Elliptical Model Research Articles

Analytical Solutions for the Characteristic Size Distribution of the Elliptical Model in Fractured Rock Mass

Analytical Solutions for the Characteristic Size Distribution of the Elliptical Model in Fractured Rock Mass

Elliptic Dimers on Minimal Graphs and Genus 1 Harnack Curves

This paper provides a comprehensive study of the dimer model on infinite minimal graphs with Fock’s elliptic weights (Fock, Inverse spectral problem for GK integrable system. arXiv e-prints arXiv:1503.00289 , 2015). Specific instances of such models were studied in Boutillier et al. (Invent Math 208(1):109–189, 2017), Boutillier et al. (Probability theory and related fields, 2018) and de Tilière (Electron J Probab 26:1–86, 2021); we now handle the general genus 1 case, thus proving a non-trivial extension of the genus 0 results of Kenyon (Invent Math 150(2):409–439, 2002) and Kenyon and Okounkov (Duke Math J 131(3):499–524, 2006) on isoradial critical models. We give an explicit local expression for a two-parameter family of inverses of the Kasteleyn operator with no periodicity assumption on the underlying graph. When the minimal graph satisfies a natural condition, we construct a family of dimer Gibbs measures from these inverses, and describe the phase diagram of the model by deriving asymptotics of correlations in each phase. In the $$\mathbb {Z}^2$$ -periodic case, this gives an alternative description of the full set of ergodic Gibbs measures constructed in Kenyon et al. (Ann Math 163(3):1019–1056, 2006). We also establish a correspondence between elliptic dimer models on periodic minimal graphs and Harnack curves of genus 1. Finally, we show that a bipartite dimer model is invariant under the shrinking/expanding of 2-valent vertices and spider moves if and only if the associated Kasteleyn coefficients are antisymmetric and satisfy Fay’s trisecant identity.

High-intensity effects on longitudinal bunch merging in hadron synchrotrons

Longitudinal rf manipulation schemes have been widely employed for achieving various beam experiments and applications in heavy ion or proton (hadron) synchrotrons. For high-intensity hadron beams, longitudinal space charge and cavity beam loading play a key role in beam intensity limitations since they may cause beam oscillations and longitudinal emittance growth. Efficient schemes to compress such intense bunched beams and minimize the emittance blow-up during those manipulations are of practical concern. In this article, the behavior of the particle distribution in the presence of space charge and beam loading during bunch merging is investigated via a generalized elliptical bunch model and particle-in-cell (PIC) simulations. Possible schemes to minimize these intensity effects are discussed. As an application, parameters for the longitudinal rf manipulation scenario in the upcoming second phase of the China Spallation Neutron Sources (CSNS-II) are proposed. It is shown that for (slow cycling) storage rings, with an optimized set of longitudinal parameters, the emittance growth due to intensity effects can be largely dampened and a high compression efficiency is achieved. For rapid cycling synchrotrons, fast bunch merging can be achieved via a desynchronization method. The agreement between the analytical elliptical model and the PIC simulation results indicates that the extended model can be employed for the study of the intensity effects during longitudinal rf manipulations in hadron synchrotrons.

Elliptic Gaudin-type model in an external magnetic field and modified algebraic Bethe ansatz

We consider the elliptic Gaudin-type model in an external magnetic field [11–13,16,15,22] associated with non-skew-symmetric elliptic r-matrix [11] defined on 4:1 unramified covering of the Weierstrass cubic y2=(u+j1)(u+j2)(u+j3). We develop a modified algebraic Bethe ansatz for the considered elliptic r-matrix and for the algebra generated by the entries of the corresponding Lax operator with the aim of obtaining the spectra of the relevant Gaudin-type Hamiltonians in terms of solutions of modified Bethe equations. The applications of the obtained result to the diagonalization of the anisotropic quantum Euler top, quantum Zhukovsky-Volterrra top, quantum Steklov and Rubanovsky tops are given.

An elliptic velocity profile-based two-equation model in viscous film

An elliptic velocity profile-based depth-averaged two-equation model is derived for a viscous falling film in terms of the film thickness h(x, t) and the flow rate q(x, t), which is consistent up to first order in inertia terms and consistent up to second order in viscous diffusion terms. It is observed that the proposed depth-averaged two-equation model recovers the available analytical, numerical, and experimental findings of the literature very well as the free parameter involving eccentricity of the ellipse increases. In fact, the present depth-averaged two-equation model converges to the existing parabolic velocity profile-based depth-averaged two-equation model as the eccentricity approaches one because the elliptic velocity profile becomes a parabolic velocity profile. Furthermore, we see that [20, 100] is the suitable range of the free parameter for capturing the existing findings of the literature. In addition, the full second-order depth-averaged model, which is consistent up to second-order in inertia and viscous terms, is also developed in Appendix A.

Umbilic points of slowness surface in elastic orthorhombic media

AbstractFor 3D seismic data processing, azimuth plays an important role, especially in complex subsurface regions. In such regions, elliptical or anelliptical orthorhombic models are commonly used to describe wave propagation. In these models, the behaviour of the slowness surface needs more detailed analysis. Umbilic points defined by the equal principal curvatures exist in a complex 3D model. In the vicinity of the umbilic points, the traveltime surface has the shifted hyperbola form that needs to be considered in processing operations like velocity analysis. Fractured media characterized by the orthorhombic model are more likely to have umbilic points, and it is important to address their positions. If exists, umbilic points can provide additional constraints in inverting for model parameters. Through a defined condition, we examine the position of the umbilic point and derive their explicit formulas. We analyse umbilic points for elliptical and anelliptical orthorhombic models in the numerical example. For the elliptical orthorhombic model, the formulas for the umbilic point position on different symmetry planes are derived and corresponding conditions are also identified. Further, we numerically examine umbilic point positions for anelliptical orthorhombic models and observe that the umbilic points are located out of two vertical symmetry planes. Moreover, caused by interference from two neighbouring umbilic points, a more significant deviation in traveltime is found in the anelliptical orthorhombic model.

Asymptotic Formulation for the Rayleigh Wave on a Nonlocally Elastic Half-Space

This paper deals with the Rayleigh wave, propagating on a nonlocally elastic, linearly isotropic half-space, excited by a prescribed surface loading. The consideration develops the methodology of hyperbolic–elliptic models for Rayleigh and Rayleigh-type waves, and relies on the effective boundary conditions formulated recently, accounting for the crucial contributions of the nonlocal boundary layer. A slow-time perturbation scheme is established, leading to the reduced model for the Rayleigh wave field, comprised of a singularly perturbed hyperbolic equation for the longitudinal wave potential on the surface, acting as a boundary condition for the elliptic equation governing the decay over the interior. An equivalent alternative formulation involving a pseudo-differential operator acting on the loading terms, with parametric dependence on the depth coordinate, is also presented.

Faster isogeny computation on twisted Hessian curves

Isogenies between elliptic curves have been the subject of recent study due to their significance in the post quantum cryptosystem based on isogeny. Various methods for faster isogeny computation have been proposed on different elliptic curve models. In this paper, we generalize a w-coordinate system to twisted Hessian curves. Based on the w-coordinate system, the computation of scalar multiplication and isogeny on twisted Hessian curves could be notably simplified.

An Elliptical Modeling Supported System for Human Action Deep Recognition Over Aerial Surveillance

The advancement of computer vision technology has led to the development of sophisticated algorithms capable of accurately recognizing human actions from red-green-blue videos recorded by drone cameras. Hence, possessing an exceptional potential, human action recognition also faces many challenges including, tendency of humans to perform the same action in different ways, limited camera angles, and field of view. In this research article, a system has been proposed to tackle the forementioned challenges by using red-green-blue videos as input while the videos were recorded by drone cameras. First of all, the video was split into its constituent frames and then gamma correction was applied on each frame to obtain an optimized version of the image. Then the Felzenszwalb’s algorithm performed the segmentation to segment out human from the input image and human silhouette was generated. Utilizing the silhouette, skeleton was extracted to spot thirteen body key points. The key points were then used to perform elliptical modeling to estimate the individual boundaries of the body parts while the elliptical modeling was governed by the Gaussian mixture model-expectation maximization algorithm. The elliptical models of the body parts were utilized to spot fiducial points that if tracked, could provide very useful information about the performed action. Some other features that were extracted for this study include, the 3d point cloud feature vector, relative distance and velocity of the key-points, and their mutual angles. The features were then forwarded for optimization under a quadratic discriminant analysis and finally, a convolutional neural network was trained to perform the action classification. Three benchmark datasets including, the Drone-Action dataset, the UAV-Human dataset, and the Okutama-Action dataset were used for a comprehensive experimentation. The system outperformed the state-of-the-art approaches by securing accuracies of 80.03%, 48.60%, and 78.01% over the Drone-Action dataset, the UAV-Human dataset, and the Okutama-Action dataset respectively.

R-NL: Covariance Matrix Estimation for Elliptical Distributions Based on Nonlinear Shrinkage

We combine Tyler's robust estimator of the dispersion matrix with nonlinear shrinkage. This approach delivers a simple and fast estimator of the dispersion matrix in elliptical models that is robust against both heavy tails and high dimensions. We prove convergence of the iterative part of our algorithm and demonstrate the favorable performance of the estimator in a wide range of simulation scenarios. Finally, an empirical application demonstrates its state-of-the-art performance on real data.

Derivatives risks as costs in a one-period network model

In counterparty credit risk complete markets, collateral and capital requirements would be indifferent to banks. The quantification by banks of market incompleteness based on various XVA metrics ([11]) has emerged as the unintended consequence of the FRTB banking reform ([26]) and of the more demanding regulatory capital requirements ([38]). The related risks are in fact reckoned today as the major risks for banks, well ahead market risk ([35, Figure 65 page 67]). The XVA metrics have been introduced and traditionally used by investment banks for pricing and collateral/capital optimization purposes. We demonstrate in this paper that they can be fruitfully used for risk management, suggesting a sound approach to regulatory requirements. We present a one-period cost-of-capital XVA setup encompassing bilateral and centrally cleared trading in a unified framework, with explicit formulas for most quantities at hand. We illustrate possible uses of this framework for running stress test exercises on financial networks with one and two clearinghouses from a clearing member's perspective or for optimizing the porting of the portfolio of a defaulted clearing member using Monte-Carlo technique with corresponding confidence errors in elliptical models. A continuous-time extension of this approach is provided in the companion paper [7].

Влияние внезапного сужения плоского канала на вынужденную конвекцию в турбулентном газокапельном течении

Numerical modeling of the flow structure and heat transfer in a gas-droplet turbulent flow in a duct with forward-facing step is carried out. The two-dimensional RANS equations are used in the numerical solution. The Eulerian two-fluid approach is used for describing the flow dynamics and heat transfer in the gaseous and dispersed phases. The turbulence of the carrier phase is described using an elliptical Reynolds stress model with taking the presence of dispersed phase. It is shown that finely-dispersed droplets are involved in the separation recirculation motion of the gas phase. The addition of evaporating droplets to a single-phase turbulent flow in the forward-facing step leads to a significant intensification of heat transfer (more than 2 times) compared to a single-phase air flow, all other things being equal. This effect is enhanced with an increase in the initial mass fraction of the water droplets.

Effect of sudden constriction of a flat duct on forced convection in a turbulent droplet-laden mist flow

Numerical modeling of the flow structure and heat transfer in a gas-droplet turbulent flow in a duct with forward-facing step is carried out. The two-dimensional RANS equations are used in the numerical solution. The Eulerian two-fluid approach is used for describing the flow dynamics and heat transfer in the gaseous and dispersed phases. The turbulence of the carrier phase is described using an elliptical Reynolds stress model with taking the presence of dispersed phase. It is shown that finely-dispersed droplets are involved in the separation recirculation motion of the gas phase. The addition of evaporating droplets to a single-phase turbulent flow in the forward-facing step leads to a significant intensification of heat transfer (more than 2 times) compared to a single-phase air flow, all other parameters being equal. This effect is enhanced with an increase in the initial mass fraction of the water droplets. Keywords: Numerical simulation, Reynolds stress transport model, forward-facing step, droplet evaporation, turbulence, heat transfer enhancement.

OLED-on-Silicon Micro-Display Based on Asymmetric Elliptical Foveated JND Model

OLED-on-Silicon Micro-Display Based on Asymmetric Elliptical Foveated JND Model

RHM-δ-GLMB Tracking Algorithm on the Focal Plane for UAV Cluster Targets

This paper offers a new tracking algorithm for clustered targets of focal plane unmanned aerial vehicles (UAVs) by integrating the random hypersurface model (RHM) model into the δ-generalized label multi-Bernoulli (δ-GLMB) filter to guarantee a robust UAV cluster target tracking on such focal planes. We first investigated the infrared imaging features of UAV cluster targets by emphasizing the target imaging size and dispersion. Next, we designed an elliptical RHM-based measurement model to map the measurement, state parameters, scaling factors, and errors to pseudo-measurement "0", followed by establishing a pseudo-measurement equation to reflect the target’s extended shape size. Then, in order to enhance measurement estimation accuracy, the RHM model was implemented with the δ-GLMB filter and Gamma-Gaussian mixture, which can perform a real-time estimate of the targets’ centroid motion state and extended state. We also used the grid-based fast density-based spatial clustering of applications with noise (DBSCAN) segmentation algorithm to overcome the distance-based segmentation method restrictions for infrared radiation (IR) measurement data and diminish the algorithm’s complexity even more in the measurement update. Extensive simulations demonstrated that this algorithm outperformed existing matching filtering algorithms in the target centroid motion and extended states. Our investigations also revealed that the algorithm was less vulnerable to clutter and more adaptive, making it more straightforward to accomplish reliable tracking of UAV cluster targets.

Study on FR4 substrate backed flaring antenna structure for wideband applications

A class of planar antenna which offers better performance over broad band of frequencies that fits itself in wide range of applications are in need of research. The license free band from 3.1 GHz to 10.6 GHz that do not cause interference to narrowband signals is chosen as operating range of frequencies for the chosen Vivaldi antenna. The novelty of the proposed work consists in the remodeling of a mathematical equations for elliptic antenna structure and the study of the Vivaldi antenna operating over the frequency range between 2.63 GHz to 14.58 GHz that lies in Super High Frequency (SHF) bands – S, C and X bands. The designed antenna is fabricated and its radiation characteristics are studied and analyzed. Purpose. Analysis of the designed antenna on the basis of an elliptical curve mathematical model will allow the antenna to operate over wide band of frequencies thus extending its applications over the areas of application in the areas of satellite communication, military, weather radar, surface ship radar. Methods. The antenna is being designed using HFSS software and fabricated antenna is being tested at anechoic chamber. Results. A mathematical model of a structure of Vivaldi antenna was developed and studied. The performance measures of designed antenna such as return loss, gain, VSWR and radiation pattern are simulated and analyzed. The antenna is being fabricated and tested using vector network analyzer and anechoic chamber. Practical value. The analysis of designed antenna over wide band of frequencies is demonstrated. The further research directions of the designed antenna can be extended for the subsequent implementation of the results in suitable applications.

Структура течения и теплоперенос в газокапельном течении за внезапным сужением канала

The numerical study of the local flow structure and heat transfer in a gas-droplet turbulent flow behind a forward-facing step in the two-phase gas-droplet flow is carried out. Two-dimensional steady-state Reynolds-averaged Navier-Stokes (RANS) equations are used for the numerical solution. They were written taking into account the presence of a dispersed phase. The Eulerian two-fluid approach is used to describe the flow dynamics and heat and mass transfer in the gaseous and dispersed phases. The turbulence of the carrier phase was described using an elliptical model for the transport of Reynolds stress components, taking into account the presence of droplets. The effect of evaporating droplets flowing after the forward-facing step on the local flow structure, turbulence, distribution of the dispersed phase, and heat transfer inetensification is analyzed.

Optimal convergence rates in L2 for a first order system least squares finite element method

We analyze a divergence based first order system least squares method applied to a second order elliptic model problem with homogeneous boundary conditions. We prove optimal convergence in the L2(Ω) norm for the scalar variable. Numerical results confirm our findings.

Modeling canopy temperature in closed greenhouses using coupled elliptic models*

Microclimate within the canopy and at the plant surface can have a significant influence on the physiological processes of plants, as well as on the epidemiology of pathogens. Assessing greenhouse climate parameters, canopy microclimate and leaf surface microclimate is essential for developing greenhouse climate control strategies. Considering the canopy as a heterogenous porous medium and using the heat transfer theory, we developed a one-dimensional coupled elliptic system for control purposes to describe the air canopy and crop temperature, and established the existence and uniqueness of the solutions. The corresponding numerical model was derived within the finite difference framework. Simulations were conducted to evaluate the capability of the model to replicate canopy temperature for two arrangements of crops species under different behaviour and environment.

A bootstrap method for spectral statistics in high-dimensional elliptical models

A bootstrap method for spectral statistics in high-dimensional elliptical models