Effect of nonlinearity on the development of oscillatory magnetohydrodynamic Kelvin-Helmholtz instability in the weakly supercritical regime

The nonlinear stage of development of perturbations at a tangential magnetohydrodynamic discontinuity is investigated in the weakly subcritical and supercritical regimes. It is assumed that the fluid is incompressible and that the density and magnetic field, as well as the velocity, suffer a discontinuity. An equation describing the evolution of low-amplitude nonlinear perturbations is obtained. For periodic perturbations this equation reduces to an infinite system of ordinary differential equations for the amplitudes of the Fourier harmonics. The system is reduced to finite form by truncation and then integrated numerically. Calculations show that the evolution of an initially sinusoidal perturbation always ends with the appearance in the wave profile of an infinite derivative. This can take the form of either an infinitely sharp peak (knife-edge) or wave breaking.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 30–39, May–June, 1988.     

Nonlinear internal waves in a fluid of infinite depth in the presence of a horizontal magnetic field

An investigation is made into the propagation of long nonlinear weakly nonone-dimensional internal waves in an incompressible stratified fluid of infinite depth in the presence of a horizontal magnetic field. It is shown that such waves are described by an equation representing the extension of the Benjamin-Ono equation to the weakly nonone-dimensional case. The equation obtained differs from that obtained in [4], which is attributable to the anisotropy of the medium resulting from the presence of a magnetic field. The stability of a soliton with respect to flexural perturbations is investigated. A particular case of the variation of the density with height at constant Alfvén velocity is examined in detail.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 65–72, November–December, 1987.     

Propagation of nonlinear Alfvén surface waves along a tangential magnetohydrodynamic discontinuity in an incompressible fluid

The paper considers the propagation of low-amplitude nonlinear waves over a surface of magnetic discontinuity. An equation for these waves is derived. The evolution of a sinusoidal perturbation is investigated. The discontinuity formation time is numerically determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 98–105, January–February, 1985.     

Polydiacetylene-supported silica films formed at the air/water interface

Mesostructured silica films have attracted interest as potential platforms for sensing, molecular sieving, catalysis, and others. The fabrication of free-standing silica films on water, however, is challenging due to the need for scaffolding agents that would constitute effective templates. We describe the assembly of thin film at the air/water interface comprising quaternary silicates and polydiacetylene (PDA), a unique chromatic polymer forming two-dimensional conjugated networks, and the use of these films for biological sensing. PDA exhibits a dual role in the system-both as the amphiphilic matrix facilitating immobilization of the silicate colloidal units at the air/water interface and additionally a chromatic reporter that undergoes visible blue-red transitions, accompanied by fluorescence transformations, in the presence of analytes. We demonstrate the application of the silicate/PDA thin films for the detection of bacterial proliferation.     

Nonlinear waves on shallow water in the presence of a horizontal magnetic field

Benjamin [1] and Davis and Acrivos [2] derived an equation for long steady nonlinear internal waves in an infinitely deep stratified fluid when the density varies only in a layer whose thickness is small compared with the characteristic perturbation length. Ono [3] generalized this equation to the unsteady case. The resulting equation was subsequently called the Benjamin—Ono equation. Steady solutions of this equation were found by Benjamin and Ono in the form of solitons and periodic waves. In the present paper it is shown that long nonlinear waves on shallow water in the presence of a horizontal magnetic field can also be described by the Benjamin—Ono equation, and not the Korteweg—de Vries equation [4], as in the case when there is no field. Moreover, in contrast to a soliton in a stratified fluid a soliton on shallow water in a horizontal magnetic field moves with a velocity less than the velocity of infinitely long perturbations of small amplitude. The dependence of the parameters of a soliton and a periodic wave on the intensity and direction of the unperturbed magnetic field is investigated.     

Freak waves in laboratory and space plasmas

Generation of large-amplitude short-lived wave groups from small-amplitude initial perturbations in plasmas is discussed. Two particular wave modes existing in plasmas are considered. The first one is the ion-sound wave. In a plasmas with negative ions it is described by the Gardner equation when the negative ion concentration is close to critical. The results of numerical solution of the Gardner equation with the modulationally unstable initial condition are presented. These results clearly show the possibility of generation of freak ion-acoustic waves due to the modulational instability. The second wave mode is the Alfvén wave. When this wave propagates at a small angle with respect to the equilibrium magnetic field, and its wave length is comparable with the ion inertia length, it is described by the DNLS equation. Studying the evolution of an initial perturbation using the linearized DNLS equation shows that the generation of freak Alfvén waves is possible due to linear dispersive focusing. The numerical solution of the DNLS equation reveals that the nonlinear dispersive focusing can also produce freak Alfvén waves.     

A new force field (ECEPP-05) for peptides, proteins, and organic molecules

Parametrization and testing of a new all-atom force field for organic molecules and peptides with fixed bond lengths and bond angles are described. The van der Waals parameters for both the organic molecules and the peptides were taken from J. Phys. Chem. B 2003, 107, 7143 and J. Phys. Chem. B 2004, 108, 12181. First, the values of the 1-4 nonbonded and electrostatic scale factors appropriate to the new force field were determined by computing the conformational energies of six model molecules, namely, ethanol, ethylamine, propanol, propylamine, 1,2-ethanediol, and 1,3-propanediol with different values of these factors. The partial atomic charges of these molecules were obtained by fitting to the electrostatic potentials calculated with the HF/6-31G quantum-mechanical method. Two different charge models (single- and multiple-conformation-derived) were also considered. We demonstrated that the charge model has a stronger effect on the conformational energies than the 1-4 scaling. The choice of a charge model affected the conformational energies of even the smallest molecules considered, whereas the effect of the 1-4 electrostatic or nonbonded scaling was apparent only for 1,3-propanediol. The best agreement with high-level ab initio data was obtained with the multiple-conformation-derived charges and with no scaling of the 1-4 nonbonded or electrostatic interactions (scale factors of 1.0). Next, the torsional parameters of a large number of neutral and charged organic molecules, assumed to be models of the side chains of the 20 naturally occurring amino acids, were computed by fitting to rotational energy profiles obtained from ab initio MP2/6-31G calculations. The quality of the fits was high with average errors for torsional profiles of less than 0.2 kcal/mol. To derive the torsional parameters for the peptide backbone, the partial atomic charges of the 20 neutral and charged amino acids were obtained by fitting to the electrostatic potentials of terminally blocked amino acids using the HF/6-31G quantum-mechanical method. Then, the phi-psi energy maps of Ac-Ala-NMe and Ac-Gly-NMe were computed using MP2/6-31G//HF/6-31G quantum-mechanical methods. The phi-psi energy map of Ac-Ala-NMe was used for refinement of the nonbonded parameters for the backbone nitrogen and hydrogen bonded to it. Subsequently, the main-chain torsional parameters were obtained by fitting the molecular mechanics energies to the phi-psi energy maps of Ac-Ala-NMe and Ac-Gly-NMe. The transferability of the entire force field was demonstrated by reproducing the main energy minima of terminally blocked Ala3 from the literature. The performance of the force field was also evaluated by simulating crystal structures of small peptides. By comparison of simulated and experimental data, examination of the torsional-angle and atom-positional root-mean-square deviations of the energy-minimized crystal structures from the corresponding X-ray model structures demonstrated high accuracy of the force field.     

Arrangements of minors in the positive Grassmannian and a triangulation of the hypersimplex

The structure of zero and nonzero minors in the Grassmannian leads to rich combinatorics of matroids. In this paper, we investigate an even richer structure of possible equalities and inequalities between the minors in the positive Grassmannian. It was previously shown that arrangements of equal minors of largest value are in bijection with the simplices in a certain triangulation of the hypersimplex that was studied by Stanley, Sturmfels, Lam and Postnikov. Here, we investigate the entire set of arrangements and its relations with this triangulation. First, we show that second largest minors correspond to the facets of the simplices. We then introduce the notion of cubical distance on the dual graph of the triangulation and study its relations with the arrangement of t-th largest minors. Finally, we show that arrangements of largest minors induce a structure of a partially ordered set on the entire collection of minors. We use this triangulation of the hypersimplex to describe a two-dimensional grid structure on this poset.     

New investigations on ferrofluidics: ferrofluidic marbles and magnetic-field-driven drops on superhydrophobic surfaces

The motion of ferrofluidic marbles on flat polymer substrates is reported. Nanopowders of polyvinylidene fluoride and gammaFe2O3 were used for the preparation of ferrofluidic marbles. The marbles are activated easily with an external magnetic field. A microfluidic device based on ferrofluidic marbles (the ferrofluidic bearing) is described. Velocities of marbles as high as 25+/-3 cm/s were registered. The sliding of ferrofluidic drops on superhydrophobic surfaces was studied. It was demonstrated that the threshold magnetic force necessary for the drop displacement depends linearly on the drop radius, thus the motion of the drop is defined by the processes occurring in the vicinity of the triple line only.     

Mechanisms of oxidation of guanine in DNA by carbonate radical anion, a decomposition product of nitrosoperoxycarbonate

Peroxynitrite is produced during inflammation and combines rapidly with carbon dioxide to yield the unstable nitrosoperoxycarbonate, which decomposes (in part) to CO(3) (.-) and (.)NO(2) radicals. The CO(3) (.-) radicals oxidize guanine bases in DNA through a one-electron transfer reaction process that ultimately results in the formation of stable guanine oxidation products. Here we have explored these mechanisms, starting with a spectroscopic study of the kinetics of electron transfer from 20-22mer double-stranded oligonucleotides to CO(3) (.-) radicals, together with the effects of base sequence on the formation of the end-products in runs of one, two, or three contiguous guanines. The distributions of these alkali-labile lesions were determined by gel electrophoresis methods. The cascade of events was initiated through the use of 308 nm XeCl excimer laser pulses to generate CO(3) (.-) radicals by an established method based on the photodissociation of persulfate to sulfate radicals and the oxidation of bicarbonate. Although the Saito model (Saito et al., J. Am. Chem. Soc. 1995, 117, 6406-6407) predicts relative ease of one-electron oxidations in DNA, following the trend 5'-GGG > 5'-GG > 5'-G, we found that the rate constants for CO(3) (.-)-mediated oxidation of guanines in these sequence contexts (k(5)) showed only small variation within a narrow range [(1.5-3.0)x10(7) M(-1) s(-1)]. In contrast, the distributions of the end-products are dependent on the base sequence context and are higher at the 5'-G in 5'-GG sequences and at the first two 5'-guanines in the 5'-GGG sequences. These effects are attributed to a combination of initial hole distributions among the contiguous guanines and the subsequent differences in chemical reaction yields at each guanine. The lack of dependence of k(5) on sequence context indicates that the one-electron oxidation of guanine in DNA by CO(3) (.-) radicals occurs by an inner-sphere mechanism.