Table 1.

The numerous application areas associated with the potential problem, together with corresponding variables. Here, attention is restricted to two-dimensional problems. It is noted that the acoustic scenario is applicable only in the dynamic setting of course and furthermore (ρ−1)ij refers to the ijth component of the inverse of the acoustic density tensor.

applicationσieiwμij
antiplane elasticityantiplane stress vector (σ13,σ23)displacement gradient ∇wdisplacement wshear moduli μij
thermal conductivityheat flux qitemperature gradient −∇Ttemperature Tthermal conductivity kij
electrical conductivityelectrical current Jielectric field Ei=∇Φelectric potential Φelectrical conductivity σ¯ij
dielectricsdisplacement field Dielectric field Ei=∇Φelectric potential Φelectric permittivity ϵij
magnetismmagnetic induction Bimagnetic field Hi=∇Ψmagnetic potential Ψmagnetic permeability μij
porous mediaweighted velocity ηvipressure gradient ∇ppressure ppermeability kij
diffusiondiffusion flux jiconcentration gradient ∇cconcentration cdiffusivity Dij
acousticsacceleration ∂v/∂tpressure gradient −∇ppressure pinverse density tensor (ρ−1)ij