A Mathematical Analysis of the Subsidence in the Long Beach - San Pedro Area

This report presents the significant results from a mathematical study of the subsidence in the Long Beach area. The work, begun in December 1949 at the request of Mr. M.D. Hughes, Chief Petroleum Engineer, the Petroleum Division of the Long Beach Harbor Department, has been in progress for two years. During this period a large volume of physical data pertinent to the subsidence phenomena has been made available and analyzed. Additional tests suggested by the mathematical analysis have been instigated by the Petroleum Division so that a well integrated program of research has been brought to bear upon this problem

Electronic Techniques Applied to Analogue Methods of Computation

This paper describes in detail the electronic devices and principles that have been developed for the California Institute of Technology (CIT) electric analogue computer. This is a general-purpose, large-scale computer applicable to a wide range of linear and nonlinear ordinary algebraic or differential equations and linear and nonlinear partial differential equations. In addition to the basic principles of the computer, a detailed discussion is given of those elements considered to be of particular interest. These include the devices for generating the arbitrary functions of the independent variable (the excitation functions), the amplifiers for producing active linear elements such as negative impedances and for representing the nonsymmetrical terms of the matrix specifying the differential equations, the multipliers for producing arbitrary functions of the dependent variables (nonlinear elements). Performance data on these devices are presented, together with analogies and solutions of representative types of problems

Ultra-dense, curved, grating optics determines peacock spider coloration

Controlling light through photonic nanostructures is important for everyday optical components, from spectrometers to data storage and readout. In nature, nanostructured materials produce wavelength-dependent colors that are key for visual communication across animals. Here, we investigate two Australian peacock spiders, which court females in complex dances with either iridescent color patterns (Maratus robinsoni) or an approximately angle-independent blue coloration (M. nigromaculatus). Using light microscopy, FIB-SEM imaging, imaging scatterometry, and optical modeling, we show that both color displays originate from nanogratings on structured 3D surfaces. The difference in angle-dependency of the coloration results from a combination of the local scale shape and the nanograting period. The iridescence of M. robinsoni arises from ordered gratings on locally flat substrates, while the more stable blue colors of M. nigromaculatus originate from ultra-dense, curved gratings with multiscale disorder. Our results shed light on the design principle of the peacock spiders' scales and could inspire novel dispersive components, e.g. used in spectroscopic applications

Cortex Thickness Is Key for the Colors of Iridescent Starling Feather Barbules With a Single, Organized Melanosome Layer

The iridescent plumage of many birds is structurally colored due to an orderly arrangement of melanosomes in their feather barbules. Here, we investigated the blue- to purple-colored feathers of the European starling (Sturnus vulgaris) and the blue and green feathers of the Cape starling (Lamprotornis nitens). In both cases, the barbules contain essentially a single layer of melanosomes, but in S. vulgaris they are solid and rod-shaped, and in L. nitens they are hollow and rod- as well as platelet-shaped. We analyzed the coloration of the feathers by applying imaging scatterometry, bifurcated-probe- and micro-spectrophotometry. The reflectance spectra of the feathers of the European starling showed multiple peaks and a distinct, single peak for the Cape starling feathers. Assuming that the barbules of the two starling species contain a simple multilayer, consisting locally only of a cortex plus a single layer of melanosomes, we interpret the experimental data by applying effective-medium-multilayer modeling. The optical modeling provides quantitative insight into the function of the keratin cortex thickness, being the principal factor to determine the peak wavelength of the reflectance bands; the melanosome layer only plays a minor role. The air cavity in the hollow melanosomes of the Cape starling creates a strongly enhanced refractive index contrast, thus very effectively causing a high reflectance

Application of the California Institute of Technology Electric Analog Computer to Nonlinear Mechanics and Servomechanisms

This paper describes the non-linear elements and circuit techniques used with the California Institute of Technology electric analog computer. Their application to nonlinear mechanical vibratory systems and nonlinear servomotors is discussed in detail. These techniques have been found to be generally suitable for representing single valued nonlinear functions of a dependent variable. Nonlinear springs, spring loaded backlash, and nonlinear damping factors can be readily simulated as well as saturation effects and other single valued non-linearities in servomotors. Methods of analysis are illustrated for several typical problems including a nonlinear rotating mechanical system and an autopilot employing a solenoid-operated rate and position limited hydraulic motor. Numerous servos of this type have now been studied and correlation of computer solutions with actual servo test data have shown in every case that the mathematical equations presented here accurately describe this type of motor

Influence of spinal cord stimulation on evoked potentials by cutaneous electrical stimulation

In the past, limited research has been done to investigate the influence of spinal cord stimulation (SCS) for treatment of chronic pain on evoked potentials (EP). Further insight into the mechanism of SCS may provide explanations for unsatisfactory results with this therapy in certain subpopulations. It also might predict effectiveness of SCS. In previous research MEG responses were measured on median and tibial nerve stimulations in chronic pain patients with and without SCS (1). However, this stimulation method preferentially activates large myelinated proprioceptive fibres, leaving painrelated small fibres unrelated. We expect that the observation of pain processing is impaired by large amounts of non-painrelated activity

Glass scales on the wing of the swordtail butterfly Graphium sarpedon act as thin film polarizing reflectors

The wings of the swordtail butterfly Graphium sarpedon (the Common Bluebottle) have blue/green-colored patches that are covered on the underside by two types of scales: white and glass scales. Transmission and scanning electron microscopy revealed that the white scales are classically structured: the upper lamina, with prominent ridges and large open windows, is well separated by trabeculae from a flat, continuous lower lamina. In the glass scales, the upper lamina, with inconspicuous ridges and windows, is almost flat and closely apposed to the equally flat lower lamina. The glass scales thus approximate ideal thin films, in agreement with the observation that they reflect light directionally and are iridescent. Reflectance and transmittance spectra measured from the glass scales with a microspectrophotometer agree with spectra calculated for an ideal non-absorbing thin film. Imaging scatterometry of single, isolated glass scales demonstrated that the reflected light can be strongly polarized, indicating that they function as polarizing reflectors

Pigmentary and photonic coloration mechanisms reveal taxonomic relationships of the Cattlehearts (Lepidoptera: Papilionidae: Parides)

Background: The colorful wing patterns of butterflies, a prime example of biodiversity, can change dramatically within closely related species. Wing pattern diversity is specifically present among papilionid butterflies. Whether a correlation between color and the evolution of these butterflies exists so far remained unsolved. Results: We here investigate the Cattlehearts, Parides, a small Neotropical genus of papilionid butterflies with 36 members, the wings of which are marked by distinctly colored patches. By applying various physical techniques, we investigate the coloration toolkit of the wing scales. The wing scales contain two different, wavelength-selective absorbing pigments, causing pigmentary colorations. Scale ridges with multilayered lamellae, lumen multilayers or gyroid photonic crystals in the scale lumen create structural colors that are variously combined with these pigmentary colors. Conclusions: The pigmentary and structural traits strongly correlate with the taxonomical distribution of Parides species. The experimental findings add crucial insight into the evolution of butterfly wing scales and show the importance of morphological parameter mapping for butterfly phylogenetics

Electronic Techniques Applied to Analogue Methods of Computation

This paper describes in detail the electronic devices and principles that have been developed for the California Institute of Technology (CIT) electric analogue computer. This is a general-purpose, large-scale computer applicable to a wide range of linear and nonlinear ordinary algebraic or differential equations and linear and nonlinear partial differential equations. In addition to the basic principles of the computer, a detailed discussion is given of those elements considered to be of particular interest. These include the devices for generating the arbitrary functions of the independent variable (the excitation functions), the amplifiers for producing active linear elements such as negative impedances and for representing the nonsymmetrical terms of the matrix specifying the differential equations, the multipliers for producing arbitrary functions of the dependent variables (nonlinear elements). Performance data on these devices are presented, together with analogies and solutions of representative types of problems

Unique wing scale photonics of male Rajah Brooke's birdwing butterflies

Background: Ultrastructures in butterfly wing scales can take many shapes, resulting in the often striking coloration of many butterflies due to interference of light. The plethora of coloration mechanisms is dazzling, but often only single mechanisms are described for specific animals. Results: We have here investigated the male Rajah Brooke's birdwing, Trogonoptera brookiana, a large butterfly from Malaysia, which is marked by striking, colorful wing patterns. The dorsal side is decorated with large, iridescent green patterning, while the ventral side of the wings is primarily brown-black with small white, blue and green patches on the hindwings. Dense arrays of red hairs, creating a distinct collar as well as contrasting areas ventrally around the thorax, enhance the butterfly's beauty. The remarkable coloration is realized by a diverse number of intricate and complicated nanostructures in the hairs as well as the wing scales. The red collar hairs contain a broad-band absorbing pigment as well as UV-reflecting multilayers resembling the photonic structures of Morpho butterflies; the white wing patches consist of scales with prominent thin film reflectors; the blue patches have scales with ridge multilayers and these scales also have centrally concentrated melanin. The green wing areas consist of strongly curved scales, which possess a uniquely arranged photonic structure consisting of multilayers and melanin baffles that produces highly directional reflections. Conclusion: Rajah Brooke's birdwing employs a variety of structural and pigmentary coloration mechanisms to achieve its stunning optical appearance. The intriguing usage of order and disorder in related photonic structures in the butterfly wing scales may inspire novel optical materials as well as investigations into the development of these nanostructures in vivo