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Analytical and numerical computational methods to determine the location of the mode as a function of the parameters of a class of the bivariate gamma distribution are presented.
Quasinormal modes describe the ringdown of compact objects deformed by small perturbations. In generic theories of gravity that extend General Relativity, the linearized dynamics of these perturbations is described by a system of coupled linear differential equations of second order. We first show, under general assumptions, that such a system can be brought to a Schrödinger-like form. We then devise an analytic approximation scheme to compute the spectrum of quasinormal modes. We validate our approach using a toy model with a controllable mixing parameter ε and showing that the analytic approximation for the fundamental mode agrees with the numerical computation when the approximation is justified. The accuracy of the analytic approximation is at the (sub-) percent level for the real part and at the level of a few percent for the imaginary part, even when ε is of order one. Our approximation scheme can be seen as an extension of the approach of Schutz and Will [1] to the case of coupled systems of equations, although our approach is not phrased in terms of a WKB analysis, and offers a new viewpoint even in the case of a single equation.
Introduction: The highest concentration of Lu-nar water-ice stores exists within the Permanently Shadowed Regions (PSRs) of the Lunar South Pole [1-3]. As such, the ability to locate in situ water-ice stores in an accurate, systematic, and safe manner will prove vital for future Lunar activities which rely on hydrogen-based resources. Here we show how the strong absorptive properties of ice can be exploited so that surface ice located in PSRs can be easily differentiated from the surrounding frozen regolith. Testbeds which simulate an icy lunar landscape were created and then systematically imaged using a mid-wave infrared (MWIR) camera system. Testbeds were imaged under two filter modes (1) high-absorption (high-abs) mode: whereby imagery captured were confined to a single central wave-length (CWL) of 3.15 ± 0.03 μm and (2) low-absorption (low-abs) mode: whereby imagery cap-tured were confined to a single CWL of 3.80 ± 0.04 μm (Figure 1). High- and low-absorption modes are related to the absorptive properties of ice at each selected wavelength, respectively. Corresponding images from each filter mode were differenced (i.e., pixels were subtracted) to enhance contrast between ice-bearing and non-ice-bearing pixels, and then fed into a semantic segmen-tation model. The model was trained to detect and differentiate between water, ice, shadows, and lunar regolith. Results: Modeling results accurately discrimi-nated ice from other materials (such as frozen lunar regolith) and were used to visually resolve the spa-tial extent of surface ice. Further, outputs produced through semantic segmentation were used to estimate water-ice contents in collected imagery [(Pixels with Class = “Water Ice”)/(Sum of Pixels)*100]. Summary: These works prove promising for future in situ resource utilization (ISRU) missions which employ robotics in combination with infrared camera systems to advance science objectives (e.g., locate water-ice in frozen regolith) on the lunar sur-face. References: [1] Cannon K. M., Deutsch A. N., Head J. W., and Britt D. T. (2020) Geophysical Re-search Letters, 46, e2020GL088920. [2] Honniball C. I. et al. (2021) Nature Astronomy 5, no. 2, 121-127. [3] Li S. et al. (2018) Proceedings of the National Academy of Sciences, 115(36), 8907-8912.
Ambient ionization techniques enable mass spectrometry (MS) to expand into broader experimental contexts, although it is increasingly clear that results are influenced by the environmental conditions at the site of sampling. Desorption electrospray ionization (DESI), in particular, is affected by variations in relative humidity (RH) levels. Here we describe the design, development, and construction of an environmental control chassis that can actively modulate RH within ± 3% of user-defined set points across a broad humidity range (15%–70% RH). Preliminary characterization demonstrated differential analyte responses across a range of set points, with observed enhancement of leucine-enkephalin, sulfadimethoxine (negative mode), and maltose (positive mode) in response to increased humidity. The measurable differences in analyte signals across discrete humidity set points underscore the importance of environmental control in ambient ionization strategies. The humidity control system outlined here can be translated to other DESI platforms, with construction information provided herein.
This paper introduces a gain-scheduling PID controller design strategy for hydroturbine frequency control mode. This scheme first uses real data to learn the nonlinear dynamics of the hydroturbine using neural controlled differential equations and then perturbs the obtained nonlinear system at different equilibrium points, based on which a static output feedback adaptive dynamic programming algorithm is then used to optimize the PID gains for each equilibrium point. Moreover, a continuous-time version of stochastic distribution control is proposed to further fine-tune the optimized PID gains. Finally, the controller is obtained by implementing linear interpolation between the optimized PID control gains. The simulation results show that the proposed gain-scheduling PID controller can control a larger range of operation points compared with the given fixed PID controller and the baseline method. Compared with the given fixed PID controller, the proposed gain-scheduling PID controller can regulate hydroturbine frequency against disturbances induced by power-load variation with over 50% less overshoot for some operation points.
Proteinoid microspheres with stable internal compartments and internal structure are made from acidic proteinoid and basic proteinoid with calcium. The populations of microspheres are characterized by a wide diversity of structure. A model of primitive intracellular communication is suggested by the observed movement of internal particles between compartments of a multicompartmentalized unit. Differential response to pH change and to temperature change has been demonstrated within one population and suggests one mode of adaptive selection among primordial cell populations.
Lidar measurements using pseudonoise code modulated AlGaAs lasers are reported. Horizontal path lidar measurements were made at night to terrestrial targets at ranges of 5 and 13 km with 35 mW of average power and integration times of one second. Cloud and aerosol lidar measurements were made to thin cirrus clouds at 13 km altitude with Rayleigh (molecular) backscatter evident up to 9 km. Average transmitter power was 35 mW and measurement integration time was 20 minutes. An AlGaAs laser was used to characterize spectral properties of water vapor absorption lines at 811.617, 816.024, and 815.769 nm in a multipass absorption cell using derivative spectroscopy techniques. Frequency locking of an AlGaAs laser to a water vapor absorption line was achieved with a laser center frequency stability measured to better than one-fifth of the water vapor Doppler linewidth over several minutes. Differential absorption lidar measurements of atmospheric water vapor were made in both integrated path and range-resolved modes using an externally modulated AlGaAs laser. Mean water vapor number density was estimated from both integrated path and range-resolved DIAL measurements and agreed with measured humidity values to within 6.5 percent and 20 percent, respectively. Error sources were identified and their effects on estimates of water vapor number density calculated.
Constricted double-heterojunction (CDH) lasers are presented as the class of single-mode nonplanar-substrate devices for which the lasing cavity is on the least resistive electrical path between the contact and the substrate. Various types of CDH structures are considered under three general topics: liquid-phase epitaxy over channeled substrates, lateral mode control, and current control in nonplanar-substrate devices. Ridge-guide CDH lasers have positive-index lateral-mode confinement and provide: single-mode CW operation to 7 mW/facet at room temperature and to 3 mW/facet at 150 C; light-current characteristics with second-harmonic distortion as low as -57 dB below the fundamental level; threshold-current temperature coefficients, as high as 375 C (pulsed) and 310 C (CW); constant external differential quantum efficiency to 100 C; and lasing operation to 170 C CW and 280 C pulsed. Semileakyguide CDH lasers have an asymmetric leaky cavity for lateral-mode confinement and provide single-mode operation to 15 to 20 mW/facet CW and to 50 mW/facet at 50% duty cycle. Modulation characteristics and preliminary reliability data are discussed.
In this paper, the status of a high-energy, all solid-state Nd:YAG laser pumped nonlinear optics based UV converter development is discussed. The high-energy UV transmitter technology is being developed for ozone sensing applications from space based platforms using differential lidar technique. The goal is to generate greater than 200 mJ/pulse with 10-50 Hz PRF at wavelengths of 308 nm and 320 nm. A diode-pumped, all-solid-state and single longitudinal mode Nd:YAG laser designed to provide conductively cooled operation at 1064 nm has been built and tested. Currently, this pump laser provides an output pulse energy of >1 J/pulse at 50 Hz PRF and a pulsewidth of 22 ns with an electrical-to-optical system efficiency of greater than 7% and a M(sup 2) value of <2. The single frequency UV converter arrangement basically consists of an IR Optical Parametric Oscillator (OPO) and a Sum Frequency Generator (SFG) setups that are pumped by 532 nm wavelength obtained via Second Harmonic Generation (SHG). In this paper, the operation of an inter cavity SFG with CW laser seeding scheme generating 320 nm wavelength is presented. Efforts are underway to improve conversion efficiency of this mJ class UV converter by modifying the spatial beam profile of the pump laser.
Current and upcoming 21-cm experiments will soon be able to map 21-cm spatial fluctuations in three dimensions for a wide range of redshifts. However, bright foreground contamination and the nature of radio interferometry create significant challenges, making it difficult to access rich cosmological information from the Fourier modes that lie within the “foreground wedge”. Here, in this work, we introduce two approaches aiming to reconstruct the full 21-cm density field, including the missing modes in the wedge: (a) a field-level inference under an effective field theory (EFT) framework; (b) a diffusion-based deep generative model trained on simulations. Under the EFT framework, we implement a fully differentiable forward model that maps the initial conditions of matter fluctuations to the observed, foreground-filtered 21-cm maps. This enables a gradient-based sampler to simultaneously sample the initial conditions and bias parameters, allowing a physically motivated mode reconstruction. Alternatively, we apply a variational diffusion model to perform 21-cm density reconstruction at the map level. Our model is trained on semi-numerical simulations over a wide range of astrophysical parameters. Our results from both approaches should provide improved cosmological constraints from the field level and also enable cross-correlation between experiments that have little or no overlapping modes.
The possibility that magnetic clouds rotate while they propagate antisunward was investigated. Magnetic clouds are modeled as magnetic flux ropes which rotate rigidly about the axis of symmetry. An ideal magnetohydrodynamic model, in which the evolution of the magnetic structure is related to the time evolution of the angular frequency, is developed. A class of 'separable' magnetic fields is employed to reduce the problem to a nonlinear ordinary differential equation for the evolution function, and it is solved numerically. The corresponding effective potential gives rise to two modes of evolution--expansion and oscillation--depending on the energy and on the value of a dimensionless parameter, k. Parameter k depends on the gas pressure, the ratio of the magnetic field components, and the frequency of rotation. There is a critical value of k, k(sub c), above which the oscillatory regime disappears and the flux rope invariably expands, regardless of the energy. Below k(sub c) the energy determines whether the configuration is confined or unbounded. Rotation always helps expansion by lowering the potential barrier. A data example was studied and features which are interpreted as signatures of rotation are presented. The angular speed is comparable to the Alfven speed, and the core of the rotating cloud completes on average one full revolution every three days at 1 AU. The parameter k is calculated from observations, and it is found to be close to, but below, critical. Only three out of the nine clouds examined showed signatures of rotation. Theoretical analysis suggests that close to the Sun rotation effects may play a more important role in the evolution of magnetic clouds than 1 AU.
The non-equilibrium critical-layer analysis of a system of frequency-detuned resonant-triads is presented using the generalized scaling of Lee. It is shown that resonant-triads can interact nonlinearly within the common critical layer when their (fundamental) Strouhal numbers are different by a factor whose magnitude is of the order of the growth rate multiplied by the wavenumber of the instability wave. Since the growth rates of the instability modes become larger and the critical layers become thicker as the instability waves propagate downstream, the frequency-detuned resonant-triads that grow independently of each other in the upstream region can interact nonlinearly in the later downstream stage. In the final stage of the non-equilibrium critical-layer evolution, a wide range of instability waves with the scaled frequencies differing by almost an Order of (l) can nonlinearly interact. Low-frequency modes are also generated by the nonlinear interaction between oblique waves in the critical layer. The system of partial differential critical-layer equations along with the jump equations are presented here. The amplitude equations with their numerical solutions are given in Part 2. The nonlinearly generated low-frequency components are also investigated in Part 2.
A numerical method is Presented for determining the natural vibration frequencies, and the corresponding mode shapes, of a rotating cantilever beam which has a nonuniform, unsymmetrical cross section. Two coupled fourth-order differential equations of motion with variable coefficients are derived which govern the motion of such a beam having deformations in two directions. Through the development and utilization of the integrating matrix, the solution of the differential equations is obtained in the form of an eigenvalue problem. The solutions to the eigenvalue problem are determined by an iteration method based upon a special orthogonality relationship which is derived. Numerical examples, including an application to a twisted propeller blade, are presented with the results of the integrating matrix solutions being compared to exact solutions and experimental data.
The Ne-21/He-3 Zeeman maser is a recently developed device which employs co-located ensembles of Ne-21 and He-3 atoms to provide sensitive differential measurements of the noble gas nuclear Zeeman splittings as a function of time, thereby greatly attenuating common-mode systematic effects such as uniform magnetic field variations. The Ne-21 maser will serve as a precision magnetometer to stabilize the system's static magnetic field, while the He-3 maser is used as a sensitive probe for violations of CPT and Lorentz symmetry by searching for small variations in the 3He maser frequency as the spatial orientation of the apparatus changes due to the rotation of the Earth (or placement on a rotating table). In the context of a general extension of the Standard Model of particle physics, the Ne-21/He-3 maser will provide the most sensitive search to date for CPT and Lorentz violation of the neutron: better than 10(exp -32) GeV, an improvement of more than an order of magnitude over past experiments. This exceptional precision will offer a rare opportunity to probe physics at the Planck scale. A future space-based Ne-21/He-3 maser or related device could provide even greater sensitivity to violations of CPT and Lorentz symmetry, and hence to Planck-scale physics, because of isolation from dominant systematic effects associated with ground-based operation, and because of access to different positions in space-time.
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We report recent progress on technology developments at the NASA Glenn Research Center using photonic lanterns for coherent optical communications applications. In particular, the development of a spatial mode-diversity optical receiver using a photonic lantern combined with a photonic integrated circuit (PIC). The PIC is designed for compatibility with the NASA Laser Communication Relay Demonstration’s (LCRD) differential phase-shift keying signaling format. We report on the PIC design and future characterization and packaging efforts. Additionally, we report on the development of a 19-channel photonic lantern and provide updates on efforts to use the photonic lantern as a wavefront sensing device. The photonic lantern insertion loss, and spatial-mode transfer characteristics are detailed, as well as the development of a predictive framework in which the intensities in the 19 single-mode output channels are used to reconstruct the wavefront of the light entering the multi-moded input side of the lantern. Finally, we discuss concepts for potential future systems using photonic lanterns and PICs that combine both wavefront sensing and coherent communications onto a single integrated platform.
One of the more significant technological problems associated with the orbital operation of large astronomical telescope's is the fabrication and maintenance of the primary mirror surface to the tolerance required for diffraction-limited performance. An interesting approach to the solution of this problem involves continuously measuring and automatically correcting the optical surface of a thin deformable mirror by means of discrete actuators located on its rear surface: The realization of diffraction-limited performance from a telescope in space by this method rests on the ability of the designer to achieve extremely accurate control of a highly complex, interacting, multivariable system. This paper presents the results of a detailed study of the discrete control of linear distributed systems with specific application to the design of a practical controller for a plant representative of a telescope primary mirror for an orbiting astronomical observatory. The problem of controlling the distributed plant is treated by employing modal techniques to represent variations in the optical figure. Distortion of the mirror surface, which arises primarily from thermal gradients, is countered by actuators working against a backing structure to apply a corrective force distribution to the controlled surface. Each displacement actuator is in series with a spring attached to the mirror by means of a pad intentionally introduced to restrict the excitation of high-order modes. Control is then exerted over a finite number (equal.to the number of actuators) of the most significant modes. Through the application of the modal expansion technique the mirror equation of motion is transformed tb a set of uncoupled, linear, time-invariant, ordinary differential equations. The desired dynamic response and static accuracy may then be achieved by the application of classical single-variable design techniques. The formulation of a quadratic performance index which incorporates a measure of image quality permits determination of the trade-off between the-number of actuators and optical purity. A criterion for defining actuator placement and pad size is presented which minimizes the tendency of the controller to excite the unmonitored modes.
Analysis of a flexible beam with displaced end-located inertial masses is presented. The resulting three-dimensional mode shape is shown to consist of two one-plane bending modes and one torsional mode. These three components of the mode shapes are shown to be linear combinations of trigonometric and hyperbolic sine and cosine functions. Boundary conditions are derived to obtain nonlinear algebraic equations through kinematic coupling of the general solutions of the three governing partial differential equations. A method of solution which takes these boundary conditions into account is also presented. A computer program has been written to obtain unique solutions to the resulting nonlinear algebraic equations. This program, which calculates natural frequencies and three-dimensional mode shapes for any number of modes, is presented and discussed.