Riemann problem for kinematical conservation laws and geometrical features of nonlinear wavefronts

A pair of kinematical conservation laws (KCL) in a ray coordinatesystem (,t) are the basic equations governing the evolutionof a moving curve in two space dimensions. We first study elementarywave solutions and then the Riemann problem for KCL when themetric g, associated with the coordinate designating differentrays, is an arbitrary function of the velocity of propagationm of the moving curve. We assume that m>1 (m is appropriatelynormalized), for which the system of KCL becomes hyperbolic.We interpret the images of the elementary wave solutions inthe (,t)-plane to the (x,y)-plane as elementary shapes of themoving curve (or a nonlinear wavefront when interpreted in aphysical system) and then describe their geometrical properties.Solutions of the Riemann problem with different initial datagive the shapes of the nonlinear wavefront with different combinationsof elementary shapes. Finally, we study all possible interactionsof elementary shapes.     

Convergence Acceleration of Some Continued Fractions

The tails of a continued fraction satisfy a bilinear recurrent equation. Transforming iteratively these tails (in a special manner) as well as these equations one may obtain finally, for a given fraction, a new, so-called diagonal continued fraction (DF) having the same value. For many important classes of continued fractions the DF has a calculable analytical form and converges qualitatively faster. Using the same method one may transform some hypergeometrical series directly into fast convergent DFs.     

Ultrasonic Broadband Spectrometry of Liquids A Research Tool in Pure and Applied Chemistry and Chemical Physics

This review is a survey of the many scientific applications of ultrasonic broadbandspectrometry (absorption and velocity measurements with coherent sound waves)in liquids and liquid systems, covering, at present, a frequency range from nearly10 kHz to 10 GHz. Ultrasonic spectrometry has proved to be an almost universalresearch tool in many laboratories, one that is useful for investigation of variouschemical, biochemical, and physicochemical systems. Sound waves traversingliquids induce periodic perturbations in pressure and temperature, which can shiftequilibria, resulting in characteristic sound absorption and velocity dispersionspectra. An analysis of such spectra yields valuable information about thermodynamic and kinetic parameters of the particular system that is often difficult toobtain by other methods. Since such periodic perturbations imposed on the systemare incremental in nearly all cases, the system can be studied under equilibriumconditions. All nonlinear effects (heating, nonconstant fluid compressibility, andothers) are negligible, permitting, for instance, the application of linearized rateequations. In this review, various examples of measured broadband spectra arepresented. Related elementary processes are discussed. Among these are ionicand molecular reactions, including mechanisms of association and complexation,proton transfer, solvation, isomerization, interconversion, side-group rotation,hydrogen-bonding, as well as stacking processes and micelle formation. Specialattention will be given to the extensive research on chemical relaxation.Fundamental early and recent publications are cited and discussed. Many referencesare included with particular emphasis on less well known research and publicationsfrom countries of the former USSR. This review aims at a demonstration of thewidespread applications of modern ultrasonic techniques in many fields ofliquid-state research.     

On Unimodular Rows over Polynomial Rings

Let A be a commutative ring and n 3 a positive integer. In this paper, we consider unimodular rows (f₁(x),..., f_n(x)) over A[x]. We prove that, if the row of the leading coefficients of f_i(x) is unimodular over A and a A, then there exists E_n(A[x]) such that (f₁(x),...,f_n(x)) = (f₁(a),...,f_n(a)). Also, if A is a Noetherian ring with finite Krull dimension and the row of leading coefficients satisfies the same condition, then we give a bound for the length of in terms of elementary transvections.Partially supported by INTAS 93–436EXT and DFG–RFBR grant No. 96–01–00092G.2000 Mathematics Subject Classification: 19A13, 19B14, 13C10, 13B25, 13F20     

Orthogonality of the range and the kernel of some elementary operators

We prove the orthogonality of the range and the kernel of an important class of elementary operators with respect to the unitarily invariant norms associated with norm ideals of operators. This class consists of those mappings , , where is the algebra of all bounded Hilbert space operators, and , , , are normal operators, such that , and . Also we establish that this class is, in a certain sense, the widest class for which such an orthogonality result is valid. Some other related results are also given.

     

Reliability analysis of stochastic structural system considering static strength, stiffness and fatigue

Multi-failures are possible to appear in the process of using the structural system, such as dead load failure, fatigue failure and stiffness failure. The expression of residual resistance is given based on the impact of random crack propagation in- duced by the fatigue load on the critical limit stress and section modulus in this paper. The failure modes of every element of the structural system are analyzed under dead and fatigue loads, and the influence of the correlation of failure modes on reliability of the element is considered. Failure mechanism and the correlation of failure modes under dead and fatigue loads are discussed, and the method of reli- ability analysis considering static strength, fatigue and stiffness is given. A nu- merical example is analyzed, which indicates that the failure probability is different for different use life and the influence of dead and fatigue loads on reliability of the structural system is different as well. This method of reliability analysis, in the pa- per, is better than the method only considering a single factor (or static strength, or fatigue, or stiffness, etc.) in the case of practical engineering.     

Creation evidence of the second non-dispersive Zakharenko wave by helium atomic beams in superfluid helium-II at low temperatures

In this work, the experimental results of the creation of the second non-dispersive Zakharenko wave (C _ph = C _g ≠ 0) in the negative roton branch (the so-called second sound) of the bulk elementary excitations (BEEs) energy spectra are introduced. Several BEE signals detected by a bolometer situated in the isotopically pure liquid helium-II at low temperatures ∼100 mK are shown, which give evidence of negative roton creation in the liquid by helium atomic beams striking the liquid surface. The negative roton signals were clearly distinguished by the following ways: the negative roton signal created by helium atomic beams appeared earlier than the positive roton signal created by the beams, and presence of both positive and negative roton signals together. It is natural that the negative roton creation by the beams requires the ⁴He-atom energies ∼12 K, while the positive roton creation by the atomic beams requires energies ∼35 K. Therefore, successive increase in the heater power resulting in an increase in the ⁴He-atom energies gives solid evidence that the negative rotons are first created in the liquid by the helium atomic beams.      

Fracture of model polyurethane elastomeric networks

Fracture properties of model elastomeric networks of polyurethane have been investigated with a double‐edge notch geometry. The networks were synthesized from monodisperse end‐functionalized polypropylene glycol precursors and a trifunctional isocyanate. All reagents were carefully purified and nearly defect‐free ideal networks were prepared at a stoichiometry very close to the theoretical one. Three networks were prepared: an unentangled network of short chains (M_n = 4 kg mol^?1), an entangled network of longer chains (M_n = 8 kg mol^?1) and a bimodal network with 8 kg mol^?1 and 1 kg mol^?1 chains. The presence of entanglements was found to increase significantly the toughness of the rubber, in particular at room temperature, relative to the bimodal networks and to the short chains network. Fracture experiments were carried out at different strain rates and temperatures and showed for all three networks a marked decrease in fracture toughness with increasing temperature and decreasing strain rate which mirrored reasonably well the rate and temperature dependence of tan δ, the dissipative factor. However the proportionality factor between tan δ, and G_IC was very material dependent and the shift factors obtained for the master curves of the viscoelastic properties could not be used to build fracture energy master curves. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010