Approximate Analytical Expressions Research Articles

Novel active-passive hybrid piezoelectric network for vibration suppression in fluid-conveying pipes

Given the failures like fatigue and fracture of the pipes conveying fluid induced by undesired dynamics and instability and the traditional passive damping cannot effectively attenuate the vibration in the low-frequency bands, this work introduces a novel active-passive control technique, namely, the hybrid piezoelectric network consisting of the piezoelectric layer, the circuit of the resistance and inductance, voltage source, controller, and sensor, which is attached on the cantilevered fluid-conveying pipes to suppress the vibration in wider frequency-bands. Built upon the location of the neutral axis in the segment of pipes is varied due to the integration of the pipeline and piezoelectric actuator, the governing equations of the fluid-conveying pipes attached with the hybrid piezoelectric network are established by virtue of Hamilton's principle in conjunction with the assumed mode method, and approximate analytical expressions of frequency responses are derived using the Laplace transform technique. The passive damping performance is carried out to achieve insightfully using the open-loop analysis based on the circuit of the resistance and inductance is set as the passive shunt characteristic, then the closed-loop features are also investigated according to the velocity feedback control. The numerical example illustrates the presented control method is effective and feasible to realize the vibration suppression on the pipes conveying fluid. Based on this, the optimal resistance and inductance are proposed through the theoretical analysis, which can further broaden the vibration attenuation.

SLJCompact: A semiconductor-liquid junction solver for rapid band diagram insights into photoelectrochemical devices

SLJCompact is a Matlab based program that computes the band diagram and current-voltage characteristics of semiconductor photoanodes. To enable rapid insights, corresponding to various semiconductor-liquid junction (SLJ) properties and observable current-voltage characteristics, an abridged set of semi-analytical conservation equations are employed in the semiconductor region coupled with Gouy-Chapman screening within the liquid region. Electrostatic interactions between these regions across the junction are solved self-consistently through a variation on the Scharfetter-Gummel method. In this manner, the model is able to provide key band diagram insights regarding the correlated operation of photoanodes, both under illumination and in the dark, with respect to: current-voltage trends, quasi-Fermi level splitting, hole transfer rates, electron transfer rates, depletion region screening, hole inversion screening, and carrier recombination lifetimes. Motivated by Kroemer's lemma, SLJCompact is intended to further the adoption of band diagram methods within the photoelectrochemical device literature, by providing a computationally inexpensive approach residing between computationally intensive full continuity equation solvers and more approximate analytical expressions. Program summaryProgram Title: SLJCompactCPC Library link to program files:https://doi.org/10.17632/by4ddckrpt.1Developer's repository link:https://www.physics.mcgill.ca/~bevankh/Codes/SLJCompact/Licensing provisions: CC BY NC 4.0Programming language: MatlabNature of problem: Providing rapid self-consistently computed insights into the operational and band diagram characteristics of photoelectrochemical devices.Solution method: A semi-analytical approach for solving carrier transfer and recombination in the depletion region coupled self-consistently with Poisson's equation across a semiconductor-liquid junction, solved together through a variation on the Scharfetter-Gummel method.Additional comments including restrictions and unusual features: The current version is only applicable to photoanodes and forward bias trends at/beyond flat band conditions.

Ergodic Rate Analysis and Phase Design of STAR-RIS Aided NOMA With Statistical CSI

In this letter, we consider a simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-aided non-orthogonal multiple access (NOMA) downlink communication system. The base station (BS) is a uniform linear array (ULA) consisting of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -elements. The expressions of the statistic of signal-to-interference-noise ratio (SINR) are derived with the statistical characteristics of the channels and they are maximized to design the phase shift matrices for reflection and transmission. Furthermore, the approximate analytical expressions of the ergodic rate are derived and the asymptotic performance is analyzed. It is found from the approximate analytical expressions that increasing the size of the ULA at BS and the STAR-RIS size can effectively improve the ergodic rate of the system. The simulation results validate the validity of the theoretical analysis and the design of the phase shift matrices.

First-order approximate analytical expressions of oblique incident elastic wave at an interface of porous media saturated with a non-viscous fluid

The analysis technology of Amplitude Variation with Offset (AVO) is one of the important methods for oil and gas reservoir prediction. Zoeppritz equation and its approximations are the theoretical basis of AVO analysis, which assumes that the upper and lower media of a horizontal interface are single-phase media. Limited by this assumption, AVO analysis has limited prediction and identification accuracy for complex porous reservoirs. In view of this, the first-order approximate analytical expressions of oblique elastic wave at an interface of porous media are derived. Firstly, the incident and scattering characteristics of various waves at the interface of porous media are analyzed, and the displacement vectors generated by these elastic waves are described by exponential function. Secondly, the kinematic and dynamic boundary conditions at the interface of porous media are discussed. Thirdly, by substituting the displacement vectors of incident and scattered waves into boundary conditions, the exact analytical equation is derived. Then, considering the symmetry of scattering matrix in the equation, the exact analytical expressions of each scattered wave are obtained. Furthermore, under the assumptions of small incident angle, weak elasticity at an interface of porous media, and ignoring the second- and higher-order terms, the first-order approximate analytical expressions are derived. Establishing a model of sandstone porous media with different porosity in upper and lower media, the correctness of the approximate analytical expressions is verified, and the elastic wave response characteristics of lithology and pore fluids are analyzed.

Approximate Analytical Solution to a Pore Network Model of Deactivation of Immobilized Glucose Isomerase in Packed-Bed Reactors Using Akbari-Ganji’s Method

The main objective of this paper is to derive an approximate analytical solution for the mathematical model pertaining to deactivation of immobilized glucose in packed-bed reactors. The Akbari-Ganji’s method is applied to solve the previously developed mathematical model. The approximate analytical expressions corresponding to the concentration and current in the steady state condition have been derived for all values of parameters. Excellent agreement is obtained between the analytical solution and the numerical simulation. The analytical solution presented in this paper is presented for the first time. The results of this work will provide a better understanding of the mathematical model examined.

Dissipation of oscillating scalar backgrounds in an FLRW universe

We study the dissipation of oscillating scalar backgrounds in a spatially flat Friedmann-Lemaître-Robertson-Walker universe using non-equilibrium quantum field theory. To be concrete, a Z2-symmetric two-scalar model with quartic interactions is used. For quasi-harmonic oscillations, we adopt the multi-scale analysis to obtain analytical approximate expressions for the evolution of the scalar background in terms of the retarded self-energy and retarded proper four-vertex function. Different from the case in flat spacetime, we find that in an expanding universe the condensate decay in this model can be complete only if the imaginary part of the retarded self-energy is not negligibly small. The microphysical interpretation of the imaginary parts of the retarded self-energy and retarded proper four-vertex function in terms of particle production is also discussed.

Simulations of surface charge density changes during the untreated solid tumour growth.

Understanding untreated tumour growth kinetics and its intrinsic behaviour is interesting and intriguing. The aim of this study is to propose an approximate analytical expression that allows us to simulate changes in surface charge density at the cancer-surrounding healthy tissue interface during the untreated solid tumour growth. For this, the Gompertz and Poisson equations are used. Simulations reveal that the unperturbed solid tumour growth is closely related to changes in the surface charge density over time between the tumour and the surrounding healthy tissue. Furthermore, the unperturbed solid tumour growth is governed by temporal changes in this surface charge density. It is concluded that results corroborate the correspondence between the electrical and physiological parameters in the untreated cancer, which may have an essential role in its growth, progression, metastasis and protection against immune system attack and anti-cancer therapies. In addition, the knowledge of surface charge density changes at the cancer-surrounding healthy tissue interface may be relevant when redesigning the molecules in chemotherapy and immunotherapy taking into account their polarities. This can also be true in the design of completely novel therapies.

Stability Analysis of Fractional-Order Mathieu Equation with Forced Excitation

The advantage of fractional-order derivative has attracted extensive attention in the field of dynamics. In this paper, we investigated the stability of the fractional-order Mathieu equation under forced excitation, which is based on a model of the pantograph–catenary system. First, we obtained the approximate analytical expressions and periodic solutions of the stability boundaries by the multi-scale method and the perturbation method, and the correctness of these results were verified through numerical analysis by Matlab. In addition, by analyzing the stability of the k’T-periodic solutions in the system, we verified the existence of the unstable k’T-resonance lines through numerical simulation, and visually investigated the effect of the system parameters. The results show that forced excitation with a finite period does not change the position of the stability boundaries, but it can affect the expressions of the periodic solutions. Moreover, by analyzing the properties of the resonant lines, we found that when the points with k’T-periodic solutions were perturbed by the same frequency of forced excitation, these points became unstable due to resonance. Finally, we found that both the damping coefficient and the fractional-order parameters in the system have important influences on the stability boundaries and the resonance lines.

Investigating the propagation characteristics of modulated circular Airy vortex beam in free space via angular spectrum method

In this paper, the approximate analytical expression of the Hankel transform of arbitrary order circular Airy vortex beam (CAVB) is derived, which enables researchers to solve the propagation characteristics of the family of CAVB via angular spectrum method. Moreover, based on the approximate analytical expression, the propagation characteristics of Fourier space modulated and azimuthally modulated CAVB are investigated. It is found that by modulating the CAVB via a Fourier space periodic function, multiple focal points can be generated during the propagation; and by modulating the CAVB via azimuthally grafting two spiral phases, the focal point of the beam will deviate from the center of the focal plane. These results provide a simple method for flexible regulation of the number and location of the focal points of the CAVB.

Dynamics Modeling and Characterization of Sunk Screw Connection Structure in Small Rockets

Bolted flange joints are widely used in engineering structures. Sunk screw connection structures commonly used in small rockets and missiles exhibit significant nonlinear characteristics when subjected to forces. In this article, a study of the dynamic characteristics of sunk screw connection is conducted. A 3-dof trilinear dynamic model is proposed, based on the study of the stiffness characteristics of the connection structure and considering contact nonlinearities. The connection surface is simplified as two axial trilinear springs and a lateral linear spring. The motion of the system can be divided into nine regions by the turning point of the trilinear springs. So that the motion of the system in each region can be completely resolved, the dynamic characteristics of the 3-dof trilinear system under impulse load and simple harmonic load are studied by means of semi-numerical analytical method. It is found that the response frequency of the system remains unchanged under a small impulse load, and the response can be obtained by approximate analytical expressions. When the impulse load is large, the response frequency is fluctuant, which reflects the sensitivity of the nonlinear system to the magnitude of impulse load. Under the simple harmonic excitation of bending moment, the response frequency curve of the system presents good single peak characteristics when the excitation amplitude is small. When the amplitude is large, the peak frequency of the system shifts, and the phenomenon of multi-peak resonance is shown in a certain range.

The General Analytic Expression of a Harvested Logistic Model with Slowly Varying Coefficients

The harvested logistic model with a slow variation in coefficients has been considered. Two cases, which depend on the harvest rate, were identified. The first one is when the harvest is subcritical, where the population evolves to an equilibrium. The other is supercritical harvesting, where the population decreases to zero at finite times. The single analytic approximate expression, which is capable of describing both harvesting cases, is readily and explicitly obtained using the multi-time scaling method together with the perturbation approach. This solution fits for a wide range of coefficient values. In addition, such an expression is validated by utilizing numerical computations, which are obtained by using the fourth-order Runge–Kutta technique. Finally, the comparison shows a very good agreement between the two methods.

Phases of Small Worlds: A Mean Field Formulation

A network is said to have the properties of a small world if a suitably defined average distance between any two nodes is proportional to the logarithm of the number of nodes, N. In this paper, we present a novel derivation of the small-world property for Gilbert–Erdös–Renyi random networks. We employ a mean field approximation that permits the analytic derivation of the distribution of shortest paths that exhibits logarithmic scaling away from the phase transition, inferable via a suitably interpreted order parameter. We begin by framing the problem in generality with a formal generating functional for undirected weighted random graphs with arbitrary disorder, recovering the result that the free energy associated with an ensemble of Gilbert graphs corresponds to a system of non-interacting fermions identified with the edge states. We then present a mean field solution for this model and extend it to more general realizations of network randomness. For a two family class of stochastic block models that we refer to as dimorphic networks, which allow for links within the different families to be drawn from two independent discrete probability distributions, we find the mean field approximation maps onto a spin chain combinatorial problem and again yields useful approximate analytic expressions for mean path lengths. Dimorophic networks exhibit a richer phase structure, where distinct small world regimes separate in analogy to the spinodal decomposition of a fluid. We find that is it possible to induce small world behavior in sub-networks that by themselves would not be in the small-world regime.

QED medium effects in (anti)neutrino-nucleus and electron-nucleus scattering: Elastic scattering on nucleons

Interpretation of current and future neutrino oscillation and electron scattering experiments requires knowledge of lepton-nucleon and lepton-nucleus interactions at the percent level. We study the exchange of photons between charged particles and the nuclear medium for (anti)neutrino-, electron-, and muon-induced reactions inside a large nucleus. While quantum electrodynamics (QED)-medium contributions are formally suppressed by two powers of the electromagnetic coupling constant α when compared to the leading-order cross sections, low-energy modes and the nuclear size enhance the effect by orders of magnitude. They require a proper infrared regularization, which we implement as a screening of the electromagnetic interactions at atomic length scales or above. We provide approximate analytic expressions for the distortion of (anti)neutrino-nucleus and charged lepton-nucleus cross sections and evaluate the QED-medium effects for realistic values of the screening scale on the example of elastic scattering with nucleons inside the nucleus. We find new permille- to percent-level effects, which were not considered in either (anti)neutrino-nucleus or electron-nucleus scattering.

Spectrum and energy efficient multi-antenna spectrum sensing for green UAV communication

Unmanned Aerial Vehicle (UAV) communication is a promising technology that provides swift and flexible on-demand wireless connectivity for devices without infrastructure support. With recent developments in UAVs, spectrum and energy efficient green UAV communication has become crucial. To deal with this issue, Spectrum Sharing Policy (SSP) is introduced to support green UAV communication. Spectrum sensing in SSP must be carefully formulated to control interference to the primary users and ground communications. In this paper, we propose spectrum sensing for opportunistic spectrum access in green UAV communication to improve the spectrum utilization efficiency. Different from most existing works, we focus on the problem of spectrum sensing of randomly arriving primary signals in the presence of non-Gaussian noise/interference. We propose a novel and improved p-norm-based spectrum sensing scheme to improve the spectrum utilization efficiency in green UAV communication. Firstly, we construct the p-norm decision statistic based on the assumption that the random arrivals of signals follow a Poisson process. Then, we analyze and derive the approximate analytical expressions of the false-alarm and detection probabilities by utilizing the central limit theorem. Simulation results illustrate the validity and superiority of the proposed scheme when the primary signals are corrupted by additive non-Gaussian noise and arrive randomly during spectrum sensing in the green UAV communication.

Development of probabilistic FRP-to-concrete bond strength models for externally-bonded reinforcement on grooves: Bayesian approach

• FRP-to-concrete bond strength models are developed for EBROG joints. • An experimental database containing 304 test samples is collected. • Bayesian inference is adopted for probabilistic model calibration. • Analytical expressions are derived for probabilistic model prediction. • Traditional models are compared to illustrate the superior of proposed ones. Recent years have witnessed the superiorities of a grooving technique, i.e., the externally-bonded reinforcement on grooves (EBROG), over the traditional technique, i.e., externally-bonded reinforcement (EBR), in terms of strengthening reinforced-concrete members by fiber-reinforced polymer (FRP) composites. Similar to EBR, the prediction of interfacial bond strength is critical for the EBROG type of FRP-to-concrete joints. There have been a series of experiments conducted to study the bond strength of EBROG joints, however, the corresponding prediction models (especially those capable of uncertainty quantification) are rarely available. Therefore, this paper aims to develop probabilistic models able to both predict the bond strength of EBROG joints and quantify the associated uncertainties. Firstly, an experimental database containing 304 bond strength tests for EBROG joints with longitudinal grooves is collected. Secondly, two widely-accepted deterministic bond strength models are selected as candidates to be calibrated by including a model correction factor. Thirdly, the factor is expressed by power and exponential functions of the influencing variables, meanwhile the deterministic model parameters are replaced with probabilistic ones. Finally, the probabilistic models are determined by means of Bayesian inference and Markov chain Monte Carlo. Moreover, an approximate analytical expressions are derived to achieve the probabilistic bond strength prediction. The experimental database is used to investigate the model performances, and the results show that: 1) the developed models can predict the FRP-to-concrete bond strength of EBROG joints with sufficient predictive accuracies and reasonable uncertainty quantifications; 2) the groove geometry has significant influence on the model correction factor; and 3) the developed probabilistic models is only applicable to EBROG joints with longitudinal grooves, but not to ones with transverse/diagonal grooves.

Quadrature Rules for the Fm-Transform Polynomial Components

The purpose of this paper is to reduce the complexity of computing the components of the integral Fm-transform, m≥0, whose analytic expressions include definite integrals. We propose to use nontrivial quadrature rules with nonuniformly distributed integration points instead of the widely used Newton–Cotes formulas. As the weight function that determines orthogonality, we choose the generating function of the fuzzy partition associated with the Fm-transform. Taking into account this fact and the fact of exact integration of orthogonal polynomials, we obtain exact analytic expressions for the denominators of the components of the Fm-transformation and their approximate analytic expressions, which include only elementary arithmetic operations. This allows us to effectively estimate the components of the Fm-transformation for 0≤m≤3. As a side result, we obtain a new method of numerical integration, which can be recommended not only for continuous functions, but also for strongly oscillating functions. The advantage of the proposed calculation method is shown by examples.

Theoretical analysis of 2D meta-structure with inertia amplification

This study proposed a square-grid structure (SGS) attached with inertial amplification mechanisms (IAMs) to obtain a better vibration isolation effect with low frequency and wide band gaps. According to the different stiffness assumptions of the IAM connecting rods, the proposed meta-structure is defined as two different types, 10° of freedom (DOF) elastic system (E-IAM) and 2-DOF rigid system (R-IAM). The motion equations of the two systems are given based on Newton's motion theorem and Lagrange's theorem, respectively. Dispersion relations and motion modes of the infinite system are discussed to obtain lower and wider band gaps. Vibration transmission characteristics of 20 × 20 meta-structures are also conducted. For the E-IAM system, ultra-low frequency vibration isolation can be achieved when the stiffness ratio of the connecting rod is the same in both vertical and horizontal directions and less than the main spring. The approximate analytical expression of the dispersion curve of the R-IAM system is given. Because the denominator is always greater than 1, it is proved that the cut-off frequency of the R-IAM system is always lower than that of the SGS. For finite R-IAM structures, when the longitudinal stiffness is asymmetric in both directions, multiple local resonant band gaps can be obtained in the passband, which is very beneficial to vibration reduction.

Diffusiophoresis of a cylindrical colloidal particle oriented parallel to an electrolyte concentration gradient field.

We derive the general expression for the diffusiophoretic mobility of a cylindrical particle oriented parallel to an applied electrolyte concentration gradient field in a symmetrical electrolyte solution. From the general mobility expression as combined with an approximate analytic expression with negligible error for the electric potential distribution around a cylinder, an accurate analytic mobility expression is obtained, which is applicable for arbitrary values of the particle zeta potential and the electrical double layer thickness. It is also found that the low zeta potential approximation is an excellent approximation for low-to-moderate values of the particle zeta potential.

Approximate Analytic Expression for the Time-Dependent Transient Electrophoretic Mobility of a Spherical Colloidal Particle.

The general expression is derived for the Laplace transform of the time-dependent transient electrophoretic mobility (with respect to time) of a spherical colloidal particle when a step electric field is applied. The transient electrophoretic mobility can be obtained by the numerical inverse Laplace transformation method. The obtained expression is applicable for arbitrary particle zeta potential and arbitrary thickness of the electrical double layer around the particle. For the low potential case, this expression gives the result obtained by Huang and Keh. On the basis of the obtained general expression for the Laplace transform of the transient electrophoretic mobility, we present an approximation method to avoid the numerical inverse Laplace transformation and derive a simple approximate analytic mobility expression for a weakly charged particle without involving numerical inverse Laplace transformations. The transient electrophoretic mobility can be obtained directly from this approximate mobility expression without recourse to the numerical inverse Laplace transformation. The results are found to be in excellent agreement with the exact numerical results obtained by Huang and Keh.

Transition Rates and Efficiency of Collective Variables from Time-Dependent Biased Simulations

Simulations with adaptive time-dependent bias enable an efficient exploration of the conformational space of a system. However, the dynamic information is altered by the bias. Infrequent metadynamics recovers the transition rate of crossing a barrier, if the collective variables are ideal and there is no bias deposition near the transition state. Unfortunately, these conditions are not always fulfilled. To overcome these limitations, and inspired by single-molecule force spectroscopy, we use Kramers' theory for calculating the barrier-crossing rate when a time-dependent bias is added to the system. We assess the efficiency of collective variables parameter by measuring how efficiently the bias accelerates the transitions. We present approximate analytical expressions of the survival probability, reproducing the barrier-crossing time statistics and enabling the extraction of the unbiased transition rate even for challenging cases. We explore the limits of our method and provide convergence criteria to assess its validity.