Set Of Response Functions Research Articles

QuDPy: A Python-based tool for computing ultrafast non-linear optical responses

Nonlinear Optical Spectroscopy is a well-developed field with theoretical and experimental advances that have benefited multiple disciplines, including chemistry, biology, and physics. However, for the accurate interpretation of the corresponding multi-dimensional spectra, there is a need for precise quantum dynamical simulations based on model Hamiltonians. In this article, we present the initial release of our code, QuDPy (Quantum Dynamics in Python), which provides a robust numerical platform for performing quantum dynamics simulations based on model systems, including open quantum systems. A distinguishing feature of our approach is the ability to specify various high-order optical response pathways in the form of double-sided Feynman diagrams through a straightforward input syntax. This syntax outlines the time-ordering of ket-sided or bra-sided optical interactions acting on the time-evolving density matrix of the system. We utilize the quantum dynamics capabilities of QuTip to simulate the spectral response of complex systems, allowing us to compute virtually any n-th order optical response of the model system. To illustrate the utility of our approach, we provide a series of example calculations. Program summaryProgram Title:QuDPyCPC Library link to program files:https://doi.org/10.17632/5xm9pm24cz.1Developer's repository link:https://github.com/sa-shah/QuDPyLicensing provisions: MIT LicenseProgramming language: Python (v3.7)Supplementary material: Available as Google Colab Files.Example 1: https://tinyurl.com/y3j5jmmrExample 2: https://tinyurl.com/37vwntn5External packages:•QuTip (v.4.7) and dependencies i.e. Numpy, Matplotlib (https://qutip.org/)•UFSS Automatic Diagram Generator (https://github.com/peterarose/ufss)Nature of problem: Accurate quantum simulations of complex systems are required in order to understand and interpret multi-dimensional ultrafast spectroscopic signals. This code provides an open-source/multi-platform method that facilitates the generation of higher-order non-linear optical responses for an arbitrary molecular or material system given a model input Hamiltonian and bath model.Solution method: We use the double-sided Feynman diagram method [1, 2] to generate (symbolically) a set of response functions corresponding to the nth order non-linear response of the system to a series of laser pulses using the UFSS package [3] We then perform a series of accurate quantum dynamics calculations using the QuTip package [4] to generate the numerical response and spectra which correspond to specific experimental conditions.

Comparative Dynamics Analysis of Simple Mathematical Models of the Plankton Communities Considering Various Types of Response Function

The paper proposes a two-component discrete-time model of the plankton community, taking into account features of the development and interaction of phytoplankton and zooplankton. To describe the interaction between these species and to compare the system dynamics, we use the following set of response functions: type II and III Holling function and the Arditi–Ginzburg response function, each of which describes trophic interactions between phytoplankton and zooplankton. An analytical and numerical study of the model proposed is made. The analysis shows that the variation of trophic functions does not change the dynamic behavior of the model fundamentally. The stability loss of nontrivial fixed point corresponding to the coexistence of phytoplankton and zooplankton can occur through a cascade of period-doubling bifurcations and according to the Neimark–Saker scenario, which allows us to observe the appearance of long-period oscillations representing the alternation of peaks and reduction in the number of species as a result of the predator-prey interaction. As well, the model has multistability areas, where a variation in initial conditions with the unchanged values of all model parameters can result in a shift of the current dynamic mode. Each of the models is shown to demonstrate conditional coexistence when a variation of the current community structure can lead to the extinction of the entire community or its part. Considering the characteristics of the species composition, the model with the type II Holling function seems a more suitable for describing the dynamics of the plankton community. Such a system is consistent with the idea that phytoplankton is a fast variable and predator dynamics is slow; thus, long-period fluctuations occur at high phytoplankton growth rates and low zooplankton ones. The model with the Arditi–Ginzburg functional response demonstrates quasi-periodic fluctuations in a narrow parametric aria with a high predator growth rate and low prey growth rate. The quasi-periodic dynamics regions in the model with the Holling type III functional response correspond to the conception of fast and slow variables, however in this case, the stability of the system increases, and the Neimark-Sacker bifurcation occurs even at a higher growth rate of zooplankton.

APPLICATION OF RESPONSE MATRIX METHOD TO TRANSIENT SIMULATIONS OF NUCLEAR SYSTEMS

Until recently, reactor transient problems were exclusively solved by approximate deterministic methods. The increase in available computing power made it feasible to approach the transient analyses with time-dependent Monte Carlo methods. These methods offer the first-principle solution to the space-time evolution of reactor power by explicitly tracking prompt neutrons, precursors of delayed neutrons and delayed neutrons in time and space. Nevertheless, a very significant computing cost is associated with such methods. The general benefits of the Monte Carlo approach may be retained at a reduced computing cost by applying a hybrid stochastic-deterministic computing scheme. Among such schemes are those based on the fission matrix and the response matrix formalisms. These schemes aim at estimating a variant of the Greens function during a Monte Carlo transport calculation, which is later used to formulate a deterministic approach to solving a space-time dependent problem. In this contribution, we provide an overview of the time-dependent response matrix method, which describes a system by a set of response functions. We have recently suggested an approach where the functions are determined during a Monte Carlo criticality calculation and are then used to deterministically solve the space-time behaviour of the system. Here, we compare the time-dependent response matrix solution with the transient fission matrix and the time-dependent Monte Carlo solutions for a control rod movement problem in a mini-core reactor geometry. The response matrix formalism results in a set of loosely connected equations which offers favourable scaling properties compared to the methods based on the fission matrix formalism.

Stochastic-deterministic response matrix method for reactor transients

Presented is a stochastic-deterministic, response matrix method for transient analyses of nuclear systems. The method is based on the response matrix formalism, which describes a system by a set of response functions. We propose an approach in which these response functions are computed during a set of Monte Carlo criticality calculations and are later used to formulate a deterministic set of equations for solving a space-time dependent problem. Application of the response matrix formalism results in a set of loosely connected equations, which leads to a favourable linear scaling of the problem. The method offers a simplified approach compared to previously proposed response matrix methods by avoiding phase-space expansions in sets of basis functions. We describe the method starting with the fundamental neutron transport considerations, provide a demonstration on two absorber movement transients in a 3 × 3 assembly PWR mini-core geometry, and compare the solutions against time-dependent Monte Carlo simulations.

Sensitivity of Aeroservoelastic Stability Characteristics Using Parametric Flutter Margins

The recently developed parametric flutter margin method is expanded to perform efficient sensitivity studies in which linear and nonlinear flutter characteristics are calculated for changes in selected parameters. Two approaches are suggested: one for structural, aerodynamic, or control parameters that can be formulated as single-input/single-output feedback loops and one for parameters that require multiple-input/multiple-output realization. The single-input/single-output analysis is based on frequency response functions, with the formulation aiming to track the important flutter mechanisms, and is arranged such that the sensitivity to different parameters, over large-variation ranges, may be based on the same set of response functions. The multiple-input/multiple-output analysis is similarly effective but is based on eigensolutions that indicate the parametric changes needed to obtain flutter. Three numerical examples using a generic transport aircraft model, in which sensitivity with respect to stiffness and mass variations were studied, are presented. The single-input/single-output and multiple-input/multiple-output approaches are also applied for calculating damping and frequency variations with velocity that may be used as traditional plots in aeroelastic design and certification tasks. The results demonstrate excellent agreement with those obtained by separate solutions of the MSC/NASTRAN code and nonlinear time marching simulations.

Response functions of cold neutron matter: Density, spin, and current fluctuations

We study the response of a single-component pair-correlated baryonic Fermi-liquid to density, spin, and their current perturbations. A complete set of response functions is derived in the low-temperature regime both within an effective theory based on a small momentum transfer expansion and within a numerical scheme valid for arbitrary momentum transfers. A comparison of these two approaches validates the perturbative approximation within the domain of its convergence. We derive the spectral functions of collective excitations associated with the density, density-current, spin, and spin-current perturbations. The dispersion relations of density and spin fluctuations are derived and it is shown that the density fluctuations lead to exciton-like undamped bound states, whereas the spin excitations correspond to diffusive modes above the pair-breaking threshold. The contribution of the collective pair-breaking modes to the specific heat of neutron matter at subnuclear densities is computed and is shown to be comparable to that of the degenerate electron gas at not too low temperatures.

A band Lanczos approach for calculation of vibrational coupled cluster response functions: simultaneous calculation of IR and Raman anharmonic spectra for the complex of pyridine and a silver cation

We describe new methods for the calculation of IR and Raman spectra using vibrational response theory. Using damped linear response functions that incorporate a Lorentzian line-shape function from the outset, it is shown how the calculation of Raman spectra can be carried out through the calculation of a set of vibrational response functions in the same manner as described previously for IR spectra. The necessary set of response functions can be calculated for both vibrational coupled cluster (VCC) and vibrational configuration interaction (VCI) anharmonic vibrational wave-functions. For the efficient and simultaneous calculation of the full set of necessary response functions, a non-hermitian band Lanczos algorithm is implemented for VCC, and a hermitian band Lanczos algorithm is implemented for VCI. It is shown that the simultaneous calculation of several response functions is often advantageous. Sample calculations are presented for pyridine and the complex between pyridine and the silver cation.

Calibration of a Bonner sphere spectrometer in quasi-monoenergetic neutron fields of 244 and 387 MeV

This paper describes the results of calibration measurements for a Bonner sphere spectrometer (BSS) with 3He proportional counter performed in quasi-monoenergetic neutron fields at the Research Center for Nuclear Physics (RCNP) at the University of Osaka, Japan. Using 246 MeV and 389 MeV proton beams, neutron fields with nominal peak energies of 244 MeV and 387 MeV were generated via 7Li(p,n)7Be reactions. At high energies, the neutron spectra were measured by means of the time-of-flight (TOF) method. The low-energy part of the neutron spectra were determined by BSS measurements down to thermal energies using the MSANDB unfolding code and three different sets of response functions. These were obtained by means of Monte Carlo (MC) calculations including various codes and intra-nuclear cascade (INC) models. Unfolded BSS fluence rates were additionally confirmed by GEANT4 calculations. For calibration of the BSS, measured count rates were corrected for low-energy contributions and compared with count rates calculated using TOF data and various response functions. In addition, measured response values were compared with mono-energetic response calculations, and best agreement was found with GEANT4 results using the Bertini INC model.

STUDY ON DECONVOLUTION FOR GAMMA SPECTROSCOPY USING ML-EM ALGORITHM AND MCNP SIMULATION

In this paper, the ML-EM (Maximum Likelihood Fitting by Expectation Maximization) algorithm was used in deconvolution of continuum gamma ray for HPGe detector. A set of response functions was simulated by using MCNP4C2 code for gamma radiation emitted from point source located at 10.6cm from detector. The source energies varied from 50.1 keV to 1502.1 keV with 2.5 keV step were detected by the 8192 - channel spectrometer. The results of deconvolution for some gamma spectra of Co-60, CS-137, Eu-152 showed that the photopeak areas of the deconvoluted spectra were considerably raised in compare with ones of measured spectra in the same condition.

Robust product development for multiple quality characteristics using computer experiments and an optimization technique

Conventional parameter or tolerance designs focus on developing exact methods to minimize quality loss or manufacturing cost. The inherent assumption is that the response functions which represent the link between controllable variables and response values of quality characteristics are known before a design is developed. Moreover, parameter and tolerance values are assumed to be independent controllable variables in previous works; namely, they are determined separately in design activities. Currently, advanced computer software, such as computer-aided engineering, can help engineers to handle design problems with unknown response functions, at the stage of product design and process planning. Therefore, in this study, the software ANSYS was employed to obtain simulation data which represent the response values of quality characteristics. These response values will be used to fit a set of response functions for later analysis. However, previous works in computer simulation for design and planning usually lack consideration of the noise impact from an external design system. To approximate a realistic design environment, various levels of controllable variables, in conjunction with artificial noises created from uncontrollable variables, are used to generate simulated data for statistical analysis via Response Surface Methodology (RSM). Then, an optimization technique, such as mathematical programming, is adopted to integrate these response functions into one formulation so that optimal parameter and tolerance values are concurrently determined, with multiple quality characteristics taken into consideration. A bike-frame design was used to demonstrate the presented approach, followed by multiple quality characteristics of interest: material cost, bike-frame weight, structure reliability, and rigidity dependability. The goal is to minimize material cost and bike frame weight and to maximize structure reliability and rigidity dependability. This approach is useful for solving any complex design problems in the early stages, while providing enhanced functionality, quality, economic benefits, and a shorter design cycle.

ON THE GENERALISATION OF THE TRANSMISSIBILITY CONCEPT

A generalisation of the transmissibility concept is presented for structures with several degrees of freedom. A transmissibility matrix between two sets of response functions is built from any of the mobility matrices of the structure. In most practical cases, the known, or measured, responses shall make one of the sets, while the other set will include the responses at any of the other co-ordinates. It is shown that the transmissibility is generally a rectangular matrix, since the number of response functions in each of the sets need not be the same; nevertheless, to allow for a solution for the unknown responses, the number of known responses needs to be at least the same as the number of input forces and moments (generalised forces) applied to the structure.

Verification of unfold error estimates in the unfold operator code

Spectral unfolding is an inverse mathematical operation that attempts to obtain spectral source information from a set of response functions and data measurements. Several unfold algorithms have appeared over the past 30 years; among them is the unfold operator (UFO) code written at Sandia National Laboratories. In addition to an unfolded spectrum, the UFO code also estimates the unfold uncertainty (error) induced by estimated random uncertainties in the data. In UFO the unfold uncertainty is obtained from the error matrix. This built-in estimate has now been compared to error estimates obtained by running the code in a Monte Carlo fashion with prescribed data distributions (Gaussian deviates). In the test problem studied, data were simulated from an arbitrarily chosen blackbody spectrum (10 keV) and a set of overlapping response functions. The data were assumed to have an imprecision of 5% (standard deviation). One hundred random data sets were generated. The built-in estimate of unfold uncertainty agreed with the Monte Carlo estimate to within the statistical resolution of this relatively small sample size (95% confidence level). A possible 10% bias between the two methods was unresolved. The Monte Carlo technique is also useful in underdetermined problems, for which the error matrix method does not apply. UFO has been applied to the diagnosis of low energy x rays emitted by Z-pinch and ion-beam driven hohlraums.

Deciduous Quercus in the Mediterranean region: tree‐ring/climate relationships

summaryComparisons are made between ring‐width response functions relating to precipitation and temperature in 72 Quercus populations (Q. afares Pomel, Q. canariensis Willd., Q. pubesrens Willd. and Q. robur L.) situated in the north and south of the western Mediterranean region. A multivariate procedure applied to the whole set of response functions allows a distinction to be made of three types of response function according to the species considered. Analogies and differences between coded response functions are revealed by the calculation of a mean response, firstly for each species and for the genus, secondly for the groups of response functions derived from the multivariate analysis. For all the populations, and hence for the entire Quercus genus, a direct response to summer precipitation and an inverse response to temperature, especially minimum temperature, are obtained for the summer period. For the other seasons, each species is characterized by a particular behaviour conditioned by the characteristics of the habitat.

Thermospheric dynamics: A system theory approach

A system theory approach to thermospheric modeling is developed, based upon a linearization method which is capable of preserving nonlinear features of a dynamical system. The method is tested using a large, nonlinear, time‐varying system, namely the thermospheric general circulation model (TGCM) of the National Center for Atmospheric Research. We compare TGCM simulation results with results from our approximation procedure at Millstone Hill and Arecibo, two locations where there may be interest for using this approach. In the linearized version an equivalent system, defined for one of the desired TGCM output variables, is characterized by a set of response functions that is constructed from corresponding quasi‐steady state and unit sample response functions. The number of functions in the set depends on the degree of nonlinearity of the original system and the desired accuracy of the approximation. Using the set of response functions, we are able to approximate time‐dependent TGCM simulation results with reasonable accuracy. The linearized version of the system runs on a personal computer and produces an approximation of the desired TGCM output field height profile at a given geographic location. The approximation is obtained by performing a specialized convolution between the cross polar cap potential drop as input and the set of response functions. This enables an efficient first‐order comparison between experimental data and theoretical simulations and may provide an operationally efficient means of more realistically predicting density variations for satellite ephemeris or reentry trajectory determinations during geomagnetic quiet periods as well as during magnetic storms.

A neutron spectrometer for neutrons with energies between 1 eV and 10 keV

Epithermal neutrons with energies between 1 eV and 10 keV are of great interest in neutron capture therapy for treating deep-seated tumors. A new type of neutron spectrometer has been developed to measure neutron spectra in this energy range. Conceptually, this new spectrometer is similar to the Bonner Sphere spectrometry system, in that it has a set of response functions which peak at various positions on the logarithmic energy scale. Therefore, by collecting a set of count rates, one can unfold the neutron spectrum. The performance of the spectrometer was tested in an experiment, and the associated unfolding technique was tested numerically. The results were satisfactory.

Growth Curve Models of Repeated Binary Response

Experimental designs that include repeated measures of binary response variables over time and under different conditions are common in biology. In such settings, it is often desirable to characterize the response pattern over time. When response variables are continuous, this characterization can be made in terms of a growth model such as the Potthoff-Roy growth curve model. We illustrate how a similar growth curve modeling strategy can be implemented using weighted least squares (WLS) methods for binary response data. The growth models are constructed in terms of polynomial functions across marginal response. However, when growth models are fit to repeated binary response, the nonsignificant higher-order polynomial functions are dropped from the model, rather than used as covariates. Dropping the nonsignificant polynomials from the model will reduce the number of response functions, and help avoid small-sample problems that can occur when the number of correlated response functions is large and sample sizes are small. The reduced set of response functions are then modeled using WLS methods. We illustrate such models with an example of binary fly oviposition response (accept or reject) exhibited by two populations of flies at four ages to two types of fruit.

Sugar Beet N Fertilization and Economic Optima: Recoverable Sucrose vs. Root Yield1

AbstractSugar beet (Beta vulgaris L.) yields are frequently measured in terms of root yield but recoverable sucrose is the marketable product. The response of recoverable sucrose content to N fertilization differs from that of whole root yield. The rationale for this study was to compare N fertilization rates and associated returns under two decision rules: (1) fertilize to optimize recoverable sucrose yield and (2) fertilize to optimize whole root yield. Sets of response functions were estimated using both whole root yield and recoverable sucrose as measures of yield. Three years of data (1976‐1977‐1978) from the Northern Plains Soil and Water Research Center, Sidney, Mont., were used to derive these physical relationships. The estimated response functions were then combined with price and cost data to determine economically optimal N fertilization rates. Finally, returns for each optimal combination were calculated and compared. The results show substantially lower levels of N are required to optimize recoverable sucrose. Over the years of this analysis, it required approximately 90 kg less N per ha to optimize recoverable sucrose than whole root yield. More importantly, under the conditions of this analysis, producer returns would increase by an average of $460 per ha by using N rates consistent with recoverable sucrose rather than root yield. These observations suggest substantial economic benefits from use of recoverable sucrose in N fertilization decisions.

Lattice effects in the ferromagnetic response functions

A scheme is considered which allows the effect of a lattice on the set of response functions of a spin-polarised electron gas to be calculated. A viable computational scheme is investigated inside the density functional theory of electron systems, which contains both the local density approach and the generalised uniform gas limit as special cases. The dependence on magnetisation of the kernels involved in the Bloch wave corrections is investigated.