Dynamic density functional theory of fluids

Marconi, Umberto Marini Bettolo; Tarazona, P.

doi:10.1063/1.478705

Cited by 574 publications

(654 citation statements)

References 24 publications

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“…Adapting the calculations of [47,48,49,50,8,43] to the present context, we find that the exact vorticity field is solution of the stochastic equation…”

Section: The Exact Vorticity Fieldmentioning

confidence: 99%

Two-dimensional Brownian vortices

Chavanis

2008

Physica A: Statistical Mechanics and its Applications

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We introduce a stochastic model of two-dimensional Brownian vortices associated with the canonical ensemble. The point vortices evolve through their usual mutual advection but they experience in addition a random velocity and a systematic drift generated by the system as a whole. The statistical equilibrium state of this stochastic model is the Gibbs canonical distribution. We consider a single species system and a system made of two types of vortices with positive and negative circulations. At positive temperatures, like-sign vortices repel each other ("plasma" case) and at negative temperatures, like-sign vortices attract each other ("gravity" case). We derive the stochastic equation satisfied by the exact vorticity field and the Fokker-Planck equation satisfied by the N -body distribution function. We present the BBGKY-like hierarchy of equations satisfied by the reduced distribution functions and close the hierarchy by considering an expansion of the solutions in powers of 1/N , where N is the number of vortices, in a proper thermodynamic limit. For spatially inhomogeneous systems, we derive the kinetic equations satisfied by the smooth vorticity field in a mean field approximation valid for N → +∞. For spatially homogeneous systems, we study the two-body correlation function, in a Debye-Hückel approximation valid at the order O(1/N ). The results of this paper can also apply to other systems of random walkers with long-range interactions such as self-gravitating Brownian particles and bacterial populations experiencing chemotaxis. Furthermore, for positive temperatures, our study provides a kinetic derivation, from microscopic stochastic processes, of the Debye-Hückel model of electrolytes.

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“…Adapting the calculations of [47,48,49,50,8,43] to the present context, we find that the exact vorticity field is solution of the stochastic equation…”

Section: The Exact Vorticity Fieldmentioning

confidence: 99%

Two-dimensional Brownian vortices

Chavanis

2008

Physica A: Statistical Mechanics and its Applications

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“…Such dynamics can in certain limits be justified by more fundamental arguments [18][19][20]. However, since the energy of the PFC models incorporates elastic energy due to elastic stress this might turn out to be problematic in some cases.…”

Section: Introductionmentioning

confidence: 99%

Phase-field-crystal models and mechanical equilibrium

et al. 2014

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Phase-field-crystal (PFC) models constitute a field theoretical approach to solidification, melting, and related phenomena at atomic length and diffusive time scales. One of the advantages of these models is that they naturally contain elastic excitations associated with strain in crystalline bodies. However, instabilities that are diffusively driven towards equilibrium are often orders of magnitude slower than the dynamics of the elastic excitations, and are thus not included in the standard PFC model dynamics. We derive a method to isolate the time evolution of the elastic excitations from the diffusive dynamics in the PFC approach and set up a two-stage process, in which elastic excitations are equilibrated separately. This ensures mechanical equilibrium at all times. We show concrete examples demonstrating the necessity of the separation of the elastic and diffusive time scales. In the small-deformation limit this approach is shown to agree with the theory of linear elasticity.

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“…The theory is explicitly worked out for hydrodynamic interactions on the Rotne-Prager level and generalizes earlier formulations [16,17,18] where hydrodynamic interactions were neglected. The theory makes predictions for an arbitrary time-dependent external potential, i.e., for a general inhomogeneous nonequilibrium situation.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Density Functional Theory with Hydrodynamic Interactions and Colloids in Unstable Traps

2008

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A density functional theory for colloidal dynamics is presented which includes hydrodynamic interactions between the colloidal particles. The theory is applied to the dynamics of colloidal particles in an optical trap which switches periodically in time from a stable to unstable confining potential. In the absence of hydrodynamic interactions, the resulting density breathing mode, exhibits huge oscillations in the trap center which are almost completely damped by hydrodynamic interactions. The predicted dynamical density fields are in good agreement with Brownian dynamics computer simulations.

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Dynamic density functional theory of fluids

Cited by 574 publications

References 24 publications

Two-dimensional Brownian vortices

Two-dimensional Brownian vortices

Phase-field-crystal models and mechanical equilibrium

Dynamical Density Functional Theory with Hydrodynamic Interactions and Colloids in Unstable Traps

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