Natural motion of one-dimensional flexible objects using minimization approaches

For one-dimensional flexible objects such as ropes, chains, hair, the assumption of constant length is realistic for large-scale 3D motion. Moreover, when the motion or disturbance at one end gradually dies down along the curve defining the one-dimensional flexible objects, the motion appears ``natural''. This paper presents a purely geometric and kinematic approach for deriving more natural and length-preserving transformations of planar and spatial curves. Techniques from variational calculus are used to determine analytical conditions and it is shown that the velocity at any point on the curve must be along the tangent at that point for preserving the length and to yield the feature of diminishing motion. It is shown that for the special case of a straight line, the analytical conditions lead to the classical tractrix curve solution. Since analytical solutions exist for a tractrix curve, the motion of a piecewise linear curve can be solved in closed-form and thus can be applied for the resolution of redundancy in hyper-redundant robots. Simulation results for several planar and spatial curves and various input motions of one end are used to illustrate the features of motion damping and eventual alignment with the perturbation vector.

Analytical theory and stability analysis of an elongated nanoscale object under external torque

We consider the rotational motion of an elongated nanoscale object in a fluid under an external torque. The experimentally observed dynamics could be understood from analytical solutions of the Stokes equation, with explicit formulae derived for the dynamical states as a function of the object dimensions and the parameters defining the external torque. Under certain conditions, multiple analytical solutions to the Stokes equations exist, which have been investigated through numerical analysis of their stability against small perturbations and their sensitivity towards initial conditions. These experimental results and analytical formulae are general enough to be applicable to the rotational motion of any isolated elongated object at low Reynolds numbers, and could be useful in the design of non-spherical nanostructures for diverse applications pertaining to microfluidics and nanoscale propulsion technologies.

DETERMINATION OF THE STRONG COUPLING FROM HADRONIC TAU DECAYS USING RENORMALIZATION GROUP SUMMED PERTURBATION THEORY

Be the strong coupling constant alpha(s) from the tau hadronn width using a renormalization group summed (RGS) expansion of the QCD Adler lunction. The main theoretical uncertainty in the extraction of as is due to the manner in which renormalization group invariance is implemented, and the as yet uncalculated higher order terms in the QCD perturbative series. We show that new expansion exhibits good renormalization group improvement and the behavior of the series is similar to that of the standard RGS expansion. The value of the strong coupling in (MS) over bar scheme obtained with the RCS expansion is alpha(s) (M-tau(2)) = 0.338 +/- 0.010. The convergence properties of the new expansion can be improved by Bond transformation and analytic continuation in t he Bond plane. This is discussed elsewhere in these issues.

Expansions of tau hadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior

The moments of the hadronic spectral functions are of interest for the extraction of the strong coupling alpha(s) and other QCD parameters from the hadronic decays of the tau lepton. Motivated by the recent analyses of a large class of moments in the standard fixed-order and contour-improved perturbation theories, we consider the perturbative behavior of these moments in the framework of a QCD nonpower perturbation theory, defined by the technique of series acceleration by conformal mappings, which simultaneously implements renormalization-group summation and has a tame large-order behavior. Two recently proposed models of the Adler function are employed to generate the higher-order coefficients of the perturbation series and to predict the exact values of the moments, required for testing the properties of the perturbative expansions. We show that the contour-improved nonpower perturbation theories and the renormalization-group-summed nonpower perturbation theories have very good convergence properties for a large class of moments of the so-called ``reference model,'' including moments that are poorly described by the standard expansions. The results provide additional support for the plausibility of the description of the Adler function in terms of a small number of dominant renormalons.

Gap renormalization of molecular crystals from density-functional theory

Fundamental gap renormalization due to electronic polarization is a basic phenomenon in molecular crystals. Despite its ubiquity and importance, all conventional approaches within density-functional theory completely fail to capture it, even qualitatively. Here, we present a new screened range-separated hybrid functional, which, through judicious introduction of the scalar dielectric constant, quantitatively captures polarization-induced gap renormalization, as demonstrated on the prototypical organic molecular crystals of benzene, pentacene, and C-60. This functional is predictive, as it contains system-specific adjustable parameters that are determined from first principles, rather than from empirical considerations.

Novel procedure for the estimation of swelling pressures of compacted bentonites based on diffuse double layer theory

Bentonite clays are proven to be attractive as buffer and backfill material in high-level nuclear waste repositories around the world. A quick estimation of swelling pressures of the compacted bentonites for different clay-water-electrolyte interactions is essential in the design of buffer and backfill materials. The theoretical studies on the swelling behavior of bentonites are based on diffuse double layer (DDL) theory. To establish theoretical relationship between void ratio and swelling pressure (e versus P), evaluation of elliptic integral and inverse analysis are unavoidable. In this paper, a novel procedure is presented to establish theoretical relationship of e versus P based on the Gouy-Chapman method. The proposed procedure establishes a unique relationship between electric potentials of interacting and non-interacting diffuse clay-water-electrolyte systems. A procedure is, thus, proposed to deduce the relation between swelling pressures and void ratio from the established relation between electric potentials. This approach is simple and alleviates the need for elliptic integral evaluation and also the inverse analysis. Further, application of the proposed approach to estimate swelling pressures of four compacted bentonites, for example, MX 80, Febex, Montigel and Kunigel V1, at different dry densities, shows that the method is very simple and predicts solutions with very good accuracy. Moreover, the proposed procedure provides continuous distributions of e versus P and thus it is computationally efficient when compared with the existing techniques.

Terminal Impact Angle Constrained Guidance Laws Using Variable Structure Systems Theory

In this brief, variable structure systems theory based guidance laws, to intercept maneuvering targets at a desired impact angle, are presented. Choosing the missile's lateral acceleration (latax) to enforce sliding mode, which is the principal operating mode of variable structure systems, on a switching surface defined by the line-of-sight angle leads to a guidance law that allows the achievement of the desired terminal impact angle. As will be shown, this law does not ensure interception for all states of the missile and the target during the engagement. Hence, additional switching surfaces are designed and a switching logic is developed that allows the latax to switch between enforcing sliding mode on one of these surfaces so that the target can be intercepted at the desired impact angle. The guidance laws are designed using nonlinear engagement dynamics for the general case of a maneuvering target.

Sustaining cooperation on networks: an analytical study based on evolutionary game theory

We analytically study the role played by the network topology in sustaining cooperation in a society of myopic agents in an evolutionary setting. In our model, each agent plays the Prisoner's Dilemma (PD) game with its neighbors, as specified by a network. Cooperation is the incumbent strategy, whereas defectors are the mutants. Starting with a population of cooperators, some agents are switched to defection. The agents then play the PD game with their neighbors and compute their fitness. After this, an evolutionary rule, or imitation dynamic is used to update the agent strategy. A defector switches back to cooperation if it has a cooperator neighbor with higher fitness. The network is said to sustain cooperation if almost all defectors switch to cooperation. Earlier work on the sustenance of cooperation has largely consisted of simulation studies, and we seek to complement this body of work by providing analytical insight for the same. We find that in order to sustain cooperation, a network should satisfy some properties such as small average diameter, densification, and irregularity. Real-world networks have been empirically shown to exhibit these properties, and are thus candidates for the sustenance of cooperation. We also analyze some specific graphs to determine whether or not they sustain cooperation. In particular, we find that scale-free graphs belonging to a certain family sustain cooperation, whereas Erdos-Renyi random graphs do not. To the best of our knowledge, ours is the first analytical attempt to determine which networks sustain cooperation in a population of myopic agents in an evolutionary setting.

Energy Hyperspace for Stacking Interaction in AU/AU Dinucleotide Step: Dispersion-Corrected Density Functional Theory Study

Double helical structures of DNA and RNA are mostly determined by base pair stacking interactions, which give them the base sequence-directed features, such as small roll values for the purine-pyrimidine steps. Earlier attempts to characterize stacking interactions were mostly restricted to calculations on fiber diffraction geometries or optimized structure using ab initio calculations lacking variation in geometry to comment on rather unusual large roll values observed in AU/AU base pair step in crystal structures of RNA double helices. We have generated stacking energy hyperspace by modeling geometries with variations along the important degrees of freedom, roll, and slide, which were chosen via statistical analysis as maximally sequence dependent. Corresponding energy contours were constructed by several quantum chemical methods including dispersion corrections. This analysis established the most suitable methods for stacked base pair systems despite the limitation imparted by number of atom in a base pair step to employ very high level of theory. All the methods predict negative roll value and near-zero slide to be most favorable for the purine-pyrimidine steps, in agreement with Calladine's steric clash based rule. Successive base pairs in RNA are always linked by sugar-phosphate backbone with C3-endo sugars and this demands C1-C1 distance of about 5.4 angstrom along the chains. Consideration of an energy penalty term for deviation of C1-C1 distance from the mean value, to the recent DFT-D functionals, specifically B97X-D appears to predict reliable energy contour for AU/AU step. Such distance-based penalty improves energy contours for the other purine-pyrimidine sequences also. (c) 2013 Wiley Periodicals, Inc. Biopolymers 101: 107-120, 2014.

Design of double toggle switching mechanisms

Toggle mechanisms are ubiquitous in electrical switches. However, literature for their mechanical design is scarce. This paper defines and classifies the toggle phenomena observed during switching. The concept of double toggle introduced in this paper enables a systematic screening of kinematic structure for the suitability in high performance switches. Seven structural and three kinematic criteria are identified for this purpose. It is also demonstrated that each such feasible kinematic structure lends itself to multiple physical embodiments. Therefore, the theory and procedure presented in this work can be used for design of numerous kinematically distinct mechanisms. One representative mechanical embodiment for a novel double toggle switch, including mass and geometric shape of links has been included in the paper. The switching behavior of the design is validated using Pro/Mechanism (TM). (C) 2013 Elsevier Ltd. All rights reserved.

MRT Letter: Experimental Verification of Vectorial Theory to Determine Field at the Geometrical Focus of a Cylindrical Lens

We provide experimental evidence supporting the vectorial theory for determining electric field at and near the geometrical focus of a cylindrical lens. This theory provides precise distribution of field and its polarization effects. Experimental results show a close match (approximate to 95% using (2)-test) with the simulation results (obtained using vectorial theory). Light-sheet generated both at low and high NA cylindrical lens shows the importance of vectorial theory for further development of light-sheet techniques. Potential applications are in planar imaging systems (such as, SPIM, IML-SPIM, imaging cytometry) and spectroscopy. Microsc. Res. Tech. 77:105-109, 2014. (c) 2014 Wiley Periodicals, Inc.

Performance analysis of boron nitride embedded armchair graphene nanoribbon metal-oxide-semiconductor field effect transistor with Stone Wales defects

We study the performance of a hybrid Graphene-Boron Nitride armchair nanoribbon (a-GNR-BN) n-MOSFET at its ballistic transport limit. We consider three geometric configurations 3p, 3p + 1, and 3p + 2 of a-GNR-BN with BN atoms embedded on either side (2, 4, and 6 BN) on the GNR. Material properties like band gap, effective mass, and density of states of these H-passivated structures are evaluated using the Density Functional Theory. Using these material parameters, self-consistent Poisson-Schrodinger simulations are carried out under the Non Equilibrium Green's Function formalism to calculate the ballistic n-MOSFET device characteristics. For a hybrid nanoribbon of width similar to 5 nm, the simulated ON current is found to be in the range of 265 mu A-280 mu A with an ON/OFF ratio 7.1 x 10(6)-7.4 x 10(6) for a V-DD = 0.68 V corresponding to 10 nm technology node. We further study the impact of randomly distributed Stone Wales (SW) defects in these hybrid structures and only 2.5% degradation of ON current is observed for SW defect density of 3.18%. (C) 2014 AIP Publishing LLC.

Curvature based mobility analysis and form closure of smooth planar curves with multiple contacts

This paper presents a simple second-order, curvature based mobility analysis of planar curves in contact. The underlying theory deals with penetration and separation of curves with multiple contacts, based on relative configuration of osculating circles at points of contact for a second-order rotation about each point of the plane. Geometric and analytical treatment of mobility analysis is presented for generic as well as special contact geometries. For objects with a single contact, partitioning of the plane into four types of mobility regions has been shown. Using point based composition operations based on dual-number matrices, analysis has been extended to computationally handle multiple contacts scenario. A novel color coded directed line has been proposed to capture the contact scenario. Multiple contacts mobility is obtained through intersection of the mobility half-spaces. It is derived that mobility region comprises a pair of unbounded or a single bounded convex polygon. The theory has been used for analysis and synthesis of form closure configurations, revolute and prismatic kinematic pairs. (C) 2013 Elsevier Ltd. All rights reserved.

Simulation of inhomogeneous distributions of ultracold atoms in an optical lattice via a massively parallel implementation of nonequilibrium strong-coupling perturbation theory

We present a nonequilibrium strong-coupling approach to inhomogeneous systems of ultracold atoms in optical lattices. We demonstrate its application to the Mott-insulating phase of a two-dimensional Fermi-Hubbard model in the presence of a trap potential. Since the theory is formulated self-consistently, the numerical implementation relies on a massively parallel evaluation of the self-energy and the Green's function at each lattice site, employing thousands of CPUs. While the computation of the self-energy is straightforward to parallelize, the evaluation of the Green's function requires the inversion of a large sparse 10(d) x 10(d) matrix, with d > 6. As a crucial ingredient, our solution heavily relies on the smallness of the hopping as compared to the interaction strength and yields a widely scalable realization of a rapidly converging iterative algorithm which evaluates all elements of the Green's function. Results are validated by comparing with the homogeneous case via the local-density approximation. These calculations also show that the local-density approximation is valid in nonequilibrium setups without mass transport.

Enhanced Gas Adsorption on Graphitic Substrates via Defects and Local Curvature: A Density Functional Theory Study

Using van-der-Waals-corrected density functional theory calculations, we explore the possibility of engineering the local structure and morphology of high-surface-area graphene-derived materials to improve the uptake of methane and carbon dioxide for gas storage and sensing. We test the sensitivity of the gas adsorption energy to the introduction of native point defects, curvature, and the application of strain. The binding energy at topological point defect sites is inversely correlated with the number of missing carbon atoms, causing Stone-Wales defects to show the largest enhancement with respect to pristine graphene (similar to 20%). Improvements of similar magnitude are observed at concavely curved surfaces in buckled graphene sheets under compressive strain, whereas tensile strain tends to weaken gas binding. Trends for CO2 and CH4 are, similar, although CO2 binding is generally stronger by similar to 4 to 5 kJ mol(-1). However, the differential between the adsorption of CO2 and CH4 is much higher on folded graphene sheets and at concave curvatures; this could possibly be leveraged for CH4/CO2 flow separation and gasselective sensors.