Vacancy-induced low-energy states in undoped graphene

We demonstrate that a nonzero concentration nv of static, randomly placed vacancies in graphene leads to a density w of zero-energy quasiparticle states at the band center ε=0 within a tight-binding description with nearest-neighbor hopping t on the honeycomb lattice. We show that wremains generically nonzero in the compensated case (exactly equal number of vacancies on the two sublattices) even in the presence of hopping disorder and depends sensitively on nv and correlations between vacancy positions. For low, but not-too-low, |ε|/t in this compensated case, we show that the density of states ρ(ε) exhibits a strong divergence of the form ρ_(Dyson)(ε)∼|ε|^(-1)/[log(t/|ε|)]^((y+1)), which crosses over to the universal low-energy asymptotic form (modified Gade-Wegner scaling) expected on symmetry grounds ρ_(GW)(ε)∼|ε|^(-1)e^(-b[log(t/|ε|)]2/3) below a crossover scale ε_c≪t. ε_c is found to decrease rapidly with decreasing nv, while y decreases much more slowly

Symmetry breaking perturbations and strange attractors

The asymmetrically forced, damped Duffing oscillator is introduced as a prototype model for analyzing the homoclinic tangle of symmetric dissipative systems with \textit{symmetry breaking} disturbances. Even a slight fixed asymmetry in the perturbation may cause a substantial change in the asymptotic behavior of the system, e.g. transitions from two sided to one sided strange attractors as the other parameters are varied. Moreover, slight asymmetries may cause substantial asymmetries in the relative size of the basins of attraction of the unforced nearly symmetric attracting regions. These changes seems to be associated with homoclinic bifurcations. Numerical evidence indicates that \textit{strange attractors} appear near curves corresponding to specific secondary homoclinic bifurcations. These curves are found using analytical perturbational tools

Griffiths Effects in Random Heisenberg Antiferromagnetic S=1 Chains

I consider the effects of enforced dimerization on random Heisenberg antiferromagnetic S=1 chains. I argue for the existence of novel Griffiths phases characterized by {\em two independent dynamical exponents} that vary continuously in these phases; one of the exponents controls the density of spin-1/2 degrees of freedom in the low-energy effective Hamiltonian, while the other controls the corresponding density of spin-1 degrees of freedom. Moreover, in one of these Griffiths phases, the system has very different low temperature behavior in two different parts of the phase which are separated from each other by a sharply defined crossover line; on one side of this crossover line, the system `looks' like a S=1 chain at low energies, while on the other side, it is best thought of as a $S=1/2$ chain. A strong-disorder RG analysis makes it possible to analytically obtain detailed information about the low temperature behavior of physical observables such as the susceptibility and the specific heat, as well as identify an experimentally accessible signature of this novel crossover.Comment: 16 pages, two-column PRB format; 5 figure

Synthesis and antimicrobial activity of novel 1H-benzo[d]imidazole-aryl sulfonamide/amide derivatives

184-191A series of novel N-(6-(propylthio)-1H-benzo[d]imidazol-2-yl)-aryl sulfonamide and amide derivatives have been synthesized. The structure of all newly synthesized 1H-benzo[d]imidazole derivatives have been confirmed using spectral analysis and evaluated for antibacterial, antifungal potential. Biological evaluations study reveals that the compounds 2, 3, 5, 7 and 15 are found to have moderate to good antimicrobial activity (MIC range of 10–20 mg/mL) against the bacterial strains Staphylococcus aureus ATCC 6538 and Escherichia coli ATCC 8739 in comparison to standard Ampicillin as well as fungal strains Candida albicans ATCC 10231 and Aspergillus niger ATCC 6275 in comparison to Fluconazole. These results suggest that this could be the start of an extensive medicinal chemistry program to identify the 1Hbenzo[ d]imidazole-aryl sulfonamide based potent antimicrobial agents

Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape

Lobe dynamics and escape from a potential well are general frameworks introduced to study phase space transport in chaotic dynamical systems. While the former approach studies how regions of phase space are transported by reducing the flow to a two-dimensional map, the latter approach studies the phase space structures that lead to critical events by crossing periodic orbit around saddles. Both of these frameworks require computation with curves represented by millions of points-computing intersection points between these curves and area bounded by the segments of these curves-for quantifying the transport and escape rate. We present a theory for computing these intersection points and the area bounded between the segments of these curves based on a classification of the intersection points using equivalence class. We also present an alternate theory for curves with nontransverse intersections and a method to increase the density of points on the curves for locating the intersection points accurately.The numerical implementation of the theory presented herein is available as an open source software called Lober. We used this package to demonstrate the application of the theory to lobe dynamics that arises in fluid mechanics, and rate of escape from a potential well that arises in ship dynamics.Comment: 33 pages, 17 figure