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Results for “Stochastic Numerical Methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 577 records · Page 32
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DOE OSTI2018

A Langevin approach to multi-scale modeling

In plasmas, distribution functions often demonstrate long anisotropic tails or otherwise significant deviations from local Maxwellians. The tails, especially if they are pulled out from the bulk, pose a serious challenge for numerical simulations as resolving both the bulk and the tail on the same mesh is often challenging. A multi-scale approach, providing evolution equations for the bulk and the tail individually, could offer a resolution in the sense that both populations could be treated on separate meshes or different reduction techniques applied to the bulk and the tail population. In this paper, we propose a multi-scale method which allows us to split a distribution function into a bulk and a tail so that both populations remain genuine, non-negative distribution functions and may carry density, momentum, and energy. The proposed method is based on the observation that the motion of an individual test particle in a plasma obeys a stochastic differential equation, also referred to as a Langevin equation. Finally, this allows us to define transition probabilities between the bulk and the tail and to provide evolution equations for both populations separately.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Stochastic properties of ultralight scalar field gradients

Ultralight axion-like particles are well-motivated dark matter candidates that are the target of numerous direct detection efforts. In the vicinity of the Solar System, such particles can be treated as oscillating scalar fields. The velocity dispersion of the Milky Way determines a coherence time of about 10 6 oscillations, beyond which the amplitude of the axion field fluctuates stochastically. Any analysis of data from an axion direct detection experiment must carefully account for this stochastic behavior to properly interpret the results. This is especially true for experiments sensitive to the gradient of the axion field that are unable to collect data for many coherence times. Indeed, the direction, in addition to the amplitude, of the axion field gradient fluctuates stochastically. We present the first complete stochastic treatment for the gradient of the axion field, including multiple computationally efficient methods for performing likelihood-based data analysis, which can be applied to any axion signal, regardless of coherence time. Additionally, we demonstrate that ignoring the stochastic behavior of the gradient of the axion field can potentially result in failure to discover a true axion signal

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

A hybrid embedded discrete fracture model for simulating tight porous media with complex fracture systems

Numerical simulation considering complex fracture networks in tight oil reservoir becomes a hot issue during these years. Recently, embedded discrete fracture model (EDFM) shows great advantages over the DFM approaches in both calculation efficiency and simplicity of simulation workflow. EDFM has been widely used in tight oil/gas natural energy or enhanced oil recovery (EOR) development. If a large number of small-scale natural fractures exist in reservoir, the calculation efficiency of EDFM method may decrease. A new hybrid simulation model combining the EDFM and dual porosity (DP) model is proposed. The large-scale fractures are dealt with EDFM method while small scale fractures are dealt with DP model. Considering the low permeability of matrix, transient transfer between matrix and natural fracture is considered. The proposed hybrid model is validated compared with the local grid refinement (LGR) model and EDFM-MINC model, and the difference between transient transfer and pseudo-steady-state transfer effect on production is presented. Finally, two test cases are presented, and the sensitivity of some key parameters are investigated. Result shows that the new simulation model has higher calculation efficiency than LGR and EDFM-MINC models. Meanwhile, it honors a good accuracy. The pseudo-steady-state transfer between matrix and natural fracture leads to big error in tight oil production performance analysis both in single phase and two phases flow. Low matrix permeability and big matrix size increase the production difference between pseudo-steady-state transfer and transient transfer models. The proposed model can simulate reservoirs considering stochastic permeability distribution.

58 GEOSCIENCES↗
DOE OSTI2014

TU-F-BRF-08: Intensity Modulation Expanded to Spatio-Temporal Space; IMRT Combined with Optimal Fractionation Schedule

Purpose: Past efforts to improve the therapeutic ratio have focused on a spatial approach where highly conformal radiation dose is given to tumors while minimizing dose to normal tissues, e.g., IMRT, VMAT, and IGRT. However, the fractionation schedule, i.e., a temporal approach to radiotherapy, has been largely overlooked so far in maximizing the therapeutic ratio. We establish a rigorous mathematical spatio-temporal approach to systematically investigate the feasibility and potential benefits of simultaneously optimizing radiation dose distribution in space and time. Methods: Stochastic control formalism is constructed to maximize the average tumor BED by choosing an optimal radiation dose distribution for an optimal number of fractions subject to normal tissue BED constraints. Three separate simulations are run on two groups of phantom cases; 5 cases with prostate cancer and 5 cases with head-and-neck cancer. (1) Conventional IMRT with 70Gy/35fx for head-and-neck, and 81Gy/45fx for prostate, (2) IMRT is done independently from the fractionation schedule optimization (S-model), (3) integrated spatio-temporal approach (I-model) where radiation intensities are simultaneously optimized for the first time ever in space and time. Final tumor BEDs from the three trials are compared in prostate and head-and-neck cases. Results: Numerical simulations show that final tumor BED from I-model is 20–90% larger than conventional IMRT, and 20-50% larger than S-model for head-and-neck cancer with α/β=10 and Tdouble=2–50 days. Final tumor BED from I-model is also 90–140% larger than conventional IMRT, and 20–30% larger than S-model for prostate cancer with α/β=2 and Tdouble=5–80 days. Conclusion: Our spatio-temporal optimization of radiotherapy allows an expansion of search space for the optimal treatment plans to include the temporal distribution of radiation dose in addition to the spatial distribution. Such spatio-temporal approach shows great potential to improve the therapeutic ratio, particularly with fast growing, aggressive tumors with short doubling time and/or low α/β.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

Perspective: Explicitly correlated electronic structure theory for complex systems

The explicitly correlated approach is one of the most important breakthroughs in ab initio electronic structure theory, providing arguably the most compact, accurate, and efficient ansatz for describing the correlated motion of electrons. Since Hylleraas first used an explicitly correlated wave function for the He atom in 1929, numerous attempts have been made to tackle the significant challenges involved in constructing practical explicitly correlated methods that are applicable to larger systems. These include identifying suitable mathematical forms of a correlated wave function and an efficient evaluation of many-electron integrals. R12 theory, which employs the resolution of the identity approximation, emerged in 1985, followed by the introduction of novel correlation factors and wave function ansätze, leading to the establishment of F12 theory in the 2000s. Rapid progress in recent years has significantly extended the application range of explicitly correlated theory, offering the potential of an accurate wave-function treatment of complex systems such as photosystems and semiconductors. In conclusion, this perspective surveys explicitly correlated electronic structure theory, with an emphasis on recent stochastic and deterministic approaches that hold significant promise for applications to large and complex systems including solids.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Uncertainty quantification for Multiphase-CFD simulations of bubbly flows: a machine learning-based Bayesian approach supported by high-resolution experiments

In this paper, we developed a machine learning-based Bayesian approach to inversely quantify and reduce the uncertainties of multiphase computational fluid dynamics (MCFD) simulations for bubbly flows. The proposed approach is supported by high-resolution two-phase flow measurements, including those by double-sensor conductivity probes, high-speed imaging, and particle image velocimetry. Local distributions of key physical quantities of interest (QoIs), including the void fraction and phasic velocities, are obtained to support the Bayesian inference. In the process, the epistemic uncertainties of the closure relations are inversely quantified while the aleatory uncertainties from stochastic fluctuations of the system are evaluated based on experimental uncertainty analysis. The combined uncertainties are then propagated through the MCFD solver to obtain uncertainties of the QoIs, based on which probability-boxes are constructed for validation. The proposed approach relies on three machine learning methods: feedforward neural networks and principal component analysis for surrogate modeling, and Gaussian processes for model form uncertainty modeling. The whole process is implemented within the framework of an open-source deep learning library PyTorch with graphics processing unit (GPU) acceleration, thus ensuring the efficiency of the computation. The results demonstrate that with the support of high-resolution data, the uncertainties of MCFD simulations can be significantly reduced. The proposed approach has the potential for other applications that involve numerical models with empirical parameters.

42 ENGINEERING↗
DOE OSTI2014

A hybrid inventory management system respondingto regular demand and surge demand

This paper proposes a hybrid policy for a stochastic inventory system facing regular demand and surge demand. The combination of two different demand patterns can be observed in many areas, such as healthcare inventory and humanitarian supply chain management. The surge demand has a lower arrival rate but higher demand volume per arrival. The solution approach proposed in this paper incorporates the level crossing method and mixed integer programming technique to optimize the hybrid inventory policy with both regular orders and emergency orders. The level crossing method is applied to obtain the equilibrium distributions of inventory levels under a given policy. The model is further transformed into a mixed integer program to identify an optimal hybrid policy. A sensitivity analysis is conducted to investigate the impact of parameters on the optimal inventory policy and minimum cost. Numerical results clearly show the benefit of using the proposed hybrid inventory model. The model and solution approach could help healthcare providers or humanitarian logistics providers in managing their emergency supplies in responding to surge demands.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2013

Tracking control of colloidal particles through non-homogeneous stationary flows

We consider the problem of controlling the trajectory of a single colloidal particle in a fluid with steady non-homogeneous flow. We use a Langevin equation to describe the dynamics of this particle, where the friction term is assumed to be given by the Faxén's Theorem for the force on a sphere immersed in a stationary flow. We use this description to propose an explicit control force field to be applied on the particle such that it will follow asymptotically any given desired trajectory, starting from an arbitrary initial condition. We show that the dynamics of the controlled particle can be mapped into a set of stochastic harmonic oscillators and that the velocity gradient of the solvent induces an asymmetric coupling between them. We study the particular case of a Brownian particle controlled through a plane Couette flow and show explicitly that the velocity gradient of the solvent renders the dynamics non-stationary and non-reversible in time. We quantify this effect in terms of the correlation functions for the position of the controlled particle, which turn out to exhibit contributions depending exclusively on the non-equilibrium character of the state of the solvent. In order to test the validity of our model, we perform simulations of the controlled particle moving in a simple shear flow, using a hybrid method combining molecular dynamics and multi-particle collision dynamics. We confirm numerically that the proposed guiding force allows for controlling the trajectory of the micro-sized particle by obligating it to follow diverse specific trajectories in fluids with homogeneous shear rates of different strengths. In addition, we find that the non-equilibrium correlation functions in simulations exhibit the same qualitative behavior predicted by the model, thus revealing the presence of the asymmetric non-equilibrium coupling mechanism induced by the velocity gradient.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

A parallel discrete dislocation dynamics/kinetic Monte Carlo method to study non-conservative plastic processes

Non-conservative processes play a fundamental role in plasticity and are behind important macroscopic phenomena such as creep, dynamic strain aging, loop raft formation, etc. In the most general case, vacancy-induced dislocation climb is the operating unit mechanism. While dislocation/vacancy interactions have been modeled in the literature using a variety of methods, the approaches developed rely on continuum descriptions of both the vacancy population and its fluxes. However, there are numerous situations in physics where point defect populations display heterogeneous concentrations and/or non-smooth kinetics. Here, a kinetic Monte Carlo (kMC) approach for modeling vacancy transport in response to arbitrary stress fields is used. Vacancies are treated as point particles and are coupled to the dislocation substructure representing a deformed material via an advection term defined by the local stress gradients. The stress fields and the dislocation substructure are evolved using a discrete dislocation dynamics (DDD) module. To extend the coupled model to the treatment of large systems, we have implemented it in the massively-parallel DDD code ParaDiS. To avoid numerical incompatibilities associated with merging deterministic (DDD) and stochastic (kMC) integration algorithms, we cast the entire elasto-plastic-diffusive problem within a single stochastic framework, taking advantage of a parallel kMC algorithm to evolve the system as a single event-driven process. The large-scale implementation enables the study of the evolution of a variety of dislocation-defect scenarios governed by non-conservative transport kinetics. After carrying out an exhaustive numerical and computational analysis of our parallel algorithm, we show results that emphasize situations where inhomogeneous vacancy dynamics are of relevance, and compare discrete kinetics to continuum solutions for several cases.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Quantitative Constraints on the Reionization History from the IGM Damping Wing Signature in Two Quasars at z > 7

During reionization, neutral hydrogen in the intergalactic medium (IGM) imprints a damping wing absorption feature on the spectrum of high-redshift quasars. A detection of this signature provides compelling evidence for a significantly neutral universe, and enables measurements of the hydrogen neutral fraction x HI (z) at that epoch. Obtaining reliable quantitative constraints from this technique, however, is challenging due to stochasticity induced by the patchy inside-out topology of reionization, degeneracies with quasar lifetime, and the unknown unabsorbed quasar spectrum close to rest-frame Lyα. Here, we combine a large-volume semi-numerical simulation of reionization topology with 1D radiative transfer through high-resolution hydrodynamical simulations of the high-redshift universe to construct models of quasar transmission spectra during reionization. Our state-of-the-art approach captures the distribution of damping wing strengths in biased quasar halos that should have reionized earlier, as well as the erosion of neutral gas in the quasar environment caused by its own ionizing radiation. Combining this detailed model with our new technique for predicting the quasar continuum and its associated uncertainty, we introduce a Bayesian statistical method to jointly constrain the neutral fraction of the universe and the quasar lifetime from individual quasar spectra. We apply this methodology to the spectra of the two quasars with the highest redshifts known, ULAS J1120+0641 and ULAS J1342+0928, and measure volume-averaged neutral fractions {x HI }(Z = 7.09) = 0.48 $+0.26\atop{-0.26}$and {x HI }(Z = 7.54) = 0.60 $+0.20\atop{-0.23}$ (posterior medians and 68% credible intervals) when marginalized over quasar lifetimes of 10 3 ≤ t q ≤ 10 8 yr.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Bayesian inferences of electrical current delivered to shocked transmission lines

Small radius Bdot measurements of electrical current delivered by pulsed power devices are routinely compromised by electrode/convolute plasmas endemic to multiterawatt transmission lines. Inferences of delivered current unaffected by these issues have recently been obtained by numerically optimizing consistency between model predictions and local experimental velocimetry data, but these are only unique for shockless velocity profiles. In the paper we describe a more general Bayesian method capable of inferring current despite the presence of shocks. Additionally, we describe uncertainty estimates and use of the technique on experimental data. This technique is the first to provide uncertainty estimates on the full current trace delivered to an inertial confinement fusion target.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Testing of Strategies for the Acceleration of the Cost Optimization

The general problem addressed in the Nuclear-Renewable Hybrid Energy System (N-R HES) project is finding the optimum economical dispatch (ED) and capacity planning solutions for the hybrid energy systems. In the present test-problem configuration, the N-R HES unit is composed of three electrical power-generating components, i.e. the Balance of Plant (BOP), the Secondary Energy Source (SES), and the Energy Storage (ES). In addition, there is an Industrial Process (IP), which is devoted to hydrogen generation. At this preliminary stage, the goal is to find the power outputs of each one of the N-R HES unit components (BOP, SES, ES) and the IP hydrogen production level that maximizes the unit profit by simultaneously satisfying individual component operational constraints. The optimization problem is meant to be solved in the Risk Analysis Virtual Environment (RAVEN) framework. The dynamic response of the N-R HES unit components is simulated by using dedicated object-oriented models written in the Modelica modeling language. Though this code coupling provides for very accurate predictions, the ensuing optimization problem is characterized by a very large number of solution variables. To ease the computational burden and to improve the path to a converged solution, a method to better estimate the initial guess for the optimization problem solution was developed. The proposed approach led to the definition of a suitable Monte Carlo-based optimization algorithm (called the preconditioner), which provides an initial guess for the optimal N-R HES power dispatch and the optimal installed capacity for each one of the unit components. The preconditioner samples a set of stochastic power scenarios for each one of the N-R HES unit components, and then for each of them the corresponding value of a suitably defined cost function is evaluated. After having simulated a sufficient number of power histories, the configuration which ensures the highest profit is selected as the optimal one. The component physical dynamics are represented through suitable ramp constraints, which considerably simplify the numerical solving. In order to test the capabilities of the proposed approach, in the present report, the dispatch problem only is tackled, i.e. a reference unit configuration is assumed, and each one of the N-R HES unit components is assumed to have a fixed installed capacity. As for the next steps, the main improvement will concern the operation strategy of the ES facility. In particular, in order to describe a more realistic battery commitment strategy, the ES operation will be regulated according to the electricity price forecasts.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2013

Dynamic phasing of multichannel cw laser radiation by means of a stochastic gradient algorithm

The phasing of a multichannel laser beam by means of an iterative stochastic parallel gradient (SPG) algorithm has been numerically and experimentally investigated. The operation of the SPG algorithm is simulated, the acceptable range of amplitudes of probe phase shifts is found, and the algorithm parameters at which the desired Strehl number can be obtained with a minimum number of iterations are determined. An experimental bench with phase modulators based on lithium niobate, which are controlled by a multichannel electronic unit with a real-time microcontroller, has been designed. Phasing of 16 cw laser beams at a system response bandwidth of 3.7 kHz and phase thermal distortions in a frequency band of about 10 Hz is experimentally demonstrated. The experimental data are in complete agreement with the calculation results. (control of laser radiation parameters)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

A Comparative Study Using Numerical Methods for Surface X Ray Doses with Conventional and Digital Radiology Equipment in Pediatric Radiology

The place of the study is a pediatrics clinic which realizes a great variety of emergency, ambulatory ad hospital examinations. The radiology compartment respects work procedures and a system to ensure the quality of X ray examinations. The results show a constant for the programmator of the digital detector machine for the tension applied to the tube. For the screen-film detector machine the applied tension increases proportionally with the physical development of the child considering the trunk thickness.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2015

Resource-efficient generation of linear cluster states by linear optics with postselection

Here we report on theoretical research in photonic cluster-state computing. Finding optimal schemes of generating non-classical photonic states is of critical importance for this field as physically implementable photon-photon entangling operations are currently limited to measurement-assisted stochastic transformations. A critical parameter for assessing the efficiency of such transformations is the success probability of a desired measurement outcome. At present there are several experimental groups that are capable of generating multi-photon cluster states carrying more than eight qubits. Separate photonic qubits or small clusters can be fused into a single cluster state by a probabilistic optical CZ gate conditioned on simultaneous detection of all photons with 1/9 success probability for each gate. This design mechanically follows the original theoretical scheme of cluster state generation proposed more than a decade ago by Raussendorf, Browne, and Briegel. The optimality of the destructive CZ gate in application to linear optical cluster state generation has not been analyzed previously. Our results reveal that this method is far from the optimal one. Employing numerical optimization we have identified that the maximal success probability of fusing n unentangled dual-rail optical qubits into a linear cluster state is equal to 1/2 n-1 ; an m-tuple of photonic Bell pair states, commonly generated via spontaneous parametric down-conversion, can be fused into a single cluster with the maximal success probability of 1/4 m-1 .

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Exact and efficient hybrid Monte Carlo algorithm for accelerated Bayesian inference of gene expression models from snapshots of single-cell transcripts

Single cells exhibit a significant amount of variability in transcript levels, which arises from slow, stochastic transitions between gene expression states. Elucidating the nature of these states and understanding how transition rates are affected by different regulatory mechanisms require state-of-the-art methods to infer underlying models of gene expression from single cell data. A Bayesian approach to statistical inference is the most suitable method for model selection and uncertainty quantification of kinetic parameters using small data sets. However, this approach is impractical because current algorithms are too slow to handle typical models of gene expression. To solve this problem, we first show that time-dependent mRNA distributions of discrete-state models of gene expression are dynamic Poisson mixtures, whose mixing kernels are characterized by a piecewise deterministic Markov process. Here, we combined this analytical result with a kinetic Monte Carlo algorithm to create a hybrid numerical method that accelerates the calculation of time-dependent mRNA distributions by 1000-fold compared to current methods. We then integrated the hybrid algorithm into an existing Monte Carlo sampler to estimate the Bayesian posterior distribution of many different, competing models in a reasonable amount of time. We demonstrate that kinetic parameters can be reasonably constrained for modestly sampled data sets if the model is known a priori. If there are many competing models, Bayesian evidence can rigorously quantify the likelihood of a model relative to other models from the data. We demonstrate that Bayesian evidence selects the true model and outperforms approximate metrics typically used for model selection.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2015

A novel SPH method for sedimentation in a turbulent fluid

A novel method for simulating sedimentation is described and applied to the sedimentation of dust in a turbulent fluid. We assume the dust grains are sufficiently numerous that they may be treated as a fluid and modelled by SPH particles. A different set of SPH particles describes the fluid. The equations of motion are therefore similar to those of Monaghan and Kocharyan [14] with the exception that the sedimentation of dust onto a solid surface is treated as if the surface mimics a sink for the dust fluid. The continuity equation for the dust then contains a sink term that can be modelled in the SPH formulation by allowing the mass of each SPH dust particle to decrease when it is sufficiently close to the boundary. We apply this method both to sedimentation in a nearly static fluid, and to sedimentation in a turbulent fluid. In the latter case we produce the turbulence by both a mechanical stirrer and by a stochastic algorithm. Our results agree very closely with the experiments of Martin and Nokes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Monte Carlo based investigation of Berry phase for depth resolved characterization of biomedical scattering samples

The propagation of light in turbid media is an active area of research with relevance to numerous investigational fields, e.g., biomedical diagnostics and therapeutics. The statistical random-walk nature of photon propagation through turbid media is ideal for computational based modeling and simulation. Ready access to super computing resources provide a means for attaining brute force solutions to stochastic light-matter interactions entailing scattering by facilitating timely propagation of sufficient (>10million) photons while tracking characteristic parameters based on the incorporated physics of the problem. One such model that works well for isotropic but fails for anisotropic scatter, which is the case for many biomedical sample scattering problems, is the diffusion approximation. In this report, we address this by utilizing Berry phase (BP) evolution as a means for capturing anisotropic scattering characteristics of samples in the preceding depth where the diffusion approximation fails. We extend the polarization sensitive Monte Carlo method of Ramella-Roman, et al.,1 to include the computationally intensive tracking of photon trajectory in addition to polarization state at every scattering event. To speed-up the computations, which entail the appropriate rotations of reference frames, the code was parallelized using OpenMP. The results presented reveal that BP is strongly correlated to the photon penetration depth, thus potentiating the possibility of polarimetric depth resolved characterization of highly scattering samples, e.g., biological tissues.

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