Energy landscape view of phase transitions and slow dynamics in thermotropic liquid crystals

Thermotropic liquid crystals are known to display rich phase behavior on temperature variation. Although the nematic phase is orientationally ordered but translationally disordered, a smectic phase is characterized by the appearance of a partial translational order in addition to a further increase in orientational order. In an attempt to understand the interplay between orientational and translational order in the mesophases that thermotropic liquid crystals typically exhibit upon cooling from the high-temperature isotropic phase, we investigate the potential energy landscapes of a family of model liquid crystalline systems. The configurations of the system corresponding to the local potential energy minima, known as the inherent structures, are determined from computer simulations across the mesophases. We find that the depth of the potential energy minima explored by the system along an isochor grows through the nematic phase as temperature drops in contrast to its insensitivity to temperature in the isotropic and smectic phases. The onset of the growth of the orientational order in the parent phase is found to induce a translational order, resulting in a smectic-like layer in the underlying inherent structures; the inherent structures, surprisingly, never seem to sustain orientational order alone if the parent nematic phase is sandwiched between the high-temperature isotropic phase and the low-temperature smectic phase. The Arrhenius temperature dependence of the orientational relaxation time breaks down near the isotropic-nematic transition. We find that this breakdown occurs at a temperature below which the system explores increasingly deeper potential energy minima.

Dynamic security assessment of power systems using structure-preserving energy functions

An application of direct methods to dynamic security assessment of power systems using structure-preserving energy functions (SPEF) is presented. The transient energy margin (TEM) is used as an index for checking the stability of the system as well as ranking the contigencies based on their severity. The computation of the TEM requires the evaluation of the critical energy and the energy at fault clearing. Usually this is done by simulating the faulted trajectory, which is time-consuming. In this paper, a new algorithm which eliminates the faulted trajectory estimation is presented to calculate the TEM. The system equations and the SPEF are developed using the centre-of-inertia (COI) formulation and the loads are modelled as arbitrary functions of the respective bus voltages. The critical energy is evaluated using the potential energy boundary surface (PEBS) method. The method is illustrated by considering two realistic power system examples.

Energy absorption behaviours of CSM-based GFRC plates with hemispherical features

In the present study, the mechanical behaviour of CSM (chopped strand mat)-based GFRC (glass fibre-reinforced composite) plates with single and multiple hemispheres under compressive loads has been investigated both experimentally and numerically. The basic stress-strain behaviours arc identified with quasi-static tests on two-ply coupon laminates and short cylinders, and these are followed up with compressive tests in a UTM (universal testing machine) on single- and multiple-hemisphere plates. The ability of an explicit LS-DYNA solver in predicting the complex material behaviour of composite hemispheres, including failure, is demonstrated. The relevance and scalability of the present class of structural components as `force-multipliers' and `energy-multipliers' have been justified by virtue of findings that as the number of hemispheres in a panel increased from one to four, peak load and average absorbed energy rose by factors of approximately four and six, respectively. The performance of a composite hemisphere has been compared to similar-sized steel and aluminium hemispheres, and the former is found to be of distinctly higher specific energy than the steel specimen. A simulation-based study has also been carried out on a composite 2 x 2-hemisphere panel under impact loads and its behaviour approaching that of an ideal energy absorber has been predicted. In summary, the present investigation has established the efficacy of composite plates with hemispherical force multipliers as potential energy-absorbing countermeasures and the suitability of CAE (computer-aided engineering) for their design.

Relationship between entropy and diffusion: A statistical mechanical derivation of Rosenfeld expression for a rugged energy landscape

Diffusion-a measure of dynamics, and entropy-a measure of disorder in the system are found to be intimately correlated in many systems, and the correlation is often strongly non-linear. We explore the origin of this complex dependence by studying diffusion of a point Brownian particle on a model potential energy surface characterized by ruggedness. If we assume that the ruggedness has a Gaussian distribution, then for this model, one can obtain the excess entropy exactly for any dimension. By using the expression for the mean first passage time, we present a statistical mechanical derivation of the well-known and well-tested scaling relation proposed by Rosenfeld between diffusion and excess entropy. In anticipation that Rosenfeld diffusion-entropy scaling (RDES) relation may continue to be valid in higher dimensions (where the mean first passage time approach is not available), we carry out an effective medium approximation (EMA) based analysis of the effective transition rate and hence of the effective diffusion coefficient. We show that the EMA expression can be used to derive the RDES scaling relation for any dimension higher than unity. However, RDES is shown to break down in the presence of spatial correlation among the energy landscape values. (C) 2015 AIP Publishing LLC.

Universal crack closure integral for SIF estimation

Numerical analysis of cracked structures often involves numerical estimation of stress intensity factors (SIFs) at a crack tip/front. A newly developed formulation called universal crack closure integral (UCCI) for the evaluation of potential energy release rates (PERRs) and the corresponding SIFs is presented in this paper. Unlike the existing element dedicated forms of crack closure integrals (MCCI, VCCI) with application limited to finite element analysis, this new numerical SIF/PERR estimation technique is independent of the basic stress analysis procedure, making it universally applicable. The second merit of this procedure is that it avoids the generally error-producing zones close to the crack tip/front singularity. The UCCI procedure, based on Irwin's original CCI, is formulated and explored using a simple 2D problem of a straight crack in an infinite sheet. It is then applied to some three-dimensional crack geometries with the stresses and displacements obtained from a boundary element program.

Ground and Excited State Intramolecular Proton Transfer in Salicylic Acid: an Ab Initio Electronic Structure Investigation

Energetics of the ground and excited state intramolecular proton transfer in salicylic acid have been studied by ab initio molecular orbital calculations using the 6-31G** basis set at the restricted Hartree-Fock (RHF) and configuration interaction-single excitation (CIS) levels and also using the semiempirical method AM1 at the RHF level as well as with single and pair doubles excitation configuration interaction spanning eight frontier orbitals (PECI = 8). The ab initio potential energy profile for intramolecular proton transfer in the ground state reveals a single minimum corresponding to the primary form, in the first excited singlet state, however, there are two minima corresponding to the primary and tautomeric forms, separated by a barrier of similar to 6 kcal/mol, thus accounting for dual emission in salicylic acid. Electron density changes with electronic excitation and tautomerism indicate no zwitterion formation. Changes in spectral characteristics with change in pH, due to protonation and deprotonation of salicylic acid, are also accounted for, qualitatively. Although the AM1 calculations suggest a substantial barrier for proton transfer in the ground as well as the first excited state of SA, it predicts the transition wavelength in near quantitative accord with the experimental results for salicylic acid and its protonated and deprotonated forms.

A Doubly curved Quadrilateral finite-element for the analysis of laminated anisotropic thin shells of revoution

The details of development of the stiffness matrix for a doubly curved quadrilateral element suited for static and dynamic analysis of laminated anisotropic thin shells of revolution are reported. Expressing the assumed displacement state over the middle surface of the shell as products of one-dimensional first order Hermite polynomials, it is possible to ensure that the displacement state for the assembled set of such elements, is geometrically admissible. Monotonic convergence of total potential energy is therefore possible as the modelling is successively refined. Systematic evaluation of performance of the element is conducted, considering various examples for which analytical or other solutions are available.

Mean-field results of a lattice-gas model of multilayer adsorption

A lattice-gas model of multilayer adsorption has been solved in the mean-field approximation by a different numerical method. Earlier workers obtained a single solution for all values of temperature and pressure. In the present work, multiple solutions have been obtained in certain regions of temperature and pressure which give rise to bysteresis in the adsorption isotherm. In addition, we have obtained a parameter which behaves like an order parameter for the transition. The potential-energy function shows a double minimum in the region of bysteresis and a single maximum elsewhere.

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.

Theoretical studies on the conformations of higher gangliosides

The possible conformations of higher gangliosides (GD3, GT1a. GT1b, GQ1b) have been determined by computing their potential energy using semi-empirical potential functions. The favoured conformation of the disialic acid fragment in these gangliosides is independent of its position (internal or terminal). The favoured conformations of these gangliosides have also been correlated to their biological activity. The results suggest that tetanus toxin and sendai virus may have a large binding site which can accommodate at least four sugar residues.

Theoretical studies on the conformations of higher gangliosides

The possible conformations of higher gangliosides (GD3, GT1a. GT1b, GQ1b) have been determined by computing their potential energy using semi-empirical potential functions. The favoured conformation of the disialic acid fragment in these gangliosides is independent of its position (internal or terminal). The favoured conformations of these gangliosides have also been correlated to their biological activity. The results suggest that tetanus toxin and sendai virus may have a large binding site which can accommodate at least four sugar residues.

X-Pro peptides. A theoretical study of the hydrogen bonded conformations of (alpha-aminoisobutyryl-L -prolyl)n sequences

Intramolecularly hydrogen bonded conformations of (Aib-Pro)n sequences have been analysed theoretically. Both 4-1 (C10 and 3-1 (C7 hydrogen bonded regular structures are shown to be stereochemically feasible. Conformational energies for the helical structures have been estimated using classical potential energy methods. Both C10 and C7 conformations have very similar energies. Pyrrolidine ring puckering has a pronounced effect on the energies, and only Cv-endo puckered Pro residues can be accommodated. The theoretical calculations using spectroscopic data suggest that the recently proposed novel 310 helical conformation for benzyloxycarbonyl(Aib-Pro)4-methyl ester is in solution, is indeed energetically and stereochemically favourable.

Complex carbohydrates: 1. Conformational studies on some oligosaccharides related to N-glycosyl proteins which interact with concanavalin A

Empirical potential energy calculations have been carried out to determine the preferred conformations of some oligosaccharides having the trimannosidic core structure (Man3GlcNAc2) and which interact with concanavalin A. In the minimum energy conformations for the trimannosidic core the mannose residue on the Man α(1–6) arm comes close to one of the N-acetylglucosamine residues of the core. The addition of N-acetylglucosamine residues to the terminal mannose residues does not alter the preferred conformation of the trimannosidic core although it alters the relative preference of some of the higher energy conformations. The minimum energy conformation broadly agrees with available X-ray data. The presence of a bisecting N-acetylglucosamine residue on the middle mannose does not push the trimannosidic core to any new conformation but it does alter the relative preference for a particular conformation.

Theoretical studies on penicillins, penicillin sulphones and their 1-oxa-1-dethia and 1-carba-1-dethia analogues: binding specificities of transeptidases and penicillinases

Empirical potential energy calculations have been carried out to determine the preferred conformations of penicillins and penicillin sulphones and their 1-oxa-1-dethia and 1-carba-1-dethia analogues. With the exception of 1-oxa-1-dethia penicillins, all the other compounds favour C2 and the C3 puckered conformations of their five-membered rings. Replacement of C2 methyl groups by hydrogen atoms as in bisnorpenicillin V or oxidation of sulphur in position 1 as in sulphones, makes the C3 puckered form much less favourable. Addition of an amino-acyl group at the C6 atom, however, makes the C3 puckered form more favoured in penicillin G or V and in 1-carba-1-dethia penicillins. Through the replacement of the sulphur atom at position 1 by an oxygen atom or by a -CH2 group increases the non-planarity of the lactam peptide bond, it significantly affects the relative disposition of the C3 carboxyl group with respect to the β-lactam ring. These conformational differences have been correlated with the biological activities of these compounds. The present study suggests that the conformation of the bicyclic ring system may be more important for initial binding with the crosslinking enzyme(s) involved in the biosynthesis of bacterial cell-wall peptidoglycan and that the mode of binding is influenced by the nature of the side-group at the C6 atom. These studies predict, in agreement with experimental results, that the 1-oxa-1-dethia penicillin nulceus is an inhibitor of penicillianses. The study also suggests that the stereospecificities of the crosslinking enzyme(s) and penicillinases are very similar with regard to the nature of the side-group at the 6 atom and the confirmation of the bicyclic ring system. However, the confirmational requirement for the bicyclic ring system appears to be more specific in the former enzyme than in the latter.

X-Pro peptides. A theoretical study of the hydrogen bonded conformations of (a-aminoisobutyryl-L -prolyl)n sequences

Intramolecularly hydrogen bonded conformations of (Aib-Pro)n sequences have been analysed theoretically. Both 4�1 (C10 and 3�1 (C7 hydrogen bonded regular structures are shown to be stereochemically feasible. Conformational energies for the helical structures have been estimated using classical potential energy methods. Both C10 and C7 conformations have very similar energies. Pyrrolidine ring puckering has a pronounced effect on the energies, and only Cγ-endo puckered Pro residues can be accommodated. The theoretical calculations using spectroscopic data suggest that the recently proposed novel 310 helical conformation for benzyloxycarbonyl(Aib-Pro)4-methyl ester is in solution, is indeed energetically and stereochemically favourable.