Collapsing lattice animals and lattice trees in two dimensions

We present high statistics simulations of weighted lattice bond animals and lattice trees on the square lattice, with fugacities for each non-bonded contact and for each bond between two neighbouring monomers. The simulations are performed using a newly developed sequential sampling method with resampling, very similar to the pruned-enriched Rosenbluth method (PERM) used for linear chain polymers. We determine with high precision the line of second order transitions from an extended to a collapsed phase in the resulting 2-dimensional phase diagram. This line includes critical bond percolation as a multicritical point, and we verify that this point divides the line into two different universality classes. One of them corresponds to the collapse driven by contacts and includes the collapse of (weakly embeddable) trees, but the other is {\it not yet} bond driven and does not contain the Derrida-Herrmann model as special point. Instead it ends at a multicritical point $P^*$ where a transition line between two collapsed phases (one bond-driven and the other contact-driven) sparks off. The Derrida-Herrmann model is representative for the bond driven collapse, which then forms the fourth universality class on the transition line (collapsing trees, critical percolation, intermediate regime, and Derrida-Herrmann). We obtain very precise estimates for all critical exponents for collapsing trees. It is already harder to estimate the critical exponents for the intermediate regime. Finally, it is very difficult to obtain with our method good estimates of the critical parameters of the Derrida-Herrmann universality class. As regards the bond-driven to contact-driven transition in the collapsed phase, we have some evidence for its existence and rough location, but no precise estimates of critical exponents.Comment: 11 pages, 16 figures, 1 tabl

Tricarbon­yl(η6-flavone)chromium(0)

In the title compound, [Cr(C15H10O2)(CO)3], the Cr(CO)3 unit exhibits a three-legged piano-stool conformation. The chromium metal centre is coordinated by the phenyl ring of the flavone ligand [Cr—(phenyl centroid) distance = 1.709 (1) Å]. The ligand is approximately planar, the dihedral angles between the γ-pyrone ring and the phenyl ring and between the γ-pyrone and the phenyl­ene ring being 2.91 (5) and 3.90 (5)°, respectively. The mol­ecular packing shows π–π stacking between the flavone ligands of neighbouring mol­ecules

Simulations of grafted polymers in a good solvent

We present improved simulations of three-dimensional self avoiding walks with one end attached to an impenetrable surface on the simple cubic lattice. This surface can either be a-thermal, having thus only an entropic effect, or attractive. In the latter case we concentrate on the adsorption transition, We find clear evidence for the cross-over exponent to be smaller than 1/2, in contrast to all previous simulations but in agreement with a re-summed field theoretic $\epsilon$-expansion. Since we use the pruned-enriched Rosenbluth method (PERM) which allows very precise estimates of the partition sum itself, we also obtain improved estimates for all entropic critical exponents.Comment: 5 pages with 9 figures included; minor change

Simulations of lattice animals and trees

The scaling behaviour of randomly branched polymers in a good solvent is studied in two to nine dimensions, using as microscopic models lattice animals and lattice trees on simple hypercubic lattices. As a stochastic sampling method we use a biased sequential sampling algorithm with re-sampling, similar to the pruned-enriched Rosenbluth method (PERM) used extensively for linear polymers. Essentially we start simulating percolation clusters (either site or bond), re-weigh them according to the animal (tree) ensemble, and prune or branch the further growth according to a heuristic fitness function. In contrast to previous applications of PERM, this fitness function is {\it not} the weight with which the actual configuration would contribute to the partition sum, but is closely related to it. We obtain high statistics of animals with up to several thousand sites in all dimension 2 <= d <= 9. In addition to the partition sum (number of different animals) we estimate gyration radii and numbers of perimeter sites. In all dimensions we verify the Parisi-Sourlas prediction, and we verify all exactly known critical exponents in dimensions 2, 3, 4, and >= 8. In addition, we present the hitherto most precise estimates for growth constants in d >= 3. For clusters with one site attached to an attractive surface, we verify the superuniversality of the cross-over exponent at the adsorption transition predicted by Janssen and Lyssy. Finally, we discuss the collapse of animals and trees, arguing that our present version of the algorithm is also efficient for some of the models studied in this context, but showing that it is {\it not} very efficient for the `classical' model for collapsing animals.Comment: 17 pages RevTeX, 29 figures include

Average Structures of a Single Knotted Ring Polymer

Two types of average structures of a single knotted ring polymer are studied by Brownian dynamics simulations. For a ring polymer with N segments, its structure is represented by a 3N -dimensional conformation vector consisting of the Cartesian coordinates of the segment positions relative to the center of mass of the ring polymer. The average structure is given by the average conformation vector, which is self-consistently defined as the average of the conformation vectors obtained from a simulation each of which is rotated to minimize its distance from the average conformation vector. From each conformation vector sampled in a simulation, 2N conformation vectors are generated by changing the numbering of the segments. Among the 2N conformation vectors, the one closest to the average conformation vector is used for one type of the average structure. The other type of the averages structure uses all the conformation vectors generated from those sampled in a simulation. In thecase of the former average structure, the knotted part of the average structure is delocalized for small N and becomes localized as N is increased. In the case of the latter average structure, the average structure changes from a double loop structure for small N to a single loop structure for large N, which indicates the localization-delocalization transition of the knotted part.Comment: 15 pages, 19 figures, uses jpsj2.cl

Racemic tricarbonyl[(4a,5,6,7,8,8a-η)-2-phenyl-3,4-dihydro-2H-1-benzopyran]chromium(0)

The title compound, [Cr(C15H14O)(CO)3], displays a distorted envelope configuration of the dihydro­pyrane ring. The dihedral angle between the phenyl and phenyl­ene rings is 50.63 (4)°. The Cr0 atom is coordinated by three CO groups and the phenyl­ene ring of the flavan ligand in an η6 mode, with a common arene-to-metal distanc

Racemic tricarbon­yl(η6-7-meth­oxy­flavan)chromium(0)

In the title compound [systematic name: tricarbonyl(η6-7-methoxy-2-phenyl-3,4-dihydro-2H-1-benzopyran)chromium(0)], [Cr(C16H16O2)(CO)3], the Cr(CO)3 unit is coordinated by the phenyl­ene ring of the flavan ligand, exhibiting a three-legged piano-stool conformation, with a point to plane distance of 1.750 (1) Å. The phenyl ring is twisted away from the fused ring system by 36.49 (5)° (r.m.s. deviation = 0.027 Å; fitted atoms are the C6 ring and the attached fused-ring C and O atoms). The dihydro­pyran ring displays a distorted envelope configuration by displacement of the phenyl-bearing and the adjacent ring C atoms from the fused-ring system plane by 0.356 (2) and 0.402 (2) Å, respectively

Transition of plasmodium sporozoites into liver stage-like forms is regulated by the RNA binding protein pumilio

Many eukaryotic developmental and cell fate decisions that are effected post-transcriptionally involve RNA binding proteins as regulators of translation of key mRNAs. In malaria parasites (Plasmodium spp.), the development of round, non-motile and replicating exo-erythrocytic liver stage forms from slender, motile and cell-cycle arrested sporozoites is believed to depend on environmental changes experienced during the transmission of the parasite from the mosquito vector to the vertebrate host. Here we identify a Plasmodium member of the RNA binding protein family PUF as a key regulator of this transformation. In the absence of Pumilio-2 (Puf2) sporozoites initiate EEF development inside mosquito salivary glands independently of the normal transmission-associated environmental cues. Puf2- sporozoites exhibit genome-wide transcriptional changes that result in loss of gliding motility, cell traversal ability and reduction in infectivity, and, moreover, trigger metamorphosis typical of early Plasmodium intra-hepatic development. These data demonstrate that Puf2 is a key player in regulating sporozoite developmental control, and imply that transformation of salivary gland-resident sporozoites into liver stage-like parasites is regulated by a post-transcriptional mechanism

Dyck Paths, Motzkin Paths and Traffic Jams

It has recently been observed that the normalization of a one-dimensional out-of-equilibrium model, the Asymmetric Exclusion Process (ASEP) with random sequential dynamics, is exactly equivalent to the partition function of a two-dimensional lattice path model of one-transit walks, or equivalently Dyck paths. This explains the applicability of the Lee-Yang theory of partition function zeros to the ASEP normalization. In this paper we consider the exact solution of the parallel-update ASEP, a special case of the Nagel-Schreckenberg model for traffic flow, in which the ASEP phase transitions can be intepreted as jamming transitions, and find that Lee-Yang theory still applies. We show that the parallel-update ASEP normalization can be expressed as one of several equivalent two-dimensional lattice path problems involving weighted Dyck or Motzkin paths. We introduce the notion of thermodynamic equivalence for such paths and show that the robustness of the general form of the ASEP phase diagram under various update dynamics is a consequence of this thermodynamic equivalence.Comment: Version accepted for publicatio

Area distribution of the planar random loop boundary

We numerically investigate the area statistics of the outer boundary of planar random loops, on the square and triangular lattices. Our Monte Carlo simulations suggest that the underlying limit distribution is the Airy distribution, which was recently found to appear also as area distribution in the model of self-avoiding loops.Comment: 10 pages, 2 figures. v2: minor changes, version as publishe