Dissociation Constants of Weak Acids from ab Initio Molecular Dynamics Using Metadynamics: Influence of the Inductive Effect and Hydrogen Bonding on pK(a) Values

The theoretical estimation of the dissociation constant, or pK(a), of weak acids continues to be a challenging field. Here, we show that ab initio CarParrinello molecular dynamics simulations in conjunction with metadynamics calculations of the free-energy profile of the dissociation reaction provide reasonable estimates of the pK(a) value. Water molecules, sufficient to complete the three hydration shells surrounding the acid molecule, were included explicitly in the computation procedure. The free-energy profiles exhibit two distinct minima corresponding to the dissociated and neutral states of the acid, and the difference in their values provides the estimate for pK(a). We show for a series of organic acids that CPMD simulations in conjunction with metadynamics can provide reasonable estimates of pK(a) values. The acids investigated were aliphatic carboxylic acids, chlorine-substituted carboxylic acids, cis- and trans-butenedioic acid, and the isomers of hydroxybenzoic acid. These systems were chosen to highlight that the procedure could correctly account for the influence of the inductive effect as well as hydrogen bonding on pK(a) values of weak organic acids. In both situations, the CPMD metadynamics procedure faithfully reproduces the experimentally observed trend and the magnitudes of the pK(a) values.

Spatio-temporal correlations in aqueous systems: computational studies of static and dynamic heterogeneity by 2D-IR spectroscopy

Local heterogeneity is ubiquitous in natural aqueous systems. It can be caused locally by external biomolecular subsystems like proteins, DNA, micelles and reverse micelles, nanoscopic materials etc., but can also be intrinsic to the thermodynamic nature of the aqueous solution itself (like binary mixtures or at the gas-liquid interface). The altered dynamics of water in the presence of such diverse surfaces has attracted considerable attention in recent years. As these interfaces are quite narrow, only a few molecular layers thick, they are hard to study by conventional methods. The recent development of two dimensional infra-red (2D-IR) spectroscopy allows us to estimate length and time scales of such dynamics fairly accurately. In this work, we present a series of interesting studies employing two dimensional infra-red spectroscopy (2D-IR) to investigate (i) the heterogeneous dynamics of water inside reverse micelles of varying sizes, (ii) supercritical water near the Widom line that is known to exhibit pronounced density fluctuations and also study (iii) the collective and local polarization fluctuation of water molecules in the presence of several different proteins. The spatio-temporal correlation of confined water molecules inside reverse micelles of varying sizes is well captured through the spectral diffusion of corresponding 2D-IR spectra. In the case of supercritical water also, we observe a strong signature of dynamic heterogeneity from the elongated nature of the 2D-IR spectra. In this case the relaxation is ultrafast. We find remarkable agreement between the different tools employed to study the relaxation of density heterogeneity. For aqueous protein solutions, we find that the calculated dielectric constant of the respective systems unanimously shows a noticeable increment compared to that of neat water. However, the `effective' dielectric constant for successive layers shows significant variation, with the layer adjacent to the protein having a much lower value. Relaxation is also slowest at the surface. We find that the dielectric constant achieves the bulk value at distances more than 3 nm from the surface of the protein.

A novel index for identification of weak nodes for reactive compensation to improve voltage stability

In this study, a new reactive power loss index (RPLI) is proposed for identification of weak buses in the system. This index is further used for determining the optimal locations for placement of reactive compensation devices in the power system for additional voltage support. The new index is computed from the reactive power support and loss allocation algorithm using Y-bus method for the system under intact condition and as well as critical/severe network contingencies cases. Fuzzy logic approach is used to select the important and critical/severe line contingencies from the contingency list. The inherent characteristics of the reactive power in system operation is properly addressed while determining the reactive power loss allocation to load buses. The proposed index is tested on sample 10-bus equivalent system and 72-bus practical equivalent system of Indian southern region power grid. The validation of the weak buses identification from the proposed index with that from other existing methods in the literature is carried out to demonstrate the effectiveness of the proposed index. Simulation results show that the identification of weak buses in the system from the new RPLI is completely non-iterative, thus requires minimal computational efforts as compared with other existing methods in the literature.

Reliability models for existing structures based on dynamic state estimation and data based asymptotic extreme value analysis

The problem of time variant reliability analysis of existing structures subjected to stationary random dynamic excitations is considered. The study assumes that samples of dynamic response of the structure, under the action of external excitations, have been measured at a set of sparse points on the structure. The utilization of these measurements m in updating reliability models, postulated prior to making any measurements, is considered. This is achieved by using dynamic state estimation methods which combine results from Markov process theory and Bayes' theorem. The uncertainties present in measurements as well as in the postulated model for the structural behaviour are accounted for. The samples of external excitations are taken to emanate from known stochastic models and allowance is made for ability (or lack of it) to measure the applied excitations. The future reliability of the structure is modeled using expected structural response conditioned on all the measurements made. This expected response is shown to have a time varying mean and a random component that can be treated as being weakly stationary. For linear systems, an approximate analytical solution for the problem of reliability model updating is obtained by combining theories of discrete Kalman filter and level crossing statistics. For the case of nonlinear systems, the problem is tackled by combining particle filtering strategies with data based extreme value analysis. In all these studies, the governing stochastic differential equations are discretized using the strong forms of Ito-Taylor's discretization schemes. The possibility of using conditional simulation strategies, when applied external actions are measured, is also considered. The proposed procedures are exemplifiedmby considering the reliability analysis of a few low-dimensional dynamical systems based on synthetically generated measurement data. The performance of the procedures developed is also assessed based on a limited amount of pertinent Monte Carlo simulations. (C) 2010 Elsevier Ltd. All rights reserved.

Dynamic analysis and simulation of a VSC based Back-to-Back HVDC link

This paper presents the modeling and analysis of a voltage source converter (VSC) based back-to-back (BTB) HVDC link. The case study considers the response to changes in the active and reactive power and disturbance caused by single line to ground (SLG) fault. The controllers at each terminal are designed to inject a variable (magnitude and phase angle) sinusoidal, balanced set of voltages to regulate/control the active and reactive power. It is also possible to regulate the converter bus (AC) voltage by controlling the injected reactive power. The analysis is carried out using both d-q model (neglecting the harmonics in the output voltages of VSC) and three phase detailed model of VSC. While the eigenvalue analysis and controller design is based on the d-q model, the transient simulation considers both models.

On the shear deformation theory for dynamic analysis of beams

Timoshenko's shear deformation theory is widely used for the dynamical analysis of shear-flexible beams. This paper presents a comparative study of the shear deformation theory with a higher order model, of which Timoshenko's shear deformation model is a special case. Results indicate that while Timoshenko's shear deformation theory gives reasonably accurate information regarding the set of bending natural frequencies, there are considerable discrepancies in the information it gives regarding the mode shapes and dynamic response, and so there is a need to consider higher order models for the dynamical analysis of flexure of beams.

On-line Dynamic Security Assessment: Determination of Critical Transmission Lines

The main objective of on-line dynamic security assessment is to take preventive action if required or decide remedial action if a contingency actually occurs. Stability limits are obtained for different contingencies. The mode of instability is one of the outputs of dynamic security analysis. When a power system becomes unstable, it splits initially into two groups of generators, and there is a unique cutset in the transmission network known as critical cutset across which the angles become unbounded. The knowledge of critical cutset is additional information obtained from dynamic security assessment, which can be used for initiating preventive control actions, deciding emergency control actions, and adaptive out-of-step relaying. In this article, an analytical technique for the fast prediction of the critical cutset by system simulation for a short duration is presented. Case studies on the New England ten-generator system are presented. The article also suggests the applications of the identification of critical cutsets.

Active vibration suppression of beams with discrete actuators using optimal dynamic inversion

Most of the structural elements like beams, cables etc. are flexible and should be modeled as distributed parameter systems (DPS) to represent the reality better. For large structures, the usual approach of 'modal representation' is not an accurate representation. Moreover, for excessive vibrations (possibly due to strong wind, earthquake etc.), external power source (controller) is needed to suppress it, as the natural damping of these structures is usually small. In this paper, we propose to use a recently developed optinial dynamic inversion technique to design a set of discrete controllers for this purpose. We assume that the control force to the structure is applied through finite number of actuators, which are located at predefined locations in the spatial domain. The method used in this paper determines control forces directly from the partial differential equation (PDE) model of the system. The formulation has better practical significance, both because it leads to a closed form solution of the controller (hence avoids computational issues) as well as because a set of discrete actuators along the spatial domain can be implemented with relative ease (as compared to a continuous actuator).

A neuro-adaptive augmented optimal dynamic inversion approach for effective and efficient treatment of chronic myelogenous leukemia

Combining the advanced techniques of optimal dynamic inversion and model-following neuro-adaptive control design, an efficient technique is presented for effective treatment of chronic myelogenous leukemia (CML). A recently developed nonlinear mathematical model for cell dynamics is used for the control (medication) synthesis. First, taking a set of nominal parameters, a nominal controller is designed based on the principle of optimal dynamic inversion. This controller can treat nominal patients (patients having same nominal parameters as used for the control design) effectively. However, since the parameters of an actual patient can be different from that of the ideal patient, to make the treatment strategy more effective and efficient, a model-following neuro-adaptive controller is augmented to the nominal controller. In this approach, a neural network trained online (based on Lyapunov stability theory) facilitates a new adaptive controller, computed online. From the simulation studies, this adaptive control design approach (treatment strategy) is found to be very effective to treat the CML disease for actual patients. Sufficient generality is retained in the theoretical developments in this paper, so that the techniques presented can be applied to other similar problem as well. Note that the technique presented is computationally non-intensive and all computations can be carried out online.

An Estimator Algorithm For Learning Automata With Changing Number Of Actions

In many problems of decision making under uncertainty the system has to acquire knowledge of its environment and learn the optimal decision through its experience. Such problems may also involve the system having to arrive at the globally optimal decision, when at each instant only a subset of the entire set of possible alternatives is available. These problems can be successfully modelled and analysed by learning automata. In this paper an estimator learning algorithm, which maintains estimates of the reward characteristics of the random environment, is presented for an automaton with changing number of actions. A learning automaton using the new scheme is shown to be e-optimal. The simulation results demonstrate the fast convergence properties of the new algorithm. The results of this study can be extended to the design of other types of estimator algorithms with good convergence properties.

Active vibration suppression of beams with discrete actuators using optimal dynamic inversion

Most of the structural elements like beams, cables etc. are flexible and should be modeled as distributed parameter systems (DPS) to represent the reality better. For large structures, the usual approach of 'modal representation' is not an accurate representation. Moreover, for excessive vibrations (possibly due to strong wind, earthquake etc.), external power source (controller) is needed to suppress it, as the natural damping of these structures is usually small. In this paper, we propose to use a recently developed optimal dynamic inversion technique to design a set of discrete controllers for this purpose. We assume that the control force to the structure is applied through finite number of actuators, which are located at predefined locations in the spatial domain. The method used in this paper determines control forces directly from the partial differential equation (PDE) model of the system. The formulation has better practical significance, both because it leads to a closed form solution of the controller (hence avoids computational issues) as well as because a set of discrete actuators along the spatial domain can be implemented with relative ease (as compared to a continuous actuator)

Dynamic stiffness matrix of a general cable element

A computational scheme for determining the dynamic stiffness coefficients of a linear, inclined, translating and viscously/hysteretically damped cable element is outlined. Also taken into account is the coupling between inplane transverse and longitudinal forms of cable vibration. The scheme is based on conversion of the governing set of quasistatic boundary value problems into a larger equivalent set of initial value problems, which are subsequently numerically integrated in a spatial domain using marching algorithms. Numerical results which bring out the nature of the dynamic stiffness coefficients are presented. A specific example of random vibration analysis of a long span cable subjected to earthquake support motions modeled as vector gaussian random processes is also discussed. The approach presented is versatile and capable of handling many complicating effects in cable dynamics in a unified manner.

Fluctuating micro-heterogeneity in water-tert-butyl alcohol mixtures and lambda-type divergence of the mean cluster size with phase transition-like multiple anomalies

Water-tert-butyl alcohol (TBA) binary mixture exhibits a large number of thermodynamic and dynamic anomalies. These anomalies are observed at surprisingly low TBA mole fraction, with x(TBA) approximate to 0.03-0.07. We demonstrate here that the origin of the anomalies lies in the local structural changes that occur due to self-aggregation of TBA molecules. We observe a percolation transition of the TBA molecules at x(TBA) approximate to 0.05. We note that ``islands'' of TBA clusters form even below this mole fraction, while a large spanning cluster emerges above that mole fraction. At this percolation threshold, we observe a lambda-type divergence in the fluctuation of the size of the largest TBA cluster, reminiscent of a critical point. Alongside, the structure of water is also perturbed, albeit weakly, by the aggregation of TBA molecules. There is a monotonic decrease in the tetrahedral order parameter of water, while the dipole moment correlation shows a weak nonlinearity. Interestingly, water molecules themselves exhibit a reverse percolation transition at higher TBA concentration, x(TBA) approximate to 0.45, where large spanning water clusters now break-up into small clusters. This is accompanied by significant divergence of the fluctuations in the size of largest water cluster. This second transition gives rise to another set of anomalies around. Both the percolation transitions can be regarded as manifestations of Janus effect at small molecular level. (C) 2014 AIP Publishing LLC.

Ergodic control of partially observed Markov chains

The ergodic or long-run average cost control problem for a partially observed finite-state Markov chain is studied via the associated fully observed separated control problem for the nonlinear filter. Dynamic programming equations for the latter are derived, leading to existence and characterization of optimal stationary policies.

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.