Self-Assembly of 4-sided Fractals in the Two-handed Tile Assembly Model

We consider the self-assembly of fractals in one of the most well-studied models of tile based self-assembling systems known as the Two-handed Tile Assembly Model (2HAM). In particular, we focus our attention on a class of fractals called discrete self-similar fractals (a class of fractals that includes the discrete Sierpi\'nski carpet). We present a 2HAM system that finitely self-assembles the discrete Sierpi\'nski carpet with scale factor 1. Moreover, the 2HAM system that we give lends itself to being generalized and we describe how this system can be modified to obtain a 2HAM system that finitely self-assembles one of any fractal from an infinite set of fractals which we call 4-sided fractals. The 2HAM systems we give in this paper are the first examples of systems that finitely self-assemble discrete self-similar fractals at scale factor 1 in a purely growth model of self-assembly. Finally, we show that there exists a 3-sided fractal (which is not a tree fractal) that cannot be finitely self-assembled by any 2HAM system

ALCH: An Imperative Language for Chemical Reaction Network-Controlled Tile Assembly

In 2015 Schiefer and Winfree introduced the chemical reaction network-controlled tile assembly model (CRN-TAM), a variant of the abstract tile assembly model (aTAM), where tile reactions are mediated via non-local chemical signals. In this paper, we introduce ALCH, an imperative programming language for specifying CRN-TAM programs. ALCH contains common features like Boolean variables, conditionals, and loops. It also supports CRN-TAM-specific features such as adding and removing tiles. A unique feature of the language is the branch statement, a nondeterministic control structure that allows us to query the current state of tile assemblies. We also developed a compiler that translates ALCH to the CRN-TAM, and a simulator that simulates and visualizes the self-assembly of a CRN-TAM program. Using this language, we show that the discrete Sierpinski triangle can be strictly self-assembled in the CRN-TAM. This solves an open problem that the CRN-TAM is capable of self-assembling infinite shapes at scale one that the aTAM cannot. ALCH allows us to present this construction at a high level, abstracting species and reactions into C-like code that is simpler to understand. Our construction utilizes two new CRN-TAM techniques that allow us to tackle this open problem. First, it employs the branching feature of ALCH to probe the previously placed tiles of the assembly and detect the presence and absence of tiles. Second, it uses scaffolding tiles to precisely control tile placement by occluding any undesired binding sites

Characterization of reconnecting vortices in superfluid helium

When two vortices cross, each of them breaks into two parts and exchanges part of itself for part of the other. This process, called vortex reconnection, occurs in classical as well as superfluids, and in magnetized plasmas and superconductors. We present the first experimental observations of reconnection between quantized vortices in superfluid helium. We do so by imaging micron-sized solid hydrogen particles trapped on quantized vortex cores (Bewley GP, Lathrop DP, Sreenivasan KR, 2006, Nature, 441:588), and by inferring the occurrence of reconnection from the motions of groups of recoiling particles. We show the distance separating particles on the just-reconnected vortex lines grows as a power law in time. The average value of the scaling exponent is approximately 1/2, consistent with the scale-invariant evolution of the vortices

Perfect-fluid cylinders and walls - sources for the Levi-Civita space-time

The diagonal metric tensor whose components are functions of one spatial coordinate is considered. Einstein's field equations for a perfect-fluid source are reduced to quadratures once a generating function, equal to the product of two of the metric components, is chosen. The solutions are either static fluid cylinders or walls depending on whether or not one of the spatial coordinates is periodic. Cylinder and wall sources are generated and matched to the vacuum (Levi--Civita) space--time. A match to a cylinder source is achieved for -\frac{1}{2}<\si<\frac{1}{2}, where \si is the mass per unit length in the Newtonian limit \si\to 0, and a match to a wall source is possible for |\si|>\frac{1}{2}, this case being without a Newtonian limit; the positive (negative) values of \si correspond to a positive (negative) fluid density. The range of \si for which a source has previously been matched to the Levi--Civita metric is 0\leq\si<\frac{1}{2} for a cylinder source.Comment: 22 pages, LaTeX, one included figure. Revised version: three (non-perfect-fluid) interior solutions are added, one of which falsifies the original conjecture in Sec. 4, and the circular geodesics of the Levi-Civita space-time are discussed in a footnot

Microwave Gaseous Discharges

Contains reports on three research projects

Parameter Estimation and Quantitative Parametric Linkage Analysis with GENEHUNTER-QMOD

Objective: We present a parametric method for linkage analysis of quantitative phenotypes. The method provides a test for linkage as well as an estimate of different phenotype parameters. We have implemented our new method in the program GENEHUNTER-QMOD and evaluated its properties by performing simulations. Methods: The phenotype is modeled as a normally distributed variable, with a separate distribution for each genotype. Parameter estimates are obtained by maximizing the LOD score over the normal distribution parameters with a gradient-based optimization called PGRAD method. Results: The PGRAD method has lower power to detect linkage than the variance components analysis (VCA) in case of a normal distribution and small pedigrees. However, it outperforms the VCA and Haseman-Elston regression for extended pedigrees, nonrandomly ascertained data and non-normally distributed phenotypes. Here, the higher power even goes along with conservativeness, while the VCA has an inflated type I error. Parameter estimation tends to underestimate residual variances but performs better for expectation values of the phenotype distributions. Conclusion: With GENEHUNTER-QMOD, a powerful new tool is provided to explicitly model quantitative phenotypes in the context of linkage analysis. It is freely available at http://www.helmholtz-muenchen.de/genepi/downloads. Copyright (C) 2012 S. Karger AG, Base

Elastic turbulence in curvilinear flows of polymer solutions

Following our first report (A. Groisman and V. Steinberg, \sl Nature $\bf 405$, 53 (2000)) we present an extended account of experimental observations of elasticity induced turbulence in three different systems: a swirling flow between two plates, a Couette-Taylor (CT) flow between two cylinders, and a flow in a curvilinear channel (Dean flow). All three set-ups had high ratio of width of the region available for flow to radius of curvature of the streamlines. The experiments were carried out with dilute solutions of high molecular weight polyacrylamide in concentrated sugar syrups. High polymer relaxation time and solution viscosity ensured prevalence of non-linear elastic effects over inertial non-linearity, and development of purely elastic instabilities at low Reynolds number (Re) in all three flows. Above the elastic instability threshold, flows in all three systems exhibit features of developed turbulence. Those include: (i)randomly fluctuating fluid motion excited in a broad range of spatial and temporal scales; (ii) significant increase in the rates of momentum and mass transfer (compared to those expected for a steady flow with a smooth velocity profile). Phenomenology, driving mechanisms, and parameter dependence of the elastic turbulence are compared with those of the conventional high Re hydrodynamic turbulence in Newtonian fluids.Comment: 23 pages, 26 figure