23,801 research outputs found
Well-Posed Two-Temperature Constitutive Equations for Stable Dense Fluid Shockwaves using Molecular Dynamics and Generalizations of Navier-Stokes-Fourier Continuum Mechanics
Guided by molecular dynamics simulations, we generalize the
Navier-Stokes-Fourier constitutive equations and the continuum motion equations
to include both transverse and longitudinal temperatures. To do so we partition
the contributions of the heat transfer, the work done, and the heat flux vector
between the longitudinal and transverse temperatures. With shockwave boundary
conditions time-dependent solutions of these equations converge to give
stationary shockwave profiles. The profiles include anisotropic temperature and
can be fitted to molecular dynamics results, demonstrating the utility and
simplicity of a two-temperature description of far-from-equilibrium states.Comment: 19 pages with 10 figures, revised following review at Physical Review
E and with additional figure/discussion, for presentation at the
International Summer School and Conference "Advanced Problems in Mechanics"
[Saint Petersburg, Russia] 1-5 July 2010
Analytic self-similar solutions of the Oberbeck-Boussinesq equations
In this article we will present pure two-dimensional analytic solutions for
the coupled non-compressible Newtoniain Navier-Stokes
--- with Boussinesq approximation --- and the heat conduction equation. The
system was investigated from E.N. Lorenz half a century ago with Fourier series
and pioneered the way to the paradigm of chaos. We present a novel analysis of
the same system where the key idea is the two-dimensional generalization of the
well-known self-similar Ansatz of Barenblatt which will be interpreted in a
geometrical way. The results, the pressure, temperature and velocity fields are
all analytic and can be expressed with the help of the error functions. The
temperature field has a strongly damped oscillating behavior which is an
interesting feature.Comment: 13 pages, 4 figure
Lattice Boltzmann Methods for thermal flows: continuum limit and applications to compressible Rayleigh-Taylor systems
We compute the continuum thermo-hydrodynamical limit of a new formulation of
lattice kinetic equations for thermal compressible flows, recently proposed in
[Sbragaglia et al., J. Fluid Mech. 628 299 (2009)]. We show that the
hydrodynamical manifold is given by the correct compressible Fourier-
Navier-Stokes equations for a perfect fluid. We validate the numerical
algorithm by means of exact results for transition to convection in
Rayleigh-B\'enard compressible systems and against direct comparison with
finite-difference schemes. The method is stable and reliable up to temperature
jumps between top and bottom walls of the order of 50% the averaged bulk
temperature. We use this method to study Rayleigh-Taylor instability for
compressible stratified flows and we determine the growth of the mixing layer
at changing Atwood numbers up to At ~ 0.4. We highlight the role played by the
adiabatic gradient in stopping the mixing layer growth in presence of high
stratification and we quantify the asymmetric growth rate for spikes and
bubbles for two dimensional Rayleigh- Taylor systems with resolution up to Lx
\times Lz = 1664 \times 4400 and with Rayleigh numbers up to Ra ~ 2 \times
10^10.Comment: 26 pages, 13 figure
Optomechanical cooling in a continuous system
Radiation-pressure-induced optomechanical coupling permits exquisite control
of micro- and mesoscopic mechanical oscillators. This ability to manipulate and
even damp mechanical motion with light---a process known as dynamical
backaction cooling---has become the basis for a range of novel phenomena within
the burgeoning field of cavity optomechanics, spanning from dissipation
engineering to quantum state preparation. As this field moves toward more
complex systems and dynamics, there has been growing interest in the prospect
of cooling traveling-wave phonons in continuous optomechanical waveguides.
Here, we demonstrate optomechanical cooling in a continuous system for the
first time. By leveraging the dispersive symmetry breaking produced by
inter-modal Brillouin scattering, we achieve continuous mode optomechanical
cooling in an extended 2.3-cm silicon waveguide, reducing the temperature of a
band of traveling-wave phonons by more than 30 K from room temperature. This
work reveals that optomechanical cooling is possible in macroscopic linear
waveguide systems without an optical cavity or discrete acoustic modes.
Moreover, through an intriguing type of wavevector-resolved phonon
spectroscopy, we show that this system permits optomechanical control over
continuously accessible groups of phonons and produces a new form of
nonreciprocal reservoir engineering. Beyond this study, this work represents a
first step towards a range of novel classical and quantum traveling-wave
operations in continuous optomechanical systems.Comment: Manuscript with supplementary information. 17 pages, 4 Figures. Minor
correction in Fig.
Lattice ellipsoidal statistical BGK model for thermal non-equilibrium flows
A thermal lattice Boltzmann model is constructed on the basis of the ellipsoidal statistical Bhatnagar-Gross-Krook (ES-BGK) collision operator via the Hermite moment representation. The resulting lattice ES-BGK model uses a single distribution function and features an adjustable Prandtl number. Numerical simulations show that using a moderate discrete velocity set, this model can accurately recover steady and transient solutions of the ES-BGK equation in the slip-flow and early transition regimes in the small Mach number limit that is typical of microscale problems of practical interest. In the transition regime in particular, comparisons with numerical solutions of the ES-BGK model, direct Monte Carlo and low-variance deviational Monte Carlo simulations show good accuracy for values of the Knudsen number up to approximately 0:5. On the other hand, highly non-equilibrium phenomena characterized by high Mach numbers, such as viscous heating and force-driven Poiseuille flow for large values of the driving force, are more difficult to capture quantitatively in the transition regime using discretizations that have been chosen with computational efficiency in mind such as the one used here, although improved accuracy is observed as the number of discrete velocities is increased
A thermo-mechanically consistent Burnett regime continuum flow equation without Chapman-Enskog expansion
Chapman-Enskog expansion is the orthodox approach to derive continuum flow models from Boltzmann’s kinetic equation for dilute gases. Beyond the Navier-Stokes-Fourier order, these models known as Burnett hydrodynamic-regime equations violate a number of fundamental mechanical and thermodynamic principles in their original forms. This has generated a widely investigated problem in the kinetic theory of gases. In this short article, we derive a Burnett hydrodynamic-regime continuum model that is systematically consistent with all known mechanical and thermodynamic principles without using any series’ expansion. Close comparison with the conventional Burnett hydrodynamic set of equations is considered and their linear stabilities around an equilibrium point under small perturbations are presented
A study of electrochemical transport and diffuse charge dynamics using a Langevin equation
This thesis aims to develop new numerical and computational tools to study electrochemical transport and diffuse charge dynamics at small scales. Previous efforts at modeling electrokinetic phenomena at scales where the noncontinuum effects become significant have included continuum models based on the Poisson-Nernst-Planck equations and atomic simulations using molecular dynamics algorithms. Neither of them is easy to use or conducive to electrokinetic transport modeling in strong confinement or over long time scales. This work introduces a new approach based on a Langevin equation for diffuse charge dynamics in nanofluidic devices, which incorporates features from both continuum and atomistic methods. The model is then extended to include steric effects resulting from finite ion size, and applied to the phenomenon of double layer charging in a symmetric binary electrolyte between parallel-plate blocking electrodes, between which a voltage is applied. Finally, the results of this approach are compared to those of the continuum model based on the Poisson-Nernst-Planck equations
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