Past

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As part of a suite of products that provide a drive thorough vehicle tyre inspection system the assessment of wheel alignment would be useful to drivers in maintaining their vehicles and reducing tyre wear.  The current method of assessing wheel alignment involves fitting equipment to the tyre and assessment within a garage environment. 

The challenge is to develop a technique that can be used in the roadway with no equipment fitted to the vehicle.  The WheelRight equipment is already capturing images of tyres from both  front and side views.  Pressure sensors in the roadway also allow a tyre pressure footprint to be created.  Using the existing data to interpret the alignment of the wheels on each axle is a preferred way forward.

The stability of structures continues to be scientifically fascinating and technically important.  Shell buckling emerged as one of the most challenging nonlinear problems in mechanics more than fifty years ago when it was intensively studied.  It has returned to life with new challenges motivated not only by structural applications but also by developments in the life sciences and in soft materials.  It is not at all uncommon for slightly imperfect thin cylindrical shells under axial compression or spherical shells under external pressure to buckle at 20% of the buckling load of the perfect shell.  A historical overview of shell buckling will be presented followed by a discussion of recent work by the speaker and his collaborators on the buckling of spherical shells.  Experimental and theoretical work will be described with a focus on imperfection-sensitivity and on viewing the phenomena within the larger context of nonlinear stability. 

We prove higher differentiability of bounded local minimizers to some degenerate functionals satisfying anisotropic growth conditions. In the two-dimensional case we also study the Lipschitz regularity of such minimizers without any limitation on the exponents of anisotropy.