Chiral surfaces self-assembling in one-component systems with isotropic interactions

We show that chiral symmetry can be broken spontaneously in one-component systems with isotropic interactions, i.e. many-particle systems having maximal a priori symmetry. This is achieved by designing isotropic potentials that lead to self-assembly of chiral surfaces. We demonstrate the principle on a simple chiral lattice and on a more complex lattice with chiral super-cells. In addition we show that the complex lattice has interesting melting behavior with multiple morphologically distinct phases that we argue can be qualitatively predicted from the design of the interaction.Comment: 4 pages, 4 figure

Quasi-two-day wave in an unstable summer atmosphere - some numerical results on excitation and propagation

International audienceBased on numerical calculations we demonstrate that small changes in the smooth climatological background atmosphere may lead to an unstable mean zonal wind distribution in the summer middle atmosphere. We relate these changes to small ones because locations and power of the main circulation structures are conserved, except for the acceleration of the easterly jet in the stratosphere/mesosphere. The instability forces oscillations propagating westward with a period of about 2 days and zonal wave numbers s=3 and/or 4. There are variations in the mean zonal wind distribution due to the excitation and transient propagation of these waves, and the numerical results correspond to features of these variations observed in experimental studies. The growing waves tend to remove the source of excitation. This process is effective enough to reduce the strong easterly jet and to remove the strong negative gradient of the zonal mean potential vorticity in the region of the instability. Therefore, when these parameters are calculated as mean values over a long time interval, the obtained values are too small to provide the instability. Strong 2-day waves, in turn, are unstable and can generate secondary waves with longer periods and lower zonal wave numbers. This effect is only significant for extremely strong 2-day waves. Another process is found to be more effective to produce secondary waves. We demonstrated that the 2-day wave with s=3 forced by nonlinear interaction between the 10-14 day planetary waves and the 2-day wave of zonal wave number 4 is unstable. This wave instability generates secondary waves with amplitudes that are large enough to be observed by ground-based radars, for example

On a generalization of Jacobi's elliptic functions and the Double Sine-Gordon kink chain

A generalization of Jacobi's elliptic functions is introduced as inversions of hyperelliptic integrals. We discuss the special properties of these functions, present addition theorems and give a list of indefinite integrals. As a physical application we show that periodic kink solutions (kink chains) of the double sine-Gordon model can be described in a canonical form in terms of generalized Jacobi functions.Comment: 18 pages, 9 figures, 3 table

From Lagrangian to Quantum Mechanics with Symmetries

We present an old and regretfully forgotten method by Jacobi which allows one to find many Lagrangians of simple classical models and also of nonconservative systems. We underline that the knowledge of Lie symmetries generates Jacobi last multipliers and each of the latter yields a Lagrangian. Then it is shown that Noether's theorem can identify among those Lagrangians the physical Lagrangian(s) that will successfully lead to quantization. The preservation of the Noether symmetries as Lie symmetries of the corresponding Schr\"odinger equation is the key that takes classical mechanics into quantum mechanics. Some examples are presented.Comment: To appear in: Proceedings of Symmetries in Science XV, Journal of Physics: Conference Series, (2012

Modular Solutions to Equations of Generalized Halphen Type

Solutions to a class of differential systems that generalize the Halphen system are determined in terms of automorphic functions whose groups are commensurable with the modular group. These functions all uniformize Riemann surfaces of genus zero and have $q$--series with integral coefficients. Rational maps relating these functions are derived, implying subgroup relations between their automorphism groups, as well as symmetrization maps relating the associated differential systems.Comment: PlainTeX 36gs. (Formula for Hecke operator corrected.

Novel self-assembled morphologies from isotropic interactions

We present results from particle simulations with isotropic medium range interactions in two dimensions. At low temperature novel types of aggregated structures appear. We show that these structures can be explained by spontaneous symmetry breaking in analytic solutions to an adaptation of the spherical spin model. We predict the critical particle number where the symmetry breaking occurs and show that the resulting phase diagram agrees well with results from particle simulations.Comment: 4 pages, 4 figure

Metal-Induced Specific and Nonspecific Oligonucleotide Folding Studied by FRET and Related Biophysical and Bioanalytical Implications

This is the peer reviewed version of the following article: Kiy, M. M., Jacobi, Z. E., & Liu, J. (2012). Metal-Induced Specific and Nonspecific Oligonucleotide Folding Studied by FRET and Related Biophysical and Bioanalytical Implications. Chemistry - A European Journal, 18(4), 1202–1208, which has been published in final form at http://dx.doi.org/10.1002/chem.201102515 This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.Metal induced nucleic acid folding has been extensively studied with ribozymes, DNAzymes, tRNA and riboswitches. These RNA/DNA molecules usually have a high content of double-stranded regions to support a rigid scaffold. On the other hand, such rigid structural features are not available for many in vitro selected or rationally designed DNA aptamers; they adopt flexible random coil structures in the absence of target molecules. Upon target binding, these aptamers adaptively fold into a compact structure with a reduced end-to-end distance, making fluorescence resonance energy transfer (FRET) a popular signaling mechanism. However, nonspecific folding induced by mono- or divalent metal ions can also reduce the end-to-end distance and thus lead to false positive results. In this study we used a FRET pair labeled HgII binding DNA and monitored metal-induced folding in the presence of various cations. While nonspecific electrostatically mediated folding can be very significant, at each tested salt condition, HgII induced folding was still observed with a similar sensitivity. We also studied the biophysical meaning of the acceptor/donor fluorescence ratio that allowed us to explain the experimental observations. Potential solutions for this ionic strength problem have been discussed. For example, probes designed to signal the formation of double-stranded DNA showed a lower dependency on ionic strength.University of Waterloo || Canadian Foundation for Innovation Ontario ministry of Research and Innovation || Natural Sciences and Engineering Research Council |

Using the uncertainty principle to design simple interactions for targeted self-assembly

We present a method that systematically simplifies isotropic interactions designed for targeted self-assembly. The uncertainty principle is used to show that an optimal simplification is achieved by a combination of heat kernel smoothing and Gaussian screening of the interaction potential in real and reciprocal space. We use this method to analytically design isotropic interactions for self-assembly of complex lattices and of materials with functional properties. The derived interactions are simple enough to narrow the gap between theory and experimental implementation of theory based designed self-assembling materials

Environmental Response Management Application

The Coastal Response Research Center (CRRC), a partnership between the University of New Hampshire (UNH) and NOAA\u27s Office of Response and Restoration (ORR), is leading an effort to develop a data platform capable of interfacing both static and real-time data sets accessible simultaneously to a command post and assets in the field with an open source internet mapping server. The Environmental Response Management Application (ERMA™) is designed to give responders and decision makers ready access to geographically specific data useful during spill planning/drills, incident response, damage assessment and site restoration. In addition to oil spill and chemical release response, this website can be relevant to other environmental incidents and natural disasters, responses and regional planning efforts. The platform is easy to operate, without the assistance of Information Technology or Geographic Information Systems (GIS) specialists. It allows users to access individual data layer values, overlay relevant data sets, and zoom into segments of interest. The platform prototype is being developed specifically for Portsmouth Harbor and the Great Bay Estuary, NH. The prototype demonstrates the capabilities of an integrated data management platform and serves as the pilot for web-based GIS platforms in other regions

Visual detection of lead(II) using a label-free DNA-based sensor and its immobilization within a monolithic hydrogel

Lead is highly toxic and its detection has attracted a lot of research interests. In recent years, DNA has been used for Pb2+ recognition and many fluorescent sensors with low to sub-nM detection limits have been reported. These figures of merit were typically measured using a spectrophotometer that can detect nM DNA with a high signal-to-noise ratio. For visual detection, however, μM DNA or dye was required, making it difficult to detect low nM targets. We recently achieved a visual sensitivity of 10 nM Hg2+ by immobilizing a DNA probe in a hydrogel. This was made possible because the gel was able to actively adsorb Hg2+. In this work, we aim to test whether this method can be extended to the detection of Pb2+. First, a new Pb2+ sensor was designed based on a guanine-rich DNA and DNA binding dyes such as thiazole orange and SYBR Green I. The free DNA showed a detection limit of 8 nM Pb2+ using 40 nM DNA. For visual detection in solution with 1 μM of the DNA probe, however, ∼300 nM Pb2+ was required. After immobilization in a monolithic polyacrylamide hydrogel, even 20 nM Pb2+ could be visually detected with a sample volume of 50 mL. Therefore, sensitive detection without signal amplification was achieved. Finally, we demonstrated simultaneous detection of both Hg2+ and Pb2+ in the same water sample with shape encoded hydrogel sensors.University of Waterloo || Canada Foundation for Innovation || Natural Sciences and Engineering Research Council || Ontario Ministry of Research and Innovation |