Rigidity

The presence of excessive EMG at "rest" might be an important factor in the genesis of Parkinson's disease (PD) rigidity, and we studied it in the first dorsal interosseous muscle (FDI) of 8 idiopathic PD patients. We had 8 age-and sex-matched normal controls. In the PD group, the average area of the surface EMG at "rest" correlated significantly with the clinical evaluation of rigidity and remained abnormally enhanced for lo-15 min after a command to "relax." Later, it tended to decline, but its entity was still much greater than in controls. The EMG "at rest" consisted of unwilled motor unit (MU) firing. A larger MU number was recruited in patients than in controls at "rest." MU rate coding was similar in both groups. Eventually, patients could get periods of EMG silence which, however, were interrupted by short EMG bursts, even if there was no muscle stretch. These bursts were interpreted as residual fragments of the original excessive EMG at "rest." MUs first recruited during such bursts showed high, but not total, overlapping with those first recruited by a gentle voluntary contraction or by a weak transcranial magnetic stimulus to motor cortex. We conclude that EMG activity at "rest" was made up of the discharge of low-threshold MUs, with a recruitment order similar to that resulting from descending cortico-spinal volleys. However, we cannot exclude other possible input sources to the cy-motoneurones at "rest."

A method is proposed for deriving dynamical equations for systems with both rigid and flexible components. During the derivation, each flexible component of the system is represented by a ``surrogate element'''' which captures the response characteristics of that component and is easy to mathematically manipulate. The derivation proceeds essentially as if each surrogate element were a rigid body. Application of an extended form of Lagrange''s equation yields a set of simultaneous differential equations which can then be transformed to be the exact, partial differential equations for the original flexible system. This method''s use facilitates equation generation either by an analyst or through application of software-based symbolic manipulation.

Postural instability has a big impact on the quality of life of patients with Parkinson's disease (PD) as it often leads to an insecure stance and fall. We investigated if postural stability in these patients improves by decreasing rigidity with a dopaminergic agonist.

Expanded polystyrene (EPS) geofoam seismic buffers can be used to reduce earthquake-induced loads acting on rigid retaining wall structures. A numerical study was carried out to investigate the influence of wall height; EPS geofoam type, thickness, and stiffness; and excitation record on seismic buffer performance. The numerical simulations were carried out using a verified FLAC code. The influence of parameter values was examined by computing the maximum forces on the walls, the buffer compressive strains, and the relative efficiency of the buffer system. In general, the closer the predominant frequency of excitation to the fundamental frequency of the wall model, the greater the seismic loads and buffer compression. The choice of earthquake record is shown to affect the magnitude of maximum earth force and isolation efficiency. However, when the wall response for walls 3 to 9 m in height are presented in this study in terms of isolation efficiency, the data from scaled accelerogra...

The displacement field for an edge dislocation in an Earth model consisting of • l•yer welded to • h•lf-sp•ce of different m•terial is found in the form of • Fourier integral following the method given by Weeks et al. [1968]. There are four elementary solutions to be considered: the dislocation is either in the half-space or the l•yer •nd the Burgers vector is either p•rallel or perpendicular to the layer. A general two-dimensional solution for • dip-slip faulting or dike injection (arbitrary dip) c•n be constructed from • superposition of these elementary solutions. Surface deformations h•ve been c•lcul•ted for •n edge dislocation located •t the interface with Burgers vector inclined 0 ø, 30 ø, 60 ø, •nd 90 ø to the interface for the case where the rigidity of the l•yer is h•lf of that of the half-space and the Poisson ratios •re the same. Those displacement fields h•ve been compared to the displacement fields generated by similarly situated edge dislocations in a uniform half-space.

The fact that natural language proper names are rigid designators is an empirical discovery about natural language. However, unlike other empirical discoveries about language made in the past few decades, it is one which has been taken to have great philosophical significance. One reason for this is that it helped simplify the formal semantical representation of ordinary modal discourse. But the central reason is that the discovery threatens a certain picture of the content of names, the descriptive picture, upon which a great deal of philosophy was premised.

Clinical diagnosis of Parkinson's disease (PD) is not always coincident with pathological findings. A better characterization of the disease from the results of studies in various areas of neuroscience can help in improving the rate of diagnostic certainty. Neurophysiology is among the techniques with better chances to furnish specific diagnostic cues on motor aspects of the disease. Neurophysiology provides quantifiable data using non-invasive, relatively inexpensive, methods. Neurophysiological tests can be applied with no previous preparation, and repeated many times without dangerous consequences. To be rewarding, however, neurophysiological examination should be done in close cooperation between the clinician who detects relevant specific signs, and the neurophysiologist who devises the most demonstrative methods to document those signs. In this review, we describe the neurophysiological correlate of symptoms and signs in patients with PD, and particularly their pathophysiological meaning, with special focus on those that could be more helpful to the neurologists in establishing differences with respect to other diseases presenting with parkinsonism. q

The conditions prevailing in the industrial applications in which enzymes are used are rather extreme, especially with respect to temperature and pH. Therefore, there is a continuing demand to improve the stability of enzymes and to meet the requirements set by specific applications. In this respect, thermostable enzymes have been proposed to be industrially relevant. In this review, α-amylase, a well-established representative of thermostable enzymes, providing an attractive model for the investigation of the structural basis of thermostability of proteins, has been discussed.

A verified fast Lagrangian analysis of continua (FLAC) numerical model is used to investigate the influence of horizontal toe stiffness on the performance of reinforced soil segmental retaining walls under working stress (operational) conditions. Results of full-scale shear testing of the interface between the bottom of a typical modular block and concrete or crushed stone levelling pads are used to back-calculate toe stiffness values. The results of numerical simulations demonstrate that toe resistance at the base of a reinforced soil segmental retaining wall can generate a significant portion of the resistance to horizontal earth loads in these systems. This partially explains why reinforcement loads under working stress conditions are typically overestimated using current limit equilibrium-based design methods. Other parameters investigated are wall height, interface shear stiffness between blocks, wall facing batter, reinforcement stiffness, and reinforcement spacing. Computed reinforcement loads are compared with predicted loads using the empirical-based K-stiffness method. The K-stiffness method predictions are shown to better capture the qualitative trends in numerical results and be quantitatively more accurate compared with the AASHTO simplified method.

This study uses a semi-analytical technique (the scaled boundary finite-element method) to evaluate the loaddisplacement response of rigid circular footings embedded in a non-homogeneous elastic half-space. Results are presented in terms of dimensionless elastic stiffness coefficients. The footings are subjected to vertical, horizontal, moment and torsional loads. The cross-coupling between the horizontal and moment load case is also evaluated. The variation of soil shear modulus with depth may correspond to normally consolidated sand or clay, and the footing geometries considered cover a range of footings commonly encountered in engineering practice.

Gelatin gels formed in D 2 O have greater rigidity than gels of equal concentration formed in H 2 O. In D 2 O the junction zones (regions of collagen triple helix structure) were smaller (i.e. involved fewer amino acid residues) than in H 2 O. The contribution per amino acid residue to the free energy of formation of junction zones was 2 0.51 kJ/mol in D 2 O compared with 2 0.34 kJ/mol in H 2 O, consistent with the fact that hydrogen bonds are stronger in D 2 O than in H 2 O. Gels formed in D 2 O also have higher melting temperatures (T m ) than corresponding gels formed in H 2 O. This increase in T m accounted for the faster rate of gelation in D 2 O compared with H 2 O. q

Optimal cross-section design of beams plays a distinctive role which involve the rigidity of the member in bending, shear and torsion load conditions. Practically modern overhead crane girders, railway bridge girders or rail tracks etc. require constant cross-section along the axial direction as the load location changes all the time. Conventional topological optimization modeling procedures in such cases prove inadequate for the reason that these procedures generate non-uniform topologies along the axis of the bending member. To examine optimal topology of those structural bending members which commonly possess constant cross-section along the axis the topology optimization with extrusion manufacturing constraint is more appropriate. The extrusion constraint method suggests a fresh approach to investigate optimal topologies of beam cross-section under the influence of realistic loading condition across the section and along the beam at the beginning of design cycle. Presented study is focused upon the influence of various configuration and location of the load and boundary conditions on the topology of the of the beam cross-section which was not possible prior to the materialization of the extrusion or stamping constraint methods in Optistuct and TOSCA. Several realistic loads and boundary conditions including moving load condition have been applied on the 3D beam model and optimal cross-section topologies obtained have uniform compliance history and convergent solutions. The lowest compliance criteria have been suggested to choose topologies for furthers shape and size optimization candidates during beam design process.

This article deals with the effect of cellulosic fiber from commercially available writing paper, bleached kraft pulp, and commercially available rice flour on the foaming of polyurethane based on polyol derived from soy bean oil. The presence of cellulosic materials was observed to have a notable influence on the density of the foams. Changes in the density of different foams were correlated with possible chemical structures generated in the presence of the fiber and were analyzed by Fourier transform infrared spectroscopy and thermogra-vimetric analysis. Furthermore, differential scanning calorimetry analysis was performed to lend support to possible changes in foaming behavior in the presence of refined fiber. Scanning electron microscopy observations were in line with the observation of structures generated in the presence of cellulosic fibers from different sources.

1] Using up to 11 years of data from a global network of Global Positioning System (GPS) stations, including 12 stations well distributed across the Pacific Plate, we derive present-day Euler vectors for the Pacific Plate more precisely than has previously been possible from space geodetic data. After rejecting on statistical grounds the velocity of one station on each of the Pacific and North American plates, we find that the quality of fit of the horizontal velocities of 11 Pacific Plate (PA) stations to the best fitting PA Euler vector is similar to the fit of 11 Australian Plate (AU) velocities to the AU Euler vector and $20% better than the fit of nine North American Plate (NA) velocities to the NA Euler vector. The velocities of stations on the Pacific and Australian Plates each fit a rigid plate model with an RMS residual of 0.4 mm/yr, while the North American velocities fit a rigid plate model with an RMS velocity of 0.6 mm/yr. Our best fitting PA/AU relative Euler vector is located $170 km southeast of the NUVEL-1A pole but is not significantly different at the 95% confidence level. It is also close (<70 km in position and <3% in rate) to a pole derived from transform faults identified from satellite altimetry, suggesting that the vector has not changed significantly over the past 3 Myr. Our relative Euler vector is also consistent with all known geological and geodetic evidence concerning the AU/PA plate boundary through New Zealand. The GPS sites offshore of southern California are presently moving 4-5 ± 1 mm/yr relative to predicted Pacific velocity, with their residual velocities in approximately the opposite direction to PA/NA relative motion. Likewise, the easternmost sites in South Island, New Zealand, are moving $3 ± 1 mm/yr relative to predicted Pacific velocity, with the residuals in approximately the opposite direction to PA/AU relative motion. These velocity residuals are in the same sense as predicted by elastic strain accumulation on known plate boundary faults but are of a significantly higher magnitude in both southern California and New Zealand, implying that the plate boundary zones in both regions are wider than previously believed.

This article explores Gareth Evans's idea that there are such things as descriptive names, i.e. referring expressions introduced by a definite description which have, unlike ordinary names, a descriptive content. Several ignored semantic and modal aspects of this idea are spelled out, including a hitherto little explored notion of rigidity, super-rigidity. The claim that descriptive names are (rigidified) descriptions, or abbreviations thereof, is rejected. It is then shown that Evans's theory leads to certain puzzles concerning the referential status of descriptive names and the evaluation of identity statements containing them. A tentative solution to these puzzles is suggested, which centres on the treatment of definite descriptions as referring expressions.

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Force and vision sensors provide complementary information, yet they are fundamentally different sensing modalities. This implies that traditional sensor integration techniques that require common data representations are not appropriate for combining the feedback from these two disparate sensor. In this paper, we introduce the concept of vision and force sensor resolvability as a means of comparing the ability of the two sensing modes to provide useful information during robotic manipulation tasks. By monitoring the resolvability of the two sensing modes with respect to the task, the information provided by the disparate sensors can be seamlessly assimilated during task execution. A nonlinear force/vision servoing algorithm that uses force and vision resolvability to switch between sensing modes is proposed. The advantages of the assimilation technique is demonstrated during contact transitions between a stiff manipulator and rigid environment, a system configuration that easily becomes unstable when force control alone is used. Experimental results show that robust contact transitions are made by the proposed nonlinear controller while simultaneously satisfying the conflicting task requirements of fast approach velocities, maintaining stability, minimizing impact forces, and suppressing bounce between contact surfaces. iv v

According to the New Theory of Reference, proper names (and indexicals) and natural kind terms are semantically similar to each other but crucially different from definite descriptions and “ordinary” predicates, respectively. New Theorists say that a name, unlike a definite description, is a directly referential nondescriptional rigid designator, which refers “without a mediation of the content” and is not functional (i.e. lacks a Carnapian intension). Natural kind terms, such as ‘horse’ and ‘water’, are held to have similar distinctions, in contrast to other predicates. However, the New Theory contains some problems related to reference, descriptionality, content and meaning. In view of these problems, it will be argued that the distinctive shared feature of proper names and natural kind terms, while technically corresponding to nonfunctionality, is to be explicated in terms of independence of possible worlds, rather than in terms of reference and content: natural kind terms are world-independent predicates, making “worldless” predications. Just as, say, ‘Elvis’ names Elvis even with respect to “Elvisless” worlds, or, rather, names Elvis independently of worlds, natural kind terms are in an important sense “worldless” as well: to talk about Elvis is to talk about him irrespective of moments of time and possible worlds, and is to talk about a human, also irrespective of moments and worlds, while it is not to talk about, say, a drug-addict irrespective of moments, nor about a singer irrespective of worlds. There is no genuinely timeless and worldless predication of the sort “Elvis is (was) bald”, but there is, it seems, such a predication “Elvis is (was) human”. This notion of independence of times and worlds is detached from those of descriptionality and content mediation.

In this research, the effect of CO 2 laser on various properties of polyester fabric specially dyeing was studied. Three disperse dyes of red, yellow, and blue were used and irradiation was performed before and after dyeing. To evaluate the color changes due to laser treatment, CIELAB DE Ã ab color difference values were calculated. The morphology of the irradiated surfaces was examined by scanning electron microscopy. Other properties including color fastness, bending rigidity, wettability, and crystal size were also examined. The results revealed that laser treatment had an increasing effect on the color difference value. Among the three laser parameters examined in this work, laser power had the strongest effect. While no significant color fastness improvement with low laser intensity was observed, high-intensity laser irradiation increased the light and rubbing fastness. Properties such as wettability and bending rigidity were negatively affected by an increase in laser intensity.

Given a metric continuum X, we consider the following hyperspaces of X: 2 X , Cn(X) and Fn(X) (n ∈ N). Let F 1 (X) = {{x} : x ∈ X}. A hyperspace K(X) of X is said to be rigid, provided that for every homeomorphism h : K(X) → K(X), we have h(F 1 (X)) = F 1 (X). In this paper, we study conditions under which a continuum X has a rigid hyperspace Cn(X). Among others, we consider families of continua, such as dendroids, Peano continua, hereditarily indecomposable continua and smooth fans.

Conventional methods of tectonic zoning are frequently characterized by two deficiencies. The first one is the large uncertainty involved in tectonic zoning based on non-quantitative and subjective analysis. Failure to interpret accurately a large amount of data ''by eye'' is the second. In order to alleviate each of these deficiencies, the multivariate statistical method of cluster analysis has been utilized to seek and separate zones with similar tectonic pattern and construct automated self-organized multivariate tectonic zoning maps. This analytical method of tectonic regionalization is particularly useful for showing trends in tectonic evolution of a region that could not be discovered by any other means. To illustrate, this method has been applied for producing a general-purpose numerical tectonic zoning map of Iran. While there are some similarities between the self-organized multivariate numerical maps and the conventional maps, the cluster solution maps reveal some remarkable features that cannot be observed on the current tectonic maps. The following specific examples need to be noted: (1) The much disputed extent and rigidity of the Lut Rigid Block, described as the microplate of east Iran, is clearly revealed on the self-organized numerical maps. (2) The cluster solution maps reveal a striking similarity between this microplate and the northern Central Iran-including the Great Kavir region. (3) Contrary to the conventional map, the cluster solution maps make a clear distinction between the East Iranian Ranges and the Makran Mountains. (4) Moreover, an interesting similarity between the Azarbaijan region in the northwest and the Makran Mountains in the southeast and between the Kopet Dagh Ranges in the northeast and the Zagros Folded Belt in the southwest of Iran are revealed in the clustering process. This new approach to tectonic zoning is a starting point and is expected to be improved and refined by collection of new data. The method is also a useful tool in studying neotectonics, seismotectonics, seismic zoning, and hazard estimation of the seismogenic regions. r

The objective of the present work is to develop empirical models to predict end-use properties of poly(ethylene/propylene) resins as functions of more fundamental molecular and morphological properties of the polymer resins. The final properties analyzed are two mechanical properties, rigidity and impact strength, and one thermal property, glass transition temperature. Two additional properties of practical importance are also modeled: the melt index and the xylene soluble content. Molecular and morphological properties selected for resin characterization are molecular weight distribution, polymer composition, degree of crystallinity, spherulite size distribution and rubbery phase dispersion. End-use, molecular and morphological properties were evaluated experimentally for 19 different commercial polypropylene copolymer grades. Statistical correlation analysis was performed for all variables and used as the basis for proper choice of inputs to each output model. Models developed are able to reproduce and predict experimental data within experimental accuracy and show that both polymerization and final resin processing variables may be of fundamental importance for definition of the final property balance of the polymer material.

Neurotypical individuals cope flexibly with the full range of semantic relations expressed in human language, including metaphoric relations. This impressive semantic ability may be associated with distinct and flexible patterns of hemispheric interaction, including higher right hemisphere (RH) involvement for processing novel metaphors. However, this ability may be impaired in specific clinical conditions, such as Asperger syndrome (AS) and schizophrenia. The impaired semantic processing is accompanied by different patterns of hemispheric interaction during semantic processing, showing either reduced (in Asperger syndrome) or excessive (in schizophrenia) RH involvement. This paper interprets these individual differences using the terms Rigidity, Chaos and Integration, which describe patterns of semantic memory network states that either lead to semantic well-being or are disruptive of it. We argue that these semantic network states lie on a rigidity-chaos semantic continuum. We define these terms via network science terminology and provide network, cognitive and neural evidence to support our claim. This continuum includes left hemisphere (LH) hyper-rigid semantic memory state on one end (e.g., in persons with AS), and RH chaotic and over-flexible semantic memory state on the other end (e.g., in persons
with schizophrenia). In between these two extremes lie different states of semantic
memory structure which are related to individual differences in semantic creativity.
We suggest that efficient semantic processing is achieved by semantic integration, a
balance between semantic rigidity and semantic chaos. Such integration is achieved
via intra-hemispheric communication. However, impairments to this well-balanced and
integrated pattern of hemispheric interaction, e.g., when one hemisphere dominates the
other, may lead to either semantic rigidity or semantic chaos, moving away from semantic integration and thus impairing the processing of metaphoric language.

Proper estimation of soil reinforcement loads and strains is key to accurate internal stability design of reinforced soil structures. Current design methodologies use limit equilibrium concepts to estimate reinforcement loads for internal stability design of geosynthetic and steel reinforced soil walls. For geosynthetic walls, however, it appears that these methods are excessively conservative based on the performance of geosynthetic walls to date. This paper presents a new method, called the K-stiffness method, that is shown to give more accurate estimates of reinforcement loads, thereby reducing reinforcement quantities and improving the economy of geosynthetic walls. The paper is focused on the new method as it applies to geosynthetic walls constructed with granular (noncohesive, relatively low silt content) backfill soils. A database of 11 full-scale geosynthetic walls was used to develop the new design methodology based on working stress principles. The method considers the sti...

There is a certain popular argument, deriving from Ruth Barcan and Saul Kripke, from the conjunction of the Principle of the Indiscernibility of Identicals (PInI, for short) and the Principle of the Necessity of Self-Identity to the Thesis of the Necessity of Identity. My purpose is to show that this argument does not work, at least not in the form it is often presented. I also give a correct formulation of the argument and point out that PInI is not even needed in the argument for the necessity of identity.

It is conjectured that a certain rigidity property of a triple of primes (p 1 , p 2 , p 3 ) in an algebraic group G limits the number of corresponding finite simple groups of Lie type which can be (p 1 , p 2 , p 3 )-generated. Further, in linear groups this rigidity property has been linked to a concept of rigid class tuples.

Neurotypical individuals cope flexibly with the full range of semantic relations expressed in human language, including metaphoric relations. This impressive semantic ability may be associated with distinct and flexible patterns of hemispheric interaction, including higher right hemisphere (RH) involvement for processing novel metaphors. However, this ability may be impaired in specific clinical conditions, such as Asperger syndrome (AS) and schizophrenia. The impaired semantic processing is accompanied by different patterns of hemispheric interaction during semantic processing, showing either reduced (in Asperger syndrome) or excessive (in schizophrenia) RH involvement. This paper interprets these individual differences using the terms Rigidity, Chaos and Integration, which describe patterns of semantic memory network states that either lead to semantic well-being or are disruptive of it. We argue that these semantic network states lie on a rigidity-chaos semantic continuum. We define these terms via network science terminology and provide network, cognitive and neural evidence to support our claim. This continuum includes left hemisphere (LH) hyper-rigid semantic memory state on one end (e.g., in persons with AS), and RH chaotic and over-flexible semantic memory state on the other end (e.g., in persons with schizophrenia). In between these two extremes lie different states of semantic memory structure which are related to individual differences in semantic creativity. We suggest that efficient semantic processing is achieved by semantic integration, a balance between semantic rigidity and semantic chaos. Such integration is achieved via intra-hemispheric communication. However, impairments to this well-balanced and integrated pattern of hemispheric interaction, e.g., when one hemisphere dominates the other, may lead to either semantic rigidity or semantic chaos, moving away from semantic integration and thus impairing the processing of metaphoric language.

Spacecraft periodic-disturbance rejection using a realistic spacecraft hardware simulator and its associated models is investigated. The effectiveness of the dipole-type disturbance rejection filter on the current realistic nonlinear rigid-body spacecraft model is validated. However, it is shown that the rejection filter is not robust to disturbance frequency uncertainty. Therefore, system identification techniques are needed if the disturbance frequency is unknown or changing. Based on experience with the current test bed, two simple closed-loop system identification methods are introduced to experimentally identify the disturbance frequency using data from the control input torque signal. It is shown that an incorrect filter frequency results in beating of the control input torque. Examination of the beat envelope leads to tuning of the rejection filter.

Citrate synthase (CS) catalyses the entry of carbon into the citric acid cycle and is highlyconserved structurally across the tree of life. Crystal structures of dimeric CSs are known in both "open" and "closed" forms, which differ by a substantial domain motion that closes the substrate-binding clefts. We explore both the static rigidity and the dynamic flexibility of CS structures from mesophilic and extremophilic organisms from all three evolutionary domains. The computational expense of this wide-ranging exploration is kept to a minimum by the use of rigidity analysis and rapid all-atom simulations of flexible motion, combining geometric simulation and elastic network modelling. CS structures from thermophiles display increased

Panarchy theory has been utilized to first conceptualize the entrenched conflict that lasted for nearly 30 years between Aceh and Indonesia and second, the development of peace prior to and shortly following the tsunami of 2004. The purpose of this paper is to show how panarchy or complex adaptive systems theory can be used to explain the previous
state of the Aceh-Indonesia conflict as a sustained maladaptive system and how it was eventually changed into an adaptive system harboring the potential for peaceful sustainability. There are four main questions that this thesis answers. First, how can the Aceh-Indonesia conflict be explained as a rigidity trap? Second, what were the main elements or inputs from cyclical systems below or above the Aceh-Indonesia conflict
scale that led to the collapse of the rigidity trap and the generation of a healthy or complex adaptive system? Third, what role, if any, did the tsunami of December 2004 play in achieving the peace of the new complex adaptive system and fourth, what elements or inputs into the new healthy system may or may not lead to the systems peaceful sustainability? The conflict and the peace achieved between the two former antagonists appears to be an example of a maladapted cyclical socio-economic and political rigidity trap that was acted upon by new inputs from cyclical scales above the Aceh-Indonesia conflict scale. It is thought that this is the first time panarchy theory has been applied to an aspect of conflict transformation modeling. It is hoped that this initial 4 attempt will encourage others to test panarchy theory; maladaptive and adaptive system models, in the field of conflict transformation.

The floating frame of reference formulation is currently the most widely used approach in flexible multibody simulations. The use of this approach, however, has been limited to small deformation problems. In this investigation, the computer implementation of the newabsolute nodal co-ordinate formulationand its use in the small and large deformation analysis of flexible multibody systems that consist of interconnected bodies are discussed. While in the floating frame of reference formulation a mixed set of absolute reference and local elastic co-ordinates are used, in the absolute nodal co-ordinate formulation only absolute co-ordinates are used. In the absolute nodal co-ordinate formulation, new interpretation of the nodal co-ordinates of the finite elements is used. No infinitesimal or finite rotations are used as nodal co-ordinates from beams and plates, instead, global slopes are used to define the element nodal co-ordinates. Using this interpretation of the element co-ordinates, beams and plates can be considered as isoparametric elements, and as a result, exact modelling of the rigid body dynamics can be obtained using the element shape function and the absolute nodal co-ordinates. Unlike the floating frame of reference approach, no co-ordinate transformation is required in order to determine the element inertia. The mass matrix of the finite elements is a constant matrix, and therefore, the centrifugal and Coriolis forces are equal to zero when the absolute nodal co-ordinate formulation is used. Another advantage of using the absolute nodal co-ordinate formulation in the dynamic simulation of multibody systems is its simplicity in imposing some of the joint constraints and also its simplicity in formulating the generalized forces due to spring-damper elements. The results obtained in this investigation show an excellent agreement with the results obtained using the floating frame of reference formulation when large rotation–small deformation problems are considered.

Let (M n , g), n 3, be a smooth closed Riemannian manifold with positive scalar curvature R g . There exists a positive constant C = C(M, g) defined by mean curvature of Euclidean isometric immersions, which is a geometric invariant, such that R g n(n − 1)C. In this paper we prove that R g = n(n − 1)C if and only if (M n , g) is isometric to the Euclidean sphere S n (C) with constant sectional curvature C. Also, there exists a Riemannian metric g on M n such that the scalar curvature satisfies the pinched condition n 2 (n − 2)

Observations, experiments and simulations often generate large numbers of snapshots of configurations of complex many-body systems. It is important to find methods of extracting useful information from these ensembles of snapshots in order to document the motion as the system evolves in time. Some of the most interesting information is contained in the relative motion of individual constituents, rather than their absolute motion. We present a novel statistical method for identifying hierarchies of plastically connected objects in a system from a series of two or more snapshot configurations. These plastic clusters are distinctive in that although their members tend to remain loosely connected, the clusters may be deformed plastically. This method is demonstrated for a number of systems, including an exactly soluble freely jointed polymer chain model, a two-dimensional simulation of two species of interacting bodies and a protein. These concepts are implemented as TIMME, the Tool for Identifying Mobility in Macromolecular Ensembles.