arXiv subjects

J. Málek

Publications and source records attributed to J. Málek.

5 recordsLinked to original sources

arXiv2026

Kinetic derivation of thermal viscous models for nematic liquid crystal dynamics

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) type. The kinetic description incorporates mean-field alignment interactions through a Vlasov potential and relies on a separation of time scales, with orientational relaxation occurring on a faster time scale than translational momentum relaxation. At the continuum level, we establish the balance equations for mass, linear and angular momentum, energy, and entropy. Using the zeroth and first order Chapman-Enskog expansions, we derive a constitutive equation for the Helmholtz free energy and identify the associated structural form of the entropy production rate. We then exploit additional information from the kinetic description to determine a constitutive relation for the entropy production rate itself. Finally, by applying the constrained maximisation procedure of Rajagopal and Srinivasa, we obtain constitutive equations for the Cauchy stress and couple-stress tensors, as well as for the energy and entropy fluxes. In this way we generalise the recent inviscid kinetic theory of Farrell, Russo, and Zerbinati to account for viscous, thermal, and spin-diffusive effects, using the simplest BGK-type approximation of the collision operator. Both compressible and incompressible variants of the theory are presented.

math-ph↗

arXiv2023

Development of boundary layers in Euler fluids that on "activation'' respond like Navier-Stokes fluids

We consider the flow of a fluid whose response characteristics change due the value of the norm of the symmetric part of the velocity gradient, behaving as an Euler fluid below a critical value and as a Navier-Stokes fluid at and above the critical value, the norm being determined by the external stimuli. We show that such a fluid, while flowing past a bluff body, develops boundary layers which are practically identical to those that one encounters within the context of the classical boundary layer theory propounded by Prandtl. Unlike the classical boundary layer theory that arises as an approximation within the context of the Navier-Stokes theory, here the development of boundary layers is due to a change in the response characteristics of the constitutive relation. We study the flow of such a fluid past an airfoil and compare the same against the solution of the Navier-Stokes equations. We find that the results are in excellent agreement with regard to the velocity and vorticity fields for the two cases.

math.NA↗

arXiv2017

Numerical simulations of an incompressible piezoviscous fluid flowing in a plane slider bearing

We provide numerical simulations of an incompressible pressure-thickening and shear-thinning lubricant flowing in a plane slider bearing. We study the influence of several parameters, namely the ratio of the characteristic lengths $\varepsilon>0$ (with $\varepsilon\searrow0$ representing the Reynolds lubrication approximation); the coefficient of the exponential pressure--viscosity relation $α^*\geq0$; the parameter $G^*\geq0$ related to the Carreau--Yasuda shear-thinning model and the modified Reynolds number $\mathrm{Re}_\varepsilon\geq0$. The finite element approximations to the steady isothermal flows are computed without resorting to the lubrication approximation. We obtain the numerical solutions as long as the variation of the viscous stress $\mathbf{S}=2η(p,\mathrm{tr}\mathbf{D}^2)\mathbf{D}$ with the pressure is limited, say $|\partial\mathbf{S}/\partial p|\leq1$. We show conclusively that the existing practice of avoiding the numerical difficulties by cutting the viscosity off for large pressures leads to results that depend sorely on the artificial cut-off parameter. We observe that the piezoviscous rheology generates pressure differences across the fluid film.

physics.flu-dyn↗

arXiv2005

Charge Transfer Excitations in Insulating Copper Oxides

A semi-quantitative cluster approach is developed to describe the charge transfer (CT) electron-hole excitations in insulating cuprates in a rather wide energy range up to 10- 15 eV. It generalizes the Zhang-Ng (ZN) model of CT excitons by considering the complete set of Cu3d and O2p orbitals within the CuO4 embedded molecular cluster method and by introducing one-center (intra-center) Frenkel-like and two-center (inter-center) excitons. Special attention is paid to the transition matrix element effects both in optical and electron energy loss spectra (EELS). In the latter case we obtain the momentum dependence of matrix elements both for intra-center and inter-center transitions. We are able to give a semi-quantitative description of the optical and EELS spectra for a large number of 0D (like CuB2O4), 1D (Sr2CuO3) and 2D (like Sr2CuO2Cl2) insulating cuprates in a unifying manner. By comparing our analysis with the experimental data we find that the CT gap in insulating cuprates is determined by nearly degenerate intra-center localized excitations and inter-center CT excitons. The corresponding EELS intensity is found to be strongly k-dependent: even for isolated exciton it sharply decreases by approaching the Brillouin zone (BZ) boundary. It is shown that the interaction of two-center excitons can result in destructive interference effects with an intensity compensation point.

cond-mat.str-el↗

arXiv1997

Solitonic approach to the dimerization problem in correlated one-dimensional systems

Using exact diagonalizations we consider self-consistently the lattice distortions in odd Peierls-Hubbard and spin-Peierls periodic rings in the adiabatic harmonic approximation. From the tails of the inherent spin soliton the dimerization d_\infty of regular even rings is found by extrapolations to infinite ring lengths. Considering a wide region of electron-electron onsite interaction values U>0 compared with the band width 4t_0 at intermediately strong electron-phonon interaction g, known relationships obtained by other methods are reproduced and/or refined within one unified approach: such as the maximum of d_\infty at U \simeq 3 t_0 for g \simeq 0.5 and its shift to zero for g \to g_c \approx 0.7. The hyperbolic tangent shape of the spin soliton is retained for any U and g <~ 0.6. In the spin-Peierls limit the d_\infty are found to be in agreement with results of DMRG computations.

cond-mat.str-el↗