Force and energy dissipation variations in non-contact atomic force spectroscopy on composite carbon nanotube systems

UHV dynamic force and energy dissipation spectroscopy in non-contact atomic force microscopy were used to probe specific interactions with composite systems formed by encapsulating inorganic compounds inside single-walled carbon nanotubes. It is found that forces due to nano-scale van der Waals interaction can be made to decrease by combining an Ag core and a carbon nanotube shell in the Ag@SWNT system. This specific behaviour was attributed to a significantly different effective dielectric function compared to the individual constituents, evaluated using a simple core-shell optical model. Energy dissipation measurements showed that by filling dissipation increases, explained here by softening of C-C bonds resulting in a more deformable nanotube cage. Thus, filled and unfilled nanotubes can be discriminated based on force and dissipation measurements. These findings have two different implications for potential applications: tuning the effective optical properties and tuning the interaction force for molecular absorption by appropriately choosing the filling with respect to the nanotube.Comment: 22 pages, 6 figure

Integrating demography and distribution modeling for the iconic <i>Leontopodium alpinum</i> Colm. in the Romanian Carpathians.

Both climate change and human exploitation are major threats to plant life in mountain environments. One species that may be particularly sensitive to both of these stressors is the iconic alpine flower edelweiss (Leontopodium alpinum Colm.). Its populations have declined across Europe due to over-collection for its highly prized flowers. Edelweiss is still subject to harvesting across the Romanian Carpathians, but no study has measured to what extent populations are vulnerable to anthropogenic change.Here, we estimated the effects of climate and human disturbance on the fitness of edelweiss. We combined demographic measurements with predictions of future range distribution under climate change to assess the viability of populations across Romania.We found that per capita and per-area seed number and seed mass were similarly promoted by both favorable environmental conditions, represented by rugged landscapes with relatively cold winters and wet summers, and reduced exposure to harvesting, represented by the distance of plants from hiking trails. Modeling these responses under future climate scenarios suggested a slight increase in per-area fitness. However, we found plant ranges contracted by between 14% and 35% by 2050, with plants pushed into high elevation sites.Synthesis. Both total seed number and seed mass are expected to decline across Romania despite individual edelweiss fitness benefiting from a warmer and wetter climate. More generally, our approach of coupling species distribution models with demographic measurements may better inform conservation strategies of ways to protect alpine life in a changing world

Interpolation Method Needed for Numerical Uncertainty

Using Computational Fluid Dynamics (CFD) to predict a flow field is an approximation to the exact problem and uncertainties exist. There is a method to approximate the errors in CFD via Richardson's Extrapolation. This method is based off of progressive grid refinement. To estimate the errors, the analyst must interpolate between at least three grids. This paper describes a study to find an appropriate interpolation scheme that can be used in Richardson's extrapolation or other uncertainty method to approximate errors

On the maximal number of cubic subwords in a string

We investigate the problem of the maximum number of cubic subwords (of the form $www$) in a given word. We also consider square subwords (of the form $ww$). The problem of the maximum number of squares in a word is not well understood. Several new results related to this problem are produced in the paper. We consider two simple problems related to the maximum number of subwords which are squares or which are highly repetitive; then we provide a nontrivial estimation for the number of cubes. We show that the maximum number of squares $xx$ such that $x$ is not a primitive word (nonprimitive squares) in a word of length $n$ is exactly $\lfloor \frac{n}{2}\rfloor - 1$, and the maximum number of subwords of the form $x^k$, for $k\ge 3$, is exactly $n-2$. In particular, the maximum number of cubes in a word is not greater than $n-2$ either. Using very technical properties of occurrences of cubes, we improve this bound significantly. We show that the maximum number of cubes in a word of length $n$ is between $(1/2)n$ and $(4/5)n$. (In particular, we improve the lower bound from the conference version of the paper.)Comment: 14 page

Numerical Uncertainty Analysis for Computational Fluid Dynamics using Student T Distribution -- Application of CFD Uncertainty Analysis Compared to Exact Analytical Solution

Computational Fluid Dynamics (CFD) is the standard numerical tool used by Fluid Dynamists to estimate solutions to many problems in academia, government, and industry. CFD is known to have errors and uncertainties and there is no universally adopted method to estimate such quantities. This paper describes an approach to estimate CFD uncertainties strictly numerically using inputs and the Student-T distribution. The approach is compared to an exact analytical solution of fully developed, laminar flow between infinite, stationary plates. It is shown that treating all CFD input parameters as oscillatory uncertainty terms coupled with the Student-T distribution can encompass the exact solution

On Maximal Unbordered Factors

Given a string $S$ of length $n$, its maximal unbordered factor is the longest factor which does not have a border. In this work we investigate the relationship between $n$ and the length of the maximal unbordered factor of $S$. We prove that for the alphabet of size $\sigma \ge 5$ the expected length of the maximal unbordered factor of a string of length~$n$ is at least $0.99 n$ (for sufficiently large values of $n$). As an application of this result, we propose a new algorithm for computing the maximal unbordered factor of a string.Comment: Accepted to the 26th Annual Symposium on Combinatorial Pattern Matching (CPM 2015

Finding All Solutions of Equations in Free Groups and Monoids with Involution

The aim of this paper is to present a PSPACE algorithm which yields a finite graph of exponential size and which describes the set of all solutions of equations in free groups as well as the set of all solutions of equations in free monoids with involution in the presence of rational constraints. This became possible due to the recently invented emph{recompression} technique of the second author. He successfully applied the recompression technique for pure word equations without involution or rational constraints. In particular, his method could not be used as a black box for free groups (even without rational constraints). Actually, the presence of an involution (inverse elements) and rational constraints complicates the situation and some additional analysis is necessary. Still, the recompression technique is general enough to accommodate both extensions. In the end, it simplifies proofs that solving word equations is in PSPACE (Plandowski 1999) and the corresponding result for equations in free groups with rational constraints (Diekert, Hagenah and Gutierrez 2001). As a byproduct we obtain a direct proof that it is decidable in PSPACE whether or not the solution set is finite.Comment: A preliminary version of this paper was presented as an invited talk at CSR 2014 in Moscow, June 7 - 11, 201