Stochastic Mean-Field Approach to Fluid Dynamics

It is shown that the incompressible Navier–Stokes equation can be derived from an infinite-dimensional mean-field stochastic differential equation.     

Diophantine geometry over groups I: Makanin-Razborov diagrams

Manucsrit re?u le 4 janvier 2000.     

TiO2-nonstoichiometry dependence on piezoelectric properties and depolarization temperature of (Bi0.5Na0.5)0.94Ba0.06TiO3 lead-free ceramics

(Bi_0.5Na_0.5)_0.94Ba_0.06Ti_xO_1+2x lead-free piezoceramics with x varying from 0.97 to 1.03 were fabricated and characterized in order to investigate the effects of TiO₂-nonstoichiometry on the piezoelectric properties and depolarization temperature of (Bi_0.5Na_0.5)_0.94Ba_0.06TiO₃ composition. X-ray diffraction (XRD) analysis showed that all samples have a single phase of perovskite structure with rhombohedral symmetry. Piezoelectric and dielectric measurements revealed that deficiency of TiO₂ leads to an increase in the piezoelectric coefficient (d₃₃), free relative permittivity (), and loss tangent (tan δ) besides an increase in the electromechanical coupling coefficient (k_p) within a certain amount, while excess of TiO₂ results in a decrease in k_p, d₃₃, and , but an increase in tan δ. Depolarization temperature (T_d) measurement indicated a decrease and an increase in T_d as a result of increasing TiO₂ deficiency and TiO₂ excess, respectively. This TiO₂-nonstoichiometry also induced changes in the remanent polarization (P_r) and coercive field (E_c) of the ceramics.     

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.     

The Entropy of a Binary Hidden Markov Process

The entropy of a binary symmetric Hidden Markov Process is calculated as an expansion in the noise parameter ε. We map the problem onto a one-dimensional Ising model in a large field of random signs and calculate the expansion coefficients up to second order in ε. Using a conjecture we extend the calculation to 11th order and discuss the convergence of the resulting series     

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.     

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     

A general route for the synthesis of β,β-difluorocarboxylic acids

A new method for the preparation of β,β-difluoro- (and other gem-difluoro) acids has been developed. It is based on the fact that 3-oxocarboxylic esters are easy to make and convert to the corresponding dithiane derivatives. These dithianes reacted with BrF₃, a commercial, but rarely used reagent in organic chemistry, under very mild conditions to form the corresponding difluoroesters, which in turn could be quantitatively hydrolyzed to the free gem-difluoroacids.     

Effect of fiber modification with carboxymethyl cellulose on the efficiency of a microparticle flocculation system

Carboxymethyl cellulose (CMC) has been used widely to enhance dry strength of paper and uniformity of sheet in the papermaking industry. Besides these positive effects, it may affect the fines retention and dewatering processes negatively. These negative effects are mainly seen when fiber modifications with high CMC dosages are studied in laboratory scale. In this paper, the effect of fiber modification with CMC on the deposition of precipitated calcium carbonate (PCC) and on the dewatering process in the presence of cationic polyacrylamide (CPAM)/bentonite microparticle flocculation system is examined. It was determined that fiber modification with 10 mg g⁻¹ of CMC decreased PCC deposition at the initial addition of CPAM and gave better PCC deposition at 2 mg g⁻¹ of CPAM. It was also observed that PCC deposition on unmodified fibers is higher at lower CPAM concentration. PCC deposition was found as almost stable after a maximum value obtained at 0.5 mg g⁻¹ of bentonite concentration for fiber modified with 40 mg g⁻¹ of CMC. This indicates that interaction between CPAM and bentonite particles changed due to higher surface charge and CMC conformation on fibers. Results of the dewatering experiments showed that CMC modification increased the drainage time due to a denser and more plugged sheet. This negative effect was compensated with higher concentrations of CPAM and bentonite. On the other hand, dewatering is also affected by the mass ratio of CMC and CPAM, which was not the optimum one in this study at lower of CPAM. Thus, the increase in the drainage time in the presence of CMC on the fiber surface could be also caused by incorrect ratios of chemicals because the effect of CMC on the drainage time was not observed at higher concentrations of CPAM.     

NMR assignments and histone specificity of the ING2 PHD finger

The ING2 plant homeodomain (PHD) finger is recruited to the nucleosome through specific binding to histone H3 trimethylated at lysine 4 (H3K4me3). Here, we describe backbone and side chain assignments of the ING2 PHD finger, analyze its binding to the unmodified and modified histone and p53 peptides, and map the histone H3 and H3K4me3 binding sites based on chemical shift perturbation analysis. Copyright © 2009 John Wiley & Sons, Ltd.