Concept of field modes and the behavior of the magnetohydrodynamic field

A method for studying the behavior of fields by splitting their behavior into independent field modes is presented. The method is used to explore the characteristics of steady, two-dimensional, linearized magnetohydrodynamic fields with finite viscosity and resistivity and arbitrary orientation of the magnetic vector relative to the velocity vector.It is shown that in general boundary layers and wakes cease to exist in magnetohydrodynamics. Their place is taken by diffusing waves which, in reality, are the fields of a set of viscous-resistive sources, vortices, poles and currents whose field lines are strongly oriented along the characteristic wave directions. When the viscosity and resistivity are equal, these waves diffuse in a simple and independent way, but when these quantities are not equal, the diffusing waves generate a new kind of wake which is located, veil-like, in the fan-shaped region between the two wave directions. These wakes are fed from the differential diffusion of the primary waves. In the special case for which the resistivity is much greater than the viscosity, a new type of pseudo boundary layer is shown to exist in the velocity field. When the viscosity is much greater than the resistivity, this pseudo boundary layer occurs in the magnetic field

The Transient Behavior of Nonlinear Systems

It is shown that the classical perturbation procedure for treating nonlinear systems leads to solutions expressed as Fourier-like series with slowly varying coefficients. These slowly varying coefficients contain the information about the long term behavior of the system. Inconsistently, the classical perturbation procedure expresses these coefficients as power series, a mode of expression which has notoriously poor long term validity. An operational procedure is presented for treating oscillations having slowly variable amplitudes and frequencies. An extension of the usual impedance concepts is presented for expressing the frequency characteristics of both linear and nonlinear elements when oscillations with many frequencies are present simultaneously and when these oscillations vary in both frequency and amplitude. From these methods, a perturbation procedure is devised which permits the behavior of systems to be computed with any order of accuracy, using only the algebraic processes which are characteristic of operational procedures. This procedure avoids expressing its results in terms of the local time. Instead, it expresses them in terms of the fundamental characteristics of the oscillations which axe present. As a consequence, the final solutions have the much desired long term validity and they may be used to obtain asymptotic estimates of the behavior of the system. The method is able to treat systems containing nonlinear perturbing elements and elements which we have described as moderately nonlinear. By means of examples it is shown that it is a straightforward process to treat systems to second order accuracy. This level of accuracy covers a large number of the intercoupling effects that characterize the more sophisticated nonlinear phenomena

Interview with Francis H. Clauser

An interview in March 1983 with Francis H. Clauser, Clark B. Millikan Professor of Engineering, emeritus, and chairman of the Division of Engineering and Applied Science from 1969 to 1974. He recalls his arrival at Caltech in 1969 to head the engineering division; discusses the broadening of Caltech’s engineering option during the 1960s, including a shift toward fundamental research and an increase in the size of the faculty and the graduate program, enabled in part by a generous Ford Foundation grant. Comments on the current state of the division, with numerous retirements coming up and the opportunity for new hires. Recalls the establishment of the Environmental Quality Laboratory and the applied physics option. Discusses the development of computer science at Caltech and his efforts to build up communications science by recruiting John Pierce from Bell Labs. Comments on Caltech’s contributions to earthquake engineering. He concludes the interview by discussing his initiation of the Sherman Fairchild Distinguished Scholars Program

Characteristic modes and fundamental singularities of partial differential equations

Systems of linear partial differential equations with constant coefficients, like their ordinary differential equation counterparts, can be characterized by the properties of the matrices that form the coefficients of the differential operators. The question arises: Do the matrix operators that result from partial differential equations possess eigenvalues and eigensolutions in the same way that ordinary differential matrix operators do? The answer to this question is explored in some detail using as an example the linearized flow of a viscous fluid. It is shown that eigenfactors do exist for these equations, and that, of necessity, these involve hypercomplex algebra. This fact introduces significant new features to the problem. It is shown that eigenmodes exist and that each of these has its distinctive fundamental singularity. The fluid mechanical significance of these is examined in some detail. In addition, a representative group of other partial differential equations is examined and their eigenmodes and fundamental singularities are determined. It is shown that a number of basic differences exist between the eigenfunction theory for ordinary and for partial differential equations

Endocrine therapy for breast cancer: a model of hormonal manipulation

Oestrogen receptor (ER) is the driving transcription factor in 70% of breast cancer. Endocrine therapies targeting the ER represent one of the most successful anticancer strategies to date. In the clinic, novel targeted agents are now being exploited in combination with established endocrine therapies to maximise efficacy. However, clinicians must balance this gain against the risk to patients of increased side effects with combination therapies. This article provides a succinct outline of the principles of hormonal manipulation in breast cancer, alongside the key evidence that underpins current clinical practice. As the role of endocrine therapy in breast cancer continues to expand, the challenge is to interpret the data and select the optimal strategy for a given clinical scenario

A Real-Time Method for Estimating Viscous Forebody Drag Coefficients

This paper develops a real-time method based on the law of the wake for estimating forebody skin-friction coefficients. The incompressible law-of-the-wake equations are numerically integrated across the boundary layer depth to develop an engineering model that relates longitudinally averaged skin-friction coefficients to local boundary layer thickness. Solutions applicable to smooth surfaces with pressure gradients and rough surfaces with negligible pressure gradients are presented. Model accuracy is evaluated by comparing model predictions with previously measured flight data. This integral law procedure is beneficial in that skin-friction coefficients can be indirectly evaluated in real-time using a single boundary layer height measurement. In this concept a reference pitot probe is inserted into the flow, well above the anticipated maximum thickness of the local boundary layer. Another probe is servomechanism-driven and floats within the boundary layer. A controller regulates the position of the floating probe. The measured servomechanism position of this second probe provides an indirect measurement of both local and longitudinally averaged skin friction. Simulation results showing the performance of the control law for a noisy boundary layer are then presented

Un cadre général et un package R pour la détection du fonctionnement différentiel d'items dichotomiques

Differential item functioning (DIF) is an important issue of interest in psychometrics and educational measurement. Several methods have been proposed in the last decades to identify items that function differently between two (or more) groups of examinees. Starting from a framework for classifying DIF detection methods and from a comparative overview of the most traditional methods, an R package for nine methods, called difR, is presented. The commands and options are briefly described, and the package is illustrated through the analysis of a data set on verbal aggression