Multi-valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems

Multi-valued solutions are constructed for 2 × 2 first-order systems using a generalization of the hodograph transformation. The solution is found as a complex analytic function on a complex Riemann surface for which the branch points move as part of the solution. The branch point singularities are envelopes for the characteristics and thus move at the characteristic speeds. We perform an analysis of stability of these singularities with respect to perturbations of the initial data. The generic singularity types are folds, cusps, and nondegenerate umbilic points with non-zero 3-jet. An isolated singularity is generically a square root branch point corresponding to a fold. Two types of collisions between singularities are generic: At a “tangential” collision between two singularities moving at the same characteristic speed, a cube root branch point is formed, corresponding to a cusp. A “non-tangential” collision, between two square root branch points moving at different characteristic speeds, remains a square root branch point at the collision and corresponds to a nondegenerate umbilic point. These results are also valid for a diagonalizable n-th order system for which there are exactly two speeds. © 1993 John Wiley & Sons, Inc.     

Evolution of physics-based methodology for exploring the conformational energy landscape of proteins

The evolution of our physics-based computational methods for determining protein conformation without the introduction of secondary-structure predictions, homology modeling, threading, or fragment coupling is described. Initial use of a hard-sphere potential captured much of the structural properties of polypeptide chains, and subsequent more refined force fields, together with efficient methods of global optimization provide indications that progress is being made toward an understanding of the interresidue interactions that underlie protein folding.     

Spectroscopic characterization of human and mouse primary cells,cell lines and malignant cells

Fourier transform infrared (FTIR) spectroscopy is currently being developed as a new optical approach to the diagnosis and characterization of cell or tissue pathology. The advantage of FTIR microspectroscopy over conventional FTIR spectroscopy in the diagnosis of malignancies is that it facilitates inspection of restricted regions of the cell culture or tissue. In this study, we set out to evaluate FTIR microspectroscopy as a diagnostic tool for identifying retrovirus-induced malignancies. Our study showed significant and consistent differences between cultures of different types of cells of both mouse and human origin, i.e. primary fibroblast cells (one to two passages in cell culture), fibroblast cell lines and malignant cells transformed by murine sarcoma virus. An impressive decrease in the levels of phosphate and other metabolites was seen in malignant cells compared with primary cells. The levels of these metabolites in the cell lines were significantly lower than in the primary cells but higher than in the malignant cells. In addition, the peak attributed to the PO2- symmetric stretching mode at 1082 cm(-1) in primary cells shifted significantly to 1085 cm(-1) for the cell line and to 1087 cm(-1) for the malignant cells. These differences taken together with differences in the shapes of various bands throughout the spectrum strongly support the possibility of developing FTIR microspectroscopy for the detection and study of malignant--and possibly premalignant--cells.     

The sonochemical coating of cotton withstands 65 washing cycles at hospital washing standards and retains its antibacterial properties

Hospital-acquired nosocomial infections are a major health, and consequently financial issue, in the world healthcare system. The problem of bacterial infections in general, and in hospitals in particular, has led to extensive scientific and industrial efforts to fabricate antibacterial textiles. A sonochemical coating machine was developed and built and its ability to coat antibacterial nanoparticles (NPs) onto 40–50 meter length of materials on a roll to roll basis at a speed of 22 cm/min. Cotton coated sonochemically with copper oxide nanoparticles (CuO NPs) was found to maintain its antibacterial properties even after 65 cycles of washings according to hospital protocols of hygienic washing (75 °C). This demonstrates the good quality and high stability of this sonochemically produced NPs coating on textiles. Durable antibacterial textiles such as these may be suitable for wide spread use in future hospital environments where hygiene control is of paramount importance.     

Are accurate computations of the 13C′ shielding feasible at the DFT level of theory?

The goal of this study is twofold. First, to investigate the relative influence of the main structural factors affecting the computation of the ¹³C′ shielding, namely, the conformation of the residue itself and the next nearest‐neighbor effects. Second, to determine whether calculation of the ¹³C′ shielding at the density functional level of theory (DFT), with an accuracy similar to that of the ¹³C^α shielding, is feasible with the existing computational resources. The DFT calculations, carried out for a large number of possible conformations of the tripeptide Ac‐G XY ‐NMe, with different combinations of X and Y residues, enable us to conclude that the accurate computation of the ¹³C′ shielding for a given residue X depends on the: (i) (?,ψ) backbone torsional angles of X ; (ii) side‐chain conformation of X ; (iii) (?,ψ) torsional angles of Y ; and (iv) identity of residue Y . Consequently, DFT‐based quantum mechanical calculations of the ¹³C′ shielding, with all these factors taken into account, are two orders of magnitude more CPU demanding than the computation, with similar accuracy, of the ¹³C^α shielding. Despite not considering the effect of the possible hydrogen bond interaction of the carbonyl oxygen, this work contributes to our general understanding of the main structural factors affecting the accurate computation of the ¹³C′ shielding in proteins and may spur significant progress in effort to develop new validation methods for protein structures. © 2013 Wiley Periodicals, Inc.     

Effect of electron cyclotron waves on the structure of a weak collisionless shock wave

An analytic study is made of the structure of a weak collisionless shock wave propagating in a magnetized plasma at right angles to the magnetic field. Dissipation is produced by an instability associated with electron cyclotron oscillations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti 1 Gaza, No. 2, pp. 187–190, March–April, 1982.I thank V. B. Baranov for suggesting the problem and constant interest in the work, and also A. V. Ershov for discussing the results.     

Structure and stability of quasiparallel small-amplitude magnetohydrodynamic shocks

The structure and stability of quasiparallel magnetohydrodynamic shock waves of small but finite amplitude are investigated. Only those waves whose propagation velocities are close to the Alfvén velocity are considered, i.e., fast shock waves in a medium in which the Alfvén velocity is greater than the speed of sound and slow shock waves in a medium in which the Alfvén velocity is less than the speed of sound and, moreover, intermediate (nonevolutionary) shock waves.In conclusion, the author wishes to thank A. A. Barmin for discussing his results and offering useful comments.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 153–160, July–August, 1989.     

Waves in a plasma with Hall dispersion

In a magnetohydrodynamic approximation, an investigation is made of the propagation of waves in a plasma, whose characteristic frequency is much less than the collision frequency of the electrons _e ^–1. It is assumed that the magnetic field is sufficiently strong so that the equality _ee1 will be satisfied, where _e is the cyclotron frequency of the rotation of the electrons. With large magnetic Reynolds numbers (R_m1), which are characteristic for many astrophysical problems, this latter condition leads to a need to take account of dispersion effects connected with Hall currents, in the absence of Joule dissipation. The dispersion equation for the propagation of small perturbations is analyzed in the limiting cases of weak dispersion and of a wave propagating along the magnetic field. In the case of weak dispersion, an equation is derived for nonlinear waves. The solutions are found in the form of stationary solitons. The region of such solutions is analyzed. A typical example of a medium with Hall dispersion is an interplanetary plasma, in which the parameter _ee is generally great.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 108–113, May–June, 1974.