Shock fluctuations in the asymmetric simple exclusion process

Summary We consider the one dimensional nearest neighbors asymmetric simple exclusion process with ratesq andp for left and right jumps respectively;q<p. Ferrari et al. (1991) have shown that if the initial measure isv _, , a product measure with densities and to the left and right of the origin respectively, <, then there exists a (microscopic) shock for the system. A shock is a random positionX _t such that the system as seen from this position at timet has asymptotic product distributions with densities and to the left and right of the origin respectively, uniformly int. We compute the diffusion coefficient of the shockD=lim _t t ^–1(E(X _t )²–(EX _t )²) and findD=(p–q)(–)^–1((1–)+(1–)) as conjectured by Spohn (1991). We show that in the scale the position ofX _t is determined by the initial distribution of particles in a region of length proportional tot. We prove that the distribution of the process at the average position of the shock converges to a fair mixture of the product measures with densities and . This is the so called dynamical phase transition. Under shock initial conditions we show how the density fluctuation fields depend on the initial configuration.     

Curves of marginal stability, and weak- and strong-coupling BPS spectra in N = 2 supersymmetric QCD

We explicitly determine the global structure of the SL(2, ) bundle over the Coulomb branch of the moduli space of asymptotically free N = 2 supersymmetric Yang-Mills theories with gauge group SU(2) when massless hypermultiplets are present. For each relevant number of flavours, we show that there is a curve of marginal stability of the Coulomb branch, diffeomorphic to a circle, across which the BPS spectrum is discontinuous. We determine rigorously and completely the BPS spectra inside and outside the curve. In all cases, the spectrum inside the curve consists of only those BPS states that are responsible for the singularities of the low energy effective action (in addition to the massless abelian gauge multiplet which is always present). The predicted decay patterns across the curve of marginal stability are perfectly consistent with all quantum numbers carried by the BPS states. As a byproduct, we also show that the electric and magnetic quantum numbers of the massless states at the singularities proposed by Seiberg and Witten are the only possible ones.     

An exact numerical analysis of coupled planar electron waveguides with asymmetric rectangular potential profiles

An exact numerical analysis is given of electron waves in a pair of coupled semiconductor heterojunction electron waveguides modelled by a rectangular potential distribution. The waveguide lengths required for electron current transfer between the guides agree asymptotically with estimates from Yariv's coupled mode theory and are usefully more accurate. Moreover the electron wave coupling due to an ideal launcher can be worked out, leading to estimates of the off/on current ratio occurring in the waveguides when regarded as an ultrafast switch. For a Poisson probability distribution of the number of electrons N making up a bit-pulse, we have calculated the minimum average N, dependent upon , which would be required to keep the switching bit-error rate below prescribed limits. Pulse rise times and switching delays are derived from the explicit forms for the longitudinal electron wave group velocity. Combining the bit-error and switching-time calculations leads to estimates of the waveguide current densities which would be required in practice. Some normalized sets of curves relating to our analysis are given and used to predict the performance of particular examples of recently proposed AlGaAs/GaAs heterojunction electron waveguide switch/couplers.     

Dark and Photochemical Interactions of Dimethyltetrahydrobenzoangelicin with DNA

A study of dark interaction and photoreaction between 4,6-dimethyltetrahydrobenzoangelicin (THBA) and DNA is described. 4,6-Dimethyltetrahydrobenzoangelicin is a furocoumarin derivative in which 4'and 5'carbons are linked by a four-methylene bridge. In spite of the bulky aliphatic ring, THBA forms a complex with DNA in the dark and, on UVA irradiation, reacts with pyrimidine bases of DNA yielding monoadducts only involving its furan side double bond. Two main photoproducts form: they derive from a C₄-cycloaddition to thymine and cytosine, respectively, and account for 56% and 39% of the total photoreaction yield. Both show cis-syn configuration. Two other isomers, one with thymine and one with cytosine, formed with so much lower yield ( ca 3 and 1%, respectively) that their structure could not be assigned. Furthermore, in spite of its angular structure, THBA induces a small number of crosslinks in DNA.     

Metal ion catalysis in the beta-elimination reactions of N-[2-(4-pyridyl)ethyl]quinuclidinium and N-[2-(2-pyridyl)ethyl]quinuclidinium in aqueous solution

Catalysis of the beta-elimination reaction of N-[2-(4-pyridyl)ethyl]quinuclidinium (1) and N-[2-(2-pyridyl)ethyl]quinuclidinium (2) by Zn(2+) and Cd(2+) in OH(-)/H(2)O (pH = 5.20-6.35, 50 degrees C, and mu = 1 M KCl) has been studied. In the presence of Zn(2+), the elimination reactions of both isomers occur from the Zn(2+)-complexed substrates (C). The equilibrium constants for the dissociation of the Zn(2+)-complexes are as follows: K(d) = 0.012 +/- 0.003 M (isomer 1) and K(d) = 0.065 +/- 0.020 M (isomer 2). The value of k(C)(H2O) for isomer 1 is 4.81 x 10(-6) s(-1). For isomer 2 both the rate constants for the "water" and OH(-)-induced reaction of the Zn(2+)-complexed substrate could be measured, despite the low concentration of OH(-) in the investigated reaction mixture [k(C)H2O)= 1.97 x 10(-6) s(-1) and k(C)(OH-)= 21.9 M(-1) s(-1), respectively]. The measured metal activating factor (MetAF), i.e., the reactivity ratio between the complexed and the uncomplexed substrate, is 8.1 x 10(4) for the OH(-)-induced elimination of 2. This high MetAF can be compared with the corresponding proton activating factor (Alunni, S.; Conti, A.; Palmizio Errico, R. J. Chem. Soc., Perkin Trans. 2 2000, 453), PAF = 1.5 x 10(6) and is in agreement with an E1cb irreversible mechanism (A(xh)D(E)* + D(N)) (Guthrie, R. D.; Jencks, W. P. Acc. Chem. Res. 1989, 22, 343). A value of k(C)(H2O)>or= 23 x 10(-7) s(-1) is estimated for the Cd(2+)-complexed isomer 2, while catalysis by Cd(2+) has not been observed for isomer 1.     

Reactions of dodecacarbonyltriosmium with dienic ligands

Dodecacabonyltriosmium reacts with diene ligands (D) such as 2,4-trans, trans- and 2,4-cis, trans-hexadiene and 1,6- and 1,5-heptadiene to give H₂Os₃D(CO)₉, H₄Os₄(CO)₁₂ and two isomers of molecular formula HOs₃-(D  H)(CO)₉ in addition to Os₂(D  2H)(CO)₆ and OsD(CO)₃. The structures of the trimetal complexes show that dehydrogenation, isomerization and rearrangement of the organic substrates occur before the coordination to the metal cluster. 2,3-Dimethyl-1,3-butadiene and dodecacabonyltriosmium give only the well known bi- and mono-metal complexes. The results are compared with those obtained in the reactions of the some organic molecules with dodecacabonyltriruthenium.