Fluctuation-dissipation theorem, kinetic stochastic integral and efficient simulations

Hütter, Markus; Öttinger, Hans Christian

doi:10.1039/a800422f

Cited by 42 publications

(67 citation statements)

References 8 publications

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“…These can be handled via a standard Brownian dynamics simulation or Fokker-Planck equation approach. 1,38,[52][53][54] Only a few special cases of the results obtained here were spread in the literature. The presented unifying description allows us to extend the calculations to arbitrary convex shapes dissolved in an arbitrary nonuniform gas ͑beyond Grad's 13 moment approximation͒ conveniently.…”

Section: Discussionmentioning

confidence: 99%

Unifying kinetic approach to phoretic forces and torques onto moving and rotating convex particles

Kröger

Hütter

2006

The Journal of Chemical Physics

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We derive general expressions and present several examples for the phoretic forces and torques acting on a translationally moving and rotating convex tracer particle, usually a submicrosized aerosol particle, assumed to be small compared to the mean free path of the surrounding nonequilibrium gas. Point of departure is an expression of the stress tensor in terms of half-sphere integrals to be evaluated with the inhomogeneous velocity distribution function of the surrounding gas, more specifically, its approximation in terms of a finite number of moments. A worked out example covers Grad’s 13 moment approximation in and out of the so-called hydrodynamic approximation. We implement an accommodation coefficient characterizing the collision process in order to derive the tracer particle’s complete equations of motion in a form which offers the possibility for immediate numerical implementation, and the analytical exploration of the effect of particle shape and size on phoretic drift velocity. Explicit expressions for axisymmetric, spherical, cylindrical, and also cuboidal particles are presented, discussed, and successfully compared with the rarely available, previously treated special cases, thus supporting the unifying approach presented in this manuscript.

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Section: Discussionmentioning

confidence: 99%

Unifying kinetic approach to phoretic forces and torques onto moving and rotating convex particles

Kröger

Hütter

2006

The Journal of Chemical Physics

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“…Such operation, however, is computationally expensive. 40 In situations of confinement different from the one considered here, also, a precomputed table for the mobility matrix in all possible system configurations is generally not available. To overcome this problem in general terms, we present an extension of the RFD approximation of the spatial divergence, originally introduced in Delong et al, 41 to the divergence on the unit sphere.…”

Section: Random Finite Difference (Rfd)mentioning

confidence: 99%

“…39 In integrating the SDE, we prefer to avoid the difficulties related to the interpretation of a stochastic integral containing a multiplicative noise. 39,40 We present instead the Langevin equation directly in a discretized form, which is readily solved. 31 The evolution of a trajectory of a uniaxial particle is fully characterized by its center of mass position vector r(t) and the unit orientation vector p(t) that are represented in Fig.…”

Section: A Langevin Equationmentioning

confidence: 99%

Hydrodynamics and Brownian motions of a spheroid near a rigid wall

Corato

Greco

D’Avino

et al. 2015

The Journal of Chemical Physics

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Articles you may be interested in PHYSICS 142, 194901 (2015) Hydrodynamics and Brownian motions of a spheroid near a rigid wall In this work, we study in detail the hydrodynamics and the Brownian motions of a spheroidal particle suspended in a Newtonian fluid near a flat rigid wall. We employ 3D Finite Element Method (FEM) simulations to compute how the mobility tensor of the spheroid varies with both the particle-wall separation distance and the particle orientation. We then study the Brownian motion of the spheroid by means of a discretized Langevin equation. We specifically focus on the additional drift terms arising from the position and orientational dependence of the mobility matrix. In this respect, we also propose a numerically convenient approximation of the orientational divergence of the mobility matrix that is required in the solution of the Langevin equation. Our results illustrate that both hydrodynamics and Brownian motions of a spheroidal particle near a confining wall display novel features from those of a sphere in the same type of confinement. C 2015 AIP Publishing LLC. [http://dx

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“…The equalities for the two time derivatives can be inserted into Eq. (19). This will give constraints on the allowed forms for the tensors A and D. The determination of these constraints is complicated by the fact that the conditional probability for t i+1 = t i is a ␦ function.…”

Section: ͑20͒mentioning

confidence: 99%

“…It is a generalization of the kinetic integral [19]. The ‫ؠ‬ symbol indicates the Stratonovich dot product.…”

Section: ͪͬͮ=0 ͑A7͒mentioning

confidence: 99%

Detailed fluctuation theorem for mesoscopic modeling

Peters

2004

Phys. Rev. E

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The detailed fluctuation theorem is derived. The basic assumptions are phase space incompressibility (Liouville's theorem) and time reversibility on the microscopic level. The theorem relates the conditional probability to end up in a mesoscopic state ⌫ B at time t B , starting from ⌫ A at time t A , to the time-reversed process. The ratio of these two probability densities is related to the entropy difference of the two mesoscopic states. The fluctuation theorem remains valid even far from equilibrium as long as the local equilibrium condition is obeyed. It is shown that the theorem imposes constraints on the form mesoscopic equations can take. For stochastic differential equations a generalized kinetic form is derived. The fluctuation theorem can be used to derive thermodynamically consistent simulation techniques. At the end of this paper the relation with the GENERIC formalism is discussed.

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Fluctuation-dissipation theorem, kinetic stochastic integral and efficient simulations

Cited by 42 publications

References 8 publications

Unifying kinetic approach to phoretic forces and torques onto moving and rotating convex particles

Unifying kinetic approach to phoretic forces and torques onto moving and rotating convex particles

Hydrodynamics and Brownian motions of a spheroid near a rigid wall

Detailed fluctuation theorem for mesoscopic modeling

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