The rapidly increasing congestion in the low Earth environment makes the modeling of uncertainty in atmospheric drag force a critical task, affecting space situational awareness (SSA) activities like the probability of collision estimation. A key element in atmospheric drag modeling is the assessment of uncertainty in the atmospheric drag coefficient estimate. While atmospheric drag coefficients for
space objects with known characteristics can be computed numerically, they suffer from large computational costs for practical applications. In this work, we use cost-effective data-driven stochastic methods for modeling the drag coefficients of objects in the low Earth orbit (LEO) region. The training data is generated using the numerical Test Particle Monte Carlo (TPMC) method. TPMC is simulated
with Cercignani–Lampis–Lord (CLL) gas-surface interaction (GSI) model. Mehta et al. [1] use a Gaussian process regression (GPR) model to predict satellite drag coefficient, but the authors did not estimate the predictive uncertainty. The first part of this research extends the work by Mehta et al. [1] by fitting a GPR model to the training data and performing predictive uncertainty estimation. The results of the Gaussian fit are then compared against a deep neural network (DNN) model aided by the Monte Carlo dropout approach. To the best of our knowledge, this is the first study to use the aforementioned stochastic deep learning algorithm to perform predictive uncertainty estimation of the estimated satellite drag coefficient.
Apart from the accuracy of the models, we also undertake the task of calibrating the models. Simulations are carried out for a spherical satellite followed by the Champ satellite. Finally, quantification of the effect of drag coefficient uncertainty on orbit prediction is carried out for different solar activity and geomagnetic
activity levels.
more »
« less
Boundary homogenization for patchy surfaces trapping patchy particles
Trapping diffusive particles at surfaces is a key step in many systems in chemical and biological physics. Trapping often occurs via reactive patches on the surface and/or the particle. The theory of boundary homogenization has been used in many prior works to estimate the effective trapping rate for such a system in the case that either (i) the surface is patchy and the particle is uniformly reactive or (ii) the particle is patchy and the surface is uniformly reactive. In this paper, we estimate the trapping rate for the case that the surface and the particle are both patchy. In particular, the particle diffuses translationally and rotationally and reacts with the surface when a patch on the particle contacts a patch on the surface. We first formulate a stochastic model and derive a five-dimensional partial differential equation describing the reaction time. We then use matched asymptotic analysis to derive the effective trapping rate, assuming that the patches are roughly evenly distributed and occupy a small fraction of the surface and the particle. This trapping rate involves the electrostatic capacitance of a four-dimensional duocylinder, which we compute using a kinetic Monte Carlo algorithm. We further use Brownian local time theory to derive a simple heuristic estimate of the trapping rate and show that it is remarkably close to the asymptotic estimate. Finally, we develop a kinetic Monte Carlo algorithm to simulate the full stochastic system and then use these simulations to confirm the accuracy of our trapping rate estimates and homogenization theory.
more »
« less
- NSF-PAR ID:
- 10421793
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 158
- Issue:
- 9
- ISSN:
- 0021-9606
- Page Range / eLocation ID:
- 094104
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
more » « less
Abstract Additive manufacturing, no longer reserved exclusively for prototyping components, can create parts with complex geometries and locally tailored properties. For example, multiple homogenous material sources can be used in different regions of a print or be mixed during printing to define properties locally. Additionally, heterogeneous composites provide an opportunity for another level of tuning properties through processing. For example, within particulate-filled polymer matrix composites before curing, the presence of an applied electric and/or magnetic fields can reorient filler particles and form hierarchical structures depending on the fields applied. Control of particle organization is important because effective material properties are highly dependent on the distribution of filler material within composites once cured. While previous work in homogenization and effective medium theories have determined properties based upon ideal analytic distributions of particle orientations and spatial location, this work expands upon these methods generating discrete distributions from quasi-Monte Carlo simulations of the electromagnetic processing event. Results of simulations provide predicted microarchitectures from which effective properties are determined via computational homogenization.
These particle dynamics simulations account for dielectric and magnetic forces and torques in addition to hydrodynamic forces and hard particle separation. As such, the distributions generated are processing field dependent. The effective properties for a composite represented by this distribution are determined via computational homogenization using finite element analysis (FEA). This provides a path from constituents, through processing parameters to effective material properties. In this work, we use these simulations in conjunction with a multi-objective optimization scheme to resolve the relationships between processing conditions and effective properties, to inform field-assisted additive manufacturing processes.
The constituent set providing the largest range of properties can be found using optimization techniques applied to the aforementioned simulation framework. This key information provides a recipe for tailoring properties for additive manufacturing design and production. For example, our simulation results show that stiffness for a 10% filler volume fraction can increase by 34% when aligned by an electric field as compared to a randomly distributed composite. The stiffness of this aligned sample is also 29% higher in the direction of the alignment than perpendicular to it, which only differs by 5% from the random case [1]. Understanding this behavior and accurately predicting composite properties is key to producing field processed composites and prints. Material property predictions compare favorably to effective medium theory and experimentation with trends in elastic and magnetic effective properties demonstrating the same anisotropic behavior as a result of applied field processing. This work will address the high computational expense of physics simulation based objective functions by using efficient algorithms and data structures. We will present an optimization framework using nested gradient searches for micro barium hexaferrite particles in a PDMS matrix, optimizing on composite magnetization to determine the volume fraction of filler that will provide the largest range of properties by varying the applied electric and magnetic fields.
-
The purpose of this work is to discuss the well-posedness theory of singular vortex patches. Our main results are of two types: well-posedness and ill-posedness. On the well-posedness side, we show that globally m m -fold symmetric vortex patches with corners emanating from the origin are globally well-posed in natural regularity classes as long as m ≥ 3. m\geq 3. In this case, all of the angles involved solve a closed ODE system which dictates the global-in-time dynamics of the corners and only depends on the initial locations and sizes of the corners. Along the way we obtain a global well-posedness result for a class of symmetric patches with boundary singular at the origin, which includes logarithmic spirals. On the ill-posedness side, we show that any other type of corner singularity in a vortex patch cannot evolve continuously in time except possibly when all corners involved have precisely the angle π 2 \frac {\pi }{2} for all time. Even in the case of vortex patches with corners of angle π 2 \frac {\pi }{2} or with corners which are only locally m m -fold symmetric, we prove that they are generically ill-posed. We expect that in these cases of ill-posedness, the vortex patches actually cusp immediately in a self-similar way and we derive some asymptotic models which may be useful in giving a more precise description of the dynamics. In a companion work from 2020 on singular vortex patches, we discuss the long-time behavior of symmetric vortex patches with corners and use them to construct patches on R 2 \mathbb {R}^2 with interesting dynamical behavior such as cusping and spiral formation in infinite time.more » « less
-
more » « less
Abstract Telescopic observations have detected an exosphere around Ceres, composed of either water vapor or its photolytic products. Proposed mechanisms for its formation include sublimation or sputtering from solar energetic particles of buried ice, surface ice, or an optically thin seasonal polar cap. We estimate the amount of water vapor produced by known exposures of water ice, detected in Dawn spacecraft image and spectral data and by ice exposures from subresolution impact craters. We use thermal and sublimation modeling to take into account slope, orientation, and, in the case of water ice within craters, shadowing due to crater walls. We use a Monte Carlo approach to calculate the number of ice‐exposing impacts, where they occur on Ceres' surface, and how long the ice within the impact crater remains bright (e.g., less than one monolayer of sublimation lag). We find that the observed water ice patches on Ceres could account for ~0.06 kg/s of water vapor to (with Oxo crater as the main contributor) and that ice‐exposing impacts that remain bright in appearance after one Ceres year supply 0.08–0.56 kg/s of vapor, depending on the regolith volume fraction of the ice. While water ice has not been detected to date at Occator crater, if it were present we find that Occator is unlikely to be a major contributor of vapor. We find a typical background water vapor production rate from all of Ceres, combining surface and buried ice, of about a few tenths of a kilogram per second.
-
We propose a bootstrap‐based calibrated projection procedure to build confidence intervals for single components and for smooth functions of a partially identified parameter vector in moment (in)equality models. The method controls asymptotic coverage uniformly over a large class of data generating processes. The extreme points of the calibrated projection confidence interval are obtained by extremizing the value of the function of interest subject to a proper relaxation of studentized sample analogs of the moment (in)equality conditions. The degree of relaxation, or critical level, is calibrated so that the function of θ , not θ itself, is uniformly asymptotically covered with prespecified probability. This calibration is based on repeatedly checking feasibility of linear programming problems, rendering it computationally attractive. Nonetheless, the program defining an extreme point of the confidence interval is generally nonlinear and potentially intricate. We provide an algorithm, based on the response surface method for global optimization, that approximates the solution rapidly and accurately, and we establish its rate of convergence. The algorithm is of independent interest for optimization problems with simple objectives and complicated constraints. An empirical application estimating an entry game illustrates the usefulness of the method. Monte Carlo simulations confirm the accuracy of the solution algorithm, the good statistical as well as computational performance of calibrated projection (including in comparison to other methods), and the algorithm's potential to greatly accelerate computation of other confidence intervals.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0135048
