Single molecule DNA sequencing via transverse electronic transport using a graphene nanopore: A tight-binding approach

We report a tight-binding model study of two-terminal graphene nanopore based device, for sequential determination of DNA bases. Using Greens function approach we calculate conductance spectra, I-V response and also the changes in local density of states (LDOS) profile as four different nucleobases inserted one by one into the pore embedded in the zigzag graphene nanoribbon (ZGNR). We find distinct features in LDOS profile for different nucleotides and the same is also present in conductance and I-V response. We propose the actual working principle of the device, by setting the bias across the pore to a fixed voltage (this voltage gives maximum discrimination between characteristic current of the four nucleotides) and translocating the ss-DNA through the nanopore using a transverse electric field while recording the characteristic current of the nucleotides. Not only the typical current output is much larger than previous results, but the seaparation between them for different bases are also definite. Our investigation provides high accuracy and significant amount of distinction between different nucleotides.Comment: 6 pages, 5 figure

Maximal distance travelled by N vicious walkers till their survival

We consider $N$ Brownian particles moving on a line starting from initial positions ${\bf{u}}\equiv \{u_1,u_2,\dots u_N\}$ such that $0<u_1 < u_2 < \cdots < u_N$. Their motion gets stopped at time $t_s$ when either two of them collide or when the particle closest to the origin hits the origin for the first time. For $N=2$, we study the probability distribution function $p_1(m|{\bf{u}})$ and $p_2(m|{\bf{u}})$ of the maximal distance travelled by the $1^{\text{st}}$ and $2^{\text{nd}}$ walker till $t_s$. For general $N$ particles with identical diffusion constants $D$, we show that the probability distribution $p_N(m|{\bf u})$ of the global maximum $m_N$, has a power law tail $p_i(m|{\bf{u}}) \sim {N^2B_N\mathcal{F}_{N}({\bf u})}/{m^{\nu_N}}$ with exponent $\nu_N =N^2+1$. We obtain explicit expressions of the function $\mathcal{F}_{N}({\bf u})$ and of the $N$ dependent amplitude $B_N$ which we also analyze for large $N$ using techniques from random matrix theory. We verify our analytical results through direct numerical simulations.Comment: 28 pages, 9 figure

Exact distributions of the number of distinct and common sites visited by N independent random walkers

We study the number of distinct sites S_N(t) and common sites W_N(t) visited by N independent one dimensional random walkers, all starting at the origin, after t time steps. We show that these two random variables can be mapped onto extreme value quantities associated to N independent random walkers. Using this mapping, we compute exactly their probability distributions P_N^d(S,t) and P_N^d(W,t) for any value of N in the limit of large time t, where the random walkers can be described by Brownian motions. In the large N limit one finds that S_N(t)/\sqrt{t} \propto 2 \sqrt{\log N} + \widetilde{s}/(2 \sqrt{\log N}) and W_N(t)/\sqrt{t} \propto \widetilde{w}/N where \widetilde{s} and \widetilde{w} are random variables whose probability density functions (pdfs) are computed exactly and are found to be non trivial. We verify our results through direct numerical simulations.Comment: 5 pages, 3 figure

A Reaction Diffusion Model Of Pattern Formation In Clustering Of Adatoms On Silicon Surfaces

We study a reaction diffusion model which describes the formation of patterns on surfaces having defects. Through this model, the primary goal is to study the growth process of Ge on Si surface. We consider a two species reaction diffusion process where the reacting species are assumed to diffuse on the two dimensional surface with first order interconversion reaction occuring at various defect sites which we call reaction centers. Two models of defects, namely a ring defect and a point defect are considered separately. As reaction centers are assumed to be strongly localized in space, the proposed reaction-diffusion model is found to be exactly solvable. We use Green's function method to study the dynamics of reaction diffusion processes. Further we explore this model through Monte Carlo (MC) simulations to study the growth processes in the presence of a large number of defects. The first passage time statistics has been studied numerically. Copyright 2012 Author(s). This article is distributed under a Creative Commons Attribution 3.0 Unported License. [http://dx.doi.org/10.1063/1.4757592]Microelectronics Research Cente

Exact gap statistics for the random average process on a ring with a tracer

We study statistics of the gaps in Random Average Process (RAP) on a ring with particles hopping symmetrically, except one tracer particle which could be driven. These particles hop either to the left or to the right by a random fraction $\eta$ of the space available till next particle in the respective directions. The random fraction $\eta \in [0,~1)$ is chosen from a distribution $R(\eta)$. For non-driven tracer, when $R(\eta)$ satisfies a necessary and sufficient condition, the stationary joint distribution of the gaps between successive particles takes an universal form that is factorized except for a global constraint. Some interesting explicit forms of $R(\eta)$ are found which satisfy this condition. In case of driven tracer, the system reaches a current-carrying steady state where such factorization does not hold. Analytical progress has been made in the thermodynamic limit, where we computed the single site mass distribution inside the bulk. We have also computed the two point gap-gap correlation exactly in that limit. Numerical simulations support our analytical results.Comment: 19 pages, 6 figure

Two dimensional imaging observations of meter-decameter bursts associated with the February 1986 flare activity

An analysis is presented of the two dimensional imaging observations of a flare observed on 3 Feb. l986 using the Clark Lake Multifrequency Radioheliograph. The flare produced almost all types of Meter-decimeter radio emission: enhanced storm radiation, type III/V bursts, II and IV and flare continuum. The flare continuum had early (FCE) and late (FC II) components and the type II occurred during the period between these two components. Comparing the source positions of type III/V and FCE it was found that these bursts must have occurred along adjacent open and closed field lines, respectively. The positional analysis of type II and FC II implies that the nonthermal electrons responsible for FC II need not be accelerated by type II shock and this conclusion is further supported by the close association of FC II with a microwave peak. Using the positional and temporal analysis of all these bursts and the associated hard X-ray and microwave emissions, a schematic model is developed for the magnetic field configuration in the flaring region in which the nonthermal particles responsible for these bursts are confined or along which they propagate