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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences RSS feed -- current issue1471-2946December 6, 2017Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences1364-5021<![CDATA[Buckling of a stiff thin film on an elastic graded compliant substrate]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2208/20170410?rss=1
The buckling of a stiff film on a compliant substrate has attracted much attention due to its wide applications such as thin-film metrology, surface patterning and stretchable electronics. An analytical model is established for the buckling of a stiff thin film on a semi-infinite elastic graded compliant substrate subjected to in-plane compression. The critical compressive strain and buckling wavelength for the sinusoidal mode are obtained analytically for the case with the substrate modulus decaying exponentially. The rigorous finite element analysis (FEA) is performed to validate the analytical model and investigate the postbuckling behaviour of the system. The critical buckling strain for the period-doubling mode is obtained numerically. The influences of various material parameters on the results are investigated. These results are helpful to provide physical insights on the buckling of elastic graded substrate-supported thin film.
]]>2017-12-13T00:05:16-08:00info:doi/10.1098/rspa.2017.0410hwp:master-id:royprsa;rspa.2017.04102017-12-13Research articles47322082017041020170410<![CDATA[On modelling the interaction between two rotating bodies with statistically distributed features: an application to dressing of grinding wheels]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2208/20170466?rss=1
The mechanisms of interaction between bodies with statistically arranged features present characteristics common to different abrasive processes, such as dressing of abrasive tools. In contrast with the current empirical approach used to estimate the results of operations based on attritive interactions, the method we present in this paper allows us to predict the output forces and the topography of a simulated grinding wheel for a set of specific operational parameters (speed ratio and radial feed-rate), providing a thorough understanding of the complex mechanisms regulating these processes. In modelling the dressing mechanisms, the abrasive characteristics of both bodies (grain size, geometry, inter-space and protrusion) are first simulated; thus, their interaction is simulated in terms of grain collisions. Exploiting a specifically designed contact/impact evaluation algorithm, the model simulates the collisional effects of the dresser abrasives on the grinding wheel topography (grain fracture/break-out). The method has been tested for the case of a diamond rotary dresser, predicting output forces within less than 10% error and obtaining experimentally validated grinding wheel topographies. The study provides a fundamental understanding of the dressing operation, enabling the improvement of its performance in an industrial scenario, while being of general interest in modelling collision-based processes involving statistically distributed elements.
]]>2017-12-06T00:05:14-08:00info:doi/10.1098/rspa.2017.0466hwp:master-id:royprsa;rspa.2017.04662017-12-06Research articles47322082017046620170466<![CDATA[The complex and quaternionic quantum bit from relativity of simultaneity on an interferometer]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2208/20170596?rss=1
The patterns of fringes produced by an interferometer have long been important testbeds for our best contemporary theories of physics. Historically, interference has been used to contrast quantum mechanics with classical physics, but recently experiments have been performed that test quantum theory against even more exotic alternatives. A physically motivated family of theories are those where the state space of a two-level system is given by a sphere of arbitrary dimension. This includes classical bits, and real, complex and quaternionic quantum theory. In this paper, we consider relativity of simultaneity (i.e. that observers may disagree about the order of events at different locations) as applied to a two-armed interferometer, and show that this forbids most interference phenomena more complicated than those of complex quantum theory. If interference must depend on some relational property of the setting (such as path difference), then relativity of simultaneity will limit state spaces to standard complex quantum theory, or a subspace thereof. If this relational assumption is relaxed, we find one additional theory compatible with relativity of simultaneity: quaternionic quantum theory. Our results have consequences for current laboratory interference experiments: they have to be designed carefully to avoid rendering beyond-quantum effects invisible by relativity of simultaneity.
]]>2017-12-06T00:05:18-08:00info:doi/10.1098/rspa.2017.0596hwp:master-id:royprsa;rspa.2017.05962017-12-06Research articles47322082017059620170596<![CDATA[On the characterization of vortex configurations in the steady rotating Bose-Einstein condensates]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2208/20170602?rss=1
Motivated by experiments in atomic Bose–Einstein condensates (BECs), we compare predictions of a system of ordinary differential equations (ODEs) for dynamics of one and two individual vortices in the rotating BECs with those of the Gross–Pitaevskii mean-field model written as a partial differential equation (PDE). In particular, we characterize orbitally stable vortex configurations in a symmetric harmonic trap due to a cubic repulsive interaction and a steady rotation. The ODE system is analysed in detail and the PDE model is approximated numerically. Good agreement between the two models is established in the semi-classical (Thomas–Fermi) limit that corresponds to the BECs at large values of the chemical potential.
]]>2017-12-06T00:05:13-08:00info:doi/10.1098/rspa.2017.0602hwp:master-id:royprsa;rspa.2017.06022017-12-06Research articles47322082017060220170602