Harmonically confined, semiflexible polymer in a channel: response to a stretching force and spatial distribution of the endpoints

We consider an inextensible, semiflexible polymer or worm-like chain which is confined in the transverse direction by a parabolic potential and subject to a longitudinal force at the ends, so that the polymer is stretched out and backfolding is negligible. Simple analytic expressions for the partition function, valid in this regime, are obtained for chains of arbitrary length with a variety of boundary conditions at the ends. The spatial distribution of the end points or radial distribution function is also analyzed.Comment: 14 pages including figure

Assessment of the environmental and economic performance of agroforestry along a European gradient

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A comparison of the cognitive difficulties posed by SPARQL query constructs

This study investigated difficulties in the comprehension of SPARQL. In particular, it compared the declarative and navigational styles present in the language, and various operators used in SPARQL property paths. The study involved participants selecting possible answers given a SPARQL query and knowledgebase. In general, no significant differences were found in terms of the response time and accuracy with which participants could answer questions expressed in either a declarative or navigational form. However, UNION did take significantly longer to comprehend than both braces and verti- cal line in property paths; with braces being faster than vertical line. Inversion and negated property paths both proved difficult, with their combination being very difficult indeed. Questions involving MINUS were answered more accu- rately than those involving negation in property paths, in particular where pred- icates were inverted. Both involve negation, but the semantics are different. With the MINUS questions, negation and inversion can be considered separate- ly; with property paths, negation and inversion need to be considered together. Participants generally expressed a preference for data represented graphically, and this preference was significantly correlated with accuracy of comprehen- sion. Implications for the design and use of query languages are discussed

Nanoconfinement-enhanced conformational response of single DNA molecules to changes in ionic environment

We show that the ionic environment plays a critical role in determining the configurational properties of DNA confined in silica nanochannels. The extension of DNA in the nanochannels increases as the ionic strength is reduced, almost tripling over two decades in ionic strength for channels around 100x100 nm in dimension. Surprisingly, we find that the variation of the persistence length alone with ionic strength is not enough to explain our results. The effect is due mainly to increasing self-avoidance created by the reduced screening of electrostatic interactions at low ionic strength. To quantify the increase in self-avoidance, we introduce a new parameter into the de Gennes theory: an effective DNA width that gives the increase in the excluded volume due to electrostatic repulsion

Amplified stretch of bottlebrush-coated DNA in nanofluidic channels

The effect of a cationic-neutral diblock polypeptide on the conformation of single DNA molecules confined in rectangular nanochannels is investigated with fluorescence microscopy. An enhanced stretch along the channel is observed with increased binding of the cationic block of the polypeptide to DNA. A maximum stretch of 85% of the contour length can be achieved inside a channel with a cross-sectional diameter of 200 nm and at a 2-fold excess of polypeptide with respect to DNA charge. With site-specific fluorescence labelling, it is demonstrated that this maximum stretch is sufficient to map large-scale genomic organization. Monte Carlo computer simulation shows that the amplification of the stretch inside the nanochannels is owing to an increase in bending rigidity and thickness of bottlebrush-coated DNA. The persistence lengths and widths deduced from the nanochannel data agree with what has been estimated from the analysis of atomic force microscopy images of dried complexes on silica.Singapore-MIT Alliance for Research and TechnologyNational Science Foundation (U.S.

The pre-WDVV ring of physics and its topology

We show how a simplicial complex arising from the WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) equations of string theory is the Whitehouse complex. Using discrete Morse theory, we give an elementary proof that the Whitehouse complex $\Delta_n$ is homotopy equivalent to a wedge of $(n-2)!$ spheres of dimension $n-4$. We also verify the Cohen-Macaulay property. Additionally, recurrences are given for the face enumeration of the complex and the Hilbert series of the associated pre-WDVV ring.Comment: 13 pages, 4 figures, 2 table

A Tool to Recover Scalar Time-Delay Systems from Experimental Time Series

We propose a method that is able to analyze chaotic time series, gained from exp erimental data. The method allows to identify scalar time-delay systems. If the dynamics of the system under investigation is governed by a scalar time-delay differential equation of the form $dy(t)/dt = h(y(t),y(t-\tau_0))$, the delay time $\tau_0$ and the functi on $h$ can be recovered. There are no restrictions to the dimensionality of the chaotic attractor. The method turns out to be insensitive to noise. We successfully apply the method to various time series taken from a computer experiment and two different electronic oscillators

Dragging a polymer chain into a nanotube and subsequent release

We present a scaling theory and Monte Carlo (MC) simulation results for a flexible polymer chain slowly dragged by one end into a nanotube. We also describe the situation when the completely confined chain is released and gradually leaves the tube. MC simulations were performed for a self-avoiding lattice model with a biased chain growth algorithm, the pruned-enriched Rosenbluth method. The nanotube is a long channel opened at one end and its diameter $D$ is much smaller than the size of the polymer coil in solution. We analyze the following characteristics as functions of the chain end position $x$ inside the tube: the free energy of confinement, the average end-to-end distance, the average number of imprisoned monomers, and the average stretching of the confined part of the chain for various values of $D$ and for the number of monomers in the chain, $N$. We show that when the chain end is dragged by a certain critical distance $x^*$ into the tube, the polymer undergoes a first-order phase transition whereby the remaining free tail is abruptly sucked into the tube. This is accompanied by jumps in the average size, the number of imprisoned segments, and in the average stretching parameter. The critical distance scales as $x^*\sim ND^{1-1/\nu}$. The transition takes place when approximately 3/4 of the chain units are dragged into the tube. The theory presented is based on constructing the Landau free energy as a function of an order parameter that provides a complete description of equilibrium and metastable states. We argue that if the trapped chain is released with all monomers allowed to fluctuate, the reverse process in which the chain leaves the confinement occurs smoothly without any jumps. Finally, we apply the theory to estimate the lifetime of confined DNA in metastable states in nanotubes.Comment: 13pages, 14figure