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A system, method, and apparatus for an avalanche photodiode with an enhanced multiplier layer are disclosed herein. In particular, the present disclosure teaches an avalanche photodiode having a multiplier with alternating layers of one or more quantum wells and one or more spacers. A method of making the avalanche photodiode includes growing the multiplier on a substrate.
A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be sued to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.
A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be used to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.
The Modified Barrier Functions (MBF) have elements of both Classical Lagrangians (CL) and Classical Barrier Functions (CBF). The MBF methods find an unconstrained minimizer of some smooth barrier function in primal space and then update the Lagrange multipliers, while the barrier parameter either remains fixed or can be updated at each step. The numerical realization of the MBF method leads to the Newton MBF method, where the primal minimizer is found by using Newton's method. This minimizer is then used to update the Lagrange multipliers. In this paper, we examine the Newton MBF method for the Quadratic Programming (QP) problem. It will be shown that under standard second-order optimality conditions, there is a ball around the primal solution and a cut cone in the dual space such that for a set of Lagrange multipliers in this cut cone, the method converges quadratically to the primal minimizer from any point in the aforementioned ball, and continues to do so after each Lagrange multiplier update. The Lagrange multipliers remain within the cut cone and converge linearly to their optimal values. Any point in this ball will be called a "hot start". Starting at such a "hot start", at most Omicron(1n 1n epsilon(exp -1)) Newton steps are sufficient to perform the primal minimization which is necessary for the Lagrange multiplier update. Here, epsilon > 0 is the desired accuracy. Because of the linear convergence of the Lagrange multipliers, this means that only Omicron(1n epsilon(exp -1))omicron(ln 1n epsilon(exp-1)) Newton steps are required to reach an epsilon-approximation to the solution from any "hot start". In order to reach the "hot start", one has to perform Omicron(square root(m) 1n C) Newton steps, where m characterizes the size of the problem and C > 0 is the condition number of the QP problem. This condition number will be characterized explicitly in terms of key parameters of the QP problem, which in turn depend on the input data and the size of the problem.
A method is presented for calculating wing characteristics by lifting-line theory using nonlinear section lift data. Material from various sources is combined with some original work into the single complete method described. Multhopp's systems of multipliers are employed to obtain the induced angle of attack directly from the spanwise lift distribution. Equations are developed for obtaining these multipliers for any even number of spanwise stations, and values are tabulated for 10 stations along the semispan for asymmetrical, symmetrical, and antisymmetrical lift distributions. In order to minimize the computing time and to illustrate the procedures involved, simplified computing forms containing detailed examples are given for symmetrical lift distributions. Similar forms for asymmetrical and antisymmetrical lift distributions, although not shown, can be readily constructed in the same manner as those given. The adaptation of the method for use with linear section lift data is also illustrated. The adaptation has been found to require less computing time than most existing methods.
The Mars Organic Mass Analyzer is being developed at Goddard Space Flight Center to identify organics and possible biological compounds on Mars. In the process of characterizing mass spectrometer size, weight, and power consumption, the use of pulse counting was considered for ion detection. Pulse counting has advantages over analog-mode amplification of the electron multiplier signal. Some advantages are reduced size of electronic components, low power consumption, ability to remotely characterize detector performance, and avoidance of analog circuit noise. The use of pulse counting as a detection method with ion trap instruments is relatively rare. However, with the recent development of high performance electrical components, this detection method is quite suitable and can demonstrate significant advantages over analog methods. Methods A prototype quadrupole ion trap mass spectrometer with an internal electron ionization source was used as a test setup to develop and evaluate the pulse-counting method. The anode signal from the electron multiplier was preamplified. The an1plified signal was fed into a fast comparator for pulse-level discrimination. The output of the comparator was fed directly into a Xilinx FPGA development board. Verilog HDL software was written to bin the counts at user-selectable intervals. This system was able to count pulses at rates in the GHz range. The stored ion count nun1ber per bin was transferred to custom ion trap control software. Pulse-counting mass spectra were compared with mass spectra obtained using the standard analog-mode ion detection. Prelin1inary Data Preliminary mass spectra have been obtained for both analog mode and pulse-counting mode under several sets of instrument operating conditions. Comparison of the spectra revealed better peak shapes for pulse-counting mode. Noise levels are as good as, or better than, analog-mode detection noise levels. To artificially force ion pile-up conditions, the ion trap was overfilled and ions were ejected at very high scan rates. Pile-up of ions was not significant for the ion trap under investigation even though the ions are ejected in so-called 'ion-micro packets'. It was found that pulse counting mode had higher dynamic range than analog mode, and that the first amplification stage in analog mode can distort mass peaks. The inherent speed of the pulse counting method also proved to be beneficial to ion trap operation and ion ejection characterization. Very high scan rates were possible with pulse counting since the digital circuitry response time is so much smaller than with the analog method. Careful investigation of the pulse-counting data also allowed observation of the applied resonant ejection frequency during mass analysis. Ejection of ion micro packets could be clearly observed in the binned data. A second oscillation frequency, much lower than the secular frequency, was also observed. Such an effect was earlier attributed to the oscillation of the total plasma cloud in the ion trap. While the components used to implement pulse counting are quite advanced, due to their prevalence in consumer electronics, the cost of this detection system is no more than that of an analog mode system. Total pulse-counting detection system electronics cost is under $250
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The fundamental concepts of the optimality criteria method of structural optimization are presented. The effect of the separability properties of the objective and constraint functions on the optimality criteria expressions is emphasized. The single constraint case is treated first, followed by the multiple constraint case with a more complex evaluation of the Lagrange multipliers. Examples illustrate the efficiency of the method.
The pulsed neutron technique is a powerful, dynamic method to assay the reactivity of a multiplying system. This work presents the novel application of the pulsed neutron technique to the Inherently Safe Subcritical Assembly, an experimental configuration accepted by the International Criticality Safety Benchmark Evaluation Project Handbook. The experiments were replicated with COG11.3, a continuous-energy Monte Carlo code. The pulsed neutron data were analyzed using the Sjöstrand and Gozani area-ratio methods and by extracting the prompt neutron decay constant. Subsequent static k-eigenvalue and 𝛼-eigenvalue simulations were also performed for the same configurations. Neutron detector dead-time effects from the experiments were corrected using the Backwards Extrapolation Method and shown to have a negligible impact on the estimated reactivities. The results highlight that capturing time-dependent effects like delayed neutron precursor buildup are essential to accurately reproduce experimental results. They also highlight the importance of shielding the detectors from generator source neutrons in deeply subcritical configurations.
A domain-decomposed A-ϕ formulation based on Lagrange multipliers is proposed to simulate low-frequency elec- tromagnetic problems. This method partitions the computational domain into smaller subdomains, allowing each subdomain to be independently formulated using Lagrange multipliers as Dirichlet boundary conditions, while ensuring continuity of the fields across the interfaces. A mixed finite element method, utilizing both vector and scalar basis functions, is employed to discretize the formulation, resulting in a global system to be solved. The proposed method is validated using TEAM Problem 7 at 50 Hz, demonstrating its effectiveness in handling complex geometries and addressing the low-frequency breakdown issues commonly encountered in traditional finite element methods.
The development of a general analytic approach to constrained balancing that is consistent with past influence coefficient methods is described. The approach uses Lagrange multipliers to impose orbit and/or weight constraints; these constraints are combined with the least squares minimization process to provide a set of coupled equations that result in a single solution form for determining correction weights. Proper selection of constraints results in the capability to: (1) balance higher speeds without disturbing previously balanced modes, thru the use of modal trial weight sets; (2) balance off-critical speeds; and (3) balance decoupled modes by use of a single balance plane. If no constraints are imposed, this solution form reduces to the general weighted least squares influence coefficient method. A test facility used to examine the use of the general constrained balancing procedure and application of modal trial weight ratios is also described.
A novel domain decomposition method based on a hybrid variational principle is presented. Prior to any computation, a given finite element mesh is torn into a set of totally disconnected submeshes. First, an incomplete solution is computed in each subdomain. Next, the compatibility of the displacement field at the interface nodes is enforced via discrete, polynomial and/or piecewise polynomial Lagrange multipliers. In the static case, each floating subdomain induces a local singularity that is resolved very efficiently. The interface problem associated with this domain decomposition method is, in general, indefinite and of variable size. A dedicated conjugate projected gradient algorithm is developed for solving the latter problem when it is not feasible to explicitly assemble the interface operator. When implemented on local memory multiprocessors, the proposed methodology requires less interprocessor communication than the classical method of substructuring. It is also suitable for parallel/vector computers with shared memory and compares favorably with factorization based parallel direct methods.
Despite being an important closo-borate in the condensed phase boron chemistry, isolated B 10 H 10 2- is electronically unstable and has never been detected in the gas phase. Herein, we report a successful capture of this fleeting species through binding with an octamethylcalix[4]pyrrole (omC4P) molecule to form a stable gaseous omC4P·[B 10 H 10 ] 2- complex and its characterizations utilizing negative ion photoelectron spectroscopy (NIPES). The recorded NIPE spectrum, contributed from both omC4P and [B 10 H 10 ] 2- , is deconvoluted by subtracting the omC4P contribution to yield a [B 10 H 10 ] 2- spectrum. The obtained [B 10 H 10 ] 2- spectrum consists of four major bands spanning electron binding energy (EBE) range from 1 to 5 eV with the EBE gaps matching excellently with the energy intervals of computed highly lying occupied molecular orbitals of the B 10 H 10 2- dianion. Finally, this study showcases a generic method to utilize omC4P to capture unstable multiply charged anions in the gas phase for experimental determination of their electronic structures.
Using covariance analysis methods, we study the fragmentation dynamics of multiply ionized 1- and 2-iodopropane. Signatures of isomer-specific nuclear motion occurring during sequential fragmentation pathways are identified.
A method is presented for using satellite measurements to interpolate vertical temperature soundings between radiosonde stations. The method finds a set of coefficients, which when multiplied by corresponding measured radiance quantities, yield zero temperature error at a radiosonde station. This derived set of coefficients is then applied to satellite radiance measurements at places between radiosonde stations. The computations show, for example, that the average absolute error in the layer 1000-800 mbs is only 0.3K when the corresponding 'minimum-information' method error was 2.9K. The method may be most applicable to measurements from geostationary satellites, but should also be applicable to measurements from polar orbiting satellites under certain conditions.
This paper presents a method for using satellite measurements to interpolate vertical temperature soundings between radiosonde stations. The calculations presented show that especially in the 1000-800 mb layer, where linear methods of temperature retrieval usually contain large errors, the proposed method reduces the errors substantially. The method finds a set of coefficients, which when multiplied by corresponding measured radiance quantities, yield zero temperature error at a radiosonde station. This derived set of coefficients is then applied to satellite radiance measurements at places between the radiosonde stations. The computations show, for example, that the average absolute error in the layer 1000-800 mb is only 0.3 K when the corresponding 'minimum-information' method error was 2.9 K. The method may be most applicable to measurements from geostationary satellites, but should also be applicable to measurements from polar orbiting satellites under certain conditions.
A coupled multiple-method analysis procedure for use late in conceptual design or early in preliminary design of aircraft structures is described. Using this method, aircraft wing structures are represented with equivalent plate models, and structural details such as engine/pylon structure, landing gear, or a 'stick' model of a fuselage are represented with beam finite element models. These two analysis methods are implemented in an integrated multiple-method formulation that involves the assembly and solution of a combined set of linear equations. The corresponding solution vector contains coefficients of the polynomials that describe the deflection of the wing and also the components of translations and rotations at the joints of the beam members. Two alternative approaches for coupling the methods are investigated; one using transition finite elements and the other using Lagrange multipliers. The coupled formulation is applied to the static analysis and vibration analysis of a conceptual design model of a fighter aircraft. The results from the coupled method are compared with corresponding results from an analysis in which the entire model is composed of finite elements.
As computational devices continue to shrink, the cost of manufacturing such devices is expected to grow exponentially. One alternative to the costly, detailed design and assembly of conventional computers is to place the nano-electronic components randomly on a chip. The price for such a trivial assembly process is that the resulting chip would not be programmable by conventional means. In this work, we show that such random nanocomputers can be adaptively programmed using multi-agent methods. This is accomplished through the optimization of an associated high dimensional error function. By representing each of the independent variables as a reinforcement learning agent, we are able to achieve convergence must faster than with other methods, including simulated annealing. Standard combinational logic circuits such as adders and multipliers are implemented in a straightforward manner. In addition, we show that the intrinsic flexibility of these adaptive methods allows the random computers to be reconfigured easily, making them reusable. Recovery from faults is also demonstrated.