Autocatalytic Sets and the Growth of Complexity in an Evolutionary Model

A model of $s$ interacting species is considered with two types of dynamical variables. The fast variables are the populations of the species and slow variables the links of a directed graph that defines the catalytic interactions among them. The graph evolves via mutations of the least fit species. Starting from a sparse random graph, we find that an autocatalytic set (ACS) inevitably appears and triggers a cascade of exponentially increasing connectivity until it spans the whole graph. The connectivity subsequently saturates in a statistical steady state. The time scales for the appearance of an ACS in the graph and its growth have a power law dependence on $s$ and the catalytic probability. At the end of the growth period the network is highly non-random, being localized on an exponentially small region of graph space for large $s$.Comment: 13 pages REVTEX (including figures), 4 Postscript figure

Emergence and Growth of Complex Networks in Adaptive Systems

We consider the population dynamics of a set of species whose network of catalytic interactions is described by a directed graph. The relationship between the attractors of this dynamics and the underlying graph theoretic structures like cycles and autocatalytic sets is discussed. It is shown that when the population dynamics is suitably coupled to a slow dynamics of the graph itself, the network evolves towards increasing complexity driven by autocatalytic sets. Some quantitative measures of network complexity are described.Comment: 10 pages (including figures), 3 Postscript figure

Geometric phase for neutrino propagation in magnetic field

The geometric phase for neutrinos propagating in an adiabatically varying magnetic field in matter is calculated. It is shown that for neutrino propagation in sufficiently large magnetic field the neutrino eigenstates develop a significant geometric phase. The geometric phase varies from 2$\pi$ for magnetic fields $\sim$ fraction of a micro gauss to $\pi$ for fields $\sim 10^7$ gauss or more. The variation of geometric phase with magnetic field parameters is shown and its phenomenological implications are discussed

Mannich Bases of 2-Substituted Benzimidazoles - A Review

Mannich bases are the end products of mannich reaction and are known as beta amino ketone carrying compounds. Mannich reaction is a carbon carbon bond forming nucleophilic addition reaction which helps in synthesizing N-methyl derivatives and many other drug molecules. Mannich base derivatives of benzimidazoles possess many pharmacological properties such as anti-oxidant, anti-inflammatory, anticancer, antiviral, anthelmintic and play an important role in medical field. As these drugs are clinically useful in treatment of microbial infections and exhibit other therapeutic activities also, so this encouraged the development of more potent, novel and clinically significant compounds. In this review synthesis and various biological activities of new mannich bases of benzimidazole derivatives reported is discussed

Synthesis,Characterization and Biological studies on Mannich Bases of 2-Substituted Benzimidazole Derivatives

In the present study novel derivatives of 2-substituted benzimidazoles were prepared via Mannich reaction and evaluated for their in vitro antimicrobial activity against two gram negative strains (Escherichia coli and Pseudomonas aeruginosa), two gram positive strains (Bacillus subtilis and Staphylococcus aureus) and fungal strains (Candida albicans and Aspergillus niger).The synthesized compounds were also screened for antioxidant activity.The newly synthesized compounds were characterized by spectral and analytical techniques.The results revealed that all the synthesized compounds have a significant antioxidant and biological activity against the tested microorganisms

Probing the Shape of a Graphene Nanobubble

Gas molecules trapped between graphene and various substrates in the form of bubbles are observed experimentally. The study of these bubbles is useful in determining the elastic and mechanical properties of graphene, adhesion energy between graphene and substrate, and manipulating the electronic properties via strain engineering. In our numerical simulations, we use a simple description of elastic potential and adhesion energy to show that for small gas bubbles ($\sim 10$ nm) the van der Waals pressure is in the order of 1 GPa. These bubbles show universal shape behavior irrespective of their size, as observed in recent experiments. With our results the shape and volume of the trapped gas can be determined via the vibrational density of states (VDOS) using experimental techniques such as inelastic tunneling and inelastic neutron scattering. The elastic energy distribution in the graphene layer which traps the nanobubble is homogeneous apart from its edge, but the strain depends on the bubble size thus variation in bubble size allows control of the electronic and optical properties.Comment: 5 Figures (Supplementary: 1 Figure), Accepted for publication in PCC

Structural characterization of carbon nanotubes via the vibrational density of states

The electrical and chemical properties of carbon nanotubes vary significantly with different chirality and diameter, making the experimental determination of these structural properties important. Here, we show that the vibrational density of states (VDOS) contains information on the structure of carbon nanotubes, particularly at low frequencies. We show that the diameter and chirality of the nanotubes can be determined from the characteristic low frequency $L$ and $L'$ modes in the VDOS. For zigzag nanotubes, the $L$ peak splits into two peaks giving rise to another low energy $L"$ peak. The significant changes in the frequencies and relative intensities of these peaks open up a route to distinguish among structurally different nanotubes. A close study of different orientations of Stone-Wales defects with varying defect density reveals that different structural defects also leave distinct fingerprints in the VDOS, particularly in the $L$ and $L'$ modes. With our results, more structural information can be obtained from experiments which can directly measure the VDOS, such as inelastic electron and inelastic neutron spectroscopy.Comment: 5 Figures, Accepted for publication in Carbo