Robustness of a perturbed topological phase

We investigate the stability of the topological phase of the toric code model in the presence of a uniform magnetic field by means of variational and high-order series expansion approaches. We find that when this perturbation is strong enough, the system undergoes a topological phase transition whose first- or second-order nature depends on the field orientation. When this transition is of second order, it is in the Ising universality class except for a special line on which the critical exponent driving the closure of the gap varies continuously, unveiling a new topological universality class.     

Single crystalline La0.7Sr0.3MnO3 molecular sieve nanowires with high temperature ferromagnetism

Porous mixed-valent manganese oxides are a group of multifunctional materials that can be used as molecular sieves, catalysts, battery materials, and gas sensors. However, material properties and thus activity can vary significantly with different synthesis methods or process conditions, such as temperature and time. Here, we report on a new synthesis route for MnO(2) and LaSr-doped molecular sieve single crystalline nanowires based on a solution chemistry methodology combined with the use of nanoporous polymer templates supported on top of single crystalline substrates. Because of the confined nucleation in high aspect ratio nanopores and of the high temperatures attained, new structures with novel physical properties have been produced. During the calcination process, the nucleation and crystallization of ε-MnO(2) nanoparticles with a new hexagonal structure is promoted. These nanoparticles generated up to 30 μm long and flexible hexagonal nanowires at mild growth temperatures (T(g) = 700 °C) as a consequence of the large crystallographic anisotropy of ε-MnO(2). The nanocrystallites of MnO(2) formed at low temperatures serve as seeds for the growth of La(0.7)Sr(0.3)MnO(3) nanowires at growth temperatures above 800 °C, through the diffusion of La and Sr into the empty 1D-channels of ε-MnO(2). Our particular growth method has allowed the synthesis of single crystalline molecular sieve (LaSr-2 × 4) monoclinic nanowires with composition La(0.7)Sr(0.3)MnO(3) and with ordered arrangement of La(3+) and Sr(2+) cations inside the 1D-channels. These nanowires exhibit ferromagnetic ordering with strongly enhanced Curie temperature (T(c) > 500 K) that probably results from the new crystallographic order and from the mixed valence of manganese.     

Multidimensional generalization of the Korous inequality

This paper deals with some qualitative properties of orthogonal polynomials in several variables. The boundedness and relations between two sets of orthonormal polynomials associated with an arbitrary weight function and its extension are investigated. It presents an analogy to Korous' result for general orthogonal polynomials in one variable.     

Stabilized phosphatidylinositol-5-phosphate analogues as ligands for the nuclear protein ING2: chemistry, biology, and molecular modeling

The interaction of PtdIns(5)P with the tumor suppressor protein ING2 has been implicated in the regulation of chromatin modification. To enhance the stability of PtdIns(5)P for studies of the biological role in vivo, two phosphatase-resistant moieties were used to replace the labile 5-phosphate. The total asymmetric synthesis of the 5-methylenephosphonate (MP) and 5-phosphothionate (PT) analogues of PtdIns(5)P is described herein, and the resulting metabolically stabilized lipid analogues were evaluated in three ways. First, liposomes containing either the dioleoyl MP or PT analogues bound to recombinant ING2 similar to liposomes containing dipalmitoyl PtdIns(5)P, indicating that the replacement of the hydrolyzable 5-phosphate group does not compromise the binding. Second, the dioleoyl MP and PT PtdIns(5)P analogues were equivalent to dipalmitoyl PtdIns(5)P in augmenting cell death induced by a DNA double-strand break in HT1080 cells. Finally, molecular modeling and docking of the MP or PT analogues to the C-terminus PtdInsP-binding region of ING2 (consisting of a PHD finger and a polybasic region) revealed a number of complementary surface and electrostatic contacts between the lipids and ING2.     

One-Dimensional Parametric Determining form for the Two-Dimensional Navier–Stokes Equations

The evolution of a determining form for the 2D Navier–Stokes equations (NSE) which is an ODE on a space of trajectories is completely described. It is proved that at every stage of its evolution, the solution is a convex combination of the initial trajectory and a chosen, fixed steady state, with a dynamical convexity parameter \(\theta \), which will be called the characteristic determining parameter. That is, we show a separation of variables formula for the solution of the determining form. Moreover, for a given initial trajectory, the dynamics of the infinite-dimensional determining form are equivalent to those of the characteristic determining parameter \(\theta \) which is governed by a one-dimensional ODE. This one-dimensional ODE is used to show that if the solution to the determining form converges to the fixed state it does so no faster than \({\mathcal {O}}(\tau ^{-1/2})\), otherwise it converges to a projection of some other trajectory in the global attractor of the NSE, but no faster than \({\mathcal {O}}(\tau ^{-1})\), as \(\tau \rightarrow \infty \), where \(\tau \) is the evolutionary variable in determining form. The one-dimensional ODE is also exploited in computations which suggest that the one-sided convergence rate estimates are in fact achieved. The ODE is then modified to accelerate the convergence to an exponential rate. It is shown that the zeros of the scalar function that governs the dynamics of \(\theta \), which are called characteristic determining values, identify in a unique fashion the trajectories in the global attractor of the 2D NSE     

Assessment of Oxidative Stress in Patients with an Isolated Traumatic Brain Injury Using Disposable Electrochemical Test Strips

The barriers to using plasma redox potential as a measure of oxidative stress in patients are the use of specialized equipment, necessity of sterilization between tests, and inconsistent electrode surfaces and cell geometry. These problems are resolved using disposable test strips with built in electrochemical cells. Measuring the electrode potential at a small current yields a stable value that is ～50 mV higher for isolated traumatic brain injury (ITBI) patients than for healthy individuals. Even with natural variations within blood chemistry, this simple method may be clinically useful for assessing the degree of oxidative stress and injury severity in ITBI patients.     

Biomolecular Densely Grafted Brush Polymers: Oligonucleotides,Oligosaccharides and Oligopeptides

In this Minireview, we describe synthetic polymers densely functionalized with sequence-defined biomolecular sidechains. We focus on synthetic brush polymers of oligonucleotides, oligosaccharides, and oligopeptides, prepared via graft-through polymerization from biomolecule functionalized monomers. The resulting structures are brush polymers wherein a biomolecular graft is positioned at each monomer backbone unit. We describe key synthetic milestones, identify synthetic opportunities, and highlight recent advances in the field, including biological applications.     

The structure of ions and zwitterionic lipids regulates the charge of dipolar membranes

In pure water, zwitterionic lipids form lamellar phases with an equilibrium water gap on the order of 2 to 3 nm as a result of the dominating van der Waals attraction between dipolar bilayers. Monovalent ions can swell those neutral lamellae by a small amount. Divalent ions can adsorb onto dipolar membranes and charge them. Using solution X-ray scattering, we studied how the structure of ions and zwitterionic lipids regulates the charge of dipolar membranes. We found that unlike monovalent ions that weakly interact with all of the examined dipolar membranes, divalent and trivalent ions adsorb onto membranes containing lipids with saturated tails, with an association constant on the order of ～10 M(-1). One double bond in the lipid tail is sufficient to prevent divalent ion adsorption. We suggest that this behavior is due to the relatively loose packing of lipids with unsaturated tails that increases the area per lipid headgroup, enabling their free rotation. Divalent ion adsorption links two lipids and limits their free rotation. The ion-dipole interaction gained by the adsorption of the ions onto unsaturated membranes is insufficient to compensate for the loss of headgroup free-rotational entropy. The ion-dipole interaction is stronger for cations with a higher valence. Nevertheless, polyamines behave as monovalent ions near dipolar interfaces in the sense that they interact weakly with the membrane surface, whereas in the bulk their behavior is similar to that of multivalent cations. Advanced data analysis and comparison with theory provide insight into the structure and interactions between ion-induced regulated charged interfaces. This study models biologically relevant interactions between cell membranes and various ions and the manner in which the lipid structure governs those interactions. The ability to monitor these interactions creates a tool for probing systems that are more complex and forms the basis for controlling the interactions between dipolar membranes and charged proteins or biopolymers for encapsulation and delivery applications.     

Mixed chromium(III) complexes with pyridinedicarboxylato and oxalato ligands: kinetic studies in HClO<Subscript>4</Subscript> solutions

Three chromium(III) complexes of general formula [Cr(ox)₂(pdaH)]²⁻ (where ox = C₂O₄ ²⁻ and pdaH⁻ is N,O-bonded 2,3-, 2,4- or 2,5-pyridinedicarboxylic acid anion) were obtained and characterized in solution. Acid-catalysed aquation of [Cr(ox)₂(pdaH)]²⁻ gave two products: [Cr(ox)(pdaH)(H₂O)₂]⁰ (P₁) and cis-[Cr(ox)₂(H₂O)₂]²⁻ (P₂). The kinetics of these reactions were studied spectrophotometrically, within the 0.1–1.0 M HClO₄ range, and the pseudo-first-order rate constants for the oxalato (k _obs1) and pdaH⁻ (k _obs2) ligands dissociation were calculated based on the determined pseudo-first-order rate constants (k _obs) and P₁:P₂ molar ratio. The dependencies of the pseudo-first-order rate constants on [H⁺] are as follows: k _obs1 = b ₁[H⁺] and k _obs2 = b ₂[H⁺], where b ₁ and b ₂ are the second-order rate constants for the oxalato and pdaH⁻ ligands dissociation, respectively. Kinetic parameters were determined and the mechanism of the pdaH⁻ ligand dissociation is proposed.