Helicity and electron correlation effects on transport properties of double-walled carbon nanotubes

We analytically demonstrate helicity determined selection rules for intershell tunneling in double-walled nanotubes with commensurate (c-DWNTs) and incommensurate (i-DWNTs) shells. For i-DWNTs the coupling is negligible between lowest energy subbands, but it becomes important as the higher subbands become populated. In turn the elastic mean free path of i-DWNTs is reduced for increasing energy, with additional suppression at subband onsets. At low energies, a Luttinger liquid theory for DWNTs with metallic shells is derived. Interaction effects are more pronounced in i-DWNTs.Comment: 4 pages, 3 figure

Efficient sum-of-exponentials approximations for the heat kernel and their applications

In this paper, we show that efficient separated sum-of-exponentials approximations can be constructed for the heat kernel in any dimension. In one space dimension, the heat kernel admits an approximation involving a number of terms that is of the order $O(\log(\frac{T}{\delta}) (\log(\frac{1}{\epsilon})+\log\log(\frac{T}{\delta})))$ for any x\in\bbR and $\delta \leq t \leq T$, where $\epsilon$ is the desired precision. In all higher dimensions, the corresponding heat kernel admits an approximation involving only $O(\log^2(\frac{T}{\delta}))$ terms for fixed accuracy $\epsilon$. These approximations can be used to accelerate integral equation-based methods for boundary value problems governed by the heat equation in complex geometry. The resulting algorithms are nearly optimal. For $N_S$ points in the spatial discretization and $N_T$ time steps, the cost is $O(N_S N_T \log^2 \frac{T}{\delta})$ in terms of both memory and CPU time for fixed accuracy $\epsilon$. The algorithms can be parallelized in a straightforward manner. Several numerical examples are presented to illustrate the accuracy and stability of these approximations.Comment: 23 pages, 5 figures, 3 table

Conditioning the logistic branching process on non-extinction

We consider a birth and death process in which death is due to both `natural death' and to competition between individuals, modelled as a quadratic function of population size. The resulting `logistic branching process' has been proposed as a model for numbers of individuals in populations competing for some resource, or for numbers of species. However, because of the quadratic death rate, even if the intrinsic growth rate is positive, the population will, with probability one, die out in finite time. There is considerable interest in understanding the process conditioned on non-extinction. In this paper, we exploit a connection with the ancestral selection graph of population genetics to find expressions for the transition rates in the logistic branching process conditioned on survival until some fixed time $T$, in terms of the distribution of a certain one-dimensional diffusion process at time $T$. We also find the probability generating function of the Yaglom distribution of the process and rather explicit expressions for the transition rates for the so-called Q-process, that is the logistic branching process conditioned to stay alive into the indefinite future. For this process, one can write down the joint generator of the (time-reversed) total population size and what in population genetics would be called the `genealogy' and in phylogenetics would be called the `reconstructed tree' of a sample from the population. We explore some ramifications of these calculations numerically

Electronic spectra of commensurate and incommensurate DWNTs in parallel magnectic field

We study the electronic spectra of commensurate and incommensurate double-wall carbon nanotubes (DWNTs) of finite length. The coupling between nanotube shells is taken into account as an inter-shell electron tunneling. Selection rules for the inter-shell coupling are derived. Due to the finite size of the system, these rules do not represent exact conservation of the crystal momentum, but only an approximate one; therefore the coupling between longitudinal momentum states in incommensurate DWNTs becomes possible. The use of the selection rules allows a fast and efficient calculation of the electronic spectrum. In the presence of a magnetic field parallel to the DWNT axis, we find spectrum modulations that depend on the chiralities of the shells

Multiscale Analysis of Adaptive Population Dynamics

In this thesis we study a spatial population model based on a class of interacting locally regulated branching processes. The results consist of three parts which are independent of each other. The first part, which is the main part of this thesis as presented in Chapter 2 and 3, is concerned with a three-time-scale analysis of a spatially structured population specified with adaptive fitness landscape. More precisely, we obtain a new model, the so-called trait substitution tree (TST), in the limiting system by taking a rare mutation limit against a slow migration limit. These limits can be either simultaneous with a large population limit from a microscopic point of view (Chapter 3), or based on a deterministic approximation (Chapter 2). The TST process is a measure-valued Markov jump process with a well-described branching tree structure. The novelty of our work is that every phenotype, which may nearly die out on the migration time scale, has a chance to recover and further to be stabilized on the mutation time scale because of a change in the fitness landscape due to a new-entering mutant. The second part (Chapter 4) deals with the neutral mutation case, i.e., the fixation probability of an advantageous mutant is of order $\frac{1}{K^\lambda}$ ($0 In the last part (Chapter 5) we study the fluctuation limit of the locally regulated population, and we obtain a limiting process as the solution both of a martingale problem and of a generalized Langevin equation. Under appropriate conditions we prove that the fluctuation limit and the long term limit are interchangeable