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We demonstrate deterministic two-qudit gates using the time and frequency degrees of freedom of a single photon, showing the potential of our scheme for deterministic quantum computing in high-dimensional Hilbert spaces.
In the article, we model deterministic broadband (-7.5 Hz) ground motion from an M w 7.1 bilateral strike-slip earthquake scenario with dynamic rupture propagation along a rough-fault topography embedded in a medium including small-scale velocity and density perturbations. Spectral accelerations (SAs) at periods 0.2-3 s and Arias intensity durations show a similar distance decay (at the level of 1-2 interevent standard deviations above the median) when compared to Next Generation Attenuation-West2 (NGA)-West2 ground-motion prediction equations (GMPEs) using a Q(f) power-law exponent of 0.6-0.8 above 1 Hz in models with a minimum V S of 750 m/s. With a trade-off from Q(f), the median ground motion is slightly increased by scattering from statistical models of small-scale heterogeneity with standard deviation (σ) of the perturbations at the lower end of the observed range (5%) but reduced by scattering attenuation at the upper end (10%) when using a realistic 3D background velocity model. The ground-motion variability is strongly affected by the addition of small-scale media heterogeneity, reducing otherwise large values of intraevent standard deviation closer to those of empirical observations. These simulations generally have intraevent standard deviations for SAs lower than the GMPEs for the modeled bandwidth, with an increasing trend with distance (most pronounced in low-to-moderate scattering media) near the level of observations at distances greater than 35 km from the fault. Durations for the models follow the same increasing trend with distance, in which σ~5% produces the best match to GMPE values. We find that a 3D background-velocity model reduces the pulse period into the expected range by breaking up coherent waves from directivity, generating a lognormal distribution of ground-motion residuals. These results indicate that a strongly heterogeneous medium is needed to produce realistic deterministic broadband ground motions. Finally, the addition of a thin surficial layer with low, frequency-independent Q in the model (with a minimum V S of 750 m/s) controls the high-frequency decay in energy, as measured by the parameter κ, that may be necessary to include as simulations continue to extend to higher frequencies.
There is growing interest to extend low-rank matrix decompositions to multi-way arrays, or tensors. One fundamental low-rank tensor decomposition is the canonical polyadic decomposition (CPD). The challenge of fitting a low-rank, nonnegative CPD model to Poisson-distributed count data is of particular interest. Several popular algorithms use local search methods to approximate the global maximum likelihood estimator from local minima. Simultaneously, a recent trend in theoretical computer science and numerical linear algebra leverages randomization to solve very large, hard problems. The typical approach is to use randomization for a fast approximation and determinism for refinement to yield effective algorithms with theoretical guarantees. Two popular algorithms for Poisson CPD reflect that emergent dichotomy: CP Alternating Poisson Regression is a deterministic algorithm and Generalized Canonical Polyadic decomposition makes use of stochastic algorithms in several variants. This work extends recent work to develop two new methods that leverage randomized and deterministic algorithms for improved accuracy and performance.
We propose a deterministic sampling framework using Score-Based Transport Modeling for sampling an unnormalized target density π given only its score ∇ log π. Our method approximates the Wasserstein gradient flow on KL($f_t$∥π) by learning the time-varying score ∇ log $f_t$ on the fly using score matching. While having the same marginal distribution as Langevin dynamics, our method produces smooth deterministic trajectories, resulting in monotone noise-free convergence. We prove that our method dissipates relative entropy at the same rate as the exact gradient flow, provided sufficient training. Numerical experiments validate our theoretical findings: our method converges at the optimal rate, has smooth trajectories, and is often more sample efficient than its stochastic counterpart. Experiments on high-dimensional image data show that our method produces high-quality generations in as few as 15 steps and exhibits natural exploratory behavior. The memory and runtime scale linearly in the sample size.
Abstract. This work considers the characteristics and drivers of the loads experienced by wind turbine main bearings. Simplified load response models of two different hub and main-bearing configurations are presented, representative of both inverting direct-drive and four-point-mounted geared drivetrains. The influences of deterministic wind field characteristics, such as wind speed, shear, yaw offset, and veer, on the bearing load patterns are then investigated for similarity scaled 5, 7.5, and 10 MW reference wind turbine models. Main-bearing load response in cases of deterministic gusts and extreme changes in wind direction are also considered for the 5 MW model. Perhaps surprisingly, veer is identified as an important driver of main-bearing load fluctuations. Upscaling results indicate that similar behaviour holds as turbines become larger, but with mean loads and load fluctuation levels increasing at least cubically with the turbine rotor radius. Strong links between turbine control and main-bearing load response are also observed.
Block encoding of discrete, memoryless sources with equiprobable outputs subject to a fidelity criterion is discussed. The encoder is assumed to be deterministic and a lower bound is derived on the amount of computational work required to encode such sources as a function of the code rate and fidelity of the encoding. An example is given to show that the bound cannot be substantially improved. These bounds apply primarily to sources and distortion measures which are such that the minimum distortion given by the rate-distortion bound is not achievable with a finite block length, deterministic encoder.
A technique is presented by which deterministic optimization techniques, for example, the maximum principle of Pontriagin, can be applied to stochastic optimal control problems formulated around linear systems with Gaussian noises and general cost criteria. Using this technique, the stochastic nature of the problem is suppressed but for two expectation operations, the optimization being deterministic. The use of the technique in treating problems with quadratic and nonquadratic costs is illustrated.
Two wind profiles were determined from STS-1 entry flight data based on preliminary best estimate trajectory (BET). The deterministic process used in deriving the atmospheric winds requires inertial estimates of the spacecraft angle-of-attack (alpha) and side-slip angle (beta) from the BET in conjunction with some air data system measurements of the actual angles. The current orbiter air data system (OADS) provides the necessary alpha information. Two beta profiles were adopted. The first profile assumed that the spacecraft would weathervane into any prevailing wind. The second assumed a conservative side-slip history computed from measured accelerations in the spacecraft body axes. It is shown that there are no major differences between the deterministic winds computed using both methods. Further, comparisons of these winds with raw measurements from Tehachapi, California, and preliminary winds obtained from the LaRC LAIRS file and the JSC/TRW descent BET are presented.
A simple mass-spring model is used to systematically examine the dynamical behavior introduced by fault zone heterogeneities. The model consists of two sliding blocks coupled to each other and to a constant velocity driver by elastic springs. The state of this system can be characterized by the positions of the two blocks relative to the driver. A simple static/dynamic friction law is used. When the system is symmetric, cyclic behavior is observed. For an asymmetric system, where the frictional forces for the two blocks are not equal, the solutions exhibit deterministic chaos. Chaotic windows occur repeatedly between regions of limit cycles on bifurcation diagrams. The model behavior is similar to that of the one-dimensional logistic map. The results provide substantial evidence that earthquakes are an example of deterministic chaos.
The three-dimensional viscous flow in a low speed centrifugal compressor stage is simulated using an average passage Navier-Stokes analysis. The impeller discharge flow is of the jet/wake type with low momentum fluid in the shroud-pressure side corner coincident with the tip leakage vortex. This nonuniformity introduces periodic unsteadiness in the vane frame of reference. The effect of such deterministic unsteadiness on the time-mean is included in the analysis through the average passage stress, which allows the analysis of blade row interactions. The magnitude of the divergence of the deterministic unsteady stress is of the order of the divergence of the Reynolds stress over most of the span, from the impeller trailing edge to the vane throat. Although the potential effects on the blade trailing edge from the diffuser vane are small, strong secondary flows generated by the impeller degrade the performance of the diffuser vanes.
Petri nets augmented with timing specifications gained a wide acceptance in the area of performance and reliability evaluation of complex systems exhibiting concurrency, synchronization, and conflicts. The state space of time-extended Petri nets is mapped onto its basic underlying stochastic process, which can be shown to be Markovian under the assumption of exponentially distributed firing times. The integration of exponentially and non-exponentially distributed timing is still one of the major problems for the analysis and was first attacked for continuous time Petri nets at the cost of structural or analytical restrictions. We propose a discrete deterministic and stochastic Petri net (DDSPN) formalism with no imposed structural or analytical restrictions where transitions can fire either in zero time or according to arbitrary firing times that can be represented as the time to absorption in a finite absorbing discrete time Markov chain (DTMC). Exponentially distributed firing times are then approximated arbitrarily well by geometric distributions. Deterministic firing times are a special case of the geometric distribution. The underlying stochastic process of a DDSPN is then also a DTMC, from which the transient and stationary solution can be obtained by standard techniques. A comprehensive algorithm and some state space reduction techniques for the analysis of DDSPNs are presented comprising the automatic detection of conflicts and confusions, which removes a major obstacle for the analysis of discrete time models.
The cause of the long-suspected excessive conservatism in the prevailing structural deterministic safety factor has been identified as an inherent violation of the error propagation laws when reducing statistical data to deterministic values and then combining them algebraically through successive structural computational processes. These errors are restricted to the applied stress computations, and because mean and variations of the tolerance limit format are added, the errors are positive, serially cumulative, and excessively conservative. Reliability methods circumvent these errors and provide more efficient and uniform safe structures. The document is a tutorial on the deficiencies and nature of the current safety factor and of its improvement and transition to absolute reliability.
Simulation of unsteady viscous turbomachinery flowfields is presently impractical as a design tool due to the long run times required. Designers rely predominantly on steady-state simulations, but these simulations do not account for some of the important unsteady flow physics. Unsteady flow effects can be modeled as source terms in the steady flow equations. These source terms, referred to as Lumped Deterministic Stresses (LDS), can be used to drive steady flow solution procedures to reproduce the time-average of an unsteady flow solution. The goal of this work is to investigate the feasibility of using inviscid lumped deterministic stresses to model unsteady combustion hot streak migration effects on the turbine blade tip and outer air seal heat loads using a steady computational approach. The LDS model is obtained from an unsteady inviscid calculation. The LDS model is then used with a steady viscous computation to simulate the time-averaged viscous solution. Both two-dimensional and three-dimensional applications are examined. The inviscid LDS model produces good results for the two-dimensional case and requires less than 10% of the CPU time of the unsteady viscous run. For the three-dimensional case, the LDS model does a good job of reproducing the time-averaged viscous temperature migration and separation as well as heat load on the outer air seal at a CPU cost that is 25% of that of an unsteady viscous computation.
A computationally effective method is described to evaluate the non-deterministic dynamic instability (probabilistic dynamic buckling) of thin composite shells. The method is a judicious combination of available computer codes for finite element, composite mechanics, and probabilistic structural analysis. The solution method is incrementally updated Lagrangian. It is illustrated by applying it to thin composite cylindrical shell subjected to dynamic loads. Both deterministic and probabilistic buckling loads are evaluated to demonstrate the effectiveness of the method. A universal plot is obtained for the specific shell that can be used to approximate buckling loads for different load rates and different probability levels. Results from this plot show that the faster the rate, the higher the buckling load and the shorter the time. The lower the probability, the lower is the buckling load for a specific time. Probabilistic sensitivity results show that the ply thickness, the fiber volume ratio and the fiber longitudinal modulus, dynamic load and loading rate are the dominant uncertainties, in that order.
The NCRP has recently defined RBE values and a new quantity (Gy-Eq) for use in estimation of deterministic effects in space shielding and operations. The NCRP's RBE for neutrons is left ambiguous and not fully defined. In the present report we will suggest a complete definition of neutron RBE consistent with the NCRP recommendations and evaluate attenuation properties of deterministic effects (Gy-Eq) in comparison with other dosimetric quantities.
In an effort to manufacture high-angular-resolution, grazing-incidence, x-ray optics, Marshall Space Flight Center (MSFC) is taking measures to improve its electroformed replicated optics. A key development is the use of computer-numerical control (CNC) polishing to deterministically improve the surface of electroless nickel mandrels used to replicate grazing- incidence optics. Metrology, control software and polishing parameters must function together seamlessly to reach the specifications required to replicate sub-arcsecond optics. Each change in polishing parameters effects the wear pattern of the polishing head. Using Richardson-Lucy deconvolution, the controller software fits the wear pattern to metrology data to calculate the changing feedrates across the mandrel. Here we present an overview of our process, and early results showing the effectiveness of deterministic polishing for replicated optics.
With today's petascale supercomputers, applications often exhibit low efficiency, such as poor communication and I/O performance, that can be diagnosed by analysis tools. However, these tools either produce extremely large trace files that complicate performance analysis, or sacrifice accuracy to collect high-level statistical information using crude averaging. This work contributes Scala-H-Trace, which features more aggressive trace compression than any previous approach, particularly for applications that do not show strict regularity in SPMD behavior. Scala-H-Trace uses histograms expressing the probabilistic distribution of arbitrary communication and I/O parameters to capture variations. Yet, where other tools fail to scale, Scala-H-Trace guarantees trace files of near constant size, even for variable communication and I/O patterns, producing trace files orders of magnitudes smaller than using prior approaches. We demonstrate the ability to collect traces of applications running on thousands of processors with the potential to scale well beyond this level. We further present the first approach to deterministically replay such probabilistic traces (a) without deadlocks and (b) in a manner closely resembling the original applications. Our results show either near constant sized traces or only sub-linear increases in trace file sizes irrespective of the number of nodes utilized. Even with the aggressively compressed histogram-based traces, our replay times are within 12% to 15% of the runtime of original codes. Such concise traces resembling the behavior of production-style codes closely and our approach of deterministic replay of probabilistic traces are without precedence.
There has been increasing interest in using Quantitative Risk Assessment [QRA] to help improve the safety of hydrogen infrastructure and applications. Hydrogen infrastructure for transportation (e.g. fueling fuel cell vehicles) or stationary (e.g. back-up power) applications is a relatively new area for application of QRA vs. traditional industrial production and use, and as a result there are few tools designed to enable QRA for this emerging sector. There are few existing QRA tools containing models that have been developed and validated for use in small-scale hydrogen applications. However, in the past several years, there has been significant progress in developing and validating deterministic physical and engineering models for hydrogen dispersion, ignition, and flame behavior. In parallel, there has been progress in developing defensible probabilistic models for the occurrence of events such as hydrogen release and ignition. While models and data are available, using this information is difficult due to a lack of readily available tools for integrating deterministic and probabilistic components into a single analysis framework. This paper discusses the first steps in building an integrated toolkit for performing QRA on hydrogen transportation technologies and suggests directions for extending the toolkit.