9 papers
A Kinetic Theory Approach To Ordered Fluids: Direct Simulation Monte Carlo Methods
José A. Carrillo, Patrick E. Farrell, Andrea Medaglia +1
We present a direct simulation Monte Carlo (DSMC) method for the kinetic theory of ordered fluids recently introduced by the authors. The microscopic constituents of these fluids c…
Kinetic derivation of thermal viscous models for nematic liquid crystal dynamics
P. E. Farrell, J. Málek, O. Souček +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…
A kinetic interpretation of thermomechanical restrictions of continua
Patrick E. Farrell, Josef Málek, Ondřej Souček +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…
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…
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…
PETScML: Second-order solvers for training regression problems in Scientific Machine Learning
Stefano Zampini, Umberto Zerbinati, George Turkiyyah +1
In recent years, we have witnessed the emergence of scientific machine learning as a data-driven tool for the analysis, by means of deep-learning techniques, of data produced by co…
Kinetic derivation of a compressible Leslie--Ericksen equation for rarified calamitic gases
Patrick E. Farrell, Giovanni Russo, Umberto Zerbinati
Nematic ordering describes the phenomenon where anisotropic molecules tend to locally align, like matches in a matchbox. This ordering can arise in solids (as nematic elastomers),…
When rational functions meet virtual elements: The lightning Virtual Element Method
M. L. Trezzi, U. Zerbinati
We propose a lightning Virtual Element Method that eliminates the stabilisation term by actually computing the virtual component of the local VEM basis functions using a lightning…