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At least 343 records · Page 19

Fluid Transient Analysis during Priming of Evacuated Line

Water hammer analysis in pipe lines, in particularly during priming into evacuated lines is important for the design of spacecraft and other in-space application. In the current study, a finite volume network flow analysis code is used for modeling three different geometrical configurations: the first two being straight pipe, one with atmospheric air and other with evacuated line, and the third case is a representation of a complex flow network system. The numerical results show very good agreement qualitatively and quantitatively with measured data available in the literature. The peak pressure and impact time in case of straight pipe priming in evacuated line shows excellent agreement.

Bandyopadhyay, Alak↗

Development of three-dimensional models for WIPP performance assessment using PFLOTRAN - 15073

The Waste Isolation Pilot Plant (WIPP), located in southeastern New Mexico, has been developed by the U.S. Department of Energy (DOE) for the deep geologic disposal of transuranic (TRU) waste. WIPP performance assessment (PA) calculations estimate the probability and consequence of potential radionuclide releases from the repository to the accessible environment for a regulatory period of 10,000 years after facility closure. To date, WIPP PA calculations have employed multiple 2D numerical models requiring simplification of the mesh and processes. Introducing 3D numerical models within WIPP PA enables increasingly realistic representations of the WIPP subsurface domain and improved flexibility for incorporating relevant features. Furthermore, the increased computing capacity afforded by modern hardware architectures enables this 3D modeling. Modeling in 3D will be more flexible because less homogenization is required and better accuracy of the results can be obtained by making fewer assumptions and/or simplifications. The use of PFLOTRAN, a state-of-art massively parallel subsurface flow and reactive transport code, will enable this 3D modeling, and eliminate the need for multiple related, but decoupled 2D models. However, there are capabilities that PFLOTRAN must be demonstrated in order to fulfill requirements for WIPP PA. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Development of a Convolutional Neural Network Classifier for Data Starved Spectra - 20199

The Institute for Clean Energy Technology (ICET) at Mississippi State University is exploring the utility of machine learning in augmenting its mobile radiation surveying platforms, which are currently being developed as means to survey depleted uranium contaminated areas in support of remediation and decommissioning efforts. Mobile survey platforms provide a means to efficiently scan large areas of interest while reducing human exposure to radiation and other hazards. The survey platforms can also be used for scanning for any gamma emitting isotope in addition to depleted uranium. The spectral data that the platforms collect may be data starved with relatively low counts and poorly defined spectral features depending on the speed of the platforms and scintillation detector selection. Such data-starved spectra are difficult to use for isotope identification, requiring advanced knowledge of the possible radionuclides that could be present and environmental factors that could attenuate signals or introduce background noise. These factors in combination with the volume of survey data increases the time it takes to perform analysis of survey data when the source type is unknown. There are a number of algorithms in the field of machine learning that can be used to classify data that would be challenging and time-consuming for a human to identify. Supervised machine learning algorithms train models based on extensive amounts of human-labeled training data. Once sufficiently trained, these models can be used to quickly make high-fidelity predictions on new data. Convolutional neural networks are machine learning algorithms that excel in learning representations of 'shapes'. They do this by taking numerical input data and convolving them with spatial feature detectors referred to as filters. These filters are incrementally adjusted to reduce the prediction error on the data during the backpropagation step of training. Discussed in this paper is the development of a convolutional neural network classifier (CNNC) that can utilize spectral survey data for source discrimination and isotope identification. Bench-top laboratory experiments data using LaBr{sub 3}(Ce) scintillation detectors were used to train and evaluate the performance of the developed CNNC. The CNNC is capable of discriminating a variety of gamma emitting source types, differentiating different forms of uranium (depleted vs. natural), and estimating the amount of uranium for a known geometry. The discussed CNNC may be useful in scenarios where survey systems are deployed in situations where hazardous radioactive material maybe present, but the type is unknown. When used in remediation applications the CNNC can be used to screen-out false positives, helping reduce remediation costs. (authors)

07 ISOTOPE AND RADIATION SOURCES↗

Auxiliary matrix formalism for interaction representation transformations, optimal control, and spin relaxation theories

Auxiliary matrix exponential method is used to derive simple and numerically efficient general expressions for the following, historically rather cumbersome, and hard to compute, theoretical methods: (1) average Hamiltonian theory following interaction representation transformations; (2) Bloch-Redfield-Wangsness theory of nuclear and electron relaxation; (3) gradient ascent pulse engineering version of quantum optimal control theory. In the context of spin dynamics, the auxiliary matrix exponential method is more efficient than methods based on matrix factorizations and also exhibits more favourable complexity scaling with the dimension of the Hamiltonian matrix.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Experimental and Numerical Investigation of the NASA High Efficiency Centrifugal Compressor Vaned Stage Geometry and Aerodynamic Performance

Since its inception in the early 2010s, the NASA High Efficiency Centrifugal Compressor (HECC) has been enigmatic for the propulsion research community: experimental data and numerical simulations of the stage have generally not aligned in their quantifications of performance metrics. Typically, the fault for these disagreements is assigned to the numerical simulations as the simulations are models, and models are inherently incomplete representations of the experiment. This “incompleteness” may manifest in assumptions regarding roughness or heat transfer, simplifications of the flow path (i.e., neglecting bleed flows), or the oft-scapegoated turbulence model. In the case of HECC, recent work showed unexpected discrepancies between the intended impeller geometry defined in the design report (termed Design-Intent) and the manufactured impeller used in the experimental campaigns (termed As-Manufactured). That work used numerical simulations to establish that the geometric differences between the Design-Intent and As-Manufactured impellers were significant enough to result in drastically different performance predictions for the HECC vaneless diffuser configuration. The Design-Intent impeller simulations over predicted the performance relative to the experiment, whereas the As-Manufactured simulations better represented the experimental data, both in terms of one-dimensional performance metrics and spanwise flow profiles. This effort expands on that work by examining in detail the geometry and aerodynamic performance of the HECC vaned diffuser configuration. Further differences between the Design-Intent and As-Manufactured geometries have been discovered in the vaned diffuser and exit guide vanes, and these differences are documented herein. The summations of the geometric differences for all of the components were used to create two numerical models of HECC vaned diffuser configuration: the Design-Intent simulations which are generated from the original geometry definitions given in the design report and the As-Manufactured simulations which are the best available representation of the manufactured compressor hardware used in the experimental test campaigns. In congruence with the earlier vaneless diffuser work, the numerical predictions of the Design-Intent choked mass flow rate, total pressure ratio, and efficiency were notably greater than that of the As-Manufactured simulations. To increase confidence in the experimental dataset, measurements from a recent test campaign conducted in 2024 are used to validate the original experimental data acquired from 2012 to 2014 with good repeatability overall, especially considering the passage of time and differences in the data acquisition systems between the test campaigns. Both numerical simulations were then extensively evaluated against the experimental data. The As-Manufactured simulations provided better estimates of the stage performance than the Design-Intent cases in terms of most performance metrics. Nonetheless, more detailed results still show opportunities for improvement. Despite a more accurate representation of the physical hardware, characterization of the impeller work input remains a challenge even for rigorously developed numerical models.

vaned diffuser↗

Experimental and Numerical Investigation of the NASA High Efficiency Centrifugal Compressor Vaned Stage Geometry and Aerodynamic Performance

Since its inception in the early 2010s, the NASA High Efficiency Centrifugal Compressor (HECC) has been enigmatic for the propulsion research community: experimental data and numerical simulations of the stage have generally not aligned in their quantifications of performance metrics. Typically, the fault for these disagreements is assigned to the numerical simulations as the simulations are models, and models are inherently incomplete representations of the experiment. This “incompleteness” may manifest in assumptions regarding roughness or heat transfer, simplifications of the flow path (i.e., neglecting bleed flows), or the oft-scapegoated turbulence model. In the case of HECC, recent work showed unexpected discrepancies between the intended impeller geometry defined in the design report (termed Design-Intent) and the manufactured impeller used in the experimental campaigns (termed As-Manufactured). That work used numerical simulations to establish that the geometric differences between the Design-Intent and As-Manufactured impellers were significant enough to result in drastically different performance predictions for the HECC vaneless diffuser configuration. The Design-Intent impeller simulations over predicted the performance relative to the experiment, whereas the As-Manufactured simulations better represented the experimental data, both in terms of one-dimensional performance metrics and spanwise flow profiles. This effort expands on that work by examining in detail the geometry and aerodynamic performance of the HECC vaned diffuser configuration. Further differences between the Design-Intent and As-Manufactured geometries have been discovered in the vaned diffuser and exit guide vanes, and these differences are documented herein. The summations of the geometric differences for all of the components were used to create two numerical models of HECC vaned diffuser configuration: the Design-Intent simulations which are generated from the original geometry definitions given in the design report and the As-Manufactured simulations which are the best available representation of the manufactured compressor hardware used in the experimental test campaigns. In congruence with the earlier vaneless diffuser work, the numerical predictions of the Design-Intent choked mass flow rate, total pressure ratio, and efficiency were notably greater than that of the As-Manufactured simulations. To increase confidence in the experimental dataset, measurements from a recent test campaign conducted in 2024 are used to validate the original experimental data acquired from 2012 to 2014 with good repeatability overall, especially considering the passage of time and differences in the data acquisition systems between the test campaigns. Both numerical simulations were then extensively evaluated against the experimental data. The As-Manufactured simulations provided better estimates of the stage performance than the Design-Intent cases in terms of most performance metrics. Nonetheless, more detailed results still show opportunities for improvement. Despite a more accurate representation of the physical hardware, characterization of the impeller work input remains a challenge even for rigorously developed numerical models.

centrifugal compressor↗

Complex Representation of Potentials and Fields for the Nonlinear Magnetic Insert of the Integrable Optics Test Accelerator

An alternative representation for the vector potential of the nonlinear magnetic insert for the Integrable Optics Test Accelerator (IOTA), first described in Sec. V.A. of (Danilov and Nagaitsev), is determined from first principles using standard complex variable methods. In particular, it is shown that the coupled system consisting of the 2D Laplace equation and the Bertrand-Darboux equation is equivalent to a single ordinary differential equation in the complex plane, and a simple solution is constructed. The results are consistent with (Danilov and Nagaitsev), and this concise representation provides computational advantages for particle tracking through the nonlinear insert by avoiding numerical errors caused by small denominators that appear when evaluating transverse derivatives of the vector potential near the midplane. A similar representation is provided for the spatial dependence of the two invariants of motion.

43 PARTICLE ACCELERATORS↗

A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations I: Derivation and algorithms

We propose a dynamically bi-orthogonal method (DyBO) to solve time dependent stochastic partial differential equations (SPDEs). The objective of our method is to exploit some intrinsic sparse structure in the stochastic solution by constructing the sparsest representation of the stochastic solution via a bi-orthogonal basis. It is well-known that the Karhunen–Loeve expansion (KLE) minimizes the total mean squared error and gives the sparsest representation of stochastic solutions. However, the computation of the KL expansion could be quite expensive since we need to form a covariance matrix and solve a large-scale eigenvalue problem. The main contribution of this paper is that we derive an equivalent system that governs the evolution of the spatial and stochastic basis in the KL expansion. Unlike other reduced model methods, our method constructs the reduced basis on-the-fly without the need to form the covariance matrix or to compute its eigendecomposition. In the first part of our paper, we introduce the derivation of the dynamically bi-orthogonal formulation for SPDEs, discuss several theoretical issues, such as the dynamic bi-orthogonality preservation and some preliminary error analysis of the DyBO method. We also give some numerical implementation details of the DyBO methods, including the representation of stochastic basis and techniques to deal with eigenvalue crossing. In the second part of our paper [11], we will present an adaptive strategy to dynamically remove or add modes, perform a detailed complexity analysis, and discuss various generalizations of this approach. An extensive range of numerical experiments will be provided in both parts to demonstrate the effectiveness of the DyBO method.

97 MATHEMATICS AND COMPUTING↗

Fast computation of synthetic seismograms within a medium containing remote localized perturbations: a numerical solution to the scattering problem

We derive a fast discrete solution to the scattering problem. This solution allows us to compute accurate synthetic seismograms or waveforms for arbitrary locations of sources and receivers within a medium containing localized perturbations. The key to efficiency is that wave propagation modelling does not need to be carried out in the entire volume that encompasses the sources and the receivers but only within the subvolume containing the perturbations or scatterers. The proposed solution has important applications, for example, it permits the imaging of remote targets located in regions where no sources or receivers are present. Our solution relies on domain decomposition: within a small volume that contains the scatterers, wave propagation is modelled numerically, while in the surrounding volume, where the medium isn't perturbed, the response is obtained through wavefield extrapolation. The originality of this work is the derivation of discrete formulas for representation theorems and Kirchhof–Helmholtz integrals that naturally adapt to the numerical scheme employed for modelling wave propagation. Our solution applies, for example, to finite difference methods or finite/spectral elements methods. The synthetic seismograms obtained with our solution can be considered ‘exact’ as the total numerical error is comparable to that of the method employed for modelling wave propagation. We detail a basic implementation of our solution in the acoustic case using the finite difference method and present numerical examples that demonstrate the accuracy of the method. We show that ignoring some terms accounting for higher order scattering effects in our solution has a limited effect on the computed seismograms and significantly reduces the computational effort. Finally, we show that our solution can be used to compute localized sensitivity kernels and we discuss applications to target oriented imaging. Extension to the elastic case is straightforward and summarized in a dedicated section.

97 MATHEMATICS AND COMPUTING↗

Lax-Oleinik-Type Formulas and Efficient Algorithms for Certain High-Dimensional Optimal Control Problems

Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high dimension. In this paper, we provide analytical solutions to certain optimal control problems whose running cost depends on the state variable and with constraints on the control. We also provide Lax-Oleinik-type representation formulas for the corresponding Hamilton-Jacobi partial differential equations with state-dependent Hamiltonians. Additionally, we present an efficient, grid-free numerical solver based on our representation formulas, which is shown to scale linearly with the state dimension, and thus, to overcome the curse of dimensionality. Using existing optimization methods and the min-plus technique, we extend our numerical solvers to address more general classes of convex and nonconvex initial costs. We demonstrate the capabilities of our numerical solvers using implementations on a central processing unit (CPU) and a field-programmable gate array (FPGA). In several cases, our FPGA implementation obtains over a 10 times speedup compared to the CPU, which demonstrates the promising performance boosts FPGAs can achieve. Furthermore, our numerical results show that our solvers have the potential to serve as a building block for solving broader classes of high-dimensional optimal control problems in real-time.

97 MATHEMATICS AND COMPUTING↗

A Parametric Study of Fine-scale Turbulence Mixing Noise

The present paper is a study of aerodynamic noise spectra from model functions that describe the source. The study is motivated by the need to improve the spectral shape of the MGBK jet noise prediction methodology at high frequency. The predicted spectral shape usually appears less broadband than measurements and faster decaying at high frequency. Theoretical representation of the source is based on Lilley's equation. Numerical simulations of high-speed subsonic jets as well as some recent turbulence measurements reveal a number of interesting statistical properties of turbulence correlation functions that may have a bearing on radiated noise. These studies indicate that an exponential spatial function may be a more appropriate representation of a two-point correlation compared to its Gaussian counterpart. The effect of source non-compactness on spectral shape is discussed. It is shown that source non-compactness could well be the differentiating factor between the Gaussian and exponential model functions. In particular, the fall-off of the noise spectra at high frequency is studied and it is shown that a non-compact source with an exponential model function results in a broader spectrum and better agreement with data. An alternate source model that represents the source as a covariance of the convective derivative of fine-scale turbulence kinetic energy is also examined.

Khavaran, Abbas↗

Direct numerical simulations of a reacting turbulent mixing layer by a pseudospectral-spectral element method

An account is given of the implementation of the spectral-element technique for simulating a chemically reacting, spatially developing turbulent mixing layer. Attention is given to experimental and numerical studies that have investigated the development, evolution, and mixing characteristics of shear flows. A mathematical formulation is presented of the physical configuration of the spatially developing reacting mixing layer, in conjunction with a detailed representation of the spectral-element method's application to the numerical simulation of mixing layers. Results from 2D and 3D calculations of chemically reacting mixing layers are given.

Mcmurtry, Patrick A.↗

Quantifying the Influence of Size, Shape, and Density of Microplastics on Their Transport Modes: A Modeling Approach

Microplastics (MPs) pose significant risks to marine ecosystems and human health, necessitating accurate predictions of their distributions in aquatic environments for effective risk mitigation. However, understanding MP transport dynamics is challenging because of the inadequate representation of MP characteristics such as size, shape, and density in numerical models. Further, the accuracy of the MP vertical profiles in existing models has not been thoroughly validated. Thus, we developed an MP transport model within the Finite Volume Community Ocean Model framework (FVCOM-MP) by integrating MP characteristics. We validated FVCOM-MP against experimental and analytical data, focusing on various MP transport modes and transitions. FVCOM-MP successfully replicates MP profiles in different transport modes, including the bedload, surface-load, suspended-load, and mixed-load modes. Additionally, we introduce phase diagrams for classifying MP transport modes based on particle characteristics, enhancing our understanding of MP dynamics in aquatic systems. The transport modes for a number of real-world MP particles, including fishing line, plastic bag/bottle fragments, synthetic fibers, tire wear particles, polyvinyl chloride and expanded polystyrene pellets, were analyzed with these phase diagrams.

Microplastic transport, Settling velocity, Rising ↗

Advancements in the Representation of Cloud-Aerosol Microphysics in the GEOS-5 AGCM

Despite numerous challenges, the physical parameterization of cloud-aerosol interactions in atmospheric GCMs has become a top priority for advancement because of our need to simulate and understand past, current, and future indirect effects of aerosols on clouds. The challenges stem from the involvement of wide range of cloud-scale dynamics and aerosol activation physical processes. Cloud dynamics modulate cloud areal extent and condensate, while aerosol activation depends on aerosol mass load, size distribution, internal mixing state, and nucleating properties, and ultimately determines cloud optical properties via particle sizes. Both macro- and micro-scale processes are obviously important for cloud-radiation interactions. We will present the main features of cloud microphysical properties in the GEOS- 5 Atmospheric GCM (AGCM) as simulated by the McRAS-AC (Microphysics of Clouds with Relaxed Arakawa-Schubert and Aerosol-Cloud interaction) scheme. McRAS-AC uses Fountoukis and Nenes (2005) aerosol activation for liquid clouds, and has an option for either Liu and Penner (2005) or Barahona and Nenes (2008, 2009) aerosol activation for ice clouds. Aerosol loading (on-line or climatological) comes from GOCART, with an assumed log-normal size distribution. Other features of McRAS-AC are level-by-level cloud-scale thermodynamics, and Seifert-Beheng (2001)-type precipitation microphysics, particularly from moist convection. Results from Single-Column Model simulations will be shown to demonstrate how cloud radiative properties, lifetimes, and precipitation are influenced by different parameterization assumptions. Corresponding fields from year-long simulations of the full AGCM will also be presented with geographical distributions of cloud effective particle sizes compared to satellite retrievals. While the primary emphasis will be on current climate, simulation results with perturbed aerosol loadings will also be shown to expose the radiative sensitivity of the microphysical parameterization.

Lee, D.↗

WORKSHOP ON URBAN SCALE PROCESSES AND THEIR REPRESENTATION IN HIGH SPATIAL RESOLUTION EARTH SYSTEM MODELS

It is essential that numerical models used to study physics, chemistry, and biology affecting the Earth system at regional and global scales represent the effects of urban areas on climate and the effects of changing the climate on urban areas. At the same time, it is essential to develop state of the art, simple and accurate urban models to better understand the relevant processes and also toaddress issues related to urban security against the spectra of chemical, biological and radiological (CBR) hazards. Towards bringing these communities together, a 2.5-day international workshop was held at Argonne National Laboratory (ANL) in the Chicago area on May 22-24, 2019. This workshop brought together national and international experts to develop a roadmap for a better understanding of the issues associated with urban areas and at enhancing the capabilities of regional and global Earth System models (ESMs) in representing the atmospheric dynamics and chemistry, unique aspects of the biosphere and land use, and human dimensions of the urban environment. This workshop was especially important to those developing very high-resolution versions of regional and global models. The workshop also discussed existing datasets, including in situ and satellite observations, and the emerging smart city sensing technologies and their possible use in model development (e.g., the NSF-funded Array of Things network currently operating in Chicago and expanding to other cities).

54 ENVIRONMENTAL SCIENCES↗

Fast arithmetic in MacLISP

MacLISP provides a compiler which produces numerical code competitive in speed with some FORTRAN implementations and yet compatible with the rest of the MacLISP system. All numerical programs can be run under the MacLISP interpreter. Additional declarations to the compiler specify type information which allows the generation of optimized numerical code which generally does not require the garbage collection of temporary numerical results. Array accesses are almost as fast as in FORTRAN, and permit the use of dynamically allocated arrays of varying dimensions. The implementation decisions regarding user interface, data representations, and interfacing conventions are discussed which allow the generation of fast numerical LISP code.

Steele, G. L., Jr.↗

Stochastic level-set variational implicit-solvent approach to solute-solvent interfacial fluctuations

Recent years have seen the initial success of a variational implicit-solvent model (VISM), implemented with a robust level-set method, in capturing efficiently different hydration states and providing quantitatively good estimation of solvation free energies of biomolecules. The level-set minimization of the VISM solvation free-energy functional of all possible solute-solvent interfaces or dielectric boundaries predicts an equilibrium biomolecular conformation that is often close to an initial guess. In this work, we develop a theory in the form of Langevin geometrical flow to incorporate solute-solvent interfacial fluctuations into the VISM. Such fluctuations are crucial to biomolecular conformational changes and binding process. We also develop a stochastic level-set method to numerically implement such a theory. We describe the interfacial fluctuation through the “normal velocity” that is the solute-solvent interfacial force, derive the corresponding stochastic level-set equation in the sense of Stratonovich so that the surface representation is independent of the choice of implicit function, and develop numerical techniques for solving such an equation and processing the numerical data. We apply our computational method to study the dewetting transition in the system of two hydrophobic plates and a hydrophobic cavity of a synthetic host molecule cucurbit[7]uril. Numerical simulations demonstrate that our approach can describe an underlying system jumping out of a local minimum of the free-energy functional and can capture dewetting transitions of hydrophobic systems. In the case of two hydrophobic plates, we find that the wavelength of interfacial fluctuations has a strong influence to the dewetting transition. In addition, we find that the estimated energy barrier of the dewetting transition scales quadratically with the inter-plate distance, agreeing well with existing studies of molecular dynamics simulations. Our work is a first step toward the inclusion of fluctuations into the VISM and understanding the impact of interfacial fluctuations on biomolecular solvation with an implicit-solvent approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Gamow shell model description of proton scattering on 18 Ne

Background: The structure of weakly bound/unbound nuclei close to particle drip lines is different from that around the valley of beta stability. A comprehensive description of these systems goes beyond the standard shell model (SM) and demands an open quantum system description of the nuclear many-body system. Purpose: For that purpose, we are using the Gamow shell model (GSM) in this study, which provides a fully microscopic description of bound and unbound nuclear states, nuclear decays, and reactions. Here, we formulate the GSM in coupled-channel (GSM-CC) representation to describe low-energy elastic and inelastic scattering of protons on $\mathrm{^{18}Ne}$. Method: The GSM-CC formalism is applied to a translationally invariant Hamiltonian with an effective finite-range two-body interaction. We discuss in detail the GSM-CC formalism in coordinate space and give the description of the novel equivalent potential method for solving the GSM-CC system of integrodifferential equations. This method is then applied for the description of ($p, p'$) reaction cross-sections. The reactions channels are built by GSM wave functions for the ground state $\mathrm{0^+}$ and the first excited $\mathrm{2^+}$ of $\mathrm{^{18}Ne}$ and a proton wave function expanded in different partial waves. The completeness of this basis is verified by comparing GSM and GSM-CC energies of low-energy resonant states in $\mathrm{^{19}Na}$. The differences between the two calculations provide a measure of the missing configurations in the GSM-CC calculation of low-energy states of $\mathrm{^{19}Na}$ due to the restriction on the number of excited states of $\mathrm{^{18}Ne}$. Results: We present the first application of the GSM-CC formalism for the calculation of excited states of $\mathrm{^{18}Ne}$ and $\mathrm{^{19}Na}$, the excitation function, and the elastic/inelastic differential cross-sections in the $\mathrm{^{18}Ne}$ ($p,p'$) reaction at different energies. This is the first unified description of the spectra and reaction cross-sections in the GSM formalism. The method is shown to be both feasible and accurate. The approximate equivalence of GSM and GSM-CC in describing spectra of $\mathrm{^{19}Na}$ has been demonstrated numerically. Conclusions: The GSM in the coupled-channel representation opens a possibility for the unified description of low-energy nuclear structure and reactions using the same Hamiltonian. While both GSM and GSM-CC can describe energies, widths, and wave functions of the many-body states, the GSM-CC can in addition yield reaction cross-sections. The combined application of GSM and GSM-CC to describe energies of resonant states allows to test the exactitude of calculated cross-sections for a given many-body Hamiltonian.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗