An Engineering Approach to Nonlinear Estimation
Linear analog operation followed by nonlinear digital signal processing for nonlinear parameter approximation
APPROXIMATION METHOD↗
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Low-gravity electrodeposition and growth of polymer thin films with large third-order optical nonlinearities by electrochemical processes for devices: Thiophene-based polymers
It has been proposed that NLO thin film properties may be improved by low-gravity processing. Strong candidates for NLO thin film applications are the polythiophenes. Polymeric thiophenes are attractive materials due to their ease of preparation, stability, and high X(exp 3). A simple and convenient method for preparation of polythiophenes is electrochemical oxidation. We will apply some of our experience and lessons learned in low-gravity metal, metal/cermet electrode position to improve the quality of polythiophene(s) thin films. In low gravity electrode position of Ni at a high rate on an Au substrate often results in the production of an x-ray non diffracting surface. Cobalt metal deposition does not give this result nor does Ni when deposited similarly on a glassy carbon substrate. Co/Ni alloy composition produced during electrode position is strongly dependent upon the amount of convection. Code position of neutral inert cermets with metals is influenced significantly by the presence of gravity and the size of the cermets. Tracks left in the 1-g surfaces by unsuccessful particle occlusion indicate suspension of the large particles is not the only reason for poor volume percentages of the larger particles in the deposits. All size particles are more homogeneously distributed in the deposits in low-gravity electrocodeposition than in 1-g. Low gravity gives larger volume percentages for the larger particles in the deposits, while 1-g gives larger volume percentages for the smaller particles. Intermediate size particles give mixed results. The experimental cells were constructed with flat electrode end plates such that 1-g bench reference electrode positions could be carried out at various orientations with respect to gravity. A series of bench studies using similar designed cells are suggested so that convection modification can be applied to electrochemical thin film preparation. Convection effects can then be coupled with other parameter variations in current, temperature, concentration, solvent, electrolyte, and anode substrates to optimize the properties of NLO thin films before resorting to low-gravity processing.
Penn, Benjamin G.↗
A Population Pharmacokinetic Model for Disposition in Plasma, Saliva and Urine of Scopolamine after Intranasal Administration to Healthy Human Subjects
An intranasal gel formulation of scopolamine (INSCOP) was developed for the treatment of Space Motion Sickness. The bioavailability and pharmacokinetics (PK) were evaluated under the Food and Drug Administration guidelines for clinical trials with an Investigative New Drug (IND) protocol. The aim of this project was to develop a PK model that can predict the relationship between plasma, saliva and urinary scopolamine concentrations using data collected from the IND clinical trials with INSCOP. Methods: Twelve healthy human subjects were administered three dose levels (0.1, 0.2 and 0.4 mg) of INSCOP. Serial blood, saliva and urine samples were collected between 5 min and 24 h after dosing and scopolamine concentrations were measured by using a validated LC‐MS‐MS assay. Pharmacokinetic Compartmental models, using actual dosing and sampling times, were built using Phoenix (version 1.2). Model selection was based on the likelihood ratio test on the difference of criteria (‐2LL) and comparison of the quality of fit plots. Results: The best structural model for INSCOP (minimal ‐2LL= 502.8) was established. It consisted of one compartment each for plasma, saliva and urine, respectively, which were connected with linear transport processes except the nonlinear PK process from plasma to saliva compartment. The best‐fit estimates of PK parameters from individual PK compartmental analysis and Population PK model analysis were shown in Tables 1 and 2, respectively. Conclusion: A population PK model that could predict population and individual PK of scopolamine in plasma, saliva and urine after dosing was developed and validated. Incorporating a non‐linear transfer from plasma to saliva compartments resulted in a significantly improved model fitting. The model could be used to predict scopolamine plasma concentrations from salivary and urinary drug levels, allowing non‐invasive therapeutic monitoring of scopolamine in space and other remote environments.
Wu, L.↗
Information Processing Capacity of Spintronic Oscillator
Physical reservoir computing is a framework that enables energy‐efficient information processing by using physical systems. Nonlinear dynamics in physical systems provide a computational capability that is unique to reservoirs. It is, however, difficult to find an appropriate task for a reservoir because of the complexity of nonlinear information processing. The information processing capacity has recently been used to clarify systematically the tasks that are solved by reservoirs; it quantifies the memory capacity of reservoirs in accordance with the order of nonlinearity. Herein, an experimental evaluation of the information processing capacity of a spintronic oscillator consisting of nanostructured ferromagnets is reported. The spintronic reservoir state is electrically manipulated by adding a delayed‐feedback circuit. The total capacity reaches a maximum of 5.6 at the edge of the echo state property. A trade‐off between the linear and nonlinear components of the capacity is also found. The result can be used to better understand the nonlinear information processing in reservoirs and to find good matches between reservoirs and tasks. As an example, a function‐approximation task is performed and it is found that it can be efficiently solved when the reservoir state is appropriately tuned so that its information processing capacity matches that of the task.
97 MATHEMATICS AND COMPUTING↗
Enhanced extreme ultraviolet high-harmonic generation from chromium-doped magnesium oxide
High-order harmonic generation (HHG) from crystals is emerging as a new ultrashort source of coherent extreme ultraviolet (XUV) light. Doping the crystal structure can offer a new way to control the source properties. Here, we present a study of HHG enhancement in the XUV spectral region from an ionic crystal, using dopant-induced vacancy defects, driven by a laser centered at a wavelength of 1.55 μm. Our numerical simulations based on solutions of the semiconductor Bloch equations and density-functional theory are supported by our experimental observations and demonstrate an increase in the XUV high harmonic yield from doped bulk magnesium oxide (MgO) compared to undoped MgO, even at a low defect concentration. The anisotropy of the harmonic emission as a function of the laser polarization shows that the pristine crystal's symmetry is preserved. Our study paves the way toward the control of HHG in solids with complex defects caused by transition-metal doping.
36 MATERIALS SCIENCE↗
Nonlinear encoding in diffractive information processing using linear optical materials
Nonlinear encoding of optical information can be achieved using various forms of data representation. Here, we analyze the performances of different nonlinear information encoding strategies that can be employed in diffractive optical processors based on linear materials and shed light on their utility and performance gaps compared to the state-of-the-art digital deep neural networks. For a comprehensive evaluation, we used different datasets to compare the statistical inference performance of simpler-to-implement nonlinear encoding strategies that involve, e.g., phase encoding, against data repetition-based nonlinear encoding strategies. We show that data repetition within a diffractive volume (e.g., through an optical cavity or cascaded introduction of the input data) causes the loss of the universal linear transformation capability of a diffractive optical processor. Therefore, data repetition-based diffractive blocks cannot provide optical analogs to fully connected or convolutional layers commonly employed in digital neural networks. However, they can still be effectively trained for specific inference tasks and achieve enhanced accuracy, benefiting from the nonlinear encoding of the input information. Our results also reveal that phase encoding of input information without data repetition provides a simpler nonlinear encoding strategy with comparable statistical inference accuracy to data repetition-based diffractive processors. Our analyses and conclusions would be of broad interest to explore the push-pull relationship between linear material-based diffractive optical systems and nonlinear encoding strategies in visual information processors.
42 ENGINEERING↗
Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines
Direct measurements are reported of the excited singlet-state absorption cross section and the associated nonlinear refractive cross section using picosecond pulses at 532 nm in solutions of phthalocyanine and naphthalocyanine dyes. By monitoring the transmittance and far-field spatial beam distortion for different pulsewidths in the picosecond regime, it is shown that both the nonlinear absorption and refraction are fluence (energy-per-unit-area) rather than irradiance dependent. Thus, excited-state absorption is the dominant nonlinear absorption process, and the observed nonlinear refraction is also due to real population excitation.
Wei, T. H.↗
Nonlinear Coherent Optical Image Processing Using Logarithmic Transmittance of Bacteriorhodopsin Films
The transmission properties of some bacteriorhodopsin-film spatial light modulators are uniquely suited to allow nonlinear optical image-processing operations to be applied to images with multiplicative noise characteristics. A logarithmic amplitude-transmission characteristic of the film permits the conversion of multiplicative noise to additive noise, which may then be linearly filtered out in the Fourier plane of the transformed image. I present experimental results demonstrating the principle and the capability for several different image and noise situations, including deterministic noise and speckle. The bacteriorhodopsin film studied here displays the logarithmic transmission response for write intensities spanning a dynamic range greater than 2 orders of magnitude.
Downie, John D.↗
Feedback loop compensates for rectifier nonlinearity
Signal processing circuit with two negative feedback loops rectifies two sinusoidal signals which are 180 degrees out of phase and produces a single full-wave rectified output signal. Each feedback loop incorporates a feedback rectifier to compensate for the nonlinearity of the circuit.
Source record↗
Inferring Instantaneous, Multivariate and Nonlinear Sensitivities for the Analysis of Feedback Processes in a Dynamical System: Lorenz Model Case Study
A new approach is presented for the analysis of feedback processes in a nonlinear dynamical system by observing its variations. The new methodology consists of statistical estimates of the sensitivities between all pairs of variables in the system based on a neural network modeling of the dynamical system. The model can then be used to estimate the instantaneous, multivariate and nonlinear sensitivities, which are shown to be essential for the analysis of the feedbacks processes involved in the dynamical system. The method is described and tested on synthetic data from the low-order Lorenz circulation model where the correct sensitivities can be evaluated analytically.
Aires, Filipe↗
Magnetic field reconnection
A reasonably detailed description is obtained of the current status of our understanding of magnetic field reconnection. The picture that emerges is of a process, simple in concept but extremely complicated and multifaceted in detail. Nonlinear MHD processes in the external flow region, governed by distant boundary conditions, are coupled to nonlinear microscopic plasma processes in the diffusion region, in a manner not clearly understood. It appears that reconnection may operate in entirely different ways for different plasma parameters and different external boundary conditions. Steady reconnection may be allowed in some cases, forbidden in others, with intermediate situations involving impulsive or pulsative events.
Sonnerup, U. O.↗
Numerical analysis of a time discretized method for nonlinear filtering problem with Lévy process observations
Abstract In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is an unnormalized probability density function of the filter solution. Then, we apply a splitting-up technique to decompose the Zakai equation into three stochastic differential equations, based on which we construct a splitting-up approximate solution and prove its half-order convergence. Furthermore, we apply a finite difference method to construct a time semi-discrete approximate solution to the splitting-up system and prove its half-order convergence to the exact solution of the Zakai equation. Finally, we present some numerical experiments to demonstrate the theoretical analysis.
Mathematics↗
Application of Novel Nonlinear Optical Materials to Optical Processing
We describe wave mixing and interactions in nonlinear photorefractive polymers and disodium flourescein. Higher diffracted orders yielding forward phase conjugation can be generated in a two-wave mixing geometry in photorefractive polymers, and this higher order can be used for image edge enhancement and correlation. Four-wave mixing and phase conjugation is studied using nonlinear disodium floureschein, and the nature and properties of gratings written in this material are investigated.
Banerjee, Partha P.↗
2-D nonlinear IIR-filters for image processing - An exploratory analysis
A new nonlinear IIR filter structure is introduced and its deterministic properties are analyzed. It is shown to be better suited for image processing applications than its linear shift-invariant counterpart. The new structure is obtained from causality inversion of a 2D quarterplane causal linear filter with respect to the two directions of propagation. It is demonstrated, that by using this design, a nonlinear 2D lowpass filter can be constructed, which is capable of effectively suppressing Gaussian or impulse noise without destroying important image information.
Bauer, P. H.↗
A theory of continuous nonlinear recursive- filtering with application to optimum analog demodulation.
Continuous nonlinear recursive filtering based on Markov processes and state-variable concepts for application to optimum analog demodulation
MARKOV PROCESS↗
Gasdynamics and shock dynamics of weak shock waves
Experiments in weak-shock dynamics were conducted using a 17-in. diameter shock tube. Weak shocks were generated in air by a compressed nitrogen driver gas; the incident shock waves were brought to a focus by reflecting them from concave cylindrical reflectors at the endwall of the tube. It was found that the behavior of a shock discontinuity at a focus is determined by nonlinear gasdynamic processes. Consideration is also given to nonlinear resonance phenomena, i.e., phenomena associated with oscillatory motion in ducts, with amplitude so large that weak shocks occur. Attention is given to nonlinear resonance in open and closed tubes and to thermal and relaxation effects.
Sturtevant, B.↗
The Nonlinear Magnetosphere: Expressions in MHD and in Kinetic Models
Like most plasma systems, the magnetosphere of the Earth is governed by nonlinear dynamic evolution equations. The impact of nonlinearities ranges from large scales, where overall dynamics features are exhibiting nonlinear behavior, to small scale, kinetic, processes, where nonlinear behavior governs, among others, energy conversion and dissipation. In this talk we present a select set of examples of such behavior, with a specific emphasis on how nonlinear effects manifest themselves in MHD and in kinetic models of magnetospheric plasma dynamics.
Hesse, Michael↗
Whistler damping at oblique propagation - Laminar shock precursors
This paper addresses the collisionless damping of whistlers observed as precursors standing upstream of oblique, low-Mach number terrestrial bow shocks. The linear theory of electromagnetic waves in a homogeneous Vlasov plasma with Maxwellian distribution functions and a magnetic field is considered. Numerical solutions of the full dispersion equation are presented for whistlers propagating at an arbitrary angle with respect to the magnetic field. It is demonstrated that electron Landau damping attenuates oblique whistlers and that the parameter which determines this damping is beta-e. In a well-defined range of parameters, this theory provides damping lengths which are the same order of magnitude as those observed. Thus electron Landau damping is a plausible process in the dissipation of upstream whistlers. Nonlinear plasma processes which may contribute to precursor damping are also discussed, and criteria for distinguishing among these are described.
Gary, S. P.↗