Stability Estimates Research Articles

Effect of personalized spinal profile on its biomechanical response in an EMG-assisted optimization musculoskeletal model of the trunk

Recent developments in musculoskeletal (MS) modeling have been geared towards model customization. Personalization of the spine profile could affect estimates of spinal loading and stability, particularly in the upright standing posture where large inter-subject variations in the lumbar lordosis have been reported. This study investigates the biomechanical consequences of changes in the spinal profile.In 31 participants (healthy and with back pain), (1) the spine external profile was measured, (2) submaximal contractions were recorded in a dynamometer to calibrate the EMG-driven MS model and finally (3) static lifting in the upright standing challenging spine stability while altering load position and magnitude were considered. EMG signals of 12 trunk muscles and angular kinematics of 17 segments were recorded. For each participant, the MS model was constructed using either a generic or a personalized spinal profile and 17 biomechanical outcomes were computed, including individual muscle forces, ratios of muscle group forces, spinal loading and stability parameters.According to the ANOVA results and corresponding effect sizes, personalizing the spine profile induced medium and large effects on about half MS model outcomes related to the trunk muscle forces and negligible to small effects on spinal loading and stability as more aggregate outcomes.These effects are explained by personalized spine profiles that were a little more in extension as well as more pronounced spine curvatures (lordosis and kyphosis). These findings suggest that spine profile personalization should be considered in MS spine modeling as it may impact muscle force prediction and spinal loading.

A stability estimate for data assimilation subject to the heat equation with initial datum

A stability estimate for data assimilation subject to the heat equation with initial datum

PERANCANGAN MEKANISASI PANEN TANAMAN BATANG RUMPUT DENGAN PEMOTONG TIPE SIRKULAR MENGGUNAKAN PEMODELAN INVENTOR®

In general, traditional farmers still use the manual method which requires a large number of workers and takes longer for one hectare. With this mechanization, it is hoped that the time and cost at harvest will be faster and cheaper. It is hoped that this harvester can not only be used on one type of grass stalks plant (eg. rice) but can also be used for other types of grass stalks plants (lemongrass, sticky rice, straw). This paper produces a design using Inventor 3D to describe a mechanization system for harvesting grass stalks using a circular harvester. The crucial analysis carried out on the carrier, focuses on three things, namely the estimation of power system requirements, estimation of harvest capacity and system stability. Fits the speed-adjusting lever and the lever adjusts the height of the cutter. In its application can be used on wet land or dry land. The conclusion from the calculation is that the driving force is sufficient to move the body and cutting blades, the design capacity exceeds twice that of the manual method, and in practice the body is still stable when passing through land with an elevation of 30 degrees.

Stability and error estimates of Strang splitting method for the nonlocal ternary conservative Allen–Cahn model

The nonlocal model has attracted a great attention in materials science for describing various types of material heterogeneities and defects. In this study, we consider a nonlocal ternary conservative Allen–Cahn model, where the standard Laplace operator is intentionally replaced with a spatial convolution term that aims at describing long-range interactions among particles. A linear energy stable scheme is developed based on the operator splitting method. The mass conservation, energy stability and global convergence of the new scheme are analyzed rigorously. Numerical stability and convergence of the present numerical scheme are analyzed theoretically. Two and three dimensional numerical experiments are performed to validate the theoretical analysis and the efficiency of the method.

Stability estimates for an inverse problem for Schrödinger operators at high frequencies from arbitrary partial boundary measurements

In this paper, we study the partial data inverse boundary value problem for the Schrödinger operator at a high frequency in a bounded domain with smooth boundary in , . Assuming that the potential is known in a neighborhood of the boundary, we obtain the logarithmic stability when both Dirichlet data and Neumann data are taken on arbitrary open subsets of the boundary where the two sets can be disjointed. Our results also show that the logarithmic stability can be improved to the one of Hölder type in the high frequency regime. To achieve those goals, we used a method by combining the CGO solution, Runge approximation and Carleman estimate.

The bodily threat monitoring scale: Development and preliminary validation in adult and childhood cancer survivors.

Bodily threat monitoring is a core clinical feature of Fear of cancer recurrence (FCR) and is targeted in psycho-oncology treatments, yet no comprehensive self-report measure exists. The aim of this study was the theory-informed development and initial validation of the Bodily Threat Monitoring Scale (BTMS). Adult survivors of breast and gynaecological cancers (Study 1: N=306, age=37-81years) and childhood cancer survivors (Study 2: N=126, age=10-25years) completed the BTMS, designed to assess how individuals monitor for and interpret uncertain symptoms as indicating that something is wrong with their body. Participants completed measures to assess construct and criterion validity of the BTMS, and childhood cancer survivors (Study 2) completed the BTMS again 2weeks later to assess test-retest reliability. The 19-item BTMS demonstrated excellent internal consistency across adult and childhood cancer samples (α=0.90-0.96). Factor analyses indicated two subscales capturing 1. Monitoring of bodily sensations and 2. Threatening interpretations of bodily sensations. Two-week stability estimates were acceptable. For construct validity, the BTMS correlated with body vigilance and anxiety sensitivity. The BTMS also demonstrated criterion validity, yielding significant associations with FCR, intolerance of uncertainty, help-seeking behaviours, and quality of life. The BTMS was associated with FCR while controlling for body vigilance and anxiety sensitivity, indicating a unique contribution of this theory-informed measure. The BTMS shows evidence of sound psychometric properties and could be used to elucidate the role of bodily threat monitoring in the maintenance and management of FCR.

Stability estimates for the expected utility in Bayesian optimal experimental design

We study stability properties of the expected utility function in Bayesian optimal experimental design. We provide a framework for this problem in a non-parametric setting and prove a convergence rate of the expected utility with respect to a likelihood perturbation. This rate is uniform over the design space and its sharpness in the general setting is demonstrated by proving a lower bound in a special case. To make the problem more concrete we proceed by considering non-linear Bayesian inverse problems with Gaussian likelihood and prove that the assumptions set out for the general case are satisfied and regain the stability of the expected utility with respect to perturbations to the observation map. Theoretical convergence rates are demonstrated numerically in three different examples.

Three-Level Schemes with Double Change in the Time Step

Nonstationary problems are solved numerically by applying multilevel (with more than two levels) time approximations. They are easy to construct and relatively easy to study in the case of uniform grids. However, the numerical study of application-oriented problems often involves approximations with a variable time step. The construction of multilevel schemes on nonuniform grids is associated with maintaining the prescribed accuracy and ensuring the stability of the approximate solution. In this paper, three-level schemes for the approximate solution of the Cauchy problem for a second-order evolution equation are constructed in the special case of a doubled or halved step size. The focus is on the approximation features in the transition between different step sizes. The study is based on general results of the stability (well-posedness) theory of operator-difference schemes in a finite-dimensional Hilbert space. Estimates for stability with respect to initial data and the right-hand side are obtained in the case of a doubled or halved time step.

A STABILITY ESTIMATE IN THE SOURCE PROBLEM FOR THE RADIATIVE TRANSFER EQUATION

It is given a stability estimate of a solution of a source problem for the stationary radiative transfer equation. It is suppose that the source is an isotropic distribution. Earlier stability estimates for this problem were known in a partial case of the emission tomography problem only, when the scattering operator vanishes, and for the complete transfer equation under additional and difficult in checking conditions for the absorption coefficient and the scattering kernel. In the present work, we suggest a new and enough simple approach for obtaining a stability estimate for the problem under the consideration. The transfer equation is considered in a circle of the two-dimension space. In the forward problem, it is assumed that incoming radiation is absent. In the inverse problem for recovering the unknown source some data for solutions of the forward problem related to outgoing radiation are given. The obtained result can be used for an estimation of the summary density of distributed sources of the radiation.

Stability of the Quermassintegral Inequalities in Hyperbolic Space

For the quermassintegral inequalities of horospherically convex hypersurfaces in the (n+1)-dimensional hyperbolic space, where nge 2, we prove a stability estimate relating the Hausdorff distance to a geodesic sphere by the deficit in the quermassintegral inequality. The exponent of the deficit is explicitly given and does not depend on the dimension. The estimate is valid in the class of domains with upper and lower bound on the inradius and an upper bound on a curvature quotient. This is achieved by some new initial value-independent curvature estimates for locally constrained flows of inverse type.

Convolution kernel determination problem for the time-fractional diffusion equation

In this work, we study the inverse problem of determining the convolution kernel in the Cauchy problem for the time-fractional diffusion equation by a single observation at the point x=0 of the diffusion process. To represent the solution of the direct problem, the fundamental solution of the time-fractional diffusion equation is constructed. In particular, using estimates of the fundamental solution and its derivatives, an estimate for the solution of the direct problem is obtained in terms of the norm of the unknown kernel function which will be used for the study inverse problem. The inverse problem is reduced to the equivalent integral equation of the Volterra type. By the contracted mapping principle, the local existence and global uniqueness results are proven. Also the stability estimate is obtained.

Stability and error estimates of GPAV-based unconditionally energy-stable scheme for phase field crystal equation

In this article, we propose a linear, second-order, semi-discrete time stepping scheme for the phase field crystal equation based on generalized positive auxiliary variable (GPAV) approach. This scheme reduces the operation counts by half compared to the GPAV and the scalar auxiliary variable methods in previous works. We prove the unconditionally energy stability and provide bounds and error estimates for the field function. Numerical experiments are carried out to verify our theoretical results and demonstrate the robustness and accuracy of the proposed scheme.

New Zealand Fault-Rupture Depth Model v.1.0: A Provisional Estimate of the Maximum Depth of Seismic Rupture on New Zealand’s Active Faults

ABSTRACT We summarize estimates of the maximum rupture depth on New Zealand’s active faults (“New Zealand Fault-Rupture Depth Model v.1.0”), as used in the New Zealand Community Fault Model v1.0 and as a constraint for the latest revision of the New Zealand National Seismic Hazard Model (NZ NSHM 2022). Rupture depth estimates are based on a combination of two separate model approaches (using different methods and datasets). The first approach uses regional seismicity distribution from a relocated earthquake catalog to calculate the 90% seismicity cutoff depth (D90), representing the seismogenic depth limit. This is multiplied by an overshoot factor representing the dynamic propagation of rupture into the conditional stability zone, and accounting for the difference between regional seismicity depths and the frictional properties of a mature fault zone to arrive at a seismic estimate of the maximum rupture depth. The second approach uses surface heat flow and rock type to compute depths that correspond to the thermal limits of frictional instabilities on seismogenic faults. To arrive at a thermally-based maximum rupture depth, these thermal limits are also multiplied by an overshoot factor. Both the models have depth cutoffs at the Moho and/or subducting slabs. Results indicate the maximum rupture depths between 8 (Taupō volcanic zone) and >30 km (e.g., southwest North Island), strongly correlated with regional thermal gradients. The depths derived from the two methods show broad agreement for most of the North Island and some differences in the South Island. A combined model using weighting based on relative uncertainties is derived and validated using constraints from hypocenter and slip model depths from recent well-instrumented earthquakes. We discuss modifications to the maximum rupture depths estimated here that were undertaken for application within the NZ NSHM 2022. Our research demonstrates the utility of combining seismicity cutoff and thermal stability estimates to assess the down-dip dimensions of future earthquake ruptures.

A quantitative stability result for the Prékopa–Leindler inequality for arbitrary measurable functions

We prove that if a triplet of functions satisfies almost-equality in the Prékopa–Leindler inequality, then these functions are close to a common log-concave function, up to multiplication and rescaling. Our result holds for general measurable functions in all dimensions, and provides a quantitative stability estimate with computable constants.

An Operator Method for Investigation of the Stability of Time-Dependent Source Identification Telegraph Type Differential Problems

This article is devoted to the study of the stability of time-dependent source identification telegraph type differential problems with dependent coefficients. Time-dependent source identification problems (SIPs) for telegraph differential equations (TDEs) with constant coefficients can be solved by classical integral-transform methods. However, these classical methods can be used, basically, in cases where the differential equation has constant coefficients. We establish the basic theorem of the stability of the time-dependent SIPs for the second-order linear differential equation (DE) in a Hilbert space with a self-adjoint positive definite operator (SAPDO) and damping term. In practice, stability estimates for the solution of the three types of SIPs for one-dimensional and for multidimensional TDEs with dependent coefficients and classic and non-classic conditions are obtained.

Nonlinear vibrational analysis and linearization error investigation in size-dependent resonant pressure microsensors

Dynamic and vibrational behavior of nonlinear resonant pressure micro sensors is studied in this paper using a proposed dynamic model. The basic part of the device is a microplate deflects due to external pressure in presence of electrostatic actuation. The frequency changes because of the microplate deformation is used to estimate the external pressure. For modeling of the micro sensor, the nonlinear governing equation of size dependent microplate in polar coordinate system and based on the modified couple stress theory is presented. Assuming specified number of Taylor expansion terms for electrostatic force, the linear and nonlinear ODE is obtained and nonlinear equation is solved both with multiple time scales method (MTS) and finite difference numerical method. Results indicate that considering finite terms of Taylor expansion (1 term for linear and three terms for MTS method) is the source of error in estimation of pressure or system stability. Using sufficient terms of Taylor Expansion, the error in linear and MTS solutions is vanished. Therefore, the limited values of microplate vibrational amplitude is extracted to increase the accuracy of the sensor in linear action. The effect of size dependency, applied voltage on nonlinear behavior and linearization error is also studied.

Large Time Behavior and Stability for Two-Dimensional Magneto-Micropolar Equations with Partial Dissipation

This paper is devoted to the stability and decay estimates of solutions to the two-dimensional magneto-micropolar fluid equations with partial dissipation. Firstly, focus on the 2D magneto-micropolar equation with only velocity dissipation and partial magnetic diffusion, we obtain the global existence of solutions with small initial in H^s({mathbb {R}}^2)(s>1), and by fully exploiting the special structure of the system and using the Fourier splitting methods, we establish the large time decay rates of solutions. Secondly, when the magnetic field has partial dissipation, we show the global existence of solutions with small initial data in dot{B}^0_{2,1}({mathbb {R}}^2). In addition, we explore the decay rates of these global solutions are correspondingly established in dot{B}^m_{2,1}({mathbb {R}}^2) with 0 le m le s, when the initial data belongs to the negative Sobolev space dot{H}^{-l}({mathbb {R}}^2) (for each 0 le l <1).

Convexification for the viscocity solution for a coefficient inverse problem for the radiative transfer equation

A coefficient inverse problem for the radiative transport equation is considered. The globally convergent numerical method, the so-called convexification, is developed. For the first time, the viscosity solution is considered for a boundary value problem for the resulting system of two coupled partial differential equations. A Lipschitz stability estimate is proved for this boundary value problem using a Carleman estimate for the Laplace operator. Next, the global convergence analysis is provided via that Carleman estimate. Results of numerical experiments demonstrate a high computational efficiency of this approach.

A local energy-based discontinuous Galerkin method for fourth-order semilinear wave equations

Abstract This paper proposes an energy-based discontinuous Galerkin scheme for fourth-order semilinear wave equations, which we rewrite as a system of second-order spatial derivatives. Compared to the local discontinuous Galerkin methods, the proposed scheme uses fewer auxiliary variables and is more computationally efficient. We prove several properties of the scheme. For example, we show that the scheme is unconditionally stable and that it achieves optimal convergence in $L^2$ norm for both the solution and the auxiliary variables without imposing penalty terms. A key part of the proof of the stability and convergence analysis is the special choice of the test function for the auxiliary equation involving the time derivative of the displacement variable, which leads to a linear system for the time evolution of the unknowns. Then we can use standard mathematical techniques in discontinuous Galerkin methods to obtain stability and optimal error estimates. We also obtain energy dissipation and/or conservation of the scheme by choosing simple and mesh-independent interelement fluxes. Several numerical experiments are presented to illustrate and support our theoretical results.

Real-time transient stability estimation of power system considering nonlinear limiters of excitation system using deep machine learning: An actual case study in Iran

One of the most important features of a reliable power system is its capability to supply the demand continuously. This continuous supply has been maintained by the transient stability of the system against large disturbances. The study of this type of stability is examined through different indicators. One of the common indicators to evaluate the transient stability of the power system is the well-known Critical Clearing Time (CCT) index. Conventional methods for calculating CCT have presented good accuracy, however, their computational cost is very high which makes them not suitable for real-time applications and real large-scale networks. Considering their ability to feature extraction of big data, deep neural networks can be utilized as reliable tools to cover these deficiencies. In this regard, to cover the shortcomings of the conventional methods, this paper proposes a method based on deep Convolutional Neural Networks (CNN) to estimate the CCT index in real-time power system applications. Moreover, to analyze a realistic case, nonlinear limiters of the excitation systems which have a considerable effect on transient stability index are considered in this study. Thanks to the using of several deep layers and the comprehensive established database, the accuracy of proposed method is appropriately high. Numerical studies on IEEE standard networks as well as a real case in Iran Power Grid (IPG) represents the advantages of the proposed method.