Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Review articles
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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences RSS feed -- recent Review articles articles1471-2946Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences1364-5021<![CDATA[How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2207/20170607?rss=1
The mechanical response of a homogeneous isotropic linearly elastic material can be fully characterized by two physical constants, the Young’s modulus and the Poisson’s ratio, which can be derived by simple tensile experiments. Any other linear elastic parameter can be obtained from these two constants. By contrast, the physical responses of nonlinear elastic materials are generally described by parameters which are scalar functions of the deformation, and their particular choice is not always clear. Here, we review in a unified theoretical framework several nonlinear constitutive parameters, including the stretch modulus, the shear modulus and the Poisson function, that are defined for homogeneous isotropic hyperelastic materials and are measurable under axial or shear experimental tests. These parameters represent changes in the material properties as the deformation progresses, and can be identified with their linear equivalent when the deformations are small. Universal relations between certain of these parameters are further established, and then used to quantify nonlinear elastic responses in several hyperelastic models for rubber, soft tissue and foams. The general parameters identified here can also be viewed as a flexible basis for coupling elastic responses in multi-scale processes, where an open challenge is the transfer of meaningful information between scales.
]]>2017-11-29T01:11:16-08:00info:doi/10.1098/rspa.2017.0607hwp:master-id:royprsa;rspa.2017.06072017-11-29Review articles47322072017060720170607<![CDATA[Analysing causal structures with entropy]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2207/20170483?rss=1
A central question for causal inference is to decide whether a set of correlations fits a given causal structure. In general, this decision problem is computationally infeasible and hence several approaches have emerged that look for certificates of compatibility. Here, we review several such approaches based on entropy. We bring together the key aspects of these entropic techniques with unified terminology, filling several gaps and establishing new connections, all illustrated with examples. We consider cases where unobserved causes are classical, quantum and post-quantum, and discuss what entropic analyses tell us about the difference. This difference has applications to quantum cryptography, where it can be crucial to eliminate the possibility of classical causes. We discuss the achievements and limitations of the entropic approach in comparison to other techniques and point out the main open problems.
]]>2017-11-01T03:11:33-07:00info:doi/10.1098/rspa.2017.0483hwp:master-id:royprsa;rspa.2017.04832017-11-01Review articles47322072017048320170483<![CDATA[Nonlinear graphene plasmonics]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2206/20170433?rss=1
The rapid development of graphene has opened up exciting new fields in graphene plasmonics and nonlinear optics. Graphene's unique two-dimensional band structure provides extraordinary linear and nonlinear optical properties, which have led to extreme optical confinement in graphene plasmonics and ultrahigh nonlinear optical coefficients, respectively. The synergy between graphene's linear and nonlinear optical properties gave rise to nonlinear graphene plasmonics, which greatly augments graphene-based nonlinear device performance beyond a billion-fold. This nascent field of research will eventually find far-reaching revolutionary technological applications that require device miniaturization, low power consumption and a broad range of operating wavelengths approaching the far-infrared, such as optical computing, medical instrumentation and security applications.
]]>2017-10-25T00:05:19-07:00info:doi/10.1098/rspa.2017.0433hwp:master-id:royprsa;rspa.2017.04332017-10-25Review articles47322062017043320170433<![CDATA[Twistor theory at fifty: from contour integrals to twistor strings]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2206/20170530?rss=1
We review aspects of twistor theory, its aims and achievements spanning the last five decades. In the twistor approach, space–time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex threefold—the twistor space. After giving an elementary construction of this space, we demonstrate how solutions to linear and nonlinear equations of mathematical physics—anti-self-duality equations on Yang–Mills or conformal curvature—can be encoded into twistor cohomology. These twistor correspondences yield explicit examples of Yang–Mills and gravitational instantons, which we review. They also underlie the twistor approach to integrability: the solitonic systems arise as symmetry reductions of anti-self-dual (ASD) Yang–Mills equations, and Einstein–Weyl dispersionless systems are reductions of ASD conformal equations. We then review the holomorphic string theories in twistor and ambitwistor spaces, and explain how these theories give rise to remarkable new formulae for the computation of quantum scattering amplitudes. Finally, we discuss the Newtonian limit of twistor theory and its possible role in Penrose’s proposal for a role of gravity in quantum collapse of a wave function.
]]>2017-10-11T00:28:31-07:00info:doi/10.1098/rspa.2017.0530hwp:master-id:royprsa;rspa.2017.05302017-10-11Review articles47322062017053020170530