Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.
Transformation theory has long been known to be a mechanism for
the design of metamaterials. It gives rise to the required properties of the
material in order to direct waves in the manner desired. This talk will
focus on the mathematical theory underpinning the design of acoustic and
elastodynamic metamaterials based on transformation theory and aspects of
the experimental confirmation of these designs. In the acoustics context it
is well-known that the governing equations are transformation invariant and
therefore a whole range of microstructural options are available for design,
although designing materials that can harness incoming acoustic energy in
air is difficult due to the usual sharp impedance contrast between air and
the metamaterial in question. In the elastodynamic context matters become
even worse in the sense that the governing equations are not transformation
invariant and therefore we generally require a whole new class of materials.
In the acoustics context we will describe a new microstructure that consists
of rigid rods that is (i) closely impedance matched to air and (ii) slows
down sound in air. This is shown to be useful in a number of configurations
and in particular it can be employed to half the resonant frequency of the
standard quarter-wavelength resonator (or alternatively it can half the size
of the resonator for a specified resonant frequency) .
In the elastodynamics context we will show that although the equations are
not transformation invariant one can employ the theory of waves in
pre-stressed hyperelastic materials in order to create natural elastodynamic
metamaterials whose inhomogeneous anisotropic material properties are
generated naturally by an appropriate pre-stress. In particular it is shown
that a certain class of hyperelastic materials exhibit this so-called
“invariance property” permitting the creation of e.g. hyperelastic cloaks
[2,3] and invariant metamaterials. This has significant consequences for the
design of e.g. phononic media: it is a well-known and frequently exploited
fact that pre-stress and large deformation of hyperelastic materials
modifies the linear elastic wave speed in the deformed medium. In the
context of periodic materials this renders materials whose dynamic
properties are “tunable” under pre-stress and in particular this permits
tunable band gaps in periodic media . However the invariant hyperelastic
materials described above can be employed in order to design a class of
phononic media whose band-gaps are invariant to deformation . We also
describe the concept of an elastodynamic ground cloak created via pre-stress
 Rowley, W.D., Parnell, W.J., Abrahams, I.D., Voisey, S.R. and Etaix, N.
(2018) “Deepening subwavelength acoustic resonance via metamaterials with
universal broadband elliptical microstructure”. Applied Physics Letters 112,
 Parnell, W.J. (2012) “Nonlinear pre-stress for cloaking from antiplane
elastic waves”. Proc Roy Soc A 468 (2138) 563-580.
 Norris, A.N. and Parnell, W.J. (2012) “Hyperelastic cloaking theory:
transformation elasticity with pre-stressed solids”. Proc Roy Soc A 468
 Bertoldi, K. and Boyce, M.C. (2008) “Mechanically triggered
transformations of phononic band gaps in periodic elastomeric structures”.
Phys Rev B 77, 052105.
 Zhang, P. and Parnell, W.J. (2017) “Soft phononic crystals with
deformation-independent band gaps” Proc Roy Soc A 473, 20160865.
 Zhang, P. and Parnell, W.J. (2018) “Hyperelastic antiplane ground
cloaking” J Acoust Soc America 143 (5)
- Industrial and Applied Mathematics Seminar
The mechanisms underlying the initiation and perpetuation of cardiac arrhythmias are inherently multi-scale: whereas arrhythmias are intrinsically tissue-level phenomena, they have a significant dependence cellular electrophysiological factors. Spontaneous sub-cellular calcium release events (SCRE), such as calcium waves, are a exemplars of the multi-scale nature of cardiac arrhythmias: stochastic dynamics at the nanometre-scale can influence tissue excitation patterns at the centimetre scale, as triggered action potentials may elicit focal excitations. This latter mechanism has been long proposed to underlie, in particular, the initiation of rapid arrhythmias such as tachycardia and fibrillation, yet systematic analysis of this mechanism has yet to be fully explored. Moreover, potential bi-directional coupling has been seldom explored even in concept.
A major challenge of dissecting the role and importance of SCRE in cardiac arrhythmias is that of simultaneously exploring sub-cellular and tissue function experimentally. Computational modelling provides a potential approach to perform such analysis, but requires new techniques to be employed to practically simulate sub-cellular stochastic events in tissue-scale models comprising thousands or millions of coupled cells.
This presentation will outline the novel techniques developed to achieve this aim, and explore preliminary studies investigating the mechanisms and importance of SCRE in tissue-scale arrhythmia: How do independent, small-scale sub-cellular events overcome electrotonic load and manifest as a focal excitation? How can SCRE focal (and non-focal) dynamics lead to re-entrant excitation? How does long-term re-entrant excitation interact with SCRE to perpetuate and degenerate arrhythmia?
- Mathematical Biology and Ecology Seminar
Julia Wolf is University Lecturer in the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge, and the Director of Taught Postgraduate Education in the Faculty of Mathematics.
More details will follow. Please email firstname.lastname@example.org to register.
The Oxford Mathematics Public Lectures are generously supported by XTX Markets.
- Public Lecture