Time evolution of entanglement and bistability of two coupled quantum dots in a driven cavity

Abstract

The time evolution of entanglement between two quantum dots (QDs) trapped inside a cavity driven by a coherent quantized field is studied. In the presence of dissipation, entanglement shows many interesting features such as sudden death and revival, and finite steady state value after sudden death. We also investigate dependence of entanglement on dot variables and its relation to bistability. It is found that entanglement vanishes when the cavity field intensity approaches the upper branch of the bistability curve. When the cavity is driven by a modulated field in the presence of dissipation, it can periodically generate entanglement, which is much larger than the maximum value attained in the steady-state for this system but the dots are never fully entangled.     

Inspection resource assignment in a multistage manufacturing system with an inspection error model

Producing high-quality products at low cost is always one concern for a multi-stage manufacturing system. That is, production costs and inspection efficiency should receive equal importance. Inspection planning to allocate inspection stations should then be performed to manage limited inspection resources during process planning. Product quality and the possible costs can then be concurrently considered when evaluating a manufacturing plan. Except for finite inspection station classes, the limited number of inspection stations of each inspection station class is considered to solve the inspection allocation problem in this research. Rather than utilizing a constant inspection error or a specified inspection error probability distribution determined by previous observations, the inspection allocation problem is solved using relative cost models in which the inspection error model is embedded. The inspection allocation problem can then be solved by practically reflecting the inspection error when tolerances are rapidly changed to satisfy customer requirements. Since determining the optimal inspection allocation plan seems impractical as the problem size becomes quite large, two heuristic methods have been developed by considering the defective rate, manufacturing cost and earliest stage priority in this research. The performance of each method is measured in comparison with the enumeration method that generates the optimal solution. A feasible manufacturing plan can then be determined and confirmed during process planning by concurrently solving the inspection allocation problem.     

Decomposition of singular large sparse matrix by adding dummy links and dummy degrees

Abstract

This paper proposes a simple scheme to decompose an n×n nonpositive definite matrix, A, associated with simultaneous equations, A X = B, into a triple‐factors (lower triangular, diagonal, and upper triangular matrices), i.e., Å = L D U, without interchanging rows or columns of A, but with A expanded with new rows and new columns to an m×m matrix Å. Whenever a near‐zero diagonal element, say ā_ii , is encountered and used as a pivoting element, an appropriate positive real number, say p, is added to this diagonal element, and a new term —px_k is also added to the i‐th equation, where x_k is a new variable called “dummy variable'’. If we also add a new equation —px_i + px_k = 0 to enforce the new added variable x_k equal to x_i then the modified i‐th equation has the same effect as the original equation. Therefore, the original solution X can be found directly from the expanded solution of the modified expanded equation. The method is very useful in solving the following problems: (1) nonlinear problems near the limit state, (2) postbuckling analysis, (3) system equations with constraint conditions, and (4) getting eigenvectors from eigenvalues.     

Seismic response prediction of base-isolated structures with high damping rubber bearings

To characterize the highly nonlinear hysteretic behavior of high damping rubber (HDR) bearings, a previously developed mathematical hysteresis model, rather than a simplified bilinear hysteresis model, is adopted in this study. Unilateral and bilateral seismic simulation tests of a scaled-down multistory structure isolated with HDR bearings subjected to three recorded earthquakes were conducted. Based on the unilateral test results, different sets of model parameters can be identified. The fidelity of the adopted hysteresis model is investigated by comparing the analytical predictions using all sets of identified parameters with results measured from the tests. The significant influence ascribed to different ground motion characteristics such as the effects of near-field and far-field earthquakes on modeling the hysteretic behavior of HDR bearings is observed. Besides, a feasibility study on applying the identified parameters of the adopted hysteresis model to predict the bilateral seismic responses is performed. Even though the prediction accuracy of the seismic responses is satisfactory in two orthogonally horizontal directions, the bilateral hysteretic modeling of HDR bearings requires further intensive studies considering the coupling effect under bilateral excitations.     

Adaptive epileptic seizure prediction system

Current epileptic seizure "prediction" algorithms are generally based on the knowledge of seizure occurring time and analyze the electroencephalogram (EEG) recordings retrospectively. It is then obvious that, although these analyses provide evidence of brain activity changes prior to epileptic seizures, they cannot be applied to develop implantable devices for diagnostic and therapeutic purposes. In this paper, we describe an adaptive procedure to prospectively analyze continuous, long-term EEG recordings when only the occurring time of the first seizure is known. The algorithm is based on the convergence and divergence of short-term maximum Lyapunov exponents (STLmax) among critical electrode sites selected adaptively. A warning of an impending seizure is then issued. Global optimization techniques are applied for selecting the critical groups of electrode sites. The adaptive seizure prediction algorithm (ASPA) was tested in continuous 0.76 to 5.84 days intracranial EEG recordings from a group of five patients with refractory temporal lobe epilepsy. A fixed parameter setting applied to all cases predicted 82% of seizures with a false prediction rate of 0.16/h. Seizure warnings occurred an average of 71.7 min before ictal onset. Similar results were produced by dividing the available EEG recordings into half training and testing portions. Optimizing the parameters for individual patients improved sensitivity (84% overall) and reduced false prediction rate (0.12/h overall). These results indicate that ASPA can be applied to implantable devices for diagnostic and therapeutic purposes.     

Dissolution rates of limestones of different sources

The dissolution characteristics of limestones from six sources in Taiwan have been studied by using the pH-stat method in a stirred tank at 60 degrees C, pH values of 4 and 6, stirrer speeds of 500-1000 rpm, and a particle size of 75-125 microm aperture width. The dissolution rates of the limestones were found to be controlled by the mass transfer of hydrogen ions with chemical reactions in the liquid film surrounding the limestone particle. The measured value of mass transfer coefficient increases with an increasing pH value and stirrer speed and remains constant with particle size. For the six limestones at the same particle size, the measured dissolution rates per unit area are the same due to the mass-transfer control kinetics; however, the time taken to reach a certain fraction of dissolution is proportional to the molar concentration of the soluble species in the limestone and the initial particle size.     

Minimizing the total weighted completion time on a single machine under linear deterioration

This paper investigates a single-machine problem in which processing times of jobs are start time dependent and the aim is to minimize the total weighted completion time. Recent research has shown the complexity of this problem to be NP-hard; however, no optimal or heuristic algorithms have been proposed. In this paper, we explore the exact solution and propose several heuristic algorithms derived based on the impacts of model parameters. The effects of normal processing times and deterioration rates are also studied.     

Physiographic Drainage-Inundation Model Based Flooding Vulnerability Assessment

Flooding vulnerability assessment is an important issue in Taiwan since Taiwan lies within the most active tropical cyclone formation zone of the Western Pacific. Huge economic damages and losses of human lives are occurred almost every year. This study aims to evaluate flooding vulnerability of a given area subject to large-scale land developments. A scoring-based approach associated with a physiographic drainage-inundation model is developed to quantitatively evaluate vulnerability for flooding. The flooding vulnerability index defined as the product of an exposure score and a hazard score. The exposure score assesses relative losses exposed to flooding, which is determined by land-uses classification. The hazard score measures flooding severity, which is simultaneously determined by inundation depth and duration that are obtained from the inundation model for a design storm. The Yenshui River basin located in southwestern Taiwan is used an example to illustrate the proposed method. The results show that the projected urbanization plan within the Yenshui River basin would increase flooding vulnerability from 0.371 to 0.472. However, this value is reduced to 0.388 when the mitigation measure has been implemented. The obtained spatial distribution of flooding vulnerability for a design storm provides decision-makers useful information to identify hotspots of the study area and evaluate effects of flood-mitigation measure on flooding risk-reduction.     

Highly stable strained layer leaky-mode diode laser arrays

A simple fabrication process for InGaAs strained quantum well leaky-mode laser arrays is demonstrated. The arrays are ten-element devices grown by two-step metal-organic chemical vapor deposition. The structure consists of a strained quantum well InGaAs graded index-separate confinement active region and a thin (0.12 μm), transparent GaAs waveguide region. The near-field pattern typical of leaky-mode phase-locked arrays was measured. Fundamental mode oscillation was observed up to 2 A (threshold was as low as 175 mA). The authors observed a 1 μs pulsed optical output power of 172 mW per facet and a far-field angle (full width at half maximum) of 1.6 times the diffraction limit at 1 A. This is the first reported operation of a strained quantum well leaky-mode laser utilizing a built-in index step     

Fitting Drought Duration and Severity with Two-Dimensional Copulas

This study aims to model the joint drought duration and severity distribution using two-dimensional copulas. The method of inference function for margins (IFM method) is employed to construct copulas. Two separate maximum likelihood estimations of univariate marginal distributions are performed first, then followed by a maximization of the bivariate likelihood as a function of the dependence parameters. The drought duration and severity are assumed to be exponential and gamma distributions, respectively. Several copulas are tested to determine the best data fitted copula. Droughts, defined using the Standardized Precipitation Index (SPI), of Wushantou (Taiwan) are employed as an example to illustrate the proposed methodology. The copula fitting results for drought duration and severity are quite satisfactory. The bivariate drought analyses, including the joint probabilities and bivariate return periods, based on the derived copula-based joint distribution are also investigated to demonstrate the advantages of bivariate modeling of droughts.