field theory
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2022 ◽  
Vol 9 (2) ◽  
pp. 136-141
Amer D. Al-Oqali ◽  

Lagrangians which depend on higher-order derivatives appear frequently in many areas of physics. In this paper, we reformulate Podolsky's Lagrangian in fractional form using left-right Riemann-Liouville fractional derivatives. The equations of motion are obtained using the fractional Euler Lagrange equation. In addition, the energy stress tensor and the Hamiltonian are obtained in fractional form from the Lagrangian density. The resulting equations are very similar to those found in classical field theory.

10.1142/q0333 ◽  
2022 ◽  
Andràs Kovàcs ◽  
Giorgio Vassallo ◽  
Paul O'Hara ◽  
Francesco Celani ◽  
Antonino Oscar Di Tommaso

2022 ◽  
Vol 33 (1) ◽  
pp. 41
Sara Angelica Cortes-Llamas ◽  
José Miguel Velázquez-López ◽  
Irma Idalia Rangel-Salas ◽  
Morelia Eunice López-Reyes ◽  
Alfredo Rosas-Sánchez ◽  

2022 ◽  
Vol 13 (1) ◽  
Michael Czajkowski ◽  
Corentin Coulais ◽  
Martin van Hecke ◽  
D. Zeb Rocklin

AbstractDeformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate symmetry due to the presence of a designer soft strain pathway. Here we show that low energy deformations of designer dilational metamaterials will be governed by a scalar field theory, conformal elasticity, in which the nonuniform, nonlinear deformations observed under generic loads correspond with the well-studied—conformal—maps. We validate this approach using experiments and finite element simulations and further show that such systems obey a holographic bulk-boundary principle, which enables an analytic method to predict and control nonuniform, nonlinear deformations. This work both presents a unique method of precise deformation control and demonstrates a general principle in which mechanisms can generate special classes of soft deformations.

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