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Introduction to the Modern Theory of Dynamical Systems

Silk spinning by insects and spiders leads to the formation of fibres that exhibit high strength and toughness. The lack of understanding of the protein processing in silk glands has prevented the recapitulation of these properties in vitro from reconstituted or genetically engineered silks. Here we report the identification of emulsion formation and micellar structures from aqueous solutions of reconstituted silkworm silk fibroin as a first step in the process to control water and protein-protein interactions. The sizes (100-200 nm diameter) of these structures could be predicted from hydrophobicity plots of silk protein primary sequence. These micelles subsequently aggregated into larger 'globules' and gel-like states as the concentration of silk fibroin increased, while maintaining solubility owing to the hydrophilic regions of the protein interspersed among the larger hydrophobic regions. Upon physical shearing or stretching structural transitions, increased birefringence and morphological alignment were demonstrated, indicating that this process mimics the behaviour of similar native silk proteins in vivo. Final morphological features of these silk materials are similar to those observed in native silkworm fibres.

Mechanism of silk processing in insects and spiders

Premises of creation of Internet portal designed to provide access to participants of educational and scientific process for the joint creation, consolidation, concentration and rapid spreading of educational and scientific information resources in its own depository are considered. CMS-based portal content management systems’ potentiality is investigated. Architecture for Internet portal of MES of Ukraine’s information resources is offered.

Створення порталу інформаційно-довідкових ресурсів міністерства освіти і науки україни

This article reports on the International Nanofluid Property Benchmark Exercise, or INPBE, in which the thermal conductivity of identical samples of colloidally stable dispersions of nanoparticles or “nanofluids,” was measured by over 30 organizations worldwide, using a variety of experimental approaches, including the transient hot wire method, steady-state methods, and optical methods. The nanofluids tested in the exercise were comprised of aqueous and nonaqueous basefluids, metal and metal oxide particles, near-spherical and elongated particles, at low and high particle concentrations. The data analysis reveals that the data from most organizations lie within a relatively narrow band (±10% or less) about the sample average with only few outliers. The thermal conductivity of the nanofluids was found to increase with particle concentration and aspect ratio, as expected from classical theory. There are (small) systematic differences in the absolute values of the nanofluid thermal conductivity among the various experimental approaches; however, such differences tend to disappear when the data are normalized to the measured thermal conductivity of the basefluid. The effective medium theory developed for dispersed particles by Maxwell in 1881 and recently generalized by Nan et al. [J. Appl. Phys. 81, 6692 (1997)], was found to be in good agreement with the experimental data, suggesting that no anomalous enhancement of thermal conductivity was achieved in the nanofluids tested in this exercise.

A Benchmark Study on the Thermal Conductivity of Nanofluids

The article tells about the diversity of green spaces in London, the citizens’ attitude toward these spaces, and what Russian cities can learn from this experience.

Nature in London

In this work we studied the effect of oscillatory stress and temperature on the ageing dynamics of aqueous suspension of laponite At the higher magnitude of stress, elastic and viscous moduli of the system underwent a sharp rise with the ageing time The age at the onset of rise and the sharpness of the same increased with the magnitude of stress We propose that at the beginning of ageing, the strain associated with the oscillatory stress field affects the lower modes in the relaxation time distribution The higher modes, which are not significantly affected by the deformation field, continue to grow increasing the viscosity of the system thereby lowering the magnitude of the deformation field Progressive decrease in the later reduces the range of relaxation modes affected by it This dynamics eventually leads to an auto‐catalytic increase in the elastic and viscous moduli An increase in temperature accelerates the ageing process by shifting the ageing dynamics to a lower ageing time This is due the microscopic relaxation dynamics, which causes ageing, becomes faster with increase in the temperature

Ageing under Shear: Effect of Stress and Temperature Field

In this work the ageing dynamics of soft solids of aqueous suspension of laponite has been investigated under the oscillatory stress field. We observed that at small stresses elastic and viscous moduli showed a steady rise with the elastic modulus increasing at a faster rate than the viscous modulus. However at higher stresses both the moduli underwent a sudden rise by several orders of magnitude with the onset of rise getting shifted to a higher age for a larger shear stress. We believe that the observed behavior is due to interaction of barrier height distribution of the potential energy wells in which the particle is trapped and strain induced potential energy enhancement of the particles. Strain induced in the material causes yielding of the particles that are trapped in the shallower wells. Those trapped in the deeper wells continue to age enhancing the cage diffusion timescale and thereby the viscosity which lowers the magnitude of strain allowing more particles to age. This coupled dependence of strain, viscosity and ageing causes forward feedback for a given magnitude of stress leading to sudden rise in both the moduli. Changing the microstructure of the laponite suspension by adding salt affected the barrier heights distribution that showed a profound influence on the ageing behavior. Interestingly, this study suggests a possibility that any apparently yielded material with negligible elastic modulus, may get jammed at a very large waiting time.

Ageing under oscillatory stress: Role of energy barrier distribution in soft glassy materials

The principle of causality leads to linear Kramers–Kronig relations (KKR) that relate the real and imaginary parts of the complex modulus [Formula: see text] through integral transforms. Using the multiple integral generalization of the Boltzmann superposition principle for nonlinear rheology, and the principle of causality, we derived nonlinear KKR, which relate the real and imaginary parts of the [Formula: see text] order complex modulus [Formula: see text]. For [Formula: see text], we obtained nonlinear KKR for medium amplitude parallel superposition (MAPS) rheology. A special case of MAPS is medium amplitude oscillatory shear (MAOS); we obtained MAOS KKR for the third-harmonic MAOS modulus [Formula: see text]; however, no such KKR exists for the first harmonic MAOS modulus [Formula: see text]. We verified MAPS and MAOS KKR for the single mode Giesekus model. We also probed the sensitivity of MAOS KKR when the domain of integration is truncated to a finite frequency window. We found that (i) inferring [Formula: see text] from [Formula: see text] is more reliable than vice versa, (ii) predictions over a particular frequency range require approximately an excess of one decade of data beyond the frequency range of prediction, and (iii) [Formula: see text] is particularly susceptible to errors at large frequencies.

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Kramers–Kronig relations for nonlinear rheology. Part I: General expression and implications

A system undergoing sol-gel transition passes through a unique point, known as the critical gel state, where it forms the weakest space spanning percolated network. We investigate the nonlinear viscoelastic behavior of a colloidal dispersion at the critical gel state using large amplitude oscillatory shear rheology. The colloidal gel at the critical point is subjected to oscillatory shear flow with increasing strain amplitude at different frequencies. We observe that the first harmonic of the elastic and viscous moduli exhibits a monotonic decrease as the material undergoes a linear to nonlinear transition. We analyze the stress waveform across this transition and obtain the nonlinear moduli and viscosity as a function of frequency and strain amplitude. The analysis of the nonlinear moduli and viscosities suggests intracycle strain stiffening and intracycle shear thinning in the colloidal dispersion. Based on the insights obtained from the nonlinear analysis, we propose a potential scenario of the microstructural changes occurring in the nonlinear region. We also develop an integral model using the time-strain separable Kaye-Bernstein-Kearsley-Zapas constitutive equation with a power-law relaxation modulus and damping function obtained from experiments. The proposed model with a slight adjustment of the damping function inferred using a spectral method, compares well with experimental data at all frequencies.

Large amplitude oscillatory shear study of a colloidal gel near the critical state.

In this work we investigate creep flow of aqueous suspension of Laponite, a model soft glassy material, at different aging times and stresses. We observe that this system shows time - aging time - stress superposition over a range of aging times and stresses when real time scale is transformed into effective time scale. Existence of superposition in an effective time domain facilitates prediction of long and very short time rheological behavior. Analysis of the observed behavior from effective time approach suggests that superposition is possible only when the shape of a relaxation time spectrum is preserved at various aging times and stresses. We also observe that creep curves at low aging times and greater stresses demonstrate delayed but sudden yielding. The critical time, at which material yields, increases with increase in aging time and decrease in stress. We argue that local rejuvenation of part of the glassy material causes variation in the rate of evolution of relaxation modes. The resulting interplay between aging and rejuvenating modes lead to delayed yielding as observed experimentally.

Yogesh M. Joshi

Papers

Ageing under Shear: Effect of Stress and Temperature Field

Ageing under oscillatory stress: Role of energy barrier distribution in soft glassy materials

Kramers–Kronig relations for nonlinear rheology. Part I: General expression and implications

Large amplitude oscillatory shear study of a colloidal gel near the critical state.

Delayed Yielding in Creep, Time - Stress Superposition and Effective Time Theory for a Soft Glass