Elliptical Model Research Articles

Self-oscillating jets in cooling applications

In the present computational study, an assessment of self-oscillating jets for use in cooling applications is investigated. The jet exits from a square nozzle into a narrow rectangular cavity at a Reynolds number of 54,000 based on nozzle hydraulic diameter and average jet exit velocity. The heated devices, such as electronic chips, are located externally on the surface of the cavity. A three-dimensional numerical simulation of the flow is conducted by solving the unsteady Reynolds-Averaged Navier-Stokes and energy equations to assess the thermal features of the flow field. The unsteady Elliptic Blending Reynolds Stress Model, which consists of transport equations for each of the stress tensor components, was used to model turbulence. The cooling performance of a self-oscillating jet is compared with that of a wall jet and a channel flow for the same flow conditions and the same arrangement of the hot devices. The cooling efficacy of two different arrangements of the heated devices is also evaluated. The self-oscillating jet provides a higher heat transfer for the heated blocks which are located farther from the central region, while the wall jet improves heat transfer around the central region. Self-oscillating jets can improve heat transfer over a larger area when the heated devices are aligned orthogonal to the axis of the nozzle. On a Nusselt number comparative basis, the channel flow provides the least desirable heat transfer performance.

Broadband Strong Ground Motion Modeling Using Planar Dynamic Rupture With Fractal Parameters

AbstractDynamic rupture modeling represents a promising physics‐based approach to strong ground motion simulations. However, its application in a broad frequency range (0–10 Hz), interesting for engineering studies, is challenging. The main reason is that widely used and relatively simple planar fault models with smooth distributions of initial stress and frictional parameters, or even self‐similar initial stress, result in ground motions depleted in high‐frequency content. Here we propose an efficient approach for the linear slip‐weakening friction model on a planar fault based on the Ide and Aochi (2005, https://doi.org/10.1029/2004jb003591) multiscale model with a small‐scale random fractal distribution of the slip‐weakening distance Dc. We propose a way to combine these variations with a large‐scale deterministic dynamic model. We illustrate the approach on an elliptical model and a smooth model of the 2016 Mw 6.2 Amatrice, Italy, earthquake from low‐frequency dynamic rupture inversion. To intensify the incoherence of the rupture propagation, we also include a variation of the strength and initial stress, both correlated with Dc. These additions result in sustained high‐frequency radiation during the whole rupture propagation and omega‐square source time functions. The new model of the Amatrice earthquake generates synthetics that agree with the local ground motion model up to 5 Hz in terms of spectral accelerations while preserving the average and integral dynamic rupture parameters (e.g., stress drop, fracture and radiated energy). The fractal dynamic model can be easily implemented in any dynamic rupture propagation code and is thus readily applicable in broadband physics‐based ground motion predictions for earthquake scenarios in seismic hazard assessment.

An inversion scheme for sizing crack from signals of the motion-induced eddy current testing method based on a new formula of signal gradient of ferromagnetic materials

In this paper, an inversion scheme for the profile reconstruction of a fatigue crack in rails from the motion-induced eddy current testing (MIECT) signals is proposed based on the conjugate gradient (CG) optimization method and the fast MIECT forward simulator developed by authors. To calculate the gradient of MIECT signals with respect to the crack parameters, a simplified analytical gradient formula is deduced, which enables a high efficiency crack reconstruction from MIECT signals for a crack in ferromagnetic material. The validity of the inversion schemes is demonstrated at first by reconstructing cracks with numerical simulated signals for ferromagnetic materials with an oblique elliptic crack model. The good reconstruction results reveal that the new signal grandient formula is efficient for reconstructing crack in ferromagnetic material with the CG algorithm. Finally, sizing of artificial cracks are carried out with use of measured MIECT signals due to cracks in plates of both non-magnetic and ferromagnetic materials. The reconstructed crack parameters are in good agreement with the true values, which experimentally proved the validity and efficiency of the proposed inversion scheme and the new signal gradient formula for MIECT inversion.

Estimating macroscopic conductivity of randomly elliptic inclusion model with imperfect interfaces

The paper introduces some solutions for computing the effective conductivity of randomly elliptic inclusion with imperfect interfaces in two-dimensional space. Based on the coated-ellipse inclusion model and the polarization approximation, one can determine the effective conductivity of the ellipse inclusions with the approximation for lowly conducting imperfect interface (ALI) and the approximation for highly conducting imperfect interface (AHI). Some solutions, including the equivalent inclusion approximations (ALI and AHI), differential approximations (DAs), Hamilton–Crosser approximations (HAs), and fast Fourier transformation (FFT) method will be applied to determine the effective conductivity of the randomly ellipse model with AHI and ALI in two-dimensional space. The ALI and AHI results agree well with DA, HA, and FFT results showing the effectiveness of the methods.

Tracer dispersion due to non-Newtonian fluid flows in hydraulic fractures with different geometries and porous walls

Tracer transport in hydraulic fractures is substantially affected by the rock matrix surrounding them. Nevertheless, there is not yet an expression in literature to address the relationship among the transport coefficients, porous walls, hydraulic fracture geometries, and non-Newtonian fluid properties. Therefore, the tracer dispersion due to non-Newtonian fluid flows in hydraulic fractures with different geometries and porous walls is mathematically derived and studied in the current work. Rectangular, triangular, and elliptical models and power-law model are considered here to describe the hydraulic fracture geometry and the non-Newtonian fluid rheology, respectively. The results reveal that as the flow behavior index grows, the coefficient of the shear dispersion term in the case of the shear thinning and Newtonian fluids follows an order of triangular > elliptical > rectangular and in the case of the shear thickening while the same order is followed at the beginning, it turns first to triangular > rectangular > elliptical, then to rectangular > triangular > elliptical, and finally to rectangular > elliptical > triangular. The coefficient of the shear dispersion term increases sharply for each geometrical model with the flow behavior index when the fluid is shear thinning while it first increases slightly and then flattens when the fluid is shear thickening. However, the coefficient of the shear dispersion term for porous walls is lower than the one for nonporous walls. It is also found that the average tracer dispersion coefficients in rectangular, triangular, and elliptical nonporous-walled and porous-walled hydraulic fractures and their ratio dictate that the hydraulic fracture-rock matrix communication through the continuity of the tracer concentration and the mass flux needs to be considered for determination of the tracer dispersion during the transition for intermediate Peclet numbers and the advection-dominated tracer transport for large Peclet numbers. This study along with its findings can pave the way for future investigations on the tracer dispersion in a network of hydraulic fractures with rough and porous walls.

A Parametric Model of Elliptic Orbits for Annual Evolutions of Northern Hemisphere Stratospheric Polar Vortex and Their Interannual Variability

The year-to-year varying annual evolutions of the stratospheric polar vortex (SPV) have an important downward impact on the weather and climate from winter to summer and thus potential implications for seasonal forecasts. This study constructs a parametric elliptic orbit model for capturing the annual evolutions of mass-weighted zonal momentum at 60° N (MU) and total air mass above the isentropic surface of 400 K (M) over the latitude band of 60–90° N from 1 July 1979 to 30 June 2021. The elliptic orbit model naturally connects two time series of a nonlinear oscillator. As a result, the observed coupling relationship between MU and M associated with SPV as well as its interannual variations can be well reconstructed by a limited number of parameters of the elliptic orbit model. The findings of this study may pave a new way for short-time climate forecasts of the annual evolutions of SPV, including its temporal evolutions over winter seasons as well as the spring and fall seasons, and timings of the sudden stratospheric warming events by constructing its elliptic orbit in advance.

Stable 3D particle manipulation using rotating elliptical Gauss–Schell model vortex partially coherent light sources

The Partially coherent light source can be applied to the noninvasive capture of particles, and increasing the freedom of capturing different types of particles simultaneously is of great significance. This paper studies the optical field distribution of a rotating elliptical Gaussian-Schell model vortex beam focused by a lens and the radiation force acting on Rayleigh particles. The beam’s rotation parameter, the vortex’s topological charge, and the spatial coherence length have different effects on the light intensity, which will determine the optical capture ability of Rayleigh particles with other refractive indices and generate equilibrium points at different positions. The longitudinal equilibrium points of high-refractive-index particles and the transverse equilibrium points of low-refractive-index particles are increased by adjusting the value of the rotation parameter and the topological charge. Finally, the appropriate size range for trapping Rayleigh particles is analyzed according to the comparison of Brownian force and radiant force. The results show that this partially coherent light source has a high degree of freedom in capturing particles with different refractive indices, which provides a new way for optical capture technology and three-dimensional (3D) particle manipulation.

Elliptic BCS-Richardson model and the modified algebraic Bethe ansatz

We consider the elliptic Gaudin-type model in an external magnetic field (Skrypnyk T 2005 Phys. Lett. A 334 390–9; Skrypnyk T 2005 Phys. Lett. A 347 266–7; Skrypnyk T 2006 J. Geom. Phys. 57 53–67; Skrypnyk T 2006 J. Math. Phys. 47; Skrypnyk T 2007 J. Phys. A 40 1611–23; Skrypnyk T 2019 Nucl. Phys. B 941 225–48) associated with non-skew-symmetric elliptic r-matrix (Skrypnyk T 2005 Phys. Lett. A 334 390–9; Skrypnyk T 2005 Phys. Lett. A 347 266–7; Skrypnyk T 2006 J. Geom. Phys. 57 53–67; Skrypnyk T 2006 J. Math. Phys. 47). Using them we construct a new integrable fermion Hamiltonian of the Richardson type. We use the modified algebraic Bethe ansatz obtained for integrable models with the considered elliptic r-matrix in (Skrypnyk T 2023 Nucl. Phys. B 988 116102) and find the spectrum of the obtained Richardson-type Hamiltonian in terms of solutions of the modified Bethe equations. The obtained results generalize our previous results on Richardson-type models (Skrypnyk T 2022 Nucl. Phys. B 975 115679).

Hybrid partial differential elliptical Rubik’s cube algorithm on image security analysis

Purpose Several chaotic system-based encryption techniques have been presented in recent years to protect digital images using cryptography. The challenges of key distribution and administration make symmetric encryption difficult. The purpose of this paper is to address these concerns, the novel hybrid partial differential elliptical Rubik’s cube algorithm is developed in this study as an asymmetric image encryption approach. This novel algorithm generates a random weighted matrix, and uses the masking method on image pixels with Rubik’s cube principle. Security analysis has been conducted, it enhances and increases the reliability of the proposed algorithm against a variety of attacks including statistical and differential attacks. Design/methodology/approach In this light, a differential elliptical model is designed with two phases for image encryption and decryption. A modified image is achieved by rotating and mixing intensities of rows and columns with a masking matrix derived from the key generation technique using a unique approach based on the elliptic curve and Rubik’s cube principle. Findings To evaluate the security level, the proposed algorithm is tested with statistical and differential attacks on a different set of test images with peak signal-to-noise ratio, unified average changed intensity and number of pixel change rate performance metrics. These results proved that the proposed image encryption method is completely reliable and enhances image security during transmission. Originality/value The elliptic curve–based encryption is hard to break by hackers and adding a Rubik’s cube principle makes it even more complex and nearly impossible to decode. The proposed method provides reduced key size.

Study on the Micro-Mechanical Mechanism of Fine-Grained Marine Sediments Subjected to Shallow Gas Invasion

Marine sediment is an important channel for methane leakage from the earth interior to the atmosphere. The investigation of gas invasion in fine-grained marine sediments is of great theoretical and practical significance in marine science and engineering. To study the mechanical mechanisms of fine-grained marine sediments subjected to shallow gas invasion, a gas injection test with a self-developed experimental apparatus was performed, and the gas invasion behavior was investigated. The results showed that the behavior of gas invasion in fine-grained sediments can be divided into different phases; the fracturing direction β gradually changes from vertical to horizontal, and finally fractures along the roof. Based on the 2D undrained elliptical cavity model and the tensile strength of sediments, considering both tensile and shear failure modes, a discrimination criteria of gas invasion was proposed. It revealed that gas invasion gradually changes from shear failure to tensile failure, and the fracturing angle θ predicted by the criteria is consistent with the experimental phenomenon.

Air Flow Analysis for Protective Clothing Ventilation Elements with and Without Constant Cross-Section Area Opening

Abstract In this paper a ventilation element is designed with the constant cross-sectional area of 3.14 mm2 with the outer ring, to study the efficiency of ventilation at three different inlet air velocities (2, 5 and 8 m/s). There are five different cases analysed in the study, in which four cases are with different coordinate values of outer ring and core while the fifth case is studied with ventilation element without outer ring. The results of all five cases are analysed and compared to see the efficiency of ventilation element design. These ventilation elements are attached at ventilation hole at the inner part of the protective jacket. The attached ventilation element increases mechanical strength of the clothing by covering ventilation hole and restricting direct access of insects to the body. Moreover, ventilation elements permit smooth flow of air inside jacket. The objective is to determine which element’s geometrical configuration results in the minimum flow energy losses in the cell flow channel from the inlet to the outlet, which are represented by the pressure difference. Flow energy losses increase with increasing pressure difference (ΔP), and the body cooling reduces if the flow is weakened or there is of lost energy. SolidWorks Flow Simulation is used to calculate the pressure, temperature, and heat flux for the simplified elliptical model of the human body with a protective jacket. The obtained results are compared and analysed to study the concept of constant cross-sectional area in the design of ventilation elements with and without outer ring. The pressure and temperature difference for each case are calculated for the comparison and the obtained results show that the element design without outer ring provides better overall results and less flow energy loss in the cell flow channel than that of element design with outer ring.

Analysis of Elliptical-Jet Acoustic Directivity and Efficiency Using a Vortex-Sheet-Based Wave-Packet Model

The hydrodynamic characteristics and associated far-field acoustics of installed elliptical jets were studied using linear models based on the Navier–Stokes equations. A compressible elliptical vortex-sheet model predicted that the growth rates of the varicose and wagging modes decreased with the aspect ratio, whereas the growth rate of the flapping mode increased, which was consistent with previous studies using finite-thickness stability models. Using a propagation model adapted from the Lighthill acoustic analogy, it was found that the acoustic efficiency of the “varicose” mode is significantly higher than the “flapping” and “wagging” modes for both free- and installed jets. Increasing the aspect ratio of the elliptical jet produces a slight reduction in sound for the mode, a significant decrease in the mode, and a significant increase for the mode. A similar trend was observed for the installed case. An exponential relationship between the jet–plate distance and scattered sound was found for elliptical jets, as observed for circular jets. Other geometric parameters such as the orientation angle of the ellipse were also analyzed.

Enzyme-Triggered l-α/d-Peptide Hydrogels as a Long-Acting Injectable Platform for Systemic Delivery of HIV/AIDS Drugs.

Eradicating HIV/AIDS by 2030 is a central goal of the World Health Organization. Patient adherence to complicated dosage regimens remains a key barrier. There is a need for convenient long-acting formulations that deliver drugs over sustained periods. This paper presents an alternative platform, an injectable in situ forming hydrogel implant to deliver a model antiretroviral drug (zidovudine [AZT]) over 28 days. The formulation is a self-assembling ultrashort d or l-α peptide hydrogelator, namely phosphorylated (naphthalene-2-ly)-acetyl-diphenylalanine-lysine-tyrosine-OH (NapFFKY[p]-OH), covalently conjugated to zidovudine via an ester linkage. Rheological analysis demonstrates phosphatase enzyme instructed self-assembly, with hydrogels forming within minutes. Small angle neutron scattering data suggest hydrogels form narrow radius (≈2nm), large length fibers closely fitting the flexible cylinder elliptical model. d-Peptides are particularly promising for long-acting delivery, displaying protease resistance for 28 days. Drug release, via hydrolysis of the ester linkage, progress under physiological conditions (37°C, pH 7.4, H2 O). Subcutaneous administration of Napffk(AZT)Y[p]G-OH in Sprague Dawley rats demonstrate zidovudine blood plasma concentrations within the half maximal inhibitory concentration (IC50 ) range (30-130ng mL-1 ) for 35 days. This work is a proof-of-concept for the development of a long-acting combined injectable in situ forming peptide hydrogel implant. These products are imperative given their potential impact on society.

Failure probability estimation through high-dimensional elliptical distribution modeling with multiple importance sampling

This paper addresses the challenge of performing importance sampling in high-dimensional space (several hundred inputs) in order to estimate the failure probability of a physical system subject to randomness. It is assumed that the failure domain defined in the input space can possibly include multiple failure regions. A new approach is developed to construct auxiliary importance sampling densities sequentially for each failure region identified as part of the failure domain. The search for failure regions is achieved through optimization. A stochastic decomposition of the elliptically distributed inputs is exploited in the structure of the auxiliary densities, which are expressed as the product of a parametric conditional distribution for the radial component, and a parametric von Mises–Fisher distribution for the directional vector. The failure probability is then estimated by multiple importance sampling with a mixture of the densities. To demonstrate the efficiency of the proposed method in high-dimensional space, several numerical examples are considered involving the multivariate Gaussian and Student distributions, which are commonly used elliptical distributions for input modeling. In comparison with other simulation methods, the numerical cost of the proposed approach is found to be quite low when the gradient of the performance function defining the failure domain is available.

Superadditivity and Convex Optimization for Globally Optimal Cell Segmentation Using Deformable Shape Models.

Cell nuclei segmentation is challenging due to shape variation and closely clustered or partially overlapping objects. Most previous methods are not globally optimal, limited to elliptical models, or are computationally expensive. In this work, we introduce a globally optimal approach based on deformable shape models and global energy minimization for cell nuclei segmentation and cluster splitting. We propose an implicit parameterization of deformable shape models and show that it leads to a convex energy. Convex energy minimization yields the global solution independently of the initialization, is fast, and robust. To jointly perform cell nuclei segmentation and cluster splitting, we developed a novel iterative global energy minimization method, which leverages the inherent property of superadditivity of the convex energy. This property exploits the lower bound of the energy of the union of the models and improves the computational efficiency. Our method provably determines a solution close to global optimality. In addition, we derive a closed-form solution of the proposed global minimization based on the superadditivity property for non-clustered cell nuclei. We evaluated our method using fluorescence microscopy images of five different cell types comprising various challenges, and performed a quantitative comparison with previous methods. Our method achieved state-of-the-art or improved performance.

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.