Compatibility Equations of Nonlinear Elasticity for Non-Simply-Connected Bodies

Compatibility equations of elasticity are almost 150 years old. Interestingly, they do not seem to have been rigorously studied, to date, for non-simply-connected bodies. In this paper we derive necessary and sufficient compatibility equations of nonlinear elasticity for arbitrary non-simply-connected bodies when the ambient space is Euclidean. For a non-simply-connected body, a measure of strain may not be compatible, even if the standard compatibility equations (“bulk” compatibility equations) are satisfied. It turns out that there may be topological obstructions to compatibility; this paper aims to understand them for both deformation gradient F and the right Cauchy-Green strain C = F ^T F. We show that the necessary and sufficient conditions for compatibility of deformation gradient F are the vanishing of its exterior derivative and all its periods, that is, its integral over generators of the first homology group of the material manifold. We will show that not every non-null-homotopic path requires supplementary compatibility equations for F and linearized strain e. We then find both necessary and sufficient compatibility conditions for the right Cauchy-Green strain tensor C for arbitrary non-simply-connected bodies when the material and ambient space manifolds have the same dimensions. We discuss the well-known necessary compatibility equations in the linearized setting and the Cesàro-Volterra path integral. We then obtain the sufficient conditions of compatibility for the linearized strain when the body is not simply-connected. To summarize, the question of compatibility reduces to two issues: i) an integrability condition, which is d(F dX) = 0 for the deformation gradient and a curvature vanishing condition for C, and ii) a topological condition. For F dx this is a homological condition because the equation one is trying to solve takes the form dφ = F dX. For C, however, parallel transport is involved, which means that one needs to solve an equation of the form dR/ ds = RK, where R takes values in the orthogonal group. This is, therefore, a question about an orthogonal representation of the fundamental group, which, as the orthogonal group is not commutative, cannot, in general, be reduced to a homological question.     

Secondary wake instabilities of a blunt trailing edge profiled body as a basis for flow control

Flow in the wake of a blunt trailing edge profiled body, comprised of an elliptical leading edge and a rectangular trailing edge, has been investigated experimentally, to identify and characterize the secondary instabilities accompanying the von Kármán vortices. The experiments, which involve laser-induced fluorescence for visualization and particle image velocimetry for quantitative measurement of the wake instabilities, cover Reynolds numbers ranging from 250 to 2,150 based on thickness of the body, to include the wake transition regime. The dominant secondary instability appears as spanwise undulations in von Kármán vortices, which evolve into pairs of counter-rotating vortices, with features resembling the instability mechanism predicted by Ryan et al. (J Fluid Mech 538:1–29, 2005). Feasibility of a flow control approach based on interaction with the secondary instability using a series of discrete trailing edge injectors has also been investigated. The control approach mitigates the adverse effects of vortex shedding in certain conditions, where it is able to amplify the secondary instability effectively.     

A comprehensive overview on the structure and comparison of magnetic properties of nanocrystalline synthesized by a thermal treatment method

This study reports the simple synthesis of MFe₂O₄ (where M=Zn, Mn and Co) nanostructures by a thermal treatment method, followed by calcination at various temperatures from 723 to 873 K. Poly(vinyl pyrrolidon) (PVP) was used as a capping agent to stabilize the particles and prevent them from agglomeration. The pyrolytic behaviors of the polymeric precursor were analyzed by use of simultaneous thermo-gravimetry analyses (TGA) and derivative thermo-gravimetry (DTG) analyses. The characterization studies were conducted by X-ray diffraction (XRD) and transmission electron microscopy (TEM). Fourier transform infrared spectroscopy (FT-IR) confirmed the presence of metal oxide bands for all the calcined samples. Magnetic properties were demonstrated by a vibrating sample magnetometer (VSM), which displayed that the calcined samples exhibited different types of magnetic behavior. The present study also substantiated that magnetic properties of ferrite nanoparticles prepared by the thermal treatment method, from viewing microstructures of them, can be explained as the results of the two important factors: cation distribution and impurity phase of α-Fe₂O₃. These two factors are subcategory of the preparation method which is related to macrostructure of ferrite. Electron paramagnetic resonance (EPR) spectroscopy showed the existence of unpaired electrons ZnFe₂O₄ and MnFe₂O₄ nanoparticles while it did not exhibit resonance signal for CoFe₂O₄ nanoparticles.     

Silver Nanoparticle Fabrication by Laser Ablation in Polyvinyl Alcohol Solutions

A laser ablation technique is applied for synthesis of silver nanoparticles in different concentrations of polyvinyl alcohol （PVA） aqueous solution. The ablation of high pure silver plate in the solution is carried out by a nanosecond Q-switched Nd：YAG pulsed laser. X-ray diffraction and transmission electron microscopy are implemented to explore the particles sizes. The effects of PYA concentrations on the absorbance of the silver nanoparticles are studied as well, by using a UV-vis spectrophotometer. The preparation process is carried out for deionized water as a reference sample. The comparison of the obtained results with the reference sample shows that the formation efficiency of nanoparticles in PYA is much higher and the sizes of particles are also smaller.     

Thermal mode-switching of a passively Q-switched microchip Nd:YAG laser

In the present article, the thermal distribution inside the gain medium of a passively Q-switched microchip laser is modeled and simulated for actual practical values associated with an available microchip laser constructed in our laboratory. The effects of the non-uniform heat distribution on the spectral properties of the output laser beam have been investigated and simulated with the variation of diode-pump power and pulse repetition rate. It is observed that the gain bandwidth as well as Optical Path Difference (OPD) values of the propagating pulses are significantly decreased, while the Nd:YAG chip is cooled down to a certain value. The validity of the utilized model is checked by setting and characterizing the spectral properties of a fabricated laboratory microchip laser under different heating conditions. It is verified that when the temperature of the gain material is changed by an electronically controlled Peltier device, the spectrum of the output laser beam can be switched between single- and dual-mode situations. This physical character has shown good agreement between the presented model and obtained experimental results.     

Cerium(IV) oxide as a neutral catalyst for aldehyde-induced decarboxylative coupling of l-proline with triethyl phosphite and nitromethane

The application of cerium(IV) oxide (CeO₂) as a neutral and heterogeneous catalyst for aldehyde-induced decarboxylative coupling of l-proline with triethyl phosphite and nitromethane is described. In addition, a [3+2] cycloaddition reaction of the in situ generated 1,3-dipolar intermediate with benzaldehyde in the absence of a nucleophile is also reported.     

Covariantization of nonlinear elasticity

In this paper we make a connection between covariant elasticity based on covariance of energy balance and Lagrangian field theory of elasticity with two background metrics. We use Kucha?’s idea of reparametrization of field theories and make elasticity generally covariant by introducing a “covariance field”, which is a time-independent spatial diffeomorphism. We define a modified action for parameterized elasticity and show that the Doyle-Ericksen formula and spatial homogeneity of the Lagrangian density are among its Euler–Lagrange equations.     

Tools to Simulate Distributive Mixing in Twin‐Screw Extruders

The application of the mapping method in finite element modeling is extended to quantitatively compare mixing in different twin‐screw extruder layouts. The mapping method provides volumetric quantities, which are crucial for the analysis and optimization of mixing based on the tracking of particles in the velocity field. A new approach to the mapping method is developed to analyze mixing in complex, dynamic open geometries. Several screw configurations and different types of conveying screws are compared, changing the pitch and gap widths. The volume‐weighted intensity of segregation is used as a mixing measure.

     

Interactive effect of oxygen diffusion and volatiles advection on transient thermal degradation of poly methyl methacrylate (PMMA)

A transient, one-dimensional model has been presented to formulate the substantial role of polymer gasification in the early stages of fire growth. The present model comprises the interaction between the oxygen diffusion and the released volatiles on the rate of polymer gasification, when the polymeric sample is subjected to an external radiative source. The model also includes different mechanisms affecting the degradation process such as in-depth thermal and oxidative decomposition, in-depth absorption of radiation and heat and mass transfer in the both gas and solid phases. The results for two different radiative heat sources (17 and 40 kW m⁻²) are reported and yielded realistic results, comparing to the published experimental data. It was found that an increase in the oxygen concentration will lead to a considerable decrease in the surface temperature as well as significant increase of gasification rate at 17 kW m⁻²; nevertheless this effect is less apparent at 40 kW m⁻².     

Microwave-Assisted Chemoselective Regeneration of Carbonyl Compounds from Oximes by Silica Chromate/WET SiO2 Under Solvent-Free Conditions

The regeneration of carbonyl compounds from oximes were performed by using silica chromate and wet SiO ₂ (w/w 50%) under microwave irradiation and solvent-free conditions with excellent yields.