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Report discusses methods for numerical simulation of Navier-Stokes equations of viscous, incompressible flow, with emphasis on pseudocompressibility method. Advanced computational techniques reviewed contribute to improved designs by rapidly providing detailed information about conditions at all points in flow fields of proposed designs.
A physical principle (more precisely, a principle that incorporates mathematical models used in physics) has been conceived as the basis of a method of generating randomness in Monte Carlo simulations. The principle eliminates the need for conventional random-number generators. The Monte Carlo simulation method is among the most powerful computational methods for solving high-dimensional problems in physics, chemistry, economics, and information processing. The Monte Carlo simulation method is especially effective for solving problems in which computational complexity increases exponentially with dimensionality. The main advantage of the Monte Carlo simulation method over other methods is that the demand on computational resources becomes independent of dimensionality. As augmented by the present principle, the Monte Carlo simulation method becomes an even more powerful computational method that is especially useful for solving problems associated with dynamics of fluids, planning, scheduling, and combinatorial optimization. The present principle is based on coupling of dynamical equations with the corresponding Liouville equation. The randomness is generated by non-Lipschitz instability of dynamics triggered and controlled by feedback from the Liouville equation. (In non-Lipschitz dynamics, the derivatives of solutions of the dynamical equations are not required to be bounded.)
Simulating molecules using the Variational Quantum Eigensolver method is one of the promising applications for NISQ-era quantum computers. Designing an efficient ansatz to represent the electronic wave function is crucial in such simulations. Standard unitary coupled-cluster with singles and doubles (UCCSD) ansatz tends to have a large number of insignificant terms that do not lower the energy of the system. In this work, we present a unitary selective coupled-cluster method, a way to construct a unitary coupled-cluster ansatz iteratively using a selection procedure with excitations up to fourth order. This approach uses the electronic Hamiltonian matrix elements and the amplitudes for excitations already present in the ansatz to find the important excitations of higher order and to add them to the ansatz. The important feature of the method is that it systematically reduces the energy error with increasing ansatz size for a set of test molecules. {The main advantage of the proposed method is that the effort to increase the ansatz does not require any additional measurements on a quantum computer.}
Manual flight control and emergency procedure task skill degradation was evaluated after time intervals of from 1 to 6 months. The tasks were associated with a simulated launch through the orbit insertion flight phase of a space vehicle. The results showed that acceptable flight control performance was retained for 2 months, rapidly deteriorating thereafter by a factor of 1.7 to 3.1 depending on the performance measure used. Procedural task performance showed unacceptable degradation after only 1 month, and exceeded an order of magnitude after 4 months. The effectiveness of static rehearsal (checklists and briefings) and dynamic warmup (simulator practice) retraining methods were compared for the two tasks. Static rehearsal effectively countered procedural skill degradation, while some combination of dynamic warmup appeared necessary for flight control skill retention. It was apparent that these differences between methods were not solely a function of task type or retraining method, but were a function of the performance measures used for each task.
Simulation of atmospheric turbulence as seen by a rotating blade element involves treatment of cyclostationary processes. Conventional filtering techniques do not lend themselves well to the generation of such turbulence sample functions as are required in rotorcraft flight dynamics simulation codes. A method to generate sample functions containing second order statistics of mean and covariance is presented. Compared to ensemble averaging involving excessive computer time, the novelty is to exploit cycloergodicity and thereby, replace ensemble averaging by averaging over a single path sample function of long duration. The method is validated by comparing its covariance results with the analytical and ensemble averaged results for a widely used 1-D turbulence approximation.
Simulation of atmospheric turbulence as seen by a rotating blade element involves treatment of cyclostationary processes. Conventional filtering techniques do not lend themselves well to the generation of such turbulence sample functions as are required in rotorcraft flight dynamics simulation codes. A method to generate sample functions containing second-order statistics of mean and covariance is presented. Compared to ensemble averaging involving excessive computer time, the novelty is to exploit cycloergodicity and thereby, replace ensemble averaging by averaging over a single-path sample function of long duration. The method is validated by comparing its covariance results with the analytical and ensemble-averaged results for a widely used one-dimensional turbulence approximation.
Method for simulating Van Allen belt proton energy spectra
Simulated strain-gage balance calibration data is used to compare the accuracy of two balance calibration model building methods for different noise environments and calibration experiment designs. The first building method obtains a math model for the analysis of balance calibration data after applying a candidate math model search algorithm to the calibration data set. The second building method uses stepwise regression analysis in order to construct a model for the analysis. Four balance calibration data sets were simulated in order to compare the accuracy of the two math model building methods. The simulated data sets were prepared using the traditional One Factor At a Time (OFAT) technique and the Modern Design of Experiments (MDOE) approach. Random and systematic errors were introduced in the simulated calibration data sets in order to study their influence on the math model building methods. Residuals of the fitted calibration responses and other statistical metrics were compared in order to evaluate the calibration models developed with different combinations of noise environment, experiment design, and model building method. Overall, predicted math models and residuals of both math model building methods show very good agreement. Significant differences in model quality were attributable to noise environment, experiment design, and their interaction. Generally, the addition of systematic error significantly degraded the quality of calibration models developed from OFAT data by either method, but MDOE experiment designs were more robust with respect to the introduction of a systematic component of the unexplained variance.
District cooling systems are widely used in urban residential communities in China. Most of such systems are oversized, which leads to wasted investment, low operational efficiency and, thus, waste of energy. The accurate prediction of district cooling loads that can support the rightsizing of cooling plant equipment remains a challenge. This study develops a novel stochastic modeling method that consists of (1) six prototype house models representing most apartments in a district, (2) occupant behavior models of residential buildings reflecting their spatial and temporal diversity as well as their complexity based on a large-scale residential survey in China, and (3) a stochastic sampling process to represent all apartments and occupants in the district. The stochastic method was applied to a case study using the Designer's Simulation Toolkit (DeST) to simulate the cooling loads of a residential district in Wuhan, China. The simulation results agreed well with the measured data based on five performance metrics representing the aggregated cooling consumption, the peak cooling loads, the spatial load distribution, the temporal load distribution and the load profiles. Two prevalent simulation methods were also employed to simulate the district cooling loads. Here, the results showed that oversimplified assumptions about occupant behavior could lead to significant overestimation of the peak cooling load and the total cooling loads in the district. Future work will aim to simplify the workflow and data requirements of the stochastic method for its application, and to explore its use in predicting district heating loads and in commercial or mixed-use districts.
The authors describe a computationally efficient and accurate method for simulating a dc SQUID's V-Phi (voltage-flux) and I-V characteristics which has proven valuable in evaluating and improving various SQUID readout methods. The simulation of the SQUID is based on fitting of previously acquired data from either a real or a modeled device using the Fourier transform of the V-Phi curve. This method does not predict SQUID behavior, but rather is a way of replicating a known behavior efficiently with portability into various simulation programs such as SPICE. The authors discuss the methods used to simulate the SQUID and the flux-locking control electronics, and present specific examples of this approach. Results include an estimate of the slew rate and linearity of a simple flux-locked loop using a characterized dc SQUID.
A fast and efficient method for simulating potential interactions between space objects is presented. The specialized hazard analysis simulation is run at the Russian Space Surveillance Center. It simulates the motion of objects in space and determines close encounters between these objects. First, ephemerides are predicted for all space objects over the time interval of concern. Second, using the predicted ephemerides, pairs of satellites that would likely collide are grouped together. Throughout the process, the pairs initially chosen are refined until all pairs of satellites are found which come within a certain miss distance of each other. In addition to the miss distance, other characteristics of the encounter including angle of incidence, relative velocity, type of approaching object, and probability of collision come out of the simulation. There are many potential applications of this simulation and its results to missing planning and mission safety. Artificial objects can be introduced to the simulation to examine potential encounters between the new objects and current objects for mission design applications. The simulation can be run many times to create data for statistical analysis of encounter parameters. These as well as many other potential applications are presented and discussed.
Purpose: This work presents the development of a phantom to verify the treatment planning system (TPS) algorithms used for high-dose-rate (HDR) brachytherapy. It is designed to measure the relative dose in a heterogeneous media. The experimental details used, simulation methods, and comparisons with a commercial TPS are also provided. Methods: To simulate heterogeneous conditions, four materials were used: Virtual Water™ (VM), BR50/50™, cork, and aluminum. The materials were arranged in 11 heterogeneity configurations. Three dosimeters were used to measure the relative response from a HDR {sup 192}Ir source: TLD-100™, Gafchromic{sup ®} EBT3 film, and an Exradin™ A1SL ionization chamber. To compare the results from the experimental measurements, the various configurations were modeled in the PENELOPE/penEasy Monte Carlo code. Images of each setup geometry were acquired from a CT scanner and imported into BrachyVision™ TPS software, which includes a grid-based Boltzmann solver Acuros™. The results of the measurements performed in the heterogeneous setups were normalized to the dose values measured in the homogeneous Virtual Water™ setup and the respective differences due to the heterogeneities were considered. Additionally, dose values calculated based on the American Association of Physicists in Medicine-Task Group 43 formalism were compared to dose values calculated with the Acuros™ algorithm in the phantom. Calculated doses were compared at the same points, where measurements have been performed. Results: Differences in the relative response as high as 11.5% were found from the homogeneous setup when the heterogeneous materials were inserted into the experimental phantom. The aluminum and cork materials produced larger differences than the plastic materials, with the BR50/50™ material producing results similar to the Virtual Water™ results. Our experimental methods agree with the PENELOPE/penEasy simulations for most setups and dosimeters. The TPS relative differences with the Acuros™ algorithm were similar in both experimental and simulated setups. The discrepancy between the BrachyVision™, Acuros™, and TG-43 dose responses in the phantom described by this work exceeded 12% for certain setups. Conclusions: The results derived from the phantom measurements show good agreement with the simulations and TPS calculations, using Acuros™ algorithm. Differences in the dose responses were evident in the experimental results when heterogeneous materials were introduced. These measurements prove the usefulness of the heterogeneous phantom for verification of HDR treatment planning systems based on model-based dose calculation algorithms.
As it evolves, aviation will continue to require integration of a wide range of safety systems and practices, some of which are already in place and others that are yet to be developed. New concepts in system safety thinking have emerged to consider not only what may go wrong, but also what can be learned when things go right during commercial flight operations. Taken together, these complementary perspectives form a more comprehensive approach to systemsafety thinking that can help to recognize and preserve the resilient performance capabilities currently provided by humans. A need exists, however, for research methods to enable better understanding of the human contributions to aviation safety. NASA’s System-Wide Safety Project supports research on using flight simulation methods to study operator resilience and safety-producing behaviors. Building on prior NASA efforts investigating procedural non-adherences during area navigation standard terminal route arrivals, a high-fidelity commercial aviation line operational simulation (LOS) experiment has been designed to study how flight crews anticipate, monitor for, respond to, and learn from expected and unexpected disturbances during these operations. A diverse set of LOS scenarios were developed to simulate highly realistic, complex, but routinely encountered operational situations. Each scenario provided multiple opportunities to collect data on how flight crews manage threats and errors, as well as novel opportunities to observe resilient and safety-producing behaviors. The experimental design, implications for the study of safety-producing behaviors using simulation, and considerations for airline pilot training will be discussed.
Purpose: Surgical procedures require dexterity, expertise and repetition to reach optimal patient outcomes. However, efficient training opportunities are usually limited. This work presents a simulator system with realistic haptic force-feedback and full, real-time ultrasounds image simulation. Methods: The simulator is composed of a custom-made Linear-DELTA force-feedback robotic platform. The needle tip is mounted on a force gauge at the end effector of the robot, which responds to needle insertion by providing reaction forces. 3D geometry of the tissue is using a tetrahedral finite element mesh (FEM) mimicking tissue properties. As the needle is inserted/retracted, tissue deformation is computed using a mass-tensor nonlinear visco-elastic FEM. The real-time deformation is fed to the L-DELTA to take into account the force imparted to the needle, providing feedback to the end-user when crossing tissue boundaries or needle bending. Real-time 2D US image is also generated synchronously showing anatomy, needle insertion and tissue deformation. The simulator is running on an Intel I7 6- core CPU at 3.26 MHz. 3D tissue rendering and ultrasound display are performed on a Windows 7 computer; the FEM computation and L-DELTA control are executed on a similar PC using the Neutrino real-time OS. Both machines communicate through an Ethernet link. Results: The system runs at 500 Hz for a 8333-tetrahedron tissue mesh and a 100-node angular spring needle model. This frame rate ensures a relatively smooth displacement of the needle when pushed or retracted (±20 N in all directions at speeds of up to 2 m/s). Unlike commercially-available haptic platforms, the oblong workspace of the L-DELTA robot complies with that required for brachytherapy needle displacements of 0.1m by 0.1m by 0.25m. Conclusion: We have demonstrated a real-life, realistic brachytherapy simulator developed for prostate implants (LDR/HDR). The platform could be adapted to other sites or training for other types of needle-based procedures.
Purpose: Scatter-to-primary ratio (SPR) is an important dosimetric quantity that describes the contribution from the scatter photons in an external photon beam. The purpose of this study is to develop an improved analytical formula to describe SPR as a function of circular field size (r) and depth (d) using Monte Carlo (MC) simulation. Methods: MC simulation was performed for Mohan photon spectra (Co-60, 4, 6, 10, 15, 23 MV) using EGSNRC code. Point-spread scatter dose kernels in water are generated. The scatter-to-primary ratio (SPR) is also calculated using MC simulation as a function of field size for circular field size with radius r and depth d. The doses from forward scatter and backscatter photons are calculated using a convolution of the point-spread scatter dose kernel and by accounting for scatter photons contributing to dose before (z' d) reaching the depth of interest, d, where z' is the location of scatter photons, respectively. The depth dependence of the ratio of the forward scatter and backscatter doses is determined as a function of depth and field size. Results: We are able to improve the existing 3-parameter (a, w, d0) empirical formula for SPR by introducing depth dependence for one of the parameter d0, which becomes 0 for deeper depths. The depth dependence of d0 can be directly calculated as a ratio of backscatter-to-forward scatter doses for otherwise the same field and depth. With the improved empirical formula, we can fit SPR for all megavoltage photon beams to within 2%. Existing 3-parameter formula cannot fit SPR data for Co-60 to better than 3.1%. Conclusion: An improved empirical formula is developed to fit SPR for all megavoltage photon energies to within 2%.
Purpose: This work proposes an accurate method for simulating dose reduction in digital mammography starting from a clinical image acquired with a standard dose. Methods: The method developed in this work consists of scaling a mammogram acquired at the standard radiation dose and adding signal-dependent noise. The algorithm accounts for specific issues relevant in digital mammography images, such as anisotropic noise, spatial variations in pixel gain, and the effect of dose reduction on the detective quantum efficiency. The scaling process takes into account the linearity of the system and the offset of the detector elements. The inserted noise is obtained by acquiring images of a flat-field phantom at the standard radiation dose and at the simulated dose. Using the Anscombe transformation, a relationship is created between the calculated noise mask and the scaled image, resulting in a clinical mammogram with the same noise and gray level characteristics as an image acquired at the lower-radiation dose. Results: The performance of the proposed algorithm was validated using real images acquired with an anthropomorphic breast phantom at four different doses, with five exposures for each dose and 256 nonoverlapping ROIs extracted from each image and with uniform images. The authors simulated lower-dose images and compared these with the real images. The authors evaluated the similarity between the normalized noise power spectrum (NNPS) and power spectrum (PS) of simulated images and real images acquired with the same dose. The maximum relative error was less than 2.5% for every ROI. The added noise was also evaluated by measuring the local variance in the real and simulated images. The relative average error for the local variance was smaller than 1%. Conclusions: A new method is proposed for simulating dose reduction in clinical mammograms. In this method, the dependency between image noise and image signal is addressed using a novel application of the Anscombe transformation. NNPS, PS, and local noise metrics confirm that this method is capable of precisely simulating various dose reductions.
Modeling and simulation are essential for predicting and verifying the behavior of fabricated quantum circuits, but existing simulation methods are either impractically costly or require an unrealistic simplification of error processes. In this paper, we present a method of simulating noisy Clifford circuits that is both accurate and practical in experimentally relevant regimes. In particular, the cost is weakly exponential in the size and the degree of non-Cliffordness of the circuit. Our approach is based on the construction of exact representations of quantum channels as quasiprobability distributions over stabilizer operations, which are then sampled, simulated, and weighted to yield unbiased statistical estimates of circuit outputs and other observables. As a demonstration of these techniques, we simulate a Steane [[7,1,3]]-encoded logical operation with non-Clifford errors and compute its fault tolerance error threshold. Finally, we expect that the method presented here will enable studies of much larger and more realistic quantum circuits than was previously possible.
Purpose: We evaluated the effect of very high-energy electron (VHEE) beam parameters on the planning of a lung cancer case by means of Monte Carlo simulations. Methods: We simulated VHEE radiotherapy plans using the EGSnrc/BEAMnrc-DOSXYZnrc code. We selected a lung cancer case that was treated with 6MV photon VMAT to be planned with VHEE. We studied the effect of beam energy (80 MeV, 100 MeV, and 120 MeV), number of equidistant beams (16 or 32), and beamlets sizes (3 mm, 5 mm or 7 mm) on PTV coverage, sparing of organs at risk (OARs) and dose conformity. Inverse-planning optimization was performed in a research version of RayStation (RaySearch Laboratories AB) using identical objective functions and constraints for all VHEE plans. Results: Similar PTV coverage and dose conformity was achieved by all the VHEE plans. The 100 MeV and 120 MeV VHEE plans were equivalent amongst them and were superior to the 80 MeV plan in terms of OARs sparing. The effect of using 16 or 32 equidistant beams was a mean difference in average dose of 2.4% (0%–7.7%) between the two plans. The use of 3 mm beamlet size systematically reduced the dose to all the OARs. Based on these results we selected the 100MeV-16beams-3mm-beamlet-size plan to compare it against VMAT. The selected VHEE plan was more conformal than VMAT and improved OAR sparing (heart and trachea received 125% and 177% lower dose, respectively) especially in the low-dose region. Conclusion: We determined the VHEE beam parameters that maximized the OAR dose sparing and dose conformity of the actually delivered VMAT plan of a lung cancer case. The selected parameters could be used for the planning of other treatment sites with similar size, shape, and location. For larger targets, a larger beamlet size might be used without significantly increasing the dose. B Palma: None. M Bazalova: None. B Hardemark: Employee, RaySearch Americas. E Hynning: Employee, RaySearch Americas. B Qu: None. B Loo Jr.: Research support, RaySearch, Varian. P Maxim: Research support, RaySearch, Varian.