Elasticity near the vulcanization transition

Signatures of the vulcanization transition--amorphous solidification induced by the random crosslinking of macromolecules--include the random localization of a fraction of the particles and the emergence of a nonzero static shear modulus. A semi-microscopic statistical-mechanical theory is presented of the latter signature that accounts for both thermal fluctuations and quenched disorder. It is found (i) that the shear modulus grows continuously from zero at the transition, and does so with the classical exponent, i.e., with the third power of the excess cross-link density and, quite surprisingly, (ii) that near the transition the external stresses do not spoil the spherical symmetry of the localization clouds of the particles.Comment: REVTEX, 5 pages. Minor change

High Resolution 3D Earth Observation Data Analysis for Safeguards Activities

This paper provides an overview of the investigations performed at DLR with respect to the application of high resolution SAR and optical data for 3D analysis in the context of Safeguards. The Research Center Jülich and the adjacent open cut mines were used as main test sites, and a comprehensive stack of ascending and descending TerraSAR data was acquired over two years. TerraSAR data acquisition was performed, and various ways to visualize and analyze stacks of radar images were evaluated. Building height estimation was performed using a combination of ascending-descending radar images, as well as height-form-shadow and height-from-layover. A tutorial on building signatures from SAR images highlighted the sensor specific imaging characteristics. These topics were particularly relevant in safeguards activity with a “small-budget” as only a single image – or a couple - were employed. Interferometric coherence map interpretation allows the detection of traffic on dirt roads. Digital surface models (DSM) were generated from TanDEM-X interferometric data and from optical VHR data. Sub-meter Worldview-2 and GeoEye-1 data was processed into highly detailed DSM with a grid spacing of 1 m, showing building structures. 3D change and volume detection was performed with both optical and radar DSMs. The TanDEM-X DSMs proved useful for volume change detection and computation in mining areas, and DSMs generated from optical satellite data show details on the building level. Virtual 3D fly-throughs were found to be a good tool to provide an intuitive understanding of site structure and might be useful for inspector briefing

Universal Formulae for Percolation Thresholds

A power law is postulated for both site and bond percolation thresholds. The formula writes $p_c=p_0[(d-1)(q-1)]^{-a}d^{\ b}$, where $d$ is the space dimension and $q$ the coordination number. All thresholds up to $d\rightarrow \infty$ are found to belong to only three universality classes. For first two classes $b=0$ for site dilution while $b=a$ for bond dilution. The last one associated to high dimensions is characterized by $b=2a-1$ for both sites and bonds. Classes are defined by a set of value for $\{p_0; \ a\}$. Deviations from available numerical estimates at $d \leq 7$ are within $\pm 0.008$ and $\pm 0.0004$ for high dimensional hypercubic expansions at $d \geq 8$. The formula is found to be also valid for Ising critical temperatures.Comment: 11 pages, latex, 3 figures not include

Effective interactions between star polymers

We study numerically the effective pair potential between star polymers with equal arm lengths and equal number $f$ of arms. The simulations were done for the soft core Domb-Joyce model on the simple cubic lattice, to minimize corrections to scaling and to allow for an unlimited number of arms. For the sampling, we used the pruned-enriched Rosenbluth method (PERM). We find that the potential is much less soft than claimed in previous papers, in particular for $f\gg 1$. While we verify the logarithmic divergence of $V(r)$, with $r$ being the distance between the two cores, predicted by Witten and Pincus, we find for $f>20$ that the Mayer function is hardly distinguishable from that for a Gaussian potential.Comment: 5 pages, 5 figure

Charge renormalization and phase separation in colloidal suspensions

We explore the effects of counterion condensation on fluid-fluid phase separation in charged colloidal suspensions. It is found that formation of double layers around the colloidal particles stabilizes suspensions against phase separation. Addition of salt, however, produces an instability which, in principle, can lead to a fluid-fluid separation. The instability, however, is so weak that it should be impossible to observe a fully equilibrated coexistence experimentally.Comment: 7 pages, Europhysics Letters (in press

Effective interactions between star polymers and colloidal particles

Using monomer-resolved Molecular Dynamics simulations and theoretical arguments based on the radial dependence of the osmotic pressure in the interior of a star, we systematically investigate the effective interactions between hard, colloidal particles and star polymers in a good solvent. The relevant parameters are the size ratio q between the stars and the colloids, as well as the number of polymeric arms f (functionality) attached to the common center of the star. By covering a wide range of q's ranging from zero (star against a flat wall) up to about 0.75, we establish analytical forms for the star-colloid interaction which are in excellent agreement with simulation results. A modified expression for the star-star interaction for low functionalities, f < 10 is also introduced.Comment: 37 pages, 14 figures, preprint-versio

Microscopic formulation of the Zimm-Bragg model for the helix-coil transition

A microscopic spin model is proposed for the phenomenological Zimm-Bragg model for the helix-coil transition in biopolymers. This model is shown to provide the same thermophysical properties of the original Zimm-Bragg model and it allows a very convenient framework to compute statistical quantities. Physical origins of this spin model are made transparent by an exact mapping into a one-dimensional Ising model with an external field. However, the dependence on temperature of the reduced external field turns out to differ from the standard one-dimensional Ising model and hence it gives rise to different thermophysical properties, despite the exact mapping connecting them. We discuss how this point has been frequently overlooked in the recent literature.Comment: 11 pages, 2 figure

Statistical Models on Spherical Geometries

We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such a walk by studying the phase diagram of a percolation problem. We find a line of second and first order phase transitions separated by a tricritical point. Then, we analyze the adsorption-desorption transition for a polymer growing near the attractive boundary of a cylindrical cell membrane. We find that the fraction of adsorbed monomers on the boundary vanishes exponentially when the adsorption energy decreases towards its critical value.Comment: 8 pages, latex, 2 figures in p

Stretching Semiflexible Polymer Chains: Evidence for the Importance of Excluded Volume Effects from Monte Carlo Simulation

Semiflexible macromolecules in dilute solution under very good solvent conditions are modeled by self-avoiding walks on the simple cubic lattice ($d=3$ dimensions) and square lattice ($d=2$ dimensions), varying chain stiffness by an energy penalty $\epsilon_b$ for chain bending. In the absence of excluded volume interactions, the persistence length $\ell_p$ of the polymers would then simply be $\ell_p=\ell_b(2d-2)^{-1}q_b^{-1}$ with $q_b= \exp(-\epsilon_b/k_BT)$, the bond length $\ell_b$ being the lattice spacing, and $k_BT$ is the thermal energy. Using Monte Carlo simulations applying the pruned-enriched Rosenbluth method (PERM), both $q_b$ and the chain length $N$ are varied over a wide range $(0.005 \leq q_b \leq 1, \; N \leq 50000$), and also a stretching force $f$ is applied to one chain end (fixing the other end at the origin). In the absence of this force, in $d=2$ a single crossover from rod-like behavior (for contour lengths less than $\ell_p$) to swollen coils occurs, invalidating the Kratky-Porod model, while in $d=3$ a double crossover occurs, from rods to Gaussian coils (as implied by the Kratky-Porod model) and then to coils that are swollen due to the excluded volume interaction. If the stretching force is applied, excluded volume interactions matter for the force versus extension relation irrespective of chain stiffness in $d=2$, while theories based on the Kratky-Porod model are found to work in $d=3$ for stiff chains in an intermediate regime of chain extensions. While for $q_b \ll 1$ in this model a persistence length can be estimated from the initial decay of bond-orientational correlations, it is argued that this is not possible for more complex wormlike chains (e.g. bottle-brush polymers). Consequences for the proper interpretation of experiments are briefly discussed.Comment: 23 pages, 17 figures, 2 tables, to be published in J. Chem. Phys. (2011