Discrete Coordinates Research Articles

Controllable single-photon transport in a one-dimensional coupled-resonator waveguide coupled to two nanocavities interacting with atoms

We investigate controllable single-photon transport in a one-dimensional coupled-resonator waveguide coupled to two nanocavities interacting with atoms. The reflection and transmission coefficients for a single photon propagating in such a system are deduced by using the discrete coordinates approach. The resonator–nanocavity coupling strength, atom–nanocavity coupling coefficient, and the detuning between the incident photon and the atom, respectively, which affect the transport properties of the single photon, are analyzed. It is found that some useful information, such as the atom–nanocavity coupling strength, can be extracted from the single-photon transmission spectrum under proper parameter settings. We also study how the coupling between two nanocavities affects the single-photon transmission property.

Single Photon Scattering Properties in Coupled-Resonator Waveguide Coupling with a Nanocavity Interacting with an External Mirror**Supported by the National Natural Science Foundation of China under Grant Nos. 11105001 and 61472282, the Anhui Provincial Natural Science Foundation under Grant Nos. 1408085QA22, 1608085MA09, and 1508085MF129.

We investigate theoretically single photon transport properties in coupled-resonator waveguide coupling with a nanocavity interacting with an external mirror. By using the discrete coordinates approach, transmission and reflection amplitudes of the propagating single photon in the waveguide are obtained. The influence of the coupling strength between the nanocavity and the external mirror on the single photon scattering spectra is discussed. We also extend the results to the waveguide with linear and quadratic form dispersion relations.

On the selection of 2D Krawtchouk moments for face recognition

Sparse representation of images using orthogonal two-dimensional Krawtchouk moments (2D KCMs) for face recognition is motivated by their ability to capture region-based higher-order hidden nonlinear structures from discrete coordinates of finitely supported images and the invariance of affine transformations of these moments to common geometric distortions. This paper presents the effectiveness of selecting the discriminatory set of KCMs as the global and local face features as opposed to traditional features obtained from heuristic choice of fixed-order moments or projection of the moments for recognizing an identity. The selection of significantly sparse 2D KCM-based features according to the proposed approach results in highly efficient face recognition method as compared to the other methods that use orthogonal moments such as the 2D Zernike, 2D Tchebichef or 2D Gaussian-Hermite. Experiments on challenging databases (viz., FRGC and CK-AUC) and comparisons with the well established projection, texture, and moment-based methods indicate superior recognition performance in terms of mean accuracy and robustness of the proposed holistic- or hybrid-type discriminative KCM-based method, especially when sample sizes are small and the intraclass faces have significant variations due to expressions.

Mean field ring polymer molecular dynamics for electronically nonadiabatic reaction rates.

We present a mean field ring polymer molecular dynamics method to calculate the rate of electron transfer (ET) in multi-state, multi-electron condensed-phase processes. Our approach involves calculating a transition state theory (TST) estimate to the rate using an exact path integral in discrete electronic states and continuous Cartesian nuclear coordinates. A dynamic recrossing correction to the TST rate is then obtained from real-time dynamics simulations using mean field ring polymer molecular dynamics. We employ two different reaction coordinates in our simulations and show that, despite the use of mean field dynamics, the use of an accurate dividing surface to compute TST rates allows us to achieve remarkable agreement with Fermi's golden rule rates for nonadiabatic ET in the normal regime of Marcus theory. Further, we show that using a reaction coordinate based on electronic state populations allows us to capture the turnover in rates for ET in the Marcus inverted regime.

Abstract W P44: Predicting Omni-directional Lesion Growth in Acute Stroke using Multimodal Intensity Profiles

Introduction: Mechanisms of lesion growth in acute stroke remain poorly characterized. Favorable imaging signatures related to regional tissue status may be disclosed with diffusion-weighted (DWI) and perfusion-weighted (PWI) imaging. Certain values of individual parameters, such as prolonged and decreased CBF, are associated with poor tissue recovery, yet scant data are available regarding the directionality of lesion growth and how different perfusion imaging parameters may be combined to best characterize lesion growth. We developed a probabilistic model that exploits DWI and multi-parametric PWI to predict likelihood of lesion growth in every 3D direction. Hypothesis: We test the hypothesis that combined intensity profiles of PWI features predict the likelihood of lesion growth, in every direction. Methods: Retrospective analysis of DWI and PWI acquired within 24 hours of symptom onset with FLAIR sequences acquired four days later. DWI and PWI were co-registered and the lesions were manually delineated on the baseline DWI and follow-up FLAIR. Intensity profiles of perfusion parameters (including CBV, CBF, MTT, TTP, Tmax) were extracted along discrete spherical coordinates (every 5 degrees). A nonlinear regression model was used to capture the relationship between the intensity profile along a direction and the amount of growth in that direction. A cross-validation was performed to evaluate the accuracy of the model in predicting the lesion growth in every direction at day 4. Results: A total of 49 patients were included in the analysis. Mean age was 68.7 (35-91). Median baseline NIHSS was 16 (2-31) and median mRS at discharge was 5 (1-6). Lowest prediction error (62 cm2 IQR [26 86]) in terms of average lesion surface and final directional growth error 7.91 mm IQR [5.2 10.3] was obtained by combining cBV, cBF, TTP, TMAX intensity profiles into a single input vector. Conclusions: For the first time, a direction-specific model of infarct growth has been developed. It provides quantitative insights about the likelihood of lesion growth surrounding a stroke. This prediction is not only based on closeness to the infarct core or the presence of penumbra but relies also on the complex dependencies between joint evidence found in multiple perfusion parameters.

A simplified method for the analysis of the stochastic response in discrete coordinates

Nowadays, the problem of the computational cost vs. the accuracy of the results is an important field of research in engineering, particularly for the analysis of the response of a stochastic system. By using a set of discrete coordinates, this response can become computationally challenging, especially when using a modal representation. Many dynamic load cases, significant for engineering applications, have random and convective properties such as wall pressure fluctuations due to the turbulent boundary layer (TBL). In this work, a new method for the evaluation of the dynamic response of a linear system excited by a TBL like load is proposed: it is named as frequency modulated pseudo-equivalent deterministic excitation (PEDEM) and it is based on the pseudo-excitation method (PEM). The latter is an exact representation since it uses the modal decomposition of the cross-spectral density matrix of the load. Unfortunately, the extraction of the eigensolutions of the load matrix is required at each frequency step and thus can become computationally unacceptable when a large number of eigensolutions is required. PEDEM tries to overcome this computational bottleneck by introducing some approximations, which are based on the analysis of the eigensolutions of the dynamic load matrix vs. frequency. Three different approximations are proposed and thus modulated for the three frequency ranges wherein the dynamic matrix of the considered random and convective load has different characteristics. A criterion to identify the above-mentioned frequency ranges is also proposed by introducing a dimensionless representation of the frequency. The results show that the proposed approximations combine a good accuracy in representing the stochastic system response with a 40 per cent of reduction of the computational costs if compared to a full stochastic response. The method is successfully applied to a simple 1D configuration, a chain of oscillators, which still presents the main features of a generic system. The extension to 2D systems is also analysed considering a preliminary test case with a flexural plate.

Hypoid Gear Three-Dimensional Modeling with Pro/E

For hypoid gear which processed by HFT (hypoid gear formate tilt) method, geometry parameters and machining parameters of hypoid gear were calculated by using Gleason card. According to the actual machining process and meshing principle, tooth surface equation was derived by coordinate transformation. Then the discrete coordinates points of tooth surface were obtained by using MATLAB tools and projection transformation principle, and data were saved in ibl format. At last the 3-demensional model of hypoid gear were established by importing the ibl format data in Pro/e.

Qualitative properties of certain piecewise deterministic Markov processes

Nous étudions une classe de processus de Markov déterministes par morceaux, sur espace d’états $\mathbb{R}^{d}\times E$ où $E$ est un ensemble fini. La composante continue du processus évolue suivant le flot d’un champ de vecteur, qui change lorsque la composante discrète saute. Les taux de saut peuvent dépendre des deux composantes. Sous l’hypothèse que le processus reste dans un ensemble compact, nous détaillons une construction possible et caractérisons son support en termes de solution d’une inclusion différentielle. Nous étudions ensuite le comportement en temps long, en faisant apparaître un certain ensemble de points accessibles, qui se trouve être fortement lié au support des mesures invariantes. Sous des conditions de type Hörmander sur les crochets de Lie entre les champs de vecteurs, nous montrons qu’il existe une unique mesure invariante vers laquelle le processus converge en variation totale. Nous donnons enfin des exemples où la condition d’unicité n’est pas vérifiée, et où le nombre de mesures invariantes dépend des taux de saut entre les flots.

Manipulating Single-Photon Transport Properties in an Asymmetrical Waveguide Coupled to a Whispering-Gallery Resonator Containing a Two-Level Atom

A hybrid system containing an asymmetrical waveguide coupled to a whispering-gallery resonator embedded with a two-level atom is designed to investigate single-photon transport properties. The transmission and reflection amplitudes are obtained via the discrete coordinates approach. Numerical simulation demonstrates that a trifrequency photon attenuator is realized by controlling the couplings between the asymmetrical waveguide and the whispering-gallery resonator. The phase shift, group delay and dissipation effects of the transmitted single-photon are also discussed.

Use of Airborne LiDAR To Estimate Forest Stand Characteristics

Small-Footprint Airborne LiDAR(light detection and ranging) remote sensing is a breakthrough technology for deriving forest canopy structural characteristics. Because the technique is relatively new as applied to canopy measurement in China, there is a tremendous need for experiments that integrate field work, LiDAR remote sensing and subsequent analyses for retrieving the full complement of structural measures critical for forestry applications. Data storage capacity and high processing speed available today have made it possible to digitally sample and store the entire reflected waveform, instead of only extracting the discrete coordinates which form the so-called point clouds. Return waveforms can give more detailed insights into the vertical structure of surface objects, surface slope, roughness and reflectivity than the conventional echoes. In this paper, an improved Expectation Maximum (EM) algorithm is adopted to decompose raw waveform data. Derived forest biophysical parameters, such as vegetation height, subcanopy topography, crown volume, ground reflectivity, vegetation reflectivity and canopy closure, are able to describe the horizontal and vertical forest canopy structure.

An Application of the Maximum Shear Strain Increment in Searching Sliding Surfaces

A slope landslides generally at the place where the shear strain increment is the largest. This position is considered as the standard of defining sliding surfaces to assess the slope stability under the action of the foundation. A new method is proposed to determine the potential sliding surface, which is based on the largest shear strain increment. Firstly, the stress and strain in the slope were calculated by using the finite difference software-FALC3D. Secondly, a series of vertical line would be set in the calculating section. And then the discrete coordinates of the sliding surface, where the shear strain is largest on the vertical line, would be found through programming fish program. At last the position and shape of the sliding surface can be obtained through carrying on curve fitting of the discrete points by using the least squares method. The concept of this method is clear and can reflect the true form of the sliding surface through contrasting with the limit equilibrium method. Sliding surfaces of different depths and distances of slope are researched and a quadratic function is put forward which can describe the trends of glide direction. Three coefficients of the quadratic function were analyzed and the corresponding expression was obtained which can provide a reference to specification revision and engineering.

Single-Photon Transmission Characteristics in a Pair of Coupled-Resonator Waveguides Linked by a Nanocavity Containing a Quantum Emitter

Single-photon scattering in a pair of coupled-resonator arrays of waveguides linked by a nanocavity embedded with a two-level system is investigated theoretically. By using the discrete coordinates approach, we deduce the analytical expressions for the transmission and reflection amplitudes. The calculations reveal that the transport properties of the single photon can be controlled by adjusting the coupled strength between the nanocavity and the coupled-resonator array. Quantum switching and a 1/4 beam splitter for the band-edge photon based on this structure are also discussed.

Properties of a discrete quantum field theory

A scalar quantum field theory defined on a discrete spatial coordinate is examined. The renormalization of the lattice propagator is discussed with an emphasis on the periodic nature of the associated momentum coordinate. The analytic properties of the scattering amplitudes indicate the development of a second branch point on which the branch cut from the optical theorem terminates.

Semi-Automatic Modeling Technique of Torque Converter Flow Passage

The modeling technique of hydrodynamic torque converter flow passage was investigated. The semi-automatic modeling technique of torque converter flow passage was proposed. The flow passage model of each converter wheel is considered as a revolution entity sliced by two curved surfaces. In order to generate the revolution entity, a new approximation method, condition optimum arc approximation, was proposed. The method was used to approximate the meridional streamlines of the inner and outer wall. As a result, the three-dimensional revolution entity can be conveniently generated. In order to create slice surfaces, the central stream surface of flow passage was approximated with a quadric surface. The normal vector of the quadric surface and the thickness/thickness-function of bade were used to calculate the discrete point coordinates of blade surfaces. Via the rotation transformation to the coordinates, the discrete point coordinates of slice surfaces were obtained. A parameterized program code used for the hydrodynamic torque converter design and semi-automatic modeling was developed. Modeling errors were calculated and analyzed. The flow passage model was generated in several minutes with the help of the program code, Auto CAD and Solidworks software. Finally, the model was inputted into Gambit, and the pre-processing task used for the numerical simulation of torque converter flow field was successfully completed. The investigation results show that the semi-automatic modeling not only can ensure the accuracy of modeling, but also librates the research and design workers of torque converter from the time-consuming modeling work, which paves the way for the numerical simulation of the complex flow field of the hydrodynamic torque converter.

Generalized uncertainty principles and localization of a particle in discrete space

Generalized uncertainty principles are able to serve as useful descriptions of some of the phenomenology of quantum gravity effects, providing an intuitive grasp on non-trivial space-time structures such as a fundamental discreteness of space, a universal bandlimit or an irreducible extendedness of elementary particles. In this article, uncertainty relations are derived by a moment expansion of states for quantum systems with a discrete coordinate, and correspondingly a periodic momentum. Corrections to standard uncertainty relations are found, with some similarities but also key differences to what is often assumed in this context. The relations provided can be applied to discrete models of matter or space-time, including loop quantum cosmology.

Coherent Control of Photon Transmission in a Coupled-Resonator Waveguide Embedded in a Semiconductor Quantum Dot

We theoretically investigate the single photon transport in a coupled resonator waveguide embedded in a semiconductor quantum dot with a V-type system. The transmission and reflection amplitudes are obtained by using a discrete coordinates approach. It is shown that the photon transport properties can be controlled by the energy detuning between the two excited states of the V-type system, and the coupling strength between the photon and the V-type system. We also compare the single photon transport properties in the waveguide with sinusoidal and linear dispersion relations.

Transmission Characteristics in a Coupled-Resonator Waveguide Interacting with a Two-Mode Nanocavity Containing a Three-Level Emitter

The photon transport in a coupled-resonator waveguide coupled to a two-mode nanocavity embedded with a three-level emitter is investigated. The transmission and reflection amplitudes are obtained by using the discrete coordinates approach. We show that the coherent transport properties of a single photon can be well controlled by detuning the coupling strength between the two-mode nanocavity and the emitter, and the coupling strength between the nanocavity and the coupled-resonator waveguide. These results may be useful for the design of photonic devices such as optical filters.

Study on derivation and optimization algorithm about thin plate bending large deformation higher-order nonlinear partial differential equations

For a thin plate bending large deformation problem, variational principle is applied, and higher-order nonlinear partial differential equations about thin plate bending large deformation is established. Based on difference method and dynamic design variable optimization method, making unknown deflection of discrete coordinate points as design variables, differential equations sets of the discrete coordinates points as building objective function, a dynamic design variable optimization algorithm for computing thin plate bending deflection is proposed. Universal computing program is designed. Practical example about rectangular thin plate with fixed boundary under uniform load is analyzed. Comparing the program computing result with finite element solution. Effectiveness and feasibility of the method are verified. This method can be used to solve engineering problem.

Quantitative ergodicity for some switched dynamical systems

We provide quantitative bounds for the long time behavior of a class of Piecewise Deterministic Markov Processes with state space $\mathbb{R}^d\times E$ where $E$ is a finite set. The continous component evolves according to a smooth vector field that it switched at the jump times of the discrete coordinate. The jump rates may depend on the whole position of the process. Under regularity assumptions on the jump rates and stability conditions for the vector fields we provide explicit exponential upper bounds for the convergence to equilibrium in terms of Wasserstein distances.

Single photon transport in one-dimensional coupled-resonator waveguide coupling to a whispering gallery resonator interacting with a semiconductor quantum dot

We theoretically investigate the hybrid mechanism for transmission of a single photon in one-dimensional coupled microcavity waveguide coupled to a whispering-gallery resonator interacting with a semiconductor quantum dot (QD). The QD is modeled as a V-type three-level system. The reflection and transmission coefficients for a single photon propagating in the hybrid system are deduced by using the discrete coordinates approach. The resonator–QD coupling strength, intermode backscattering, and the detuning between the resonator and the QD, respectively, which affect the transport properties of the single photon, are analyzed. We also compare the single photon transport properties in the waveguides with sinusoidal, linear, and quadratic form dispersion relations.