arXiv subjects

G. Gompper

Publications and source records attributed to G. Gompper.

At least 19 recordsLinked to original sources

arXiv2015

Conformations, hydrodynamic interactions, and instabilities of sedimenting semiflexible filaments

The conformations and dynamics of semiflexible filaments subject to a homogeneous external (gravitational) field, e.g., in a centrifuge, are studied numerically and analytically. The competition between hydrodynamic drag and bending elasticity generates new shapes and dynamical features. We show that the shape of a semiflexible filament undergoes instabilities as the external field increases. We identify two transitions that correspond to the excitation of higher bending modes. In particular, for strong fields the filament stabilizes in a non-planar shape, resulting in a sideways drift or in helical trajectories. For two interacting filaments, we find the same transitions, with the important consequence that the new non-planar shapes have an effective hydrodynamic repulsion, in contrast to the planar shapes which attract themselves even when their osculating planes are rotated with respect to each other. For the case of planar filaments, we show analytically and numerically that the relative velocity is not necessarily due to a different drag of the individual filaments, but to the hydrodynamic interactions induced by their shape asymmetry.

physics.bio-ph↗

arXiv2014

Rheological properties of sheared vesicle and cell suspensions

Numerical simulations of vesicle suspensions are performed in two dimensions to study their dynamical and rheological properties. An hybrid method is adopted, which combines a mesoscopic approach for the solvent with a curvature-elasticity model for the membrane. Shear flow is induced by two counter-sliding parallel walls, which generate a linear flow profile. The flow behavior is studied for various vesicle concentrations and viscosity ratios between the internal and the external fluid. Both the intrinsic viscosity and the thickness of depletion layers near the walls are found to increase with increasing viscosity ratio.

cond-mat.soft↗

arXiv2013

Non-equilibrium structure and dynamics in a microscopic model of thin film active gels

In the presence of ATP, molecular motors generate active force dipoles that drive suspensions of protein filaments far from thermodynamic equilibrium, leading to exotic dynamics and pattern formation. Microscopic modelling can help to quantify the relationship between individual motors plus filaments to organisation and dynamics on molecular and supra-molecular length scales. Here we present results of extensive numerical simulations of active gels where the motors and filaments are confined between two infinite parallel plates. Thermal fluctuations and excluded-volume interactions between filaments are included. A systematic variation of rates for motor motion, attachment and detachment, including a differential detachment rate from filament ends, reveals a range of non-equilibrium behaviour. Strong motor binding produces structured filament aggregates that we refer to as asters, bundles or layers, whose stability depends on motor speed and differential end-detachment. The gross features of the dependence of the observed structures on the motor rate and the filament concentration can be captured by a simple one-filament model. Loosely bound aggregates exhibit super-diffusive mass transport, where filament translocation scales with lag time with non-unique exponents that depend on motor kinetics. An empirical data collapse of filament speed as a function of motor speed and end-detachment is found, suggesting a dimensional reduction of the relevant parameter space. We conclude by discussing the perspectives of microscopic modelling in the field of active gels.

physics.bio-ph↗

arXiv2013

Dynamics and Rheology of Vesicle Suspensions in Wall-Bounded Shear Flow

The dynamics and rheology of suspensions of fluid vesicles or red blood cells is investigated by a combination of molecular dynamics and mesoscale hydrodynamics simulations in two dimensions. The vesicle suspension is confined between two no-slip walls, which are driven externally to generate a shear flow with shear rate $\dotγ$. The flow behavior is studied as a function of $\dotγ$, the volume fraction of vesicles, and the viscosity contrast between inside and outside fluids. Results are obtained for the encounter and interactions of two vesicles, the intrinsic viscosity of the suspension, and the cell-free layer near the walls.

cond-mat.soft↗

arXiv2011

Simple and complex micelles in amphiphilic mixtures: a coarse-grained mean-field study

Binary mixtures of amphiphiles in solution can self-assemble into a wide range of structures when the two species individually form aggregates of different curvatures. In this paper, we focus on small, spherically-symmetric aggregates in a solution of sphere-forming amphiphile mixed with a smaller amount of lamella-forming amphiphile. Using a coarse-grained mean-field model (self-consistent field theory, or SCFT), we scan the parameter space of this system and find a range of morphologies as the interaction strength, architecture and mixing ratio of the amphiphiles are varied. When the two species are quite similar in architecture, or when only a small amount of lamella-former is added, we find simple spherical micelles with cores formed from a mixture of the hydrophobic blocks of the two amphiphiles. For more strongly mismatched amphiphiles and higher lamella-former concentrations, we instead find small vesicles and more complex micelles. In these latter structures, the lamella-forming species is encapsulated by the sphere-forming one. For certain interaction strengths and lamella-former architectures, the amount of lamella-forming copolymer encapsulated may be large, and the implications of this for the solubilization of hydrophobic chemicals are considered. The mechanisms behind the formation of the above structures are discussed, with a particular emphasis on the sorting of amphiphiles according to their preferred curvature.

cond-mat.soft↗

arXiv2011

Tumbling of polymers in semidilute solution under shear flow

The tumbling dynamics of individual polymers in semidilute solution is studied by large-scale non-equilibrium mesoscale hydrodynamic simulations. We find that the tumbling time is equal to the non-equilibrium relaxation time of the polymer end-to-end distance along the flow direction and strongly depends on concentration. In addition, the normalized tumbling frequency as well as the widths of the alignment distribution functions for a given concentration-dependent Weissenberg number exhibit a weak concentration dependence in the cross-over regime from a dilute to a semidilute solution. For semidilute solutions a universal behavior is obtained. This is a consequence of screening of hydrodynamic interactions at polymer concentrations exceeding the overlap concentration.

cond-mat.soft↗

arXiv2011

Bilayers in amphiphilic mixtures connected by threadlike micelles: a self-consistent field theory study

Binary mixtures of amphiphiles in solution can self-assemble into a wide range of structures when the two species individually form aggregates of different curvatures. A specific example of this is seen in solutions of lipid mixtures where the two species form lamellar structures and spherical micelles respectively. Here, vesicles connected by thread-like micelles can form in a narrow concentration range of the sphere-forming lipid. We present a self-consistent field theory (SCFT) study of these structures. Firstly, we show that the addition of sphere-forming lipid to a solution of lamella-former can lower the free energy of cylindrical, thread-like micelles and hence encourage their formation. Next, we demonstrate the coupling between composition and curvature; specifically, that increasing the concentration of sphere-former in a system of two bilayers connected by a thread leads to a transfer of amphiphile to the thread. We further show that the two species are segregated within the structure, with the concentration of sphere-former being significantly higher in the thread. Finally, the addition of larger amounts of sphere-former is found to destabilize the junctions linking the bilayers to the cylindrical micelle, leading to a breakdown of the connected structures. The degree of segregation of the amphiphiles and the amount of sphere-former required to destabilize the junctions is shown to be sensitive to the length of the hydrophilic block of the sphere-forming amphiphiles.

cond-mat.soft↗

arXiv2008

Multi-Particle Collision Dynamics -- a Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids

In this review, we describe and analyze a mesoscale simulation method for fluid flow, which was introduced by Malevanets and Kapral in 1999, and is now called multi-particle collision dynamics (MPC) or stochastic rotation dynamics (SRD). The method consists of alternating streaming and collision steps in an ensemble of point particles. The multi-particle collisions are performed by grouping particles in collision cells, and mass, momentum, and energy are locally conserved. This simulation technique captures both full hydrodynamic interactions and thermal fluctuations. The first part of the review begins with a description of several widely used MPC algorithms and then discusses important features of the original SRD algorithm and frequently used variations. Two complementary approaches for deriving the hydrodynamic equations and evaluating the transport coefficients are reviewed. It is then shown how MPC algorithms can be generalized to model non-ideal fluids, and binary mixtures with a consolute point. The importance of angular-momentum conservation for systems like phase-separated liquids with different viscosities is discussed. The second part of the review describes a number of recent applications of MPC algorithms to study colloid and polymer dynamics, the behavior of vesicles and cells in hydrodynamic flows, and the dynamics of viscoelastic fluids.

cond-mat.soft↗

arXiv2007

Mesoscale simulations of polymer dynamics in microchannel flows

The non-equilibrium structural and dynamical properties of flexible polymers confined in a square microchannel and exposed to a Poiseuille flow are investigated by mesoscale simulations. The chain length and the flow strength are systematically varied. Two transport regimes are identified, corresponding to weak and strong confinement. For strong confinement, the transport properties are independent of polymer length. The analysis of the long-time tumbling dynamics of short polymers yields non-periodic motion with a sublinear dependence on the flow strength. We find distinct differences for conformational as well as dynamical properties from results obtained for simple shear flow.

cond-mat.soft↗

arXiv2005

Dynamic regimes of fluids simulated by multiparticle-collision dynamics

We investigate the hydrodynamic properties of a fluid simulated with a mesoscopic solvent model. Two distinct regimes are identified, the `particle regime' in which the dynamics is gas-like, and the `collective regime' where the dynamics is fluid-like. This behavior can be characterized by the Schmidt number, which measures the ratio between viscous and diffusive transport. Analytical expressions for the tracer diffusion coefficient, which have been derived on the basis of a molecular-chaos assumption, are found to describe the simulation data very well in the particle regime, but important deviations are found in the collective regime. These deviations are due to hydrodynamic correlations. The model is then extended in order to investigate self-diffusion in colloidal dispersions. We study first the transport properties of heavy point-like particles in the mesoscopic solvent, as a function of their mass and number density. Second, we introduce excluded-volume interactions among the colloidal particles and determine the dependence of the diffusion coefficient on the colloidal volume fraction for different solvent mean-free paths. In the collective regime, the results are found to be in good agreement with previous theoretical predictions based on Stokes hydrodynamics and the Smoluchowski equation.

cond-mat.soft↗

arXiv2005

DNA condensation and redissolution: Interaction between overcharged DNA molecules

The effective DNA-DNA interaction force is calculated by computer simulations with explicit tetravalent counterions and monovalent salt. For overcharged DNA molecules, the interaction force shows a double-minimum structure. The positions and depths of these minima are regulated by the counterion density in the bulk. Using two-dimensional lattice sum and free energy perturbation theories, the coexisting phases for DNA bundles are calculated. A DNA-condensation and redissolution transition and a stable mesocrystal with an intermediate lattice constant for high counterion concentration are obtained.

q-bio.BM↗

arXiv2004

Helical polymer in cylindrical confining geometries

Using an algorithm for simulating equilibrium configurations, we study a fluctuating helical polymer either (i) contained in a cylindrical pore or (ii) wound around a cylindrical rod. We work in the regime where both the contour length and the persistence length of the helical polymer are much larger than the diameter of the cylinder. In case (i) we calculate the free energy of confinement and interpret it in terms of a worm-like chain in a pore with an effective diameter that depends on the parameters of the helix. In case (ii) we consider the possibility that one end of the helical polymer escapes from the rod and wanders away. The average numbers of turns at which the helix escapes or intersects the rod are measured in the simulations, as a function of the pitch $p_0$. The behavior for large and small $p_0$ is explained with simple scaling arguments.

cond-mat.soft↗

arXiv2004

DNA-condensation, redissolution and mesocrystals induced by tetravalent counterions

The distance-resolved effective interaction potential between two parallel DNA molecules is calculated by computer simulations with explicit tetravalent counterions and monovalent salt. Adding counterions first yields an attractive minimum in the potential at short distances which then disappears in favor of a shallower minimum at larger separations. The resulting phase diagram includes a DNA-condensation and redissolution transition and a stable mesocrystal with an intermediate lattice constant for high counterion concentration.

cond-mat.soft↗

arXiv2003

Attraction between DNA molecules mediated by multivalent ions

The effective force between two parallel DNA molecules is calculated as a function of their mutual separation for different valencies of counter- and salt ions and different salt concentrations. Computer simulations of the primitive model are used and the shape of the DNA molecules is accurately modelled using different geometrical shapes. We find that multivalent ions induce a significant attraction between the DNA molecules whose strength can be tuned by the averaged valency of the ions. The physical origin of the attraction is traced back either to electrostatics or to entropic contributions. For multivalent counter- and monovalent salt ions, we find a salt-induced stabilization effect: the force is first attractive but gets repulsive for increasing salt concentration. Furthermore, we show that the multivalent-ion-induced attraction does not necessarily correlate with DNA overcharging.

cond-mat.soft↗

arXiv2003

Adsorption of mono- and multivalent cat- and anions on DNA molecules

Adsorption of monovalent and multivalent cat- and anions on a deoxyribose nucleic acid (DNA) molecule from a salt solution is investigated by computer simulation. The ions are modelled as charged hard spheres, the DNA molecule as a point charge pattern following the double-helical phosphate strands. The geometrical shape of the DNA molecules is modelled on different levels ranging from a simple cylindrical shape to structured models which include the major and minor grooves between the phosphate strands. The densities of the ions adsorbed on the phosphate strands, in the major and in the minor grooves are calculated. First, we find that the adsorption pattern on the DNA surface depends strongly on its geometrical shape: counterions adsorb preferentially along the phosphate strands for a cylindrical model shape, but in the minor groove for a geometrically structured model. Second, we find that an addition of monovalent salt ions results in an increase of the charge density in the minor groove while the total charge density of ions adsorbed in the major groove stays unchanged. The adsorbed ion densities are highly structured along the minor groove while they are almost smeared along the major groove. Furthermore, for a fixed amount of added salt, the major groove cationic charge is independent on the counterion valency. For increasing salt concentration the major groove is neutralized while the total charge adsorbed in the minor groove is constant. DNA overcharging is detected for multivalent salt. Simulations for a larger ion radii, which mimic the effect of the ion hydration, indicate an increased adsorbtion of cations in the major groove.

cond-mat.soft↗

arXiv2003

Bicontinuous surfaces in self-assembling amphiphilic systems

Amphiphiles are molecules which have both hydrophilic and hydrophobic parts. In water- and/or oil-like solvent, they self-assemble into extended sheet-like structures due to the hydrophobic effect. The free energy of an amphiphilic system can be written as a functional of its interfacial geometry, and phase diagrams can be calculated by comparing the free energies following from different geometries. Here we focus on bicontinuous structures, where one highly convoluted interface spans the whole sample and thereby divides it into two separate labyrinths. The main models for surfaces of this class are triply periodic minimal surfaces, their constant mean curvature and parallel surface companions, and random surfaces. We discuss the geometrical properties of each of these types of surfaces and how they translate into the experimentally observed phase behavior of amphiphilic systems.

cond-mat.soft↗

arXiv2001

Semi-Flexible Polymer in a Uniform Force Field in Two Dimensions

The conformational properties of a semi-flexible polymer chain, anchored at one end in a uniform force field, are studied in a simple two-dimensional model. Recursion relations are derived for the partition function and then iterated numerically. We calculate the angular fluctuations of the polymer about the direction of the force field and the average polymer configuration as functions of the bending rigidity, chain length, chain orientation at the anchoring point, and field strength.

cond-mat.soft↗

arXiv2001

Multi-particle-collision dynamics: Flow around a circular and a square cylinder

A particle-based model for mesoscopic fluid dynamics is used to simulate steady and unsteady flows around a circular and a square cylinder in a two-dimensional channel for a range of Reynolds number between 10 and 130. Numerical results for the recirculation length, the drag coefficient, and the Strouhal number are reported and compared with previous experimental measurements and computational fluid dynamics data. The good agreement demonstrates the potential of this method for the investigation of complex flows.

cond-mat.soft↗