Dual Series Research Articles

Motion prediction via online instantaneous frequency estimation for vision-based beating heart tracking

The beating heart tracking based on stereo endoscope remains challenging due to highly dynamic scenes and poor imaging conditions in minimally invasive surgery. This paper proposes a new prediction method for robust tracking of heart motion. The dual time-varying Fourier series is used for modeling the motion of points of interest (POI) on heart surfaces, which is driven jointly by breathing and heartbeat motion. A dual Kalman filtering scheme is used to estimate the frequencies and Fourier coefficients of the model respectively. A novel orthogonal decomposition algorithm is developed to measure the instantaneous frequencies of breathing and heartbeat motion online from the 3D trajectory of the POI. The difference in direction between breathing and heartbeat motion is exploited by using principal component analysis on the past trajectory, and optimal 1D principal component signals are extracted for measuring the corresponding frequencies. The frequencies calculated from the orthogonal subbands are fused based on an additive noise model for optimal frequency measurement. The proposed method is evaluated and compared with other available prediction methods based on the simulated data and the real-measured signals from the videos recorded by the daVinci® surgical robot. The prediction algorithm is finally incorporated into a well-established visual tracking method to handle long-term occlusions.

Diagrammatic Monte Carlo for dual fermions

We introduce a numerical algorithm to stochastically sample the dual fermion perturbation series around the dynamical mean field theory, generating all topologies of two-particle interaction vertices. We show results in the weak and strong coupling regime of the half-filled Hubbard model in two dimensions, illustrating that the method converges quickly where dynamical mean field theory is a good approximation, and show that corrections are large in the strong correlation regime at intermediate interaction. The fast convergence of dual corrections to dynamical mean field results illustrates the power of the approach and opens a practical avenue towards the systematic inclusion of non-local correlations in correlated materials simulations. An analysis of the frequency scale shows that only low-frequency propagators contribute substantially to the diagrams, putting the inclusion of higher order vertices within reach.

Diffraction of surface water waves by an undulating bed topography in the presence of vertical barrier

In this paper, the problem of diffraction of surface water waves by an undulating bed and a vertical barrier is examined. Here, two different barrier configurations are studied, namely, (i) a partially immersed barrier and (ii) a bottom standing barrier. Perturbation analysis containing a dimensionless parameter which describe the smallness of bottom undulation is employed to find the solution of the mixed boundary value problem (BVP). This analysis reduces the BVP into two BVPs up to first order. The zeroth order BVP represents the problem of scattering of water waves by a vertical barrier. Using eigenfunction expansion method this zeroth order BVP leads to a pair of dual series relations which are solved by the application of least-squares method. The first order BVP containing the solution of the zeroth order BVP is solved by suitable application of the Green's function technique. From the solution of the first order BVP, the physical quantities, namely, the first order reflection and transmission coefficients are obtained in terms of integrals involving the shape function representing the bottom undulation and the solution of the zeroth order BVP. A patch of sinusoidal ripples which closely corresponds to some obstacles produced by nature due to ripple growth and alluviation of sand is considered for which the explicit expressions for the first order reflection and transmission coefficients are obtained. The variation of these coefficients on the barrier length, gap above or below the barrier, ripple amplitude and the number of ripples at the bottom is illustrated graphically. The other important factors of the study, namely, the hydrodynamic force and the moment are also studied and depicted graphically. Furthermore, the energy balance relation which ensures the correctness of the numerical results, is derived and verified.

Crop Monitoring Based on SPOT-5 Take-5 and Sentinel-1A Data for the Estimation of Crop Water Requirements

Optical and microwave images have been combined for land cover monitoring in different agriculture scenarios, providing useful information on qualitative and quantitative land cover changes. This study aims to assess the complementarity and interoperability of optical (SPOT-5 Take-5) and synthetic aperture radar (SAR) (Sentinel-1A) data for crop parameter (basal crop coefficient (Kcb) values and the length of the crop’s development stages) retrieval and crop type classification, with a focus on crop water requirements, for an irrigation perimeter in Angola. SPOT-5 Take-5 images are used as a proxy of Sentinel-2 data to evaluate the potential of their enhanced temporal resolution for agricultural applications. In situ data are also used to complement the Earth Observation (EO) data. The Normalized Difference Vegetation Index (NDVI) and dual (VV + VH) polarization backscattering time series are used to compute the Kcb curve for four crop types (maize, soybean, bean and pasture) and to estimate the length of each phenological growth stage. The Kcb values are then used to compute the crop’s evapotranspiration and to subsequently estimate the crop irrigation requirements based on a soil water balance model. A significant R2 correlation between NDVI and backscatter time series was observed for all crops, demonstrating that optical data can be replaced by microwave data in the presence of cloud cover. However, it was not possible to properly identify each stage of the crop cycle due to the lack of EO data for the complete growing season.

Dual and triple equations and q-orthogonal polynomials

In this paper, we solve dual and triple sequences involving q-orthogonal polynomials. We also introduce and solve a system of dual series equations when the kernel is the q-Laguerre polynomials. Examples are included.

The Influence of Changing PV Array Interconnections under a Non-uniform Irradiance

Usually, the output characteristics of a photovoltaic (PV) array are significantly affected by non-uniform irradiance which is caused by ambient obstacles, clouds, orientations, tilts, etc. Some local maximum power points (LMPP) in the current-voltage (I-V) curves of a PV array can result in power losses of the array. However, the output power at the global maximum power point (GMPP) is different in different interconnection schemes in a PV array. Therefore, based on the theoretical analysis and mathematical derivation of different topological structures of a PV array, this paper investigated the output characteristics of dual series PV arrays with different interconnections. The proposed mathematical models were also validated by experimental results. Finally, this paper also concluded that in terms of performance, the total cross tied (TCT) interconnection was not always the optimal structure, especially in a dual series PV array. When one of the PV modules was severely mismatched, the TCT worked worse than the series parallel (SP) structure. This research can provide guidance for switching the interconnection to gain the greatest energy yield in a changeable- structure PV system.

Analytical solution of the dynamic contact problem of anisotropic materials indented with a rigid wavy surface

This article establishes a dynamic wavy contact model of anisotropic materials subject to a rigid indenter, which moves at a constant speed. There is a gap between the indenter and the substrate prior to deformation. The Galilean transformation is introduced to make the equations of motion tractable. Applying the generalized Almansi’s theorem, general solutions for anisotropic governing equations are given for three root cases by using potential theory. The stated problem is reduced to dual series equations, which are solved exactly. Displacement and stress are given in the infinite series forms. Numerical tests have been done to examine the convergence of the infinite series. It is found that maximum magnitudes of the stress can be relieved by adjusting the relative velocity and the elastic constant ratio.

Illegal intra-corporeal packets: can dual energy CT be used for the evaluation of cocaine concentration? A cross sectional study.

BackgroundThe recent implementation of the dual energy technology on CT-scanners has opened new perspectives in tissue and material characterization. This study aims to evaluate whether dual energy CT can be used to assess the concentration of cocaine of intra-intestinal illegal packets.MethodsThe study was approved by the institutional review board of our institution (CER 13_027_R). From November 2010 to May 2013, all consecutive conveyors in whom a low-dose abdominal CT (LDCT) revealed the presence of illegal intra-corporeal drug packets underwent a dual energy CT series (gemstone spectral imaging) targeted on one container. The mean radiological density (HU) of these packets was measured on the LDCT series, and on the monochromatic dual energy series, at 40 and 140 keV. The difference between the HU at 40 and 140 keV was reported as ∆HU. The effective atomic number Z(eff) was also measured on the monochromatic series. A chemical analysis was performed after expulsion to select cocaine containing packets, and to determine their cocaine concentrations. A correlation analysis was performed between HU, ∆HU and Z(eff), with regard to the percentage of cocaine.ResultsFifty-four cocaine conveyors were included. The mean cocaine content of the packets was 36.8 % (range 11.2–80, SD 15.4), the mean radiologic density 105 HU, the mean Z(eff) 8.7 and the mean ∆HU 163. The cocaine content was correlated with the ∆HU (0.57, p < 0.001), with the Z(eff) (r = 0.56, p < 0.001) but not with radiologic density (r = 0.25, p = 0.064). ∆HU >200 was 0.9 (9 of 10) sensitive and 0.82 (36 of 44) specific to predict a cocaine concentration higher than 50 %.ConclusionMeasuring ∆HU or Z(eff) on dual energy monochromatic CT series can be used to detect ingested packets with cocaine concentration >50 %.

The stability analysis of a rectangular plate supported at points of the corners

The stability problem of a rectangular plate supported at points of corners under uniform pressures in its median plane is studied by using the reciprocal theorem. At first, according to the differential equation of transversal buckling displacement function for a thin rectangular plate, dual trigonometric series, and the reciprocal theorem, the equation of the deflection surface for a rectangular plate with four simple supported edges under uniform pressures in its median plane and a transversal concentrated unit load is established. Secondly, using the reciprocal theorem, the buckling equation for a rectangular plate supported at points of corners is derived. The unknowns here can be determined by the boundary conditions. The exact solution of critical load is given. Finally, as an example, a square plate has been calculated. The results show that the method is accurate and effective to solve the stability problem of rectangular plates. It can serve as technical reference for engineering designs.

Enhancement of Voltage Stability of DC Smart Grid During Islanded Mode by Load Shedding Scheme

Abstract This paper presents the voltage stability of a DC smart grid based on renewable energy resources during grid connected and isolated modes. During the islanded mode the load shedding, based on the state of charge of the battery and distribution line voltage, was proposed for voltage stability and reservation of critical load power. The analyzed power system comprises a wind turbine, a photovoltaic generator, storage battery as controllable load, DC loads, and power converters. A fuzzy logic control strategy was applied for power consumption control of controllable loads and the grid-connected dual active bridge series resonant converters. The proposed DC Smart Grid operation has been verified by simulation using MATLAB® and PLECS® Blockset. The obtained results show the effectiveness of the proposed method.

Fuzzy Logic Controlled Dual Active Bridge Series Resonant Converter for DC Smart Grid Application

Fuzzy Logic Controlled Dual Active Bridge Series Resonant Converter for DC Smart Grid Application

A general solution approach to dynamic contact between a sinusoidal rigid solid and piezoelectric materials with anisotropy

Applying the operator method, general solutions for dynamic governing equations involving anisotropic piezoelectric materials are derived. Based on the general solutions, a rigid solid with a sinusoidal surface moving along the surface of anisotropic piezoelectric materials is concerned. Dual series equations are obtained and solved analytically. Then, the electro-elastic fields are determined in series forms. A full contact problem leads to more simple forms. Numerical analysis is performed for the anisotropic piezoelectric material \({0^{\circ }}\) Graphite-epoxy, in which an illustrative example concerning the vertical mechanical displacement on the surface is displayed to validate the present approach. Results demonstrate that the contact behavior is considerably affected by both the velocity and material properties.

Motion prediction using dual Kalman filter for robust beating heart tracking.

A novel prediction method for robust beating heart tracking is proposed. The dual time-varying Fourier series is used to model the heart motion. The frequency parameters and Fourier coefficients in the model are estimated respectively by using a dual Kalman filter scheme. The instantaneous frequencies of breathing and heartbeat motion are measured online from the 3D trajectory of the point of interest using an orthogonal decomposition algorithm. The proposed method is evaluated based on both the simulated signals and the real motion signals, which are measured from the videos recorded using the da Vinci surgical system.

Scattering Of Internal Waves By Vertical Barrier In A Channel Of Stratified Fluid

The problem of two dimensional internal wave scattering by a vertical barrier in the form of a submerged plate, or a thin wall with a gap in an exponentially stratified fluid of uniform finite depth bounded by a rigid plane at the top, is considered in this paper. Assuming linear theory and the Boussinesq approximation, the problem is formulated in terms of the stream function. In the regions of the two sides of the vertical barrier, the scattered stream function is represented by appropriate eigen function expansions. By the use of appropriate conditions on the barrier and the gap, a dual series relation involving the unknown elements of the scattering matrix is produced. By defining a function with these unknown elements as its Fourier sine expansion series, it is found that this function satisfies a Carleman type integral equation on the barrier whose solution is immediate. The elements of the scattering matrix are then obtained analytically as well as numerically corresponding to any mode of the incident internal wave train for each barrier configuration. A comparison with earlier results available in the literature shows good agreement. To visualize the effect of the barrier on the fluid motion, the stream lines for an incident internal wave train at the lowest mode are plotted.

Partial contact in two-layered piezoelectric structure with interface occupying periodic profiles

The present article establishes a partial contact model to reveal how the contact strength of two piezoelectric materials is influenced by the wavy surface topography. General solutions of governing equations of the piezoelectric materials are presented. Dual series equations are obtained and solved by considering the Werner formulas and Mehler integral. For evaluating various stresses and electric displacements, the related explicit expressions are presented. Numerical tests are conducted to examine in what way the external loading and the piezoelectric coefficient ratio affect the contact performances between two piezoelectric materials. Results delineate that the external loading has a bigger contribution on forming the contact region between two different piezoelectric materials compared with the piezoelectric coefficient ratio.

Scattering and absorption of terahertz waves by a free-standing infinite grating of graphene strips: analytical regularization analysis

The plane wave scattering and absorption by an infinite flat graphene strip grating in the free space are studied in the THz range in the H- and E-polarization regimes. Accurate numerical treatment is based on the dual series equations and the analytical regularization technique. The resulting numerical algorithm possesses guaranteed convergence and controlled accuracy of computations. Reflectance, transmittance and absorbance by the graphene-strip gratings are studied as a function of various parameters. In the H-polarization case, the dominant feature is the excitation of the surface plasmon resonances on each strip. In the E-polarization case, Rayleigh anomalies are the only observable features.

A robust FACTS PV-smart grid interface scheme for efficient energy utilisation

In the last two decades, wind and PV system have been increased remarkably. A novel FACTS-based PV-DC-AC interface scheme using VSI-6 pulse scheme with a switched filter compensator (SFC) scheme developed by the first author is validated for efficient energy utilisation and decoupled DC-AC interface with robust stand under normal and faults (open and short circuit) conditions. The proposed FACTS scheme enhances power quality and ensures efficient energy utilisation and stabilised interface to the smart grid. The FACTS scheme is based on a hybrid power filter-capacitive compensation scheme with SPWM-dual switching strategy using a dual series and shunt capacitor banks. The hybrid control scheme uses a modified fast acting dynamic error driven time-descaled/decoupled multi-regulation loops with an additional inter-coupled weighted controller. The proposed FACTS-scheme is tested using the MATLAB-Simulink Simulation Environment. The unified AC study system was tested under different operating/fault conditions including normal loading and open/short circuit fault conditions.

Triple Simultaneous Fourier Series Equations Involving Associated Legendre Function

In this paper, we have considered the two sets of triple series equations of the first kind and second kind, which are the generalization of dual series equations involving Associated Legendre functions & solved the two sets of series equations. such simultaneous Fourier equations occur in many problems in hydrodynamics, elasticity and electromagnetism, involving a spherical or spheroidal boundary when different conditions are prescribed on different parts of the boundary.

Dual series method for solving Helmholtz equation with mixed boundary conditions of the third kind

The paper involves with the application of the dual series equation to the problem of Helmholtz equation of cylindrical coordinates subject to inhomogeneous mixed boundary conditions of the third kind located on the surface of the cylinder of bounded radius and infinite high. By choosing the Hankel integral transform, the dual series equations were reduced to a Fredholm integral equation of the second kind which is solved conveniently by using numerical techniques. Keywords : Helmholtz Equation, Dual Series Equations, Mixed Boundary Conditions.

APPLICATION OF DUAL SERIES EQUATIONS TO WAVY CONTACT BETWEEN PIEZOELECTRIC MATERIALS AND AN ELASTIC SOLID

In this paper, the wavy contact between piezoelectric materials and an isotropic solid is considered. The Papkovich–Neuber potentials for the isotropic solid and three harmonic functions for piezoelectric materials are also presented. The stated problem is reduced to a pair of dual series equations and then recast as an integral equation of the Abel type. Employing the product relation for trigonometric functions and the Mehler integral yields an exact solution of the reduced Abel type integral equation. The relationship between contact length and the level of loading, and the distribution of the surface normal stress are given in terms of elementary functions. The derived results agree well with the previous ones for the purely elastic solid. It is found that a critical loading exists for the disturbance. For limiting cases, such as the low level of loading case and full contact case, corresponding contact behaviors are presented. Numerical analyses are done to reveal the influence of the level of loading on the contact behaviors.