Efficiency and persistence in models of adaptation

A cut-and-paste model which mimics a trial-and-error process of adaptation is introduced and solved. The model, which can be thought of as a diffusion process with memory, is characterized by two properties, efficiency and persistence. We establish a link between these properties and determine two transitions for each property, a percolation transition and a depinning transition. If the adaptation process is iterated, the antipersistent state becomes an attractor of the dynamics. Extensions to higher dimensions are briefly discussed.Comment: 4 pages, 4 figures, submitted to publicatio

Collapse transition of a square-lattice polymer with next nearest-neighbor interaction

We study the collapse transition of a polymer on a square lattice with both nearest-neighbor and next nearest-neighbor interactions, by calculating the exact partition function zeros up to chain length 36. The transition behavior is much more pronounced than that of the model with nearest-neighbor interactions only. The crossover exponent and the transition temperature are estimated from the scaling behavior of the first zeros with increasing chain length. The results suggest that the model is of the same universality class as the usual theta point described by the model with only nearest-neighbor interaction.Comment: 14 pages, 5 figure

1-Methyl-2,4-bis­(2-methoxy­phen­yl)-3-aza­bicyclo­[3.3.1]nonan-9-one

The crystal structure of the title compound, C23H27NO3, shows that the compound exists in a chair–chair conformation with an equatorial disposition of 2-methoxy­phenyl groups at an angle of 39.94 (3)° with respect to each other. An inter­molecular N—H⋯π inter­action is observed in the crystal packing

2,4-Bis(2-methyl­phen­yl)-3-aza­bicyclo[3.3.1]nonan-9-one O-methyl­oxime

The mol­ecule of the title compound, C23H28N2O, exists in a twin-chair conformation, with equatorial orientation of the ortho-tolyl groups on both sides of the secondary amino group. The title oxime compound and its ketone precursor 2,4-bis­(2-methyl­phen­yl)-3-aza­bicyclo­[3.3.1]nonan-9-one exhibit similar stereochemistries, with the orientation of the o-tolyl rings almost identical in both compounds. In the title compound, the tolyl rings are at an angle of 23.77 (3)° with respect to one another; the angle in the precursor is 29.4 (1)° [Vijayalakshmi, Parthasarathi, Venkatraj & Jeyaraman (2000 ▶), Acta Cryst. C56, 1240–1241]. The cyclo­hexane ring and the oxime ether are disordered over two alternative orientations, with a refined site-occupancy ratio of 0.813 (2):0.186 (4). The crystal structure of the title compound is stabilized by inter­molecular N—H⋯π inter­actions

2,4-Bis(4-propoxyphen­yl)-3-aza­bicyclo­[3.3.1]nonan-9-one

In the title compound, C26H33NO3, a crystallographic mirror plane bis­ects the mol­ecule (two C atoms, one O atom and one N atom lie on the mirror plane). The mol­ecule exists in a twin-chair conformation with equatorial orientations of the 4-propoxyphenyl groups. The dihedral angle between the 4-propoxyphenyl groups is 31.58 (3)°

Exotic magnetism on the quasi-FCC lattices of the d3d^3 double perovskites La2_2NaB′'O6_6 (B′' == Ru, Os)

We find evidence for long-range and short-range ($\zeta$ $=$ 70 \AA~at 4 K) incommensurate magnetic order on the quasi-face-centered-cubic (FCC) lattices of the monoclinic double perovskites La$_2$NaRuO$_6$ and La$_2$NaOsO$_6$ respectively. Incommensurate magnetic order on the FCC lattice has not been predicted by mean field theory, but may arise via a delicate balance of inequivalent nearest neighbour and next nearest neighbour exchange interactions. In the Ru system with long-range order, inelastic neutron scattering also reveals a spin gap $\Delta$ $\sim$ 2.75 meV. Magnetic anisotropy is generally minimized in the more familiar octahedrally-coordinated $3d^3$ systems, so the large gap observed for La$_2$NaRuO$_6$ may result from the significantly enhanced value of spin-orbit coupling in this $4d^3$ material.Comment: 5 pages, 4 figure

Exact Partition Function Zeros of a Polymer on a Simple-Cubic Lattice

We study conformational transitions of a polymer on a simple-cubic lattice by calculating the zeros of the exact partition function, up to chain length 24. In the complex temperature plane, two loci of the partition function zeros are found for longer chains, suggesting the existence of both the coil-globule collapse transition and the melting-freezing transition. The locus corresponding to coil-globule transition clearly approaches the real axis as the chain length increases, and the transition temperature could be estimated by finite-size scaling. The form of the logarithmic correction to the scaling of the partition function zeros could also be obtained. The other locus does not show clear scaling behavior, but a supplementary analysis of the specific heat reveals a first-order-like pseudo-transition.Comment: 21 pages, 4 figure

Critical Exponents of the Four-State Potts Model

The critical exponents of the four-state Potts model are directly derived from the exact expressions for the latent heat, the spontaneous magnetization, and the correlation length at the transition temperature of the model.Comment: LaTex, 7 page