Analytical and numerical solutions of the space and time fractional bloch-torrey equation

Fractional order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brown-ian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As MRI is applied with increasing temporal and spatial resolution, the spin dynamics are being examined more closely; such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments where processes are often anisotropic. Anomalous diffusion in the human brain using fractional order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (see R.L. Magin et al., J. Magnetic Resonance, 190 (2008) 255-270). However effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE, and the stability and convergence of the INM are investigated. We prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.

The effects of lane-changing on the immediate follower : anticipation, relaxation, and change in driver characteristics

This paper investigates the effects of lane-changing in driver behavior by measuring (i) the induced transient behavior and (ii) the change in driver characteristics, i.e., changes in driver response time and minimum spacing. We find that the transition largely consists of a pre-insertion transition and a relaxation process. These two processes are different but can be reasonably captured with a single model. The findings also suggest that lane-changing induces a regressive effect on driver characteristics: a timid driver (characterized by larger response time and minimum spacing) tends to become less timid and an aggressive driver less aggressive. We offer an extension to Newell’s car-following model to describe this regressive effect and verify it using vehicle trajectory data.

Motivations for eWOM exchanges in an online community : self-development, problem solving support, relaxation

Electronic word-of-mouth (eWOM) has gained significant attention from academics and practitioners since it has become an important source of consumers’ product information, which can influence consumer purchase intentions (Cheung & Lee, 2012). eWOM exchanges exist in two types of online communities: online communities of practice and online communities of interest. A few prior studies in online communities of interest have examined members’ motivations for product knowledge exchange (Hung & Li, 2007; Ma & Agarwal, 2007). However, there is a lack of understanding of member motivations for exchanging social bonds and enjoyment in addition to exchanging knowledge pertaining to products in the community. It is important to have an initial comprehension of motivation as an antecedent of these three eWOM exchanges so as to be able to determine the driving factors that lead members to generate eWOM communication. Thus, the research problem "What are the driving factors for members to exchange eWOM in an online community?" was justified for investigation. The purpose of this study was to examine different member motivations for exchanging three types of eWOM. Resource exchange theory and theory on consumer motivation and behavior were applied to develop a conceptual framework for this study. This study focused on an online beauty community since there is an increasing trend of consumers turning to online beauty resources so as to exchange useful beauty product information (SheSpot, 2011). As this study examined consumer motivation in an online beauty community, a web-based survey was the most effective and efficient way to gain responses from beauty community members and these members were appropriate samples from which to draw a conclusion about the whole population. Multiple regression analysis was used to test the relationships between member motivations and eWOM exchanges. It was found that members have different motivations for exchanging knowledge, social bonds, and enjoyment related to products: self-development, problem solving support, and relaxation, respectively. This study makes three theoretical contributions. First, this study identifies the influence of self-development motivation on knowledge exchange in an online community of interest, just as this motivation has previously been found in online communities of practice. This study highlights that members of the two different types of online communities share similar goals of knowledge exchange, despite the two communities evincing different attributes (e.g., member characteristics and tasks’ objectives). Further, this study will assist researchers to understand other motivations identified by prior research in online communities of practice since such motivations may be applicable to online communities of interest. Second, this study offers a new perspective on member motivation for social bonding. This study indicates that in addition to social support from friends and family, consumers are motivated to build social bonds with members in an online community of interest since they are an important source of problem solving support in regard to products. Finally, this study extends the body of knowledge pertaining to member motivation for enjoyment exchange. This study provides a basis for researchers to understand that members in an online community of interest value experiential aspects of enjoyable consumption activities, and thus based on group norms, members have a mutual desire for relaxation from enjoyment exchange. The major practical contribution is that this study provides an important guideline for marketing managers to develop different marketing strategies based on member motivations for exchanging three types of eWOM in an online community of interest, such as an online beauty community. This will potentially help marketing managers increase online traffic and revenue, and thus bring success to the community. Although, this study contributes to the literature by highlighting three distinctive member motivations for eWOM exchanges in an online community of interest, there are some possible research limitations. First, this study was conducted in an online beauty community in Australia. Hence, further research should replicate this study in other industries and nations so as to give the findings greater generalisability. Next, online beauty community members are female skewed. Thus, future research should examine whether similar patterns of motivations would emerge in other online communities that tend to be populated by males (e.g., communities focused on football). Further, a web-based survey has its limitations in terms of self-selection and self-reporting (Bhatnagar & Ghose, 2004). Therefore, further studies should test the framework by employing different research methods in order to overcome these weaknesses.

The location of Ti atom in sodium alanate : an ab initio spin-polarised study

In this work, ab initio spin-polarised Density Functional Theory (DFT) calculations are performed to study the interaction of a Ti atom with a NaAlH4(001) surface. We confirm that an interstitially located Ti atom in the NaAlH4 subsurface is the most energetically favoured configuration as recently reported (Chem. Comm. (17) 2006, 1822). On the NaAlH4(001) surface, the Ti atom is most stable when adsorbed between two sodium atoms with an AlH4 unit beneath. A Ti atom on top of an Al atom is also found to be an important structure at low temperatures. The diffusion of Ti from the Al-top site to the Na-bridging site has a low activation barrier of 0.20 eV and may be activated at the experimental temperatures (∼323 K). The diffusion of a Ti atom into the energetically favoured subsurface interstitial site occurs via the Na-bridging surface site and is essentially barrierless.

Vacancy mediated desorption of hydrogen from a sodium alanate surface : An ab initio spin-polarized study

Ab initio spin-polarized density functional theory calculations are performed to explore the effect of single Na vacancy on NaAlH4(001) surface on the initial dehydrogenation kinetics. The authors found that two Al–H bond lengths become elongated and weakened due to the presence of a Na vacancy on the NaAlH4(001) surface. Spontaneous recombination from the surface to form molecular hydrogen is observed in the spin-polarized ab initio molecular dynamics simulation. The authors’ results indicate that surface Na vacancies play a critical role in accelerating the dehydrogenation kinetics in sodium alanate. The understanding gained here will aid in the rational design and development of complex hydride materials for hydrogen storage

Spin-polarization and ferromagnetism of graphitic carbon nitride materials

Polymeric graphitic carbon nitride materials have attracted increasing attention in recent years owning to their potential applications in energy conversion, environment protection, and so on. Here, from first-principles calculations, we report the electronic structure modification of graphitic carbon nitride (g-C3N4) in response to carbon doping. We showed that each dopant atom can induce a local magnetic moment of 1.0 μB in non-magnetic g-C3N4. At the doping concentration of 1/14, the local magnetic moments of the most stable doping configuration which has the dopant atom at the center of heptazine unit prefer to align in a parallel way leading to long-range ferromagnetic (FM) ordering. When the joint N atom is replaced by C atom, the system favors an antiferromagnetic (AFM) ordering at unstrained state, but can be tuned to ferromagnetism (FM) by applying biaxial tensile strain. More interestingly, the FM state of the strained system is half-metallic with abundant states at the Fermi level in one spin channel and a band gap of 1.82 eV in another spin channel. The Curie temperature (Tc) was also evaluated using a mean-field theory and Monte Carlo simulations within the Ising model. Such tunable electron spin-polarization and ferromagnetism are quite promising for the applications of graphitic carbon nitride in spintronics.

Spin-coated carbon

We describe a novel and facile approach to covalently graft molecules containing stable free radicals onto carbon surfaces including graphene, carbon nanotubes, glassy carbon and carbon fibres. The new technique employs a stable aryl nitroxide radical diazonium tetrafluoroborate salt. The salt may be isolated and added to carbon surfaces in solution, suspension or electrochemically and represents a convenient, versatile and highly efficient means to adorn graphitic materials with large numbers of free radical spin systems

Equilibrium and relaxation of particulate charge in fluorocarbon plasmas

Charging of micron-size particulates, often appearing in fluorocarbon plasma etching experiments, is considered. It is shown that in inductively coupled and microwave slot-excited plasmas of C4F8 and Ar gas mixtures, the equilibrium particle charge and charge relaxation processes are controlled by a combination of microscopic electron, atomic (Ar+ and F+), and molecular ion (CF+ 3, CF+ 2, and CF+) currents. The impact of molecular ion currents on the particulate charging and charge relaxation processes is analyzed. It is revealed that in low-power (<0.5 kW) microwave slot-excited plasmas, the impact of the combined molecular ion current to the total positive microscopic current on the particle can be as high as 40%. The particulate charge relaxation rate in fluorocarbon plasmas appears to exceed 108 s-1, which is almost one order of magnitude higher than that from purely argon plasmas. This can be attributed to the impact of positive currents of fluorocarbon molecular ions, as well as to the electron density fluctuations with particle charge, associated with electron capture and release by the particulates.

Semantic context and visual feature effects in object naming : an fMRI study using arterial spin labeling

Previous behavioral studies reported a robust effect of increased naming latencies when objects to be named were blocked within semantic category, compared to items blocked between category. This semantic context effect has been attributed to various mechanisms including inhibition or excitation of lexico-semantic representations and incremental learning of associations between semantic features and names, and is hypothesized to increase demands on verbal self-monitoring during speech production. Objects within categories also share many visual structural features, introducing a potential confound when interpreting the level at which the context effect might occur. Consistent with previous findings, we report a significant increase in response latencies when naming categorically related objects within blocks, an effect associated with increased perfusion fMRI signal bilaterally in the hippocampus and in the left middle to posterior superior temporal cortex. No perfusion changes were observed in the middle section of the left middle temporal cortex, a region associated with retrieval of lexical-semantic information in previous object naming studies. Although a manipulation of visual feature similarity did not influence naming latencies, we observed perfusion increases in the perirhinal cortex for naming objects with similar visual features that interacted with the semantic context in which objects were named. These results provide support for the view that the semantic context effect in object naming occurs due to an incremental learning mechanism, and involves increased demands on verbal self-monitoring.

Stress relaxation analysis of single chondrocytes using porohyperelastic model based on AFM experiments

The aim of this study is to investigate the stress relaxation behavior of single chondrocytes using the Porohyperelastic (PHE) model and inverse Finite Element Analysis (FEA). Firstly, based on Atomic Force Microscopy (AFM) technique, we have found that the chondrocytes exhibited stress relaxation behavior. We explored the mechanism of this stress relaxation behavior and concluded that the intracellular fluid exuding out from the cells during deformation plays the most important role in the stress relaxation. Next, we have applied the inverse FEA technique to determine necessary material parameters for PHE model to simulate this stress relaxation behavior as this model is proven capable of capturing the non-linear behavior and the fluid-solid interaction during the stress relaxation of the single chondrocytes. It is observed that this PHE model can precisely capture the stress relaxation behavior of single chondrocytes and would be a suitable model for cell biomechanics.

One-step macroscopic alignment of conjugated polymer systems by epitaxial crystallization during spin-coating

The one-step preparation of highly anisotropic polymer semiconductor thin films directly from solution is demonstrated. The conjugated polymer poly(3-hexylthiophene) (P3HT) as well as P3HT:fullerene bulk-heterojunction blends can be spin-coated from a mixture of the crystallizable solvent 1,3,5-trichlorobenzene (TCB) and a second carrier solvent such as chlorobenzene. Solidification is initiated by growth of macroscopic TCB spherulites followed by epitaxial crystallization of P3HT on TCB crystals. Subsequent sublimation of TCB leaves behind a replica of the original TCB spherulites. Thus, highly ordered thin films are obtained, which feature square-centimeter-sized domains that are composed of one spherulite-like structure each. A combination of optical microscopy and polarized photoluminescence spectroscopy reveals radial alignment of the polymer backbone in case of P3HT, whereas P3HT:fullerene blends display a tangential orientation with respect to the center of spherulite-like structures. Moreover, grazing-incidence wide-angle X-ray scattering reveals an increased relative degree of crystallinity and predominantly flat-on conformation of P3HT crystallites in the blend. The use of other processing methods such as dip-coating is also feasible and offers uniaxial orientation of the macromolecule. Finally, the applicability of this method to a variety of other semi-crystalline conjugated polymer systems is established. Those include other poly(3-alkylthiophene)s, two polyfluorenes, the low band-gap polymer PCPDTBT, a diketopyrrolopyrrole (DPP) small molecule as well as a number of polymer:fullerene and polymer:polymer blends. Macroscopic spherulite-like structures of the conjugated polymer poly(3-hexylthiophene) (P3HT) grow directly during spin-coating. This is achieved by processing P3HT or P3HT:fullerene bulk heterojunction blends from a mixture of the crystallizable solvent 1,3,5-trichlorobenzene and a second carrier solvent such as chlorobenzene. Epitaxial growth of the polymer on solidified solvent crystals gives rise to circular-symmetric, spherulite-like structures that feature a high degree of anisotropy.

Iron(II) spin transition complexes with dendritic ligands, Part I

The ligands G1- and G2-oligo (benzyl ether) (PBE) dendrons and their iron(II) complexes [Fe(Gn-PBE)3]A2·xH2O (with n = 1, 2 and A = triflate, tosylate) were prepared. The magnetic properties of the complexes were investigated by a SQUID magnetometer. All complexes exhibit gradual spin transition below room temperature. At very low temperatures the magnetic behaviour reflects zero-field splitting (ZFS) effects. 57Fe-Mössbauer spectroscopy was performed to distinguish between ZFS of high spin species and spin state conversion into the low spin state. Further characterisation was carried out by thermogravimetric analysis (TGA) and FT-IR spectroscopy. Structural features have been determined by powder XRD measurements.

Iron(II) spin-transition complexes with dendritic ligands, part II

The dendritic triazole-based complexes \[Fe(G1-BOC)3](triflate) 2·xH2O (1; G1-BOC = tert-butyl {3-\[3-(3-tert- butoxycarbonylaminopropyl)-5-(\[1,2,4]triazol-4-ylcarbamoyl)-phenyl]propyl} carbamate, triflate = CF3SO3-), \[Fe(G1-BOC) 3]-(tosylate)2·xH2O(2;tosylate = p-CH3PhSO3-),\[Fe(G1-DPBE)3]-(triflate) 2·xH2O {3; G1-DPBE = 3,5-bis(3,5- didodecaoxybenzyloxy)-N-\[1,2,4]triazol-4-ylbenzamide}, \[Fe(G1-DPBE) 3]-(tosylate)2·xH2O (4) and \[Fe(G1-DPBE)3](BF4)2·xH2O (5) were designed and synthesized. Magnetic and thermal properties of these novel complexes were characterized by magnetic susceptibility measurements, 57Fe Mössbauer spectroscopy and thermogravimetric analysis or differential scanning calorimetry, respectively. All dendritic complexes under study show different spin-transition behaviour with respect to the nature of different dendritic ligands and counteranions. Complexes 1 and 2 have pronounced effects of a spin-state change during the first heating process and gradual spintransition properties for further temperature treatments, whereas 3 and 4 exhibited a very sharp spin-state change in the first heating procedures. Complex 5 showed a gradual spin-transition curve. In this paper, we report how the magnetic properties of these complexes are correlated with noncoordinated water molecules and their effects on spin states.

Spin polarized DFT calculations of metal borides

The metal borides, in particular the diborides and hexaborides, contain stoichiometric forms that include insulators, semiconductors and superconductors. In addition, their end-member structures have high symmetry and two atoms although, in general, substitution(s) of multi-valent ions into the metal site occurs consistent with Vegard’s law. These characteristics allow for fundamental comparison of important physical properties such as superconductivity and insulation within a relatively simple structure type. Our early work1,2 has demonstrated this for the hexaborides and this work compares similar attributes across a broader suite of boride structures. In all cases, theoretical calculations are referenced to structures determined via high resolution neutron or X-ray diffraction experiments.

An investigation of problem-solving support and relaxation motivations on e-WOM

As a consequence of greater computer-mediated consumer-to-consumer communication within the firm's marketing communications, there has been a growing need to understand these digital interactions more explicitly. That is, we still know little about the exact extrinsic and intrinsic motivations that drive electronic word-of-mouth. The purpose of the paper is to better understand why members within community-based websites develop a need to exchange and/or develop a social bond within the community. Questionnaire data were gathered from 147 members of an online beauty forum in Australia. The findings highlight that those members seeking problem-solving support in combination with elements of relaxation will be more inclined to exchange with other community members and develop a social bond within that community. Marketing managers can capitalise these findings by strengthening problem-solving support systems and creating environments where community members can also relax and unwind to increase the exchange between members and also increase the social bonds within the community.