A linear differential equation with a time-periodic damping coefficient: stability diagram and an application

In this paper the second-order differential equation with time-dependent damping coefficientx + cos (2t) x + x = 0,will be studied. In particular the coexistence of periodic solutions corresponding with the vanishing of domains of instability is investigated. The coexistence of -periodic solutions occurs for 4n ² where n is integer. This implies that the instability area which is emanating from =4n ² in the – stability diagram disappears. In applications, this equation can be considered as a model equation for the study of rain-wind-induced vibrations of a special oscillator.on leave as a PhD reseacher at Delft University of Technology, The Netherlands     

Heat transfer in plane film formation

A mathematical model is obtained for the process of cooling with formation of a planar film. The solution obtained is verified experimentally.Notation mean axial velocity gradient - v_x current axial velocity - v_o initial polymer velocity - v₁ sampling velocity - K draw ratio - deformation rate tensor - x, y, z spatial coordinates - X, Y dimensionless coordinates - L() differential operator - T temperature - T_o initial temperature - T_c temperature of surrounding medium - dimensionless temperature - dimensionless temperature averaged over film thickness - thermal-diffusivity coefficient - 2_o initial film thickness - thermal conductivity - heat-transfer coefficient - f(X) distance function - Bi Biot criterion, Bi_o, Biot criterion calculated for initial film thickness - Gz* modified Graetz criterion - V dimensionless velocity - ₁, ₂, ₃ heat-transfer coefficients produced by radiation, free convection, and forced convection - v_c, _c mean velocity and film half-thickness in formation zone - T₁ calculated temperature value - T₂ experimental temperature value - l formation zone length Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 854–858, November, 1979.     

Transport results from untwinned YBCO: Washboard frequency of the vortex lattice,and the quasiparticle mean free path

The washboard frequency of the moving vortex lattice in untwinned YBa₂ Cu₃ O_6.93 may be observed through mode-locking to an externally applied ac current of frequency _ext. The interference between and _ext results in jumps in the dc current-voltage characteristics when and _ext are harmonically related¹. The interference effect disappears in the vortex liquid state. The Hall conductivity _xy below T_c in YBCO contains contributions² from a positive quasiparticle (qp) term (H) and a negative vortex term (1/H). The qp term is surprisingly large well below T_c and implies a large gap anisotropy and a long qp mean free path (mfp). The thermal Hall effect³ _xy is closely related to the qp _xy; _xy is produced by asymmetric scattering of qp by pinned vortices. The qp mfp at H = 0, extracted from _xy and extended to low T by _xy, increases remarkably from 90 Å at T_c to more than 0.5m at 22 K.     

Investigation of the excitonic insulator phase in bismuth-antimony alloys

Pressure-induced metal-semiconductor transitions in bismuth-antimony alloys in a strong magnetic field (up to 70 kOe) at helium temperatures have been investigated. It is found that for values of the overlap-gap |G|1 meV the alloy forms an excitonic insulator (EI) in magnetic fields above a certain threshold (30–40 kOe). It is inferred that the EI energy gap increases with the magnetic field. The maximum gap observed in fields of 70 kOe turns out to be ₀₀7.5 K. An analysis of the results shows that transitions to the EI phase are observed from both the semimetal and the semiconducting states. The critical transition temperatureT _c is related to the EI gap by the expressionT _c0.7. Arguments are advanced in support of the fact that the formation of the EI phase involves the pairing of electrons at theL point with holes at theT point.     

Optical thermophysical characteristics of the condensed phase of combustion products and heatproof materials

An unconventional unit for experimentally studying the optical thermophysical properties of materials over a wide temperature range is described. Results are presented of studying the temperature function and dispersion of the absorption index for the condensed phase of the combustion products of a metalbearing fuel and of the emittance of fiber fireproof materials.Notation K spectral absorption coefficient - D spectral transmission coefficient - spectral absorption index - wavelength - d sample thickness - d_s surface layer thickness - I spectral intensity of radiation - , spectral and total emittances Kirov Polytechnical Institute. Kazan Chemical Engineering Institute, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 3, pp. 330–336. March, 1993     

Microstructure and mechanical properties of rapidly quenched L20 and L20+L12 alloys in Ni-Al-Fe and Ni-Al-Co systems

Ductile L2₀-type wires and+L1₂-type duplex wires with high strengths and large elongation in the Ni-Al-Fe and Ni-Al-Co ternary systems have been manufactured directly from the liquid state by an in-rotating-water spinning method. The wire diameter was in the range 80 to 180m and the average grain size was 2 to 4m for the wires and 0.2 to 1.0m for the+ wires. _y, _f and _p of the wires were found to be about 360 to 760 MPa, 560 to 960 MPa, and 0.2 to 5.5%, respectively, for the Ni-Al-Fe system, those of the+ wires were about 395 to 660 MPa, 670 to 1285 MPa, and 3.5 to 17%, respectively, for the Ni-Al-Fe system, and about 260 to 365 MPa, 600 to 870 MPa, and 4.0 to 7.0%, respectively, for the Ni-Al-Co system. Cold-drawing caused a significant increase in _y and _f and the values attained were about 1850 and 2500 MPa, respectively, for Ni-20Al-30Fe and Ni-25Al-30Co wires drawn to about 90% reduction in area. The high strengths, large elongation and good cold-workability of the melt-quenched and+ compound wires have been inferred to be due to the structural change into a low-degree ordered state containing a high density of phase boundaries, suppression of grain-boundary segregation and refinement of grain size.     

Transport properties of helium near the liquid-vapor critical point. II. Thermal conductivity of a3He-4He mixture

Measurements of the thermal conductivity are reported for an 80%³He-20%⁴He mixture above the critical point along several isotherms and near-critical isochores, using the same techniques and apparatus described for a study of³He. Using again the assumption that the observed conductivity can be decomposed into a sum of a regular and a singular contribution _reg and _sing, it is shown that along two near-critical isochores, _sing diverges. In particular, along the isochore showing the largest at the phase transition, the divergence is nearly the same as for³He and can be roughly characterized by a simple power law (T-T_c)^– with 0.58. This observation is contrary to predictions that foresee _sing0 asT _c is approached. The relaxation times characterizing the attainment of steady state conditions after switching the heat flux on and off show a similar behaviour as a function of reduced temperature as do those for pure³He. This result might indicate a substantial coupling between concentration and entropy diffusion. In the Appendix, the correlation length for³He nearT _c is calculated from heat conductivity, viscosity, and specific heat data.Work supported by Grant DMR 8024056 of the National Science Foundation.     

Solution of thermal conductivity problems with boundary condition of the third kind and arbitrary coordinate and time dependence of the biot number

An analytical solution of the thermal conductivity problem with boundary conditions of the third kind and arbitrary coordinate and time dependence of the Biot number is found in the form of a converging series of quadratures.Notation , z dimensionless coordinates - dimensionless temperature - Q dimensionless volume heat-liberation density per unit time - Fo=/² Fourier number - Bi₁(, Fo)=(, Fo) · / Biot number - thermal diffusivity coefficient - plate thickness - time - (, Fo) heat-liberation coefficient - thermal conductivity coefficient - i summation index - Jo zero order Bessel function of the first kind Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 536–540, September, 1981.     

Differential-flow-induced instability in a cubic autocatalator system

The formation of spatio-temporal stable patterns is considered for a reaction-diffusion-convection system based upon the cubic autocatalator, A + 2B 3B, B C, with the reactant A being replenished by the slow decay of some precursor P via the simple step P A. The reaction is considered in a differential-flow reactor in the form of a ring. It is assumed that the reactant A is immobilised within the reactor and the autocatalyst B is allowed to flow through the reactor with a constant velocity as well as being able to diffuse. The linear stability of the spatially uniform steady state (a, b) = (µ^–1, µ), where a and b are the dimensionless concentrations of the reactant A and autocatalyst B, and µ is a parameter reflecting the initial concentration of the precursor P, is discussed first. It is shown that a necessary condition for the bifurcation of this steady state to stable, spatially non-uniform, flow-generated patterns is that the flow parameter > _c(µ, ) where _c(µ,) is a (strictly positive) critical value of and is the dimensionless diffusion coefficient of the species B and also reflects the size of the system. Values of _c at which these bifurcations occur are derived in terms of µ and . Further information about the nature of the bifurcating branches (close to their bifurcation points) is obtained from a weakly nonlinear analysis. This reveals that both supercritical and subcritical Hopf bifurcations are possible. The bifurcating branches are then followed numerically by means of a path-following method, with the parameter as a bifurcation parameter, for representatives values of µ and . It is found that multiple stable patterns can exist and that it is also possible that any of these can lose stability through secondary Hopf bifurcations. This typically gives rise to spatio-temporal quasiperiodic transients through which the system is ultimately attracted to one of the remaining available stable patterns.     

Mapping co-word structures: A comparison of multidimensional scaling and leximappe

The LEXIMAPPE method and Multidimensional Scaling (MDS) are discussed as methods to visualize (map) characteristics of structures of word-occurrence (co-word) relations. Utilization of MDS is proposed as an alternative mapping method able to circumvent problematic features of LEXIMAPPE maps of the total co-word structure. A comparison of both methods on the same real-life co-word matrix demonstrates topological advantages of an extended MDS-mapping.     

Specific analysis of EBSD data to study the texture inheritance due to the β → α phase transformation

A specific processing of EBSD data is proposed to study the texture inheritance of titanium or zirconium alloys. A non standard misorientation map is calculated to localise the colonies inherited from the same parent grain. The calculation of the parent orientation from its inherited variants detailed in previous works has been adapted to the data obtained from an automated EBSD analysis. Finally, a method to derive the orientation map of the parent phase from that of the inherited phase is proposed. The resulting and COMs are used to study some aspects of the variant selection occurring in the transformation of a T40 sample.     

Simultaneous determination of the thermal conductivity and diffusivity of metals using an electronic heater

A nonstationary method allowing simultaneous determination of the thermal conductivity and diffusivity of metals using an electronic heater is described.Notation q_e heat flux density - t temperature - x distance to thermocouple - heating time - t₀ temperature at time zero - thermal conductivity of material examined - a thermal diffusivity of material - c coefficient describing the energy losses - X₁, x₂, x₃ distance to first, second, and third thermocouples, respectively - ₁, ₂, ₃ times during which specimen is heated to temperature t at points X₁, x₂, X₃, respectively     

Study of Broadband Long-Focus Optics for Synchrotron Infrared Diagnosis of Low-Energy Electron Beams

A special optical device for measuring the geometry and current parameters in electron rings by synchrotron infrared radiation is designed, fabricated, and studied. The optical elements of the device are made of an optical ceramic and operate at 1–8 m. The study results are presented.     

Nonlinear asymptotic theory of hypersonic flow past a circular cone

Summary The hypersonic small-disturbance theory is reexamined in this study. A systematic and rigorous approach is proposed to obtain the nonlinear asymptotic equation from the Taylor-Maccoll equation for hypersonic flow past a circular cone. Using this approach, consideration is made of a general asymptotic expansion of the unified supersonic-hypersonic similarity parameter together with the stretched coordinate. Moreover, the successive approximate solutions of the nonlinear hypersonic smalldisturbance equation are solved by iteration. Both of these approximations provide a closed-form solution, which is suitable for the analysis of various related flow problems. Besides the velocity components, the shock location and other thermodynamic properties are presented. Comparisons are also made of the zeroth-order with first-order approximations for shock location and pressure coefficient on the cone surface, respectively. The latter (including the nonlinear effects) demonstrates better correlation with exact solution than the zeroth-order approximation. This approach offers further insight into the fundamental features of hypersonic small-disturbance theory.Notation a speed of sound - H unified supersonic-hypersonic similarity parameter, - K hypersonic similarity parameter, M - M freestream Mach number - P pressure - T temperature - S entropy - u, v radial, polar velocities - V freestream velocity - shock angle - cone angle - density - density ratio, /() - ratio of specific heats - polar angle - stretched polar angle, / - (), (), () gage functions     

Axisymmetric stagnation-point flow impinging on a transversely oscillating plate with suction

The viscous fluid motion generated by axisymmetric stagnation-point flow of strain rate a impinging on a flat plate oscillating in its own plane with velocity amplitude U0 and frequency , including uniform suction of strength W0 is considered. A coordinate decomposition transforms the full Navier-Stokes equations into a primary equation describing the steady flow and a secondary equation describing the unsteady motion coupled to the primary solution. The solution to the boundary-value problem is governed by two dimensionless groups: the suction parameter S = W0 a and the frequency parameter = /a, where is the kinematic viscosity. Numerical integrations performed with a Runge-Kutta routine provide an exact solution to the Navier-Stokes equations. Values of the steady shear stress are found to agree with asymptotic results for large values of |S|, with S>0 representing suction and S<0 representing blowing. The magnitude and phase of the unsteady shear stress are given over a range of frequencies sufficient to recover analytical asymptotic results at large values of . The unsteady shear stress lags the wall motion by radians for 0 and by 5/4 radians when . Velocity profiles at selected parameter values during a period of plate oscillation are presented and discussed.     

Geometrical factors for parts of an infinite cylindrical surface

A method is described for calculating geometrical factors, allowing for attenuation of radiation by the medium, and computing radiative heat transfer between coaxial strips forming part of a cylinder.Notation mean generalized geometrical factor - local generalized geometrical factor for a closed infinite cylindrical surface - F surface area - l length of ray between elements dF_m - D and H diameter and length of cylinder - k ray attenuation coefficient - equivalent solid angle [1] determined from the condition _mm=1 at =0 for a closed surface - f () indicatrix of the specific radiation intensity (a quantity analogous to the specific luminous intensity [1]) - angle between the normal to an element of surface and the ray linking the surface elements - and angles in a section of the surface - angle between the radius and the chord subtending the projections of dF_mon the section - angle between the radius and the chord subtending the projection of element dF_mon the section and the edge of the surface - acute angle between rayl and the generator of the cylinder - ₀ half subtended angle for the arc of a section of the surface - S₂ and M generalized local geometrical factors in the notation of [2] (s₂ and is shown in Table 2 - M local factor for an infinite cylinder with a semicircular cross section for a point in the middle of the plane part of the surface; a table of values of M is given in [2]) - n number of strips     

Application of a new iterative method for elastic-plastic stress analysis

A new iterative method for elastic-plastic stress analysis based on a new approximation of the constitutive equations is proposed and compared with standard methods on the accuracy and the computational time in a test problem. The proposed method appears to be better than the conventional methods on the accuracy and comparable with others on the computational time. Also the present method is applied to a crack problem and the results are compared with experimental ones. The agreement of both results are satisfactory.List of symbols u = (u ₁, u ₂) displacements u ^(H) = u ⁽ⁿ⁺¹⁾ - u ⁽ⁿ⁾ u _k ⁽ⁿ⁾ = u _(k ^{(n + 1)} - u ⁽ⁿ⁾ (n, k = 0, 1, 2, ...) - = ₁₁, ₂₂, ₁₂) stresses - = (₁₁, ₂₂, ₁₂) strains - = (₁₁, ₂₂, ₁₂) center of yield surface - D elastic coeffficient matrix, C = D ^–1 - von Mises yield function. The initial yielding is given by f() = _Y - f {f/} - ^* transposed f - H hardening parameter (assumed to be a positive constant for kinematic hardening problems) - time derivative of - [K] total elastic stiffness matrix - T traction vector - = [B] relation between nodal displacements and strains     

Eutectic solidification characteristics of Bridgman grown AI-3Fe-0.1V alloy

Eutectic solidification characteristics of Al-2.85 wt%Fe-0.12 wt% Valloy have been investigated by steady-state growth over the range of solidification front velocity from 51 to 1030m/s and temperature gradient 8 to 15 K/mm. Increasing growth velocity displaced the Al-Al3Fe eutectic by Al-AlxFe eutectic rather than by the Al-Al6Fe eutectic obtained for the binary Al-3 wt%Fe alloy. A fully Al-AlxFe eutectic structure has been obtained for the first time in the vanadium-containing alloy over the growth velocity range from 71 to1030m/s except at 100 and 510m/s where some Al dendrites were present in the eutectic matrix. TheAl-AlxFe eutectic was observed to undergo a morphological transition from lamellar to rod-like with increasing growth velocity concurrently with formation of a cellular eutectic structure. It was found that the relationship = Av–1/2, between eutectic spacing and growth velocity v, was applicable with A = 22.4 ± 1.8 and 13.8 ± 2.1 m3/2s–1/2 for lamellar and rod-like Al-AlxFe eutectics, respectively.     

The neural net of neural network research

In this paper we discuss the limits and potentials of bibliometric mapping based on a specific co-word analysis. The subject area is neural network research. Our approach is a simulation of expert assessment by offering the reader a narrative of the field which can be used as background information when reading the bibliometric maps. The central issue in the applicability of bibliometric maps is whether these maps may supply additional intelligence to users. In other words, whether such a bibliometric tool has an epistemological value, in the sense that it ecriches existing knowledge by supplying unexpected relations between specific pieces of knowledge (synthetic value) or by supplying unexpected problems (creative value). We argue that sophisticated bibliometric mapping techniques are indeed valuable for open new avenues to study science as a self-organizing system in the form of a neural network like structure of which the bibliometric map is a first-order aproximation. In that sense, this paper deals with the neural net of neural network research as our bibliometric techniques in fact mimic a connectionistic approach.     

γ ? α2 Phase transformation in fractured high temperature stress rupture Ti-48Al-2Nb(at.%)

The ₂ phase transformation in fractured high temperature stress rupture Ti-48Al-2Nb(at.%) alloy has been studied by analytical electron microscopy. ₂ and phases were found at grain boundaries. ₂ layers that suspended in layers and interfacial ledge higher than 2d ₍₁₁₁₎ at /₂ interfaces were observed in the lamellar grains. These facts indicated that ₂ phase transformation and dynamic recrystallization have occurred during high temperature stress rupture deformation. It can be concluded that deformation induced ₂ phase transformation and dynamic recrystallization resulted in the presence of particles at grain boundaries. A structural and compositional transition area between deformation-induced ₂(or ) and its adjacently original (or ₂) phases was found by HREM and EDS and is suggested as a way to transform between and ₂ phase during high temperature stress rupture deformation. The transition area was formed by slide of partial dislocations on close-packed planes and diffusion of atoms.