David Jasnow

Coarse‐grained description of thermo‐capillary flow

A mesoscopic or coarse‐grained approach is presented to study thermo‐capillary induced flows. An order parameter representation of a two‐phase binary fluid is used in which the interfacial region separating the phases naturally occupies a transition zone of small width. The order parameter satisfies the Cahn–Hilliard equation with advective transport. A modified Navier–Stokes equation that incorporates an explicit coupling to the order parameter field governs fluid flow. It reduces, in the limit of an infinitely thin interface, to the Navier–Stokes equation within the bulk phases and to two interfacial forces: a normal capillary force proportional to the surface tension and the mean curvature of the surface, and a tangential force proportional to the tangential derivative of the surface tension. The method is illustrated in two cases: thermo‐capillary migration of drops and phase separation via spinodal decomposition, both in an externally imposed temperature gradient.

Designing synthetic vesicles that engulf nanoscopic particles

We examine the interaction of a lipid bilayer membrane with a spherical particle in solution using dissipative particle dynamics, with the aim of controlling the passage of foreign objects into and out of vesicles. Parameters are chosen such that there is a favorable adhesive interaction between the membrane and the particle. Under these conditions, the membrane wraps the particle in a process resembling phagocytosis in biological cells. We find that, for a homogeneous membrane with a uniform attraction to the particle, the membrane is unable to fully wrap the particle when the adhesion strength is below a certain value. This is observed even in the limit of zero membrane tension. When the adhesion strength is increased above the threshold value, the membrane fully wraps the particle. However, the wrapped particle remains tethered to the larger membrane. We next consider an adhesive domain, or raft, in an otherwise nonadhesive membrane. We find that, when the particle is wrapped by the raft, the line tension at the raft interface promotes fission, allowing the wrapped particle to detach from the larger membrane. This mechanism could be used to allow particles to cross a vesicle membrane.

Simulation of Hard Particles in a Phase-Separating Binary Mixture

We simulate the motion of spherical particles in a phase-separating binary mixture. By combining cell dynamical equations with Langevin dynamics for particles, we show that the addition of hard particles significantly changes both the speed and the morphology of the phase separation. At the late stage of the spinodal decomposition process, particles significantly slow down the domain growth, in qualitative agreement with earlier experimental data. {copyright} {ital 1999} {ital The American Physical Society}

Efficient and verified simulation of a path ensemble for conformational change in a united-residue model of calmodulin

The computational sampling of rare, large-scale, conformational transitions in proteins is a well appreciated challenge—for which a number of potentially efficient path-sampling methodologies have been proposed. Here, we study a large-scale transition in a united-residue model of calmodulin using the “weighted ensemble” (WE) approach of Huber and Kim. Because of the models relative simplicity, we are able to compare our results with brute-force simulations. The comparison indicates that the WE approach quantitatively reproduces the brute-force results, as assessed by considering (i) the reaction rate, (ii) the distribution of event durations, and (iii) structural distributions describing the heterogeneity of the paths. Importantly, the WE method is readily applied to more chemically accurate models, and by studying a series of lower temperatures, our results suggest that the WE method can increase efficiency by orders of magnitude in more challenging systems.

Finite-size scaling and the renormalization group

Renormalization group calculations ind = 4 andd = 4 −ɛ are performed for a system of finite size. A form of mean-field theory is used which yields a rounded transition for a finite system, and this allows a sensible expansion in fluctuations. A combination of Ewald and Poisson sum techniques is used to produce explicit numerical results for the specific heat ind = 4 which, with the setting of two nonuniversal metrical factors and the fourth-order coupling constant may be compared with simulations. The numerical visibility of logarithmic corrections is investigated. The universal scaling function for the specific heat to relativeO(ɛ) is also evaluated numerically.

Interface and contact line motion in a two phase fluid under shear flow

We use a coarse grained description to study the steady state interfacial configuration of a two phase fluid under steady shear. Dissipative relaxation of the order parameter leads to interfacial slip at the contact line, even with no-slip boundary conditions on the fluid velocity. This relaxation occurs within a characteristic length scale l(0) = sqrt[xiD/V0], with xi the (microscopic) interfacial thickness, D an order parameter diffusivity, and V0 the boundary velocity. The steady state interfacial configuration is shown to satisfy a scaling form involving the ratio l(0)/L, where L is the width of the fluid layer, for a passive interface, and the capillary number as well for an active interface.

Finite-Size Scaling and the Renormalization Group

Renormalization group calculations ind = 4 andd = 4 −ɛ are performed for a system of finite size. A form of mean-field theory is used which yields a rounded transition for a finite system, and this allows a sensible expansion in fluctuations. A combination of Ewald and Poisson sum techniques is used to produce explicit numerical results for the specific heat ind = 4 which, with the setting of two nonuniversal metrical factors and the fourth-order coupling constant may be compared with simulations. The numerical visibility of logarithmic corrections is investigated. The universal scaling function for the specific heat to relativeO(ɛ) is also evaluated numerically.

Compatibilizing A/B blends with AB diblock copolymers: Effect of copolymer molecular weight

We use numerical self‐consistent field (SCF) calculations to determine the interfacial behavior of AB diblocks in a blend of immiscible homopolymers, A and B. In particular, we compare the compatibilizing effect of relatively short and long AB copolymers. In the calculations, we explicitly take into account the formation of micellar or multilamellar phases. The results show that the interfacial tension can be reduced to zero only if the blocks in the diblock are longer than the corresponding homopolymer. Our two‐dimensional SCF calculations reveal that short diblocks form multilamellar structures in the blend, whereas a microemulsion is formed when relatively long copolymers are added to the A/B mixture. These observations are compared with experiments on blends of polystyrene (PS), polymethyl methacrylate (PMMA), and PS‐PMMA symmetric diblock copolymers. By measuring the contact angle of PS droplets on the PMMA layer, we can obtain a direct estimate for the interfacial tension at the PS/PMMA interface. T...

Transition-event durations in one-dimensional activated processes

Despite their importance in activated processes, transition-event durations--which are much shorter than first passage times--have not received a complete theoretical treatment. The authors therefore study the distribution rhob(t) of durations of transition events over a barrier in a one-dimensional system undergoing overdamped Langevin dynamics. The authors show that rhob(t) is determined by a Fokker-Planck equation with absorbing boundary conditions and obtain a number of results, including (i) the analytic form of the asymptotic short-time transient behavior, which is universal and independent of the potential function; (ii) the first nonuniversal correction to the short-time behavior leading to an estimate of a key physical time scale; (iii) following previous work, a recursive formulation for calculating, exactly, all moments of rhob based solely on the potential function-along with approximations for the distribution based on a small number of moments; and (iv) a high-barrier approximation to the long-time (t-->infinity) behavior of rhob(t). The authors also find that the mean event duration does not depend simply on the barrier-top frequency (curvature) but is sensitive to details of the potential. All of the analytic results are confirmed by transition-path-sampling simulations implemented in a novel way. Finally, the authors discuss which aspects of the duration distribution are expected to be general for more complex systems.

Periodic droplet formation in chemically patterned microchannels.

Simulations show that, when a phase-separated binary AB fluid is driven to flow past chemically patterned substrates in a microchannel, the fluid exhibits unique morphological instabilities. For the pattern studied, these instabilities give rise to the simultaneous, periodic formation of monodisperse droplets of A in B and B in A. The system bifurcates between time-independent behavior and different types of regular, nondecaying oscillations in the structural characteristics. The surprisingly complex behavior is observed even in the absence of hydrodynamic interactions and arises from the interplay between the fluid flow and patterned substrate, which introduces nonlinearity into the dynamical system.