6 papers
Kinetic derivation of thermal viscous models for nematic liquid crystal dynamics
P. E. Farrell, J. Málek, O. SouÄek +1
We develop a macroscopic thermodynamic theory of nematic liquid crystals starting from a kinetic theory of ordered fluids with a collision operator of Bhatnagar-Gross-Krook (BGK) t…
On the convergence of iterated penalty methods for structure-preserving discretizations of saddle point problems
Patrick E. Farrell, Michael Neilan, Charles Parker +1
We present new convergence estimates for the iterated penalty method applied to structure-preserving discretizations of linear generalized saddle point systems. The method may be v…
Analysis and numerical analysis of the Helmholtz-Korteweg equation
Patrick E. Farrell, Tim van Beeck, Umberto Zerbinati
We analyse the nematic Helmholtz-Korteweg equation, a variant of the classical Helmholtz equation that describes time-harmonic wave propagation in calamitic fluids in the presence…
A kinetic interpretation of thermomechanical restrictions of continua
Patrick E. Farrell, Josef Málek, OndÅej SouÄek +1
Rajagopal and Srinivasa's thermodynamic framework derives constitutive relations in continuum mechanics from two scalar functions describing energy storage and entropy production v…
A Kinetic Theory Approach to Ordered Fluids
José A. Carrillo, Patrick E. Farrell, Andrea Medaglia +1
We develop a unified kinetic theory for ordered fluids, which systematically extends the phase space with the appropriate generalized angular momenta. Our theory yields a uniquely…
Time-harmonic waves in Korteweg and nematic-Korteweg fluids
Patrick E. Farrell, Umberto Zerbinati
We derive the Helmholtz--Korteweg equation, which models acoustic waves in Korteweg fluids. We further derive a nematic variant of the Helmholtz-Korteweg equation, which incorporat…