Semi-analytical Results Research Articles

Nonlinear dynamics and safety aspects of pressure relief valves

Direct spring operated pressure relief valves are regular elements of high-pressure hydraulic systems; however, valve vibrations may still occur endangering the valve and the protected system. The damping of these vibrations is a crucial issue, whereas the external viscous damping at the valve cannot be increased boundlessly based on safety aspects. The vibrations emerge via Hopf bifurcations of either super- or subcritical type, and the nonlinear characteristics have an important role in the valve dynamics. Thorough nonlinear analysis is needed to guarantee safe operation. The linear stability analysis is extended by local and global bifurcation analysis to reveal the stable domains bounded by subcritical Hopf points and the possible bistabilities that exclude the safe operation. Afterwards, the effect of a downstream pipe is analysed, which can also carry safety risks based on the literature; however, the time delay originated in the wave propagation in the pipe may also have stabilising effects. The nonlinear analysis of the presented system compares analytical, semi-analytical and numerical results and assigns the safe parameter domains of the valve with respect to a wide range of relevant parameter variations.

Shear wave transmissivity and wave-induced vorticity diffusion through conversion scattering to slow-shear diffusion wave

In the poroelasticity theory of de la Cruz and Spanos, fluid shearing within the viscous boundary layer, i.e. fluid vorticity, manifests as an independent process, namely the diffusive slow shear wave. Quantifying its impact on elastic wave propagation remains a research challenge. We analyse the transmissivity of a horizontally polarized shear wave travelling across a stack of porous fluid-saturated layers. The fluid shearing developed at each contact is captured, in a macroscopic sense, through conversion scattering into this diffusive slow shear wave. Generalizing the reflectivity method for elastic waves to the poroelastic case, we develop semi-analytical results for an arbitrary number of layers. We find that the conversion scattering into this diffusion wave reduces the shear wave amplitude, and this reduction accumulates with the number of layers. In the limit when the layer thickness corresponds to the pore diameter, the resulting wave quality factor is close to the predictions of previously reported attempts to capture the fluid vorticity. However, our approach is distinctively different since it is purely based on a wave-theoretic analysis of interacting waves, acknowledging vorticity diffusion as an independent process, thereby avoiding the problems arising when incorporating a pore-scale phenomenon in a macroscopic wave propagation theory.

Mathematical modelling of the biofiltration treating mixtures of toluene and N-propanol in the biofilm and gas phase

This paper presents a mathematical model in the biofilm phase and in the gas phase that has been successfully applied to investigate various aspects of the biofiltration process. The mixtures of volatile organic compounds (VOCs) are emitted from a wide range of industries, such as chemical, petrochemical, pharmaceutical, pulp paper mills, printing and paint workshops, etc. The objective of the present study is, presence of high n-propanol loading negatively affected the toluene removal; however, n-propanol removal was not affected by the presence of toluene and was effectively removed in the biofilter despite high toluene loadings. A model for toluene and n-propanol biofiltration could predict the cross-inhibition effect of n-propanol on toluene removal. Further, we studied the effects of many physical and biological parameters on model prediction. The mathematical equations (2.12)-(2.16) which are non-linear partial differential equations are solved by using the homotopy perturbation technique. Also, we derived the semi-analytical results for toluene and n -propanol concentrations for saturated and unsaturated kinetics. It is verified that the proposed solution is validated by comparing it with numerical solutions.

Study of the intermediate mass ratio black hole binary merger up to 1000:1 with numerical relativity

We explicitly demonstrate that current numerical relativity techniques are able to accurately evolve black hole binaries with mass ratios of the order of 1000:1. This proof of principle is relevant for future third generation gravitational wave detectors and space mission LISA, as by purely numerical methods we would be able to accurately compute gravitational waves from the last stages of black hole mergers, as directly predicted by general relativity. We perform a sequence of simulations in the intermediate to small mass ratio regime, , with the small hole starting from rest at a proper distance . We compare these headon full numerical evolutions with the corresponding semianalytic point particle perturbative results finding an impressive agreement for the total gravitational radiated energy and linear momentum as well as for the waveform spectra. We display numerical convergence of the results and identify the minimal numerical resolutions required to accurately solve for these very low amplitude gravitational waves. This work represents a first step towards the considerable challenge of applying numerical-relativity waveforms to interpreting gravitational-wave observations by LISA and next-generation ground-based gravitational-wave detectors.

Numerical study of magnetized Powell–Eyring hybrid nanomaterial flow with variable heat transfer in the presence of artificial bacteria: Applications for tumor removal and cancer cell destruction

This investigation determined the effectiveness of an exterior magnetic field on bacteria enclosed by thousands of magnetite nanoparticles. Variable thermal conductivity and Joule heating were used in the interstitial nano liquid in which artificial bacteria were swimming in a biotic cell. The unsteady motions of a Powell–Eyring fluid in two dimensions were assumed. The porous extending wall was used as a bent surface shape. To convert the governing non-linear PDEs into non-linear ODEs, suitable transformations were exploited. The homotopy analysis technique (HAM) was utilized to resolve the semi-analytical results of non-linear ODEs. Plots were utilized to investigate the impact of significant parameters of velocity distribution, temperature profile, bacterial density field, nutrient concentration field, skin friction, Nusselt number, and nutrient concentration density. Clinical disease has shown that daring tumors have reduced blood flow. The results of this study showed that augmenting the values of unsteady parameters improved the blood velocity profile. The velocity distribution decreased for higher magnetite volume fraction values, as well as porosity and magnetic parameters. As the concentration of magnetite nanoparticles increased, so did the blood temperature distribution. As a result, the immersion of magnetite nanoparticles improved the physical characteristics of the blood. These findings also demonstrated that magnetic parameters and Eckert number play an essential role in increasing heat transfer rates.

Maps unlock the full dynamics of targeted energy transfer via a vibro-impact nonlinear energy sink

We consider a model of a vibro-impact nonlinear energy sink (VI-NES), where a ball moves within a cavity of an externally forced mass, impacting either end of the cavity. These impacts result in energy transfer from the mass to the ball, thus limiting the oscillations of the larger system. We develop a semi-analytical map-based approach, recently used for an inclined impact pair model, in the setting where there is energy transfer between the mass and the ball. With this approach we analytically derive exact expressions for the full dynamics of the VI-NES system without restricting the range of parameters, in contrast to other recent work in which an approximate reduced model is valid only for small mass of the ball, small amplitude, and a limited frequency range. We develop the bifurcation analysis for the full VI-NES system, based on exact maps between the states at successive impacts. This analysis yields parameter ranges for complex periodic responses and stability analyses for O(1) mass of the ball, forcing frequencies that are not the same as the natural frequency, and large amplitude forcing. The approach affords the flexibility to analytically study the dynamics of different periodic solutions and their stability, including a variety of impact sequences in the full two degree-of-freedom model of VI-NES. Comparisons of quantities that characterize the energy transfer point to the significance of different types of periodic behavior, which may occur for different parameter combinations. Our semi-analytical results also provide the impact phase, which plays an important role in the efficiency of the energy transfer.

Probing neutrino interactions and dark radiation with gravitational waves

After their generation, cosmological backgrounds of gravitational waves propagate nearly freely but for the expansion of the Universe and the anisotropic stress of free-streaming particles. Primordial signals — both that from inflation and the infrared spectrum associated to subhorizon production mechanisms — would carry clean information about the cosmological history of these effects. We study the modulation of the standard damping of gravitational waves by free-streaming radiation due to the decoupling (or recoupling) of interactions. We focus on nonstandard neutrino interactions in effect after the decoupling of weak interactions as well as more general scenarios in the early Universe involving other light relics. We develop semianalytic results in fully free-streaming scenarios to provide intuition for numerical results that incorporate interaction rates with a variety of temperature dependencies. Finally, we compute the imprint of neutrino interactions on the B-mode polarization of the cosmic microwave background, and we comment on other means to infer the presence of such effects at higher frequencies.

Continuous simultaneous measurement of position and momentum of a particle

We formulate a model of a quantum particle continuously monitored by detectors measuring simultaneously its position and momentum. We implement the postulate of wave-function collapse by assuming that upon detection the particle is found in one of the meters' states chosen as a discrete subset of coherent states. The dynamics, as observed by the meters, is thus a random sequence of jumps between coherent states. We generate such trajectories using the quantum Monte Carlo wave-function method. For sparsely distributed detectors, we use methods from renewal theory of stochastic processes to obtain some semianalytic results. In particular, the different regimes of dynamics of the free particle are identified and quantitatively discussed: from stroboscopic motion in the case of low interrogation frequency, to delayed dynamics reminiscent of the Zeno effect if monitoring is frequent. For a semicontinuous spatial distribution of meters the emergence of classical trajectories is shown. Their statistical properties are discussed and compared to other detection schemes in which the operation on the system due to measurement corresponds to ``spatial filtering'' of the wave function.

Rolling Bearing Fault Diagnosis Based on Exact Moment Dynamics for Underdamped Periodic Potential Systems

This research is to build a more general bridge over the model investigation on stochastic resonance (SR) and the laboratory design in rolling bearing faults. To this end, we generalize the derivative matching moment closure method to the underdamped biased periodic potential systems to disclose the non-monotonic evolution of the spectral amplification factor. With the exact moment dynamics available, a two-layer loop algorithm for detecting the incipient bearing faults is then developed. With the outer loop to optimize the output SNR for the best time scale factor and the inner loop to maximize the spectral amplification factor for optimal system parameter, the semi-analytic results are directly related with this laboratory application. The analog and experimental verification based on different datasets show that the proposed method can perform as well as the existing SR method, even under strong noise background. Particularly, the proposed method does not depend on the amplitude of input signal when optimizing parameters, but only on noise intensity and characteristic fault frequency, thus it has higher detection efficiency than the existing simulation based SR methods.

Incipient Bearing Fault Diagnosis Based on the Two-State Theory for Stochastic Resonance Systems

The principle of stochastic resonance (SR) has been intensively used in designing algorithms for incipient bearing fault diagnosis based on stochastic simulation. In order to directly apply the semi-analytic result to the laboratory designs, an incipient bearing fault diagnosis algorithm based on the method of moments for stochastic resonant systems was proposed, with its real-time monitoring efficiency being assured by an available table of the involving stationary moments. Nevertheless, since the noise that buried the fault signal can only be estimated after sampling, calculation of such stationary moments might be an inconvenience. To fix this inconvenience, a brand-new fault diagnosis algorithm is designed in this paper based on the two-state theory for a biased underdamped bistable stochastic resonant system. The capability and the efficiency of the algorithm in identifying the characteristic frequency of the hidden fault signal are confirmed with the experimental data sets. This investigation actually opens a new way for improving the existing SR-based diagnosis algorithms.

Post-buckling shear capacity of the corroded end panels of H-shaped steel beams

The shear capacity of steel beams can be affected by corrosion when the effective thickness is reduced. However, the contribution to shear capacity of beams with corroded steel web from support stiffener and flange has not been quantified until now. Thus, this work aims to reveal the changing rules of the shear capacity of randomly corroded steel beam while considering the nonlinear buckling behavior of the corroded web. The established numerical model is first validated through code-based semi analytical results. The contribution from support stiffener and flange are then investigated in detail. The influences of corrosion location, corroded thickness, thickness of support stiffener or flange, corrosion size, and corrosion severity on the reduction of shear capacity are investigated. Both the constant and random corroded depths are considered. The results show that the shear capacity corresponding to local corrosion is lower than uniform corrosion. This is caused by the corrosion located at different positions, which can influence the shear capacity in varying degree. Furthermore, the diameter of the corrosion pit has no influence on residual shear capacity and can be taken as a constant value. The influence of corrosion parameters on reduction factor is also quantified. The conclusions derived in this work can be directly applied to steel beams under actual conditions.

Effects of Efimov states on quench dynamics in a three-boson trapped system

We investigate the effects of Efimov states on the postquench dynamics of a system of three identical bosons with contact interactions in a spherically symmetric three-dimensional harmonic trap. The quench we consider is in the $s$-wave contact interaction, and we focus on quenches from the noninteracting to strongly interacting regimes and vice versa. The calculations use the hyperspherical solutions of the three-body problem and enable us to evaluate the semianalytical results of the Ramsey and particle separation, postquench. In the case where the interactions are quenched from the noninteracting to strongly interacting regime we find convergent aperiodic solutions for both the Ramsey signal and the particle separation. In contrast, for quenches from the strongly interacting regime to the noninteracting regime both the Ramsey signal and particle separation are periodic functions. However, in this case we find that the solutions for the particle separation diverge, indicating that in such a system large oscillations may be observable.

Three-Dimensional Thermo-Mechanical Elastic Analysis of Functionally Graded Five Layers Composite Sandwich Plate on Winkler Foundations

In this work, the first shear deformation theory (FSDT) is used for the thermo-mechanical analysis of a simply supported five-layer functionally Graded (FG) sandwich plate resting on a Winkler elastic foundation. The sandwich plate consists of five layers (two functionally graded face sheets (AL−AL2O3), with aluminum (Al) as the metal and Alumina (AL2O3) as ceramic phases. Two vinyl ester adhesive layers bond the face sheets to an Elastollan core. The governing equations are obtained using the principle of virtual displacements. A uniform distributed load q with constant magnitude is applied on the top face sheet while all layers experience a steady temperature equal to T. We adapted layerwise theory (LT) to solve each layer’s stress distribution. Navier solution is employed to produce the semi-analytical solution results, which are compared with those of three-dimensional finite element analysis obtained by ABAQUS software. A parametric study is presented to observe the effect of the material gradation, variation in plate dimensions, variation in the thermo-mechanical load, and elastic foundation on the deflections and stresses in the functionally graded sandwich plate. For a composite sandwich plate with mechanical load, in the absence of thermal load, results of the first-order shear layer theory obtained by using the Navire method are relatively good in comparison to the normal stresses obtained for investigated points, which are obtained by finite element.

Free vibration analysis of grid-stiffened composite truncated spherical shells

In this paper, the vibrational behavior of grid-stiffened truncated composite spherical shells has been studied. Using a smeared stiffener technique, the stiffness contribution of the non-uniform grid structures are superimposed with those of the shell. The helical stiffeners have been considered as truss, which are able to bear the axial forces. The equations of motion have been derived within the framework of the classical Donnell’s thin shell theory and then solved by means of Galerkin method in order to extract the natural frequencies and vibration modes. The simply supported, clamped and combination of these two boundary conditions have been considered for the shell ends. In order to validate the semi-analytical results and also conduct an extensive parametric study, a 3-D finite element model has been built using ABAQUS CAE software. Comparing the results obtained via the two approaches, good agreement has been achieved. The effects of spherical shell’s geometrical parameters, lamination angle and different configurations of the stiffening structure have been examined as well. The results are new and can be considered as a benchmark for further studies.

Sound diffusion with spatiotemporally modulated acoustic metasurfaces

Traditional sound diffusers are quasi-random phase gratings attached to reflecting surfaces to introduce spatiotemporal incoherence into the backscattered acoustic field. Early designs consisted of periodically tiled diffuser grating unit cells to cover large surfaces. However, spatial periodicity leads to coherent constructive and destructive interference, which is undesirable for achieving acoustic diffusivity. This problem was partially addressed by using aperiodic tiling of unit cells based on pseudorandom sequences. While an aperiodic diffuser spacing can overcome the problems introduced by spatial periodicity, the improvements in performance come at the expense of increased thickness. In this work, we investigate spatiotemporal modulation of the surface acoustic admittance of a metasurface diffuser to improve sound diffusion. Using semi-analytical and finite element models, we demonstrate that the effects of the spatial periodicity can be mitigated without introducing an aperiodic spatial spacing, thus simultaneously minimizing diffuser thickness and improving diffusivity of the backscattered field. We develop a semi-analytical model that employs Fourier series expansion to determine the scattered sound field from a surface admittance consisting of a quadratic residue diffuser whose individual well admittances are modulated in a traveling wave fashion with modulation frequency, ωm, amplitude, Ym, and a wavenumber that matches the unit cell length, Λ. We observe significant improvement in diffusion due to the fact that the spatiotemporal modulation scatters sound into additional frequency-wavenumber pairs associated with harmonics of ωm and their diffraction orders. The semi-analytical model results are verified using a time-domain finite element model and compared with periodic and aperiodic diffuser designs.

Numerical simulations of stochastic inflation using importance sampling

We show how importance sampling can be used to reconstruct the statistics of rare cosmological fluctuations in stochastic inflation. We have developed a publicly available package, PyFPT,[https://github.com/Jacks0nJ/PyFPT.] that solves the first-passage time problem of generic one-dimensional Langevin processes. In the stochastic-δ N formalism, these are related to the curvature perturbation at the end of inflation. We apply this method to quadratic inflation, where the existence of semi-analytical results allows us to benchmark our approach. We find excellent agreement within the estimated statistical error, both in the drift- and diffusion-dominated regimes. The computation takes at most a few hours on a single CPU, and can reach probability values corresponding to less than one Hubble patch per observable universe at the end of inflation. With direct sampling, this would take more than the age of the universe to simulate even with the best current supercomputers. As an application, we study how the presence of large-field boundaries might affect the tail of the probability distribution. We also find that non-perturbative deviations from Gaussianity are not always of the simple exponential type.

Infrared radiation feedback does not regulate star cluster formation

ABSTRACT We present 3D radiation-hydrodynamical (RHD) simulations of star cluster formation and evolution in massive, self-gravitating clouds, whose dust columns are optically thick to infrared (IR) photons. We use VETTAM – a recently developed, novel RHD algorithm, which uses the Variable Eddington Tensor closure – to model the IR radiation transport through the cloud. We also use realistic temperature (T) dependent IR opacities (κ) in our simulations, improving upon earlier works in this area, which used either constant IR opacities or simplified power laws (κ ∝ T2). We investigate the impact of the radiation pressure of these IR photons on the star formation efficiency of the cloud, and its potential to drive dusty winds. We find that IR radiation pressure is unable to regulate star formation or prevent accretion on to the star clusters, even for very high gas surface densities ($\Sigma \gt 10^5 \, \mathrm{M}_{\odot } \, \mathrm{pc}^{-2}$), contrary to recent semi-analytic predictions and simulation results using simplified treatments of the dust opacity. We find that the commonly adopted simplifications of κ ∝ T2 or constant κ for the IR dust opacities leads to this discrepancy, as those approximations overestimate the radiation force. By contrast, with realistic opacities that take into account the microphysics of the dust, we find that the impact of IR radiation pressure on star formation is very mild, even at significantly high dust-to-gas ratios (∼3 times solar), suggesting that it is unlikely to be an important feedback mechanism in controlling star formation in the ISM.

PAPR Reduction of OFDM Waveform in Integrated Passive Radar and Communication Systems

For the dual-function radar and communication (DFRC) system based on the orthogonal frequency division multiplexing (OFDM) signal, low peak-to-average power ratio (PAPR) design of the waveform is very important to improve the transmitting efficiency and overall performance. In this paper we consider this problem in the context of the integrated passive radar and communication (IPRC) system in which the channel state information (CSI) and transmitting waveform are unknown to the passive radar. In this context, the traditional constellation extension method is applicable but the effect of PAPR reduction is limited by the constellation size. To solve this problem, we propose a low PAPR waveform design method suitable for a large constellation size. The new method makes two improvements to significantly reduce the PAPR by increasing the constellation point participating in the extension and expanding the extension regions, which is independent of the CSI. Specifically, we adjust the extension regions by the scaling factor to obtain different PAPR, while remaining the pilot data unchanged. Furthermore, the communication performance is semi-analytically analyzed, and the consistency of semi-analytical results and simulation results verifies the effectiveness of the proposed method. Analysis and numerical results demonstrate that the proposed method can achieve good comprehensive performance of communication and passive radar detection compared with other methods in the case of large constellation size.

Cross-scale energy transfer of chaotic oscillator chain in stiffness-dominated range

The investigations on the dynamics of hierarchical oscillator chains provide basic theories for the fields of acoustic metamaterial and passive guidance of energy flow. In the present study, the characteristics of stiffness-dominated energy transfer of a reduced cross-scale oscillator chain that generates chaotic vibrations are studied. The semi-analytical solutions are obtained by the complexification-averaging method and the least-square method for thoroughly searching the branches of responses. Then, the energy transfer patterns of the oscillator chain are analyzed based on Runge–Kutta method. Moreover, chaotic responses are determined using the displacements and Lyapunov exponents of the system. The average energy and normalized energy flux are defined to evaluate the energy distribution in each oscillator and the energy transfer between oscillators, respectively. The semi-analytical results show that the oscillator chain produces complex unstable branches of response around the resonance frequency of the linear oscillator. It is found that the detached higher branches of response of the chain are similar to that of a system consisting of one linear oscillator and one cubic oscillator. When chaotic responses occur, the energy transfer patterns that reflected by average energy and normalized energy flux are similar in the same branch of response for different excitation frequencies. However, energy transfer patterns in different branches of response are quite different even at the same excitation frequency, and the higher branch generates the lower energy transfer. Furthermore, analyses of the input energy and the scale between cubic oscillators demonstrate that variations of the two parameters slightly affect the normalized energy flux.

Athermal GES-based solar plasma stability with sphero-logabarotropic special effects

A model formalism for the small-scale radial fluctuations excitable in the athermal (non-thermal) solar plasma system on the basis of the non-extensive gravito-electrostatic sheath (GES) model fabric is reported. A unique speciality here is that it intercouples the solar interior plasma (SIP) and the solar wind plasma (SWP) gravito-electrostatically via the interfacial diffused solar surface boundary (SSB). The constitutive electrons are thermostatistically framed in the κ-distribution laws via the Tsallis thermostatistics. In contrast, the heavier ions are treated as an inhomogeneous fluid. The turbulent degrees of freedom are accounted through the Larson nonlinear logabarotropic equation of state in curved geometry. A spherically symmetric wave analysis over the perturbed GES structure results in a unique pair of distinct linear dispersion laws (SIP plus SWP) without any typical quasi-classic approximation. A numerical illustrative platform for the dispersion analysis specifically shows that an antikink-type (kink-type) impulsive rarefactive (compressive) propagatory boost due to irregular dispersion is experienced by the fluctuations at the heliospheric core (photospheric SSB). We see that the thermostatistical parameter (Tsallis power-law tail index κ) acts as a unique form of acceleration agency for both the SIP and SWP instabilities to proliferate. At the last, the explorative semi-analytic results are contextually compared with the realistic domains of the collective excitation of the helioseismic waves and SSB oscillations.