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At least 37 records · Page 2

Identifying Differential Equations in Fourier Domain (FourierIdent)

We investigate identifying differential equations in the frequency domain. Fourier analysis is an important tool in theoretical analysis and numerical solvers of differential equations, yet there is limited work in exploring this connection in the identification of differential equations. This paper aims to identify the underlying differential equation in the frequency domain, from a given single realization of the differential equation perturbed by noise. Such setting imposes difficulties which are different from other identification methods where computation is carried out in the physical domain. We propose several ways to mitigate the challenges arising from noise in data and large differences in the magnitudes of frequency responses. The main takeaways are that identifying differential equations solely in the frequency domain is challenging, the method we propose is based on a form of domain partitions in the frequency domain, and this method shows benefits for complex data even with high level of noise. We introduce a Fourier feature denoising, and define the meaningful data region and the core regions of features to reduce the effect of noise in the frequency domain and to enhance the accuracy in coefficient identification. The proposed method is tested on various differential equations with linear, nonlinear, and high-order derivative feature terms, and shows advantages on complex data with many frequency modes, even under high level of noise.

97 MATHEMATICS AND COMPUTING

4-Coumarate:coenzyme A ligase and isoperoxidase expression in Zinnia mesophyll cells induced to differentiate into tracheary elements

When cultured in inductive medium containing adequate auxin and cytokinin, isolated mesophyll cells of Zinnia elegans L. cv Envy differentiate into tracheary elements with lignified secondary wall thickenings. Differentiation does not occur when cells are cultured in control medium, which has reduced levels of auxin and/or cytokinin. The activities of two enzymes involved in lignin synthesis, 4-coumarate:coenzyme A ligase and peroxidase, were examined. An induction-specific cationic isoperoxidase, visualized by low pH polyacrylamide gel electrophoresis, is detectable in soluble and wall fractions of cultured Zinnia cells long before tracheary elements visibly differentiate and is thus an early marker of differentiation. Compounds (such as antiauxins, anticytokinins, and tunicamycin) that inhibit or delay differentiation alter the expression of this isoperoxidase. 4-Coumarate:coenzyme A ligase activity increases dramatically only as cells differentiate. Together, these results suggest that the onset of lignification in differentiating Zinnia cells might be controlled by the availability of precursors synthesized by way of 4-coumarate:coenzyme A ligase. These precursors would then be polymerized into lignin in the cell wall by the induction-specific isoperoxidase.

NASA Discipline Plant Biology

Ferroelectric Field-Effect Transistor Differential Amplifier Circuit Analysis

There has been considerable research investigating the Ferroelectric Field-Effect Transistor (FeFET) in memory circuits. However, very little research has been performed in applying the FeFET to analog circuits. This paper investigates the use of FeFETs in a common analog circuit, the differential amplifier. The two input Metal-Oxide-Semiconductor (MOS) transistors in a general MOS differential amplifier circuit are replaced with FeFETs. Resistors are used in place of the other three MOS transistors. The FeFET model used in the analysis has been previously reported and was based on experimental device data. Because of the FeFET hysteresis, the FeFET differential amplifier has four different operating modes depending on whether the FeFETs are positively or negatively polarized. The FeFET differential amplifier operation in the different modes was analyzed by calculating the amplifier voltage transfer and gain characteristics shown in figures 2 through 5. Comparisons were made between the FeFET differential amplifier and the standard MOS differential amplifier. Possible applications and benefits of the FeFET differential amplifier are discussed.

Phillips, Thomas A.

Radar Differential Phase Signatures of Ice Orientation for the Prediction of Lightning Initiation and Cessation

The majority of lightning-related casualties typically occur during thunderstorm initiation (e.g., first flash) or dissipation (e.g., last flash). The physics of electrification and lightning production during thunderstorm initiation is fairly well understood. As such, the literature includes a number of studies presenting various radar techniques (using reflectivity and, if available, other dual-polarimetric parameters) for the anticipation of initial electrification and first lightning flash. These radar techniques have shown considerable skill at forecasting first flash. On the other hand, electrical processes and lightning production during thunderstorm dissipation are not nearly as well understood and few, if any, successful techniques have been developed to anticipate the last flash and subsequent cessation of lightning. One promising approach involves the use of dual-polarimetric radar variables to infer the presence of oriented ice crystals in lightning producing storms. In the absence of strong vertical electric fields, ice crystals fall with their largest (semi-major) axis in the horizontal associated with gravitational and aerodynamic forces. In thunderstorms, strong vertical electric fields (100-200 kV m(sup -1)) have been shown to orient small (less than 2 mm) ice crystals such that their semi-major axis is vertical (or nearly vertical). After a lightning flash, the electric field is typically relaxed and prior radar research suggests that ice crystals rapidly resume their preferred horizontal orientation. In active thunderstorms, the vertical electric field quickly recovers and the ice crystals repeat this cycle of orientation for each nearby flash. This change in ice crystal orientation from primarily horizontal to vertical during the development of strong vertical electric fields prior to a lightning flash forms the physical basis for anticipating lightning initiation and, potentially, cessation. Research has shown that radar reflectivity (Z) and other co-polar back-scattering radar measurements like differential reflectivity (Z(sub dr)) typically measured by operational dual-polarimetric radars are not sensitive to these changes in ice crystal orientation. However, prior research has demonstrated that oriented ice crystals cause significant propagation effects that can be routinely measured by most dual-polarimetric radars from X-band (3 cm) to S-band (10 cm) wavelengths using the differential propagation phase shift (often just called differential phase, phi(sub dp)) or its range derivative, the specific differential phase (K(sub dp)). Advantages of the differential phase include independence from absolute or relative power calibration, attenuation, differential attenuation and relative insensitivity to ground clutter and partial beam occultation effects (as long as the signal remains above noise). In research mode, these sorts of techniques have been used to anticipate initial cloud electrification, lightning initiation, and cessation. In this study, we develop a simplified model of ice crystal size, shape, orientation, dielectric, and associated radar scattering and propagation effects in order to simulate various idealized scenarios of ice crystals responding to a hypothetical electric field and their dual-polarimetric radar signatures leading up to lightning initiation and particularly cessation. The sensitivity of the K(sub dp) ice orientation signature to various ice properties and radar wavelength will be explored. Since K(sub dp) is proportional to frequency in the Rayleigh- Gans scattering regime, the ice orientation signatures should be more obvious at higher (lower) frequencies (wavelengths). As a result, simulations at radar wavelengths from 10 cm down to 1 cm (Ka-band) will be conducted. Resonance effects will be considered using the T-matrix method. Since most K(sub dp) Vbased observations have been shown at S-band, we will present ice orientation signatures from C-band (UAH/NASA ARMOR) and X-bd (UAH MAX) dual-polarimetric radars located in Northern Alabama. Issues related to optimal radar scanning for the detection of oriented ice will be discussed. Preliminary suggestions on how these differential phase signatures of oriented ice could contribute to lightning initiation and cessation algorithms will be presented.

Carey, L.D.

Constant-Differential-Pressure Two-Fluid Accumulator

A two-fluid accumulator has been designed, built, and demonstrated to provide an acceptably close approximation to constant differential static pressure between two fluids over the full ranges of (1) accumulator stroke, (2) rates of flow of the fluids, and (3) common static pressure applied to the fluids. Prior differential- pressure two-fluid accumulators are generally not capable of maintaining acceptably close approximations to constant differential pressures. The inadequacies of a typical prior differential-pressure two-fluid accumulator can be summarized as follows: The static differential pressure is governed by the intrinsic spring rate (essentially, the stiffness) of an accumulator tank. The spring rate can be tailored through selection of the tank-wall thickness, selection of the number and/or shape of accumulator convolutions, and/or selection of accumulator material(s). Reliance on the intrinsic spring rate of the tank results in three severe limitations: (1) The spring rate and the expulsion efficiency tend to be inversely proportional to each other: that is to say, as the stiffness (and thus the differential pressure) is increased, the range of motion of the accumulator is reduced. (2) As the applied common static pressure increases, the differential pressure tends to decrease. An additional disadvantage, which may or may not be considered limiting, depending on the specific application, is that an increase in stiffness entails an increase in weight. (3) The additional weight required by a low expulsion efficiency accumulator eliminates the advantage given to such gas storage systems. The high expulsion efficiency provided by this two-fluid accumulator allows for a lightweight, tightly packaged system, which can be used in conjunction with a fuel cell-based system.

Piecuch, Benjamin

Special Component Designs for Differential-Amplifier MMICs

Special designs of two types of electronic components transistors and transmission lines have been conceived to optimize the performances of these components as parts of waveguide-embedded differential-amplifier monolithic microwave integrated circuits (MMICs) of the type described in the immediately preceding article. These designs address the following two issues, the combination of which is unique to these particular MMICs: Each MMIC includes a differential double-strip transmission line that typically has an impedance between 60 and 100 W. However, for purposes of matching of impedances, transmission lines having lower impedances are also needed. The transistors in each MMIC are, more specifically, one or more pair(s) of InP-based high-electron-mobility transistors (HEMTs). Heretofore, it has been common practice to fabricate each such pair as a single device configured in the side-to-side electrode sequence source/gate/drain/gate/source. This configuration enables low-inductance source grounding from the sides of the device. However, this configuration is not suitable for differential operation, in which it is necessary to drive the gates differentially and to feed the output from the drain electrodes differentially. The special transmission-line design provides for three conductors, instead of two, in places where lower impedance is needed. The third conductor is a metal strip placed underneath the differential double-strip transmission line. The third conductor increases the capacitance per unit length of the transmission line by such an amount as to reduce the impedance to between 5 and 15 W. In the special HEMT-pair design, the side-to-side electrode sequence is changed to drain/gate/source/gate/ drain. In addition, the size of the source is reduced significantly, relative to corresponding sizes in prior designs. This reduction is justified by the fact that, by virtue of the differential configuration, the device has an internal virtual ground, and therefore there is no need for a low-resistance contact between the source and the radio-frequency circuitry. The source contact is needed only for DC biasing. These designs were implemented in a single-stage-amplifier MMIC. In a test at a frequency of 305 GHz, the amplifier embedded in a waveguide exhibited a gain of 0 dB; after correcting for the loss in the waveguide, the amplifier was found to afford a gain of 0.9 dB. In a test at 220 GHz, the overall gain of the amplifier- and-waveguide assembly was found to be 3.5 dB.

Kangaslahti, Pekka

Impedance Discontinuity Reduction Between High-Speed Differential Connectors and PCB Interfaces

High-speed serial communication (i.e., Gigabit Ethernet) requires differential transmission and controlled impedances. Impedance control is essential throughout cabling, connector, and circuit board construction. An impedance discontinuity arises at the interface of a high-speed quadrax and twinax connectors and the attached printed circuit board (PCB). This discontinuity usually is lower impedance since the relative dielectric constant of the board is higher (i.e., polyimide approx. = 4) than the connector (Teflon approx. = 2.25). The discontinuity can be observed in transmit or receive eye diagrams, and can reduce the effective link margin of serial data networks. High-speed serial data network transmission improvements can be made at the connector-to-board interfaces as well as improving differential via hole impedances. The impedance discontinuity was improved by 10 percent by drilling a 20-mil (approx. = 0.5-mm) hole in between the pin of a differential connector spaced 55 mils (approx. = 1.4 mm) apart as it is attached to the PCB. The effective dielectric constant of the board can be lowered by drilling holes into the board material between the differential lines in a quadrax or twinax connector attachment points. The differential impedance is inversely proportional to the square root of the relative dielectric constant. This increases the differential impedance and thus reduces the above described impedance discontinuity. The differential via hole impedance can also be increased in the same manner. This technique can be extended to multiple smaller drilled holes as well as tapered holes (i.e., big in the middle followed by smaller ones diagonally).

Navidi, Sal

Differential equations for cosmological correlators

Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations satisfied by cosmological correlation functions. In this work, we provide a broader perspective on the origin and structure of these differential equations. As a concrete example, we study conformally coupled scalar fields in a power-law cosmology. The wavefunction coefficients in this model have integral representations, with the integrands being the product of the corresponding flat-space results and “twist factors” that depend on the cosmological evolution. Similar twisted integrals arise for loop amplitudes in dimensional regularization, and their recent study has led to the discovery of rich mathematical structures and powerful new tools for computing multi-loop Feynman integrals in quantum field theory. The integrals of interest in cosmology are also part of a finite-dimensional basis of master integrals, which satisfy a system of first-order differential equations. We develop a formalism to derive these differential equations for arbitrary tree graphs. The results can be represented in graphical form by associating the singularities of the differential equations with a set of graph tubings. Upon differentiation, these tubings grow in a local and predictive fashion. In fact, a few remarkably simple rules allow us to predict — by hand — the equations for all tree graphs. While the rules of this “kinematic flow” are defined purely in terms of data on the boundary of the spacetime, they reflect the physics of bulk time evolution. We also study the analogous structures in tr ϕ 3 theory, and see some glimpses of hidden structure in the sum over planar graphs. This suggests that there is an autonomous combinatorial or geometric construction from which cosmological correlations, and the associated spacetime, emerge.

Cosmological models

Regulation of collagenase-3 and osteocalcin gene expression by collagen and osteopontin in differentiating MC3T3-E1 cells

Both collagenase-3 and osteocalcin mRNAs are expressed maximally during the later stages of osteoblast differentiation. Here, we demonstrate that collagenase-3 mRNA expression in differentiating MC3T3-E1 cells is dependent upon the presence of ascorbic acid, is inhibited in the presence of the collagen synthesis inhibitor, 3,4-dehydroproline, and is stimulated by growth on collagen in the absence of ascorbic acid. Transient transfection studies show that collagenase-3 promoter activity increases during cell differentiation and requires the presence of ascorbic acid. Additionally, we show that, in differentiating MC3T3-E1 cells, collagenase-3 gene expression increases in the presence of an anti-osteopontin monoclonal antibody that binds near the RGD motif of this protein, whereas osteocalcin expression is inhibited. Furthermore, an RGD peptidomimetic compound, designed to block interaction of ligands to the alpha(v) integrin subunit, increases osteocalcin expression and inhibits collagenase-3 expression, suggesting that the RGD peptidomimetic initiates certain alpha(v) integrin signaling in osteoblastic cells. Overall, these studies demonstrate that stimulation of collagenase-3 expression during osteoblast differentiation requires synthesis of a collagenous matrix and that osteopontin and alpha(v) integrins exert divergent regulation of collagenase-3 and osteocalcin expression during osteoblast differentiation.

NASA Discipline Musculoskeletal

Skeletal unloading inhibits the in vitro proliferation and differentiation of rat osteoprogenitor cells

Loss of weight bearing in the growing rat decreases bone formation, osteoblast numbers, and bone maturation in unloaded bones. These responses suggest an impairment of osteoblast proliferation and differentiation. To test this assumption, we assessed the effects of skeletal unloading using an in vitro model of osteoprogenitor cell differentiation. Rats were hindlimb elevated for 0 (control), 2, or 5 days, after which their tibial bone marrow stromal cells (BMSCs) were harvested and cultured. Five days of hindlimb elevation led to significant decreases in proliferation, alkaline phosphatase (AP) enzyme activity, and mineralization of BMSC cultures. Differentiation of BMSCs was analyzed by quantitative competitive polymerase chain reaction of cDNA after 10, 15, 20, and 28 days of culture. cDNA pools were analyzed for the expression of c-fos (an index of proliferation), AP (an index of early osteoblast differentiation), and osteocalcin (a marker of late differentiation). BMSCs from 5-day unloaded rats expressed 50% less c-fos, 61% more AP, and 35% less osteocalcin mRNA compared with controls. These data demonstrate that cultured osteoprogenitor cells retain a memory of their in vivo loading history and indicate that skeletal unloading inhibits proliferation and differentiation of osteoprogenitor cells in vitro.

NASA Discipline Musculoskeletal

Study of fully coupled three-dimensional envelope instability using automatic differentiation

Automatic differentiation is a powerful tool for computing derivatives of simulation results with respect to given parameters. In this Letter, we have applied this tool to investigate the instability of a dynamical system governed by 21 ordinary differential equations. This second-order instability (named envelope instability) is driven by space-charge effects and has a significant impact on the operational regimes of particle accelerators. Our study delves into the three-dimensional envelope instability, incorporating both transverse and longitudinal coupling. Conventionally, analyzing this complex system would necessitate solving 441 ordinary differential equations, which is computationally intractable. However, by employing automatic differentiation, we were able to track only 21 equations. This approach allowed us to uncover an additional instability stopband, which arises from space-charge-induced coupling and has not been reported in previous studies. This research highlights the significant advantages of automatic differentiation in analyzing complicated dynamical systems involving a large number of ordinary differential equations.

Qiang, Ji [Lawrence Berkeley National Laboratory (

The Memory Scaling of Reverse-Mode Differentiation in Particle Accelerator Simulations with Space Charge

The recent development of differentiable simulation codes for particle accelerators has enabled gradient-based workflows that promise finer control and more realistic modeling of accelerator facilities. However, when using reverse-mode automatic differentiation, the memory usage continuously increases during the simulation, and can potentially exceed the available hardware memory - especially when costly space charge computation is included. To study the memory requirements for differentiable simulations, we have implemented space charge in Cheetah, a PyTorch-based beam tracking code that supports reverse-mode differentiation. We find that the memory usage for reverse-mode differentiation grows linearly with the number of macroparticles and cells, and that it is proportional to the number of space charge kicks involved in the simulation. This general scaling can be used to evaluate whether a given differentiable simulation is feasible given hardware memory constraints.

Dhamrait, Arjun

Absolute elastic differential electron scattering cross sections in the intermediate energy region. IV - CO

Using a crossed electron beam-molecular beam scattering geometry and a relative-flow technique, ratios of elastic differential cross sections of CO to those of He have been measured at electron impact energies of 3, 5, 7.5, 9.9, 15, 20, 30, 50, 75, and 100 eV. At each energy, an angular range of 15 to 130 deg has been covered. These ratios have been multiplied by previously known He elastic differential cross sections to obtain elastic differential cross sections for CO. Since pure rotational excitations were not resolved, the elastic differential cross sections are a sum of elastic and pure rotational excitations at room temperature. From a knowledge of differential cross sections (DCS), integral and momentum transfer cross sections have been calculated. Both the DCS and integral cross sections are compared at 50, 75, and 100 eV to a recent two-potential theory of e-molecule scattering. Present results show that the isoelectronic molecules CO and N2 have very similar magnitudes and shapes of their differential cross sections.

Tanaka, H.

Differentiating matrices for arbitrarily spaced grid points

Differentiating matrices allow the numerical differentiation of functions defined at points of a discrete grid. A type of differentiating matrix based on local approximation on a sequence of sliding subgrids is considered. Previous derivations of this type of matrix have been restricted to grids with uniformly spaced points, and the resulting derivative approximations have lacked precision, especially at endpoints. The new formulation allows grids which have arbitrarily space points. It is shown that high accuracy can be achieved through use of differentiating matrices on non-uniform grids which include near-boundary points. Use of the differentiating matrix as an operator to solve eigenvalue problems involving ordinary differential equations is also considered.

Lakin, W. D.

Differentiating matrices for arbitrarily spaced grid points

Differentiating matrices allow the numerical differentiation of functions defined at points of a discrete grid. Previous derivations of these matrices have been restricted to grids with uniformly spaced points, and the resulting derivative approximations have lacked precision, especially at endpoints. The present work derives differentiating matrices on grids with arbitrarily spaced points. It is shown that high accuracy can be achieved through use of differentiating matrices on non-uniform grids through the expedient of including 'near boundary' points. Use of the differentiating matrix as an operator in the solution of problems involving ordinary differential equations is also considered.

Lakin, W. D.

A unified approach to the helioseismic forward and inverse problems of differential rotation

A general, degenerate perturbation theoretic treatment of the helioseismic forward and inverse problem for solar differential rotation is presented. For the forward problem, differential rotation is represented as the axisymmetric component of a general toroidal flow field using velocity spherical harmonics. This approach allows each degree of differential rotation to be estimated independently from all other degrees. In the inverse problem, the splitting caused by differential rotation is expressed as an expansion in a set of orthonormal polynomials that are intimately related to the solution of the forward problem. The combined use of vector spherical harmonics as basis functions for differential ratio and the Clebsch-Gordon coefficients to represent splitting provides a unified approach to the forward and inverse problems of differential rotation which greatly simplify inversion.

Ritzwoller, Michael H.

Differential phase acoustic microscope for micro-NDE

A differential phase scanning acoustic microscope (DP-SAM) was developed, fabricated, and tested in this project. This includes the acoustic lens and transducers, driving and receiving electronics, scanning stage, scanning software, and display software. This DP-SAM can produce mechanically raster-scanned acoustic microscopic images of differential phase, differential amplitude, or amplitude of the time gated returned echoes of the samples. The differential phase and differential amplitude images provide better image contrast over the conventional amplitude images. A specially designed miniature dual beam lens was used to form two foci to obtain the differential phase and amplitude information of the echoes. High image resolution (1 micron) was achieved by applying high frequency (around 1 GHz) acoustic signals to the samples and placing two foci close to each other (1 micron). Tone burst was used in this system to obtain a good estimation of the phase differences between echoes from the two adjacent foci. The system can also be used to extract the V(z) acoustic signature. Since two acoustic beams and four receiving modes are available, there are 12 possible combinations to produce an image or a V(z) scan. This provides a unique feature of this system that none of the existing acoustic microscopic systems can provide for the micro-nondestructive evaluation applications. The entire system, including the lens, electronics, and scanning control software, has made a competitive industrial product for nondestructive material inspection and evaluation and has attracted interest from existing acoustic microscope manufacturers.

Waters, David D.

Differential Canard deflection for generation of yawing moment on the X-31 with and without the vertical tail

The feasibility of augmenting the available yaw control power on the X-31 through differential deflection of the canard surfaces was studied as well as the possibility of using differential canard control to stabilize the X-31 with its vertical tail removed. Wind-tunnel tests and the results of departure criteria and linear analysis showed the destabilizing effect of the reduction of the vertical tail on the X-31. Wind-tunnel testing also showed that differential canard deflection was capable of generating yawing moments of roughly the same magnitude as the thrust vectoring vanes currently in place on the X-31 in the post-stall regime. Analysis showed that the X-31 has sufficient aileron roll control power that with the addition of differential canard as a yaw controller, the wind-axis roll accelerations will remain limited by yaw control authority. It was demonstrated, however, that pitch authority may actually limit the maximum roll rate which can be sustained. A drop model flight test demonstrated that coordinated, wind axis rolls could be performed with roll rates as high as 50 deg/sec (full scale equivalent) at 50 deg angle of attack. Another drop model test was conducted to assess the effect of vertical tail reduction, and an analysis of using differential canard deflection to stabilize the tailless X-31 was performed. The results of six-degree-of-freedom, non-linear simulation tests were correlated with the drop model flights. Simulation studies then showed that the tailless X-31 could be controlled at angles of attack at or above 20 deg using differential canard as the only yaw controller.

Whiting, Matthew Robert