156 research outputs found
Limitations of stationary Vlasov-Poisson solvers in probe theory
Physical and numerical limitations of stationary Vlasov-Poisson solvers based on backward Liouville methods are investigated with five solvers that combine different meshes, numerical integrators, and electric field interpolation schemes. Since some of the limitations arise when moving from an integrable to a non-integrable configuration, an elliptical Langmuir probe immersed in a Maxwellian plasma was considered and the eccentricity (ep) of its cross-section used as integrability-breaking parameter. In the cylindrical case, ep=0, the energy and angular momentum are both conserved. The trajectories of the charged particles are regular and the boundaries that separate trapped from non-trapped particles in phase space are smooth curves. However, their computation has to be done carefully because, albeit small, the intrinsic numerical errors of some solvers break these conservation laws. It is shown that an optimum exists for the number of loops around the probe that the solvers need to classify a particle trajectory as trapped. For ep≠0, the angular momentum is not conserved and particle dynamics in phase space is a mix of regular and chaotic orbits. The distribution function is filamented and the boundaries that separate trapped from non-trapped particles in phase space have a fractal geometry. The results were used to make a list of recommendations for the practical implementation of stationary Vlasov-Poisson solvers in a wide range of physical scenarios.This work was supported by the European Union's Horizon 2020 Research and Innovation Programme under grant agreement No 828902 (E.T.PACK project). GSA work is supported by the Ministerio de Ciencia, Innovación of Spain under the Grant RYC-2014-15357. The authors thank the Reviewers for their valuable comments and suggestions about the use of energy-conserving numerical integrators
Thermophoresis in Colloidal Suspensions
This dissertation examines the motion of colloids in a temperature gradient, a non-equilibrium
phenomenon also known as thermophoresis. Chapter 1 gives an introduction to the existing
applications and basic concepts of thermophoresis and outlines some of the experimental and
theoretical challenges that serve as a motivation for this PhD project. In Chapter 2, a general
theoretical description for thermophoresis is formulated using the theory of non-equilibrium
thermodynamics. The colloidal flux is split up into an interfacial single-colloid contribution
and a bulk contribution, followed by a determination of transport coefficients based on
Onsager’s reciprocal relations. It is further shown how the phenomenological expression
of the thermophoretic flux can be recovered when the fluid is at steady-state. The results
issuing from this description are then discussed and compared to other existing approaches,
some of which are shown to neglect the hydrodynamic character of colloidal thermophoresis.
Chapter 3 is dedicated to the validation of the introduced theoretical framework by means
of computer simulations, using a simulation technique known as multi-particle collision
dynamics. More specifically, the dependence of the thermophoretic force on different system
parameters is examined and deviations from the theoretical prediction are explained by an
advective distortion of interfacial fluid properties at the colloidal surface. Chapter 4 presents
steady-state measurements of functionalised colloids in a temperature gradient, showing
how the addition of molecular surface groups increases the experimental complexity of
thermophoretic motion. The relaxation process behind this steady-state is also studied, to
determine how the relaxation speed depends on the applied temperature gradient. In chapter
5, a general conclusion is drawn from the presented work and its implications are briefly
discussed in relation to the current state of knowledge. Finally, the discussion is closed with
an outlook on remaining challenges in understanding colloidal motion that could be the
subject of future research
On the dynamics of correlations in Scaling limits of interacting particle systems
In this work, we analyze the properties of two-particle correlations in the weak-coupling and plasma limit of interacting particle systems motivated by Bogolyubov's formal derivation of kinetic equations. We prove that the leading order evolution in the weak-coupling scaling limit is stable on the macroscopic timescale, and yields the nonlinear Landau equation as kinetic equation. This result shows the transition from the non-Markovian dynamics of the interacting particle system to the Markovian, parabolic evolution in the kinetic limit. Since the system is non-dissipative before taking the limit, we introduce a time-averaged notion of stability to derive an a priori estimate on the solution. Moreover, we prove the global stability of the truncated correlation function in the plasma limit, for a time independent background distribution and soft potentials. In the case of systems with Coulombian interaction, we prove the onset of the Debye screening length and show that the limit evolution is driven by the interaction of particles with impact parameter much smaller than the Debye length
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