Parameter Dependence Research Articles

Wind Farm Power Maximisation via Wake Steering: A Gaussian Process‐Based Yaw‐Dependent Parameter Tuning Approach

ABSTRACTMaximising the power production of wind farms is vital to meet the growing demand for wind energy and reduce its cost. Wake effects, resulting from the aerodynamic interactions between turbines in a wind farm, significantly impact farm efficiency, leading to substantial annual power losses. Wake steering, an influential control strategy, involves mitigating wake effects by strategically yaw misaligning upstream turbines to deflect their wakes. Conventional wake steering approaches typically rely on physics‐based analytical wake models with their parameters often calibrated using higher fidelity data. However, these approaches determine a fixed set of parameters prior to conducting wake steering, neglecting each parameter's dependency on yaw misalignment (i.e. the optimisation variables) exhibited throughout the optimisation process, potentially affecting its accuracy. To address this limitation, this paper introduces a novel data‐driven parameter tuning approach that integrates higher fidelity power measurements using Gaussian processes to continuously adapt parameters in lower fidelity wake models based on the current farm's yaw configuration. The effectiveness of the proposed approach is demonstrated on a wind farm and a layout corresponding to the Horns Rev wind farm, where various wind directions are investigated. The results reveal that the approach can enable a lower fidelity model to capture more complex physics, thereby improving its accuracy in wake steering optimisation, while maintaining robustness and computational efficiency. This method holds promise for real‐time control applications and can be extended to other control strategies and closed‐loop frameworks.

Assessment of a multiphase formulation of one-dimensional turbulence using direct numerical simulation of a decaying turbulent interfacial flow

The interaction between turbulence and surface tension is studied numerically using the one-dimensional-turbulence (ODT) model. ODT is a stochastic model simulating turbulent flow evolution along a notional one-dimensional line of sight by applying instantaneous maps that represent the effects of individual turbulent eddies on property fields. It provides affordable high resolution of interface creation and property gradients within each phase, which are key for capturing the local behavior as well as overall trends, and has been shown to reproduce the main features of an experimentally determined regime diagram for primary jet breakup. Here ODT is used to investigate the interaction of turbulence with an initially planar interface. The notional flat interface is inserted into a periodic box of decaying homogeneous isotropic turbulence, simulated for a variety of turbulent Reynolds and Weber numbers. Unity density and viscosity ratios serve to focus solely on the interaction between fluid inertia and the surface-tension force. Statistical measures of interface surface density and spatial structure along the direction normal to the initial surface are compared to corresponding direct-numerical-simulation (DNS) data. Allowing the origin of the lateral coordinate system to follow the location of the median interface element improves the agreement between ODT and DNS, reflecting the absence of lateral nonvortical displacements in ODT. Beyond the DNS-accessible regime, ODT is shown to obey the predicted parameter dependencies of the Kolmogorov critical scale in both the inertial and dissipative turbulent-cascade subranges. Notably, the probability density function of local fluctuations of the critical scale is found to collapse to a universal curve across both subranges. Published by the American Physical Society 2024

The Higgs boson decay h → bs in the U(1)XSSM

In the U(1)XSSM, we delve into the quark flavor violation of h → bs, where h is identified as the SM-like Higgs boson discovered at the LHC. As the U(1) extension of the minimal supersymmetric standard model (MSSM), the U(1)XSSM has new super fields such as right-handed neutrinos and three Higgs singlets. We conduct a thorough analysis of the underlying mechanisms and parameter dependencies of h → bs in the U(1)XSSM. In the U(1)XSSM, we discover that the Br(h → bs) for the Higgs decay to bs could significantly differ from the expectation in the standard model (SM), depending on the values of the new parameters introduced in the model. Our research not only contributes to a deeper understanding of Higgs physics within the U(1)XSSM, but also provides valuable guidance for new physics (NP).

Existence of Three Positive Solutions for Boundary Value Problem of Fourth Order with Sign-Changing Green’s Function

In this paper, we examine a fourth-order equation that has parameter dependency and boundary conditions in three different places. We prove some of the features of the relevant asymmetric Green’s function and infer its exact form. The resulting solutions are still positive and decreasing functions on the entire interval of the Green’s function definition, and they are concave in a specific subinterval, despite the fact that the function’s sign changes on the square of its definition. The fixed point theorem of Krasnoselskii is the foundation of the existence arguments. Next, using the Leggett–Williams fixed point theorem, it is concluded that there are at least three positive solutions. Lastly, an example is provided, to highlight the primary findings of the manuscript.

Analysis of a brake squeal functional model using a linear parameter varying perspective

Brake squeal is a limit cycle vibration induced by mode coupling instability that depends on operating conditions such as applied pressure, temperature, and disc velocity. This work proposes a simplified functional model of brake squeal that reproduces the main characteristics observed in a full-scale industrial test campaign: vibration growth, limit cycle saturation, vibration decay and parametric dependence. The proposed functional model differs from the well-known Hoffmann model by the introduction of a nonlinear contact law and a quasi-static pressure loading. First, using a harmonic balance perspective, non-linear forces are shown to lead to a pressure and amplitude dependent contact stiffness. This Linear Parameter Varying perspective allows complex mode computations in the pressure/amplitude domain which are then correlated with a series of transient responses of the nonlinear modes for three different pressure profiles. The chosen profiles represent usual experiments: drag where a constant pressure is applied, pressure ramps and pressure oscillations mimicking the effect of wheel spin on the contact surfaces.

An impedance spectroscopy study to unravel the effect of water on proton and oxygen transport in PEM fuel cells

A recent physics-based model for liquid and gaseous water transport in the cathode catalyst layer (CCL) is incorporated into our 1d ＋ 1d model for the PEM fuel cell impedance. The model includes parametric dependencies of the CCL oxygen diffusivity and proton conductivity on the liquid saturation. Fitting of the 1d ＋ 1d model to experimental impedance spectra of a PEM fuel cell reveals two intriguing effects. Contrary to common belief, the liquid water saturation in the CCL is nearly independent of cell current density due to the growing liquid pressure gradient that drives liquid water removal from the CCL. Further, the “dry” oxygen diffusivity of the catalyst layer increases with cell current density. Apparently, at small current density, electrochemical conversion proceeds primarily in narrow pores, where the Knudsen oxygen diffusivity is low. With growing current density, larger and better connected pores with higher oxygen diffusivity dominate in the current conversion, leading to increase in effective oxygen diffusivity observed in impedance spectroscopy data.

Reliability analysis of cutting tools using transformed inverse Gaussian process-based wear modelling considering parameter dependence

Reliability analysis is crucial for ensuring the performability of the desired function. The cutting tool performs the machining operation at varied conditions to manufacture diverse products. During operation, the tool degrades stochastically in the form of wear. To avoid the unfavourable consequences occurring from severe tool wear, appropriate formulation of the tool reliability, considering threshold degradation level as the failure criterion, is crucial. However, the degradation of the tool during machining is impacted by the current state of the tool wear and operating conditions. Considering these, the present study proposes a state-dependent transformed inverse Gaussian (TIG) process incorporating the effects of operating conditions to develop the tool wear model. In order to evaluate the proposed method, tool wear experiments are conducted at different operating conditions following the Taguchi orthogonal array experimental design. The experimental data are utilised to estimate the parameters of the developed model using the Bayesian approach. Following the parameter estimation, tool reliability is evaluated under varying operating conditions. The comparison of the estimated median time to failure of the tools with the failure time observed in the validation experiments ensures the effectiveness of the proposed model. The proposed approach has the potential to estimate the reliability of the industrial products subjected to state-dependent degradation under varied operating conditions.

Tayler Instability Revisited

Tayler instability of toroidal magnetic fields B ϕ is broadly invoked as a trigger for turbulence and angular momentum transport in stars. This paper presents a systematic revision of the linear stability analysis for a rotating, magnetized, and stably stratified star. For plausible configurations of B ϕ , instability requires diffusive processes: viscosity, magnetic diffusivity, or thermal/compositional diffusion. Our results reveal a new physical picture, demonstrating how different diffusive effects independently trigger instability of two types of waves in the rotating star: magnetostrophic waves and inertial waves. It develops via overstability of the waves, whose growth rate sharply peaks at some characteristic wavenumbers. We determine instability conditions for each wave branch and find the characteristic wavenumbers. The results are qualitatively different for stars with magnetic Prandtl number Pm ≪ 1 (e.g., the Sun) and Pm ≫ 1 (e.g., protoneutron stars). The parameter dependence of unstable modes suggests a nonuniversal scaling of the possible Tayler–Spruit dynamo.

Parameter dependence of depth and lateral resolution of transmission Kikuchi diffraction

The spatial resolution of transmission Kikuchi diffraction (TKD) depends on experimental parameters such as atomic number, accelerating voltage, sample backtilt and thickness. In this work, the dependence of spatial resolution on these parameters is explored by using bilayered coarse-grained/nanocrystalline samples to determine the depth resolution. Digital image correlation of the Kikuchi patterns across grain boundaries is used to measure the lateral resolution. The depth resolutions of TKD in aluminium, copper and platinum at 30 kV for an untilted sample were 80, 32 and 14 nm respectively. These worsened with increasing sample backtilt and slightly improved with decreasing accelerating voltage. The best physical lateral resolution obtained was 6 nm, at 30 keV in a 41 nm thick aluminium sample with no backtilt. The lateral resolution worsened with increasing sample thickness and backtilt, contrasting with some previous reports. Accelerating voltage and atomic number did not have a significant impact on the measured lateral resolution within the scatter in the data.

Irreversibility analysis of CNT‐enhanced Williamson nanofluid flow in a stretching cylinder

AbstractThis study presents a novel exploration into the intricate interplay of slanted magnetohydrodynamic and radiative fluxes within a Williamson fluid incorporating single‐walled carbon nanotubes (SWCNTs) and multi‐walled carbon nanotubes (MWCNTs) in a water‐based system. Utilizing an exponentially stretching cylinder model, the research holistically integrates entropy production, encompassing thermal radiation, porosity, buoyant forces, and heat source/sink constraints within the governing equations. To solve the resulting governing equations with boundary conditions, the shooting technique is employed to convert them into initial value problems. Subsequently, the Runge–Kutta–Fehlberg 4–5th order method is used to obtain numerical solutions. Unveiling unprecedented insights, the investigation reveals distinctive parameter dependencies governing fluid behavior. It delineates how variations in different factors distinctly impact fluid velocity, thermal profiles, entropy generation, Bejan number, drag force, and heat transfer rates across different nanofluid compositions. Furthermore, the study highlights the transformative impact of nanocomposites on altering the thermal properties of the fluid and orchestrating nanofluid mobility. The results show that MWCNTs have an enhanced entropy generation rate when compared to SWCNTs. These findings bear substantial promise for real‐world applications involving water‐based nanofluids, shedding light on their manipulation and optimization in various technological domains.

Existence and uniqueness of positive solution to a new class of nonlocal elliptic problem with parameter dependency

In this paper, we prove that under weak assumptions on the reaction terms and diffusion coefficients, a positive solution exists for a one-dimensional case and a positive radial solution to a multidimensional case of a nonlocal elliptic problem. Additionally, we establish the uniqueness of the solution, with the fixed point theorem being the primary tool employed. Our results are new and generalize several existing results.

Analysis of Mechanical Properties and Parameter Dependency of Novel, Doubly Re-Entrant Auxetic Honeycomb Structures.

This study proposes a new, doubly re-entrant auxetic unit-cell design that is based on the widely used auxetic honeycomb structure. Our objective was to develop a structure that preserves and enhances the advantages of the auxetic honeycomb while eliminating all negative aspects. The doubly re-entrant geometry design aims to enhance the mechanical properties, while eliminating the buckling deformation characteristic of the re-entrant deformation mechanism. The effects of the geometric modification are described and evaluated using two parameters, offset and deg. A series of experiments were conducted on a wide range of parameters based on these two parameters. Specimens were printed via the vat photopolymerization process and were subjected to a compression test. Our aim was to investigate the mechanical properties (energy absorption and compressive force) and the deformation behaviour of these specimens in relation to the relevant parameters. The novel geometry achieved the intended properties, outperforming the original auxetic honeycomb structure. Increasing the offset and deg parameters results in increasing the energy absorption capability (up to 767%) and the maximum compressive force (up to 17 times). The right parameter choice eliminates buckling and results in continuous auxetic behaviour. Finally, the parameter dependency of the deformation behaviour was predicted by analytical approximation as well.

Exploiting locality in sparse polynomial approximation of parametric elliptic PDEs and application to parameterized domains

This work studies how the choice of the representation for parametric, spatially distributed inputs to elliptic partial differential equations (PDEs) affects the efficiency of a polynomial surrogate, based on Taylor expansion, for the parameter-to-solution map. In particular, we show potential advantages of representations using functions with localized supports. As model problem, we consider the steady-state diffusion equation, where the diffusion coefficient and right-hand side depend smoothly but potentially in a highly nonlinear way on a parameter y ∈ [−1, 1]N. Following previous work for affine parameter dependence and for the lognormal case, we use pointwise instead of norm-wise bounds to prove ℓp-summability of the Taylor coefficients of the solution. As application, we consider surrogates for solutions to elliptic PDEs on parametric domains. Using a mapping to a nominal configuration, this case fits in the general framework, and higher convergence rates can be attained when modeling the parametric boundary via spatially localized functions. The theoretical results are supported by numerical experiments for the parametric domain problem, illustrating the efficiency of the proposed approach and providing further insight on numerical aspects. Although the methods and ideas are carried out for the steady-state diffusion equation, they extend easily to other elliptic and parabolic PDEs.

Near-optimal learning of Banach-valued, high-dimensional functions via deep neural networks

The past decade has seen increasing interest in applying Deep Learning (DL) to Computational Science and Engineering (CSE). Driven by impressive results in applications such as computer vision, Uncertainty Quantification (UQ), genetics, simulations and image processing, DL is increasingly supplanting classical algorithms, and seems poised to revolutionize scientific computing. However, DL is not yet well-understood from the standpoint of numerical analysis. Little is known about the efficiency and reliability of DL from the perspectives of stability, robustness, accuracy, and, crucially, sample complexity. For example, approximating solutions to parametric PDEs is a key task in UQ for CSE. Yet, training data for such problems is often scarce and corrupted by errors. Moreover, the target function, while often smooth, is a potentially infinite-dimensional function taking values in the PDE solution space, which is generally an infinite-dimensional Banach space. This paper provides arguments for Deep Neural Network (DNN) approximation of such functions, with both known and unknown parametric dependence, that overcome the curse of dimensionality. We establish practical existence theorems that describe classes of DNNs with dimension-independent architecture widths and depths, and training procedures based on minimizing a (regularized) ℓ2-loss which achieve near-optimal algebraic rates of convergence in terms of the amount of training data m. These results involve key extensions of compressed sensing for recovering Banach-valued vectors and polynomial emulation with DNNs. When approximating solutions of parametric PDEs, our results account for all sources of error, i.e., sampling, optimization, approximation and physical discretization, and allow for training high-fidelity DNN approximations from coarse-grained sample data. Our theoretical results fall into the category of non-intrusive methods, providing a theoretical alternative to classical methods for high-dimensional approximation.

D meson production in p+Pb collisions with the analytical transverse momentum distribution from the color dipole models* *Supported by the National Natural Science Foundation of China Joint for Large Scientific Units (U1832120), the Hebei Province Outstanding Youth Fund (A2020210012), the S&T Program of Hebei (Grant No. 236Z4601G), and the Scientific Research Foundation for the Introducing Returned Overseas Chinese Scholars of

D meson production in proton–lead (p+Pb) collisions is globally investigated within the color dipole framework. To simplify the Fourier transform, the analytical transverse momentum distribution functions extracted from different color dipole models are used. With the Glauber–Gribov method, the impact parameter dependence is considered for the nuclear modification of the gluon density. We obtain from comparison with recent experimental data from the LHCb and ALICE Collaborations that the theoretical results from the Kovchegov, Lu and Rezaeian (KLR) model are in good agreement with the experimental data at small P T, and the results from the Golec–Biernat–Wüsthoff (GBW) and Bartels, Golec-Biernat and Kowalski (BGK) model are reasonable at all rapidity bins. Then, the influence of the initial-state energy loss effect on D meson production in p+Pb collisions is analyzed. A clear reduction of the nuclear modification factor is shown at backward rapidity. Finally, the predictive results for D0 and D+ production differential cross section versus rapidity (Y) in p+Pb collisions are given.

Q-balls in the presence of attractive force

Q-balls are non-topological solitons in field theories whose stability is typically guaranteed by the existence of a global conserved charge. A classic realization is the Friedberg-Lee-Sirlin (FLS) Q-ball in a two-scalar system where a real scalar χ triggers symmetry breaking and confines a complex scalar Φ with a global U(1) symmetry. A quartic interaction κχ2|Φ|2 with κ > 0 is usually considered to produce a nontrivial Q-ball configuration, and this repulsive force contributes to its stability. On the other hand, the attractive cubic interaction Λχ|Φ|2 is generally allowed in a renormalizable theory and could induce an instability. In this paper, we study the behavior of the Q-ball under the influence of this attractive force which has been overlooked. We find approximate Q-ball solutions in the limit of weak and moderate force couplings using the thin-wall and thick-wall approximations respectively. Our analytical results are consistent with numerical simulations and predict the parameter dependencies of the maximum charge. A crucial difference with the ordinary FLS Q-ball is the existence of the maximum charge beyond which the Q-ball solution is classically unstable. Such a limitation of the charge fundamentally affects Q-ball formation in the early Universe and could plausibly lead to the formation of primordial black holes.

A two-step identification approach for an extended nonlinear double-capacitor model

Equivalent circuits are one of the most used models for Li-ion cells in the automotive area. However, it is a challenge to these models to be able to capture the cell discharge capacity under different loads, while still being accurate on both continuous charge and dynamic tests, fast to compute, and easy to parametrize from non-specialized data. To tackle this challenge, this paper proposes an extension of the nonlinear double capacitor model by increasing its order, parameter dependency with C-rate, and an identification procedure that exploits the pseudo-linear nature of the problem to find the parameter maps. An analogy between the parts of the circuit and the single particle model is also presented to reduce the search space of the identification algorithm and to enhance model interpretability. The performance of the proposed model extension is analyzed and compared to a state-of-the-art model on a challenging LiFePO4 dataset with different characteristics and validated on a realistic drive cycle, obtaining a mean absolute average error of around 20 mV for both training and validation tests.

Nuclear acoustic envelope soliton in a relativistically degenerate magneto-rotating stellar plasma

The study explores a model called Relativistic Degenerate Magneto-Rotating Quantum Plasma (RDMRQP), which comprises a static heavy nucleus, an inertial non-degenerate light nucleus, and warm non-relativistic or ultra-relativistic electrons. The focus is on observing the emergence of Nucleus-Acoustic Envelope Solitons (NAESs). Using the reductive perturbation method, a Nonlinear Schrödinger equation (NLSE) is derived to characterize the properties of NAESs. We have analysed the Peregrine breather soliton solution. The investigation reveals that the temperature of warm degenerate species, plasma system’s rotational speed, and the presence of heavy nucleus species can alter the fundamental features (height and width) of NAESs in the WDMRQP system. The study emphasizes the existence of only positive NA wave potential. Additionally, a phase plane analysis is conducted to gain a deeper understanding of the parametric dependencies. Through detailed mathematical and numerical analysis, the study avoids overloading with complex mathematics while demonstrating parametric dependence via phase portrait analysis. The research augments the envelop soliton model with breather mode solutions and discusses modulation instability using the Benjamin-Feir Index, highlighting the significance of solitons in star formation. Envelop solitons, stable waves within stars and proto-stars, influence energy transport and stellar evolution, playing a crucial role in the accretion process and formation of stable structures. Key findings include the effects of various parameters on NAESs’ generation and propagation in which non-relativistic and ultra-relativistic electrons support NAESs, with amplitude and width influenced by temperature, rotational frequency, inclination angle, and the presence of a static heavy nucleus. The research is applicable to hot white dwarfs and neutron stars, suggesting further exploration of quantum effects and non-planar or arbitrary amplitude NAESs.

Multi-Frequency Entropy for Quantifying Complex Dynamics and Its Application on EEG Data.

Multivariate entropy algorithms have proven effective in the complexity dynamic analysis of electroencephalography (EEG) signals, with researchers commonly configuring the variables as multi-channel time series. However, the complex quantification of brain dynamics from a multi-frequency perspective has not been extensively explored, despite existing evidence suggesting interactions among brain rhythms at different frequencies. In this study, we proposed a novel algorithm, termed multi-frequency entropy (mFreEn), enhancing the capabilities of existing multivariate entropy algorithms and facilitating the complexity study of interactions among brain rhythms of different frequency bands. Firstly, utilizing simulated data, we evaluated the mFreEn's sensitivity to various noise signals, frequencies, and amplitudes, investigated the effects of parameters such as the embedding dimension and data length, and analyzed its anti-noise performance. The results indicated that mFreEn demonstrated enhanced sensitivity and reduced parameter dependence compared to traditional multivariate entropy algorithms. Subsequently, the mFreEn algorithm was applied to the analysis of real EEG data. We found that mFreEn exhibited a good diagnostic performance in analyzing resting-state EEG data from various brain disorders. Furthermore, mFreEn showed a good classification performance for EEG activity induced by diverse task stimuli. Consequently, mFreEn provides another important perspective to quantify complex dynamics.

[formula omitted] order subharmonic waves of two cavitation bubbles

In the work, the 1/2 order subharmonic wave of two coupling cavitation bubbles is investigated numerically via Fourier spectrum analysis. By analyzing the dynamics of bubble, we find that the mutual interaction between bubbles can affect the appearance of 1/2 order subharmonic. The results of parameter dependence show that the intensity of 1/2 order subharmonic would be promoted or inhibited with the increase of mutual interaction. The higher the driving amplitude or the smaller the distance between bubbles, the stronger the mutual interaction is, and also the greater the promotion or suppression of the 1/2 order subharmonic is. Moreover, while the 1/2 order subharmonic occurs, the energy of bubble would alternate between two different peaks, and the temperature inside bubble has a similar fluctuation while the bubble collapses. This qualitative analysis suggests that the bubble′s dynamics for multi-bubble case is complex. Understanding the generation of subharmonic of bubble′s dynamics is of great significance for helpful applying of cavitation bubble.