A Geometric Theory of Growth Mechanics

In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. The time dependence of the metric represents the evolution of the stress-free (natural) configuration of the body in response to changes in mass density and “shape”. We show that the time dependency of the material metric will affect the energy balance and the entropy production inequality; both the energy balance and the entropy production inequality have to be modified. We then obtain the governing equations covariantly by postulating invariance of energy balance under time-dependent spatial diffeomorphisms. We use the principle of maximum entropy production in deriving an evolution equation for the material metric. In the case of isotropic growth, we find those growth distributions that do not result in residual stresses. We then look at Lagrangian field theory of growing elastic solids. We will use the Lagrange–d’Alembert principle with Rayleigh’s dissipation functions to derive the governing equations. We make an explicit connection between our geometric theory and the conventional multiplicative decomposition of the deformation gradient, F=F _e F _g, into growth and elastic parts. We linearize the nonlinear theory and derive a linearized theory of growth mechanics. Finally, we obtain the stress-free growth distributions in the linearized theory.     

Role of recording geometry in the performance of spectral diversity filters with spherical beam volume holograms

We present experimental demonstrations of spectral diversity filters with spherical beam volume holograms for multimodal multiplex spectroscopy. Major properties of filters under diffuse-light illumination are discussed. The comparisons of spectral diversity between the transmission geometry holograms and the reflection geometry holograms are also studied. The results show that there is a trade-off between the degree of the spatial coherence of the source and the spectral diversity of the filter. We also conclude that the reflection geometry holograms have better spectral diversity and less sensitivity to the spatial coherence of the source.     

A framework for synthetic validation of 3D echocardiographic particle image velocimetry

Particle image velocimetry (PIV) has been significantly advanced since its conception in early 1990s. With the advancement of imaging modalities, applications of 2D PIV have far expanded into biology and medicine. One example is echocardiographic particle image velocimetry that is used for in vivo mapping of the flow inside the heart chambers with opaque boundaries. Velocimetry methods can help better understanding the biomechanical problems. The current trend is to develop three-dimensional velocimetry techniques that take advantage of modern medical imaging tools. This study provides a novel framework for validation of velocimetry methods that are inherently three dimensional such as but not limited to those acquired by 3D echocardiography machines. This framework creates 3D synthetic fields based on a known 3D velocity field \({\mathbf{V}}\) and a given 3D brightness field \({\mathbf{B}}\). The method begins with computing the inverse flow \({\mathbf{V}}^{\varvec{*}} \) based on the velocity field \({\mathbf{V}}\). Then the transformation of \({\mathbf{B}}\), imposed by \({\mathbf{V}}\), is calculated using the computed inverse flow according to \({\mathbf{B}}^{\varvec{*}} \left( {\mathbf{x}} \right) = {\mathbf{B}}\left( {{\mathbf{x}} + {\mathbf{V}}^{\varvec{*}} \left( {\mathbf{x}} \right)} \right)\), where x is the coordinates of voxels in \({\mathbf{B}}^{\varvec{*}} \), with a 3D weighted average interpolation, which provides high accuracy, low memory requirement, and low computational time. To check the validity of the framework, we generate pairs of 3D brightness fields by employing Hill’s spherical vortex velocity field. \({\mathbf{B}}\) and the generated \({\mathbf{B}}^{\varvec{*}} \) are then processed by our in-house 3D particle image velocimetry software to obtain the interrelated velocity field. The results indicates that the computed and imposed velocity fields are in agreement.     

A digital implementation of 2D Hindmarsh–Rose neuron

Nonlinear Dynamics - Different architectures and techniques have developed in the neuromorphic field to mimic and investigate the activity of biological neural networks. This paper presents a set...     

Application of Tsunoda reagent to the convenient synthesis of drug-like pyrazoles

The versatility of the under-utilised (cyanomethylene)tributylphosphorane (CMBP, Tsunoda reagent) was demonstrated on two occasions in a drug discovery context. Firstly, the high reactivity of the phosphorane allowed the alkylation of a weakly acidic pyrazole when standard Mitsunobu conditions were unsuccessful. Secondly, the clean reaction profile generally obtained using CMBP allowed the direct use of the crude mixture in a subsequent Suzuki cross coupling. This reagent has utility when isolation of the Mitsunobu reaction product (e.g. containing a boronate) is not desirable.     

Synthesis of CuS nanoparticles loaded on activated carbon composite for ultrasound‐assisted adsorption removal of dye pollutants: Process optimization using CCD‐RSM,equilibrium and kinetic studies

In this study, the CuS nanoparticles loaded on activated carbon (CuS‐NPs‐AC) composite was synthesized and then, characterized by XRD and FE‐SEM analyses. The prepared composite was used as a potential adsorbent for the simultaneous ultrasound‐assisted removal of Indigo Carmine (IC) and Safranin‐O (SO). The CuS‐NPs‐AC dose (0.01‐0.03 g), sonication time (1‐5 min), initial SO concentration (5‐15 mg L^‐1) and initial IC concentration (5‐15 mg L^‐1) as expectable effective parameters were studied by central composite design (CCD) under response surface methodology (RSM) to obtain an useful knowledge about the effect of simultaneous interaction between IC and SO on their removal percentage. The optimum SO and IC removal percentages were determined to be 98.24 and 97.15% at pH = 6, 0.03 g of the CuS‐NPs‐AC, 3 min sonication time, 12 and 10 mg L^‐1 of IC and SO. The values of coefficient of determination (R²) for SO and IC were 0.9608 and 0.9796, respectively, indicating the favorable fitness of the experimental data to the second order polynomial regression model. The isotherm data were well correlated with Freundlich model. The maximum monolayer adsorption capacities of 87.5 and 69.90 mg g^‐1 at room temperature for IC and SO in the investigated binary system expressed the high efficiency of the novel adsorbent for water cleanup within a short time. The investigation of correlation between time and rate of adsorption revealed that IC and SO adsorption onto the CuS‐NPs‐AC followed pseudo‐second‐order and intra‐particle diffusion simultaneously.     

Immobilization of a nickel complex onto functionalized Fe3O4 nanoparticles: a green and recyclable catalyst for synthesis of 5-substituted 1H-tetrazoles and oxidation reactions

Research on Chemical Intermediates - In the present research, a magnetically recoverable catalyst was easily prepared by anchoring nickel onto the surface of organically modified magnetite...     

Free vibration and stability of an axially moving thin circular cylindrical shell using multiple scales method

This paper investigates the linear free vibration of axially moving simply supported thin circular cylindrical shells with constant and time-dependent velocity considering the effect of viscous structure damping. Classical shell theory is employed to express strain-displacement relation. Linear elasticity theory is used to write stress–strain relation considering Hook’s Law. Governing equations in cylindrical coordinates are derived using the Hamilton principle. Equilibrium equations are rewritten with the help of Donnell–Mushtari shell theory simplification assumptions. Motion equations for displacements in axial and circumferential directions are solved analytically concerning to displacement in the radial direction.As the displacement in the radial direction is the combination of driven and companion modes, the third motion equation is discretized using the Galerkin method. The set of ordinary differential equation obtained from the Galerkin method is solved using the steady-state method, which in practice leads to the prediction of the exact frequencies of vibration. By employing multiple scale method the critical speed values of a circular cylindrical shell and several types of instabilities are discussed. The numerical results show that by increasing the mean velocity, the system always loses stability by the divergence instability in different modes, and the critical speed values of lower modes are higher than those of higher modes. As well as the unstable regions for the resonances between velocity function fluctuation frequencies and the linear combination of natural frequencies is gained from the solvability condition of second order multiple scale method. The accuracy of the method is checked against the available data.