Geometric Coupling Research Articles

Mathieu ray-wave structured light with self-healing elliptical accelerating vortices.

Ray-wave structured vortex beams have attracted increasing attention due to their unique spatial geometric coupling to control complex orbital angular momentum (OAM). Still, current models were constrained by circular symmetry with limited modulation freedom. Herein, we propose a generalized class of ray-wave light fields called Mathieu geometric modes (MGMs) fulfilling the form of a stationary coherent state but based on a set of helical Mathieu modes (HMMs), in which geometrically tunable elliptical accelerating vortices are obtained by tuning their eccentricity-related parameters. MGMs also possess intriguing properties of coordinate transformation, self-healing, and multilayer tunable angular acceleration upon propagation. MGMs have higher degrees of freedom to control spatial accelerating vortices, paving the way for higher-dimensional optical tweezers and complex particle manipulation.

Renormalization of networks with weak geometric coupling.

The renormalization group is crucial for understanding systems across scales, including complex networks. Renormalizing networks via network geometry, a framework in which their topology is based on the location of nodes in a hidden metric space, is one of the foundational approaches. However, the current methods assume that the geometric coupling is strong, neglecting weak coupling in many real networks. This paper extends renormalization to weak geometric coupling, showing that geometric information is essential to preserve self-similarity. Our results underline the importance of geometric effects on network topology even when the coupling to the underlying space is weak.

Moiré patterns of space-filling curves

It is shown on the examples of Moore and Gosper curves that two spatially shifted or twisted, preasymptotic space-filling curves can produce large-scale superstructures akin to moiré patterns. To study physical phenomena emerging from these patterns, a geometrical coupling coefficient based on the Neumann integral is introduced. It is found that moiré patterns appear most defined at the peaks of those coefficients. A physical interpretation of these coefficients as a measure for inductive coupling between radiofrequency resonators leads to a design principle for strongly overlapping resonators with vanishing mutual inductance, which might be interesting for applications in MRI. These findings are demonstrated in graphical, numerical, and physical experiments. Published by the American Physical Society 2024

Spin-Charge Conversion in Chiral Polymers with Hopping Conduction.

Organic and biological materials are often chiral. Chiral polymers, as recent experiments indicate, facilitate spin-charge conversion: a charge current results in a spin polarization and vice versa, dubbed chirality-induced spin selectivity (CISS) and inverse CISS (ICISS). While CISS/ICISS in crystalline chiral systems such as tellurium can be understood in terms of their chirality- and spin-dependent band structure, such a picture becomes inapplicable to disordered chiral polymers, where carrier transport is via hopping rather than band conduction. Here, we develop a microscopic theory to describe CISS and ICISS in disordered chiral organics, in which chirality-induced geometric spin-orbit coupling leads to a purely geometric spin-dependent Berry phase in electron hops involving triads, whose orientations are dictated by the material's chirality. Our theory reveals a central role of spin-flip hopping, which suppresses CISS but enables ICISS.

The Suppression Effect of an Imaging System on the Geometric Tilt-to-Length Coupling in a Test Mass Interferometer

Tilt-to-length (TTL) coupling noise arises from angular misalignments of interfering beams in optical path length (OPL) measurements and significantly impacts the accuracy of interferometry measurement systems. This paper focuses on geometric TTL coupling in a test mass (TM) interferometer and examines how an imaging system influences TTL noise suppression. First, the analytical expression of the geometric TTL coupling in a TM interferometer with alignment errors is derived and confirmed through numerical simulation. Subsequently, an imaging system is incorporated into the geometric model and the corresponding analytical expressions are obtained under two common conjugate relationships. Nevertheless, the TTL coupling remains beyond the requirement of TM interferometer, as the residual TTL coupled with alignment errors persists even with the imaging system. Therefore, an optimal position of the imaging system capable of eliminating the second-order term of the TTL coupling is determined. Meanwhile, the first-order term can be mitigated through in-orbit calibrations. These findings offer valuable guidance for the design and adjustment of imaging systems in space-borne gravitational wave detection missions, which require high-precision laser interferometry.

Application of meshless generalized finite difference method (GFDM) in single-phase coupled heat and mass transfer problem in three-dimensional porous media

This paper achieves effective and precise meshless modeling of three-dimensional (3D) single-phase coupled heat and mass transfer problems based on the generalized finite difference method (GFDM). It utilizes the Taylor formula and the weighted least squares method in the node influence domains to derive a generalized finite difference scheme for spatial derivatives of pressure and temperature. Consequently, a sequential coupled discrete scheme for the pressure diffusion equation and heat convection–conduction equation is formulated, resulting in the determination of pressure and temperature. An example conducts sensitivity analysis with different schemes of node collocation and different radius of influence domains. The calculation results demonstrate that this method exhibits good convergence. Two 3D model examples with regular and irregular boundaries illustrate the advantages of the GFDM in handling complex geometric problems within the computational domain, showcasing its superior flexibility and simplicity. This paper demonstrates the significant potential of GFDM in addressing complex geometric multi-physics field coupling challenges, offering innovative ideas for geothermal resource development, groundwater management, and thermal recovery in oil and gas reservoirs.

Generalized Yang Chizhong filtering and interpolation method without stationarity assumption

The stationarity assumption of geostatistical methods is difficult to satisfy in practice. To overcome this limitation, this study proposed a geometric and statistical coupling strategy for modeling spatial dependence structures and developed a generalized Yang Chizhong filtering and interpolation (GYangCZ) method without the assumption of stationarity. In this work, we theoretically prove the effectiveness of Yang Chizhong filtering in fitting spatial dependence structures from a geometric perspective, and develop an orientation-constrained Yang Chizhong filtering to fit the local and discontinuous spatial dependence structures. To measure nonstationary spatial dependence structure, we define a local statistical indicator (i.e., fundamental variation function) by comparing the variance of the original data and the fitted geometric surfaces obtained under different filtering radii. The fundamental variation function is used as the kernel function to obtain the approximate best linear unbiased estimators at unobserved locations. We theoretically demonstrate that when only a linear drift exists in local areas, GYangCZ does not require the stationarity assumption. GYangCZ was used to estimate the gold grade of the Xiadian gold deposit in China. The results show that GYangCZ outperformed ordinary kriging, moving window kriging, and kriging convolution networks. GYangCZ is easy to implement with wide applications in geoscience.

Accurate error compensation method for multi-axis parallel machine via singularized jacobi geometric parameter correction and coupling error evaluation

The Jacobian model is a prevalent tool for error compensation in multi-axis parallel mechanisms. However, discrepancies between the model's nominal and actual geometrical parameters, combined with equivalent replacements and high-order rounding in the modeling process, lead to equation solving challenges and modeling errors. These inaccuracies result in residual errors in the Jacobian model compensation. To address these problems, this paper proposes an optimal Jacobian correction approach. This is based on a geometrical parameter singularized Jacobian correction model, and a module for the evaluation of coupling errors for multi-axis parallel mechanisms was incorporated. Instead of relying on iterative processes, a singularized geometrical error solution method (SESM) was developed. Through this method, precise derivation of the Jacobian correction parameters is ensured, effectively addressing the indefinite equation challenge and partial posture non-solution problem. Moreover, modeling errors resulting from equivalent infinitesimal replacements and the overlooking of high-order minor values are compensated for by the SESM. It was observed that varying singularized geometrical parameters in the Jacobian model can produce different coupling effects and compensation outcomes. Therefore, a sensitivity-based error predictive evaluation method (EPEM) was introduced. By this method, the optimal correction parameter of the Jacobian model across the entire workspace is identified, ensuring precise pose error compensation. The proposed method was validated using a three-axis parallel mechanism. Through these tests, its superior efficacy was revealed. In comparison to the traditional uncorrected Jacobian compensation, reductions in position and orientation errors by 64.93% and 55.29%, respectively, were achieved. This method provides a new approach for error modeling, equation solving, and parameter correction for multi-axis mechanism error compensation and precision equipment development.

Random graphs and real networks with weak geometric coupling

Geometry can be used to explain many properties commonly observed in real networks. It is therefore often assumed that real networks, especially those with high average local clustering, live in an underlying hidden geometric space. However, it has been shown that finite-size effects can also induce substantial clustering, even when the coupling to this space is weak or nonexistent. In this paper, we study the weakly geometric regime, where clustering is absent in the thermodynamic limit but present in finite systems. Extending Mercator, a network embedding tool based on the popularity×similarity S1/H2 static geometric network model, we show that, even when the coupling to the geometric space is weak, geometric information can be recovered from the connectivity alone for networks of any size. The fact that several real networks are best described in this quasigeometric regime suggests that the transition between nongeometric and geometric networks is not a sharp one. Published by the American Physical Society 2024

Effect of slug characteristics on the nonlinear dynamic response of a long flexible fluid-conveying cylinder

Hydrocarbon flows in a marine riser may appear in multiple phases with varying flow patterns, among which, slug flows are known to exhibit complex flow characteristics due to fluctuations in multiphase mass, velocities, and pressure changes. Bulk of the literature concerning internal single and two-phase flow induced vibrations have largely focused on the use of a linearized tension beam model. In this study, the fluid-structure interaction phenomena of a submerged long flexible cylinder conveying two-phase slug flows is investigated taking into account the geometric and hydrodynamic nonlinearities. A semi-empirical theoretical model which consists of nonlinear structural equations of coupled out-of-plane, in-plane and axial structural motions is presented for the analysis and prediction of two-phase slug flow induced vibrations (SIV). The model includes equations involving centrifugal and Coriolis forces to capture mass variations in the slug flow regime. A numerical space-time finite difference approach combined with a frequency domain analysis is used for analyzing the highly nonlinear three-dimensional responses. The model assumes constant geometric properties across the span of the cylinder and utilizes an idealized slug unit concept, wherein slug properties are considered to be fully developed and undisturbed by pipe oscillations. Model validations are performed through comparisons with published experimental internal flow-induced vibration results. Parametric study captures the effects of several key slug characteristics on the vibration responses of a fluid-conveying cylinder. The results demonstrate amplitude-modulation response, mean displacements, three-dimensional cylinder displacements due to geometric nonlinear couplings and the influence of internal flow velocities. Higher dominant modes and oscillation frequencies were observed when the cylinder experiences large amplitude motions at specific slug formations. A new dimensionless parameter is introduced to predict scenarios of high amplitude oscillations for long flexible cylinders carrying two-phase slug flows.

More on β-symmetry

Recent work has proposed a method for imposing T-duality on the metric, B-field, and dilaton of the classical effective action of string theory without using Kaluza-Klein reduction. Specifically, the D-dimensional effective action should be invariant under global O(D,D) transformations, provided that the partial derivatives along the β-parameters of the non-geometrical elements of the O(D,D) group become zero. In this paper, we speculate that the global β-symmetry can be utilized to identify both bulk and boundary couplings.We demonstrate that the Gibbons-Hawking term at the leading order of α′ is reproduced by this symmetry. Additionally, for closed spacetime manifolds at order α′, we show that the 20 independent geometrical couplings at this order are fixed by this symmetry up to field redefinitions. Specifically, we show that the invariance of the most general covariant and gauge invariant bulk action at order α′ under the most general covariant deformed β-transformation at order α′ fixes the action up to 13 parameters. These parameters reflect the field redefinitions freedom for the closed spacetime manifolds. For particular values of these parameters, we recover the effective action in the Metsaev-Tseytlin and in the Meissner schemes.

Mould free laminated composites using eccentric fibre prestressing

Mould free fibre reinforced composites are an emerging manufacturing process that allows for complex shapes to be produced, independently from complex moulding. Previous examples demonstrated reconfiguration through thermal stresses induced by an asymmetrical stacking sequence within a laminate. However, asymmetry within the laminate can adversely influence the stiffness and geometric coupling which results in heavier structures. This paper presents eccentric prestressing as a novel method to produce more structurally efficient mould free laminated composites. Euler-Bernoulli beam theory and finite element methods were employed to predict the strain and deformation of laminated composites with selective fibre prestress. The internal and external strains were measured with chirped fibre bragg grating sensors, and surface mounted strain gauges respectively to validate the numerical and analytical predictions where a difference of 3.13% was reported. Finally, a comparative study was conducted to show the benefits of eccentric prestress over asymmetric 4D printed laminates.

Probability measures of fermions on branes

In our research, we explore the impact of a geometric non-minimal coupling between fermions and curvature scalars on the positioning of fermions within a brane structure. Our investigation encompasses massless fermionic modes and massive modes, revealing that specifically fermionic modes with left chirality are situated within the brane. This insight allows us to gain a more direct understanding of how the system’s geometry influences the placement of fermion fields on the brane. To delve deeper into the precise localization of massless fermionic modes, we employ entropic information measurements. By varying the parameters that govern the curvature scalars, we observe the ability to adjust the localization of these fermionic modes on the brane. Importantly, the BBM uncertainty relation remains satisfied in all scenarios, particularly for f1,2,3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{1,2,3}$$\\end{document}. We leverage the Shannon entropy as a highly effective metric to yield accurate results regarding the positioning of massless fermionic modes within our model. In the case of massive fermionic modes, we utilize relative probability analysis to pinpoint the resonant modes, and we identify the existence of these resonant modes in both f1,2,3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{1,2,3}$$\\end{document} cases. Ultimately, we ascertain that these parameters influence the placement of resonant modes by increasing the amplitude of the massive modes in the core of the brane.

A fast steering mirror with ultra-low geometric tilt-to-length coupling noise for space-borne gravitational wave detection

The misalignment between the geometric center and rotation center in fast steering mirrors (FSMs) poses a challenge for space-borne gravitational wave detection, as it results in geometric tilt-to-length (TTL) coupling noise. To address this issue, we have proposed a FSM structure that exhibits ultra-low geometric TTL coupling noise. The geometric TTL coupling noise is analyzed and evaluated strictly considering the FSM non-ideal tilt of the plane and the center shift characteristic of cartwheel flexure hinges under a small rotational angle. Compared to traditional FSM designs, our new design offers superior noise suppression capabilities and is capable of meeting the stringent piston effect noise requirements of 0.2 in the frequency band of under ideal conditions.

Passive aeroelastic study of large and flexible wind turbine blades for load reduction

In this paper, passive aeroelastic coupling of wind turbine blades for load reduction is realized by introducing bending-twist coupling (BTC) and geometric sweep coupling (GSC). The BTC is implemented by composite fiber off-axis of the blade spar cap, and the GSC is achieved by defining sweep curves of the blade reference axis. To investigate the passive coupling effect and load reduction of the large and flexible blades, the IEA 15 MW blades are considered. BTC are introduced into the three-dimensional finite element (FE) models and the residual stiffness coefficient is obtained. Meanwhile, geometrically exact beam theory (GEBT) is used to build the flexible blade. Both BTC and GSC are introduced into the beam model, and the effect elastic deformation on blade load is also considered. Multi-objective optimization (MOO) process of rotating blades for load reduction is proposed under steady-state rated conditions. The results show that the highest coupling efficiency can be obtained when the fiber off-axis angle is between 12° and 15°. The BTC of the blade can reduce the load of blade root with a small fiber off-axis angle. Meanwhile, the GSC can further reduce the axis torque. Compared with the initial design of IEA 15 MW steady-state rotating blade, the maximum thrust, flapwise moment and axis torque of the blade can be reduced by 8.8 %, 13.4 % and 22.9 % respectively.

One-To-One-To-One Internal Resonance Analysis of a Double-Cable-Stayed Flexible Beam-Structure Mounted with a Manipulator System

This paper deals with the theoretical studies to investigate the in-plane eigenvalue problems and the one-to-one-to-one internal resonance behaviors of a double-cable-stayed flexible beam-structure mounted with a manipulator system (DCFBMS) under constant rotational speed. A more precise and rigorous dynamic model with proper boundary conditions has been developed in which geometric nonlinearity and coupling nonlinearity of cables and beam are considered while the manipulator has been modeled as a rigid link. The in-plane eigenvalue problem of the model considering the boundary and continuous conditions has been evaluated and graphically demonstrated. Then, the ordinary differential equations (ODEs) are obtained by Galerkin’s method and multiple scales method has been employed to further analyze the vibration attributes of steady-state responses and their stability under internal resonance condition. The nonlinear response, stability and bifurcations for one-to-one-to-one internal resonance have also been investigated by varying system parameters. Analytically obtained results have been verified by Runge–Kutta method and found to be in good agreement. The present theoretical results deliver a useful insight into the nonlinear dynamic behavior and operational stability of DCFBMS.

Effective action of heterotic string theory at order α′2

Upon examining the effective action of the heterotic string theory at order α′2, an inconsistency between the Chern-Simons coupling Ω2 and T-duality has been discovered. To address this issue, we introduce 60 parity-even independent geometrical couplings involving the B-field, metric, and dilation at the same order, each with arbitrary coefficients. To ensure the invariance of these couplings under T-duality, we consider the Miessner action for the couplings at order α′ and rigorously determine the coefficients of the 60 couplings in terms of the Chern-Simons coupling. Notably, it is found that the coefficients of the Riemann cubed terms must be zero, which aligns with the results of S-matrix calculations. Additionally, the parity odd couplings at order α′2 are obtained through T-duality. Overall, our analysis successfully resolves the inconsistency between the Chern-Simons coupling and T-duality, providing a more comprehensive understanding of the behavior of the heterotic string theory at order α′2.

Fermion localization mechanisms in f(T,𝒯 )-brane

In this work, we investigate two mechanisms for locating fermions on the brane in a modified teleparallel gravity [Formula: see text], where [Formula: see text] is the torsion scalar and [Formula: see text] is the trace of the energy–momentum tensor. The first mechanism is a Yukawa-type minimal coupling between the fermion and the background scalar field. The second mechanism is a nonminimal coupling between the fermion and the torsion. The geometric coupling presents a greater sensitivity to the influence of torsion and to the trace of the energy–momentum tensor.

Asymmetries of frequency splittings of dipolar mixed modes: A window on the topology of deep magnetic fields

Context. Space asteroseismology is revolutionizing our knowledge of the internal structure and dynamics of stars. A breakthrough is ongoing with the recent discoveries of signatures of strong magnetic fields in the core of red giant stars. The key signature for such a detection is the asymmetry these fields induce in the frequency splittings of observed dipolar mixed gravito-acoustic modes. Aims. We investigate the ability of the observed asymmetries of the frequency splittings of dipolar mixed modes to constrain the geometrical properties of deep magnetic fields. Methods. We used the powerful analytical Racah-Wigner algebra used in quantum mechanics to characterize the geometrical couplings of dipolar mixed oscillation modes with various realistically plausible topologies of fossil magnetic fields. We also computed the induced perturbation of their frequencies. Results. First, in the case of an oblique magnetic dipole, we provide the exact analytical expression of the asymmetry as a function of the angle between the rotation and magnetic axes. Its value provides a direct measure of this angle. Second, considering a combination of axisymmetric dipolar and quadrupolar fields, we show how the asymmetry is blind to the unraveling of the relative strength and sign of each component. Finally, in the case of a given multipole, we show that a negative asymmetry is a signature of non-axisymmetric topologies. Conclusions. Asymmetries of dipolar mixed modes provide a key bit of information on the geometrical topology of deep fossil magnetic fields, but this is insufficient on its own. Asteroseismic constraints should therefore be combined with spectropolarimetric observations and numerical simulations, which aim to predict the more probable stable large-scale geometries.

Two-Stage Link Loss Optimization of Divergent Gaussian Beams for Narrow Field-of-View Receivers in Line-of-Sight Indoor Downlink Optical Wireless Communication (Invited)

The predominant focus of research in high-speed optical wireless communication (OWC) lies in line-of-sight (LOS) links with narrow infrared beams. However, the implementation of precise tracking and steering necessitates delicate active devices, thereby presenting a formidable challenge in establishing a cost-effective wireless transmission. Other than using none-line-of-sight (NLOS) links with excessive link losses and multi-path distortions, the simplification of the tracking and steering process can be alternatively achieved through the utilization of divergent optical beams in LOS. This paper addresses the issue by relaxing the stringent link budget associated with divergent Gaussian-shaped optical beams and narrow field-of-view (FOV) receivers in LOS OWC through the independent optimization of geometrical path loss and fiber coupling loss. More importantly, the geometrical path loss is effectively mitigated by modifying the transverse intensity distribution of the optical beam using manipulations of multi-mode fibers (MMFs) in an all-fiber configuration. In addition, the sufficiently excited higher order modes (HOMs) of MMFs enable a homogenized distribution of received optical powers (ROPs) within the coverage area, which facilitates the mobility of end-users. Comparative analysis against back-to-back links without free-space transmission demonstrates the proposed scheme’s ability to achieve low power penalties. With the minimized link losses, experimental results demonstrate a 10 Gbps error-free (BER < 10−13) LOS OWC downlink transmission at 2.5 m over an angular range of 10° × 10° without using any optical pre-amplifications at a typical PIN receiver. The proposed scheme provides a simple and low-cost solution for high-speed and short-range indoor wireless applications.