Non-periodic finite-element formulation of orbital-free density functional theory

We propose an approach to perform orbital-free density functional theory calculations in a non-periodic setting using the finite-element method. We consider this a step towards constructing a seamless multi-scale approach for studying defects like vacancies, dislocations and cracks that require quantum mechanical resolution at the core and are sensitive to long range continuum stresses. In this paper, we describe a local real-space variational formulation for orbital-free density functional theory, including the electrostatic terms and prove existence results. We prove the convergence of the finite-element approximation including numerical quadratures for our variational formulation. Finally, we demonstrate our method using examples.     

Application of Gyarmati's variational principle to laminar stagnation flow problem

Gyarmati's principle for the evolution of irreversible processes has been applied to construct the variational solutions of laminar stagnation flow of incompressible Newtonian fluid in two dimensions. Variational solutions obtained in three different representations approximate closely the exact numerical result of longitudinal velocity component and the Gyarmati's principle in force representation yield the same result as obtained by Doty and Blick with the help of local potential method of Glansdorff and Prigogine.

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Die Anwendung des Variationsprinzips von Gyarmati auf die laminare Stauströmung

Zusammenfassung Gyarmatis Prinzip für die Entwicklung irreversibler Prozesse wurde verwendet, um Variationslösungen für die laminare Stauströmung einer inkompressiblen Newtonschen Flüssigkeit in zwei Dimensionen aufzustellen. In drei verschiedenen Darstellungen erhaltene Variationslösungen approximieren gut die exakte numerische Lösung der longitudinalen Geschwindigkeitskomponente; Gyarmatis Prinzip in der Kraft-Darstellung ergibt das gleiche Ergebnis, wie es Doty and Blick mit Hilfe der Methode des lokalen Potentials nach Glansdorff und Prigogine erhalten haben.

     

Analysis of elastic and plastic deformation associated with indentation testing of thin films on substrates

A study has been made of the elastic and plastic deformation associated with submicrometer indentation of thin films on substrates using the finite element method. The effects of the elastic and plastic properties of both the film and substrate on the hardness of the film/substrate composite are studied by determining the average pressure under the indenter as a function of the indentation depth. Calculations have been made for film/substrate combinations for which the substrate is either harder or softer than the film and for combinations for which the substrate is either stiffer or more compliant than the film. It is found, as expected, that the hardness increases with indentation depth when either the yield strength or the elastic modulus of the substrate is higher than that of the film. Correspondingly, the hardness decreases with indentation depth when the yield strength or elastic modulus of the substrate is lower than that of the film. Functional equations have been developed to predict the hardness variation with depth under these different conditions. Finite element simulation of the unloading portion of the load displacement curve permits a determination of the elastic compliance of the film/substrate composite as a function of indentation depth. The elastic properties of the film can be separated from those of the substrate using this information. The results are in good agreement with King's analytical treatment of this problem.     

A Theory of Anharmonic Lattice Statics for Analysis of Defective Crystals

This paper develops a theory of anharmonic lattice statics for the analysis of defective complex lattices. This theory differs from the classical treatments of defects in lattice statics in that it does not rely on harmonic and homogenous force constants. Instead, it starts with an interatomic potential, possibly with infinite range as appropriate for situations with electrostatics, and calculates the equilibrium states of defects. In particular, the present theory accounts for the differences in the force constants near defects and in the bulk. The present formulation reduces the analysis of defective crystals to the solution of a system of nonlinear difference equations with appropriate boundary conditions. A harmonic problem is obtained by linearizing the nonlinear equations, and a method for obtaining analytical solutions is described in situations where one can exploit symmetry. It is then extended to the anharmonic problem using modified Newton–Raphson iteration. The method is demonstrated for model problems motivated by domain walls in ferroelectric materials.      

Rheology of shear thickening suspensions and the effects of wall slip in torsional flow

The rheological characterisation of concentrated shear thickening materials suspensions is challenging, as complicated and occasionally discontinuous rheograms are produced. Wall slip is often apparent and when combined with a shear thickening fluid the usual means of calculating rim shear stress in torsional flow is inaccurate due to a more complex flow field. As the flow is no longer “controlled”, a rheological model must be assumed and the wall boundary conditions are redefined to allow for slip. A technique is described where, by examining the angular velocity response in very low torque experiments, it is possible to indirectly measure the wall slip velocity. The suspension is then tested at higher applied torques and different rheometer gaps. The results are integrated numerically to produce shear stress and shear rate values. This enables the measurement of true suspension bulk flow properties and wall slip velocity, with simple rheological models describing the observed complex rheograms.     

A first principle study of pristine and BN-doped graphyne family

Based on first principle calculation using generalized gradient approximation, we report electronic properties of graphyne and its related structures (graphdiyne, graphyne-3, graphyne-4). Boron and nitrogen atoms are systematically substituted into the position of carbon atom and the corresponding changes of the properties are reported. All the structures are found to be direct band gap semiconductors with band gap depending on the concentration and position of the doping material. Our band structure calculation clearly shows that the band gap can be tuned by B–N doping and the spin-polarized calculation depicts the nonmagnetic nature of these structures. The possibility of modulating the band gap provides flexibility for its use in nanoelectronic devices. Projected density of state (PDOS) analysis shed insights on the bonding nature of these novel materials, whereas from the view point of Crystal Orbital Hamilton Population (–COHP) analysis, the nature of chemical bonding between neighbouring atoms and the orbital participating in bonding and antibonding have been explored in details.     

Color Polymorphism: Understanding the Diverse Solid‐State Packing and Color in Dimethyl‐3,6‐dichloro‐2,5‐dihydroxyterephthalate

Dimethyl‐3,6‐dichloro‐2,5‐dihydroxyterephthalate (MCHT) is known to exist in three differently packed crystals having three different colors, namely yellow (Y), light yellow (LY), and white (W). Apart from the difference in their color, the molecules in the crystals also differ in their intramolecular O?H???O and O?H???Cl hydrogen bonds. Time‐dependent DFT calculations reveal the role of the various types of hydrogen bonds in controlling the color of the polymorphs. Mechanistic pathways that lead to such transformations in the crystal are elucidated by solid‐state dispersion‐corrected DFT studies. Relative stabilities of the various polymorphs rationalize the experimentally observed transformations between them. Calculations reveal that the minimum‐energy pathway for the conversion of the Y form to a W form is through stepwise disrotatory motion of the two ?OH groups through a hybrid intermediate having one intramolecular O?H???O and one O?H???Cl bond. The LY form is shown to exist on the higher‐energy pathway involving a concerted Y→W transformation.     

Electrochemical characterization of sodium and potassium doped lanthanum–titanium mixed oxides prepared by sol–gel method

Varying amounts of Na and K doped lanthanum–titanium oxides were synthesized by gel entrapment technique. These ceramics were characterized by X-ray diffraction. Microstructural investigations revealed grain growth in the doped material compared to undoped sample. Dielectric relaxations of these compounds were investigated in the temperature range 250–900 °C. A high degree of dispersion of the permittivity of un-doped lanthanum–titanium oxide and K and Na doped lanthanum–titanium oxide was observed in the frequency range <100 kHz which was attributed to oxygen vacancies. An increase in the permittivity values were observed with 1 % Na and K doped samples. The permittivity values further deteriorated with the dopant concentration. Using the Cole–Cole model, an analysis of the dielectric loss with frequency was performed, assuming a distribution of relaxation time. The dielectric loss was found to decrease by doping K in lanthanum–titanium oxide matrix. The dc conductivity studies showed that a temperature dependent hopping type mechanism is responsible for electrical conduction in the system.     

An Efficient Probe for Rapid Detection of Cyanide in Water at Parts per Billion Levels and Naked‐Eye Detection of Endogenous Cyanide

A new molecular probe based on an oxidized bis‐indolyl skeleton has been developed for rapid and sensitive visual detection of cyanide ions in water and also for the detection of endogenously bound cyanide. The probe allows the “naked‐eye” detection of cyanide ions in water with a visual color change from red to yellow (Δλ_max=80 nm) with the immediate addition of the probe. It shows high selectivity towards the cyanide ion without any interference from other anions. The detection of cyanide by the probe is ratiometric, thus making the detection quantitative. A Michael‐type addition reaction of the probe with the cyanide ion takes place during this chemodosimetric process. In water, the detection limit was found to be at the parts per million level, which improved drastically when a neutral micellar medium was employed, and it showed a parts‐per‐billion‐level detection, which is even 25‐fold lower than the permitted limits of cyanide in water. The probe could also efficiently detect the endogenously bound cyanide in cassava (a staple food) with a clear visual color change without requiring any sample pretreatment and/or any special reaction conditions such as pH or temperature. Thus the probe could serve as a practical naked‐eye probe for “in‐field” experiments without requiring any sophisticated instruments.     

Assessment of Acrylamide Degradation Potential of Pseudomonas aeruginosa BAC-6 Isolated from Industrial Effluent

Acrylamide finds diverse industrial applications but is considered an environmental threat because of its neurotoxic, carcinogenic, and teratogenic effects. Certain bacteria enzymatically degrade acrylamide to acrylic acid and ammonia. The present investigation was carried out to isolate and identify an acrylamide-degrading bacterium from industrial effluent. Bacterial growth and extent of acrylamide degradation in the presence of different acrylamide concentrations, nutrients, varied range of pH, and temperature were analyzed. Among the eight acrylamide-degrading isolates, isolate BAC-6 demonstrated the highest degradation, and based upon the partial 16S rDNA sequencing, it was identified as Pseudomonas aeruginosa. P. aeruginosa BAC-6 grew over a wide range of acrylamide concentrations, but the highest degradation was recorded at 500 mg/L concentration with concomitant cell growth. Among the carbon supplements, mannitol supported the highest growth and degradation. Maximum degradation was reported at neutral pH. A mesophilic temperature range (25–40 °C) facilitated conducive bacterial growth followed by degradation. The highest degradation and bacterial growth were observed at 30 and 35 °C, respectively. Thus, it could be inferred from the present investigation that cultural conditions strongly affected the degradation potential of P. aeruginosa BAC-6 and advocated the utilization of the isolate in bioremediation of sites polluted with acrylamide.