A finite volume cell‐centered Lagrangian hydrodynamics approach for solids in general unstructured grids

A finite volume cell‐centered Lagrangian hydrodynamics approach, formulated in Cartesian frame, is presented for solving elasto‐plastic response of solids in general unstructured grids. Because solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum, and energy conservation laws. The total stress is split into deviatoric shear stress and dilatational components. The dilatational response of the material is modeled using the Mie‐Grüneisen equation of state. A predicted trial elastic deviatoric stress state is evolved assuming a pure elastic deformation in accordance with the hypo‐elastic stress‐strain relation. The evolution equations are advanced in time by constructing vertex velocity and corner traction force vectors using multi‐dimensional Riemann solutions erected at mesh vertices. Conservation of momentum and total energy along with the increase in entropy principle are invoked for computing these quantities at the vertices. Final state of deviatoric stress is effected via radial return algorithm based on the J‐2 von Mises yield condition. The scheme presented in this work is second‐order accurate both in space and time. The suitability of the scheme is evinced by solving one‐ and two‐dimensional benchmark problems both in structured grids and in unstructured grids with polygonal cells. Copyright © 2013 John Wiley & Sons, Ltd.     

How does the ambiguity of the electronic stress tensor influence its ability to serve as bonding indicator

The electronic stress tensor is not uniquely defined. Possible bonding indicators originating from the quantum stress tensor may inherit this ambiguity. Based on a general formula of the stress tensor this ambiguity can be described by an external parameter λ for indicators derived from the scaled trace of the stress tensor (whereby the scaling function is proportional to the Thomas–Fermi kinetic energy density). The influence of λ is analyzed and the consequences for the representation of chemical bonding are discussed in detail. It is found that the scaled trace of the stress tensor may serve as suitable bonding indicator over a wide range of λ values, excluding the value range between ?0.15 and ?0.48. Focusing on the eigenvalues of the stress tensor, it is found that the sign of the eigenvalues heavily depends on the chosen representation of the stress tensor. Therefore, chemical bonding analyses which are based on the interpretation of the eigenvalue sign (e.g., the spindle structure) are strongly dependent on the chosen form of the stress tensor. © 2014 Wiley Periodicals, Inc.     

Reconstruction of n-dimensional convex bodies from surface tensors

In this paper, we derive uniqueness and stability results for surface tensors. Further, we develop two algorithms that reconstruct shape of n-dimensional convex bodies. One algorithm requires knowledge of a finite number of surface tensors, whereas the other algorithm is based on noisy measurements of a finite number of harmonic intrinsic volumes. The derived stability results ensure consistency of the two algorithms. Examples that illustrate the feasibility of the algorithms are presented.     

A thermodynamic framework to model thixotropic materials

Thixotropic materials are widely used in a variety of industrial applications. The constitutive relations to describe these materials are based on one-dimensional experiments in which the material is subjected to a shear motion and there is no unique methodology to obtain proper three-dimensional models. The path towards generalization to a three-dimensional framework is invariably carried out in a ad hoc manner. Here we propose a three-dimensional model that stems from a general thermodynamic framework that has proved to be quite robust in the development of constitutive relations, namely the application of the second law of thermodynamics together with the maximization of the entropy production. This leads to a constitutive equation that has the same form of a generalized Upper Convected Maxwell equation, if we require that changes of microstructure due to the deformation of each Maxwell element that comprises the model are reversible. Changes in microstructure are governed by a potential that is a measure of the difference between the current structure and the equilibrium structure associated with it. The equilibrium structure associated with the current structure is determined by the current value of stress, considered the main break up agent. We assume that the state of equilibrium would be achieved in a Motion With Constant Stress History, starting from the current stress state, until a steady state where the kinematics is not changing.     

Twist-bend nematics,liquid crystal dimers,structure–property relations

ABSTRACT

One of the current challenges in liquid crystal science is to understand the molecular factors leading to the formation of the intriguing twist-bend nematic phase (N_TB) and determine its properties. During our earlier hunt for the N_TB phase created on cooling directly from the isotropic phase and not the nematic phase, we had prepared 30 symmetric liquid crystal dimers. These had odd spacers and methylene links to the two mesogenic groups; desirable but clearly not essential features for the formation of the N_TB. Here, we report the phases that the dimers exhibit and their transition temperatures as functions of both the lengths of the spacer and the terminal chains. In addition we describe the transitional entropies, their optical textures, the X-ray scattering patterns and the ²H NMR spectra employed in characterising the phases. All of which may lead to important properties of the twist-bend nematic phase.     

Binary hairy nanoparticles: Recent progress in theory and simulations

Binary polymer brushes, including mixed homopolymer brushes and diblock copolymer brushes, are an attractive class of environmentally responsive nanostructured materials. Owing to microphase separation of the two chemically distinct components in the brush, multifaceted nanomaterials with functionalized and patterned surfaces can be obtained. This review summarizes recent progress on the theory and simulations related to binary polymer brushes grafted to flat, spherical, and cylindrical substrates, with a focus on patterned morphologies of multifaceted hairy nanoparticles, an intriguing class of hybrid nanostructured particles (e.g., nanospheres and nanorods). In particular, powerful field theory and particle-based simulations suitable for revealing novel structures on these patterned surfaces, including self-consistent field theory and dissipative particle dynamics simulations, are emphasized. The unsolved yet critical issues in this research field, such as dynamic response of binary polymer brushes to environmental stimuli and the hierarchical self-assembly of binary hairy nanoparticles, are briefly discussed. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1583–1599     

Protein dielectrophoresis: Key dielectric parameters and evolving theory

Globular proteins exhibit dielectrophoresis (DEP) responses in experiments where the applied field gradient factor ∇E² appears far too small, according to standard DEP theory, to overcome dispersive forces associated with the thermal energy kT of disorder. To address this a DEP force equation is proposed that replaces a previous empirical relationship between the macroscopic and microscopic forms of the Clausius–Mossotti factor. This equation relates the DEP response of a protein directly to the dielectric increment δε⁺ and decrement δε⁻ that characterize its β-dispersion at radio frequencies, and also indirectly to its intrinsic dipole moment by way of providing a measure of the protein's effective volume. A parameter Γ_pw, taken as a measure of cross-correlated dipole interactions between the protein and its water molecules of hydration, is included in this equation. For 9 of the 12 proteins, for which an evaluation can presently be made, Γ_pw has a value of ≈4600 ± 120. These conclusions follow an analysis of the failure of macroscopic dielectric mixture (effective medium) theories to predict the dielectric properties of solvated proteins. The implication of a polarizability greatly exceeding the intrinsic value for a protein might reflect the formation of relaxor ferroelectric nanodomains in its hydration shell.     

On the structure of the microscopic dielectric tensor in incommensurate crystals

A microscopic model for calculating the optical response of incommensurately modulated phases in insulating crystals is presented. The dominant contribution to the dielectric permittivity tensor is shown to originate from the lowest-index reciprocal lattice vectors, thus proving the validity of the mesoscopic approach developed in several earlier studies. The expression for the mesoscopic Fourier component of the dielectric tensor is obtained. These results may be useful in relation to the controversial problem of the optical activity observed in the incommensurate phases of some A₂BX₄ family crystals.     

Neurofibrillary tangles and plaques are not accompanied by white matter pathology in aged triple transgenic-Alzheimer disease mice

Alzheimer's disease (AD) is a progressive neurodegenerative disorder that is the most common cause of dementia in aging populations. Although senile plaques and neurofibrillary tangles are well-established hallmarks of AD, changes in cerebral white matter correlate with cognitive decline and may increase the risk of the development of dementia. We used the triple transgenic (3xTg)-AD mouse model of AD, previously used to show that white matter changes precede plaque formation, to test the hypothesis that MRI detectable changes occur in the corpus callosum, external capsule and the fornix. T₂-weighted and diffusion tensor magnetic resonance imaging and histological stains were employed to assess white matter in older (11–17 months) 3xTg-AD mice and controls. We found no statistically significant changes in white matter between 3xTg-AD mice and controls, despite well-developed neurofibrillary tangles and beta amyloid immunoreactive plaques. Myelin staining was normal in affected mice. These data suggest that the 3xTg-AD mouse model does not develop MRI detectable white matter changes at the ages we examined.