Linear Term Research Articles

DEVELOPMENT AND ASSESSMENT OF MANUAL AND AUTOMATED PID CONTROLLERS FOR THE OPTIMUM PRODUCTION OF ETHYLENE GLYCOL IN A CSTR

Industrially, one of the techniques used to enhance the optimum production of petrochemicals is the configuration of process control units such as gas chromatography (G.C. Analyzer) for concentration and thermocouple for temperature in the production system. This research focused on the application of the principles of mass and energy conservation in the development of dynamic or unsteady state models for predicting the behaviour of the system or process involved in the production of ethylene glycol from a reaction involving oxidation of ethylene-to-ethylene oxide which further undergoes hydrolysis to produce ethylene glycol in a continuous stirred tank reactor (CSTR). The high mathematical complexities of the mass and energy balance models of the Process as a result of the reaction kinetic scheme of the non-elementary reaction of the process which integrated both linear and non-linear terms into the models were resolved by the application of the principles of Taylor’s series expansion, Laplace Transform, partial fraction and matrix in the development of the dynamic models. Process simulation tool (Simulink) was utilized in the configuration of closed-loop systems with thermocouple and G. C. Analyzer, at the feed point of the reactor for process variables (temperature and concentration) control during the process using proportional, integral and derivative (PID) as controller parameters. The results of the process behaviour showed that manual tuning of different controller parameters experienced a high level of fluctuations and would not attain its stability or steady state even at a processing time above 16 seconds. Whereas, automatic tuning of desired controller gains of 1.361, 1.056 and 0.4109 for K P, K I and K D for temperature and pressure with a tuning time of 143.9 Seconds, requires a maximum time of 8 seconds for the system to attain stability. This study showed that automated tuning of the controller resulted in better performance characteristics for optimum production of ethylene glycol in a non-isotheral continuous stirred tank reactor within the shortest possible time.

Associations of actigraph sleep characteristics with blood pressure among older adults

ObjectivesMany studies have examined links between sleep and blood pressure, with mixed findings, mostly using self-reported sleep data and cross-sectional designs. We examined whether actigraph-estimated sleep characteristics are associated with concurrent blood pressure or 5-year blood pressure change in a national cohort of older adults (National Social Life, Health and Aging Project), and whether these associations differ by hypertension medication use. MethodsSubjects were 669 older adults (62-90years), 471 with 5-year follow-up data. Sleep characteristics were duration (linear plus quadratic terms); sleep percentage; and categorical onset, midpoint, and waking times. Multivariable linear models adjusted for age, race, gender, obesity, smoking, daytime napping, and hypertension medication use. Interactions between sleep characteristics and hypertension medication were tested among the 401 subjects with consistent hypertension medication status over time. ResultsWe found U-shaped cross-sectional and longitudinal relationships between duration and blood pressure, with shorter and longer sleep times associated with higher blood pressure. Later onset times were cross-sectionally associated with higher systolic blood pressure, while earlier onset times were longitudinally associated with systolic blood pressure increase. Midpoint, wake time, and sleep percentage were not significantly associated with blood pressure. Significant interaction terms suggested hypertension medications attenuated associations of sleep onset and wake time with diastolic blood pressure. ConclusionsThese results with actigraph-estimated parameters confirm some, but not all, associations reported from research based on self-reported sleep data. Our findings are consistent with recommended intermediate sleep durations for cardiovascular health and suggest hypertension medication use may attenuate some associations between sleep timing and blood pressure.

The impact of different strategies for modeling associations between medications at low doses and health outcomes: a simulation study and practical application to postpartum opioid use.

Pharmacoepidemiological studies commonly examine the association between drug dose and adverse health outcomes. In situations where no safe dose exists, the choice of modeling strategy can lead to identification of an apparent safe low dose range in the presence of a non-linear relationship or due to the modeling strategy forcing a linear relationship through a dose of 0. We conducted a simulation study to assess the performance of several regression approaches to model the drug dose-response curve at low doses in a setting where no safe range exists, including the use of a (1) linear dose term, (2) categorical dose term, and (3) natural cubic spline terms. Additionally, we introduce and apply an expansion of prior work related to modeling dose-response curves at low and infrequently used doses in the setting of no safe dose ("spike-at-zero" and "slab-and-spline"). Furthermore, we demonstrate and empirically assess the use of these regression strategies in a practical scenario examining the association between the dose of the initial postpartum opioid prescribed after vaginal delivery and the subsequent total dose of opioids prescribed in the entire postpartum period among a cohort of opioid-naïve women with a vaginal delivery enrolled in a State Medicaid program (2007-2014).

The Influence of Emotional Facial Expression Intensity on Decoding Accuracy: High Intensity Does Not Yield High Accuracy

AbstractThis study examined the relationship between the intensity of emotional expressions in facial stimuli and receivers' decoding accuracy for six basic emotions: anger, disgust, fear, happiness, sadness, and surprise. A laboratory experiment was conducted using the forced‐choice method, in which the intensity of each stimulus was manipulated at every 10% interval using the morphing technique. To explore whether a linear relationship would be observed when the intensity was finely manipulated at 10% intervals, a hierarchical multiple regression analysis was performed. The mean percentage of correct responses for each stimulus was the dependent variable, and the linear, quadratic, and cubic terms of the stimulus intensity were the independent variables. The results showed that the linear model was not adopted as the final model for all facial expressions; that is, the effect of the squared term of intensity was significant for anger, disgust, fear, and sadness, while the effect of the cubic term of intensity was significant for happiness and surprise. Our findings indicate that a higher intensity of emotional expression does not yield higher decoding accuracy.

New pairing mechanism via chiral electron–hole condensation for non-BCS superconductivity

A novel chiral electron–hole (CEH) pairing mechanism is proposed to account for non-BCS superconductivity. In contrast to BCS Cooper pairs, CEH pairs exhibit a pronounced affinity to antiferromagnetism for superconductivity. The gap equations derived from this new microscopic mechanism are analyzed for both s- and d-wave superconductivity, revealing marked departures from the BCS theory. Unsurprisingly, CEH naturally describes superconductivity in strongly-correlated systems, necessitating an exceedingly large coupling parameter (λ>1 for s-wave and λ>π/2 for d-wave) to be efficacious. The new mechanism provides a better understanding of various non-BCS features, especially in cuprate and iron-based superconductors. In particular, CEH, through quantitative comparison with experimental data, shows promise in solving long-standing puzzles such as the unexpectedly large gap-to-critical-temperature ratio Δ0/Tc, the lack of gap closure at Tc, superconducting phase diagrams, and a non-zero heat-capacity-to-temperature ratio C/T at T=0 (i.e., the “anomalous linear term”), along with its quadratic behavior near T=0 for d-wave cuprates.

State estimation and structure identification of complex networks with time‐varying delays and model uncertainty based on probabilistic graph neural network

SummaryIn this paper, the state estimation problem and structure identification problem are investigated for an array of complex networks with time‐varying delays and model uncertainty. Model uncertainty is generated by uncertain connections between nodes in complex networks. Combining probabilistic graph model and graph neural network, a probabilistic graph neural network is proposed to deal with the uncertainty, and the multiple linear terms of the errors between nodes are estimated. The purpose of the addressed state estimation problem is to design a state estimator such that, in the presence of the model uncertainty, the estimation error to converge to zero can be guaranteed and the explicit expression of the estimator parameters is given. Based on a Lyapunov function, the parameters of the estimator and the updating laws of the weights of probabilistic graph neural network can be obtained by the solutions to linear matrix inequalities. The purpose of the addressed structure identification problem is to infer a definite graph structure model based on Bayes' theorem in the presence of a stable probabilistic graph neural network and state estimator. Finally, an illustrative example is provided to demonstrate the feasibility and effectiveness of the developed state estimation and structure identification scheme.

Operation optimization of cogeneration microgrid based on deep reinforcement learning

Abstract The deep Q learning method is adopted to transform the microgrid model into the Markov decision model to realize the coordinated management and energy optimization of the microgrid. For the problem of the Markov decision model, we cleverly divide the working state of the gas turbine into different gears to meet its requirements. To reduce the fitting difficulty and improve the result accuracy and convergence stability, a linear penalty term was added to the reward function. Considering the operating and environmental costs, in addition to the purchase and sale price of a large power grid, peak and valley electricity price and operation constraints, we further reduce the peak and valley difference and reduce the operating cost. Finally, the output of the battery and the output of the distributed power supply are obtained through simulation verification. Through the peak-shifting and valley-filling function of the battery, it can effectively deal with the fluctuation of peak and valley electricity prices, reducing the peak and valley difference of electric heating load, and providing strong support for sustainable energy management.

Gravitational waves from domain wall collapses and dark matter in the SM with a complex scalar field

We study a domain wall induced by spontaneously broken Z2 symmetry and its gravitational wave signature in the standard model with a complex scalar in connection with dark matter physics. In a minimal setup, a linear term of the singlet field is added to the scalar potential as an explicit Z2 breaking term to make the domain wall unstable. We obtain its minimal size from cosmological constraints and show that the parameter space that can be probed by current and future pulsar time array experiments requires the vacuum expectation value of the singlet field to be greater than O(10–100) TeV, along with a singletlike Higgs mass of O(1–100) TeV. However, such a region is severely restricted by the dark matter relic density, which places an upper bound on the singlet vacuum expectation value at approximately 200 TeV, and limits the dark matter mass to about half of the singletlike Higgs boson mass. Published by the American Physical Society 2024

A general computational framework for Lagrangian hydrodynamic scheme. I: Unification of staggered‐grid and cell‐centered methods

AbstractThis paper focuses on a general computational framework to unify both Lagrangian staggered‐grid hydrodynamic (SGH) and cell‐centered hydrodynamic (CCH) methods. One challenge is that artificial viscosity has contained empirical parameters in the SGH method for seven decades. To address this challenge, a new relationship between pressure and velocity is constructed using specific volume as a medium. Another challenge is that entropy is increasing in isentropic flows for the CCH method. To overcome this second challenge, the forces acting on a target cell are split into linear and quadratic terms in the CCH method. The numerical results of the two methods are almost identical. The scheme is more general than both existing SGH and CCH methods.

Partially explicit splitting scheme with explicit–implicit-null method for nonlinear multiscale flow problems

In this work, we present an efficient approach to solve nonlinear high-contrast multiscale diffusion problems. We incorporate the explicit–implicit-null (EIN) method to separate the nonlinear term into a linear term and a damping term, and then utilize the implicit and explicit time marching scheme for the two parts respectively. Due to the multiscale property of the linear part, we further introduce a temporal partially explicit splitting scheme and construct suitable multiscale subspaces to speed up the computation. The approximated solution is split into these subspaces associated with different physics. The temporal splitting scheme employs implicit discretization in the subspace with small dimension that representing the high-contrast property and uses explicit discretization for the other subspace. We exploit the stability of the proposed scheme and give the condition for the choice of the linear diffusion coefficient. The convergence of the proposed scheme is provided. Several numerical tests are performed to show the efficiency and accuracy of the proposed scheme.

Linear dynamics of a thick liquid layer subjected to an oblique temperature gradient

The present study aims to demonstrate the application of the oblique temperature gradient (OTG) to manipulate the buoyancy instabilities and resulting mixing. To accomplish this, we consider a model consisting of a liquid layer supported by a perfectly conducting bottom wall from below and the upper surface is exposed to ambient inert gas in a shallow container. The stability analysis employs the pseudospectral method and perturbation energy budget approach. The imposed OTG consists of a negative vertical temperature gradient (VTG), which leads to unstable density stratification, and a negative horizontal temperature gradient (HTG) component responsible for the Hadley circulation, which can be utilised to control instabilities. Without the HTG, a Rayleigh–Bénard mode of instability exists due to the imposed VTG termed as a VTG mode. The imposed HTG induces a linear VTG term and a quintic polynomial VTG term in the bottom wall-normal coordinate $y$ . The induced linear VTG term reinforces the imposed VTG, while the induced quintic polynomial VTG term opposes the imposed VTG. For the vanishing Biot number ( $Bi$ ), the induced quintic VTG term stabilises the VTG mode for the Prandtl number, $Pr=7$ . However, for $Pr=0.01$ , the Reynolds stresses associated with the Hadley circulation destabilise the VTG mode. For non-zero $Bi$ , new streamwise and spanwise instability modes arise for $Pr=7$ due to the induced linear VTG term. Physical arguments show that the unstable density stratification near the gas–liquid interface caused by the synergistic effect of the imposed VTG and the induced linear VTG term lead to the existence of the predicted new modes. The present study thus shows that the strength of the HTG can be utilised to control the instability modes and critical parameters, thereby demonstrating the utility of the OTG in manipulating the buoyancy instabilities.

The relationship between dietary total flavonoids and thyroid function in U.S.adults, NHANES 2007-2010.

Although small studies have shown that flavonoids can affect thyroid disease, few epidemiological studies have explored the relationship between dietary total flavonoids (TFs) intake and serum thyroid function. The aim of this research was to evaluate the relationship between TFs and serum thyroid function. Our study included 4,949 adults from the National Health and Nutrition Examination Survey (NHANES) 2007-2010. Multivariable linear regression, subgroup analyses, and interaction terms were used to explore the relationships between TFs and thyroid function. And we also used restricted cubic splines (RCS) to investigate possible nonlinear relationships. After adjusting for covariates, we found that log10-transformated dietary total flavonoids intake (LgTFs) was negatively associated with total thyroxine (TT4) (β = -0.153, 95% CI = -0.222 to -0.084, P<0.001). Subgroup analyses revealed a stronger and statistically supported association in subjects with high annual family income (β = -0.367, P<0.001, P for interaction = 0.026) and subjects with high poverty to income ratio (PIR) (β = -0.622, P<0.001, P for interaction = 0.042). And we found a U-shaped curve association between LgTFs and free triiodothyronine (FT3) (inflection point for LgTFs: 2.063). The results of our study demonstrated that a higher intake of total flavonoids in the diet was negatively associated with a lower TT4. Furthermore, the associations were more pronounced in high annual family income and high PIR adults. And we found a U-shaped relationship between LgTFs and FT3. These findings provided guidance for future thyroid dysfunction diet guidelines.

Driven generalized quantum Rayleigh-van der Pol oscillators: Phase localization and spectral response.

Driven classical self-sustained oscillators have been studied extensively in the context of synchronization. Using the master equation, this work considers the classically driven generalized quantum Rayleigh-van der Pol oscillator, which is characterized by linear dissipative gain and loss terms as well as three nonlinear dissipative terms. Since two of the nonlinear terms break the rotational phase space symmetry, the Wigner distribution of the quantum mechanical limit cycle state of the undriven system is, in general, not rotationally symmetric. The impact of the symmetry-breaking dissipators on the long-time dynamics of the driven system are analyzed as functions of the drive strength and detuning, covering the deep quantum to near-classical regimes. Phase localization and frequency entrainment, which are required for synchronization, are discussed in detail. We identify a large parameter space where the oscillators exhibit appreciable phase localization but only weak or no entrainment, indicating the absence of synchronization. Several observables are found to exhibit the analog of the celebrated classical Arnold tongue; in some cases, the Arnold tongue is found to be asymmetric with respect to vanishing detuning between the external drive and the natural oscillator frequency.

Statistically consistent inverse optimal control for discrete-time indefinite linear–quadratic systems

The Inverse Optimal Control (IOC) problem is a structured system identification problem that aims to identify the underlying objective function based on observed optimal trajectories. This provides a data-driven way to model experts’ behavior. In this paper, we consider the case of discrete-time finite-horizon linear–quadratic problems where: the quadratic cost term in the objective is not necessarily positive semi-definite; the planning horizon is a random variable; we have both process noise and observation noise; the dynamics can have a drift term; and where we can have a linear cost term in the objective. In this setting, we first formulate the necessary and sufficient conditions for when the forward optimal control problem is solvable. Next, we show that the corresponding IOC problem is identifiable. Using the conditions for existence of an optimum of the forward problem, we then formulate an estimator for the parameters in the objective function of the forward problem as the globally optimal solution to a convex optimization problem, and prove that the estimator is statistical consistent. Finally, the performance of the algorithm is demonstrated on two numerical examples.

Mild Solutions for w-Weighted, Φ-Hilfer, Non-Instantaneous, Impulsive, w-Weighted, Fractional, Semilinear Differential Inclusions of Order μ ∈ (1, 2) in Banach Spaces

The aim of this work is to obtain novel and interesting results for mild solutions to a semilinear differential inclusion involving a w-weighted, Φ-Hilfer, fractional derivative of order μ∈(1,2) with non-instantaneous impulses in Banach spaces with infinite dimensions when the linear term is the infinitesimal generator of a strongly continuous cosine family and the nonlinear term is a multi-valued function. First, we determine the formula of the mild solution function for the considered semilinear differential inclusion. Then, we give sufficient conditions to ensure that the mild solution set is not empty or compact. The desired results are achieved by using the properties of both the w-weighted Φ-Laplace transform, w-weighted ψ-convolution and the measure of non-compactness. Since the operator, the w-weighted Φ-Hilfer, includes well-known types of fractional differential operators, our results generalize several recent results in the literature. Moreover, our results are novel because no one has previously studied these types of semilinear differential inclusions. Finally, we give an illustrative example that supports our theoretical results.

An extended incremental technique for solving economic dispatch with practical considerations

This work develops a mixed-integer incremental model to solve economic dispatch (ED) with practical challenges of prohibited operating zones (POZs), transmission losses, and valve loading effects (VLE). The first challenge, the POZ, disconnects ED feasible space. The second challenge arises from transmission losses and imposes bilinear terms on ED. The VLE, in the third challenge, renders the ED objective function non-smooth and nonconvex. Due to the practical challenges, a disconnected and multimodal solution space arises, requiring a tailored solver. This work presents an extended incremental (Ext-Inc) technique to fulfill the requirement. The Ext-Inc enforces the POZs by using auxiliary variables and logical constraints. Moreover, the Ext-Inc uses linear combinatorial terms to represent the nonconvex VLEs and bilinear terms. The Ext-Inc is evaluated through ED case studies. The Ext-Inc finds the optimal cost of 1,016,279 $/h, 24,512 $/h, 62,456 $/h, 32,704 $/h, 121,412 $/h, 653,645 $/h in 10-unit, 13-unit, 15-unit, 20-unit, 40-unit, and 200-unit respectively. These findings either replicate or enhance the solution documented in previous studies, demonstrating the effectiveness of the Ext-Inc in addressing real-world challenges. Moreover, the proposed method demonstrates remarkable efficiency, solving single-period ED case studies in under 3 seconds and the multi-period case study within one minute.

Convergence analysis of a decoupled pressure-correction SAV-FEM for the Cahn–Hilliard–Navier–Stokes model

In this paper, a linear, decoupled and unconditional energy-stable numerical scheme of Cahn–Hilliard–Navier–Stokes (CHNS) model is constructed and analyzed. We reformulate the CHNS model into an equivalent system based on the scalar auxiliary variable approach. The Euler implicit/explicit scheme is used for time discretization, that is, linear terms are implicitly processed, nonlinear terms are explicitly processed, and pressure-correction method of the Navier–Stokes equations is also adopted. In this way, we achieve the decoupling of phase field, velocity and pressure, and only need to solve a series of linear equations with constant coefficients at each time step, thereby improving computational efficiency. Then the finite element method is used for space discretization, and the finite element spaces of phase field, velocity and pressure are taken as Pl−Pl−Pl−1 respectively. We also verify that the proposed scheme satisfies the discrete energy dissipation law. The optimal error estimates of the fully discrete scheme is proved, which the phase field, velocity and pressure satisfy the first-order accuracy in time and the (ℓ+1,ℓ+1,ℓ)th order accuracy in space, respectively. Finally, numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.

Association between hydrometeorological conditions and infectious diarrhea in mainland China: a spatiotemporal modeling study

Infectious diarrhea imposes substantial disease burden in China, with local climate identified as a key risk factor. In this study, we aimed to explore the association between hydrometeorological conditions and the incidence of infectious diarrhea, and investigate the modification effect of urbanization, which remained unclear previously. Monthly data were collected from 1 January 2021 to 31 December 2022 from each city of mainland China on cases of infectious diarrhea other than cholera, dysentery, typhoid and paratyphoid (i.e. other infectious diarrhea, OID), temperature and precipitation. We used Palmer drought severity index (PDSI) to represent local hydrometeorological conditions (dry and wet). A spatiotemporal Bayesian hierarchical model combined with distributed lag nonlinear model was specified to explore the association between PDSI and the relative risk of OID. The effect size of hydrometeorological conditions at different urbanization levels were quantified through a linear interaction term. A total of 1999 947 OID cases were included. There was a N-shaped cumulative association between PDSI and OID incidence over a maximum lag of 4 months. The effect of extreme dry conditions persisted over lag 1–3 months and peaked at the 2-month lag (RR = 2.67, 95%CI: 2.44–2.91). By contrast, the relative risk of OID increased immediately under extreme wet conditions (RR = 1.97, 95%CI: 1.68–2.32 at lag 0 month). Children and the older population were particularly susceptible to extreme dry and wet conditions, respectively. Areas with lower urbanization rate, healthcare resources and economic levels, and higher population density showed a higher risk of OID related to extreme dry conditions. While the modification effects of these urbanization characteristics were limited for extreme wet conditions. There was a nonlinear and lagged association between hydrometeorological conditions and the incidence of OID in mainland China, which may be modified in diverse patterns by urbanization indicators. Our findings will provide valuable reference for better prevention and control of OID.

Influence of time-to-diagnosis on time-to-percutaneous coronary intervention for emergency department ST-elevation myocardial infarction patients: Time-to-electrocardiogram matters.

Earlier electrocardiogram (ECG) acquisition for ST-elevation myocardial infarction (STEMI) is associated with earlier percutaneous coronary intervention (PCI) and better patient outcomes. However, the exact relationship between timely ECG and timely PCI is unclear. We quantified the influence of door-to-ECG (D2E) time on ECG-to-PCI balloon (E2B) intervention in this three-year retrospective cohort study, including patients from 10 geographically diverse emergency departments (EDs) co-located with a PCI center. The study included 576 STEMI patients excluding those with a screening ECG before ED arrival or non-diagnostic initial ED ECG. We used a linear mixed-effects model to evaluate D2E's influence on E2B with piecewise linear terms for D2E times associated with time intervals designated as ED intake (0-10 min), triage (11-30min), and main ED (>30min). We adjusted for demographic and visit characteristics, past medical history, and included ED location as a random effect. The median E2B interval was longer (76vs 68 min, p<0.001) in patients with D2E>10 min than in those with timely D2E. The proportion of patients identified at the intake, triage, and main ED intervals was 65.8%, 24.9%, and 9.7%, respectively. The D2E and E2B association was statistically significant in the triage phase, where a 1-minute change in D2E was associated with a 1.24-minute change in E2B (95% confidence interval [CI]: 0.44-2.05, p=0.003). Reducing D2E is associated with a shorter E2B. Targeting D2E reduction in patients currently diagnosed during triage (11-30 min) may be the greatest opportunity to improve D2B and could enable 24.9% more ED STEMI patients to achieve timely D2E.

Discrete analogues in harmonic analysis: A theorem of Stein-Wainger

For d≥2,D≥1, let Pd,D denote the set of all degree d polynomials in D dimensions with real coefficients without linear terms. We prove that for any Calderón-Zygmund kernel, K, the maximally modulated and maximally truncated discrete singular integral operator,supP∈Pd,D,N⁡|∑0<|m|≤Nf(x−m)K(m)e2πiP(m)|, is bounded on ℓp(ZD), for each 1<p<∞. Our proof introduces a stopping time based off of equidistribution theory of polynomial orbits to relate the analysis to its continuous analogue, introduced and studied by Stein-Wainger:supP∈Pd,D⁡|∫RDf(x−t)K(t)e2πiP(t)dt|.