Terms Of Non-uniformity Research Articles

Singular Nature of Preferential Conducting Paths at High Electric Fields in ZnO‐Based Varistors

The ac electrical response of ZnO‐based varistors was monitored as a function of frequency (50 Hzf2 MHz) and electric field (60% ElmA/cm2EElmA/cm2, ElmA/cm2 in the critical field at 1 mA/cm2) at room temperature, and these data were represented in the complex impedance (Z*) plane. The finite depression angle observed in this plane was rationalized in terms of nonuniformity in the measured reactance between the terminals. The singular nature of the series‐parallel combination of the uniform conducting paths between the electrodes was suggested when this depression angle diminished to 0° at high electric fields (EElmA/cm2).

The integration of Burgers and Korteweg-de Vries equations with nonuniformities

In this letter we demonstrate that both Burgers and Korteweg-de Vries equations with nonuniformity terms can be reduced to a Burgers or Korteweg-de Vries equation with constant coefficients if these terms satisfy a compatibility condition.

Account of Film Turbulence for Predicting Film Cooling Effectiveness in Gas Turbine Combustors

The paper deals with a small but important part of the overall gas turbine engine combustion system and continues earlier published work on turbulence effects in film cooling to cover the case of film turbulence. Film cooling of the gas turbine combustor liner imposes certain geometric limitations on the coolant injection device. The impact of practical film injection geometry on the cooling is one of increased rates of film decay when compared to the performance from idealized injection geometries at similar injection conditions. It is important to combustor durability and life estimation to be able to predict accurately the performance obtainable from a given practical slot. The coolant film is modeled as three distinct regions, and the effects of injection slot geometry on the development of each region are described in terms of film turbulence intensity and initial circumferential non-uniformity of the injected coolant. The concept of the well-designed slot is introduced and film effectiveness is shown to be dependent on it. Only slots which can be described as well-designed are of interest in practical equipment design. A prediction procedure is provided for well-designed slots which describes growth of the film downstream of the first of the three film regions. Comparisons of predictions with measured data are made for several very different well-designed slots over a relatively wide range of injection conditions, and good agreement is shown.

The effect on tension of non‐uniform distribution of length changes applied to frog muscle fibres.

1. The stability of sarcomere lengths along single frog twitch fibres was examined, during lengthening and shortening, using a spot follower appparatus to monitor or control the length of a central segment. 2. During active shortening from sarcomere lengths beyond 2.2 micrometer the end sarcomeres shortened dramatically, while much of the fibre did not shorten at all. It is proposed that this is the cause of the tension failing to recover, after the shortening ceased, to the value of isometric tension at the shorter length. 3. During active lenghtening from sarcomere lengths beyond 2.2 micrometer, non-uniformity of stretch was seen, with the middle stretching more than the ends. Some maintained extra tension after stretch above that appropriate to the longer length was found, as were consistent changes in internal movement, and in the shape of the tension record during relaxation. 4. Measurements of stiffness during and after a lengthening suggest that no increased activation is involved. Observation of internal movement during the raised tension after a lengthening contradicts theories involving 'locked on' bridges. 5. From these and other observations, an explanation for the extra tension in terms of non-uniformity of sarcomeres is proposed. The explanation is in accord with that previously suggested for the creep phase of tension rise seen at these lengths.

The Bäcklund and Inverse Scattering Transform of the K-dV Equation with Nonuniformities

The Backlund and inverse scattering transforms are obtained for the Korteweg-do Vries equation with various nonuniformity terms u t +6 u u x + u x x x +[α( x , t ) u ] x +γ( t ) u = F x ( x , t ), provided that the three functions α( x , t ), γ( t ) and F x ( x , t ) related to the non-uniformities of the system, are constrained by the compatibility condition.

N-Soliton Solution of the K-dV Equation with Loss and Nonuniformity Terms

N -soliton solution of the Korteweg-de Vries equation with loss and nonuniformity terms \begin{aligned} u_{t}+2{\alpha}u+(C_{0}+{\alpha}x)u_{x}+6uu_{x}+u_{xxx}=0, \end{aligned} are obtained. The solutions express multisolitons damping in time without radiation and mutually colliding in nonuniform media with a relaxation effect.

A Method of Predicting the Behavior of a Turbulent Boundary Layer With Discrete Transpiration Jets

A method is proposed for predicting the behavior of a turbulent boundary layer with heat transfer under the influence of transpiration with discrete jets. The boundary layer is treated as a laterally averaged flow and the effects of nonuniformity are introduced through additional momentum and energy source terms in the equations of motion. These nonuniformity interaction terms are obtained using solutions of a set of ordinary differential equations governing the trajectory of jets. The effects of interaction between the jet and boundary layer turbulence structure are also treated. The predictions of the theory are shown to compare well with available discrete jet-boundary layer data.

Singular Perturbation Methods in Nonlinear Acoustics

The application of singular perturbation techniques to problems in nonlinear acoustics is demonstrated in two examples. In the first, we show that straightforward perturbation methods, using Lighthill's equation for aerodynamic sound, give a secular series when applied to one-dimensional simple wave flow. The nonuniform secular terms are removed by the introduction of expansions in terms of multiple scaled coordinates, and the Earnshaw solution for the shock-free region is recovered. Such an expansion technique is also applied to solve a problem in compound flow. In the second example, the method of matched asymptotic expansions (MAE) is applied to one-dimensional flow governed by Burgers' equation. If the excitation at the origin is time harmonic, Burgers' equation can be solved exactly, and the solution reduced to an intelligible form in the shock-free, saw-tooth, and saturation regions. These simplified approximate solutions are recovered by a direct application of MAE to Burgers' equation, and in work still under completion, it appears that the same process will yield a uniformly valid approximate solution of the analogous problems in two and three dimensions.

A statistical model for photomultiplier single-electron statistics

A statistical model is proposed to describe secondary electron emission in photomultipliers, based on the Polya or “negative binomial” distribution, which contains the exponential and Poisson distributions as special cases. Computations of the single-electron spectra have been carried out for a variety of stage-gains. Limited comparisons with available experimental data confirm that the effective statistical distribution of secondary emission in photomultipliers is broader than Poissonian and an interpretation in terms of non-uniformity of the dynodes is discussed.