A note on flame stability theory

The stability of normal combustion of a gas mixture with respect to small hydrodynamic perturbations is examined. An explanation is given of the physically contradictory conclusion obtained in [1] regarding the destabilizing influence of viscosity. With the aid of the author's inverse feedback condition [2] for a flame zone of finite thickness stability is investigated with allowance for viscous forces. The results show good agreement with well-known experiments [3,4] on the instability of spherical flames.     

A note on the theory of the rank effect

The possibility of using the equations of motion of a viscous compressible gas in the Kasterin-Predvoditeiev form, to describe the vortex effect, is discussed.     

A note on the stochastic theory of time-delayed epidemics

Summary Some deterministic and stochastic models for the spread of epidemics are studied. Some models are developed, which take into account a constant incubation time, but where the probability of a new infection is more general than in known models.The research for this paper was supported by the National Science Foundation under grant no. GP-18682 while on leave at the Courant Institute of Math. Sciences, New York University.     

A note on ergonomics of theory construction and use

The specialization and technical language in human-machine science leads to increasing difficulties in its understanding by many user groups. These difficulties and their remedies can probably be best understood and described by the concepts and methods of ergonomics. It is the thesis of this paper that developers of theory and applications in general, and the human-machine area in particular can benefit from the use of recent developments in pure mathematics and mathematical logic, in combination with a recent development in theoretical psychology, Psychologic. By introducing standard formalization in theory construction, and combining this with the language of Psychologic (or a formalized 'descendant' of Psychologic), developers of theories and applications in the human-machine science can better meet the different needs of the user groups, concerning both usability and user-friendliness. In the present note, the focus is on human-machine-science in general, and on rehabilitation ergonomics in particular.     

A note on finite strain theory of elasto-plasticity

Summary An alternative derivation of the elastic-plastic strain decomposition recently introduced by Lee is discussed. References to papers in which this decomposition has been effectively utilized in working out a general computer program are given.     

A note on the kernel approximation in a certain axially symmetric temperature problem

A contour integral technique and the second mean value theorem of integral calculus are used to obtain an approximation to the kernel of the integral equation associated with a certain axially symmetric temperature problem. The method of derivation also provides the scheme by which the approximation can be improved to any desired degree of accuracy. Numerical results are obtained to demonstrate the effectiveness of the scheme.     

A note on approximation of distribution function for the number of innovation activities

This note attempts to approximate the distribution function for the number of innovation activities (NIA) in the manufacturing sector using the dataset of 2002 Korean Innovation Survey. The mixture model applied here can easily capture the bimodality feature of the NIA distribution and provide some useful information such as the mean of NIA and the effect of a firm’s characteristic on whether the firm will undertake innovation activity.     

A status report on applying discrete inverse theory to ionospheric tomography

Discrete inverse theory (DIT) provides an orderly framework in which to combine measurements of total electron content (TEC) with a priori information to image the ionosphere tomographically. We have developed a DIT-based tomographic processor for use with relative TEC data. The processor's a priori information comprises the global mean of over 17,000 profiles generated from an ionospheric model, for use as a “generic background”; empirical orthogonal functions (EOFs) spanning the same model profiles, for use as vertical basis functions; and a red power-law horizontal spectrum. Relative TEC data are used to evaluate coefficients multiplying the EOFs and harmonics, thus quantifying a perturbation electron-density field. The perturbation field, which need not be small, is added to the a priori background to produce the image. We present here several images produced by employing the processor with simulated TEC data based on in situ ionospheric measurements and incoherent-scatter radar observations.©1994 John Wiley & Sons Inc     

A note on the first-passage problem and VanMarcke’s approximation — short communication

Given a scalar, stationary, Markov process, this short communication presents a closed-form solution for the first-passage problem for a fixed threshold b. The derivation is based on binary processes and the general formula of Siegert [Siegert AJF. On the first-passage time probability problem. Physical Review 1951; 81:617–23]. The relation for the probability density function of the first-passage time is identical to the commonly used formula that was derived by VanMarcke [VanMarcke E. On the distribution of the first-passage time for normal stationary random processes. Journal of Applied Mechanics ASME 1975; 42:215–20] for Gaussian processes. The present derivation is based on more general conditions and reveals the criteria for the validity of the approximation. Properties of binary processes are also used to derive a hierarchy of upper bounds for any scalar process.     

Spin fluctuations beyond the Gutzwiller approximation: A renormalised paramagnon theory

We analyze the spin fluctuations in the single-band lattice Hubbard model by using the slave-boson technique. It is shown that, at the Gaussian level beyond the saddle-point approximation, spin fluctuations obey a simple RPA-like form at all frequencies and wavevectors. Spin fluctuations, then, appear to give rise to an effective renormalized paramagnon theory opening new perspectives for the discussion of the effect of a magnetic field on Mott-Hubbard systems.     

A note on the solution of a differential equation arising in boundary-layer theory

Summary The differential equation f + ff + f² = 0 (where dashes denote differentiation with respect to the independent variable ) subject to the boundary conditions f(0)=0, f()=0 and either f(0)=1 or f(0)=–1 is considered. It is shown that by using pf as dependent variable and =C–f (where C=f()) as independent variable and then expanding in powers of , a very good approximation to the solution can be obtained using only a few terms in the expansion.     

A complementary note on Gegenbauer polynomial approximation for random response problem of stochastic structure

Recently, Gegenbauer polynomial approximation was proposed for solving the evolutionary random response problem of a random structure with bounded random parameters under evolutionary random excitations. The bounded random parameters used there are supposed to be proportional to a random variable with λ-PDF (probability density function). For this kind of random parameter, the Gegenbauer polynomial approximation is the unique correct choice for transforming a random structure into its deterministic equivalent system, which plays a central role in solving the response problem. Actually, the Gegenbauer polynomial approximation bridges the gap between the random structural response problem and the conventional methods. Just through its deterministic equivalent system, the random response problem of a random structure can be solved by any available, analytical and numerical method developed for deterministic systems. But the simple assumption on proportionality to λ-PDF may bring some unnecessary limitation on symmetry. Since λ-PDF is symmetrical about its center axis, so are these random parameters. However, not all random parameters have this kind of symmetry. Then, what can we do to lessen the limitation, if random parameters are non-symmetric per se? Besides, the graph of λ-PDF (see Fig. 1 in the text) shows its features’ dependence on λ, that is, the smaller the λ, the more dispersive the PDF. Then, what is the influence of different values of λ on the evolutionary random responses of the stochastic system? Moreover, is there any qualitative information about the dispersion in response with respect to every individual random parameter? This note is devoted to answering the above two questions and giving a supplementary note on Gegenbauer polynomial approximation. Our study shows that the symmetric limitation can be partly lessened by putting the random parameter into a polynomial function, even a quadratic one, of a random variable with λ-PDF. On the other hand, the second-order moment of the random responses of the stochastic structure relative to that of a nominal one can be used to describe qualitatively their relative dispersion with respect to each individual random parameter.     

A conserving approximation evaluation of superfluid density within the pair theory of superfluids

The evaluation of the superfluid density, defined by the weak field response of the system, within the pairing theory of pure superfluids of Fermi or Bose statistics is considered. The need for evaluating this within what Baym and Kadanoff term a conserving approximation is emphasized. A formalism for generating manifestly conserving response kernels by analytic continuation at finite temperatures is developed and applied to the problem in question. At zero temperatures this is equivalent to the work of Nambu and others. The superfluid density is obtained in terms of the solution of a linear integral equation, the kernel and inhomogeneous term of which depends on the self-consistent equilibrium solution to the pair model. It is shown in general that this superfluid density tends to the full density at the absolute zero and vanishes above the critical temperature. Finally, some numerical work on the Bose superfluid is presented which is an extension of the calculations of Evans and Imry in the sense that a pseudopotential that more closely parameterizes the dispersion spectrum in He II is employed and that the superfluid density is evaluated as a function of temperature.     

On the usual approximation used in the Rayleigh-Sommerfeld diffraction theory

The complete Rayleigh-Sommerfeld scalar diffraction formula contains (1 - ikR) in the integrand. Usually the wavelength is small compared with the distance of the observation point from the aperture and (1 - ikR) is approximated by -ikR alone. Other approximations usually made in the Rayleigh-Sommerfeld formula are addressed as well. Closed-form solutions, without approximations, are possible wherein interesting consequences of these approximations become apparent.