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At least 991 records · Page 55

Measurement incompatibility and Schrödinger-Einstein-Podolsky-Rosen steering in a class of probabilistic theories

Steering is one of the most counter intuitive non-classical features of bipartite quantum system, first noticed by Schrödinger at the early days of quantum theory. On the other hand, measurement incompatibility is another non-classical feature of quantum theory, initially pointed out by Bohr. Recently, Quintino et al. [Phys. Rev. Lett. 113, 160402 (2014)] and Uola et al. [Phys. Rev. Lett. 113, 160403 (2014)] have investigated the relation between these two distinct non-classical features. They have shown that a set of measurements is not jointly measurable (i.e., incompatible) if and only if they can be used for demonstrating Schrödinger-Einstein-Podolsky-Rosen steering. The concept of steering has been generalized for more general abstract tensor product theories rather than just Hilbert space quantum mechanics. In this article, we discuss that the notion of measurement incompatibility can be extended for general probability theories. Further, we show that the connection between steering and measurement incompatibility holds in a border class of tensor product theories rather than just quantum theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Probabilistic modeling and prediction of out-of-plane unidirectional composite lamina properties

Computational simulation provides an efficient means to predict the behavior of customized hybrid material configurations using validated, physics-based models. One limitation to this approach is the quality and quantity of available data to characterize the many constituent input properties. Therefore, a systematic approach to identify the most influential parameters on the hybrid behavior and quantify the corresponding uncertainty in predictive capabilities is required. Here, an approach using Bayesian multimodel inference and imprecise global sensitivity analysis is presented to investigate the effects of sparse constituent data on the prediction of composite material properties. The methodology allows the identification, using quantified uncertainties, of the most influential constituent material parameters for specified homogenized properties. This sensitivity analysis further enables a dimension reduction when assessing the influence of uncertainties on material properties and can be used to inform testing programs of the constituent properties that require additional testing/data collection in order to minimize uncertainty in macro-scale composite properties. The methodology is specifically demonstrated on the prediction and sensitivity analysis of out-of-plane mechanical properties of a unidirectional lamina.

36 MATERIALS SCIENCE↗

PROBABILISTIC MODEL OF BEAM–PLASMA INTERACTION IN RANDOMLY INHOMOGENEOUS PLASMA

We propose a new model that describes beam–plasma interaction in the presence of random density fluctuations with a known probability distribution. We use the property that, for the given frequency, the probability distribution of the density fluctuations uniquely determines the probability distribution of the phase velocity of waves. We present the system as discrete and consisting of small, equal spatial intervals with a linear density profile. This approach allows one to estimate variations in wave energy density and particle velocity, depending on the density gradient on any small spatial interval. Because the characteristic time for the evolution of the electron distribution function and the wave energy is much longer than the time required for a single wave–particle resonant interaction over a small interval, we determine the description for the relaxation process in terms of averaged quantities. We derive a system of equations, similar to the quasi-linear approximation, with the conventional velocity diffusion coefficient D and the wave growth rate γ replaced by the average in phase space, by making use of the probability distribution for phase velocities and by assuming that the interaction in each interval is independent of previous interactions. Functions D and γ are completely determined by the distribution function for the amplitudes of the fluctuations. For the Gaussian distribution of the density fluctuations, we show that the relaxation process is determined by the ratio of beam velocity to plasma thermal velocity, the dispersion of the fluctuations, and the width of the beam in the velocity space.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

CLASSIFYING X-RAY BINARIES: A PROBABILISTIC APPROACH

In X-ray binary star systems consisting of a compact object that accretes material from an orbiting secondary star, there is no straightforward means to decide whether the compact object is a black hole or a neutron star. To assist in this process, we develop a Bayesian statistical model that makes use of the fact that X-ray binary systems appear to cluster based on their compact object type when viewed from a three-dimensional coordinate system derived from X-ray spectral data where the first coordinate is the ratio of counts in the mid- to low-energy band (color 1), the second coordinate is the ratio of counts in the high- to low-energy band (color 2), and the third coordinate is the sum of counts in all three bands. We use this model to estimate the probabilities of an X-ray binary system containing a black hole, non-pulsing neutron star, or pulsing neutron star. In particular, we utilize a latent variable model in which the latent variables follow a Gaussian process prior distribution, and hence we are able to induce the spatial correlation which we believe exists between systems of the same type. The utility of this approach is demonstrated by the accurate prediction of system types using Rossi X-ray Timing Explorer All Sky Monitor data, but it is not flawless. In particular, non-pulsing neutron systems containing “bursters” that are close to the boundary demarcating systems containing black holes tend to be classified as black hole systems. As a byproduct of our analyses, we provide the astronomer with the public R code which can be used to predict the compact object type of XRBs given training data.

79 ASTRONOMY AND ASTROPHYSICS↗

Thermal Overloading Risk Mitigation With a Semi-Analytical Probabilistic Model on Branch Current

A semi-analytical formulation is presented in this paper for the probability computation of branch current in multiphase systems. The developed formula is derived based on the linear power flow model in rectangular coordinates. The system uncertainty injections can be renewable energy resources or loads and are modeled using a Gaussian mixture model (GMM). The developed formula can be used to compute the line current violation probability as well as integrate into optimal power flow problem as chance-constraint relaxation. Here, the proposed formula is first compared with the Matlab embedded numerical integration function to show its performance. Besides, the semi-analytical formula is validated and compared with the Monte Carlo simulation method using the IEEE 123-bus system, EPRI Ckt5, and Ckt7 systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Using probabilistic criteria in an assessment of the potential radiological consequences of the decommissioning of a nuclear research reactor

In order to assess the risk of radiological consequences of incidents and accidents in nuclear facilities it is important to contemplate their frequency of occurrence. It has to be shown that incidents and accidents occur sufficiently seldom according to their radiological consequences i. e. the occurrence frequency of radiological doses has to be limited. This is even demanded by the German radiation protection ordinance (StrlSchV), which says that in nuclear facilities other than nuclear power plants (NPP) in operation and for decommissioning, the occurrence frequency of incidents and accidents shall be contemplated in order to prove the design of safety measures and safety installations. Based on the ideas of the ICRP64, we developed a risk based assessment concept for nuclear facilities, which fulfils the requirements of the German regulations concerning dose limits in normal operation and design basis accidents. The general use of the concept is dedicated to nuclear facilities other than nuclear power plants (NPP) in operation and for decommissioning, where the regulation of risk assessment is less sophisticated. The concept specifies occurrence frequency limits for radiation exposure dose ranges, i. e. the occurrence frequency of incidents and accidents has to be limited according to their radiological effects. To apply this concept, scenarios of incidents and accidents are grouped in exposition classes according to their resulting potential effective dose to members of the general public. The occurrence frequencies of the incidents and accidents are summarized in each exposition class whereas the sum must not exceed the frequency limits mentioned above. In the following we introduce the application of this concept in the assessment of the potential radiological consequences of the decommissioning of a nuclear research reactor. We carried out this assessment for the licensing process of the decommissioning on behalf of German authorities. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Probabilistic estimates of the number of cosmic strings

The dependences of the mean expected number of cosmic strings on their redshift up to the surface of last scattering have been derived. The calculations are based on the geometric probability of a straight string segment crossing a given field and on information about the absence of strings when they are searched for via their gravitational lensing effects in optical catalogs. It is shown that there are no strings for redshifts 0 < z < 1.954, but the expected number of strings for 0 < z < 5 can be no more than 2.1 Multiplication-Sign 10{sup 3} at the 95% confidence level. The expected number of strings for redshifts up to z = 1100 can be no more than 2.4 Multiplication-Sign 10{sup 4} at the 95% confidence level. The latter estimate is sensitive to a priori information about the absence of cosmic strings in the redshift range 0 < z < 1.954 in a field of 4.48 square degrees in optical catalogs; it is smaller than the estimate without allowance for this information by 6%.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Probabilistic modeling of the indoor climates of residential buildings using EnergyPlus

The indoor air temperature and relative humidity in residential buildings significantly affect material moisture durability, HVAC system performance, and occupant comfort. Therefore, indoor climate data is generally required to define boundary conditions in numerical models that evaluate envelope durability and equipment performance. However, indoor climate data obtained from field studies is influenced by weather, occupant behavior and internal loads, and is generally unrepresentative of the residential building stock. Likewise, whole-building simulation models typically neglect stochastic variables and yield deterministic results that are applicable to only a single home in a specific climate. The

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

SAPHIRE 8 Basics An Introduction to Probabilistic Risk Assessment via the Systems Analysis Program for Hands-On Integrated Reliability Evaluations (SAPHIRE) Software P-201

The SAPHIRE Basics course material is intended to both (1) provide guidance for learning SAPHIRE during the Basics class and (2) become a stand-alone reference document after finishing the class. Thus, the format for the class material is a combination of the traditional “overhead-type” of presentation information with a structured, reference-type document.

97 MATHEMATICS AND COMPUTING↗

Advanced SAPHIRE 8 Modeling Methods for Probabilistic Risk Assessment via the Systems Analysis Program for Hands-On Integrated Reliability Evaluations (SAPHIRE) Software P-202

1.1. Overview of the Advanced SAPHIRE Material The Advanced SAPHIRE course material is intended to both (1) provide guidance for learning advanced SAPHIRE features during the class and (2) become a stand-alone reference document after finishing the class. Thus, the format for the class material is a combination of the traditional “overhead-type” of presentation information with a structured, reference-type document. Major topics that are covered in the Advanced SAPHIRE class include: Advanced data base concepts such as Model Type (e.g., random, seismic, fire, flood). Definition of house events and how they are used on a sequence-by-sequence basis to manipulate individual fault tree logic using sequence flag sets or fault tree flag sets. ? Basic event templates, compound basic event equation editors, and human error worksheets. A rule-based event tree top event substitution feature (called the Link Event Tree Rule Editor) which allows for top event substitutions. A rule-based cut set post-processing feature (called the Recovery Rules) which allows cut set manipulation. Cut set analysis based upon rule-based end state categories (called End State Analysis). Cut set generation options for both fault trees and event tree sequences. The large event tree methodology and how SAPHIRE can be used to generate sequence cut sets for this method. The transfer of data between SAPHIRE data bases and between other PRA codes (MAR-D).

97 MATHEMATICS AND COMPUTING↗

Integrated Fire Probabilistic Risk Assessment (PRA) Modeling in Support of Operational Efficiency (Final Report)

To improve the realism of Fire PRA associated with fire progression and damage modeling or manual suppression, previous research by the Socio-Technical Risk Analysis (SoTeRiA) Research Laboratory at the University of Illinois at Urbana-Champaign focused on the development of an Integrated PRA (I-PRA) methodological framework for fire risk analysis in NPPs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Probabilistic Assembly of a Ball Screw

The assembly of ball screws is considered theoretically and experimentally in the case where the screw and nut are combined with an optimal combination of systematic and random errors in the screw pitch (optimal pitch error ratio).

42 ENGINEERING↗

PROBABILISTIC CROSS-IDENTIFICATION IN CROWDED FIELDS AS AN ASSIGNMENT PROBLEM

One of the outstanding challenges of cross-identification is multiplicity: detections in crowded regions of the sky are often linked to more than one candidate associations of similar likelihoods. We map the resulting maximum likelihood partitioning to the fundamental assignment problem of discrete mathematics and efficiently solve the two-way catalog-level matching in the realm of combinatorial optimization using the so-called Hungarian algorithm. We introduce the method, demonstrate its performance in a mock universe where the true associations are known, and discuss the applicability of the new procedure to large surveys.

79 ASTRONOMY AND ASTROPHYSICS↗