Self-avoiding walks on scale-free networks

Several kinds of walks on complex networks are currently used to analyze search and navigation in different systems. Many analytical and computational results are known for random walks on such networks. Self-avoiding walks (SAWs) are expected to be more suitable than unrestricted random walks to explore various kinds of real-life networks. Here we study long-range properties of random SAWs on scale-free networks, characterized by a degree distribution $P(k) \sim k^{-\gamma}$. In the limit of large networks (system size $N \to \infty$), the average number $s_n$ of SAWs starting from a generic site increases as $\mu^n$, with $\mu = / - 1$. For finite $N$, $s_n$ is reduced due to the presence of loops in the network, which causes the emergence of attrition of the paths. For kinetic growth walks, the average maximum length, $$, increases as a power of the system size: $\sim N^{\alpha}$, with an exponent $\alpha$ increasing as the parameter $\gamma$ is raised. We discuss the dependence of $\alpha$ on the minimum allowed degree in the network. A similar power-law dependence is found for the mean self-intersection length of non-reversal random walks. Simulation results support our approximate analytical calculations.Comment: 9 pages, 7 figure

Heat capacity of α\alpha-GaN: Isotope Effects

Until recently, the heat capacity of GaN had only been measured for polycrystalline powder samples. Semiempirical as well as \textit{first-principles} calculations have appeared within the past few years. We present in this article measurements of the heat capacity of hexagonal single crystals of GaN in the 20-1400K temperature range. We find that our data deviate significantly from the literature values for polycrystalline materials. The dependence of the heat capacity on the isotopic mass has also been investigated recently for monatomic crystals such as diamond, silicon, and germanium. Multi-atomic crystals are expected to exhibit a different dependence of these heat capacities on the masses of each of the isotopes present. These effects have not been investigated in the past. We also present \textit{first-principles} calculations of the dependence of the heat capacities of GaN, as a canonical binary material, on each of the Ga and N masses. We show that they are indeed different, as expected from the fact that the Ga mass affects mainly the acoustic, that of N the optic phonons. It is hoped that these calculations will encourage experimental measurements of the dependence of the heat capacity on isotopic masses in binary and more complex semiconductors.Comment: 12 pages, 5 Figures, submitted to PR

Interacting Growth Walk - a model for hyperquenched homopolymer glass?

We show that the compact self avoiding walk configurations, kinetically generated by the recently introduced Interacting Growth Walk (IGW) model, can be considered as members of a canonical ensemble if they are assigned random values of energy. Such a mapping is necessary for studying the thermodynamic behaviour of this system. We have presented the specific heat data for the IGW, obtained from extensive simulations on a square lattice; we observe a broad hump in the specific heat above the $\theta$-point, contrary to expectation.Comment: 4 figures; Submitted to PR

Active Topological Glass Confined within a Spherical Cavity

[Image: see text] We study active topological glass under spherical confinement, allowing us to exceed the chain lengths simulated previously and determine the critical exponents of the arrested conformations. We find a previously unresolved “tank-treading” dynamic mode of active segments along the ring contour. This mode can enhance active–passive phase separation in the state of active topological glass when both diffusional and conformational relaxation of the rings are significantly suppressed. Within the observational time, we see no systematic trends in the positioning of the separated active domains within the confining sphere. The arrested state exhibits coherent stochastic rotations. We discuss possible connections of the conformational and dynamic features of the system to chromosomes enclosed in the nucleus of a living cell

Field theory of self-avoiding walks in random media

Based on the analogy with the quantum mechanics of a particle propagating in a {\em complex} potential, we develop a field-theoretical description of the statistical properties of a self-avoiding polymer chain in a random environment. We show that the account of the non-Hermiticity of the quantum Hamiltonian results in a qualitatively different structure of the effective action, compared to previous studies. Applying the renormalisation group analysis, we find a transition between the weak-disorder regime, where the quenched randomness is irrelevant, and the strong-disorder regime, where the polymer chain collapses. However, the fact that the renormalised interaction constants and the chiral symmetry breaking regularisation parameter flow towards strong coupling raises questions about the applicability of the perturbative analysis.Comment: RevTeX, 9 pages; accepted for publication in J. Phys.

Strong Attraction between Charged Spheres due to Metastable Ionized States

We report a mechanism which can lead to long range attractions between like-charged spherical macroions, stemming from the existence of metastable ionized states. We show that the ground state of a single highly charged colloid plus a few excess counterions is overcharged. For the case of two highly charged macroions in their neutralizing divalent counterion solution we demonstrate that, in the regime of strong Coulomb coupling, the counterion clouds are very likely to be unevenly distributed, leading to one overcharged and one undercharged macroion. This long-living metastable configuration in turn leads to a long range Coulomb attraction.Comment: REVTEX-published versio