Rheological behavior of molten impact-resistant polystyrene under large-amplitude vibrations superposed on a fast constant shear flow

A study has been made concerning the rheological characteristics of molton impact-resistant polystyrene, under low-frequency (up to 40 Hz) vibrations with a velocity amplitude of the same order of magnitude as the rate of a constant shear flow on which they are superposed. It is shown that under these conditions of deformation at shear rates above 100 sec^?1, a melt of this polymer behaves like an inelastic nonlinearly viscous fluid.     

Weighted norm inequalities for pseudo-pseudodifferential operators defined by amplitudes

We prove weighted norm inequalities for pseudodifferential operators with amplitudes which are only measurable in the spatial variables. The result is sharp, even for smooth amplitudes. Nevertheless, in the case when the amplitude contains the oscillatory factor ξ?ei|ξ|^1−ρ, the result can be substantially improved. We extend the Lp-boundedness of pseudo-pseudodifferential operators to certain weights. End-point results are obtained when the amplitude is either smooth or satisfies a homogeneity condition in the frequency variable. Our weighted norm inequalities also yield the boundedness of commutators of these pseudodifferential operators with functions of bounded mean oscillation.     

Four theorems on uniform estimates of oscillatory integrals

Exact order uniform estimates of oscillatory integrals with monomial phase are obtained. These results are close to the hypothesis of V. I. Arnold on uniform estimates of oscillatory integrals. Namely, for absolute values of oscillatory integrals, estimates of order ρ ^?1/k ln ^n?1 τ uniform with respect to phase and amplitude are derived for every sufficiently small perturbation of phase (i.e., the monomial \(x_1^{m_1 } \ldots x_n^{m_n }\) , m _j ≤ k, 1 ≤ k, is perturbed by monomials \(x_1^{s_1 } \ldots x_n^{s_n }\) , where s _j ≤ k, 1 ≤ j ≤ n), and for each amplitude φ ∈ C ₀ ² (R ⁿ ), n > 0. In the case |m| < nk the upper uniform estimate with the same perturbation and the same amplitude has the order τ ^?1/k ln ^n?2 τ. The estimate by order τ ^?1/k ln ^n?2 τ was proved in the case when the amplitude vanishes at the origin. In the case k = 1, a uniform estimate of order τ ^?1ln ^n?2 τ is valid. This implies a uniform estimate for a polynomial phase. Previously the upper estimate of an oscillatory integral by the value 32 ⁿ τ ^?1/k ln ^n?1(τ+2) was known for the amplitude being the characteristic function of a cube and the same phase.     

Effect of strain rate on the shear fracture-toughness characteristics of glass laminate 27–63S

The effect of strain rate on the interval from 8.3·10^?4 to 8.3·10^?6 sec^?1 on the fracture-toughness characteristics of 27–63S unidirectional glass laminate is considered. It is shown that the strain-rate effect can be described in the same way as the time dependence of the strength.     

Normal vibrations of N,N-dimethylformamide and N,N-dimethylacetamide

Infrared and Raman frequencies of N, N-dimethylformamide and N, N-dimethylacetamide as recorded by the authors, in the region 3100 cm.^?1 to 250 cm.^?1 are given. The normal co-ordinate treatment of these molecules has been carried out using general quadratic force field and the potential energy distribution of the various modes of vibrations have been calculated to study the nature of absorption frequencies arising out of the in-plane vibrations. The assignments made by the authors in the region 3100 cm.^?1 to 500 cm.^?1 are compared with those of Lumley Jones who assigned the frequencies on the basis of band contour studies. These calculations have enabled the authors also to assign the frequencies in the region 500 cm.^?1 to 250 cm.^?1 to the various bending modes of vibrations. The C-N stretching frequency in tertiary amides is considerably different from that in primary and secondary amides.     

Transmission-line analysis of gravitational pulse detector response functions

Basic notations for measuring gravity waves are recalled, and a δ-pulse of areaJ ₀=10^?12 sec^?1 chosen as a convenient unit for sensitivity calculations. Pulse excitation of a long thin bar causes stress variations following trapezoidal patterns of time dependence, with a flat top duration proportional to distance from the bar's center of mass. A suitable arrangement of piezoelectric transducers (‘PX’) provides frequency-independent matching, both mechanical and electrical, allowing a straightforward and accurate calculation of electric signals. Signal shape is given explicitly for two extreme cases:

1. whole bar is piezoelectric (parabolic arcs resembling a sine wave),
2. very short PX sections (triangular or trapezoidal, depending on position along the bar).

A suitable combination ofn (=1, 3, 5, ...) transducers generates directly a triangular wave at then-th harmonic of the fundamental bar frequency, with amplitude proportional toL/n, so that the use of a long bar as a Fourier Analyser of gravity waves appears feasible. For an estimate of the sensitivity limit, preliminary results of a noise background analysis are quoted, according to which the PX-length can be optimized. A threshold energy relation \( \sim \sqrt[4]{{kT/M^2 Q_{{\text{PX}}} }}\) is obtained in the case where amplifier noise becomes important.     

Electrodeposition of copper on copper single crystal (100) face in presence of chloride ions

Observations of copper electrodeposits on to the (100) plane of copper was made from highly purified solutions of copper sulphate containing known concentration of hydrochloric acid from 10^?10 to 10^?1 m/L. In pure solutions at current densities of 5 and 10 mA/cm.² layers and pyramids were noticed. In the presence of hydrochloric acid of concentration 10^?9 to 10^?5 m/L there is a gradual decrease of distance between successive steps. At 10^?4 m/L of HCl there was the breaking of layers giving rise to ridge type of growth. With the increase of concentration to 3·5×10^?3 m/L pyramids appear again. On increasing the concentration of HCl to 10^?2 m/L there was the formation of triangular pyramids of cuprous chloride and on still increasing the concentration, polycrystalline type of deposit was noticed. The transition from layer to ridge, ridge to pyramids and to polycrystalline deposit occurs at all c.d. studied but the critical concentration of HCl needed for the transition depends upon the current density.     

On the principles of limiting absorption and limit amplitude for a class of locally perturbed waveguides. Part 2: Time-dependent theory

In part 1

1 Math. meth. in the Appl. Sci, 10, 125–144 (1988).

we studied the principle of limiting absorption for local perturbations Ω of the n-dimensional domain Ω₀ = ?^n?1 × (0, π). In this second part we extend our investigations to the time-dependent theory and show that absence of admissible standing waves implies the validity of the principle of limiting amplitude for every frequency ω≥0 if n ≠ 3 and for ω ≠ 2, 3,… if n = 3, respectively. In particular, the principle of limiting amplitude holds for every ω≥0 in the case n ≠ 3 and for every ω ≠ 2, 3,… in the case n = 3 if Ω≠Ω₀ and ν · x ′ ?0 on ?Ω, where x ′ = (x₁,…, x_n?1, 0) and ν is the normal unit vector on ?Ω pointing into the complement of Ω This result stands in remarkable contrast to the fact that both principles are violated in the case of the unperturbed domain Ω₀ at the frequencies ω = 1, 2,… if n?3. The question of the asymptotic behaviour of the solution as t→∞ for n = 3 and ω = 2, 3,… will be discussed in two subsequent papers.     

Markov measures and extended zeta functions

In this paper we study a family of representations of the Cuntz algebras O _p where p is a prime. These algebras are built on generators and relations. They are C ^?-algebras and their representations are a part of non-commutative harmonic analysis. Starting with specific generators and relations we pass to an ambient C ^?-algebra, for example in one of the Cuntz-algebras. Our representations are motivated by the study of frequency bands in signal processing: We construct induced measures attached to those representations which turned out to be related to a class of zeta functions. For a particular case those measures give rise to a class of Markov measures and q-Bernoulli polynomials. Our approach is amenable to applications in problems from dynamics and mathematical physics: We introduce a deformation parameter q, and an associated family of q-relations where the number q is a ??quantum-deformation,?? and also a parameter in a scale of (Riemann-Ruelle) zeta functions. Our representations are used in turn in a derivation of formulas for this q-zeta function.     

The effect of rate of deformation on the mechanical characteristics of plastics

An experimental investigation of the effect of the rate of deformation on the strength and modulus of elasticity of vinyl plastic and glass-reinforced laminate is described. It is established that when the rate of relative tensile deformation of vinyl plastic at 25°C is reduced from 2000×10^–6 sec^–1 to 5×10^–6 sec^–1, and that for glass-reinforced laminate from 1000×10^–6 sec^–1 to 1.3×10^–6 sec^–1, the decrease in the modulus of elasticity is about 40% and the decrease in ultimate strength 30 and 48%, as the case may be.Mekhanika polimerov, Vol. 1, No. 1, pp. 76–81, 1965     

Role of chloride ions in relation to copper corrosion and inhibition

Corrosion rates of copper single crystal faces are determined in stirred 0·1N sulphuric acid with various chloride ion concentrations. A mechanism is proposed to explain the variation of corrosion rate with Cl^? ion concentration. Up to 7·5 × 10^?3 M Cl^? ions, the stabilities of the crystal faces are in the order (111)>(100)>(110) but this order is changed to (110)>(100)>(111) in presence of 10^?2 M Cl^? ions. The corrosion potentials of the crystal faces are less noble at all concentrations of Cl^? ions and Cl^? ion acts as a cathodic inhibitor. There is no significant orientation effect on the kinetics of dissolution of copper.     

Determination of the flux of primary cosmic ray hydrogen and helium nuclei near the geomagnetic equator using nuclear emulsions

Nuclear emulsions exposed to the cosmic radiation over Hyderabad, India, at an altitude of 31·3 km. for six hours, have been used to derermine primary cosmic ray deuteron flux. The flux of deuterons of rigidity ?16·9 GV at the top of the atmosphere is found to be <10 m.^?2 sec.^?1 sterad^?1; this may be compared with the proton fiux of 83±12 m.^?2 sec.^?1 sterad.^?1 in the same rigidity region over Hyderabad.     

On the Existence of Generalized Pólya Frequency Functions Corresponding to Entire Functions with Zeros in Angular Sectors

Generalized Pólya frequency functions are introduced through inverse Mellin transformations of the reciprocals of real entire functions with all zeros in sectors A ^? and ? A ^? for 0 ≤ ? ≤ π/4, where A ^? := {z ? C||arg z| ≤ ?}. It is shown that the constant π/4 is best possible in this context.     

Effect of the rate of deformation on the mechanical properties of compact bone tissue

Conclusions The results of this study show that the ultimate stress increases with increasing deformation rate from 10^–5 to 1 sec^–1 but the initial elasticity modulus remains virtually constant. A characteristic feature of bone tissue is the significant increase or even maximum in specific deformation energy for destruction in the range of deformation rates corresponding to normal physiological conditions for bone function. The deformation diagrams of human bone tissue for the same values of moisture content and deformation rate in tensile testing do not differ from the analogous curves for the bone tissue of cattle. Quantitatively, the ultimate stress ₁₁ and the initial elasticity modulus E₁ are 5–10% and 15–25% greater, respectively, than for cattle bone tissue, while the ultimate deformation eu is virtually the same. An increase in the moisture content of bone tissue leads to a more pronounced dependence of the mechanical parameters on the deformation rate.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 512–517, May–June, 1982.     

Variations of Dirichlet-to-Neumann map and deformation boundary rigidity of simple 2-manifolds

The Dirichlet-to-Neumann (DN) map Λ_g: C^∞ (?M) → C^∞(?M) on a compact Riemannian manifold (M, g) with boundary is defined by Λ_gh = ?u/?v¦in{t6M}, where u is the solution to the Dirichlet problem Δu = 0, u¦?M = h and v is the unit normal to the boundary. If g^t = g + t? is a variation of the metric g by a symmetric tensor field ?, then Λ_g ^t = Λ_g + tΛ_? + o(t). We study the question: How do tensor fields ? look like for which Λ_? =0? A partial answer is obtained for a general manifold, and the complete answer is given in the two cases: For the Euclidean metric and in the 2D-case. The latter result is used for proving the deformation boundary rigidity of a simple 2-manifold.     

Scheme for interpretation of approximately computed eigenvalues embedded in a continuous spectrum

It is assumed that a trapped mode (i.e., a function decaying at infinity that leaves small discrepancies of order ? ? 1 in the Helmholtz equation and the Neumann boundary condition) at some frequency κ⁰ is found approximately in an acoustic waveguide Ω⁰. Under certain constraints, it is shows that there exists a regularly perturbed waveguide Ω^? with the eigenfrequency κ^? = κ⁰ + O(?). The corresponding eigenvalue λ^? of the operator belongs to the continuous spectrum and, being naturally unstable, requires “fine tuning” of the parameters of the small perturbation of the waveguide wall. The analysis is based on the concepts of the augmented scattering matrix and the enforced stability of eigenvalues in the continuous spectrum.     

Forbidden hyperfine transitions in electron spin resonance of Mn2+ in NaCl single crystal

Forbidden hyperfine transitions are observed in the electron spin resonance spectrum of divalent Mn⁵⁵ ion in NaCl single crystal for a particular associated pair. From the measurements of the M = + 1/2 → ?1/2, Δm = ± 1 transitions the parametersQ′ and Q″ of the nuclear electric quadrupole part of the spin-Hamiltonian H_o = Q′ [I_z ² ? 1/3 I (I + 1)] + Q″ (I_x ²?I_y ²) are found to be + 1.70 × 10^?4 cm.^?1 and +0.16 × 10^?4 cm.^?1 respectively.     

Validity of lorentz invariance at extremely high energies

Experimental data on the distribution of times of arrival of electrons (and muons) in extensive air showers produced by cosmic rays in the energy range 10¹²–10¹⁹ eV have been examined to see if there is any evidence for a departure of the velocity of ultra-high energy particles from that of light as suggested by the model proposed by Pavlopoulos. No evidence for such a departure has been found. An upper limit to the “fundamental length” occurring in the theory is obtained as ～10^?21 cm.     

Free in-plane vibration analysis of a curved beam (arch) with arbitrary various concentrated elements

In the existing literature, the information regarding the exact solutions for free in-plane vibrations of the curved beams (or arches) carrying various concentrated elements is rare, particularly for the case with multiple attachments including eccentricities and mass moments of inertias. For this reason, this paper aims at presenting an effective approach to tackle the title problem. First of all, the un-coupled equation of motion for the circumferential displacement of an arch segment is derived. Next, based on the value of the discriminate parameter for a cubic equation, the exact solutions for the three types of roots of the un-coupled equation are determined and, corresponding to each type of roots, all displacement functions for the arch segment in terms of the real numbers (instead of the complex ones) are obtained. Finally, use of the compatible equations for the displacements and slopes together with the equilibrium equations for the forces and moments at each intermediate node and two ends of the entire curved beam, a frequency equation of the form ∣H(ω)∣ = 0 is obtained. It is found that the conventional approach by using the condition “∣H(ω^t)∣ ? ε” to search for the approximate value of ω^t is difficult even if the convergence tolerance ε is greater than 10⁺³ (i.e., ε > 10⁺³) instead of less than 10^?3 (i.e., ε < 10^?3), however, the half-interval method is one of the effective tools for solving the problem if all coefficients of the determinant ∣H(ω)∣ are the real numbers. In addition to comparing with the existing literature, most of the numerical results obtained from the presented method are compared with those obtained from the conventional finite element method (FEM) and good agreement is achieved.