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Gelled waxy crude oils can be considered as an elasto-viscoplastic material, exhibiting the transition from linear to nonlinear viscoelasticity. The LAOStress measurements have rarely been applied in the crude oil rheology literature to investigate the nonlinear viscoelasticity. In this study, we present results of the nonlinear viscoelastic characteristics under LAOStress by a series of analytical methods of Fourier transform rheology, Chebyshev strain decomposition, Lissajous curves analysis, energy dissipation calculation, viscoelastic measures quantification, and Pipkin diagram interpretation. Both the elastic and viscous nonlinearities were found to be first strengthened before yielding and subsequently weakened after yielding with the increase in imposed stress amplitude σ0, and a more striking nonlinear response can be captured when using a lower angular frequency ω. However, the defined viscoelastic measures and energy dissipation characteristics continue to keep getting more significant with increasing σ0, even after structural fracture. The results of Lissajous curves analysis reflect that a lower applied ω is more favorable for the structural nonlinear destruction and thus flowability enhancement of interlocking waxy network. The Pipkin diagrams were finally plotted to represent the nonlinear rheological signatures to an oscillatory input, showing a higher measured yield stress under a higher imposed ω. [ABSTRACT FROM AUTHOR]

In this study, we examined the possibility of using industrial microwave processing to enhance the gelling properties and reduce the starch digestibility of mung bean flour (MBF). MBF (12.6 % moisture) was microwaved at a power of 6 W/g to different final temperatures (100–130 °C), and then its structural and functional properties were characterized. The microwave treatment had little impact on the crystalline structure or amylose content of the starch, but it roughened the starch granule surfaces and decreased the short-range ordered structure and degree of branching. In addition, the extent of mung bean protein denaturation caused by the microwave treatment depended on the final temperature. Slightly denaturing the proteins (100 °C) did not affect the nature of the gels (protein phase dispersed in a starch phase) but the gel network became more compact. Moderately denaturing the proteins (110–120 °C) led to more compact and homogeneous starch-protein double network gels. Excessive protein denaturation (130 °C) caused the gel structure to become more heterogeneous. As a result, the facilitated tangles between starch chains by more linear starch molecules after debranching, and the protein network produced by moderate protein denaturation led to the formation of stronger gel and the improvement of plasticity during large deformation (large amplitude oscillatory shear-LAOS). Starch recrystallization, lipid complexion, and protein network retard starch digestion in the MBF gels. In conclusion, an industrial microwave treatment improved the gelling and digestive properties of MBF, and Lissajous curve has good adaptability in characterizing the viscoelasticity of gels under large deformations. [Display omitted] • Microwave treatment facilitated starch debranching and protein denaturation. • Starch debranching improved the tangle and plasticity during LAOS. • Moderate protein denaturation led to uniform starch-protein double network gels. • The denser double gel network is beneficial for retard starch digestion. [ABSTRACT FROM AUTHOR]

A point in the (N , q) -torus knot in ℝ 3 goes q times along a vertical circle while this circle rotates N times around the vertical axis. In the Lissajous-toric knot K (N , q , p) , the point goes along a vertical Lissajous curve (parametrized by t ↦ (sin (q t + ϕ) , cos (p t + ψ))) while this curve rotates N times around the vertical axis. Such a knot has a natural braid representation B N , q , p which we investigate here. If gcd (q , p) = 1 , K (N , q , p) is ribbon; if gcd (q , p) = d > 1 , B N , q , p is the d th power of a braid which closes in a ribbon knot. We give an upper bound for the 4 -genus of K (N , q , p) in the spirit of the genus of torus knots; we also give examples of K (N , q , p) 's which are trivial knots. [ABSTRACT FROM AUTHOR]

Two methods are widely used to quantitatively analyze the nonlinear stress in large amplitude oscillatory shear (LAOS) flow; one is to analyze the stress in time domain and the other in strain or strain rate domain. Distinguished from these two methods, this paper exploits the concept of work and energy to analyze the oscillatory shear stress. The inner area in the strain-stress Lissajous curve after one cycle is known to be related with work, and that of the strain rate-stress Lissajous with energy. To precisely analyze the nonlinear stress, it helps to consider work and energy not only after a complete cycle but also during the cycle. In this paper, we trace the work and energy during the oscillation, together with their derivatives. We apply this concept to perfectly elastic solid, purely viscous liquid, and viscoelastic fluid. By this approach, it is shown that a rheological behavior such as strain thinning can be originated by various origin in the perspective of work and energy, which means that the rheological behavior can be subclassified in terms of work and energy. This approach is useful because it can analyze nonlinear stress without mathematically intriguing higher harmonics and it can be easily applied to any type of material with different stress shape. [ABSTRACT FROM AUTHOR]

The crumb rubber (CR) recycled from waste tires can improve the mechanical properties of bitumen effectively. For the widely used modified bitumen today, it could work in nonlinear regime in many occasions. This study focuses on the nonlinear properties of styrene-butadiene-styrene (SBS) and CR composite modified bitumen (CMB) by analyzing the results of stress-controlled large amplitude oscillatory shear (LAOS) tests. The results show that the nonlinearity of SBS/CR CMB was significant under low load frequency, high temperature and high stress level. Lissajous curves at these conditions are distorted obviously due to the presence of higher-order harmonics. By analyzing the geometry parameters of Lissajous curves, it can be concluded that the incorporation of CR has a positive influence on the nonlinear properties of bitumen, which effectively improve the stress bearing capacity of bitumen. However, the high-order harmonic analysis indicates that improving the CR content simply does not always improve the performance of bitumen. Besides, the nonlinearity of SBS/CR CMB with lower CR content is similar to that of SBS modified bitumen through the value of I 3 / I 1 and intrinsic nonlinear parameter Q, thus there are two critical CR contents for the prospect of modifying the nonlinearity of bitumen. [ABSTRACT FROM AUTHOR]

Dispersed viscoelastic microsphere systems have preliminarily been applied in oil fields with gratifying successes. In this paper, a type of viscoelastic microsphere system with an average particle size of 100.6 μm was synthesized by employing the inverse suspension polymerization. The synthesized viscoelastic microspheres could swell 25.42 times due to the three-dimension structure. The rheological properties of dispersed viscoelastic microsphere system were researched by dynamic strain amplitude scanning measurements and the energy dissipation behaviors were investigated through mathematical method. The results showed that the dispersed system exhibited “shear-thickening” behavior when the strain was greater than the critical strain at different fixed angular frequency. The area enclosed by LISSAJOUS curves or normalized LISSAJOUS curves increased with the increasing of the strain at fixed angular frequency. The relationship between the dissipated energy ( E d ) and strain amplitude ( γ max ) is: E d = K ( γ max ) α . And the relationship between the dissipated energy exponent ( α ) and the fixed angular frequency( ω ) is: α ∝ ω 0.131±0.009 . Therefore, as the strain increases, the clusters grow up gradually and block the flow of the system, which results in “shear-thickening” and the demand of additional energy. [ABSTRACT FROM AUTHOR]

The rheological properties of waxy crude oil are important for its economical and safe pipeline transportation. In actual pipeline transportation, waxy crude oil often exhibits nonlinear rheological characteristics, among which viscoelastic-thixotropic characteristics are the main ones, while there are currently few related studies. This article carried out a study of large amplitude oscillatory shearing (LAOS) for typical Daqing waxy crude oil, and conducted analysis of the nonlinear rheological characteristics of the low temperature waxy crude oil based on the periodic strain loading mode. Using the Fourier transform rheology, Lissajous curve, and stress decomposition method, the effects of strain amplitude and frequency on the nonlinear rheological characteristics under LAOS conditions are analyzed. Results show that when the Fourier transform method analyzes the non-linear rheological characteristics area, the relative intensities of frequency triple and frequency quintuple increase with the increase of strain amplitude and frequency, and it cannot accurately reflect the non-linear rheological properties of waxy crude oil under high-frequency conditions. The Lissajous curve method is more suitable for the study of the nonlinear rheological characteristics of waxy crude oil under low frequency conditions and establishing a prediction formula of dissipated energy density. In addition, the nonlinear viscoelastic parameters obtained by the stress decomposition method can accurately characterize the nonlinear viscoelasticity of waxy crude oil. This research deeply explores the nonlinear rheological properties of waxy crude oil, which can provide theoretical guidance for practice. • The nonlinear rheological characteristics are studied by LAOS experiment. • The influencing factors of nonlinear characteristics are analyzed by three methods. • The applicability of different analysis methods of LAOS is analyzed. • The prediction formula of dissipated energy density is established. [ABSTRACT FROM AUTHOR]

• Studying the influence of voltage frequency and amplitude on the hysteresis loop of piezoelectric actuator. • Discussing the similarity and difference between Lissajous Curve and dynamic hysteresis. • Proposing a LC-PI model to describe the dynamic hysteresis of piezoelectric actuators. • Building a dynamic compensator based on the LC-PI model to suppress the dynamic hysteresis. [Display omitted] Piezoelectric actuators, which are widely used in micro-positioning systems, have hysteresis characteristics between the input and output. In particular, the hysteresis loop is complicated and difficult to be described when the input amplitude and frequency change. Most existing dynamic models cannot describe the law of dynamic hysteresis accurately, such as describing the zero drift of the hysteresis loop. In this paper, a novel and accurate model based on the Lissajous Curve is proposed to describe and compensate the dynamic hysteresis. Firstly, the performance of the piezoelectric actuator is tested, and the experimental results are quantified to research the law of dynamic hysteresis. Secondly, the Lissajous Curve Prandtl-Ishlinskii (LC-PI) model is proposed and the influence of differential order on the operator and memoryless function is discussed. Thirdly, three experiments are designed to verify the LC-PI model. Compared with the existing models, the LC-PI model can describe different types of dynamic hysteresis loops more accurately under the same modeling conditions. Finally, the LC-PI model is used to compensate the dynamic hysteresis. Experimental results show that the compensator based on this model can effectively suppress the dynamic hysteresis of the piezoelectric actuator. [ABSTRACT FROM AUTHOR]

Soy protein isolate (SPI) is often used in food processing due to the high water holding capacity and high stability. This paper explored the effect of heat treatment (HT) on the nonlinear rheological properties of acid-Induced soy protein isolate gels modified by high-pressure homogenization. The effects of HT on the storage modulus G′ , loss modulus G″ and gel rate of the SPI gel were studied through time sweep, frequency sweep and strain sweep tests. The effects of the Lissajous curve, Chebyshev stress decomposition and Fourier transformation were also investigated. The results illustrated that the HT significantly enhanced the mechanical properties of the SPI gel. The curve area and energy dissipation of the Lissajous curve after HT were significantly reduced. Chebyshev stress decomposition illustrated that HT enhanced the shear thickening behavior of SPI gel. The study also found that HT significantly improved the structure and strain resistance of the SPI gel structure. In short, HT significantly improved the nonlinear rheological properties of the SPI gel. • Gel network structure of HIPPE can be stabilized by A/S-SPIG particles. • SPI particles can improve the stability of HIPPE at low temperatures. • A/S-SPIG particle concentration is positively correlated with the emulsification stability. [ABSTRACT FROM AUTHOR]

We present a mathematical model for animating trees realistically by taking into account the influence of natural frequencies and damping ratios. To create realistic motion of branches, we choose three basic mode shapes from the modal analysis of a curved beam, and combine them with a driven harmonic oscillator to approximate Lissajous curve which is observed in pull-and-release test of real trees. The forced vibration of trees is animated by utilizing local coordinate transformation before applying the forced vibration model of curved beams. In addition, we assume petioles are flexible to create natural motion of leaves. A wind field is generated by three-dimensional 1/ f noises to interact with the trees. Besides, our animation model allows users to interactively manipulate trees. We demonstrate several examples to show the realistic motion of interactive trees without using pre-computation or GPU acceleration. Various motions of trees can be achieved by choosing different combinations of natural frequencies and damping ratios according to tree species and seasons. [ABSTRACT FROM AUTHOR]

Abstract: The effect of poly(ethylene glycol) (PEG) on the nonlinear viscoelasticity of Laponite suspensions containing NaCl was investigated with large amplitude oscillatory shear rheology. The molecular weight (M w) of PEG was 4k, 10k and 35k, and the concentration of PEG was varied from 0.063 wt% to 2.4 wt%. The dynamic strain sweep showed that the nonlinearity appeared at γ 0 > 30% with a stress overshoot at γ 0 = 50–70%. The intensity ratio I 3/1 from Fourier-transform increased with γ 0 when entering the nonlinear regime and leveled off at γ 0 ≥ 100% with higher slope and constant value for the PEG of higher M w or lower concentration. I 3/1 revealed the structure difference in the suspensions induced by adsorbing PEG in the nonlinear regime. The minimum- and large-strain rate viscosities η M and η L from the Lissajous curve were found to be sensitive to the nonlinear viscoelasticity and the peak of η M and η L appeared at lower γ 0 with higher maximum following the same dependency as I 3/1 on PEG M w and concentration. The overall nonlinearity parameters N E and N V were proposed in this paper and demonstrated to reflect the difference in the Laponite suspensions with PEG more clearly and more effectively. [Copyright &y& Elsevier]

The central nervous system (CNS) achieves a stable gait at several speeds and modes while controlling diverse instability. An essential feature of a gait is the motion of the center of body mass (CoM). CoM motion is at larger risk for trespassing the base of support in the mediolateral direction than in the anteroposterior direction. How the CoM trajectory in the frontal plane changes depending on the speed or mode can thus provide insights about the neural control of stable gaits. Here, we reveal the speed- and mode-dependent modulations of the trajectory by utilizing a Lissajous curve. The current study clarifies that speed-dependent modulations are evident in walking. Between walking and running, there were significant mode-dependent modulations. In contrast, there were no significant speed-dependent modulations during running. Deviations from standard tendencies quantified via Lissajous curve fitting could be a sign of gait impairments and recovery after treatments. [ABSTRACT FROM AUTHOR]

Studying sliding friction of hydrogels in liquid is important for understanding biological friction. This work applies the non-linear rheology approach to study the friction of elastic hydrogels against adhesive glass in water and in concentrated hyaluronan (HA) solution. Using a rheometer in parallel plate geometry, stress-strain Lissajous curves are obtained from the oscillatory strain sweep test. Non-linearity and energy dissipation are characterized the strain-hardening ratio S , and "energy dissipation occupancy" κ , respectively. For friction in water, a clear transition from a linear viscoelastic to non-linear viscoelastic response occurs at a critical strain amplitude. Whereas, in HA solution, significant friction reduction and non-linear viscoelastic response occurs, related to the rheological behaviors of HA film intercalated at the gel/glass interface. • The non-linear rheology approach was used to study friction of elastic hydrogels. • Experiments were conducted in water and in concentrated hyaluronan (HA) solution. • Non-linearity and energy dissipation are characterized. • In water, a transition from a linear to a non-linear viscoelastic response occurs. • In HA solution, friction reduction and a non-linear viscoelastic response occurs. [ABSTRACT FROM AUTHOR]

We propose a nanometer-scale displacement or vibration measurement system, using an optical quadrature interferometer and the post-processing technique that extracts the parameters necessary for characterizing the interferometric system. Using a 3 × 3 fiber-optic coupler, the entire complex interference signal could be reconstructed with two interference signals measured at two return ports of the coupler. The intrinsic phase difference between the return ports was utilized to obtain the quadratic part of the interference signal, which allowed one to reconstruct the entire complex interference signal. However, the two measured signals were appreciably affected by the unequal detector gains and non-uniform intrinsic phases of the coupler. Fortunately, we could find that the Lissajous curve plotted by the two signals of the interferometric system would form an ellipse. Therefore, by fitting the measured Lissajous curve to an ellipse, we could extract the parameters characterizing the actual system, which allowed the nanometer-scale measurement. Experimental results showed that a 20 kHz sinusoidal vibration with an amplitude of 1.5 nm could be measured with a standard deviation of 0.4 nm. [ABSTRACT FROM AUTHOR]