Illustrative Application of the 2^nd-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Reaction-Rate Detector Response

This work continues the illustrative application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2nd-CASAM) to a benchmark mathematical model that can simulate the evolution and/or transmission of particles in a heterogeneous medium. The model response considered in this work is a reaction-rate detector response, which provides the average interactions of particles with the respective detector or, alternatively, the time-average of the concentration of a mixture of substances in a medium. The definition of this model response includes both uncertain boundary points of the benchmark, thereby providing both direct and indirect contributions to the response sensitivities stemming from the boundaries. The exact expressions for the 1st- and 2nd-order response sensitivities to the boundary and model parameters obtained in this work can serve as stringent benchmarks for inter-comparing the performances of all (deterministic and statistical) sensitivity analysis methods.

Illustrative Application of the 2^nd-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Point-Detector Response

This work illustrates the application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2nd-CASAM) to a mathematical model that can simulate the evolution and/or transmission of particles in a heterogeneous medium. The model response is the value of the model’s state function (particle concentration or particle flux) at a point in phase-space, which would simulate a pointwise measurement of the respective state function. This paradigm model admits exact closed-form expressions for all of the 1st- and 2nd-order response sensitivities to the model’s uncertain parameters and domain boundaries. These closed-form expressions can be used to verify the numerical results of production and/or commercial software, e.g., particle transport codes. Furthermore, this paradigm model comprises many uncertain parameters which have relative sensitivities of identical magnitudes. Therefore, this paradigm model could serve as a stringent benchmark for inter-comparing the performances of all deterministic and statistical sensitivity analysis methods, including the 2nd-CASAM.

An efficient technique for recovering responses of parameterized structural dynamic problems

In this article,an effective technique is developed to efficiently obtain the output responses of parameterized structural dynamic problems.This technique is based on the conception of reduced basis method and the usage of linear interpolation principle.The original problem is projected onto the reduced basis space by linear interpolation projection,and subsequently an associated interpolation matrix is generated.To ensure the largest nonsingularity,the interpolation matrix needs to go through a timenode choosing process,which is developed by applying the angle of vector spaces.As a part of this technique,error estimation is recommended for achieving the computational error bound.To ensure the successful performance of this technique,the offline-online computational procedures are conducted in practical engineering.Two numerical examples demonstrate the accuracy and efficiency of the presented method.

A New Type Four-Fold Microstrip Hairpin Line Bandpass Filter at 1.82 GHz for TranslReceive Communication Systems

A conventional hairpin-line resonator size is normally very large. This paper presents the design, simulation/optimization and measured results of a four-resonator multi-folded hairpin line microstrip bandpass filter at 1.82 GHz, with great reduction in size compared to the conventional hairpin line structure. In the proposed filter, the cross couplings have been realized between adjacent and non-adjacent resonators.

A fast implementation for computing spatial impulse response of ultrasonic transducers

The spatial impulse response（SIR） method is often used as the ＇gold standard5 in simulation of transient acoustic wave fields due to its high accuracy in the linear domain.However, a high sampling frequency is often required in order to achieve the high accuracy. As a result, a large amount of data has to be processed. In this paper a fast approach for computing spatial impulse response is proposed to reduce the computation burden. The proposed approach is developed by employing the relationship of SIRs at observed points and SIRs of the projection points on the transducer surface. Two critical parameters used in the proposed approach, the calculation sampling frequency and the interpolation sampling frequency, are then analyzed.Results show that for a 2.25 MHz rectangular transducer with the size of 5 mm×10 mm,a calculation sampling frequency of 1000 MHz and an interpolation sampling frequency of500 MHz can achieve superior performance while improving the computation efficiency 18 times than the direct solving.

Some Modal Relations and Generalized Velocity Method in State Space

Real mode theory in configuration space has shown that the mode acceleration method converges faster than the mode displacement method. This paper demonstrates a similar conclusion in the state space. Some new expressions on modal parameter matrices were set up first. A generalized velocity method (GVM) is then demonstrated in a systematic way. This method is the so\|called complex mode velocity method, but the expressions and schemes are given in terms of parametric matrices in configuration space. Theoretical comparison of this GVM with the traditional complex mode method shows some interesting conclusions. The latter approach is actually a generalized displacement method (GDM). Without mode reduction, the displacement responses of the concerned system resulting from both approaches are identical. On the other hand, both approaches have to adopt mode reduction to become practical. Under this situation, GVM has advantages because it compensates for the contribution of the omitted high\|order modes to the displacement responses.