An overview on Single Apparatus Quantum Measurements

Given the state of a quantum system, one can calculate the expectation value of any observable of the system. However, the inverse problem of determining the state by performing different measurements is not a trivial task. In various experimental setups it is reasonably straightforward to reconstruct the state of a quantum system employing linear tomographic technique. In this way the elements of the density matrix can be linearly related to a set of measured quantities. But since different observables of a quantum system are not commuting with each other, one often has to perform series of successive measurements of observables which cannot be done simultaneously. Simultaneous measurement of observables cost less time and energy and is more beneficial. In this paper we review the strategy of quantum state tomography with simultaneous measurement of commuting observables. This can be done by introducing an assistant system of which the state is known. We show that the interaction between the assistant and the system of interest within different frame works allows the reconstruction of the state of the system. Specifically, we consider a two-level system and reconstruct its initial state by introducing an assistant which can be either another two-level system or a single cavity mode of the electromagnetic field.Comment: 11 pages, to be appear in journal of computational and theoretical nanoscienc

Uncertainty-Integrated Surrogate Modeling for Complex System Optimization

Approximation models such as surrogate models provide a tractable substitute to expensive physical simulations and an effective solution to the potential lack of quantitative models of system behavior. These capabilities not only enable the efficient design of complex systems, but is also essential for the effective analysis of physical phenomena/characteristics in the different domains of Engineering, Material Science, Biomedical Science, and various other disciplines. Since these models provide an abstraction of the real system behavior (often a low-fidelity representative) it is important to quantify the accuracy and the reliability of such approximation models without investing additional expensive system evaluations (simulations or physical experiments). Standard error measures, such as the mean squared error, the cross-validation error, and the Akaike\u27s information criterion however provide limited (often inadequate) information regarding the accuracy of the final surrogate model while other more effective dedicated error measures are tailored towards only one class of surrogate models. This lack of accuracy information and the ability to compare and test diverse surrogate models reduce the confidence in model application, restricts appropriate model selection, and undermines the effectiveness of surrogate-based optimization. A key contribution of this dissertation is the development of a new model-independent approach to quantify the fidelity of a trained surrogate model in a given region of the design domain. This method is called the Predictive Estimation of Model Fidelity (PEMF). The PEMF method is derived from the hypothesis that the accuracy of an approximation model is related to the amount of data resources leveraged to train the model . In PEMF, intermediate surrogate models are iteratively constructed over heuristic subsets of sample points. The median and the maximum errors estimated over the remaining points are used to determine the respective error distributions at each iteration. The estimated modes of the error distributions are represented as functions of the density of intermediate training points through nonlinear regression, assuming a smooth decreasing trend of errors with increasing sample density. These regression functions are then used to predict the expected median and maximum errors in the final surrogate models. It is observed that the model fidelities estimated by PEMF are up to two orders of magnitude more accurate and statistically more stable compared to those based on the popularly-used leave-one-out cross-validation method, when applied to a variety of benchmark problems. By leveraging this new paradigm in quantifying the fidelity of surrogate models, a novel automated surrogate model selection framework is also developed. This PEMF-based model selection framework is called the Concurrent Surrogate Model Selection (COSMOS). COSMOS, unlike existing model selection methods, coherently operates at all the three levels necessary to facilitate optimal selection, i.e., (1) selecting the model type, (2) selecting the kernel function type, and (3) determining the optimal values of the typically user-prescribed parameters. The selection criteria that guide optimal model selection are determined by PEMF and the search process is performed using a MINLP solver. The effectiveness of COSMOS is demonstrated by successfully applying it to different benchmark and practical engineering problems, where it offers a first-of-its-kind globally competitive model selection. In this dissertation, the knowledge about the accuracy of a surrogate estimated using PEMF is applied to also develop a novel model management approach for engineering optimization. This approach adaptively selects computational models (both physics-based models and surrogate models) of differing levels of fidelity and computational cost, to be used during optimization, with the overall objective to yield optimal designs with high-fidelity function estimates at a reasonable computational expense. In this technique, a new adaptive model switching (AMS) metric defined to guide the switching of model from one to the next higher fidelity model during the optimization process. The switching criterion is based on whether the uncertainty associated with the current model output dominates the latest improvement of the relative fitness function, where both the model output uncertainty and the function improvement (across the population) are expressed as probability distributions. This adaptive model switching technique is applied to two practical problems through Particle Swarm Optimization to successfully illustrate: (i) the computational advantage of this method over purely high-fidelity model-based optimization, and (ii) the accuracy advantage of this method over purely low-fidelity model-based optimization. Motivated by the unique capabilities of the model switching concept, a new model refinement approach is also developed in this dissertation. The model refinement approach can be perceived as an adaptive sequential sampling approach applied in surrogate-based optimization. Decisions regarding when to perform additional system evaluations to refine the model is guided by the same model-uncertainty principles as in the adaptive model switching technique. The effectiveness of this new model refinement technique is illustrated through application to practical surrogate-based optimization in the area of energy sustainability

Modeling single-phase flow and solute transport across scales

textFlow and transport phenomena in the subsurface often span a wide range of length (nanometers to kilometers) and time (nanoseconds to years) scales, and frequently arise in applications of CO₂ sequestration, pollutant transport, and near-well acid stimulation. Reliable field-scale predictions depend on our predictive capacity at each individual scale as well as our ability to accurately propagate information across scales. Pore-scale modeling (coupled with experiments) has assumed an important role in improving our fundamental understanding at the small scale, and is frequently used to inform/guide modeling efforts at larger scales. Among the various methods, there often exists a trade-off between computational efficiency/simplicity and accuracy. While high-resolution methods are very accurate, they are computationally limited to relatively small domains. Since macroscopic properties of a porous medium are statistically representative only when sample sizes are sufficiently large, simple and efficient pore-scale methods are more attractive. In this work, two Eulerian pore-network models for simulating single-phase flow and solute transport are developed. The models focus on capturing two key pore-level mechanisms: a) partial mixing within pores (large void volumes), and b) shear dispersion within throats (narrow constrictions connecting the pores), which are shown to have a substantial impact on transverse and longitudinal dispersion coefficients at the macro scale. The models are verified with high-resolution pore-scale methods and validated against micromodel experiments as well as experimental data from the literature. Studies regarding the significance of different pore-level mixing assumptions (perfect mixing vs. partial mixing) in disordered media, as well as the predictive capacity of network modeling as a whole for ordered media are conducted. A mortar domain decomposition framework is additionally developed, under which efficient and accurate simulations on even larger and highly heterogeneous pore-scale domains are feasible. The mortar methods are verified and parallel scalability is demonstrated. It is shown that they can be used as “hybrid” methods for coupling localized pore-scale inclusions to a surrounding continuum (when insufficient scale separation exists). The framework further permits multi-model simulations within the same computational domain. An application of the methods studying “emergent” behavior during calcite precipitation in the context of geologic CO₂ sequestration is provided.Petroleum and Geosystems Engineerin

THE NEED FOR GINGIVAL RETRACTION IN THE MANUFACTURE OF AESTHETIC STRUCTURES

After the preparation of the tooth, one of the main manipulations in the manufacture of aesthetic structures is to obtain an impression. When prosthetics with metal-ceramic and all-ceramic crowns, the refined impression technique is used using silicone or polyester impression materials. One of the main criteria for the obtained impression is the accurate representation of the tissues of the marginal periodontium, the hard tissues of the tooth in the cervical area and the gingival sulcus, which is an important step for the exact fit of the subgingival margin of the future restoration. To achieve this goal, a special manipulation is carried out - gum retraction, which consists in expanding and completely opening the periodontal sulcus

POVMs: a small but important step beyond standard quantum mechanics

It is the purpose of the present contribution to demonstrate that the generalization of the concept of a quantum mechanical observable from the Hermitian operator of standard quantum mechanics to a positive operator-valued measure is not a peripheral issue, allegedly to be understood in terms of a trivial nonideality of practical measurement procedures, but that this generalization touches the very core of quantum mechanics, viz. complementarity and violation of the Bell inequalities.Comment: Contribution to Proceedings of the Workshop `Beyond the quantum', Leiden, May/June 200