Finite Size Polyelectrolyte Bundles at Thermodynamic Equilibrium

We present the results of extensive computer simulations performed on solutions of monodisperse charged rod-like polyelectrolytes in the presence of trivalent counterions. To overcome energy barriers we used a combination of parallel tempering and hybrid Monte Carlo techniques. Our results show that for small values of the electrostatic interaction the solution mostly consists of dispersed single rods. The potential of mean force between the polyelectrolyte monomers yields an attractive interaction at short distances. For a range of larger values of the Bjerrum length, we find finite size polyelectrolyte bundles at thermodynamic equilibrium. Further increase of the Bjerrum length eventually leads to phase separation and precipitation. We discuss the origin of the observed thermodynamic stability of the finite size aggregates

P-values for high-dimensional regression

Assigning significance in high-dimensional regression is challenging. Most computationally efficient selection algorithms cannot guard against inclusion of noise variables. Asymptotically valid p-values are not available. An exception is a recent proposal by Wasserman and Roeder (2008) which splits the data into two parts. The number of variables is then reduced to a manageable size using the first split, while classical variable selection techniques can be applied to the remaining variables, using the data from the second split. This yields asymptotic error control under minimal conditions. It involves, however, a one-time random split of the data. Results are sensitive to this arbitrary choice: it amounts to a `p-value lottery' and makes it difficult to reproduce results. Here, we show that inference across multiple random splits can be aggregated, while keeping asymptotic control over the inclusion of noise variables. We show that the resulting p-values can be used for control of both family-wise error (FWER) and false discovery rate (FDR). In addition, the proposed aggregation is shown to improve power while reducing the number of falsely selected variables substantially.Comment: 25 pages, 4 figure

An Integrable Shallow Water Equation with Linear and Nonlinear Dispersion

We study a class of 1+1 quadratically nonlinear water wave equations that combines the linear dispersion of the Korteweg-deVries (KdV) equation with the nonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation, yet still preserves integrability via the inverse scattering transform (IST) method. This IST-integrable class of equations contains both the KdV equation and the CH equation as limiting cases. It arises as the compatibility condition for a second order isospectral eigenvalue problem and a first order equation for the evolution of its eigenfunctions. This integrable equation is shown to be a shallow water wave equation derived by asymptotic expansion at one order higher approximation than KdV. We compare its traveling wave solutions to KdV solitons.Comment: 4 pages, no figure

Broadleaf weed control in chickpea (Cicer arietinum) and lentil (Lens culinaris) with fall application of pursuit

Non-Peer ReviewedBroadleaf weed control options in chickpea and lentil are very limited. Preliminary trials found that spring applied Pursuit at rates from 0.25X to 0.5X resulted in severe injury to chickpea in some years. The objective of these trials was to evaluate fall application of Pursuit in chickpea and lentil, at rates from 0.25X to 0.5X, for both crop tolerance and weed control efficacy. A 4-replicate trial was set up at Saskatoon, Sask. in 2000, 2001 and 2002 and at Scott, Sask. and Swift Current, Sask. in 2002. Pursuit was surface applied, with no incorporation, in the fall, at rates of 0.25X, 0.33X, 0.4X and 0.5X. Edge (2000) or Poast Ultra (2001, 2002) were applied to improve grassy weed control. The trials were direct seeded with low disturbance openers. There was excellent crop tolerance to fall applications of Pursuit in both chickpea and lentil at all location-years. Some visual crop injury was evident at the higher rates of Pursuit; however, yield was not reduced. Broadleaf weed control was inconsistent at the 0.25X rate. Rates higher than 0.33X rates resulted in excellent control of stinkweed (Thlaspi arvense L.), wild mustard (Sinapsis arvensis L.), wild buckwheat (Polygonum convolvulus L.), lamb’s-quarters (Chenopodium album L.), redroot pigweed (Amaranthus retroflexus L.), Russian thistle (Salsola kali L.) and cleavers (Galium aparine L.) at all location-years. When compared to a post-emergence application of Sencor, fall applied Pursuit at 0.33X to 0.4X rates resulted in similar to 20% higher seed yields in lentil and chickpea, respectively. Fall applied Pursuit at 0.33X to 0.4X rate resulted in consistent broadleaf weed control, low crop injury, and high crop yield

Polyelectrolyte Bundles

Using extensive Molecular Dynamics simulations we study the behavior of polyelectrolytes with hydrophobic side chains, which are known to form cylindrical micelles in aqueous solution. We investigate the stability of such bundles with respect to hydrophobicity, the strength of the electrostatic interaction, and the bundle size. We show that for the parameter range relevant for sulfonated poly-para-phenylenes (PPP) one finds a stable finite bundle size. In a more generic model we also show the influence of the length of the precursor oligomer on the stability of the bundles. We also point out that our model has close similarities to DNA solutions with added condensing agents, hinting to the possibility that the size of DNA aggregates is under certain circumstances thermodynamically limited.Comment: 10 pages, 8 figure

Equilibria of biological aggregations with nonlocal repulsive-attractive interactions

We consider the aggregation equation $\rho_{t}-\nabla\cdot(\rho\nabla K\ast\rho) =0$ in $\mathbb{R}^{n}$, where the interaction potential $K$ incorporates short-range Newtonian repulsion and long-range power-law attraction. We study the global well-posedness of solutions and investigate analytically and numerically the equilibrium solutions. We show that there exist unique equilibria supported on a ball of $\mathbb{R}^n$. By using the method of moving planes we prove that such equilibria are radially symmetric and monotone in the radial coordinate. We perform asymptotic studies for the limiting cases when the exponent of the power-law attraction approaches infinity and a Newtonian singularity, respectively. Numerical simulations suggest that equilibria studied here are global attractors for the dynamics of the aggregation model

Ballistic and Diffuse Electron Transport in Nanocontacts of Magnetics

The transition from the ballistic electron transport to the diffuse one is experimentally observed in the study of the magnetic phase transition in Ni nanocontacts with different sizes. It is shown that the voltage $U_C$ needed for Joule heating of the near-contact region to the critical temperature does not depend on the contact size only in the diffuse mode. For the ballistic contact it increases with decrease in the nanocontact size. The reduction of the transport electron mean free path due to heating of NCs may result in change of the electron transport mode from ballistic to diffusive one.Comment: 7 pages, 2 figures accepted for the publication in JETPL (http://www.jetpletters.ac.ru). Will be published on 25 april 201

Multiband superconductivity in the heavy fermion compound PrOs4Sb12

The thermal conductivity of the heavy fermion superconductor PrOs4Sb12 was measured down to Tc/40 throughout the vortex state. At lowest temperatures and for magnetic fields H ~ 0.07Hc2, already 40% of the normal state thermal conductivity is restored. This behaviour (similar to that observed in MgB2) is a clear signature of multiband superconductivity in this compound.Comment: 12pages, version #1 20\_06\_200