Binding branched and linear DNA structures: from isolated clusters to fully bonded gels

The proper design of DNA sequences allows for the formation of well defined supramolecular units with controlled interactions via a consecution of self-assembling processes. Here, we benefit from the controlled DNA self-assembly to experimentally realize particles with well defined valence, namely tetravalent nanostars (A) and bivalent chains (B). We specifically focus on the case in which A particles can only bind to B particles, via appropriately designed sticky-end sequences. Hence AA and BB bonds are not allowed. Such a binary mixture system reproduces with DNA-based particles the physics of poly-functional condensation, with an exquisite control over the bonding process, tuned by the ratio, r, between B and A units and by the temperature, T. We report dynamic light scattering experiments in a window of Ts ranging from 10{\deg}C to 55{\deg}C and an interval of r around the percolation transition to quantify the decay of the density correlation for the different cases. At low T, when all possible bonds are formed, the system behaves as a fully bonded network, as a percolating gel and as a cluster fluid depending on the selected r.Comment: 15 pages, 11 figure

Shear flow effects on phase separation of entangled polymer blends

We introduce an entanglement model mixing rule for stress relaxation in a polymer blend to a modified Cahn-Hilliard equation of motion for concentration fluctuations in the presence of shear flow. Such an approach predicts both shear-induced mixing and demixing, depending on the relative relaxation times and plateau moduli of the two components

Dynamic crossover scaling in polymer solutions

The crossover region in the phase diagram of polymer solutions, in the regime above the overlap concentration, is explored by Brownian Dynamics simulations, to map out the universal crossover scaling functions for the gyration radius and the single-chain diffusion constant. Scaling considerations, our simulation results, and recently reported data on the polymer contribution to the viscosity obtained from rheological measurements on DNA systems, support the assumption that there are simple relations between these functions, such that they can be inferred from one another.Comment: 4 pages, 6 figures, 1 Table. Revised version to appear in Physical Review Letters. Includes supplemental material

Random walk approach to the d-dimensional disordered Lorentz gas

A correlated random walk approach to diffusion is applied to the disordered nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic expression for the diffusion constant in arbitrary number of dimensions d is obtained. The result corresponds to an Enskog-like correction to the Boltzmann prediction, being exact in the dilute limit, and better or nearly exact in comparison to renormalized kinetic theory predictions for all allowed densities in d=2,3. Extensive numerical simulations were also performed to elucidate the role of the approximations involved.Comment: 5 pages, 5 figure

Polymer translocation out of confined environments

We consider the dynamics of polymer translocation out of confined environments. Analytic scaling arguments lead to the prediction that the translocation time scales like $\tau\sim N^{\beta+\nu_{2D}}R^{1+(1-\nu_{2D})/\nu}$ for translocation out of a planar confinement between two walls with separation $R$ into a 3D environment, and $\tau \sim N^{\beta+1}R$ for translocation out of two strips with separation $R$ into a 2D environment. Here, $N$ is the chain length, $\nu$ and $\nu_{2D}$ are the Flory exponents in 3D and 2D, and $\beta$ is the scaling exponent of translocation velocity with $N$, whose value for the present choice of parameters is $\beta \approx 0.8$ based on Langevin dynamics simulations. These scaling exponents improve on earlier predictions.Comment: 5 pages, 5 figures. To appear in Phys. Rev.

Scattering solutions in a network of thin fibers: small diameter asymptotics

Small diameter asymptotics is obtained for scattering solutions in a network of thin fibers. The asymptotics is expressed in terms of solutions of related problems on the limiting quantum graph. We calculate the Lagrangian gluing conditions at vertices for the problems on the limiting graph. If the frequency of the incident wave is above the bottom of the absolutely continuous spectrum, the gluing conditions are formulated in terms of the scattering data for each individual junction of the network

Role of friction-induced torque in stick-slip motion

We present a minimal quasistatic 1D model describing the kinematics of the transition from static friction to stick-slip motion of a linear elastic block on a rigid plane. We show how the kinematics of both the precursors to frictional sliding and the periodic stick-slip motion are controlled by the amount of friction-induced torque at the interface. Our model provides a general framework to understand and relate a series of recent experimental observations, in particular the nucleation location of micro-slip instabilities and the build up of an asymmetric field of real contact area.Comment: 6 pages, 5 figure

Boundary conditions associated with the Painlev\'e III' and V evaluations of some random matrix averages

In a previous work a random matrix average for the Laguerre unitary ensemble, generalising the generating function for the probability that an interval $(0,s)$ at the hard edge contains $k$ eigenvalues, was evaluated in terms of a Painlev\'e V transcendent in $\sigma$-form. However the boundary conditions for the corresponding differential equation were not specified for the full parameter space. Here this task is accomplished in general, and the obtained functional form is compared against the most general small $s$ behaviour of the Painlev\'e V equation in $\sigma$-form known from the work of Jimbo. An analogous study is carried out for the the hard edge scaling limit of the random matrix average, which we have previously evaluated in terms of a Painlev\'e \IIId transcendent in $\sigma$-form. An application of the latter result is given to the rapid evaluation of a Hankel determinant appearing in a recent work of Conrey, Rubinstein and Snaith relating to the derivative of the Riemann zeta function

Effects of differential mobility on biased diffusion of two species

Using simulations and a simple mean-field theory, we investigate jamming transitions in a two-species lattice gas under non-equilibrium steady-state conditions. The two types of particles diffuse with different mobilities on a square lattice, subject to an excluded volume constraint and biased in opposite directions. Varying filling fraction, differential mobility, and drive, we map out the phase diagram, identifying first order and continuous transitions between a free-flowing disordered and a spatially inhomogeneous jammed phase. Ordered structures are observed to drift, with a characteristic velocity, in the direction of the more mobile species.Comment: 15 pages, 4 figure