Noncooperative algorithms in self-assembly

We show the first non-trivial positive algorithmic results (i.e. programs whose output is larger than their size), in a model of self-assembly that has so far resisted many attempts of formal analysis or programming: the planar non-cooperative variant of Winfree's abstract Tile Assembly Model. This model has been the center of several open problems and conjectures in the last fifteen years, and the first fully general results on its computational power were only proven recently (SODA 2014). These results, as well as ours, exemplify the intricate connections between computation and geometry that can occur in self-assembly. In this model, tiles can stick to an existing assembly as soon as one of their sides matches the existing assembly. This feature contrasts with the general cooperative model, where it can be required that tiles match on \emph{several} of their sides in order to bind. In order to describe our algorithms, we also introduce a generalization of regular expressions called Baggins expressions. Finally, we compare this model to other automata-theoretic models.Comment: A few bug fixes and typo correction

Topological analysis of polymeric melts: Chain length effects and fast-converging estimators for entanglement length

Primitive path analyses of entanglements are performed over a wide range of chain lengths for both bead spring and atomistic polyethylene polymer melts. Estimators for the entanglement length N_e which operate on results for a single chain length N are shown to produce systematic O(1/N) errors. The mathematical roots of these errors are identified as (a) treating chain ends as entanglements and (b) neglecting non-Gaussian corrections to chain and primitive path dimensions. The prefactors for the O(1/N) errors may be large; in general their magnitude depends both on the polymer model and the method used to obtain primitive paths. We propose, derive and test new estimators which eliminate these systematic errors using information obtainable from the variation of entanglement characteristics with chain length. The new estimators produce accurate results for N_e from marginally entangled systems. Formulas based on direct enumeration of entanglements appear to converge faster and are simpler to apply.Comment: Major revisions. Developed near-ideal estimators which operate on multiple chain lengths. Now test these on two very different model polymers

Exact Gravity Duals for Simple Quantum Circuits

Holographic complexity proposals have sparked interest in quantifying thecost of state preparation in quantum field theories and its possible dualgravitational manifestations. The most basic ingredient in defining complexityis the notion of a class of circuits that, when acting on a given referencestate, all produce a desired target state. In the present work we build onstudies of circuits performing local conformal transformations in generaltwo-dimensional conformal field theories and construct the exact gravity dualto such circuits. In our approach to holographic complexity, the gravity dualto the optimal circuit is the one that minimizes an externally chosen costassigned to each circuit. Our results provide a basis for studying exactgravity duals to circuit costs from first principles.<br

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

Multifractal behavior of linear polymers in disordered media

The scaling behavior of linear polymers in disordered media modelled by self-avoiding random walks (SAWs) on the backbone of two- and three-dimensional percolation clusters at their critical concentrations p_c is studied. All possible SAW configurations of N steps on a single backbone configuration are enumerated exactly. We find that the moments of order q of the total number of SAWs obtained by averaging over many backbone configurations display multifractal behavior, i.e. different moments are dominated by different subsets of the backbone. This leads to generalized coordination numbers \mu_q and enhancement exponents \gamma_q, which depend on q. Our numerical results suggest that the relation \mu_1 = p_ c \mu between the first moment \mu_1 and its regular lattice counterpart \mu is valid.Comment: 11 pages, 12 postscript figures, to be published in Phys. Rev.

Sub-millimeter Spectroscopy of Astrophysically Important Molecules and Ions: Metal Hydrides, Halides, and Cyanides

With the advent of SOFIA, Herschel, and SAFIR, new wavelength regions will become routinely accessible for astronomical spectroscopy, particularly at submm frequencies (0.5-1.1 THz). Molecular emission dominates the spectra of dense interstellar gas at these wavelengths. Because heterodyne detectors are major instruments of these missions, accurate knowledge of transition frequencies is crucial for their success. The Ziurys spectroscopy laboratory has been focusing on the measurement of the pure rotational transitions of astrophysically important molecules in the sub-mm regime. Of particular interest have been metal hydride species and their ions, as well as metal halides and cyanides. A new avenue of study has included metal bearing molecular ions

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

Phase diagram of mixtures of colloids and polymers in the thermal crossover from good to θ\theta solvent

We determine the phase diagram of mixtures of spherical colloids and neutral nonadsorbing polymers in the thermal crossover region between the $\theta$ point and the good-solvent regime. We use the generalized free-volume theory (GFVT), which turns out to be quite accurate as long as $q = R_g/R_c\lesssim 1$ ($R_g$ is the radius of gyration of the polymer and $R_c$ is the colloid radius). Close to the $\theta$ point the phase diagram is not very sensitive to solvent quality, while, close to the good-solvent region, changes of the solvent quality modify significantly the position of the critical point and of the binodals. We also analyze the phase behavior of aqueous solutions of charged colloids and polymers, using the extension of GFVT proposed by Fortini et al., J. Chem. Phys. 128, 024904 (2008)

Unexpected relaxation dynamics of a self-avoiding polymer in cylindrical confinement

We report extensive simulations of the relaxation dynamics of a self-avoiding polymer confined inside a cylindrical pore. In particular, we concentrate on examining how confinement influences the scaling behavior of the global relaxation time of the chain, t, with the chain length N and pore diameter D. An earlier scaling analysis based on the de Gennes blob picture led to t ~ N^2D^(1/3). Our numerical effort that combines molecular dynamics and Monte Carlo simulations, however, consistently produces different t-results for N up to 2000. We argue that the previous scaling prediction is only asymptotically valid in the limit N >> D^(5/3) >> 1, which is currently inaccessible to computer simulations and, more interestingly, is also difficult to reach in experiments. Our results are thus relevant for the interpretation of recent experiments with DNA in nano- and micro-channels.Comment: 10 pages, 11 figure