An eigenproblem approach to classical screw theory

This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general two-, three-systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. We also present novel methods for the determination of the principal screws for four-, five-systems which do not require the explicit computation of the reciprocal systems. Principal screws of the systems of different orders are identified from one uniform criterion, namely that the pitches of the principal screws are the extreme values of the pitch.The classical results of screw theory, namely the equations for the cylindroid and the pitch-hyperboloid associated with the two-and three-systems, respectively have been derived within the proposed framework. Algebraic conditions have been derived for some of the special screw systems. The formulation is also illustrated with several examples including two spatial manipulators of serial and parallel architecture, respectively.

Classical screw theory: A fresh look using dual eigenvalue approach

This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general screw systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. The formulation is illustrated with examples of practical manipulators.

Architecture Optimization of Aerospace Computing Systems

Simultaneous consideration of both performance and reliability issues is important in the choice of computer architectures for real-time aerospace applications. One of the requirements for such a fault-tolerant computer system is the characteristic of graceful degradation. A shared and replicated resources computing system represents such an architecture. In this paper, a combinatorial model is used for the evaluation of the instruction execution rate of a degradable, replicated resources computing system such as a modular multiprocessor system. Next, a method is presented to evaluate the computation reliability of such a system utilizing a reliability graph model and the instruction execution rate. Finally, this computation reliability measure, which simultaneously describes both performance and reliability, is applied as a constraint in an architecture optimization model for such computing systems. Index Terms-Architecture optimization, computation

Structural mobility and transformations in globular proteins

Although globular proteins are endowed with well defined three-dimensional structures, they exhibit substantial mobility within the framework of the given threedimensional structure. The different types of mobility found in proteins by and large correspond to the different levels of organisational hierarchy in protein architecture. They are of considerable structural and functional significance, and can be broadly classified into(a) thermal and conformational fluctuations, (b) segmental mobility, (c) interdomain mobility and (d) intersubunit mobility. Protein crystallographic studies has provided a wealth of information on all of them. The temperature factors derived from X-ray diffraction studies provide a measure of atomic displacements caused by thermal and conformational fluctuations. The variation of displacement along the polypeptide chain have provided functionally significant information on the flexibility of different regions of the molecule in proteins such as myoglobin, lysozyme and prealbumin. Segmental mobility often involves the movement of a region or a segment of a molecule with respect to the rest, as in the transition between the apo and the holo structures of lactate dehydrogenase. It may also involve rigidification of a disordered region of the molecule as in the activation of the zymogens of serine proteases. Transitions between the apo and the holo structures of alcohol dehydrogenase,and between the free and the sugar bound forms of hexokinase, are good examples of interdomain mobility caused by hinge-bending. The capability of different domains to move semi-independently contributes greatly to the versatility of immunoglobulin molecules. Interdomain mobility in citrate synthase appears to be more complex and its study has led to an alternative description of domain closure. The classical and the most thoroughly studied case of intersubunit mobility is that in haemoglobin. The stereochemical mechanism of the action of this allosteric protein clearly brings out the functional subtilities that could be achieved through intersubunit movements. In addition to ligand binding and activation,environmental changes also often cause structural transformations. The reversible transformation between 2 Zn insulin and 4 Zn insulin is caused by changes in the ionic strength of the medium. Adenylate Kinase provides a good example for functionally significant reversible conformational transitions induced by variation in pH. Available evidences indicate that reversible structural transformations in proteins could also be caused by changes in the aqueous environment, including those in the amount of water surrounding protein molecules.

Transient state work fluctuation theorem for a classical harmonic oscillator linearly coupled to a harmonic bath

Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is not restricted only to the Ohmic bath, rather it is more general, for a non-Ohmic bath. We also derive expressions of the average work done and the variance of the work done in terms of the two-time correlation function of the fluctuations of the position of the harmonic oscillator. In the case of an Ohmic bath, we use these relations to evaluate the average work done and the variance of the work done analytically and verify the transient state work fluctuation theorem quantitatively. Actually these relations have far-reaching consequences. They can be used to numerically evaluate the average work done and the variance of the work done in the case of a non-Ohmic bath when analytical evaluation is not possible.

Classical and Cosserat plasticity and viscoplasticity models for slow granular flow

We consider models for the rheology of dense, slowly deforming granular materials based of classical and Cosserat plasticity, and their viscoplastic extensions that account for small but finite particle inertia. We determine the scale for the viscosity by expanding the stress in a dimensionless parameter that is a measure of the particle inertia. We write the constitutive relations for classical and Cosserat plasticity in stress-explicit form. The viscoplastic extensions are made by adding a rate-dependent viscous stress to the plasticity stress. We apply the models to plane Couette flow, and show that the classical plasticity and viscoplasticity models have features that depart from experimental observations; the prediction of the Cosserat viscoplasticity model is qualitatively similar to that of Cosserat plasticity, but the viscosities modulate the thickness of the shear layer.

NMR relaxation study of disorder in the mixed system BP x GPI(1-x) and the low temperature transition from classical to quantum rotation

1H NMR spin-lattice relaxation time (T1) studies have been carried out in the temperature range 100 K to 4 K, at two Larmor frequencies 11.4 and 23.3 MHz, in the mixed system of betaine phosphate and glycine phosphite (BPxGPI(1-x)), to study the effects of disorder on the proton group dynamics. Analysis of T1 data indicates the presence of a number of inequivalent methyl groups and a gradual transition from classical reorientations to quantum tunneling rotations. At lower temperatures, microstructural disorder in the local environments of the methyl groups, result in a distribution in the activation energy (Ea) and the torsional energy gap (E01). For certain values of x, the magnetisation recovery shows biexponential behaviour at lower temperatures.

Classical Langevin dynamics of a charged particle moving on a sphere and diamagnetism: A surprise

It is generally known that the orbital diamagnetism of a classical system of charged particles in thermal equilibrium is identically zero —the Bohr-van Leeuwen theorem. Physically, this null result derives from the exact cancellation of the orbital diamagnetic moment associated with the complete cyclotron orbits of the charged particles by the paramagnetic moment subtended by the incomplete orbits skipping the boundary in the opposite sense. Motivated by this crucial but subtle role of the boundary, we have simulated here the case of a finite but unbounded system, namely that of a charged particle moving on the surface of a sphere in the presence of an externally applied uniform magnetic field. Following a real space-time approach based on the classical Langevin equation, we have computed the orbital magnetic moment that now indeed turns out to be non-zero and has the diamagnetic sign. To the best of our knowledge, this is the first report of the possibility of finite classical diamagnetism in principle, and it is due to the avoided cancellation.

An RNS based transform Architecture for H.264/AVC

This paper presents the architecture and the VHDL design of an integer 2-D DCT used in the H.264/AVC. The 2-D DCT computation is performed by exploiting it’s orthogonality and separability property. The symmetry of the forward and inverse transform is used in this implementation. To reduce the computation overhead for the addition, subtraction and multiplication operations, we analyze the suitability of carry-free position independent residue number system (RNS) for the implementation of 2-D DCT. The implementation has been carried out in VHDL for Altera FPGA. We used the negative number representation in RNS, bit width analysis of the transforms and dedicated registers present in the Logic element of the FPGA to optimize the area. The complexity and efficiency analysis show that the proposed architecture could provide higher through-put.

A multi-microprocessor architecture for solving partial differential equations

This paper presents the architecture of a fault-tolerant, special-purpose multi-microprocessor system for solving Partial Differential Equations (PDEs). The modular nature of the architecture allows the use of hundreds of Processing Elements (PEs) for high throughput. Its performance is evaluated by both analytical and simulation methods. The results indicate that the system can achieve high operation rates and is not sensitive to inter-processor communication delay.

A Novel Cache Architecture and Placement Framework for Packet Forwarding Engines

Packet forwarding is a memory-intensive application requiring multiple accesses through a trie structure. With the requirement to process packets at line rates, high-performance routers need to forward millions of packets every second with each packet needing up to seven memory accesses. Earlier work shows that a single cache for the nodes of a trie can reduce the number of external memory accesses. It is observed that the locality characteristics of the level-one nodes of a trie are significantly different from those of lower level nodes. Hence, we propose a heterogeneously segmented cache architecture (HSCA) which uses separate caches for level-one and lower level nodes, each with carefully chosen sizes. Besides reducing misses, segmenting the cache allows us to focus on optimizing the more frequently accessed level-one node segment. We find that due to the nonuniform distribution of nodes among cache sets, the level-one nodes cache is susceptible t high conflict misses. We reduce conflict misses by introducing a novel two-level mapping-based cache placement framework. We also propose an elegant way to fit the modified placement function into the cache organization with minimal increase in access time. Further, we propose an attribute preserving trace generation methodology which emulates real traces and can generate traces with varying locality. Performanc results reveal that our HSCA scheme results in a 32 percent speedup in average memory access time over a unified nodes cache. Also, HSC outperforms IHARC, a cache for lookup results, with as high as a 10-fold speedup in average memory access time. Two-level mappin further enhances the performance of the base HSCA by up to 13 percent leading to an overall improvement of up to 40 percent over the unified scheme.

Parallel polygon scan conversion algorithms: Performance evaluation on a shared bus architecture

In this paper, three parallel polygon scan conversion algorithms have been proposed, and their performance when executed on a shared bus architecture has been compared. It has been shown that the parallel algorithm that does not use edge coherence performs better than those that use edge coherence. Further, a multiprocessing architecture has been proposed to execute the parallel polygon scan conversion algorithms more efficiently than a single shared bus architecture.

Metal-organic framework structures - how closely are they related to classical inorganic structures?

Metal-organic frameworks (MOFs) have emerged as an important family of compounds for which new properties are increasingly being found. The potential for such compounds appears to be immense, especially in catalysis, sorption and separation processes. In order to appreciate the properties and to design newer frameworks it is necessary to understand the structures from a fundamental perspective. The use of node, net and vertex symbols has helped in simplifying some of the complex MOF structures. Many MOF structures are beginning to be described as derived from inorganic structures. In this tutorial review, we have provided the basics of the node, the net and the vertex symbols and have explained some of the MOF structures. In addition, we have also attempted to provide some leads towards designing newer structures/topologies.

Non-Abelian monopoles break color. I. Classical mechanics

Monopoles which are sources of non-Abelian magnetic flux are predicted by many models of grand unification. It has been argued elsewhere that a generic transformation of the "unbroken" symmetry group H cannot be globally implemented on such monopoles for reasons of topology. In this paper, we show that similar topological obstructions are encountered in the mechanics of a test particle in the field of these monopoles and that the transformations of H cannot all be globally implemented as canonical transformations. For the SU(5) model, if H is SU(3)C×U(1)em, a consequence is that color multiplets are not globally defined, while if H is SU(3)C×SU(2)WS×U(1)Y, the same is the case for both color and electroweak multiplets. There are, however, several subgroups KT, KT′,… of H which can be globally implemented, with the transformation laws of the observables differing from group to group in a novel way. For H=SU(3)C×U(1)em, a choice for KT is SU(2)C×U(1)em, while for H=SU(3)C×SU(2)WS×U(1)Y, a choice is SU(2)C×U(1)×U(1)×U(1). The paper also develops the differential geometry of monopoles in a form convenient for computations.

Classical solitons with no quantum counterparts and their supersymmetric revival

We demonstrate the phenomenon stated in the title, using for illustration a two-dimensional scalar-field model with a triple-well potential {fx837-1}. At the classical level, this system supports static topological solitons with finite energy. Upon quantisation, however, these solitons develop infinite energy, which cannot be renormalised away. Thus this quantised model has no soliton sector, even though classical solitons exist. Finally when the model is extended supersymmetrically by adding a Majorana field, finiteness of the soliton energy is recovered.