Linear Theoretical Model Research Articles

Monsoonal MCS Initiation, Rainfall, and Diurnal Gravity Waves over the Bay of Bengal: Observation and a Linear Model

Abstract Previous observational studies have indicated that mesoscale convective systems (MCSs) contribute the majority of precipitation over the Bay of Bengal (BoB) during the summer monsoon season, yet their initiation and propagation remain incompletely understood. To fill this knowledge gap, we conducted a comprehensive study using a combination of 20-yr satellite observations, MCS tracking, reanalysis data, and a theoretical linear model. Satellite observations reveal clear diurnal propagation signals of MCS initiation frequency and rainfall from the west coast of the BoB toward the central BoB, with the MCS rainfall propagating slightly slower than the MCS initiation frequency. Global reanalysis data indicate a strong association between the offshore-propagating MCS initiation frequency/rainfall and diurnal low-level wind perturbations, implying the potential role of gravity waves. To verify the hypothesis, we developed a 2D linear model that can be driven by realistic meteorological fields from reanalysis. The linear model realistically reproduces the characteristics of offshore-propagating diurnal wind perturbations. The wind perturbations, as well as the offshore propagation signals of MCS initiation frequency and rainfall, are associated with diurnal gravity waves emitted from the coastal regions, which in turn are caused by the diurnal land–sea thermal contrast. The ambient wind speed and vertical wind shear play crucial roles in modulating the timing, propagation, and amplitude of diurnal gravity waves. Using the linear model and satellite observations, we further show that the stronger monsoonal flows lead to faster offshore propagation of diurnal gravity waves, which subsequently control the offshore propagation signals of MCS initiation and rainfall. Significance Statement Rainfall over the Bay of Bengal (BoB) is primarily contributed by large and organized rainfall systems in the summer monsoon season. During this season, these systems are commonly observed over the east coast of India around midnight, the western BoB in the morning, and the central BoB in the afternoon. This eastward rainfall propagation is confirmed by observations, reanalysis data, and a theoretical model to have a strong association with atmospheric diurnal gravity waves. These waves are caused by land–sea thermal contrast and can trigger rainfall systems over the offshore regions. We also found that the diurnal gravity waves, as well as their triggered rainfall systems, can be greatly modulated by the large-scale monsoonal flows. All the above findings improve our understanding of diurnal rainfall cycle over the BoB and may contribute to the future improvement of rainfall forecast over the region.

In-plane elastic property prediction of straight-arc coupled auxetic structures

Auxetic metamaterials with two components exhibit a wide variety of potential engineering applications due to their exotic mechanical properties. In this work, a novel straight-arc coupled structure (SACS) is designed by introducing a circular arc structure to a classical re-entrant structure. This work aims to explore the linear and geometrical nonlinear mechanical of SACS at large strains. According to Castigliano’s second theorem, the in-plane linear theoretical model is established to obtain equivalent Poisson’s ratio and elastic modulus. A geometrical nonlinear model is further established based on large deflection theory and chain algorithm. The finite element method is used to verify the prediction of the theoretical solution, and linear and nonlinear mechanical properties of the SACS are studied by numerical simulation. The influence of geometric parameter re-entrant angle and arc radius on the mechanical properties of the SACS is investigated to compare the linear and nonlinear mechanical properties. The linear numerical simulation of SACS with two transverse ribs (SACS-TR) and classical re-entrant honeycomb structure with two transverse ribs (CRS-TR) is carried out to analyze the in-plane elastic properties. These results demonstrate that considering the geometric nonlinear model can predict the actual structural deformation more accurately, which is verified by the quasi-static compression experiment results at large strains. The SACS design can enhance the auxetic effect and structure Young’s moduli under the same dimension.

Thermophoresis beyond Local Thermodynamic Equilibrium.

We measure the thermophoresis of polysterene beads over a wide range of temperature gradients and find a pronounced nonlinear phoretic characteristic. The transition to the nonlinear behavior is marked by a drastic slowing down of thermophoretic motion and is characterized by a Péclet number of order unity as corroborated for different particle sizes and salt concentrations. The data follow a single master curve covering the entire nonlinear regime for all system parameters upon proper rescaling of the temperature gradients with the Péclet number. For low thermal gradients, the thermal drift velocity follows a theoretical linear model relying on the local-equilibrium assumption, while linear theoretical approaches based on hydrodynamic stresses, ignoring fluctuations, predict significantly slower thermophoretic motion for steeper thermal gradients. Our findings suggest that thermophoresis is fluctuation dominated for small gradients and crosses over to a drift-dominated regime for larger Péclet numbers in striking contrast to electrophoresis.

Compromised Vibration Isolator of Electric Power Generator Considering Self-Excitation and Basement Input

A previous study proposed an optimal vibration isolator for self-excitation, but the solution results showed a critical drawback for the basement input. Because the plant system is exposed to self-excitation and basement input, the vibration isolator characteristics must meet all the requirements of both excitation cases. Two performance indices of the vibration isolator were introduced to evaluate the vibration control capability over two excitation cases, self-excitation and basement input, using the theoretical linear model of the electric power generator. The compromise strategy was devoted to enhancing the vibration control capability over the basement input, owing to the acceptable margin for self-excitation. The modification of the mechanical properties of the vibration isolator focused on the isolator between the mass block and the surrounding building. Simulation results revealed that an increase in the spring coefficient and a decrease in the damping coefficient of the vibration isolator beneath the mass block could enhance the vibration reduction capability over the basement input.

Smart Manufacturing as a Management Strategy to Achieve Sustainable Competitiveness

The aim of this study is to determine whether smart technologies can bring sustainable competitiveness to manufacturing firms and this study attempts to determine it through theoretical linear modelling. This paper reflects on the importance of sustainable competitiveness and means of achieving sustainable competitiveness by highlighting it through analysis of scientific literature review. It explains competitiveness by the means of resources and capabilities, clustering, and public policy. This study also presents an analytical framework that interlinks Quintuple Helix model, Industry 5.0, and sustainable competitive. This study also emphasizes on a management strategy that explains how a manufacturing firm devise a strategy to obtain sustainable competitiveness. A theoretical linear model is developed that identifies digital technologies proven to be the source of manufacturing competitiveness. This work also shed light to the limitations in order to measure or determine competitiveness factor at national, regional, or firm level. For the future researchers, this study provides a baseline to develop a mechanism of measuring competitiveness based on smart technology.

Bond of FRP rods in damaged RC beams strengthened with NSM technique

In strengthening reinforced concrete (RC) elements with composite materials, the role of adherence between concrete and FRP assumes great importance as it guarantees the effectiveness of the consolidation method. In this paper the bond mechanisms between FRP rods and concrete second the Near Surface Mounted (NSM) technique have been analyzed by experimental results of investigation and a theoretical linear model. The experimental investigation consists of direct pull-out tests on RC elements with circular GFRP and CFRP rods inserted into a groove. Through pull-out tests main parameters of bond have been presented. The experimental results are compared with those obtained by the theoretical model.

The diurnal Yarkovsky effect of irregularly shaped asteroids

The Yarkovsky effect plays an important role in the motions of small celestial bodies. Increasingly detailed observations bring the need for high-accuracy modelling of the effect. We used the multiphysics software COMSOL to model the diurnal Yarkovsky effect in three dimensions and compare the results with those derived from the widely adopted theoretical linear model. We find that the linear model shows high accuracy for spherical asteroids in most cases. We explored the range of parameters for which the relative error of the linear model is over 10%. For biaxial ellipsoidal asteroids (particularly oblate ones), the linear model systematically overestimates the transverse Yarkovsky force by ~10%. The diurnal effect on triaxial ellipsoids is periodic, and no linear model is available for this phenomenon. Our numerical calculations show that the average effects on triaxial ellipsoids are stronger than those on biaxial ellipsoids. We also investigated the diurnal effect on asteroids of real shapes and find it be overestimated by the linear model by 16% on average, with a maximum of up to 35%. To estimate the strength of the Yarkovsky effect directly from the shape, we introduced the quantity of ‘effective area’ for asteroids of any shape, and find a significant linear relationship between the Yarkovsky migration rate and the effective area. This brings great convenience to the estimation in practice.

A Theoretical Dynamical Noninteracting Model for General Manipulation Systems Using Axiomatic Geometric Structures

This paper presents a new theoretical approach to the study of robotics manipulators dynamics. It is based on the well-known geometric approach to system dynamics, according to which some axiomatic definitions of geometric structures concerning invariant subspaces are used. In such a framework, certain typical problems in robotics are mathematically formalised and analysed in axiomatic form. The outcomes are sufficiently general that it is possible to discuss the structural properties of robotic manipulation. A generalized theoretical linear model is used, and a thorough analysis is made. The noninteracting nature of this model is also proven through a specific theorem.

The impact of moisture on thermal conductivity of fabrics

The article presents the experimental results of the thermal conductivity of absorbent fabrics for increasing relative amount of water in the fabric. Measurements confirm that the effective thermal conductivity of fabrics at low moisture level is proportional to the relative amount of water absorbed in fabrics. With increasing relative amount of water in the fabric, effective thermal conductivity stabilizes around the value comparable with the thermal conductivity of water. The experimental results are compared with the theoretical linear model.

Polyphonic workflows

Abstract The dubbing process is usually depicted as a linear model in which its participants occupy fixed roles determined by their specializations. However, Torre A, a Peruvian dubbing firm, applies alternative procedures in an emerging context of the dubbing industry. This first case study of dubbing in Peru seeks to examine the dubbing process employed by the agency Torre A based on two projects taking place during its emerging stage as a company. Participants from both projects were interviewed to reconstruct each project workflow. The workflows were then analyzed to contrast the monological, linear theoretical model found in the literature with the dialogical model arising from the participants’ voices. The results show the looping nature of the dubbing process, which is comprised of tasks performed simultaneously or repeatedly by versatile agents whose roles depend on available human and temporal resources as well as intrinsic motivation. This multiplicity of roles also influences the quality criteria used by the agents, who formulate criteria based on their professional perspectives, experiences, and general knowledge of the dubbing process. Thus, a variety of dubbing project circumstances determine how dubbing takes place. This represents a departure from the traditional, or standardized, model of dubbing.

Effects of Coulomb collisions on lower hybrid drift waves inside a laboratory reconnection current sheet

We have developed a local, linear theoretical model for lower hybrid drift waves that can be used for plasmas in the weakly collisional regime. Two cases with typical plasma and field parameters for the current sheet of the magnetic reconnection experiment have been studied. For a case with a low electron beta (βe=0.25, high guide field case), the quasi-electrostatic lower hybrid drift wave is unstable, while the electromagnetic lower hybrid drift wave has a positive growth rate for a high-βe case (βe=8.9, low guide field case). For both cases, including the effects of Coulomb collisions reduces the growth rate but collisional impacts on the dispersion and growth rate are limited (≲20%).

Linear analysis of Atwood number effects on shear instability in the elastic\u2013plastic solids

The evolution of shear instability between elastic–plastic solid and ideal fluid which is concerned in oblique impact is studied by developing an approximate linear theoretical model. With the velocities expressed by the velocity potentials from the incompressible and irrotational continuity equations and the pressures obtained by integrating momentum equations with arbitrary densities, the motion equations of the interface amplitude are deduced by considering the continuity of normal velocities and the force equilibrium with the perfectly elastic–plastic properties of solid at interface. The completely analytical formulas of the growth rate and the amplitude evolution are achieved by solving the motion equations. Consistent results are performed by the model and 2D Lagrange simulations. The characteristics of the amplitude development and Atwood number effects on the growth are discussed. The growth of the amplitude is suppressed by elastic–plastic properties of solids in purely elastic stage or after elastic–plastic transition, and the amplitude oscillates if the interface is stable. The system varies from stable to unstable state as Atwood number decreasing. For large Atwood number, elastic–plastic properties play a dominant role on the interface evolution which may influence the formation of the wavy morphology of the interface while metallic plates are suffering obliquely impact.

Electron bunch charge enhancement in laser wakefield acceleration using a flattened Gaussian laser pulse

We demonstrate the charge enhancement of the electron bunch using a flattened Gaussian laser pulse in laser wakefield accelerations. In laser wakefield accelerations, the change in laser pulse shape affects the diffraction pattern, resulting in laser intensity variation during plasma interaction. We employ a flattened Gaussian laser pulse to excite wakefields for electron acceleration. The central flattened region of the flattened Gaussian laser pulse, having the same energy as the Gaussian pulse, helps to enhance the pulse intensity via self-focusing. Thus, the evolution of flat Gaussian pulse enhances self-injection, which leads a considerable amount of electrons into the accelerating fields. A linear theoretical model is adopted to understand the wakefield generation mechanism using Gaussian and flattened Gaussian pulses. In order to broaden our understanding, quasi-three-dimensional PIC simulations are also performed. Our results show that a flattened Gaussian laser pulse with N=2 (where N is the order of the super Gaussian shape) yields a good quality electron bunch with retaining a relatively higher charge (about 300 pC) with respect to the case of a Gaussian laser pulse. We also show a twofold increase in bunch peak current when a flattened Gaussian pulse is employed. The electron bunches with high charge and high current may be promising candidates to drive next-generation compact free-electron lasers with unique X-ray properties.

On the forced oscillations in a precessing open cylindrical channel

In this paper, theoretical and experimental results of the forced oscillations in an open precessed cylindrical channel are reported. The theoretical part treats the problem using a linear inviscid irrotational approximation, where different inertial modes, such as resonance ones, are presented. A real-channel flume model was constructed for the experimental part, where three different control parameters were considered: the nutation angle, the rotation rate, and the average water depth. The experiments focused on tracking the different responses toward the provided forces to the system with comparison with the assumed theory where this was possible, as other nonlinear aspects appeared. The experimental observations were tracked using a charge-coupled device sensor type camera, which enabled the extraction of both quantitative and qualitative results. The measurement of the azimuthal velocity involved the use of an acoustic Doppler velocimeter, an approach that closely aligned with the theoretical linear model; this measured velocity was also compared with the three different control parameters. The system shows instabilities in the form of resonance collapse and triadic resonance; in addition, an experimental diagram involving variation in both Reynolds and Rossby numbers is provided.

An Optimal Model Identification Algorithm of Nonlinear Dynamical Systems With the Algebraic Method

Abstract This article proposes a nonparametric system identification technique to discover the governing equation of nonlinear dynamic systems with the focus on practical aspects. The algorithm builds on Brunton’s work in 2016 and combines the sparse regression with an algebraic calculus to estimate the required derivatives of the measurements. This reduces the required derivative data for the system identification. Furthermore, we make use of the concepts of K-fold cross validation from machine learning and information criteria for model selection. This allows the system identification with less measurements than the typically required data for the sparse regression. The result is an optimal model for the underlining system of the data with a minimum number of terms. The proposed nonparametric system identification method is applicable for multiple-input–multiple-output systems. Two examples are presented to demonstrate the proposed method. The first one makes use of the simulated data of a nonlinear oscillator to show the effectiveness and accuracy of the proposed method. The second example is a nonlinear rotary flexible beam. Experimental responses of the beam are used to identify the underlining model. The Coulomb friction in the servo motor together with other nonlinear terms of the system variables are found to be important components of the model. These are, otherwise, not available in the theoretical linear model of the system.

ZnO ALD-Coated Microsphere-Based Sensors for Temperature Measurements.

In this paper, the application of a microsphere-based fiber-optic sensor with a 200 nm zinc oxide (ZnO) coating, deposited by the Atomic Layer Deposition (ALD) method, for temperature measurements between 100 and 300 °C, is presented. The main advantage of integrating a fiber-optic microsphere with a sensing device is the possibility of monitoring the integrity of the sensor head in real-time, which allows for higher accuracy during measurements. The study has demonstrated that ZnO ALD-coated microsphere-based sensors can be successfully used for temperature measurements. The sensitivity of the tested device was found to be 103.5 nW/°C when the sensor was coupled with a light source of 1300 nm central wavelength. The measured coefficient R2 of the sensor head was over 0.99, indicating a good fit of the theoretical linear model to the measured experimental data.

Whistler Mode Waves Excited by Anisotropic Hot Electrons With a Drift Velocity in Earth's Magnetosphere: Linear Theory

AbstractWith a linear theoretical model, we have investigated the properties of whistler waves excited by anisotropic hot electrons with a drift velocity parallel to the background magnetic field, which is usually neglected in previous studies. It is found that a finite drift velocity can significantly change the properties of excited whistler waves, resulting in distinct properties for parallel and antiparallel propagating waves. In the high‐beta regime, as the drift velocity increases, the frequency of parallel propagating whistler waves increases, while that of antiparallel propagating waves is found to decline. So parallel and antiparallel propagating whistler waves appear in different frequency bands. However, the growth rate of parallel wave is always smaller than that of antiparallel wave and falls below 10−2Ωe for large drift velocities (vd/vth > 1.5), in which case the parallel wave may be too weak to be observed. Generally, the growth rate of whistler waves in both directions is enhanced with the increasing anisotropy or proportion of hot electrons. In the low‐beta regime, the trends of the frequency and linear growth rate of excited whistler waves are quite similar to those in the high‐beta regime. But with the increase of the drift velocity, the wave normal angle of parallel propagating whistler waves gradually declines until reaching 0, while that of antiparallel propagating waves continues to increase. Our study may be helpful to understand various whistler mode spectra observed in the Earth's magnetosphere.

A linear theoretical model of cavitation flow past a multihydrofoil system with a finite number of foils

Aiming to study the complicated interference phenomenon of the cavitation flow around a multihydrofoil system with a finite number of foils, we establish a linear theoretical model under the conditions of small angle of attack and small cavitation number. By solving the model numerically, we analyze the effects of different cavitation numbers and foil spacings on cavitation flow. The cavitation shape and hydrodynamics of each foil in the multihydrofoil system are obtained. The shapes of the cavities differ from each other because of the mutual interference phenomenon. Moreover, the change rule for cavitation shapes, which varied with the foil spacing and cavitation number, is very complicated, and no simple mode can be found. The linear theoretical model in this article is suitable for the problem of cavitation flow around multiple hydrofoils with different chord length, camber, and angle of attack.

Dynamics of a Partially Confined, Vertical Upward-Fluid-Conveying, Slender Cantilever Pipe with Reverse External Flow

：A linear theoretical model is established for the dynamics of a hanging vertical cantilevered pipe which is subjected concurrently to internal and reverse external axial flows. Such pipe systems may have instability by flutter (amplified oscillations) or static divergence (buckling). The pipe system under consideration is a slender flexible cantilevered pipe hanging concentrically within an inflexible external pipe of larger diameter. From the clamped end to the free end, fluid is injected through the annular passage between the external pipe and the cantilevered pipe. When exiting the annular passage, the fluid discharges in the counter direction along the cantilevered pipe. The inflexible external pipe has a variable length and it can cover a portion of the length of the cantilevered pipe. This pipe system has been applied in the solution mining and in the salt cavern underground energy storage industry. The planar motion equation of the system is solved by means of a Galerkin method, and Euler–Bernoulli beam eigenfunctions are used as comparison functions. Calculations are conducted to quantify the effects of different confinement conditions (i.e., the radial confinement degree of the annular passage and the confined-flow length) on the cantilevered pipe stability, for a long leaching-tubing-like system. For a long system, an increase in the radial confinement degree of the annular passage and the confined-flow length gives rise to a series of flutter and divergence. Additionally, the effect of the cantilevered pipe length is studied. Increasing the cantilevered pipe length results in an increase of the critical flow velocity while a decrease of the associated critical frequency. For a long enough system, the critical frequency almost disappears.

A nonlinear model for a hanging tubular cantilever simultaneously subjected to internal and confined external axial flows

A full nonlinear model is developed for the dynamics of a hanging tubular cantilever that is simultaneously subjected to internal and external axial flows. These two flows are dependent on each other and are in opposite directions. Also, the external flow is confined over the whole length of the cantilever. A nonlinear equation of motion for the cantilever is obtained via Hamilton's principle to third-order accuracy. The virtual work due to the fluid-related forces acting on the cantilever is derived, to the same accuracy, considering the non-conservative forces associated with the internal flow as well as the inviscid, viscous and hydrostatic forces related to the external one. In addition, a vortex-lift mechanism due to the external flow is considered, and the associated steady hydrodynamic forces are derived and added to the expression of the virtual work. The equation of motion is then discretized and solved using the pseudo-arclength continuation method and a direct time-integration technique. The dynamical behaviour obtained is compared to the one predicted by another linear theoretical model, from the literature, for the same system parameters. The two models are in good qualitative and quantitative agreement with each other in terms of the type of instability, namely flutter, that occurs with increasing flow velocity and its onset. However, the proposed model can also predict quantitative facets of the dynamical behaviour beyond the onset of instability, such as limit-cycle amplitude and frequency. Moreover, the influences of various system parameters are investigated theoretically, namely the degree of confinement of the external flow, gravity, mass ratio, drag coefficient, and the thickness of the tubular cantilever.