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Register a new userCollective Dynamics of Random Polyampholytes
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Added by
Kristian K. Mueller-Nedebock
Publication date
1998
fields
Physics
and research's language is
English
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We consider the Langevin dynamics of a semi-dilute system of chains which are random polyampholytes of average monomer charge $q$ and with a fluctuations in this charge of the size $Q^{-1}$ and with freely floating counter-ions in the surrounding. We cast the dynamics into the functional integral formalism and average over the quenched charge distribution in order to compute the dynamic structure factor and the effective collective potential matrix. The results are given for small charge fluctuations. In the limit of finite $q$ we then find that the scattering approaches the limit of polyelectrolyte solutions.
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We provide a theory for the dynamics of collapse of strongly charged polyelectrolytes (PEs) and flexible polyampholytes (PAs) using Langevin equation. After the initial stage, in which counterions condense onto PE, the mechanism of approach to the globular state is similar for PE and PA. In both instances, metastable pearl-necklace structures form in characteristic time scale that is proportional to N^{4/5} where N is the number of monomers. The late stage of collapse occurs by merger of clusters with the largest one growing at the expense of smaller ones (Lifshitz- Slyozov mechanism). The time scale for this process T_{COLL} N. Simulations are used to support the proposed collapse mechanism for PA and PE.
We present a multiscale simulation algorithm for amorphous materials, which we illustrate and validate in a canonical case of dense granular flow. Our algorithm is based on the recently proposed Spot Model, where particles in a dense random packing undergo chain-like collective displacements in response to diffusing spots of influence, carrying a slight excess of interstitial free volume. We reconstruct the microscopic dynamics of particles from the coarse grained dynamics of spots by introducing a localized particle relaxation step after each spot-induced block displacement, simply to enforce packing constraints with a (fairly arbitrary) soft-core repulsion. To test the model, we study to what extent it can describe the dynamics of up to 135,000 frictional, viscoelastic spheres in granular drainage simulated by the discrete-element method (DEM). With only five fitting parameters (the radius, volume, diffusivity, drift velocity, and injection rate of spots), we find that the spot simulations are able to largely reproduce not only the mean flow and diffusion, but also some subtle statistics of the flowing packings, such as spatial velocity correlations and many-body structural correlations. The spot simulations run over 100 times faster than DEM and demonstrate the possibility of multiscale modeling for amorphous materials, whenever a suitable model can be devised for the coarse-grained spot dynamics.
We have studied the collective short wavelength dynamics in deuterated DMPC bilayers by inelastic neutron scattering. The corresponding dispersion relation $hbaromega$(Q) is presented for the gel and fluid phase of this model system. The temperature dependence of the inelastic excitations indicates a phase coexistence between the two phases over a broad range and leads to a different assignment of excitations than that reported in a preceding inelastic x-ray scattering study [Phys. Rev. Lett. {bf 86}, 740 (2001)]. As a consequence, we find that the minimum in the dispersion relation is actually deeper in the gel than in the fluid phase. Finally, we can clearly identify an additional non-dispersive (optical) mode predicted by Molecular Dynamics (MD) simulations [Phys. Rev. Lett. {bf 87}, 238101 (2001)].
Circular milling, a stunning manifestation of collective motion, is found across the natural world, from fish shoals to army ants. It has been observed recently that the plant-animal worm $Symsagittifera~roscoffensis$ exhibits circular milling behaviour, both in shallow pools at the beach and in Petri dishes in the laboratory. Here we investigate this phenomenon, through experiment and theory, from a fluid dynamical viewpoint, focusing on the effect that an established circular mill has on the surrounding fluid. Unlike systems such as confined bacterial suspensions and collections of molecular motors and filaments that exhibit spontaneous circulatory behaviour, and which are modelled as force dipoles, the front-back symmetry of individual worms precludes a stresslet contribution. Instead, singularities such as source dipoles and Stokes quadrupoles are expected to dominate. A series of models is analyzed to understand the contributions of these singularities to the azimuthal flow fields generated by a mill, in light of the particular boundary conditions that hold for flow in a Petri dish. A model that treats a circular mill as a rigid rotating disc that generates a Stokes flow is shown to capture basic experimental results well, and gives insights into the emergence and stability of multiple mill systems.
We present the first inelastic neutron scattering study of the short wavelength dynamics in a phospholipid bilayer. We show that inelastic neutron scattering using a triple-axis spectrometer at the high flux reactor of the ILL yields the necessary resolution and signal to determine the dynamics of model membranes. The results can quantitatively be compared to recent Molecular Dynamics simulations. Reflectivity, in-plane correlations and the corresponding dynamics can be measured simultaneously to gain a maximum amount of information. With this method, dispersion relations can be measured with a high energy resolution. Structure and dynamics in phospholipid bilayers, and the relation between them, can be studied on a molecular length scale.
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