A differential geometric method for kinematic analysis of two- and three-degree-of-freedom rigid body motions

In this paper, we present a novel differential geometric characterization of two- and three-degree-of-freedom rigid body kinematics, using a metric defined on dual vectors. The instantaneous angular and linear velocities of a rigid body are expressed as a dual velocity vector, and dual inner product is defined on this dual vector, resulting in a positive semi-definite and symmetric dual matrix. We show that the maximum and minimum magnitude of the dual velocity vector, for a unit speed motion, can be obtained as eigenvalues of this dual matrix. Furthermore, we show that the tip of the dual velocity vector lies on a dual ellipse for a two-degree-of-freedom motion and on a dual ellipsoid for a three-degree-of-freedom motion. In this manner, the velocity distribution of a rigid body can be studied algebraically in terms of the eigenvalues of a dual matrix or geometrically with the dual ellipse and ellipsoid. The second-order properties of the two- and three-degree-of-freedom motions of a rigid body are also obtained from the derivatives of the elements of the dual matrix. This results in a definition of the geodesic motion of a rigid body. The theoretical results are illustrated with the help of a spatial 2R and a parallel three-degree-of-freedom manipulator.

Decoupling of diffusion from viscosity: Difference scenario for translational and rotational motions

Recent experiments have indicated a dramatically different viscosity dependence of the translational and the rotational diffusion coefficients in a supercooled liquid as the glass transition temperature is approached from above. While the translational motion seems to be decoupled from the rising viscosity (eta), the rotational motion seems to remain firmly coupled to eta. In order to understand the microscopic origin of this behavior, we have carried nut detailed theoretical calculations of both the quantities by using a self-consistent mode-coupling theory (MCT). it is found that when the size of the solute is same as that of the solvent molecules, the conventional MCT fails to predict the observed decoupling. The solvent inhomogeneity is found to play a decisive role in determining the decoupling. The difference in the viscosity dependence between rotation and translational diffusion coefficient is discussed.

Simulation of length-preserving motions of flexible one dimensional oObjects using optimization

During the motion of one dimensional flexible objects such as ropes, chains, etc., the assumption of constant length is realistic. Moreover,their motion appears to be naturally minimizing some abstract distance measure, wherein the disturbance at one end gradually dies down along the curve defining the object. This paper presents purely kinematic strategies for deriving length-preserving transformations of flexible objects that minimize appropriate ‘motion’. The strategies involve sequential and overall optimization of the motion derived using variational calculus. Numerical simulations are performed for the motion of a planar curve and results show stable converging behavior for single-step infinitesimal and finite perturbations 1 as well as multi-step perturbations. Additionally, our generalized approach provides different intuitive motions for various problem-specific measures of motion, one of which is shown to converge to the conventional tractrix-based solution. Simulation results for arbitrary shapes and excitations are also included.

Predicting the lithospheric stress field and plate motions by joint modeling of lithosphere and mantle dynamics

The way in which basal tractions, associated with mantle convection, couples with the lithosphere is a fundamental problem in geodynamics. A successful lithosphere-mantle coupling model for the Earth will satisfy observations of plate motions, intraplate stresses, and the plate boundary zone deformation. We solve the depth integrated three-dimensional force balance equations in a global finite element model that takes into account effects of both topography and shallow lithosphere structure as well as tractions originating from deeper mantle convection. The contribution from topography and lithosphere structure is estimated by calculating gravitational potential energy differences. The basal tractions are derived from a fully dynamic flow model with both radial and lateral viscosity variations. We simultaneously fit stresses and plate motions in order to delineate a best-fit lithosphere-mantle coupling model. We use both the World Stress Map and the Global Strain Rate Model to constrain the models. We find that a strongly coupled model with a stiff lithosphere and 3-4 orders of lateral viscosity variations in the lithosphere are best able to match the observational constraints. Our predicted deviatoric stresses, which are dominated by contribution from mantle tractions, range between 20-70 MPa. The best-fitting coupled models predict strain rates that are consistent with observations. That is, the intraplate areas are nearly rigid whereas plate boundaries and some other continental deformation zones display high strain rates. Comparison of mantle tractions and surface velocities indicate that in most areas tractions are driving, although in a few regions, including western North America, tractions are resistive. Citation: Ghosh, A., W. E. Holt, and L. M. Wen (2013), Predicting the lithospheric stress field and plate motions by joint modeling of lithosphere and mantle dynamics.

Ground motion prediction equation considering combined dataset of recorded and simulated ground motions

Himalayan region is one of the most active seismic regions in the world and many researchers have highlighted the possibility of great seismic event in the near future due to seismic gap. Seismic hazard analysis and microzonation of highly populated places in the region are mandatory in a regional scale. Region specific Ground Motion Predictive Equation (GMPE) is an important input in the seismic hazard analysis for macro- and micro-zonation studies. Few GMPEs developed in India are based on the recorded data and are applicable for a particular range of magnitudes and distances. This paper focuses on the development of a new GMPE for the Himalayan region considering both the recorded and simulated earthquakes of moment magnitude 5.3-8.7. The Finite Fault simulation model has been used for the ground motion simulation considering region specific seismotectonic parameters from the past earthquakes and source models. Simulated acceleration time histories and response spectra are compared with available records. In the absence of a large number of recorded data, simulations have been performed at unavailable locations by adopting Apparent Stations concept. Earthquakes recorded up to 2007 have been used for the development of new GMPE and earthquakes records after 2007 are used to validate new GMPE. Proposed GMPE matched very well with recorded data and also with other highly ranked GMPEs developed elsewhere and applicable for the region. Comparison of response spectra also have shown good agreement with recorded earthquake data. Quantitative analysis of residuals for the proposed GMPE and region specific GMPEs to predict Nepal-India 2011 earthquake of Mw of 5.7 records values shows that the proposed GMPE predicts Peak ground acceleration and spectral acceleration for entire distance and period range with lower percent residual when compared to exiting region specific GMPEs. Crown Copyright (C) 2013 Published by Elsevier Ltd. All rights reserved.

Condition R and proper holomorphic maps between equidimensional product domains

We consider proper holomorphic mappings of equidimensional pseudoconvex domains in complex Euclidean space, where both source and target can be represented as Cartesian products of smoothly bounded domains. It is shown that such mappings extend smoothly up to the closures of the domains, provided each factor of the source satisfies Condition R. It also shown that the number of smoothly bounded factors in the source and target must be the same, and the proper holomorphic map splits as a product of proper mappings between the factor domains. (C) 2013 Elsevier Inc. All rights reserved.

Dynamic state estimation for identifying earthquake support motions in instrumented structures

The problem of identification of multi-component and (or) spatially varying earthquake support motions based on measured responses in instrumented structures is considered. The governing equations of motion are cast in the state space form and a time domain solution to the input identification problem is developed based on the Kalman and particle filtering methods. The method allows for noise in measured responses, imperfections in mathematical model for the structure, and possible nonlinear behavior of the structure. The unknown support motions are treated as hypothetical additional system states and a prior model for these motions are taken to be given in terms of white noise processes. For linear systems, the solution is developed within the Kalman filtering framework while, for nonlinear systems, the Monte Carlo simulation based particle filtering tools are employed. In the latter case, the question of controlling sampling variance based on the idea of Rao-Blackwellization is also explored. Illustrative examples include identification of multi-component and spatially varying support motions in linear/nonlinear structures.

Proper holomorphic mappings between hyperbolic product manifolds

We prove a result on the structure of finite proper holomorphic mappings between complex manifolds that are products of hyperbolic Riemann surfaces. While an important special case of our result follows from the ideas developed by Remmert and Stein, the proof of the full result relies on the interplay of the latter ideas and a finiteness theorem for Riemann surfaces.

Surrogate Regret Bounds for Bipartite Ranking via Strongly Proper Losses

The problem of bipartite ranking, where instances are labeled positive or negative and the goal is to learn a scoring function that minimizes the probability of mis-ranking a pair of positive and negative instances (or equivalently, that maximizes the area under the ROC curve), has been widely studied in recent years. A dominant theoretical and algorithmic framework for the problem has been to reduce bipartite ranking to pairwise classification; in particular, it is well known that the bipartite ranking regret can be formulated as a pairwise classification regret, which in turn can be upper bounded using usual regret bounds for classification problems. Recently, Kotlowski et al. (2011) showed regret bounds for bipartite ranking in terms of the regret associated with balanced versions of the standard (non-pairwise) logistic and exponential losses. In this paper, we show that such (non-pairwise) surrogate regret bounds for bipartite ranking can be obtained in terms of a broad class of proper (composite) losses that we term as strongly proper. Our proof technique is much simpler than that of Kotlowski et al. (2011), and relies on properties of proper (composite) losses as elucidated recently by Reid and Williamson (2010, 2011) and others. Our result yields explicit surrogate bounds (with no hidden balancing terms) in terms of a variety of strongly proper losses, including for example logistic, exponential, squared and squared hinge losses as special cases. An important consequence is that standard algorithms minimizing a (non-pairwise) strongly proper loss, such as logistic regression and boosting algorithms (assuming a universal function class and appropriate regularization), are in fact consistent for bipartite ranking; moreover, our results allow us to quantify the bipartite ranking regret in terms of the corresponding surrogate regret. We also obtain tighter surrogate bounds under certain low-noise conditions via a recent result of Clemencon and Robbiano (2011).

PROPER HOLOMORPHIC MAPS BETWEEN BOUNDED SYMMETRIC DOMAINS REVISITED

We prove that a proper holomorphic map between two nonplanar bounded symmetric domains of the same dimension, one of them being irreducible, is a biholomorphism. Our methods allow us to give a single, all-encompassing argument that unifies the various special cases in which this result is known. We discuss an application of these methods to domains having noncompact automorphism groups that are not assumed to act transitively.

Proper holomorphic mappings of balanced domains in C-n

We extend a well-known result, about the unit ball, by H. Alexander to a class of balanced domains in . Specifically: we prove that any proper holomorphic self-map of a certain type of balanced, finite-type domain in , is an automorphism. The main novelty of our proof is the use of a recent result of Opshtein on the behaviour of the iterates of holomorphic self-maps of a certain class of domains. We use Opshtein's theorem, together with the tools made available by finiteness of type, to deduce that the aforementioned map is unbranched. The monodromy theorem then delivers the result.

A cis-Regulatory Mutation in Troponin-I of Drosophila Reveals the Importance of Proper Stoichiometry of Structural Proteins During Muscle Assembly

Rapid and high wing-beat frequencies achieved during insect flight are powered by the indirect flight muscles, the largest group of muscles present in the thorax. Any anomaly during the assembly and/or structural impairment of the indirect flight muscles gives rise to a flightless phenotype. Multiple mutagenesis screens in Drosophila melanogaster for defective flight behavior have led to the isolation and characterization of mutations that have been instrumental in the identification of many proteins and residues that are important for muscle assembly, function, and disease. In this article, we present a molecular-genetic characterization of a flightless mutation, flightless-H (fliH), originally designated as heldup-a (hdp-a). We show that fliH is a cis-regulatory mutation of the wings up A (wupA) gene, which codes for the troponin-I protein, one of the troponin complex proteins, involved in regulation of muscle contraction. The mutation leads to reduced levels of troponin-I transcript and protein. In addition to this, there is also coordinated reduction in transcript and protein levels of other structural protein isoforms that are part of the troponin complex. The altered transcript and protein stoichiometry ultimately culminates in unregulated acto-myosin interactions and a hypercontraction muscle phenotype. Our results shed new insights into the importance of maintaining the stoichiometry of structural proteins during muscle assembly for proper function with implications for the identification of mutations and disease phenotypes in other species, including humans.

Surface motions and intraplate continental deformation in Alaska driven by mantle flow

The degree to which the lithosphere and mantle are coupled and contribute to surface deformation beneath continental regions remains a fundamental question in the field of geodynamics. Here we use a new approach with a surface deformation field constrained by GPS, geologic, and seismicity data, together with a lithospheric geodynamic model, to solve for tractions inferred to be generated by mantle convection that (1) drive extension within interior Alaska generating southward directed surface motions toward the southern convergent plate boundary, (2) result in accommodation of the relative motions between the Pacific and North America in a comparatively small zone near the plate boundary, and (3) generate the observed convergence within the North American plate interior in the Mackenzie mountains in northwestern Canada. The evidence for deeper mantle influence on surface deformation beneath a continental region suggests that this mechanism may be an important contributing driver to continental plate assemblage and breakup.

Damage assessment of basaltic rock mass due to repeated blasting in a railway tunnelling project - A case study

The demand for tunnelling and underground space creation is rapidly growing due to the requirement of civil infrastructure projects and urbanisation. Blasting remains the most inexpensive method of underground excavations in hard rock. Unfortunately, there are no specific safety guidelines available for the blasted tunnels with regards to the threshold limits of vibrations caused by repeated blasting activity in the close proximity. This paper presents the results of a comprehensive study conducted to find out the effect of repeated blast loading on the damage experienced by jointed basaltic rock mass during tunnelling works. Conducting of multiple rounds of blasts for various civil excavations in a railway tunnel imparted repeated loading on rock mass of sidewall and roof of the tunnel. The blast induced damage was assessed by using vibration attenuation equations of charge weight scaling law and measured by borehole extensometers and borehole camera. Ground vibrations of each blasting round were also monitored by triaxial geophones installed near the borehole extensometers. The peak particle velocity (V-max) observations and plastic deformations from borehole extensometers were used to develop a site specific damage model. The study reveals that repeated dynamic loading imparted on the exposed tunnel from subsequent blasts, in the vicinity, resulted in rock mass damage at lesser vibration levels than the critical peak particle velocity (V-cr). It was found that, the repeated blast loading resulted in the near-field damage due to high frequency waves and far-field damage due to low frequency waves. The far field damage, after 45-50 occurrences of blast loading, was up to 55% of the near-field damage in basaltic rock mass. The findings of the study clearly indicate that the phenomena of repeated blasting with respect to number of cycles of loading should be taken into consideration for proper assessment of blast induced damage in underground excavations.

Certain Aspects Related To Computation By Modified Crack Closure Integral(MCCI)

This paper presents the proper computational approach for the estimation of strain energy release rates by modified crack closure integral (MCCI). In particular, in the estimation of consistent nodal force vectors used in the MCCI expressions for quarter-point singular elements (wherein all the nodal force vectors participate in computation of strain energy release rates by MCCI). The numerical example of a centre crack tension specimen under uniform loading is presented to illustrate the approach.