General framework for fluctuating dynamic density functional theory
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Transkript: Englisch(automatisch erzeugt)
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Hello, I'm Serafin Kalyadasis from the Chemical Engineering Department of Imperial College. What I will try to do within the next few minutes is tell you about our recent paper in the new Journal of Physics entitled General Framework for Fluctuating Dynamic Density Functional Theory. This work was driven by Senior Postdoctoral Research Associate in the group, Dr. Miguel
00:24
Durano-Livensia and was extended to include another Senior Postdoctoral Research Associate in the group, Dr. Peter Gacicin and former Postdoctoral Research Associate Dr. Ben Goddard, currently faculty in the School of Mathematics and Imperial University. The work was supported by the Engineering and Physical Sciences Research Council of
00:41
the UK and the European Research Council via its Advanced Grand Scheme. Continued mechanical approaches, such as Navier-Stokes, describe non-equilibrium systems but fail to capture noise-driven and small-scale phenomena, for instance the dynamics of a phase separation or flow through a nanopore. In this work, we show how such equations can be derived essentially from the Newtonian
01:02
dynamics, conveying the behaviour of individual particles. Half a century ago, Landau and Ifsitz proposed an empirical modification of the hydrodynamic equations. They empirically added a noise term to the Navier-Stokes equation, requiring only that the fluctuation-dissipation relation satisfied, thus introducing fluctuating hydrodynamics.
01:21
In the modern world, the behaviour of matter at the smallest scales becomes increasingly amenable to experimental exploration. This has encouraged theoreticians to provide adequate connection between the macro and macro worlds, thus rigorously justifying the intuition behind classical approaches. There are at least two aspects which make a fully macroscopic derivation of fluctuating hydrodynamics important.
01:41
First, exact definitions of quantities such as viscosity, stress tensor, pressure, transport coefficients and so on, as averages of the microscopic quantities which included individual particle coordinates, velocity center particle forces. Second, a rigorous derivation of fluctuating hydrodynamics would naturally account for the spatial inhomogeneity of various properties, such as density and pressure.
02:03
In this way, the continuum of mechanical formulas becomes applicable to the description of small-scale phenomena, such as phase transitions, contact line motion, adsorption in nanopores and so on. Regarding existing efforts to derive fluctuating hydrodynamics, most notable are the works of Dean and Kawasaki, who independently obtained the structure of the microscopic dynamical
02:23
equations. However, their final expressions contain microscopic operators, thus leaving the equations computationally intractable and disconnected from the original and all of his theory. Even more importantly, this disconnection often has led to the misconception that the Dean-Kawasaki models describe the evolution of macroscopic observables.
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In the present work, we systematically derive the equations of fluctuating hydrodynamics for arbitrarily shaped thermalized colloidal particles and formulate them in terms of observables given by proper operator averages. As a byproduct, we obtain the non-equilibrium energy functional, which has the same structure as the Helmholtz free energy.
03:02
These two aspects make our proposed framework, in principle, computationally accessible because it expresses relations between observable quantities in terms of ensemble averages, as well as giving their macroscopic definitions. Therefore, our derivation stays in tune with the intuitive treatment of the original theory of Landau-Lipshitz and alleviates the misconceptions just mentioned.
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Our formalism has also a direct link with classical dynamic density functional theory. As a matter of fact, we show that classical dynamic density functional theory is simply the most likely realization of our formalism. This advances the long-standing debate and in fact provides closure to this debate in
03:41
the classical density functional theory community about the inclusion of fluctuations in density functional theory. But even more, it opens the door to the discovery of new physical laws conveying the dynamics of soft matter systems out of equilibrium under noise-carbon conditions. To find out more about our work, please check out our website and thank you for watching.
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