An investigation into the mechanics of cutting using data from orthogonally cutting Nylon 66

Cutting force data for Nylon 66 has been examined in terms of various different models of cutting. Theory that includes significant work of separation at the tool tip was found to give the best correlation with experimental data over a wide range of rake angles for derived primary shear plane angle. A fracture toughness parameter was used as the measure of the specific work of separation. Variation in toughness with rake angle determined from cutting is postulated to be caused by mixed mode separation at the tool tip. A rule of mixtures using independently determined values of toughness in tension (mode 1) and shear (mode 11) is found to describe well the variation with rake angle. The ratio of modes varies with rake angle and, in turn, with the primary shear plane angle. Previous suggestions that cutting is a means of experimentally determining fracture toughness are now seen to be extended to identify the mode of fracture toughness as well.

Quantum mechanics studies of the tautomers of diacetylformoin, an important maillard product and odorant

Diacetylformoin (3,4-dihydroxy-3-hexene-2,5-dione) has 16 tautomers, many with several possible conformations and all have been geometry optimised using quantum mechanics at the HF/6-31+G* level. Eleven structures have been identified with energies within 10 kcal mol(-1) of the minimum energy structure. Of these eight are acyclic and three cyclic. Calculations of NMR spectra have clarified the identity of the acyclic and cyclic structures found experimentally. The mechanism for cyclisation has been investigated and transition states obtained. The lowest energy reaction path requires the loss and gain of a proton during cyclisation. (c) 2006 Elsevier B.V. All rights reserved.

Design of redundant drive joint with adjustable stiffness and damping mechanism to improve joint admittance

Improving admittance of robotic joints is the key issue for making rehabilitation robots safe. This paper describes a design of Redundant Drive Joint (RD-Joint) which allows greater flexibility in the design of robotic mechanisms. The design strategy of the RD-Joint employs a systematic approach which consists of 1) adopting a redundant joint mechanism with internal kinematical redundancy to reduce effective joint inertia, and 2) adopting an adjustable admittance mechanism with a novel Cross link Reduction Mechanism and mechanical springs and dampers as a passive second actuator. First, the basic concepts used to construct the redundant drive joint mechanism are explained, in particular the method that allows a reduction in effective inertia at the output joint. The basic structure of the RD-Joint is introduced based on the idea of reduced inertia along with a method to include effective stiffness and damping. Then, the basic design of the adjustable admittance mechanism is described. Finally, a prototype of RD-joint is described and its expected characteristics are discussed.

Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.

Models, moulds and mass production: the mechanics of stylistic influence form the Mediterranean to Bactria

Classical Greek and Roman influence on the material culture of Central Asia and northwestern India is often considered in the abstract. This article attempts to examine the mechanisms of craft production and movement of artisans and objects which made such influence possible, through four case studies: (1) Mould-made ceramics in Hellenistic eastern Bactria; (2) Plaster casts used in the production of metalware from Begram; (3) Terracotta figurines and the moulds used to produce them, from various archaeological sites; and (4) Mass production of identical gold adornments in the nomadic tombs from Tillya Tepe. The implications of such techniques for our understanding of the development of Gandhāran art are also discussed.

On the approximation of local and linear radiative damping in the middle atmosphere

The validity of approximating radiative heating rates in the middle atmosphere by a local linear relaxation to a reference temperature state (i.e., ‘‘Newtonian cooling’’) is investigated. Using radiative heating rate and temperature output from a chemistry–climate model with realistic spatiotemporal variability and realistic chemical and radiative parameterizations, it is found that a linear regressionmodel can capture more than 80% of the variance in longwave heating rates throughout most of the stratosphere and mesosphere, provided that the damping rate is allowed to vary with height, latitude, and season. The linear model describes departures from the climatological mean, not from radiative equilibrium. Photochemical damping rates in the upper stratosphere are similarly diagnosed. Threeimportant exceptions, however, are found.The approximation of linearity breaks down near the edges of the polar vortices in both hemispheres. This nonlinearity can be well captured by including a quadratic term. The use of a scale-independentdamping rate is not well justified in the lower tropical stratosphere because of the presence of a broad spectrum of vertical scales. The local assumption fails entirely during the breakup of the Antarctic vortex, where large fluctuations in temperature near the top of the vortex influence longwave heating rates within the quiescent region below. These results are relevant for mechanistic modeling studies of the middle atmosphere, particularly those investigating the final Antarctic warming.

An ‘ideal’ form of decaying two-dimensional turbulence

In decaying two-dimensional Navier-Stokes turbulence, Batchelor's similarity hypothesis fails due to the existence of coherent vortices. However, it is shown that decaying two-dimensional turbulence governed by the Harney-Hasegawa-Mima (CHM) equation ∂/∂t (V^2 φ-λ^2 φ)+J(φ,∇^2 φ)=D where D is a damping, is described well by Batchelor's similarity hypothesis for wave numbers k ≪ λ (the so-called AM regime). It is argued that CHM turbulence in the AM regime is a more `ideal' form of two-dimensional turbulence than is Navier-Stokes turbulence itself.

The physical pendulum in an advanced undergraduate course in mechanics

The physical pendulum treated with a Hamiltonian formulation is a natural topic for study in a course in advanced classical mechanics. For the past three years, we have been offering a series of problem sets studying this system numerically in our third-year undergraduate courses in mechanics. The problem sets investigate the physics of the pendulum in ways not easily accessible without computer technology and explore various algorithms for solving mechanics problems. Our computational physics is based on Mathematica with some C communicating with Mathematica, although nothing in this paper is dependent on that choice. We have nonetheless found this system, and particularly its graphics, to be a good one for use with undergraduates.

Lower-stratospheric radiative damping and polar-night jet oscillation events

The effect of stratospheric radiative damping time scales on stratospheric variability and on stratosphere–troposphere coupling is investigated in a simplified global circulation model by modifying the vertical profile of radiative damping in the stratosphere while holding it fixed in the troposphere. Perpetual-January conditions are imposed, with sinusoidal topography of zonal wavenumber 1 or 2. The depth and duration of the simulated sudden stratospheric warmings closely track the lower-stratospheric radiative time scales. Simulations with the most realistic profiles of radiative damping exhibit extended time-scale recoveries analogous to polar-night jet oscillation (PJO) events, which are observed to follow sufficiently deep stratospheric warmings. These events are characterized by weak lower-stratospheric winds and enhanced stability near the tropopause, which persist for up to 3 months following the initial warming. They are obtained with both wave-1 and wave-2 topography. Planetary-scale Eliassen–Palm (EP) fluxes entering the vortex are also suppressed, which is in agreement with observed PJO events. Consistent with previous studies, the tropospheric jets shift equatorward in response to the warmings. The duration of the shift is closely correlated with the period of enhanced stability. The magnitude of the shift in these runs, however, is sensitive only to the zonal wavenumber of the topography. Although the shift is sustained primarily by synoptic-scale eddies, the net effect of the topographic form drag and the planetary-scale fluxes is not negligible; they damp the surface wind response but enhance the vertical shear. The tropospheric response may also reduce the generation of planetary waves, further extending the stratospheric dynamical time scales.

The effect of non-uniform radiative damping on the zonal-mean dynamics of the extratropical middle atmosphere

The effect of spatial and temporal variations in the radiative damping rate on the response to an imposed forcing or diabatic heating is examined in a zonal-mean model of the middle atmosphere. Attention is restricted to the extratropics, where a linear approach is viable. It is found that regions with weak radiative damping rates are more sensitive in terms of temperature to the remote influence of the diabatic circulation. The delay in the response in such regions can mean that ‘downward’ control is not achieved on seasonal time-scales. A seasonal variation in the radiative damping rate modulates the evolution of the response and leaves a transient-like signature in the annual mean temperature field. Several idealized examples are considered, motivated by topical questions. It is found that wave drag outside the polar vortex can significantly affect the temperatures in its interior, so that high-latitude, high-altitude gravity-wave drag is not the only mechanism for warming the southern hemisphere polar vortex. Diabatic mass transport through the 100 hPa surface is found to lag the seasonal evolution of the wave drag that drives the transport, and thus cannot be considered to be in the downward control regime. On the other hand, the seasonal variation of the radiative damping rate is found to make only a weak contribution to the annual mean temperature increase that has been observed above the ozone hole. Copyright © 2002 Royal Meteorological Society.