scholarly journals A duality proof of sampling localisation in relaxation spectrum recovery

2001 ◽  
Vol 64 (2) ◽  
pp. 265-269 ◽  
Author(s):  
R. J. Loy ◽  
C. Newbury ◽  
R. S. Anderssen ◽  
A. R. Davies
Keyword(s):  
Linear Viscoelasticity ◽  
Finite Interval ◽  
Relaxation Spectrum ◽  
Relaxation Times ◽  
Oscillatory Shear ◽  
Fundamental Nature ◽  
Duality Argument ◽  
Spectrum Recovery

In a recent paper, Davies and Anderssen (1997) examined the range of relaxation times, on which the linear viscoelasticity relaxation spectrum could be reconstructed, when the oscillatory shear data were only known on a fixed finite interval of frequencies. In particular, they showed that, for such oscillatory shear data, knowledge about the relaxation spectrum could only be recovered on a specific finite interval of relaxation times. They referred to this phenomenon as sampling localisation. The purpose of this note is show how their result can be proved using a duality argument, and, thereby, establish the fundamental nature of sampling localisation in relaxation spectrum recovery.

The Lodge Rubberlike Liquid Behavior for Cheese in Large Amplitude Oscillatory Shear

2001 ◽  
Vol 11 (6) ◽  
pp. 312-319 ◽  
Author(s):  
Y.-C. Wang ◽  
S. Gunasekaran ◽  
A. J. Giacomin
Keyword(s):  
Stress Responses ◽  
Relaxation Spectrum ◽  
Large Strain ◽  
Small Strain ◽  
Oscillatory Shear ◽  
Linear Relaxation ◽  
Linear Regime ◽  
Linear Spectrum ◽  
Liquid Behavior ◽  
Scale Down

AbstractThe viscoelasticity of reduced-fat Cheddar and Mozzarella cheeses was characterized in small (parallel disk rheometer, go = 0.01) and large (sliding plate rheometer, 0.2< go <7) amplitude oscillatory shear at 40 and 60˚C. We deduced the linear relaxation spectrum from the small strain measurements. At large strain amplitudes, we found sinusoidal stress responses whose amplitudes are well below those predicted from the linear relaxation spectrum, and yet remarkably linear with strain amplitude. We call this the large strain linear regime. We discovered that the Lodge rubberlike liquid can quantitatively explain the large strain linear regime if we scale down the relaxation moduli in the linear spectrum by a constant. This large strain linear regime persists to much higher strain amplitudes for Cheddar (go £ 4) than for Mozzarella (go £ 1). This is perhaps due to oriented structure of the protein matrix in the Mozzarella cheese.

CONVERGENCE IN RELAXATION SPECTRUM RECOVERY

2016 ◽  
Vol 95 (1) ◽  
pp. 121-132 ◽  
Author(s):  
R. J. LOY ◽  
F. R. DE HOOG ◽  
R. S. ANDERSSEN
Keyword(s):  
Infinite Series ◽  
Relaxation Spectrum ◽  
Sufficient Conditions ◽  
Convolution Equation ◽  
Series Expansions ◽  
Practical Application ◽  
Rigorous Analysis ◽  
Spectrum Recovery ◽  
Derivatives Of

Because of its practical and theoretical importance in rheology, numerous algorithms have been proposed and utilised to solve the convolution equation $g(x)=(\text{sech}\,\star h)(x)\;(x\in \mathbb{R})$ for $h$, given $g$. There are several approaches involving the use of series expansions of derivatives of $g$, which are then truncated to a small number of terms for practical application. Such truncations can only be expected to be valid if the infinite series converge. In this note, we examine two specific truncations and provide a rigorous analysis to obtain sufficient conditions on $g$ (and equivalently on $h$) for the convergence of the series concerned.

Determination of the relaxation spectrum from oscillatory shear data

1991 ◽  
Vol 35 (6) ◽  
pp. 1035-1049 ◽  
Author(s):  
Nese Orbey ◽  
John M. Dealy
Keyword(s):  
Relaxation Spectrum ◽  
Oscillatory Shear

scholarly journals Measurements of the Electrical Properties of Ice Ih Single Crystals by Admittance and Thermally Stimulated Depolarization Techniques

1978 ◽  
Vol 21 (85) ◽  
pp. 219-230 ◽  
Author(s):  
Arturo Loria ◽  
Ezio Mazzega ◽  
Umberto del Pennino ◽  
Giovanni Andreotti
Keyword(s):  
Activation Energy ◽  
Relaxation Time ◽  
Electrical Properties ◽  
Single Crystals ◽  
Relaxation Spectrum ◽  
Relaxation Times ◽  
Dielectric Strength ◽  
Inert Gas ◽  
Complex Admittance ◽  
Thermally Stimulated Depolarization

Abstract Ice Ih single crystals were investigated by complex admittance and thermally stimulated depolarization (TSD) techniques, in the relaxation-time ranges 10–5–10 s and 10–104 s respectively. The relaxation spectrum was resolved and three components of it were studied. Second-order kinetics had to be assumed for two of the TSD spectra to obtain Arrhenius-type relaxation times. The “Debye spectrum” had an activation energy for the relaxation time of 0.64 eV at the high temperatures and its dielectric strength revealed a possible defect cross-over at T c = 190 K. Far below this temperature the activation energy was 0.38 eV, that is about half of that necessary for a pair of ion defects to form. In comparison with the results of other authors, a lower concentration of ionic defects, or possibly of Bjerrum–ion aggregates, was deduced to occur in our crystals. Inert-gas host molecules were proposed as a possible origin of the two other spectra, having relaxation times shorter than the “Debye spectrum” and energies of 0.33 eV and 0.37 eV. Moreover the 0.33 eV spectrum, whose dielectric strength appears at a temperature below T c, might alternatively be related to the cross-over of the “Debye spectrum”.

Influence of Vibrations on the Viscoelastic Behavior of Monodisperse Polybutadienes

1972 ◽  
Vol 45 (4) ◽  
pp. 1082-1093
Author(s):  
G. V. Vinogradov ◽  
Yu G. Yanovsky ◽  
A. I. Isayev ◽  
V. P. Shatalov ◽  
V. G. Shalganova
Keyword(s):  
Linear Theory ◽  
Cyclic Deformation ◽  
Relaxation Spectrum ◽  
Relaxation Times ◽  
Viscoelastic Behavior ◽  
Logarithmic Scale ◽  
Continuous Deformation ◽  
Long Time ◽  
Short Time ◽  
Theory Of Viscoelasticity

Abstract The viscoelastic behavior of monodisperse polybutadienes is studied at different amplitudes of cyclic deformation. The concept of initial relaxation spectrum is introduced, this spectrum corresponding to small amplitudes. Under the action of high amplitudes the relaxation spectrum changed. This changed-effective spectrum can be calculated by means of the linear theory of viscoelasticity. The initial spectra of monodisperse polybutadienes have maxima. Under the action of high amplitudes the long-time parts of the spectra are truncated and the maxima shift into the short-time regions. There is an unambiguous correspondence between the amplitude of the deformation rate on cyclic deformation and the rate of shear on continuous deformation. It is shown that the length of the high-elasticity plateau, estimated on a logarithmic scale of relaxation times, and the maximum relaxation times of polybutadienes, as well as their initial Newtonian viscosities are dependent on molecular weight to a power of 3.6. The apparent viscosity is calculated, making use of the approximate initial relaxation spectrum concept, the law of change of its long-time boundary with the shear rate, and the commonly known relation of the linear theory of viscoelasticity. The results of these calculations were found to agree approximately with the data obtained under conditions of continuous deformation.

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