By means of computer simulations of a coarse-grained DNA model we show that the DNA hairpin zippering dynamics is anomalous, i.e. the characteristic time τ scales non-linearly with N , the hairpin length: τ ∼ N α with α > 1. This is in sharp contrast with the prediction of the zipper model for which τ ∼ N . We show that the anomalous dynamics originates from an increase in the friction during zippering due to the tension built in the closing strands. From a simple polymer model we get α = 1 + ν ≈ 1.59 with ν the Flory exponent, a result which is in agreement with the simulations. We discuss transition path times data where such effects should be detected. The folding dynamics of DNA (or RNA) hairpins, which are single stranded molecules forming a stem-loop structure, has been a topic of broad interest within the biophysics community for a long time [1][2][3][4][5][6][7]. Hairpin folding is a prototype example of secondary structure formation [8] and shares common features with the more complex case of protein folding [9]. In both cases the folding process is described by a one-dimensional reaction coordinate performing a diffusive motion across a free energy potential barrier (see e.g. [10]). Recent advances in experimental single molecule techniques allow to monitor the folding of hairpins [7] and of proteins [11] with an unprecedented time resolution. These and future experiments are expected to elucidate many aspects of the folding dynamics [12], the reason being that the actual conformational changes occur on timescales which can be typically a few orders of magnitudes smaller than the total folding time [11].The aim of this letter is to investigate the folding dynamics of DNA hairpins, focusing in particular on the rapid zippering which follows the formation of a stable nucleus of a few base pairs. The latter process is generally much slower as initially the hairpin undergoes a large number of failed nucleation attempts. We show here that the zippering time τ scales with the hairpin length N as τ ∼ N α with α > 1. This conclusion is based on extensive simulations of coarse-grained model of DNA and on scaling arguments for polymer dynamics. Our results are at odds with the zipper model [13] which assumes that the hairpin closes like a zipper following a biased random walk dynamics, which implies α = 1. The results give insights on the forces involved in the folding process and in particular in the role of frictional forces. In addition, as argued at the end of this letter, recent experiments on transition path times [7] appear to be better described by a non-linear dependence of zippering time vs. N , supporting the results reported here.

The rare β-decay channel of 6 He into the α + d continuum was investigated at the REX-ISOLDE facility. Bunches of postaccelerated 6 He ions were implanted into the optical time projection chamber (OTPC), where the decays with emission of charged particles were recorded. This novel technique allowed us to extend the low-energy end of the spectrum down to 150 keV in α + d center of mass, corresponding to a deuteron energy of 100 keV. The branching ratio for this process amounts to [2.78 ± 0.07(stat) ± 0.17(sys)] × 10 −6. The shape of the spectrum is found to be in a good agreement with a three-body model, while the total intensity is about 20% larger than the predicted one.

In this paper, we present an analytical subsurface scattering model, derived with the explicit assumption of strong forward scattering. Our model is not based on di usion theory, but follows from a connection that we identi ed between the functional integral formulation of radiative transport and the partition function of a worm-like chain in polymer physics. Our resulting model does not need a separate Monte Carlo solution for unscattered or single-scattered contributions, nor does it require ad-hoc regularization procedures. It has a single singularity by design, corresponding to the initial unscattered propagation, which can be accounted for by the extensive analytical importance sampling scheme that we provide. Our model captures the full behaviour of forward scattering media, ranging from unscattered straight-line propagation to the fully di usive limit. Moreover, we derive a novel forward scattering BRDF as limiting case of our subsurface scattering model, which can be used in a level of detail hierarchy. We show how our model can be integrated in existing Monte Carlo rendering algorithms, and make comparisons to previous approaches. CCS Concepts: • Computing methodologies → Rendering; Ray tracing;

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Computing ray-object intersections is a key operation of ray tracers. Two wellknown data structures to accelerate this computation are the kd-tree (which partitions space) and the Bounding Volume Hierarchy (BVH, which partitions the primitives). A third type of structure is a Constrained Convex Space Partitioning (CCSP), whichlike the kd-tree -partitions space, but it does this in such a way that the geometric primitives exactly overlap with the boundaries of its cells. As a consequence, it is robust against ill-fitting cells that plague methods with axis-aligned cells (kd-tree, BVH) and it permits an efficient, stackless traversal.Within the computer graphics community, such CCSPs have received some attention in both 2D and 3D, but their construction methods were never directly aimed at minimizing their traversal cost -even having fundamentally opposing goals for Delaunay-type methods. Instead, for an isotropic and translation-invariant ray distribution the traversal cost is minimized when minimizing the weight: the total boundary size of all cells in the structure.We study the two-dimensional case using triangulations as CCSPs and explicitly minimize their total edge length using a simulated annealing process that allows for topological changes and varying vertex count. Standard Delaunay-based triangulation techniques have total edge lengths ranging from 10% higher to twice as high as our optimized triangulations for a variety of scenes, with a similar difference in traversal cost when using the triangulations for ray tracing. Compared to a idealised roped kdtree with stackless traversal, our triangulations require less traversal steps for all scenes that we tested and they are robust against the kd-tree's pathological behaviour when geometry becomes misaligned with the world axes. Moreover, the stackless traversal of our triangulations strongly outperforms a BVH, which always requires a top-down descent in the hierarchy. In fact, we show several scenes where the number of traversal operations for our triangulations decreases as the number of geometric primitives N increases, in contrast to the increasing log N behaviour of a BVH.