Small Amplitude Research Articles

Ion-acoustic solitons in a relativistic Fermi plasma at finite temperature.

The theory of ion-acoustic solitons in nonrelativistic fully degenerate plasmas and nonrelativistic and ultra-relativistic degenerate plasmas at low temperatures is known. We consider a multi-component relativistic degenerate electron-positron-ion plasma at finite temperatures. Specifically, we focus on the intermediate region where the particle's thermal energy and the rest mass energy do not differ significantly, i.e., . However, the Fermi energy is larger than the thermal energy and the normalized chemical energy ( ) is positive and finite. Two different parameter regimes with and , relevant for astrophysical plasmas, are defined, and the existence of small amplitude ion-acoustic solitons in these regimes are studied, including the critical cases where the known KdV (Korteweg-de Vries) theory fails. We show that while the solitons with both the positive (compressive) and negative (rarefactive) potentials coexist in the case of , only compressive solitons can exist in the other regime . Furthermore, while the rarefactive solitons within the parameter domains of and can evolve with increasing amplitude and hence increasing energy, the energy of compressive solitons reaches a steady state.

Experimental and theoretical studies of sea ice effects on internal solitary waves

Internal solitary waves in polar regions have attracted much interest recently. It is important to understand how sea ice affects them as this may have a profound influence on human activities and the environment. In this study, experiments on internal solitary waves with and without two types of sea ice (ice sheet and ice keel) are presented, as well as corresponding simulations using the Korteweg-de Vries (KdV) equation, the Benjamin-Ono (BO) equation, and the variable-coefficient Korteweg-de Vries (vKdV) equation, which is a derivation of the KdV equation. Comparison between experiments without sea ice and simulations using the KdV and BO equations proves the suitability of the former over the latter for this study. The experiments with sea ice and theoretical simulations using the vKdV equation provide evidence for wave deformation, oscillation occurring in the rear of the wave, and a decrease in amplitude. The latter suggests possibilities of energy dissipation or the emission of small amplitude linear waves. The sharp vertices of the ice result in occasional inconsistency with the vKdV predictions. Nonetheless, the vKdV equation is still suitable for modeling internal solitary waves under sea ice, giving generally accurate results that can assist further studies. This is the first time the vKdV equation has been applied to investigate the impacts of sea ice on internal solitary waves.

Review on peak detect and hold circuits and their applicability in partial discharge detection

Abstract This article reviews various designs of electrical peak detect and hold circuits and tests their applicability for the detection of partial discharge pulses. Since partial discharges are very short pulses in the nanosecond range, the peak detector circuit must be very fast and thus work precisely over a wide bandwidth up to the GHz range. The article begins with a comprehensive literature review and gives an overview of the state of the art of peak detector circuits. As a result of the literature research, four different peak detector designs are identified that appear suitable for measuring partial discharges. These four circuits are then simulatively tested for their performance in measuring the pulse height of various partial discharge pulses. It turns out that two of the identified circuits are able to measure nanosecond pulses of small amplitude. These two circuits must be further optimized for partial discharge detection in the future. In addition, the circuit should be tested prototypically with real partial discharge pulses.

Computational and experimental studies of vibration-protective properties of a pneumatic wheel of the MTZ-82 BELARUS tractor with external spring-hydraulic mini-suspension

BACKGROUND: Currently used in various sectors of the national economy, numerous wheeled suspensionless vehicles on pneumatic tires have a low level of vibration protection of the frame and limited cross-country ability. Therefore, the development and study of the design characteristics of a pneumatic wheel with increased elastic-damping properties and cross-country ability is a relevant technical problem. AIM: Development of the design and study the vibration-protective properties of a pneumatic wheel with an external spring-hydraulic mini-suspension to improve the ride smoothness and cross-country ability of large-sized suspensionless vehicles. METHODS: A description of the design of a wheel with mini-suspension and a support roller is presented. The wheel modeling was carried out in the PascalABC software, which takes into account the nonlinearity of the total force of the pneumatic tire and the spring-hydraulic mini-suspension, which is installed parallel to the tire at an angle to the vertical axis of the wheel. The test method consisted of comparison of free and forced vibrations of the rear pneumatic wheel of the MTZ-82 BELARUS tractor with a 400-965/15.5-38 tire, which operated without and with mini-suspension at a vertical load of 0.6 tons and various excessive pressure in the tire. RESULTS: The results of computational and experimental studies show that if the tire is radially compressed by 75 mm, the excess pressure inside the pneumatic wheel almost does not change, and if the pressure in the tire decreases from 1.6 to 0.4 bar, the resonant vibration frequency of the standard wheel axle decreases by 25%, while the dynamic coefficient remains unacceptably high (more than 5), leading to the tire breakaway from the supporting surface. Installing a mini-suspension parallel to the wheel in the form of a spring-hydraulic shock-absorbing strut leads to an increase in the resonant frequency by 1 Hz, however, the resonant peaks are reduced by almost 3 times to a dynamic coefficient of 2.5...2, which significantly increases the ride smoothness of suspensionless vehicles and reduces the likelihood of wheel breakaway from the supporting surface. CONCLUSION: It was found with the studies that the proposed wheel with a mini-suspension as a spring-hydraulic strut and a support roller has a relatively simple design, ensures high vibration-protective properties with small amplitudes of kinematic disturbance and can be used to improve the ride smoothness and cross-country ability of wheeled suspensionless vehicles.

Dynamic Control of Piezoelectric Sandwich Beams with Multi-Frequency Excitations

In this work, we present a non-linear analysis of the dynamics of a sandwich beam with piezoelectric patches under multi-frequency excitations. The model takes into account geometrical non-linearities, piezoelectric non-linearities, and inertia. Hamilton’s principle is used to determine the electromechanical equation of motion, and Garlekin’s technique is used to determine the equivalent model of the piezoelectric generator. A mathematical methodology based on the multi-scale method for vibration control and stability is reviewed in this work to determine a system of amplitude and phase equations. The control of primary and secondary mode resonances is developed, and feedback effects are analyzed for small and large amplitudes of vibrations of sandwich beams. Frequency response curves are presented and discussed for various gain parameters.

Effect of chitosan molecular weight and protein to polysaccharide ratio on the rheological and physicochemical properties of milk proteins–chitosan complex coacervate

The small amplitude oscillatory shear (SAOS) rheological properties of complex coacervate of milk proteins with high (HMC), medium (MMC), and low (LMC) molecular weight chitosan in the optimal ratios of milk proteins to chitosan (15:1, 10:1, and 5:1, respectively) were measured. In addition, the morphological (SEM), structural (XRD), and thermal (DSC) properties of the complex coacervates were investigated in comparison with the milk protein concentrate. Complex coacervates showed the shear-thinning behavior due to a linear decrease of complex viscosity with increasing frequency. Furthermore, the highest complex modulus and the more compact structure under optimal conditions, in terms of the ratio of protein to chitosan and pH, revealed strong electrostatic bonding between proteins and chitosan. All coacervates showed a G′ > G″ (Tanδ<1), indicating the formation of an interconnected gel-like structure that was described by the power law model. The maximum fracture stress was obtained at optimum conditions (R = 15:1, pH =6.7 for HMC; R = 10:1, pH =5.5 for MMC and R = 5:1, pH =4.6 for LMC), indicating the highest intermolecular interaction between milk proteins and chitosan. The coacervates had a completely amorphous structure similar to MPC, and according to DSC results, the ionic bonds between milk proteins and chitosan were not destroyed up to 300 °C. Coacervation leads to purified milk proteins at a low cost. In addition, the coacervates can be used for the encapsulation of heat-sensitive compounds, and also as a stabilizer to improve the texture of food.

Cellulose nanocrystal dispersion-ability in polylactides with various molecular weights prepared in dichloromethane/dimethyl sulfoxide solvents for electrospinning applications

In this study, effects of polylactide molecular weight, i.e., high (HPLA), medium (MPLA), low (LPLA), and dichloromethane (DCM)/dimethyl sulfoxide (DMSO) blend ratio on cellulose nanocrystal (CNC) dispersion quality in solution casted PLA/CNC nanocomposites were investigated via small amplitude oscillatory shear rheological analysis, while crystallization behavior, thermal degradation, morphological structure of the nanocomposites were also reported. Due to its low dielectric constant, none of the nanocomposites with 100DCM indicated a change in their complex viscosity as a result of poor CNC dispersion. This is while the increase in DMSO content (50%vv−1) improved CNC dispersion. The superior CNC dispersion-ability in PLAs with lower molecular weight was confirmed. The poorer CNC dispersion in HPLA attributes to hindering effect of higher molecular weight on solvent and nanoparticle diffusion. The better dispersed CNCs influenced crystal nucleation behavior of PLAs and increased crystallinity degree. In addition, the impact of well-dispersed CNCs on fiber formation quality of nanocomposites was reported. Introducing finely dispersed CNCs (1 wt%) in LPLA refined fiber diameters around 1200 nm with more homogenous structure. Besides, the use of 100DCM and the use of DMSO at high contents (50%vv−1) deteriorated fiber formation, respectively, due to low conductivity of DCM and high boiling temperature of DMSO.

On the Large-x Asymptotic of the Classical Solutions to the Non-Linear Benjamin Equation in Fractional Sobolev Spaces

In this work, we study the large-x asymptotic of classical solutions to the non-linear Benjamin equation modeling propagation of small amplitude internal waves in a two fluid system. In our analysis, we extend known Hs-well-posedness results to the case of the variable-weight Sobolev spaces. The spaces provide a direct control over the asymptotics of classical solutions and their weak derivatives, and permit us to compute the bulk large-x asymptotic of classical solutions explicitly in terms of input data. The asymptotic formula provides a precise description of the qualitative behaviour of classical solutions in weighted spaces and yields a number of weighted persistence and continuation results automatically.

A One-Dimensional Model for Investigating Scale-separated Approaches to the Interaction of Oceanic Internal Waves

Abstract High-frequency wave propagation in near-inertial wave shear has, for four decades, been considered fundamental in setting the spectral character of the oceanic internal wave continuum and for transporting energy to wave-breaking. We compare idealized ray tracing numerical results with metrics derived using a wave turbulence derivation for the kinetic equation and a path integral to study this specific process. Statistical metrics include the changing ensemble mean vertical wavenumber, referred to as a mean drift, dispersion about the mean drift, time lagged correlation estimates of wavenumber and phase locking of the wave packets with the background. The path integral permits us to identify the mean drift as a resonant process and dispersion about that mean drift as non-resonant. At small inertial wave amplitudes; ray tracing, wave turbulence and the path integral provide consistent descriptions for the mean drift of wavepackets in the spectral domain and dispersion about the mean drift. Extrapolating these results to the background internal wavefield over-predicts downscale energy transports by an order of magnitude. At oceanic amplitudes, however, the numerics support diminished transport and dispersion that coincide with the mean drift time scale becoming similar to the lagged correlation time scale. We parse this as the transition to a non-Markovian process. Despite this decrease, numerical estimates of downscale energy transfer are still too large. We argue that residual differences result from an unwarranted discard of Bragg scattering resonances. Our results support replacing the long standing interpretive paradigm of extreme scale-separated interactions with a more nuanced slate of ‘local’ interactions in the kinetic equation.

Field study on proactive pipe condition assessment using hydroacoustic noise

Condition assessment of water transmission pipelines is of important necessity for prioritizing rehabilitation and preventing catastrophic pipe failure. Hydraulic transient analysis has been investigated for three decades for this purpose and applied to many field studies. However, the significant pipe vibrations caused by the transient generation process and the limited energy and bandwidth of conventional discrete transient pressure waves (e.g., step and pulse waves) limit the accuracy and resolution of the analysis. This paper reports a pilot field study of noninvasive and nondestructive pipe condition assessment using small amplitude and persistent hydroacoustic noise instead of conventional large and discrete hydraulic transient waves. By opening a discharge valve installed at an existing access point, such as an air valve, on the field pipe, hydroacoustic noise was generated at the valve due to the turbulence of the discharge. The hydroacoustic noise was measured by pressure transducers at this access point as well as some other access points along the field pipe. A signal deconvolution process was then applied to the measured hydraulic pressures to transfer them to a compositional impulse response function (IRF), which is composed of IRFs of different pipe sections. A mathematical model was derived to interpret the anomaly-induced spikes on the deconvolution trace. A time-shifting process on the compositional IRFs was proposed to find the locations with pipe condition changes from a specific direction of the pipe. The field study has shown that small-amplitude persistent hydroacoustic noise can replace conventional large hydraulic transient waves for pipe condition assessment.

Particulate flow of a viscous fluid driven by a torsionally oscillating disk

Abstract A novel hydrodynamic model is used to study oscillatory flow of a particle-laden fluid driven by a torsionally oscillating disk. The present model is featured by a modified form of Navier-Stokes equations which is conceptually different than existing related models and enjoys relatively concise mathematical formulation. Explicit expressions are derived for the radial, azimuthal and axial velocities using the method of power series expansions of small amplitude parameter, and the derived solutions reduce to Rosenblat's earlier results for a clear fluid driven by a torsionally oscillating disk in the absence of suspended particles. The implications of the present results to dusty gases are discussed in detail with particular interest in the effects of suspended particles on the decay indexes and wavelengths of the induced oscillatory velocity fields. The results obtained in this work can be used to quantify the effects of suspended particles on particulate flow driven by a torsionally oscillating disk.

Toughening Immiscible Polymer Blends: The Role of Interface-Crystallization-Induced Compatibilization Explored Through Nanoscale Visualization.

This study explores the novel approach of interface-crystallization-induced compatibilization (ICIC) via stereocomplexation as a promising method to improve the interfacial strength in thermodynamically immiscible polymers. Herein, two distinct reactive interfacial compatibilizers, poly(styrene-co-glycidyl methacrylate)-graft-poly(l-lactic acid) (SAL) and poly(styrene-co-glycidyl methacrylate)-graft-poly(d-lactic acid) (SAD) are synthesized via reactive melt blending in an integrated grafting and blending process. This approach is demonstrated to enhance the interfacial strength of immiscible polyvinylidene fluoride/poly l-lactic acid (PVDF/PLLA) 50/50 blends via ICIC. IR nanoimaging indicates a cocontinuous morphology in the blends. The blend compatibilized with SAD exhibits a higher storage modulus, as unveiled by small amplitude oscillatory shear (SAOS) in the melt state at a temperature below the melting temperature of the stereocomplex (SC) crystals and by DMTA measurements in the solid state. This increase is attributed to the formation of a 200-300 nm thick rigid interfacial SC crystalline layer that is directly visible using AFM imaging and chemically characterized via IR nanospectroscopy. This ICIC also results in a significant toughening of the blend, with the elongation at break increasing more than 20-fold. Moreover, the fracture toughness factor obtained from single edge-notch bending (SENB) tests is doubled with ICIC as compared to the uncompatibilized blend, indicating the strong crack-resistance capability as a result of ICIC. This improvement is also evident in SEM images, where thinner and longer fibrillation is observed on the fractured surface in the presence of ICIC.

Oblique Wave Scattering by a Pair of Asymmetric Inverse Π-Shaped Breakwater

Abstract The topic of wave scattering by different breakwaters has unfolded over the past few decades, largely driven by the profound impacts of global climate change. In this study, a completely new type of breakwater, inverse Π-shaped breakwater, has been taken into account for serving both purposes from analytical as well as an application point of view. During the formulation, the actual physical problem is transferred into a boundary value problem by employing the small amplitude water wave theory. With the aid of eigenfunction expansion, the problem is reduced to a set of integral equations having square-root singularities at the submerged edges of thin structures. To address such singularities, a multi-term Galerkin approximation technique is used along with Chebyshev polynomials (multiplied with suitable weights) as basis functions. The numerical methodology employed here validates with different previous literatures as special cases. Then, numerical solutions of the reflection and transmission coefficients, hydrodynamic forces are graphically illustrated across various dimensionless structural parameters. In summary, the present paper offers valuable insights into the dynamics of wave scattering by a pair of asymmetric inverse bottom-mounted Π-shaped breakwater, emphasizing the role of different non-dimensional parameters in this system.

The influence of lumped mass deployment on the performance of a hybrid galloping energy harvester

This article delves into a hybrid galloping energy harvester featuring a longitudinally aligned triangular-shaped bluff body. Numerically, it analyzes how the position of a lumped mass influences the average output power of the harvester under concurrent base excitation and galloping. In comparison with traditional hybrid energy harvesters, the impact of three factors—low airflow velocity, small base excitation amplitude, and low frequency—is examined for each case of lumped mass deployment. The findings reveal that optimal mass positioning markedly enhances the harvester’s average power output when there are low airflow velocities, small base excitation amplitudes, and low frequencies, constituting a novel contribution to the field. Through numerous numerical simulations, it is determined that the optimal position for deploying the lumped mass is approximately 60–70% along the length of the cantilever beam substrate.

Nonlinear Ion Acoustic Waves in Multicomponent Plasmas with Nonthermal Electrons-positron and Bipolar Ions

Abstract This paper studied the propagating characteristics of (2+1) dimensional nonlinear ion acoustic waves in a multicomponent plasma with nonthermal electrons, positrons and bipolar ions. The dispersion relations are initially explored by using the small amplitude wave's dispersion relation. Then, the Sagdeev potential method is employed to study large amplitude ion acoustic waves. The analysis involves examining the system's phase diagram, Sagdeev potential function, and solitary wave solutions through numerical solution of an analytical process in order to investigate the propagation properties of nonlinear ion acoustic waves under various parameters. It is found that the propagation of nonlinear ion acoustic waves is subject to the influence of various physical parameters, including the ratio of number densities between the unperturbed positrons, electrons to positive ions, nonthermal parameters, the masses ratio of positive ions to negative ions, and the charge numbers ratio of negative ions to positive ions, the ratio of the electrons’ temperature to positrons’ temperature. In addition, the multicomponent plasma system has a compressive solitary waves with amplitude greater than zero or a rarefactive solitary waves with amplitude less than zero, in the meantime, compressive and rarefactive ion acoustic wave characteristics depend on the charge numbers ratio of negative ions to positive ions.

What guides the judgment of learning: Memory or heuristics? An event-related potential study

Memory monitoring ability is essential for the effectiveness of learning processes. Judgment of Learning (JOL), a metacognitive judgment, is commonly used to measure this ability. An ongoing debate questions whether JOL is an outcome of an inferential or recollective experience, as suggested by different hypotheses regarding the underlying cognitive mechanisms of this judgment. To address this question through a neuroscientific perspective, we aimed to investigate the temporal dynamic of JOL adopting event-related potential (ERP) methodology. Seventy-two young adults participated in an episodic memory task involving word-pairs as stimuli. Their JOLs were obtained through categorical choices in a delayed condition. Additionally, their memory performance was tested in the recognition phase. ERP components were compared for different JOL levels, as well as for the hit responses in the recognition test according to their JOL levels. The analyses showed that JOL processes are observable within an early time window after stimulus presentation, as evidenced by elicitation of the P100, N100, P200, N200, and P300 components across all JOL levels. However, only the amplitude of the N100 varied among these levels. A negative ERP component with 330–500 ms latency was also evident for all JOL levels in the central and parietal electrodes, which did not differ in amplitude. The analyses of the recognition phase ERPs showed that the hit responses did not exhibit a significant difference in the familiarity-related mid-frontal old/new effect (FN400) amplitude; however, those with high level of JOL elicited recollection-related parietal old-new effect with a smaller amplitude. These findings support both hypotheses suggesting that JOL is influenced by heuristics and the retrievability of information.

A first order in time wave equation modeling nonlinear acoustics

In this paper we focus on a small amplitude approximation of a Navier-Stokes-Fourier system modeling nonlinear acoustics. Omitting all third and higher order terms with respect to certain small parameters, we obtain a first order in time system containing linear and quadratic pressure and velocity terms. Subsequently, the well-posedness of the derived system is shown using the classical method of Galerkin approximation in combination with a fixed point argument. We first prove the well-posedness of a linearized equation using energy estimates and then the well-posedness of the nonlinear system using a Newton-Kantorovich type argument. Based on this, we also obtain global in time well-posedness for small enough data and exponential decay. This is in line with semigroup results for a linear part of the system that we provide as well.

Self-induced transparency of long water waves over bathymetry: the dispersive shock mechanism

The shoreline hazard posed by ocean long waves such as tsunamis and meteotsunamis critically depends on the fraction of energy transmitted across the shallow near-shore shelf. In linear setting, bathymetric inhomogeneities of length comparable to the incident wavelength act as a protective high-pass filter, reflecting long waves and allowing only shorter waves to pass through. Here, we show that, for weakly nonlinear waves, the transmitted energy flux fraction can significantly depend on the amplitude of the incoming wave. The basis of this mechanism is the formation of dispersive shock waves (DSWs), a salient feature of nonlinear evolution of long water waves, often observed in tidal bores and tsunami/meteotsunami evolution. Within the framework of the Boussinesq equations, we show that the DSWs efficiently transfer wave energy into the high wavenumber band, where reflection is negligible. This is phenomenologically similar to self-induced transparency in nonlinear optics: small amplitude long waves are reflected by the bathymetric inhomogeneity, while larger amplitude waves that develop DSWs blueshift into the transparency regime and pass through. We investigate this mechanism in a simplified setting that retains only the key processes of DSW disintegration and reflection, while the effects such as bottom dissipation and breaking are ignored. The results suggests that the phenomenon is a robust, order-one effect. In contrast, the increased transmission due to the growth of bound harmonics associated with the steepening of the wave is weak. The results of the simplified modelling are validated by simulations with the FUNWAVE-TVD Boussinesq model.

Shock Waves in Nonlinear Transmission Lines

In the first half of the article, interaction between the small amplitude travelling waves (“sound”) and the shock waves in the transmission line containing both nonlinear capacitors and nonlinear inductors is considered. Herein, the “sound” wave coefficient of reflection from (coefficient of transmission through) the shock wave is calculated. These coefficients are expressed in terms of the speeds of the “sound” waves relative to the shock and the wave impedances. In the second half of the article, the dissipation in the system is explicitly included into consideration, introducing Ohmic resistors shunting the inductors and also in series with the capacitors. This allows us to justify the conditions on the shocks, postulated in the first half of the article. This also allows us to describe the shocks as physical objects of finite width and study their profiles, same as the profiles of the waves closely connected with the shocks—the kinks. The profiles of the latter, and in some particular cases, the profiles of the former are obtained in terms of elementary functions.

Assessing the impact of degree of fusion and muscle fibre twitch shape variation on the accuracy of motor unit discharge time identification from ultrasound images

ObjectiveUltrasound (US) images during a muscle contraction can be decoded into individual motor unit (MU) activity, i.e., trains of neural discharges from the spinal cord. However, current decoding algorithms assume a stationary mixing matrix, i.e. equal mechanical twitches at each discharge. This study aimed to investigate the accuracy of these approaches in non-ideal conditions when the mechanical twitches in response to neural discharges vary over time and are partially fused in tetanic contractions. MethodsWe performed an in silico experiment to study the decomposition accuracy for changes in simulation parameters, including the twitch waveforms, spatial territories, and motoneuron-driven activity. Then, we explored the consistency of the in silico findings with an in vivo experiment on the tibialis anterior muscle at varying contraction forces. ResultsA large population of MU spike trains across different excitatory drives, and noise levels could be identified. The identified MUs with varying twitch waveforms resulted in varying amplitudes of the estimated sources correlated with the ground truth twitch amplitudes. The identified spike trains had a wide range of firing rates, and the later recruited MUs with larger twitch amplitudes were easier to identify than those with small amplitudes. Finally, the in silico and in vivo results were consistent, and the method could identify MU spike trains in US images at least up to 40% of the maximal voluntary contraction force. ConclusionThe decoding method was accurate irrespective of the varying twitch-like shapes or the degree of twitch fusion, indicating robustness, important for neural interfacing applications.