Admissible Parameter Research Articles

Stabilization of a weak viscoelastic wave equation in Riemannian geometric setting with an interior delay under nonlinear boundary dissipation

The stabilization of a weak viscoelastic wave equation with variable coefficients in the principal part of elliptic operator and an interior delay is considered. The dynamics is subject to a nonlinear boundary dissipation. This leads to a non-dissipative dynamics. The existence of solution is demonstrated by means of Faedo–Galerkin method combined with monotone operator theory in handling nonlinear boundary conditions. The main result pertains to exponential decay rates for energy, which depend on the geometry of the spatial domain, viscoelastic effects, the strength of delay and the strength of mechanical boundary damping. An important feature of the model is the fact that the delay term and stabilizing mechanism are not collocated geometrically — in contrast with many other works on the subject. This aspect of the problem requires the appropriate tools in order to exhibit propagation of the dissipation from one location to another. The precise ranges of admissible parameters characterizing the model and ensuring the stability are provided. The methods of proofs are routed in Riemannian geometry.

An analysis of the Crossbred Algorithm for the MQ Problem

The Crossbred algorithm is currently the state-of-the-art method for solving overdetermined multivariate polynomial systems over 𝔽 2 . Since its publication in 2017, several record breaking implementations have been proposed and demonstrate the power of this hybrid approach. Despite these practical results, the complexity of this algorithm and the choice of optimal parameters for it are difficult open questions. In this paper, we prove a bivariate generating series for potentially admissible parameters of the Crossbred algorithm.

Evaluation of a decomposition-based interpolation method for fourth-order fiber-orientation tensors: An eigensystem approach

We propose and assess a new decomposition-based interpolation method on fourth-order fiber-orientation tensors. This method can be used to change the resolution of discretized fields of fiber-orientation tensors, e.g., obtained from flow simulations or computer tomography, which are common in the context of short- and long-fiber–reinforced composites. The proposed interpolation method separates information on structure and orientation using a parametrization which is based on tensor components and a unique eigensystem. To identify this unique eigensystem of a given fourth-order fiber-orientation tensor in the absence of material symmetry, we propose a sign convention on tensor coefficients. We explicitly discuss challenges associated with material symmetries, e.g., non-distinct eigenvalues of the second-order fiber-orientation tensor and propose algorithms to obtain a unique set of parameters combined with a minimal number of eigensystems of a given fourth-order fiber-orientation tensor. As a side product, we specify for the first time, parametrizations and admissible parameter ranges of cubic, tetragonal, and trigonal fiber-orientation tensors. Visualizations in terms of truncated Fourier series, quartic plots, and tensor glyphs are compared.

A modified dyon solution in a non-Abelian gauge model

A modified SU(2) Georgi-Glashow model is considered here, and it is shown that besides the well-known Julia-Zee dyon solution, the model can also have a modified dyon solution. The properties of the modified dyon solution are studied using analytical and numerical methods. A comparative analysis of the modified dyon and the Julia-Zee dyon shows that their properties are significantly different. In particular, except for the BPS case, the energy and electric charge of the modified dyons exceed considerably those of the Julia-Zee dyons. At the same time, the energy and electric charge of the modified dyon are bounded for all admissible parameter values, whereas those of the Julia-Zee dyon can be arbitrarily large in the BPS case.

High-precision modelling of deformation of sandwich structures under bilateral symmetric and oblique-symmetric loading

The analysis and assessment of the stress-strain state (STS) of multilayer plates with orthotropic layers under the action of stationary transverse and tangential loads is an urgent task. It includes calculations on the strength and deformability of various homogeneous and multi-layered plates with layers of constant thickness but arbitrary structure according to the thickness of the plate. Combining materials with isotropic and transversely isotropic physical characteristics into a multilayer package allows you to create multifunctional structures. The SSS of such structures, due to their structural heterogeneity and relatively low transverse stiffness of the individual layers, is significantly associated with the influence of transverse shear deformations and transverse compression deformations. Therefore, the problem of refined modeling of SSS plates, which would take into account these types of deformations, is urgent. Based on the decomposition of the SSS plate into flexural and unflexural components, it is proposed to optimize the design scheme of deformation of a rectangular multilayer plate. This significantly simplifies its modeling. For unflexural and exclusively flexural SSS, a two-dimensional, high-degree iterative approximation, but three-dimensional models of deformation of multilayer rectangular plate on a rigid foundation with isotropic, transverse-isotropic and orthotropic layers are constructed in an elastic formulation. That models takes full account deformation of transverse shear and transverse compression at transverse and the tangential loading of a plate. The model is continuous, that is, the number of equations and the order of differentiation of the calculation system of equations does not depend on the number of layers in the slab. This order of differentiation and the number of calculation equations can depend only on the order of iterative approximation of the model. A way of precise satisfaction of all defining correlations of the layers of material under keeping the conditions of their contact is found, while in the known continual models the dependence between the cross normal stress and cross deformation is only integral.The results of the analytical solution of the problem of deformation of a rectangular plate under boundary conditions of the Navier type under the action of transverse and tangential loads are given. By solving the test problems of the deformation of two-layer plates with transversally isotropic layers and three-layer plates with orthotropic layers and comparing the solutions with the exact three-dimensional solutions of these problems obtained by known methods, an assessment of the accuracy of the proposed refined models is given. The limits of admissible parameters of elastic characteristics of transversely isotropic and orthotropic plates for application of the offered models are established.

Reliable stabilization of discrete-time nonlinear singular systems with time-varying delays

The problem of delay-dependent reliable control for uncertain discrete-time nonlinear singular system with time-varying delays is investigated. A new set of delay-dependent sufficient conditions are established for the existence of a reliable controller which ensures the singular system to be regular, causal (absence of impulses) and stable for all admissible parameter uncertainties. First, the controller for singular system in the presence of known actuator fault matrix is designed. Further, the result is extended to study the robust stabilization of singular systems with unknown actuator fault matrix. The sensor failures of actuator are considered by a variable, which is varying in a given interval. The conditions for the existence of proposed controller design are established in the form of linear matrix inequality (LMI), which can be easily solved via standard numerical software. Finally, numerical examples with simulation results are provided to illustrate the usefulness of control design and results are compared with existing results to show the less conservatism of the proposed theory.

Attractive Ellipsoid Technique for a Decentralized Passivity-Based Voltage Tracker for Islanded DC Microgrids

A new passivity-based voltage tracker for islanded Direct Current (DC) microgrids is presented in this paper. The proposed design develops a new sufficient condition for passivity-based state feedback with proportional and integral control using the attracting ellipsoid method. In this paper, we consider the time behavior of the extended vector, which completely describes the principle properties of the closed-loop system such as the boundedness of the trajectories within some ellipsoid and the dependence of its “size” on the feedback gains. The next step, which we are realizing in this paper, is the minimization of the attractive ellipsoid by selecting the “best” admissible feedback parameters. Here, it is important to note that the applied feedback is of PD-type (proportional differential) on the system state and I-type (integral) on the output. This is a new construction of the suggested feedback which gives several advantages for a designer. The suggested control is decentralized and uses only the local states; it is cost-effective and avoids the time delays in the communication networks which are needed if centralized control is used. The suggested control is carried out in the bilinear matrix inequality (BMI) framework. Extensive simulation is performed on a test system composed of renewable energy sources, under plug and play (PnP) operations, and uncertainties in distribution lines and loads. The performance of the proposed decentralized voltage controller is compared with that of a voltage tracker present in the literature. The comparison shows the improvements introduced by the proposed control ensure the stability of the dc bus voltage and a quick response under different scenarios of operating conditions.

TAIL RISK MONOTONICITY IN GARCH(1,1) MODELS

The stationary distribution of a GARCH(1,1) process has a power law decay, under broadly applicable conditions. We study the change in the exponent of the tail decay under temporal aggregation of parameters, with the distribution of innovations held fixed. This comparison is motivated by the fact that GARCH models are often fit to the same time series at different frequencies. The resulting models are not strictly compatible so we seek more limited properties we call forecast consistency and tail consistency. Forecast consistency is satisfied through a parameter transformation. Tail consistency leads us to derive conditions under which the tail exponent increases under temporal aggregation, and these conditions cover most relevant combinations of parameters and innovation distributions. But we also prove the existence of counterexamples near the boundary of the admissible parameter region where monotonicity fails. These counterexamples include normally distributed innovations.

On the Averaging and Closure of Fiber Orientation Tensors in Virtual Process Chains

Fiber orientation tensors (FOT) are widely used to approximate statistical orientation distributions of fibers within fiber-reinforced polymers. The design process of components made of such fiber-reinforced composites is usually accompanied by a virtual process chain. In this virtual process chain, process-induced FOT are computed in a flow simulation and transferred to the structural simulation. Within the structural simulation, effective macroscopic properties are identified based on the averaged information contained in the FOT. Solving the field equations in flow simulations as well as homogenization of effective stiffnesses necessitates the application of a closure scheme, computing higher-order statistical moments based on assumptions. Additionally, non-congruent spatial discretizations require an intermediate mapping operation. This mapping operation is required, if the discretization, i.e., mesh, of the flow simulation differs from the discretization of the structural simulation. The main objective of this work is to give an answer to the question: Does the sequence of closure and mapping influence the achieved results? It will turn out, that the order influences the result, raising the consecutive question: Which order is beneficial? Both questions are addressed by deriving a quantification of the closure-related uncertainty. The two possible sequences, mapping followed by closure and closure followed by mapping, yield strongly different results, with the magnitude of the deviation even exceeding the magnitude of a reference result. Graphical consideration reveals that for both transversely isotropic and planar FOT-input, invalid results occur if the mapping takes place prior to closure. This issue is retrieved by orientation averaging stiffness tensors. As a by-product, we explicitly define for the first time the admissible parameter space of orthotropic fourth-order fiber orientation tensors and define a distance measure in this parameter space.

EXPERIENCE OF SYNTHESIS OF MULTITOOL SETTINGS IN APPLICATION TO MODERN CONDITIONS

The trends in the production of special equipment for mass production are analyzed and the prospects for the use of multi-tool blocks for such equipment are established. The questions of synthesis of variants of multi-tool machining for parts with a large number of machined sides and machining surfaces are considered. Three groups of factors of a technological, geometrical and technical nature are established, which have a dominant influence on the compatibility of machining with tools in one tool block. Their allowable values and the proposed matrix of compatibility of technological operations performed are established. Based on the research carried out, a refined method for the synthesis of multi-tool blocks of special machine tools is proposed, the layout of which is based on the maximum use of unified modules and assemblies. This approach does not depend on the technological operations performed and on which modules can be used for the design implementation of the proposed tool block layout. The proposed method is focused on the use of computer-aided design systems in the process of creating machine tools with an aggregate-modular layout for mass production. It is based on the wide use of the knowledge base of the technical characteristics and technological capabilities of the modules used and makes it possible to initially configure the synthesis system for specific tasks solved at the enterprise by establishing admissible boundary parameters.

On the private and social incentives to adopt environmentally and socially responsible practices in a monopoly industry

This paper studies the incentives to adopt Environmental Corporate Social Responsibility (ECSR) in a multiproduct monopoly. In our framework, products are horizontally differentiated, production is polluting and a time-consistent government levies a tax on emissions. The ECSR monopolist may invest in R&D activities to reduce polluting emissions, while emission-reducing innovation may spillover from one product to the other. We show that the monopolist has no incentive to engage in ECSR, unless a regulatory measure is introduced. By contrast, a time consistent tax induces the adoption of a ECSR statute. Under admissible parameter conditions, profits are concave and single-peaked in the ECSR intensity. Finally, ECSR monotonically increases social welfare, by raising consumer surplus and curbing environmental damage.

The stability of present-day Antarctic grounding lines – Part 2: Onset of irreversible retreat of Amundsen Sea glaciers under current climate on centennial timescales cannot be excluded

Abstract. Observations of ocean-driven grounding-line retreat in the Amundsen Sea Embayment in Antarctica raise the question of an imminent collapse of the West Antarctic Ice Sheet. Here we analyse the committed evolution of Antarctic grounding lines under the present-day climate. To this aim, we first calibrate a sub-shelf melt parameterization, which is derived from an ocean box model, with observed and modelled melt sensitivities to ocean temperature changes, making it suitable for present-day simulations and future sea level projections. Using the new calibration, we run an ensemble of historical simulations from 1850 to 2015 with a state-of-the-art ice sheet model to create model instances of possible present-day ice sheet configurations. Then, we extend the simulations for another 10 000 years to investigate their evolution under constant present-day climate forcing and bathymetry. We test for reversibility of grounding-line movement in the case that large-scale retreat occurs. In the Amundsen Sea Embayment we find irreversible retreat of the Thwaites Glacier for all our parameter combinations and irreversible retreat of the Pine Island Glacier for some admissible parameter combinations. Importantly, an irreversible collapse in the Amundsen Sea Embayment sector is initiated at the earliest between 300 and 500 years in our simulations and is not inevitable yet – as also shown in our companion paper (Part 1, Hill et al., 2023). In other words, the region has not tipped yet. With the assumption of constant present-day climate, the collapse evolves on millennial timescales, with a maximum rate of 0.9 mm a−1 sea-level-equivalent ice volume loss. The contribution to sea level by 2300 is limited to 8 cm with a maximum rate of 0.4 mm a−1 sea-level-equivalent ice volume loss. Furthermore, when allowing ice shelves to regrow to their present geometry, we find that large-scale grounding-line retreat into marine basins upstream of the Filchner–Ronne Ice Shelf and the western Siple Coast is reversible. Other grounding lines remain close to their current positions in all configurations under present-day climate.

Optimal guaranteed cost control of discrete-time uncertain systems subjected to state saturation nonlinearity

This paper investigates the optimal guaranteed cost (GC) control problem for uncertain discrete-time (DT) systems with state saturation nonlinearities via static-state feedback. The parameter uncertainties in the system state and input matrix are considered to be norm bounded. Utilizing Lyapunov theory and sector-based characterization of saturation nonlinearities, a novel criterion for the existence of GC controllers is proposed. The criterion is expressed in the framework of linear matrix inequalities (LMIs) and is thus computationally tractable. The proposed GC controllers make the closed-loop (CL) system asymptotically stable and ensure an adequate level of performance for all admissible parameter uncertainties. To design an optimum GC controller, a convex optimization problem with LMI constraints is formulated. The effectiveness of the proposed approach is illustrated by examples.

Implementation of the Weak Link Problem for Trusses

This article examines the application of the theory of critical strain energy levels to the determination of the limiting states of rod systems. A redundant truss is chosen to illustrate the peculiarities of changes in the self-stressing states of the structure at critical strain energy levels. The removal of ties when they reach their stress or strain limits leads to a change in the state of self-stress in the structure, which is illustrated by the removal of the rods in the trusses. The matrix notation of the governing equations for the structure allows us to visualize both the formulation of the problem and the course of its solution. We present the formulation and algorithm for solving the problem of a weak link in the structure by the example of a five-core redundant truss. The basic equations of matrix structural mechanics are given, allowing us to implement the algorithm and to determine the unknown parameters of the problem in the form of the method of displacements and the method of forces. The mathematical model of the problem is presented in the form of an eigenvalues problem, which allows us to investigate the extreme properties of the structure’s strain energy in the whole area of admissible parameter values, including the boundaries. The eigenvalues and eigenvectors make it possible to determine the extreme values of the nodal reactive forces of the structure or displacements, depending on the chosen formulation of the problem. The internal forces and deformations in the rods depend on the nodal vectors of external influences. The applied design load is balanced by the internal forces of the system and remains unchanged. This follows from the equality of the work of external forces to a part of the potential energy of the structure. The remaining part of the strain energy allows us to find the limit values of the reactive response of the structure to external actions. Additional actions on the structure can lead to the bearing capacity lost if they exceed the limits of the structure’s response. Examples show an algorithm for finding the weak link in a structure and identifying the rods that will be the first to fail under external loads. The matrices of stiffness and flexibility are formed, and the eigenvalues and vectors are found, which allow for the construction of the limit surface of allowable influences on the structure.

Schematic 4-designs

We study 4-designs with three intersection numbers. By the Cameron-Delsarte theorem, the blocks form a symmetric three-class association scheme. This imposes strong restrictions on the parameters of such designs. We calculate the eigenvalues of the association scheme from the design parameters and determine all admissible parameters with at most 1000 points. An infinite family of admissible parameters is discovered. Designs with small admissible parameters exist and are related to the quadratic residue codes.

A Novel Approach to Parameter Determination of the Continuous Spontaneous Localization Collapse Model

Models of dynamical wave function collapse consistently describe the breakdown of the quantum superposition with the growing mass of the system by introducing non-linear and stochastic modifications to the standard Schrödinger dynamics. Among them, Continuous Spontaneous Localization (CSL) was extensively investigated both theoretically and experimentally. Measurable consequences of the collapse phenomenon depend on different combinations of the phenomenological parameters of the model-the strength λ and the correlation length rC-and have led, so far, to the exclusion of regions of the admissible (λ-rC) parameters space. We developed a novel approach to disentangle the λ and rC probability density functions, which discloses a more profound statistical insight.

Effective matrix designs for COVID-19 group testing

BackgroundGrouping samples with low prevalence of positives into pools and testing these pools can achieve considerable savings in testing resources compared with individual testing in the context of COVID-19. We review published pooling matrices, which encode the assignment of samples into pools and describe decoding algorithms, which decode individual samples from pools. Based on the findings we propose new one-round pooling designs with high compression that can efficiently be decoded by combinatorial algorithms. This expands the admissible parameter space for the construction of pooling matrices compared to current methods.ResultsBy arranging samples in a grid and using polynomials to construct pools, we develop direct formulas for an Algorithm (Polynomial Pools (PP)) to generate assignments of samples into pools. Designs from PP guarantee to correctly decode all samples with up to a specified number of positive samples. PP includes recent combinatorial methods for COVID-19, and enables new constructions that can result in more effective designs.ConclusionFor low prevalences of COVID-19, group tests can save resources when compared to individual testing. Constructions from the recent literature on combinatorial methods have gaps with respect to the designs that are available. We develop a method (PP), which generalizes previous constructions and enables new designs that can be advantageous in various situations.

Precautionary Saving in a Financially Constrained Firm

Abstract For a firm that cannot raise external funds, cash on hand serves as precautionary saving. We derive a closed-form expression for the target level of cash on hand in the presence of persistent cash flows. Contrary to conventional wisdom, a mean-preserving increase in the volatility of cash flow can decrease this target. Over the set of admissible parameter values, the average impact of volatility on the target is zero. Endogenous selection, reflecting termination of firms that run out of cash, leads to a positive average impact of volatility on the target level of cash, consistent with empirical findings.

ESTIMATION OF THE TOLERANCE AREA FOR CORRECTION PARAMETERS IN INDUCTION ACCELERATION SYSTEMS

The general statements of the problems of the normal functioning of the object in real modes are considered, within which the problems of evaluating the area of admissible parameters are formulated. The issues of formalizing the formulation of problems for calculating tolerances for parameters in the presence of dynamic restrictions with respect to fluctuations of the state vector of a real object are studied. For the purpose of numerical implementation of this kind of inverse problems, the application of practical stability algorithms for systems of differential equations dependent on parameters is proposed. For linear dynamic constraints on the spread of the vector of phase coordinates, a necessary and sufficient condition for the corresponding estimate of the area of deviations of the system parameters in a given structure is given. It is shown that in this concretization the problem of tolerance estimation is completely covered by the statements of stability problems. A class of problems related to the estimation of deviations of the vector of parameters from the calculated ones in the presence of a variation in the quality index is singled out. For the numerical implementation of the formulations of such problems, a linear system of differential equations depending on parameters with fixed initial conditions is studied. The analysis of the corresponding system of differential equations with respect to the spread of the state vector and parameters was carried out by methods of practical stability. Provided that the deviations of the values of the vector of parameters from the nominal are small enough, and the change in the vector of parameters within the tolerance field is linear, the expression for the variation of the quality indicator is presented in the form of a linear form. Within the framework of the formulations formulated, the area of tolerances for parameters is specified structurally in the form of an ellipsoid. The range of admissible parameters was estimated by finding the maximum of the linear form on the ellipsoid. A more complicated variant of the problem of estimating the maximum range of allowable values of the spread of the vector of parameters by the methods of practical directional stability is considered. The algorithms are extended to the case of a nonlinear change in the vector of parameters within the tolerance field and non-fixed initial conditions of the original system. In the applied plan, the considered problem statements are extended to a discrete model of an induction acceleration system for estimating the tolerance range for the correction parameters under given restrictions on the spread of the quality criterion.

Optimization of Parameters for ROI Data Compression for Nontargeted Analyses Using LC-HRMS.

Nontargeted analyses of low-concentration analytes in the information-rich data collected by liquid chromatography with high-resolution mass spectrometry detection can be challenging to accomplish in an efficient and comprehensive manner. The aim of this study is to demonstrate a workflow involving targeted parameter optimization for entire chromatograms using region of interest (ROI) data compression uncoupled from a subsequent tile-based Fisher ratio (F-ratio) analysis, a supervised discovery-based method, for the discovery of low-concentration analytes. Soil samples spiked with 18 pesticides at nominal concentrations ranging from 0.1 to 50 ppb for a total of six sample classes served as challenging samples to demonstrate the overall workflow. Optimization of two parameters proved to be the most critical for ROI data compression: the signal threshold parameter and the admissible mass deviation parameter. The parameter optimization method workflow we introduce is based upon spiking known analytes into a representative sample and determining the number of detectable spikes and the Δppm for various combinations of the signal threshold and admissible mass deviation, where Δppm is the absolute value of the difference between the theoretical m/z and the ROI m/z. Once optimal parameters are determined providing the lowest average Δppm and the greatest number of detectable analytes, the optimized parameters can be utilized for the intended analysis. Herein, tile-based F-ratio analysis was performed on the ROI compressed data of all spiked soil samples first by applying ROI parameters recommended in the literature, referred to herein as the initial ROI parameters, and finally by the combination of the two optimized parameters. Using the initial ROI parameters, three pesticides were discovered, whereas all 18 spiked pesticides were discovered by optimizing both ROI parameters.