded motion is at every time close to the equilibrium state of a finite system of growing size. This is due to time scale separation: inside wells of the random potential, there is relatively fast equilibration, while the motion across major potential barriers is ultraslow. Quantities studied by us are the time dependent mean squared displacement, the time dependent mean energy of an ensemble of particles, and the time dependent entropy of the probability distribution. Using a very fast numerical algorithm, we can explore times up top 10(17) steps and thereby also study finite-time crossover phenomena.
Recent observations have revealed remarkable insights into the gas reservoir in the circumgalactic medium (CGM) of galaxy haloes. In this paper, we characterise the gas in the vicinity of Milky Way and Andromeda analogues in the hestia (High resolution Environmental Simulations of The Immediate Area) suite of constrained Local Group (LG) simulations. The hestia suite comprise of a set of three high-resolution arepo-based simulations of the LG, run using the Auriga galaxy formation model.
For this paper, we focus only on the 𝑧 = 0 simulation datasets and generate mock skymaps along with a power spectrum analysis to show that the distributions of ions tracing low-temperature gas (H i and Si iii) are more clumpy in comparison to warmer gas tracers (O vi, O vii and O viii). We compare to the spectroscopic CGM observations of M31 and low-redshift galaxies.
hestia under-produces the column densities of the M31 observations, but the simulations are consistent with the observations of low-redshift galaxies. A possible explanation for these findings is that the spectroscopic observations of M31 are contaminated by gas residing in the CGM of the Milky Way.
Non-fullerene acceptors (NFAs) as used in state-of-the-art organic solar cells feature highly crystalline layers that go along with low energetic disorder.
Here, the crucial role of energetic disorder in blends of the donor polymer PM6 with two Y-series NFAs, Y6, and N4 is studied.
By performing temperature-dependent charge transport and recombination studies, a consistent picture of the shape of the density of state distributions for free charges in the two blends is developed, allowing an analytical description of the dependence of the open-circuit voltage V-OC on temperature and illumination intensity.
Disorder is found to influence the value of the V-OC at room temperature, but also its progression with temperature. Here, the PM6:Y6 blend benefits substantially from its narrower state distributions.
The analysis also shows that the energy of the equilibrated free charge population is well below the energy of the NFA singlet excitons for both blends and possibly below the energy of the populated charge transfer manifold, indicating a down-hill driving force for free charge formation.
It is concluded that energetic disorder of charge-separated states has to be considered in the analysis of the photovoltaic properties, even for the more ordered PM6:Y6 blend.
The formation of large polarons has been proposed as reason for the high defect tolerance, low mobility, low charge carrier trapping, and low nonradiative recombination rates of lead halide perovskites. Recently, direct evidence for large-polaron formation has been reported from a 50% effective mass enhancement in angle-resolved photoemission of CsPbBr3 over theory for the orthorhombic structure. We present in-depth band dispersion measurements of CsPbBr3 and GW calculations, which lead to similar effective masses at the valence band maximum of 0.203 1 0.016 m0 in experiment and 0.226 m0 in orthorhombic theory. We argue that the effective mass can be explained solely on the basis of electron-electron correlation and largepolaron formation cannot be concluded from photoemission data.