One of ten thousand: a way for the printmaker; thoughts and images related to involvement in Zen Buddhism

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Numerical Results for the Ground-State Interface in a Random Medium

The problem of determining the ground state of a $d$-dimensional interface embedded in a $(d+1)$-dimensional random medium is treated numerically. Using a minimum-cut algorithm, the exact ground states can be found for a number of problems for which other numerical methods are inexact and slow. In particular, results are presented for the roughness exponents and ground-state energy fluctuations in a random bond Ising model. It is found that the roughness exponent $\zeta = 0.41 \pm 0.01, 0.22 \pm 0.01$, with the related energy exponent being $\theta = 0.84 \pm 0.03, 1.45 \pm 0.04$, in $d = 2, 3$, respectively. These results are compared with previous analytical and numerical estimates.Comment: 10 pages, REVTEX3.0; 3 ps files (separate:tar/gzip/uuencoded) for figure

Intrinsic noise and discrete-time processes

A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For finite populations an approximate Gaussian scheme is devised to describe the stochastic fluctuations in the non-chaotic regime. More generally, the stochastic dynamics can be captured using a stochastic difference equation, derived through an approximation to the Markov chain. The scheme is demonstrated using the logistic map as a case study.Comment: Modified version accepted for publication in Phys. Rev. E Rapid Communications. New figures adde

Vicious Walkers in a Potential

We consider N vicious walkers moving in one dimension in a one-body potential v(x). Using the backward Fokker-Planck equation we derive exact results for the asymptotic form of the survival probability Q(x,t) of vicious walkers initially located at (x_1,...,x_N) = x, when v(x) is an arbitrary attractive potential. Explicit results are given for a square-well potential with absorbing or reflecting boundary conditions at the walls, and for a harmonic potential with an absorbing or reflecting boundary at the origin and the walkers starting on the positive half line. By mapping the problem of N vicious walkers in zero potential onto the harmonic potential problem, we rederive the results of Fisher [J. Stat. Phys. 34, 667 (1984)] and Krattenthaler et al. [J. Phys. A 33}, 8835 (2000)] respectively for vicious walkers on an infinite line and on a semi-infinite line with an absorbing wall at the origin. This mapping also gives a new result for vicious walkers on a semi-infinite line with a reflecting boundary at the origin: Q(x,t) \sim t^{-N(N-1)/2}.Comment: 5 page

Efficacy of Herbicides When Spray Solution Application Is Delayed

Information is limited concerning the impact of delaying applications of pesticides after solution preparation on efficacy. Experiments were conducted to determine weed control when diclosulam, dimethenamid-P, flumioxazin, fomesafen, imazethapyr, pendimethalin, and S-metolachlor were applied preemergence the day of solution preparation or 3, 6, and 9 days after solution preparation. Herbicide solutions were applied on the same day regardless of when prepared. Control of broadleaf signalgrass, common lambsquarters, entireleaf morningglory, and Palmer amaranth by these herbicides was not reduced regardless of when herbicide solutions were prepared. Surprisingly entireleaf morningglory control by all herbicides increased when herbicide application was delayed by 9 days. In separate experiments, control of broadleaf signalgrass by clethodim, common ragweed by glyphosate and lactofen, entireleaf morningglory by lactofen, Italian rye grass by glyphosate and paraquat, and Palmer amaranth by atrazine, dicamba, glufosinate, glyphosate, imazethapyr, lactofen, and 2,4-D was affected more by increase in weed size due to delayed application than the time between solution preparation and application

Salt forms of sulfadiazine with alkali metal and organic cations

The structures of four salt forms of sulfadiazine (SDH) with alkali metal cations are presented. Three contain the deprotonated SD anion. These are the discrete complex [Li(SD)(OH2)2], (I), and the coordination polymers [Na(SD)]n, (II), and [K(SD)(OH2)2]n, (III). The Na complex (II) is a three-dimensional coordination polymer whilst the K complex (III) has two crystallographically independent [K(SD)(OH2)2] units per asymmetric unit, Z′ = 2, and gives a two dimensional coordination polymer whose layers propagate parallel to the crystallographic ab plane. The different bonding modes of the SD anion in these three complexes is discussed. Structure (IV) contains protonated SDH2 cations and the Orange G (OG), C16H10N2O7S2, dianion in a structure with formula [SDH2]2[Na(OG)(OH2)4]2·3H2O. The [Na(OG)(OH2)4]2 dimers have antiparallel naphthol ring structures joined through two Na centres that bond to the hydrazone anions through the O atoms of the ketone and sulfonate substituents. The structures of the salts formed on reaction of SDH with 2-aminopyridine and ethanolamine are also presented as [C5H7N2][SD], (V), and [HOCH2CH2NH3][SD]·H2O, (VI), respectively. Structure (V) features a heterodimeric R2 2(8) hydrogen bond motif between the cation and the anion whilst structure (VI) has a tetrameric core of two cations linked by a central R2 2(10) hydrogen bonded motif which supports two anions linked to this core by R3 3(8) motifs

Energetics and geometry of excitations in random systems

Methods for studying droplets in models with quenched disorder are critically examined. Low energy excitations in two dimensional models are investigated by finding minimal energy interior excitations and by computing the effect of bulk perturbations. The numerical data support the assumptions of compact droplets and a single exponent for droplet energy scaling. Analytic calculations show how strong corrections to power laws can result when samples and droplets are averaged over. Such corrections can explain apparent discrepancies in several previous numerical results for spin glasses.Comment: 4 pages, eps files include