Mechanisms of kinetic trapping in self-assembly and phase transformation

In self-assembly processes, kinetic trapping effects often hinder the formation of thermodynamically stable ordered states. In a model of viral capsid assembly and in the phase transformation of a lattice gas, we show how simulations in a self-assembling steady state can be used to identify two distinct mechanisms of kinetic trapping. We argue that one of these mechanisms can be adequately captured by kinetic rate equations, while the other involves a breakdown of theories that rely on cluster size as a reaction coordinate. We discuss how these observations might be useful in designing and optimising self-assembly reactions

A Generalized Q-operator for U_q(\hat(sl_2)) Vertex Models

In this paper, we construct a Q-operator as a trace of a representation of the universal R-matrix of $U_q(\hat{sl}_2)$ over an infinite-dimensional auxiliary space. This auxiliary space is a four-parameter generalization of the q-oscillator representations used previously. We derive generalized T-Q relations in which 3 of these parameters shift. After a suitable restriction of parameters, we give an explicit expression for the Q-operator of the 6-vertex model and show the connection with Baxter's expression for the central block of his corresponding operator.Comment: 22 pages, Latex2e. This replacement is a revised version that includes a simple explicit expression for the Q matrix for the 6-vertex mode

Glassy behaviour in an exactly solved spin system with a ferromagnetic transition

We show that applying simple dynamical rules to Baxter's eight-vertex model leads to a system which resembles a glass-forming liquid. There are analogies with liquid, supercooled liquid, glassy and crystalline states. The disordered phases exhibit strong dynamical heterogeneity at low temperatures, which may be described in terms of an emergent mobility field. Their dynamics are well-described by a simple model with trivial thermodynamics, but an emergent kinetic constraint. We show that the (second order) thermodynamic transition to the ordered phase may be interpreted in terms of confinement of the excitations in the mobility field. We also describe the aging of disordered states towards the ordered phase, in terms of simple rate equations.Comment: 11 page

Analyzing mechanisms and microscopic reversibility of self-assembly

We use computer simulations to investigate self-assembly in a system of model chaperonin proteins, and in an Ising lattice gas. We discuss the mechanisms responsible for rapid and efficient assembly in these systems, and we use measurements of dynamical activity and assembly progress to compare their propensities for kinetic trapping. We use the analytic solution of a simple minimal model to illustrate the key features associated with such trapping, paying particular attention to the number of ways that particles can misbind. We discuss the relevance of our results for the design and control of self-assembly in general.Comment: 11 pages, 8 figures. Discussion clarified in response to referee coment

Quantifying reversibility in a phase-separating lattice gas: an analogy with self-assembly

We present dynamic measurements of a lattice gas during phase separation, which we use as an analogy for self-assembly of equilibrium ordered structures. We use two approaches to quantify the degree of 'reversibility' of this process: firstly, we count events in which bonds are made and broken; secondly, we use correlation-response measurements and fluctuation-dissipation ratios to probe reversibility during different time intervals. We show how correlation and response functions can be related directly to microscopic (ir)reversibility and we discuss time-dependence and observable- dependence of these measurements, including the role of fast and slow degrees of freedom during assembly.Comment: 10 pages, 8 figure

Some Exact Results on the Potts Model Partition Function in a Magnetic Field

We consider the Potts model in a magnetic field on an arbitrary graph $G$. Using a formula of F. Y. Wu for the partition function $Z$ of this model as a sum over spanning subgraphs of $G$, we prove some properties of $Z$ concerning factorization, monotonicity, and zeros. A generalization of the Tutte polynomial is presented that corresponds to this partition function. In this context we formulate and discuss two weighted graph-coloring problems. We also give a general structural result for $Z$ for cyclic strip graphs.Comment: 5 pages, late

Seasonal phosphate activity in three characteristic soils of the English uplands polluted by long-term atmospheric nitrogen deposition

Phosphomonoesterase activities were determined monthly during a seasonal cycle in three characteristic soil types of the English uplands that have been subject to long-term atmospheric nitrogen deposition. Activities (moll para-nitrophenol ri soil dry wt. h-1) ranged between 83.9 and 307 in a blanket peat (total carbon 318 mg g-1, pH 3.9), 45.2-86.4 in an acid organic grassland soil (total carbon 354 mg g-1, pH 3.7) and 10.4-21.1 in a calcareous grassland soil (total carbon 140 mg g-1, pH 7.3). These are amongst the highest reported soil phosphomonoesterase activities and confirm the strong biological phosphorus limitation in this environmen

Asymptotic Limits and Zeros of Chromatic Polynomials and Ground State Entropy of Potts Antiferromagnets

We study the asymptotic limiting function $W({G},q) = \lim_{n \to \infty}P(G,q)^{1/n}$, where $P(G,q)$ is the chromatic polynomial for a graph $G$ with $n$ vertices. We first discuss a subtlety in the definition of $W({G},q)$ resulting from the fact that at certain special points $q_s$, the following limits do not commute: $\lim_{n \to \infty} \lim_{q \to q_s} P(G,q)^{1/n} \ne \lim_{q \to q_s} \lim_{n \to \infty} P(G,q)^{1/n}$. We then present exact calculations of $W({G},q)$ and determine the corresponding analytic structure in the complex $q$ plane for a number of families of graphs ${G}$, including circuits, wheels, biwheels, bipyramids, and (cyclic and twisted) ladders. We study the zeros of the corresponding chromatic polynomials and prove a theorem that for certain families of graphs, all but a finite number of the zeros lie exactly on a unit circle, whose position depends on the family. Using the connection of $P(G,q)$ with the zero-temperature Potts antiferromagnet, we derive a theorem concerning the maximal finite real point of non-analyticity in $W({G},q)$, denoted $q_c$ and apply this theorem to deduce that $q_c(sq)=3$ and $q_c(hc) = (3+\sqrt{5})/2$ for the square and honeycomb lattices. Finally, numerical calculations of $W(hc,q)$ and $W(sq,q)$ are presented and compared with series expansions and bounds.Comment: 33 pages, Latex, 5 postscript figures, published version; includes further comments on large-q serie

Impact Exercise Increases BMC During Growth: An 8-Year Longitudinal Study

Our aim was to assess BMC of the hip over 8 yr in prepubertal children who participated in a 7-mo jumping intervention compared with controls who participated in a stretching program of equal duration. We hypothesized that jumpers would gain more BMC than control subjects. The data reported come from two cohorts of children who participated in separate, but identical, randomized, controlled, school-based impact exercise interventions and reflect those subjects who agreed to long-term follow-up (N = 57; jumpers = 33, controls = 24; 47% of the original participants). BMC was assessed by DXA at baseline, 7 and 19 mo after intervention, and annually thereafter for 5 yr (eight visits over 8 yr). Multilevel random effects models were constructed and used to predict change in BMC from baseline at each measurement occasion. After 7 mo, those children that completed high-impact jumping exercises had 3.6% more BMC at the hip than control subjects whom completed nonimpact stretching activities (p \u3c 0.05) and 1.4% more BMC at the hip after nearly 8 yr (BMC adjusted for change in age, height, weight, and physical activity; p \u3c 0.05). This provides the first evidence of a sustained effect on total hip BMC from short-term high-impact exercise undertaken in early childhood. If the benefits are sustained into young adulthood, effectively increasing peak bone mass, fracture risk in the later years could be reduced

Ground State Entropy of the Potts Antiferromagnet on Cyclic Strip Graphs

We present exact calculations of the zero-temperature partition function (chromatic polynomial) and the (exponent of the) ground-state entropy $S_0$ for the $q$-state Potts antiferromagnet on families of cyclic and twisted cyclic (M\"obius) strip graphs composed of $p$-sided polygons. Our results suggest a general rule concerning the maximal region in the complex $q$ plane to which one can analytically continue from the physical interval where $S_0 > 0$. The chromatic zeros and their accumulation set ${\cal B}$ exhibit the rather unusual property of including support for $Re(q) < 0$ and provide further evidence for a relevant conjecture.Comment: 7 pages, Latex, 4 figs., J. Phys. A Lett., in pres