Low formation energy and kinetic barrier of Stone-Wales defect in infinite and finite silicene

Stone-Wales (SW) defects in materials having hexagonal lattice are the most common topological defects that affect the electronic and mechanical properties. Using first principles density functional theory based calculations, we study the formation energy and kinetic barrier of SW-defect in infinite and finite sheets of silicene. The formation energies as well as the barriers in both the cases are significantly lower than those of graphene. Furthermore, compared with the infinite sheets, the energy barriers and formation energies are lower for finite sheets. However, due to low barriers these defects are expected to heal out of the finite sheets. (C) 2013 Elsevier B.V. All rights reserved.

A fractional order proportional integral controller for path following and trajectory tracking of miniature air vehicles

In this paper, a fractional order proportional-integral controller is developed for a miniature air vehicle for rectilinear path following and trajectory tracking. The controller is implemented by constructing a vector field surrounding the path to be followed, which is then used to generate course commands for the miniature air vehicle. The fractional order proportional-integral controller is simulated using the fundamentals of fractional calculus, and the results for this controller are compared with those obtained for a proportional controller and a proportional integral controller. In order to analyze the performance of the controllers, four performance metrics, namely (maximum) overshoot, control effort, settling time and integral of the timed absolute error cost, have been selected. A comparison of the nominal as well as the robust performances of these controllers indicates that the fractional order proportional-integral controller exhibits the best performance in terms of ITAE while showing comparable performances in all other aspects.

CANDO and the infinite drug discovery frontier

The Computational Analysis of Novel Drug Opportunities (CANDO) platform (http://protinfo.org/cando) uses similarity of compound-proteome interaction signatures to infer homology of compound/drug behavior. We constructed interaction signatures for 3733 human ingestible compounds covering 48,278 protein structures mapping to 2030 indications based on basic science methodologies to predict and analyze protein structure, function, and interactions developed by us and others. Our signature comparison and ranking approach yielded benchmarking accuracies of 12-25% for 1439 indications with at least two approved compounds. We prospectively validated 49/82 `high value' predictions from nine studies covering seven indications, with comparable or better activity to existing drugs, which serve as novel repurposed therapeutics. Our approach may be generalized to compounds beyond those approved by the FDA, and can also consider mutations in protein structures to enable personalization. Our platform provides a holistic multiscale modeling framework of complex atomic, molecular, and physiological systems with broader applications in medicine and engineering.

An integral fluctuation theorem for systems with unidirectional transitions

The fluctuations of a Markovian jump process with one or more unidirectional transitions, where R-ij > 0 but R-ji = 0, are studied. We find that such systems satisfy an integral fluctuation theorem. The fluctuating quantity satisfying the theorem is a sum of the entropy produced in the bidirectional transitions and a dynamical contribution, which depends on the residence times in the states connected by the unidirectional transitions. The convergence of the integral fluctuation theorem is studied numerically and found to show the same qualitative features as systems exhibiting microreversibility.

Optimality Conditions and Duality for Semi-Infinite Mathematical Programming Problem with Equilibrium Constraints

This article considers a semi-infinite mathematical programming problem with equilibrium constraints (SIMPEC) defined as a semi-infinite mathematical programming problem with complementarity constraints. We establish necessary and sufficient optimality conditions for the (SIMPEC). We also formulate Wolfe- and Mond-Weir-type dual models for (SIMPEC) and establish weak, strong and strict converse duality theorems for (SIMPEC) and the corresponding dual problems under invexity assumptions.

THEORY OF NEWFORMS OF HALF-INTEGRAL WEIGHT

We set up the theory of newforms of half-integral weight on Gamma(0)(8N) and Gamma(0)(16N), where N is odd and squarefree. Further, we extend the definition of the Kohnen plus space in general for trivial character and also study the theory of newforms in the plus spaces on Gamma(0)(8N), Gamma(0)(16N), where N is odd and squarefree. Finally, we show that the Atkin-Lehner W-operator W-4 acts as the identity operator on S-2k(new)(4N), where N is odd and squarefree. This proves that S-2k(-)(4) = S-2k(4).

Markov chain splitting methods in structural reliability integral estimation

Monte Carlo simulation methods involving splitting of Markov chains have been used in evaluation of multi-fold integrals in different application areas. We examine in this paper the performance of these methods in the context of evaluation of reliability integrals from the point of view of characterizing the sampling fluctuations. The methods discussed include the Au-Beck subset simulation, Holmes-Diaconis-Ross method, and generalized splitting algorithm. A few improvisations based on first order reliability method are suggested to select algorithmic parameters of the latter two methods. The bias and sampling variance of the alternative estimators are discussed. Also, an approximation to the sampling distribution of some of these estimators is obtained. Illustrative examples involving component and series system reliability analyses are presented with a view to bring out the relative merits of alternative methods. (C) 2015 Elsevier Ltd. All rights reserved.

Phase space path integral approach to harmonic oscillator with a time-dependent force constant

The quantum statistical mechanical propagator for a harmonic oscillator with a time-dependent force constant, m omega(2)(t), has been investigated in the past and was found to have only a formal solution in terms of the solutions of certain ordinary differential equations. Such path integrals are frequently encountered in semiclassical path integral evaluations and having exact analytical expressions for such path integrals is of great interest. In a previous work, we had obtained the exact propagator for motion in an arbitrary time-dependent harmonic potential in the overdamped limit of friction using phase space path integrals in the context of Levy flights - a result that can be easily extended to Brownian motion. In this paper, we make a connection between the overdamped Brownian motion and the imaginary time propagator of quantum mechanics and thereby get yet another way to evaluate the latter exactly. We find that explicit analytic solution for the quantum statistical mechanical propagator can be written when the time-dependent force constant has the form omega(2)(t) = lambda(2)(t) - d lambda(t)/dt where lambda(t) is any arbitrary function of t and use it to evaluate path integrals which have not been evaluated previously. We also employ this method to arrive at a formal solution of the propagator for both Levy flights and Brownian subjected to a time-dependent harmonic potential in the underdamped limit of friction. (C) 2015 Elsevier B.V. All rights reserved.

SOME INFINITE SUMS IDENTITIES

We find the sum of series of the form Sigma(infinity)(i=1) f(i)/i(r) for some special functions f. The above series is a generalization of the Riemann zeta function. In particular, we take f as some values of Hurwitz zeta functions, harmonic numbers, and combination of both. These generalize some of the results given in Mezo's paper (2013). We use multiple zeta theory to prove all results. The series sums we have obtained are in terms of Bernoulli numbers and powers of pi.

A modified approach to numerical solution of Fredholm integral equations of the second kind

A modified approach to obtain approximate numerical solutions of Fredholin integral equations of the second kind is presented. The error bound is explained by the aid of several illustrative examples. In each example, the approximate solution is compared with the exact solution, wherever possible, and an excellent agreement is observed. In addition, the error bound in each example is compared with the one obtained by the Nystrom method. It is found that the error bound of the present method is smaller than the ones obtained by the Nystrom method. Further, the present method is successfully applied to derive the solution of an integral equation arising in a special Dirichlet problem. (C) 2015 Elsevier Inc. All rights reserved.

Complex potentials and singular integral equation for curve crack problem in antiplane elasticity

Four types of the fundamental complex potential in antiplane elasticity are introduced: (a) a point dislocation, (b) a concentrated force, (c) a dislocation doublet and (d) a concentrated force doublet. It is proven that if the axis of the concentrated force doublet is perpendicular to the direction of the dislocation doublet, the relevant complex potentials are equivalent. Using the obtained complex potentials, a singular integral equation for the curve crack problem is introduced. Some particular features of the obtained singular integral equation are discussed, and numerical solutions and examples are given.

Dynamic SIF of interface crack between two dissimilar viscoelastic bodies under impact loading

In this paper, the transient dynamic stress intensity factor (SIF) is determined for an interface crack between two dissimilar half-infinite isotropic viscoelastic bodies under impact loading. An anti-plane step loading is assumed to act suddenly on the surface of interface crack of finite length. The stress field incurred near the crack tip is analyzed. The integral transformation method and singular integral equation approach are used to get the solution. By virtue of the integral transformation method, the viscoelastic mixed boundary problem is reduced to a set of dual integral equations of crack open displacement function in the transformation domain. The dual integral equations can be further transformed into the first kind of Cauchy-type singular integral equation (SIE) by introduction of crack dislocation density function. A piecewise continuous function approach is adopted to get the numerical solution of SIE. Finally, numerical inverse integral transformation is performed and the dynamic SIF in transformation domain is recovered to that in time domain. The dynamic SIF during a small time-interval is evaluated, and the effects of the viscoelastic material parameters on dynamic SIF are analyzed.