On helical shear of a compressible elastic circular cylindrical tube

In this paper we examine the combined azimuthal and axial shear of a compressible isotropic elastic circular cylindrical tube of finite extent, otherwise referred to as helical shear (which is an isochoric deformation). The equilibrium equations are formulated in terms of the principal stretches, and explicit necessary and sufficient conditions on the strain-energy function for the material to support this deformation are obtained and compared with those obtained previously for this problem. Several classes of strain-energy functions are derived and in some general cases complete solutions of the equilibrium equations are obtained. Existing results are recovered as special cases and some new results for the strain-energy functions derived are determined and discussed.

On extension and torsion of a compressible elastic circular cylinder

In this paper we examine the combined extension and torsion of a compressible isotropic elastic cylinder of finite extent. The equilibrium equations are formulated in terms of the principal stretches and then applied to the special case of pure torsion superimposed on a uniform extension (an isochoric deformation). Explicit necessary and sufficient conditions on the strain-energy function for the material to support this deformation with vanishing traction on the lateral surfaces of the cylinder are obtained. Some strain-energy functions satisfying these conditions are considered, existing results are recovered as special cases and new results are obtained. We also point out how the strain-energy functions generated from the considered isochoric deformation considered (of a compressible material) can be used to generate energy functions and corresponding solutions for the incompressible theory.

A conformational approach to the study of the dynamics of enzyme inhibition: studies on thermolysin

The preferred conformations of β-phenylpropionyl-Image -phenylalanine (β-PPP) and N-carbobenzoxy-L-phenylalanine (Cbz-Phe), two inhibitors of thermolysin, have been determined by computing potential energy using empirial potential energy functions. Of the 15 to 20 conformations that are favoured for each of these inhibitors only a few have the right conformation to reach the active site of the enzyme. The conformer of β-PPP that initiates binding with the enzyme is different from the bound one, while for Cbz-Phe the bound and initiating conformers are quite similar. Thus, β-PPP favours the ‘induced fit’ model while Cbz-Phe follows the ‘lock and key’ model of binding. The inhibitors differ in their alignment at the active site.

A Case Study of the Conformation of Poly(alpha-aminoisobutyric acid): alpha- or 310-Helix

The relative stabilities of a- and Blo-helical structures for polymers of a-aminoisobutyric acid (Aib) have been worked out, using the classical potential energy functions. To make a comparative study, we have used Buckingham "6-exp" and Kitaigorodsky's potential functions. Conformational analysis of the dipeptide segment with Aib residue indicates the necessity for nonplanar distortion of the peptide unit, which is a common feature in the observed crystal structures with Aib residues. In the range of Aw -10 to +loo studied, a-helical conformations are preferred in the region -3" < Aw < +loo, and Blo-helical conformations are preferred in the region -3" > Aw > -10'. Minimum energy conformations for right-handed structures are found in the +ue region of Aw and correspondingly for left-handed structures in the -ue region of Aw. For Aw - 6", a-helical structures have four- or near fourfold symmetry with h - 1.5 A. Such a helix with n = 4 and h = 1.5 A is termed an a'-helix. This structure is found to be consistent with the electron diffraction data of Malcolm3 and energetically more favorable than the standard 310-helix.

Determination of the thermodynamic stability of TiB2

The standard free energy of formation of titanium boride (TiB2) Was measured by the Electro Motive Force (EMF) method (by using yttria doped thoria (YDT) as the solid electrolyte). Two galvanic cells viz. Cell (I): Pt, TiB2 (s), TiO2 (s), B (s) vertical bar YDT vertical bar NiO (s), Ni (s), Pt and cell (II): Pt, TiB2 (s), TiO2 (s), B (s) vertical bar YDT vertical bar FeO (s). Fe (s), Pt were constructed in order to determine the Delta(f)G degrees, of TiB2. Enthalpy increments on TiB2 were measured by using inverse drop calorimetry over the temperature range 583-1769 K. The heat capacity, entropy and the free energy function have been derived from these experimental data in the temperature range 298-1800 K. The mean value of the standard enthalpy of formation of TiB2 (Delta H-f(298)degrees (TiB2)) was obtained by combining these Delta(f)G degrees, values and the free energy functions of TiB2 derived from the drop calorimetry data. The mean values of Delta H-f(298)degrees (TiB2) derived from the Delta(f)G degrees, data obtained from cell I and II were -322 +/- 1.2 kJ mol(-1) and -323.3 +/- 2.1 kJ mol(-1), respectively. These values were found to be in very good agreement with the assessed data. (C) 2009 Elsevier B.V. All rights reserved.

Theoretical studies on alpha-helix--DNA interactions

The interaction energies between (Ala)10 and alpha-helix fragment and different nucleotide sequences in right-handed B-form have been optimized using semi-empirical potential energy functions. The energies are calculated for two different orientations of the alpha-helix, viz., when the alpha-helix axis taken in the N----C direction is (i) parallel and (ii) antiparallel to the 5'-3' ascending strand of DNA, proximal to it. When both the DNA molecule as well as the alpha-helix are treated as rigid molecules it is found that a polyalanine alpha-helix has slightly more favourable contacts when it is in the proximity of a four nucleotide sequence of 5'-(N-A-T-N)-3' type, where N is either a purine or a pyrimidine. However, when the two interacting molecules are allowed to undergo local structural variations then the interaction energy appears to be independent of the base sequence confirming the non-specific nature of these interactions.

Basic equations for ferroelectrics

A set of new formula of energy functions for ferroelectrics was proposed, and then the new basic equations were derived in this paper. The finite element formulation based on the new basic equations was improved to avoid the equivalent nodal load produced by remnant polarization. With regard to the fundamentals of mathematics and physics, the new energy functions and basic equations are reasonable for the material element of ferroelectrics in finite element analysis.

Geometric elasticity for graphics, simulation, and computation

We develop new algorithms which combine the rigorous theory of mathematical elasticity with the geometric underpinnings and computational attractiveness of modern tools in geometry processing. We develop a simple elastic energy based on the Biot strain measure, which improves on state-of-the-art methods in geometry processing. We use this energy within a constrained optimization problem to, for the first time, provide surface parameterization tools which guarantee injectivity and bounded distortion, are user-directable, and which scale to large meshes. With the help of some new generalizations in the computation of matrix functions and their derivative, we extend our methods to a large class of hyperelastic stored energy functions quadratic in piecewise analytic strain measures, including the Hencky (logarithmic) strain, opening up a wide range of possibilities for robust and efficient nonlinear elastic simulation and geometry processing by elastic analogy.

Lyapunov's stability and operational margin of grid-connected photovoltaic modules

Analyses of photovoltaic power generation based on Lyapunov's theorems are presented. The characteristics of the photovoltaic module and the power conditioning unit are analyzed in order to establish energy functions that assess the stability of solutions and define safe regions of operation. Furthermore, it is shown that grid-connected photovoltaic modules driven at maximum power may become unstable under normal grid transients. In such cases, stability can be maintained by allowing an operational margin defined as the energy difference between the stable and the unstable solutions of the system. Simulations show that modules cope well with grid transients when a sufficiently large margin is used.

Nuclear shape-phase diagrams

Ground-state energy functions of even-even and odd-A nuclei are derived from simple parameter-dependent Interacting Boson Model (IBM) and Interacting Boson-Fermion Model (IBFM) Hamiltonians. Exact nuclear shape-phase diagrams in the two-parameter (eta, chi) plane are explicitly described using the energy functions on the basis of the condition of phase equilibrium.

Theoretical study on analytical potential function and spectroscopic parameters for CaF molecule

The equilibrium properties and potential energy curves of the ground electronic state of CaF have been calculated using the Brueckner Doubles calculation with a triples contribution added [BD(T)] and the gradient-corrected density functional theory with three-parameter exact exchange mixing (B3LY-P) method, with 6-311 + G*,6-311 + G(2df,2pd) and 6-311 + G(3df,3pd) basis sets. All the computational PECs are fitted to analytical potential energy functions using Murrell-Sorbie, Huxley and Tang-Toennies potentials. Based on this, the spectroscopic parameters are calculated, and then compared with some other theoretical and experimental data. (C) 2004 Elsevier B.V. All rights reserved.

Development of complex classical force fields through force matching to ab initio data: Application to a room-temperature ionic liquid

Recent experimental neutron diffraction data and ab initio molecular dynamics simulation of the ionic liquid dimethylimidazolium chloride ([dmim]Cl) have provided a structural description of the system at the molecular level. However, partial radial distribution functions calculated from the latter, when compared to previous classical simulation results, highlight some limitations in the structural description offered by force fieldbased simulations. With the availability of ab initio data it is possible to improve the classical description of [dmim]Cl by using the force matching approach, and the strategy for fitting complex force fields in their original functional form is discussed. A self-consistent optimization method for the generation of classical potentials of general functional form is presented and applied, and a force field that better reproduces the observed first principles forces is obtained. When used in simulation, it predicts structural data which reproduces more faithfully that observed in the ab initio studies. Some possible refinements to the technique, its application, and the general suitability of common potential energy functions used within many ionic liquid force fields are discussed.

Diamond machining of silicon: A review of advances in molecular dynamics simulation

Molecular dynamics (MD) simulation has enhanced our understanding about ductile-regime machining of brittle materials such as silicon and germanium. In particular, MD simulation has helped understand the occurrence of brittle–ductile transition due to the high-pressure phase transformation (HPPT), which induces Herzfeld–Mott transition. In this paper, relevant MD simulation studies in conjunction with experimental studies are reviewed with a focus on (i) the importance of machining variables: undeformed chip thickness, feed rate, depth of cut, geometry of the cutting tool in influencing the state of the deviatoric stresses to cause HPPT in silicon, (ii) the influence of material properties: role of fracture toughness and hardness, crystal structure and anisotropy of the material, and (iii) phenomenological understanding of the wear of diamond cutting tools, which are all non-trivial for cost-effective manufacturing of silicon. The ongoing developmental work on potential energy functions is reviewed to identify opportunities for overcoming the current limitations of MD simulations. Potential research areas relating to how MD simulation might help improve existing manufacturing technologies are identified which may be of particular interest to early stage researchers.

Molecular dynamics simulation (MDS) to study nanoscale machining processes

Molecular Dynamics Simulations (MDS) are constantly being used to make important contributions to our fundamental understanding of material behaviour, at the atomic scale, for a variety of thermodynamic processes. This chapter shows that molecular dynamics simulation is a robust numerical analysis tool in addressing a range of complex nanofinishing (machining) problems that are otherwise difficult or impossible to understand using other methods. For example the mechanism of nanometric cutting of silicon carbide is influenced by a number of variables such as machine tool performance, machining conditions, material properties, and cutting tool performance (material microstructure and physical geometry of the contact) and all these variables cannot be monitored online through experimental examination. However, these could suitably be studied using an advanced simulation based approach such as MDS. This chapter details how MD simulation can be used as a research and commercial tool to understand key issues of ultra precision manufacturing research problems and a specific case was addressed by studying diamond machining of silicon carbide. While this is appreciable, there are a lot of challenges and opportunities in this fertile area. For example, the world of MD simulations is dependent on present day computers and the accuracy and reliability of potential energy functions [109]. This presents a limitation: Real-world scale simulation models are yet to be developed. The simulated length and timescales are far shorter than the experimental ones which couples further with the fact that contact loading simulations are typically done in the speed range of a few hundreds of m/sec against the experimental speed of typically about 1 m/sec [17]. Consequently, MD simulations suffer from the spurious effects of high cutting speeds and the accuracy of the simulation results has yet to be fully explored. The development of user-friendly software could help facilitate molecular dynamics as an integral part of computer-aided design and manufacturing to tackle a range of machining problems from all perspectives, including materials science (phase of the material formed due to the sub-surface deformation layer), electronics and optics (properties of the finished machined surface due to the metallurgical transformation in comparison to the bulk material), and mechanical engineering (extent of residual stresses in the machined component) [110]. Overall, this chapter provided key information concerning diamond machining of SiC which is classed as hard, brittle material. From the analysis presented in the earlier sections, MD simulation has helped in understanding the effects of crystal anisotropy in nanometric cutting of 3C-SiC by revealing the atomic-level deformation mechanisms for different crystal orientations and cutting directions. In addition to this, the MD simulation revealed that the material removal mechanism on the (111) surface of 3C-SiC (akin to diamond) is dominated by cleavage. These understandings led to the development of a new approach named the “surface defect machining” method which has the potential to be more effective to implement than ductile mode micro laser assisted machining or conventional nanometric cutting.

Analytical potentials for triatomic molecules from spectroscopic data V. Application to HOX (X=F, Cl, Br, I)

Analytical potential energy functions are reported for HOX (X=F, Cl, Br, I). The surface for HOF predicts two metastable minima as well as the equilibrium configuration. These correspond to HFO (bent) and OHF (linear). Ab initio calculations performed for the HOF surface confirm these predictions. Comparisons are drawn between the two sets of results, and a vibrational analysis is undertaken for the hydrogen bonded OHF species. For HOCl, one further minimum is predicted, corresponding to HClO (bent), the parameters for which compare favourably with those reported from ab initio studies. In contrast, only the equilibrium configurations are predicted to be stable for HOBr and HOI.