An algebraic formulation of static isotropy and design of statically isotropic 6-6 Stewart platform manipulators

In this paper, we present an algebraic method to study and design spatial parallel manipulators that demonstrate isotropy in the force and moment distributions. We use the force and moment transformation matrices separately, and derive conditions for their isotropy individually as well as in combination. The isotropy conditions are derived in closed-form in terms of the invariants of the quadratic forms associated with these matrices. The formulation is applied to a class of Stewart platform manipulator, and a multi-parameter family of isotropic manipulators is identified analytically. We show that it is impossible to obtain a spatially isotropic configuration within this family. We also compute the isotropic configurations of an existing manipulator and demonstrate a procedure for designing the manipulator for isotropy at a given configuration. (C) 2008 Elsevier Ltd. All rights reserved.

Algebraic distributed space-time codes with low ML decoding complexity

"Extended Clifford algebras" are introduced as a means to obtain low ML decoding complexity space-time block codes. Using left regular matrix representations of two specific classes of extended Clifford algebras, two systematic algebraic constructions of full diversity Distributed Space-Time Codes (DSTCs) are provided for any power of two number of relays. The left regular matrix representation has been shown to naturally result in space-time codes meeting the additional constraints required for DSTCs. The DSTCs so constructed have the salient feature of reduced Maximum Likelihood (ML) decoding complexity. In particular, the ML decoding of these codes can be performed by applying the lattice decoder algorithm on a lattice of four times lesser dimension than what is required in general. Moreover these codes have a uniform distribution of power among the relays and in time, thus leading to a low Peak to Average Power Ratio at the relays.

Geometry-free stochastic analysis of BDS triple frequency signals

The paper presents a geometry-free approach to assess the variation of covariance matrices of undifferenced triple frequency GNSS measurements and its impact on positioning solutions. Four independent geometryfree/ ionosphere-free (GFIF) models formed from original triple-frequency code and phase signals allow for effective computation of variance-covariance matrices using real data. Variance Component Estimation (VCE) algorithms are implemented to obtain the covariance matrices for three pseudorange and three carrier-phase signals epoch-by-epoch. Covariance results from the triple frequency Beidou System (BDS) and GPS data sets demonstrate that the estimated standard deviation varies in consistence with the amplitude of actual GFIF error time series. The single point positioning (SPP) results from BDS ionosphere-free measurements at four MGEX stations demonstrate an improvement of up to about 50% in Up direction relative to the results based on a mean square statistics. Additionally, a more extensive SPP analysis at 95 global MGEX stations based on GPS ionosphere-free measurements shows an average improvement of about 10% relative to the traditional results. This finding provides a preliminary confirmation that adequate consideration of the variation of covariance leads to the improvement of GNSS state solutions.

Inter-helical Interactions in Membrane Proteins: Analysis Based on the Local Backbone Geometry and the Side Chain Interactions

The availability of a significant number of the Structures of helical membrane proteins has prompted us to investigate the mode of helix-helix packing. In the present study, we have considered a dataset of alpha-helical membrane proteins representing Structures solved from all the known superfamilies. We have described the geometry of all the helical residues in terms of local coordinate axis at the backbone level. Significant inter-helical interactions have been considered as contacts by weighing the number of atom-atom contacts, including all the side-chain atoms. Such a definition of local axis and the contact criterion has allowed us to investigate the inter-helical interaction in a systematic and quantitative manner. We show that a single parameter (designated as alpha), which is derived from the parameters representing the Mutual orientation of local axes, is able to accurately Capture the details of helix-helix interaction. The analysis has been carried Out by dividing the dataset into parallel, anti-parallel, and perpendicular orientation of helices. The study indicates that a specific range of alpha value is preferred for interactions among the anti-parallel helices. Such a preference is also seen among interacting residues of parallel helices, however to a lesser extent. No such preference is seen in the case of perpendicular helices, the contacts that arise mainly due to the interaction Of Surface helices with the end of the trans-membrane helices. The Study Supports the prevailing view that the anti-parallel helices are well packed. However, the interactions between helices of parallel orientation are non-trivial. The packing in alpha-helical membrane proteins, which is systematically and rigorously investigated in this study, may prove to be useful in modeling of helical membrane proteins.

Simultaneous material selection and geometry design of statically determinate trusses using continuous optimization

In this work, we explore simultaneous geometry design and material selection for statically determinate trusses by posing it as a continuous optimization problem. The underlying principles of our approach are structural optimization and Ashby’s procedure for material selection from a database. For simplicity and ease of initial implementation, only static loads are considered in this work with the intent of maximum stiffness, minimum weight/cost, and safety against failure. Safety of tensile and compression members in the truss is treated differently to prevent yield and buckling failures, respectively. Geometry variables such as lengths and orientations of members are taken to be the design variables in an assumed layout. Areas of cross-section of the members are determined to satisfy the failure constraints in each member. Along the lines of Ashby’s material indices, a new design index is derived for trusses. The design index helps in choosing the most suitable material for any geometry of the truss. Using the design index, both the design space and the material database are searched simultaneously using gradient-based optimization algorithms. The important feature of our approach is that the formulated optimization problem is continuous, although the material selection from a database is an inherently discrete problem. A few illustrative examples are included. It is observed that the method is capable of determining the optimal topology in addition to optimal geometry when the assumed layout contains more links than are necessary for optimality.

Strong motion compatible source geometry

Strong motion array records are analyzed in this paper to identify and map the source zone of four past earthquakes. The source is represented as a sequence of double couples evolving as ramp functions, triggering at different instants, distributed in a region yet to be mapped. The known surface level ground motion time histories are treated as responses to the unknown double couples on the fault surface. The location, orientation, magnitude, and risetime of the double couples are found by minimizing the mean square error between analytical solution and instrumental data. Numerical results are presented for Chi-Chi, Imperial Valley, San Fernando, and Uttarakashi earthquakes. Results obtained are in good agreement with field investigations and those obtained from conventional finite fault source inversions.

Enhanced Ion Anisotropy by Nonconventional Coordination Geometry: Single-Chain Magnet Behavior for a [{(FeL)-L-II}(2){Nb-IV(CN)(8)}] Helical Chain Compound Designed with Heptacoordinate Fe-II

Nonconventional heptacoordination in combination with efficient magnetic exchange coupling is shown to yield a 1-D heteronuclear {(FeNbIV)-Nb-II} compound with remarkable magnetic features when compared to other Fe(II)-based single chain magnets (SCM). Cyano-bridged heterometallic {3d-4d} and {3d-5d} chains are formed upon assembling Fe(II) bearing a pentadentate macrocycle as the blocking ligand with octacyano metallates, [M(CN)(8)](4-) (M = Nb-IV, Mo-IV, W-IV.) X-ray diffraction (single-crystal and powder) measurements reveal that the [{(H2O)Fe(L-1)}{M(CN)(8)}{Fe(L-1)}](infinity) architectures consist of isomorphous 1-D polymeric structures based on the alternation of {Fe(L-1)}(2+) and {M(CN)(8)}(4-) units (L-1 stands for the pentadentate macrocycle). Analysis of the magnetic susceptibility behavior revealed cyano-bridged {Fe-Nb} exchange interaction to be antiferromagnetic with J = -20 cm(-1) deduced from fitting an Ising model taking into account the noncollinear spin arrangement. For this ferrimagnetic chain a slow relaxation of its magnetization is observed at low temperature revealing a SCM behavior with Delta/k(B) = 74 K and tau(0) = 4.6 x 10(-11) s. The M versus H behavior exhibits a hysteresis loop with a coercive field of 4 kOe at 1 K and reveals at 380 mK magnetic avalanche processes, i.e., abrupt reversals in magnetization as H is varied. The origin of these characteristics is attributed to the combination of efficient {Fe-Nb} exchange interaction and significant anisotropy of the {Fe(L-1)) unit. High field EPR and magnetization experiments have revealed for the parent compound [Fe(L-1)(H2O)(2)]Cl-2 a negative zero field splitting parameter of D approximate to -17 cm(-1). The crystal structure, magnetic behavior, and Mossbauer data for [Fe(L-1)(H2O)(2)]Cl-2 are also reported.

Enhanced Ion Anisotropy by Nonconventional Coordination Geometry: Single-Chain Magnet Behavior for a [{(FeL)-L-II}(2){Nb-IV(CN)(8)}] Helical Chain Compound Designed with Heptacoordinate Fe-II

Nonconventional heptacoordination in combination with efficient magnetic exchange coupling is shown to yield a 1-D heteronuclear {(FeNbIV)-Nb-II} compound with remarkable magnetic features when compared to other Fe(II)-based single chain magnets (SCM). Cyano-bridged heterometallic {3d-4d} and {3d-5d} chains are formed upon assembling Fe(II) bearing a pentadentate macrocycle as the blocking ligand with octacyano metallates, [M(CN)(8)](4-) (M = Nb-IV, Mo-IV, W-IV.) X-ray diffraction (single-crystal and powder) measurements reveal that the [{(H2O)Fe(L-1)}{M(CN)(8)}{Fe(L-1)}](infinity) architectures consist of isomorphous 1-D polymeric structures based on the alternation of {Fe(L-1)}(2+) and {M(CN)(8)}(4-) units (L-1 stands for the pentadentate macrocycle). Analysis of the magnetic susceptibility behavior revealed cyano-bridged {Fe-Nb} exchange interaction to be antiferromagnetic with J = -20 cm(-1) deduced from fitting an Ising model taking into account the noncollinear spin arrangement. For this ferrimagnetic chain a slow relaxation of its magnetization is observed at low temperature revealing a SCM behavior with Delta/k(B) = 74 K and tau(0) = 4.6 x 10(-11) s. The M versus H behavior exhibits a hysteresis loop with a coercive field of 4 kOe at 1 K and reveals at 380 mK magnetic avalanche processes, i.e., abrupt reversals in magnetization as H is varied. The origin of these characteristics is attributed to the combination of efficient {Fe-Nb} exchange interaction and significant anisotropy of the {Fe(L-1)) unit. High field EPR and magnetization experiments have revealed for the parent compound [Fe(L-1)(H2O)(2)]Cl-2 a negative zero field splitting parameter of D approximate to -17 cm(-1). The crystal structure, magnetic behavior, and Mossbauer data for [Fe(L-1)(H2O)(2)]Cl-2 are also reported.

Geometry changes induced by negative hyperconjugative interactions involving carbonyl and thiocarbonyl groups

MNDO geometry optimizations have been carried out on a series of acyclic and cyclic unsymmetrically disubstituted carbonyl and thiocarbonyl compounds. The C=X unit shows a consistent and often sizeable tilt towards one of the substituents, following the order O > Snot, vert, similarN > C > B. Reference ab initio calculations and available experimental results support the MNDO results. The effect, which is particularly dramatic in small rings, is attributed primarily to favorable negative hyperconjugative interaction between the lone pair on X and a low lying adjacent σ* orbital. Such an interaction can lead to highly distorted structures, including perhaps to a planar molecule with an inverted sp2 carbon center.

Sliding Modes for the Simulation of Mechanical and Electrical Systems Defined by Differential-Algebraic Equations

We offer a technique, motivated by feedback control and specifically sliding mode control, for the simulation of differential-algebraic equations (DAEs) that describe common engineering systems such as constrained multibody mechanical structures and electric networks. Our algorithm exploits the basic results from sliding mode control theory to establish a simulation environment that then requires only the most primitive of numerical solvers. We circumvent the most important requisite for the conventionalsimulation of DAEs: the calculation of a set of consistent initial conditions. Our algorithm, which relies on the enforcement and occurrence of sliding mode, will ensure that the algebraic equation is satisfied by the dynamic system even for inconsistent initial conditions and for all time thereafter. [DOI:10.1115/1.4001904]

An algebraic formulation of static isotropy and design of statically isotropic 6–6 Stewart platform manipulators

In this paper, we present an algebraic method to study and design spatial parallel manipulators that demonstrate isotropy in the force and moment distributions. We use the force and moment transformation matrices separately, and derive conditions for their isotropy individually as well as in combination. The isotropy conditions are derived in closed-form in terms of the invariants of the quadratic forms associated with these matrices. The formulation is applied to a class of Stewart platform manipulator, and a multi-parameter family of isotropic manipulators is identified analytically. We show that it is impossible to obtain a spatially isotropic configuration within this family. We also compute the isotropic configurations of an existing manipulator and demonstrate a procedure for designing the manipulator for isotropy at a given configuration.

Cross-field gas breakdown in a coaxial cylinder geometry

Sparking potentials in a coaxial cylinder geometry in oxygen and dry air were measured in crossed electric and magnetic fields. From the data effective collision frequencies were calculated using the equivalent pressure concept. It is shown that the equivalent pressure concept holds good for deriving the effective collision frequencies in non-uniform electric fields.

A standard reference frame for the description of Nucleic Acid Base-Pair Geometry

A common point of reference is needed to describe the three-dimensional arrangements of bases and base-pairs in nucleic acid structures. The different standards used in computer programs created for this purpose give rise to con¯icting interpretations of the same structure.1 For example, parts of a structure that appear ``normal'' according to one computational scheme may be highly unusual according to another and vice versa. It is thus dif®cult to carry out comprehensive comparisons of nucleic acid structures and to pinpoint unique conformational features in individual structures

HELANAL: A program to characterise helix geometry in proteins,

A detailed analysis of structural and position dependent characteristic features of helices will give a better understanding of the secondary structure formation in globular proteins. Here we describe an algorithm that quantifies the geometry of helices in proteins on the basis of their C-alpha atoms alone. The Fortran program HELANAL can extract the helices from the PDB files and then characterises the overall geometry of each helix as being linear, curved or kinked, in terms of its local structural features, viz. local helical twist and rise, virtual torsion angle, local helix origins and bending angles between successive local helix axes. Even helices with large radius of curvature are unambiguously identified as being linear or curved. The program can also be used to differentiate a kinked helix and other motifs, such as helix-loop-helix or a helix-turn-helix (with a single residue linker) with the help of local bending angles. In addition to these, the program can also be used to characterise the helix start and end as well as other types of secondary structures.

An Algebraic Implicitization and Specialization of Minimum KL-Divergence Models

In this paper we study representation of KL-divergence minimization, in the cases where integer sufficient statistics exists, using tools from polynomial algebra. We show that the estimation of parametric statistical models in this case can be transformed to solving a system of polynomial equations. In particular, we also study the case of Kullback-Csiszar iteration scheme. We present implicit descriptions of these models and show that implicitization preserves specialization of prior distribution. This result leads us to a Grobner bases method to compute an implicit representation of minimum KL-divergence models.