Complex Frequency Research Articles

Study on low-mid-frequency broadband sound absorption properties of bending acoustic metamaterials with embedded porous materials

With the rapid development of the traffic industry, noise issues are becoming increasingly serious, and the traditional noise control technologies have the problems of poor low-frequency noise absorption and narrow bandwidth. This study proposes a variable-section bending acoustic metamaterial with an embedded porous material (VS_BAMP). A theoretical model of the VS_BAMP unit is developed based on the Johnson-Champoux-Allard (JCA) model and the impedance transfer method. The sound absorption unit with a thickness of 48 mm exhibits a quasi-perfect (α = 0.98) at 736 Hz, and an efficient sound absorption (α > 0.8) in the range of 574 Hz–966 Hz. Based on the complex frequency plane method, this work designs sound absorption units that exhibit perfect sound absorption at discrete frequencies. By connecting two different absorption units (PVS_BAMP) in parallel, efficient sound absorption from 424 Hz to 1500 Hz is achieved. Finally, the accuracy of the theoretical model is verified by experiments and simulations, confirming the effective sound absorption of PVS_BAMP structure in the middle and low frequency bands. The prepared PVS_BAMP is highly adjustable, has a wide bandwidth, and can be prepared through a simple manufacturing process. Our results can provide a theoretical basis for the design of compact low-mid-frequency broadband noise reduction structures for practical application.

Complex housing in adulthood state-dependently affects the excitation-inhibition balance in the infralimbic prefrontal cortex of male C57Bl/6 mice

The prefrontal cortex (PFC) plays an important role in social behavior and is sensitive to stressful circumstances. Challenging life conditions might change PFC function and put individuals at risk for maladaptive social behavior. The excitation-inhibition (EI) balance of prefrontal neurons appears to play a crucial role in this process. Here, we examined how a challenging life condition in C57BL/6JolaHsd mice, i.e. group-housing 6 mice in a complex environment for 10 days in adulthood, changes the EI-balance of infralimbic prefrontal neurons in layer 2/3, compared to standard pair-housing. Slices were prepared from “undisturbed” mice, i.e. the first mouse taken from the cage, or mice taken ∼15 min later, who were mildly aroused after removal of the first mouse. We observed a housing-condition by arousal-state interaction, with in the complex housing group an elevated EI-balance in undisturbed and reduced EI-balance in mildly aroused animals, while no differences were observed in standard housed animals. The change was explained by a shift in mIPSC and mEPSC frequency, while amplitudes remained unaffected. Female mice showed no housing-by-state interaction, but a main effect of housing was found for mIPSCs, with a higher frequency in complex- versus standard-housed females. No effects were observed in males who were complex-housed from a young age onwards. Explorative investigations support a potential mediating role of corticosterone in housing effects on the EI-balance of males. We argue that taking the arousal state of individuals into account is necessary to better understand the consequences of exposure to challenging life conditions for prefrontal function.

Measuring Transverse Relaxation with a Single-Beam 894 nm VCSEL for Cs-Xe NMR Gyroscope Miniaturization.

The spin-exchange-pumped nuclear magnetic resonance gyroscope (NMRG) is a pivotal tool in quantum navigation. The transverse relaxation of atoms critically impacts the NMRG's performance parameters and is essential for judging normal operation. Conventional methods for measuring transverse relaxation typically use dual beams, which involves complex optical path and frequency stabilization systems, thereby complicating miniaturization and integration. This paper proposes a method to construct a 133Cs parametric resonance magnetometer using a single-beam vertical-cavity surface-emitting laser (VCSEL) to measure the transverse relaxation of 129Xe and 131Xe. Based on this method, the volume of the gyroscope probe is significantly reduced to 50 cm3. Experimental results demonstrate that the constructed Cs-Xe NMRG can achieve a transverse relaxation time (T2) of 8.1 s under static conditions. Within the cell temperature range of 70 °C to 110 °C, T2 decreases with increasing temperature, while the signal amplitude inversely increases. The research lays the foundation for continuous measurement operations of miniaturized NMRGs.

A coupled finite element-discrete element method for the modelling of brake squeal instabilities

The work presented here proposes a contribution on the analysis of brake squeal phenomenon using a transient coupled finite element-discrete element method (FEM-DEM) simulation with pad surface topography evolution. To build the coupled FEM-DEM model, a non-overlapping strong coupling is first employed between the FEM and DEM subdomains. Second, a new calibration methodology of the DEM microscopic properties is proposed based on the eigenvalue analysis of the full model. The results of the coupled FEM-DEM model show a good agreement in terms of unstable frequencies and the evolution of the pad contact state history when compared to full FEM models, both for new and worn pad topographies. The evolution of the pad surface topography during the transient analysis results in a complex frequency behaviour, with abrupt shifts of instabilities and new operating deflection shapes, in agreement with reported experimental results. The proposed coupled FEM-DEM model thus seems to be a valuable tool for a better understanding of the squeal triggering due to the evolution of the pad surface topography. This contribution paves the way to advanced numerical analyses of brake squeal phenomenon, which triggering conditions are still under investigation.

Robust 3-D Path Following Control Framework for Magnetic Helical Millirobots Subject to Fluid Flow and Input Saturation.

Precise trajectory control is imperative to ensure the safety and efficacy of in vivo therapy employing the magnetic helical millirobots. However, achieving accurate 3-D path following of helical millirobots under fluid flow conditions remains challenging due to the presence of the lumped disturbances, encompassing complex fluid dynamics and input frequency saturation. This study proposes a robust 3-D path following control framework that combines a disturbance observer for perturbation estimation with an adaptive finite-time sliding mode controller for autonomous navigation along the reference trajectories. First, a magnetic helical millirobot's kinematic model based on the 3-D hand position approach is established. Subsequently, a robust smooth differentiator is implemented as an observer to estimate disturbances within a finite time. We then investigate an adaptive finite-time sliding mode controller incorporating an auxiliary system to mitigate the estimated disturbance and achieve precise 3-D path tracking while respecting the input constraints. The adaptive mechanism of this controller ensures fast convergence of the system while alleviating the chattering effects. Finally, we provide a rigorous theoretical analysis of the finite-time stability of the closed-loop system based on the Lyapunov functions. Utilizing a robotically-actuated magnetic manipulation system, experimental results demonstrate the efficacy of the proposed approach in terms of the control accuracy and convergence time.

A stochastic Schrödinger equation and matrix product state approach to carrier transport in organic semiconductors with nonlocal electron-phonon interaction.

Evaluation of the charge transport property of organic semiconductors requires exact quantum dynamics simulation of large systems. We present a numerically nearly exact approach to investigate carrier transport dynamics in organic semiconductors by extending the non-Markovian stochastic Schrödinger equation with complex frequency modes to a forward-backward scheme and by solving it using the matrix product state (MPS) approach. By utilizing the forward-backward formalism for noise generation, the bath correlation function can be effectively treated as a temperature-independent imaginary part, enabling a more accurate decomposition with fewer complex frequency modes. Using this approach, we study the carrier transport and mobility in the one-dimensional Peierls model, where the nonlocal electron-phonon interaction is taken into account. The reliability of this approach was validated by comparing carrier diffusion motion with those obtained from the hierarchical equations of motion method across various parameter regimes of the phonon bath. The efficiency was demonstrated by the modest virtual bond dimensions of MPS and the low scaling of the computational time with the system size.

Complex Dispersion Analysis of Flexural Wave Propagation in Periodic Track Structure

The periodic characteristics of the track structure have filtering characteristics for the propagation of vibration waves within it, and the dispersion analysis is of great significance to understand the vibration transmission characteristics of the track structure. The accuracy of the traditional virtual spring method depends on the value of spring stiffness, which leads to poor stability. Therefore, this paper adopts a null space method with both stability, accuracy and efficiency, and takes the CRTSIII ballastless track structure as the research object. Based on the null space method and energy functional variational principle, the damping factor and the material frequency variation effect are considered in detail, and the complex frequency dispersion of the CRTSIII ballastless track structure is analyzed. The accuracy of the proposed method is verified by comparing it with the results of the existing literature, and the influence of fastener stiffness frequency variation, fastener damping and concrete support layer damping on the complex dispersion characteristics of vibration waves of track structures is analyzed by using this method. The results show that the stiffness frequency effect, fastener damping and concrete support layer damping have a great influence on the attenuation domain and attenuation rate of vibration, which must be considered in the vibration transmission analysis of track structures.

Comparative analysis of double and single porosity effects on SH-wave induced vibrations in periodic porous lattices

The manuscript presents a novel study comparing the impact of single and double porosity on horizontally polarized shear wave (SH-wave) propagation in corrugated elastic void materials. The considered mathematical model comprises two cases; the first one depicts SH-wave propagation through a void porous layer having creased boundaries and resting over a heterogeneous anisotropic fluid-saturated fractured porous half-space, whereas according to the second case, heterogeneous anisotropic fluid-saturated porous semi-infinite medium without fractures has been considered. In both cases, rigidity and density of the half-space vary quadratically with depth. The separable variable method is used to attain the complex frequency equation for each case that leads to two different dispersion relations associated with two distinct wave fronts. The first wave front depends on the void parameters, whereas the second wave front defines the propagation of SH-waves in an elastic layer without void pores. In each case, the complex dispersion relation has been separated into two equations that illustrate the dispersion and attenuation properties of SH-waves. Using the variations in the inhomogeneity, position, fluctuation, flatness, total porosity, and anisotropy parameters, case I and case II have been compared in each graphical execution. In addition, the surface response of shear stress and displacement have been implemented graphically.

Development of EEG Response to Unpleasant, Pleasant, and Neutral Tactile Stimuli.

The study of tactile perception during a childhood is extremely important for understanding the social and communicative aspects of the child's development. Tactile perception of stimuli with different valence can have different normative stages of development. In the present study, we examined changes in linear and nonlinear electroencephalogram (EEG) parameters during the presentation of pleasant (C-tactile optimal stroking), unpleasant (ice stroking), and neutral tactile stimuli in three groups of healthy volunteers: preschoolers 4 and 5 years, school-age children from 8 to 10 years, and adults from 20 to 40 years. According to our findings, child maturation plays a significant role in the perception of pleasant and neutral tactile stimuli. Patterns of EEG dynamics related to tactile perception showed greater similarity between adult volunteers and school-aged children than preschoolers. Non-linear EEG parameters such as fractal dimension (FD), envelope mean frequency (EMF), and power spectral density (PSD) dynamics of the theta-rhythm were particularly sensitive to developmental changes in tactile perception. Hjorth complexity and peak alpha frequency (PAF) scores may serve as indicators of mature perception of С-tactile (CT)-stimuli.

Highly sensitive mapping of in vitro type II topoisomerase DNA cleavage sites with SHAN-seq.

Type II topoisomerases (topos) are a ubiquitous and essential class of enzymes that form transient enzyme-bound double-stranded breaks on DNA called cleavage complexes. The location and frequency of these cleavage complexes on DNA is important for cellular function, genomic stabilityand a number of clinically important anticancer and antibacterial drugs, e.g. quinolones. We developed a simple high-accuracy end-sequencing (SHAN-seq) method to sensitively map type II topo cleavage complexes on DNA in vitro. Using SHAN-seq, we detected Escherichia coli gyrase and topoisomerase IV cleavage complexes at hundreds of sites on supercoiled pBR322 DNA, approximately one site every ten bp, with frequencies that varied by two-to-three orders of magnitude. These sites included previously identified sites and 20-50-fold more new sites. We show that the location and frequency of cleavage complexes at these sites are enzyme-specific and vary substantially in the presence of the quinolone, ciprofloxacin, but not with DNA supercoil chirality, i.e. negative versus positive supercoiling. SHAN-seq's exquisite sensitivity provides an unprecedented single-nucleotide resolution view of the distribution of gyrase and topoisomerase IV cleavage complexes on DNA. Moreover, the discovery that these enzymes can cleave DNA at orders of magnitude more sites than the relatively few previously known sites resolves the apparent paradox of how these enzymes resolve topological problems throughout the genome.

Experimental Study on Vibration and Noise Reduction of Gear Transmission System Based on ISFD

Gear transmission systems are widely used in ship propulsion systems, but, during operations, they produce serious vibration and noise problems, reducing the fatigue life of gears and affecting the performance of ships and the comfort of operators. Taking into account the complex frequencies and vibration components of gear transmission systems, this study conducted wide-band vibration suppression and noise reduction research on a gear transmission system using an integral squeeze film damper (ISFD), providing a novel approach for reducing vibration and noise in gear transmission systems. By conducting a simulation analysis and numerical calculations, the ISFD was analyzed via a static analysis and a dynamic analysis. We developed an experimental platform for reducing vibration and noise in gear transmission systems using sliding bearings, and the experiments were conducted under different speed and load conditions to study the vibration suppression and noise reduction of gears based on the ISFD. The experimental results show that the ISFD has good vibration suppression capabilities for gears at different speeds, with a horizontal vibration reduction of 75.44% and a vertical vibration reduction of 68.48% at 2400 r/min. The ISFD has wide-band vibration suppression capabilities, especially for mesh frequency and twice-mesh frequency, with a vibration reduction of 86.96% or more. Moreover, the ISFD has good vibration suppression capabilities for gears at different load torques, with a reduction of more than 35% in all directions. In addition, the ISFD also has noise reduction capabilities, reducing the gears’ noise by 1.92 dB at different speeds.

Premature ventricular complexes after catheter ablation for atrial fibrillation: Accounting for regression to the mean.

Prior studies have indicated that the frequency of premature ventricular complexes (PVC) increases after catheter ablation for atrial fibrillation (AF). However, these studies have primarily focused on patients whose PVC burden increased rather than including the full spectrum of outcomes. We performed a single-center retrospective cohort study of consecutive patients who underwent first-time AF ablation from 1/2018 to 12/2022 for paroxysmal or persistent AF and had both preablation and postablation rhythm monitoring within 6 months of the procedure. Patients were excluded if they had prior AF or PVC ablation or were prescribed a class I or III antiarrhythmic medication. Among 2945 patients who underwent AF ablation during the study period, 130 patients underwent first-time AF ablation and received both pre and post ambulatory monitoring. The median PVC burden before ablation was <1%. Most patients (63%) had no change in PVC burden after AF ablation compared with preablation, and patients who had an increase in PVC burden were offset by those with reductions in PVCs. A paired analysis pre- and post-AF ablation showed no significant change in PVC burden (p = .495). Although an elevated PVC burden after AF ablation may be seen clinically, the majority of patients have no change in burden. Studies that suggest an increase in PVC burden after AF ablation may suffer from incomplete sample selection and thus omit the important effect of regression to the mean.

Two-station Lg wave attenuation tomography in Eastern Asia

SUMMARY Utilizing over 31 000 Lg waveforms from 136 crustal earthquakes recorded at 346 regional stations, we conduct detailed tomographic mappings of the Lg Q structure across Eastern Asia in a frequency range from 0.5 to 4.0 Hz. By improving the standard two-station (TS) method, we effectively correct non-unity site response ratios using site responses estimated at individual stations. This innovative approach combines the flexible recording geometry of the TS method with the precision of reversed two-station (RTS) and reversed two-event (RTE) methods, producing a comprehensive data set devoid of source and site effects for Q tomography. To address unsolvable 3-D structural effects in the Lg spectral amplitude modelling, we justify these as modelling errors with a Gaussian distribution. This approach supports our SVD-based tomographic method, allowing for effective inversion of attenuation parameters and quantitative assessment of model resolution and errors. Our results reveal a complex relationship between Lg Q and the tectonic characteristics of Eastern Asia. In well-resolved regions, low Qo (1-Hz Q) values correspond to areas with high heat flow, partial melt, thick sediment and recent tectonic-thermal activities, in contrast to high Qo values in stable, ancient crusts lacking recent tectonic activity. Rift basins are characterized by low Lg Qo, whereas flexural basins generally have high Qo basements. We also note that post-formation factors, such as sedimentation and crustal flow intrusion, significantly impact Qo values. Furthermore, Lg Q shows a complex frequency relationship, though the power-law approximation with positive power η remains useful. The frequency dependence power η is inversely related to Qo: the regions with low Qo typically have high η and vice versa. This study provides reliable attenuation tomographic and relative site response models for Lg waves in Eastern Asia, pertinent for relative geophysical studies.

Controlling acoustic non-Hermitian skin effect via synthetic magnetic fields

Non-Hermitian skin effect (NHSE) is an intrinsic non-Hermitian phenomenon where an extensive number of eigenmodes, called skin modes, are localized at the boundary of a system. Recent theories have suggested that the NHSE can be well-tuned by external fields, opening a route to manipulating wave localization. Here, we experimentally demonstrate the diverse interactions between NHSE and synthetic magnetic fields (SMFs) in coupled acoustic ring resonator lattices. We observe that the NHSE and SMFs can, via different physical mechanisms, compete or synergize, resulting in either the suppression or the creation of NHSE. With the aid of the complex frequency excitation technique, we experimentally observe that SMFs can suppress the NHSE by introducing Landau quantization, causing localization to move toward the bulk. In contrast, we show that the presence of SMF generates topological edge modes in the lattice, which then become corner skin modes by the second-order NHSE. Our results evidence the rich physics and diverse consequences that arise from the interplay of magnetic fields and NHSE, paving the way for actively controlling wave localization.

Characterization of Micro-seismic Activity in Northern Cyprus Using Complexity and Corner Frequency Methods

Cyprus is an island country located in the eastern Mediterranean, to the south of Türkiye and the western of Syria and Lebanon, and is a popular tourist destination. Due to being surrounded by seas on all four sides, meticulous planning of rescue, assistance, and evacuation plans is necessary in the face of disasters such as earthquakes and tsunamis. Tectonically, the southern part of the island is controlled by the Cyprus Arc, while the northern part is dominated by the Kyrenia Range. The demand for raw materials for construction and industry is met through controlled quarry blasting operations carried out by open-pit quarry companies in the districts of Kyrenia and Nicosia. As a result, both natural and artificial seismic events occur in the region, and these quakes are documented in seismic catalogs by seismology centers. However, due to the low energy content of micro-seismic events and the inadequacy of seismic stations on the island, the source types of these seismic events can be misidentified in the catalogs. In this context, the study focuses on 122 seismic events with magnitudes between 0.9≤Ml≤2.7 that occurred in Northern Cyprus during the January 2018 - December 2021 period (4 years). The seismic events recorded by the station LFK, operated by Boğaziçi University Kandilli Observatory and Earthquake Research Institute Regional Earthquake-Tsunami Monitoring Center (KOERI-RETMC), were classified using Linear and Quadratic Discriminant Functions based on complexity and corner frequency methods. According to the results obtained, 10 of the 122 seismic events were identified as natural, and 96 were determined to be artificial, resulting in a general success rate of 86.89%. However, classification results for 16 seismic events were inconclusive with the methods used. As a result, more detailed secondary analyses should be conducted to accurately determine the source types of micro-seismic events, and the seismic catalogs should be updated accordingly.

Diagnostic reliability of monitoring for premature atrial and ventricular complexes.

Short-term ambulatory electrocardiogram (ECG) monitoring is often used to assess premature atrial complex (PAC) and premature ventricular complex (PVC) frequency, but the diagnostic reliability is unknown. The objective of this study was to study the day-to-day variability of PAC and PVC frequency. We used 14-day full-disclosure mobile cardiac telemetry recordings without atrial fibrillation in 8245 US patients aged 17-103 years to calculate the diagnostic reliability of shorter ambulatory ECG recordings compared with 14-day averages. Over 14 days, 1853 patients had ≥500 PACs/day, 410 patients had ≥5000 PACs/day, and 197 patients had ≥10 000 PACs/day; 1640 patients had ≥500 PVCs/day, 354 patients had ≥5000 PVCs/day, and 175 patients had ≥10 000 PVCs/day. After 3 days, the estimated daily PAC frequency differed by ≥50% from the 14-day mean in 25% of patients; for PVCs, the corresponding duration was 7 days. Ten days of monitoring were needed to estimate PAC and PVC frequency within ±20% of the overall 14-day frequency in 80% of patients. For daily PAC and PVC frequencies ≥10 000, single-day estimation had a specificity of 99.3% [95% confidence interval (CI) 99.1-99.5] at a sensitivity of 76.6 (95% CI 70.1-80.4%) for PACs and a 99.6% (95% CI 99.4-99.7%) specificity at 79.4 (95% CI 72.7-85.2) sensitivity for PVCs. After 7 days, the sensitivity increased to 88.8% (95% CI 83.6-92.9) for PACs and 86.9% (95% CI 80.9-91.5%) for PVCs. While there is substantial daily variability across most PAC and PVC levels, findings of ≥10 000 PACs or PVCs are highly specific and do not need to be confirmed with longer recordings.

Example of the convergence of hydrodynamics in strong external fields

The anti-de-Sitter/conformal field theory (AdS/CFT) correspondence is used to provide an estimate of the radius of convergence of the linearized gradient expansion of the hydrodynamic description of N=4 supersymmetric Yang-Mills (SYM) theory minimally coupled to U(1) gauge theory subjected to strong magnetic fields. The results of this work demonstrate that the dispersion relations of hydrodynamic modes continue to converge for magnetic field strengths far beyond those values for which a hydrodynamic description is expected. For magnetic field strengths much larger then the temperature scale the bulk dual interpolates between AdS4+1 and the product of a Bañados-Teitelboim-Zanelli (BTZ) black hole and a two dimensional manifold (BTZ2+1×R2) and may be regarded as a renormalization group flow of the 3+1 dimensional CFT to a 1+1 dimensional CFT. In this regime, we clarify past literature on the quasi-normal mode (QNM) spectrum of bulk scalar fields by introducing a new way to classify the behavior of QNM collisions in the complex frequency and momentum plane. Published by the American Physical Society 2024

Improved assembly DC circuit breaker based on resonant current injection.

DC circuit breakers (DCCBs) with high breaking capacity and low cost are necessary for quick fault clearance in DC networks. The assembly DC circuit breakers (ADCCBs) have a main breaking section (MBS) and a sub-breaking sections (SBS) for each line, which greatly reduce the cost. But in conventional operation, it bears high voltage for a long time when there is a main switch grounding process in any line fault action. To address this problem, a multiport assembly circuit breaker based on current injection (CI-MPACB) is proposed, which is able to generate a resonant current with increasing amplitude by controlling the duty cycle of Integrated Gate-Commutated Thyristors (IGCTs). Then the resonant current is injected into the SBS to generate current zero crossing and arc extinction. A complex frequency domain circuit analysis is performed on the MBS to describe the action logic as well as the commutation characteristics. In addition, the parameters of each component of the MBS are subject to multiple constraints and reasonable design to ensure the fault current could be cut off quickly and reliably. The cost of existing design is greatly reduced due to the design idea of resonant current injection device parameter selection. Finally, a PSCAD/EMTDC simulation confirms the opening viability of CI-MPACB and the accuracy of the parameter design. The test results show that the designed CI-MPACB can cut off DC fault lines.

Local cochlear mechanical responses revealed through outer hair cell receptor potential measurements

Sensory hair cells, including the sensorimotor outer hair cells, which enable the sensitive, sharply tuned responses of the mammalian cochlea, are excited by radial shear between the organ of Corti and the overlying tectorial membrane. It is not currently possible to measure directly in vivo mechanical responses in the narrow cleft between the tectorial membrane and organ of Corti over a wide range of stimulus frequencies and intensities. The mechanical responses can, however, be derived by measuring hair cell receptor potentials. We demonstrate that the seemingly complex frequency- and intensity-dependent behavior of outer hair cell receptor potentials could be qualitatively explained by a two degrees of freedom system with local cochlear partition and tectorial membrane resonances strongly coupled by the outer hair cell stereocilia. A local minimum in the receptor potential below the characteristic frequency should always be observed at a frequency where the tectorial membrane mechanical impedance is minimal, i.e., at the presumed tectorial membrane resonance frequency. The tectorial membrane resonance frequency might, however, shift with stimulus intensity in accordance with a shift in the maximum of the tectorial membrane radial mechanical responses to lower frequencies, as observed in experiments.

Development of a Prototype Hydraulic Damping Device for Hot Water Heating Circuit in Pulse Mode

This paper provides a comprehensive exploration into the design and implementation of the hydraulic damping device within a pulse mode hot water heating loop. It outlines a systematic approach aimed at optimizing system performance, detailing the operational principles of the pulse mode heating circuit and presenting a structured construction scheme for the hydraulic damping apparatus. Accompanying this analysis is a simplified diagram illustrating the hydraulic damping system, offering a clear visual representation of its integration within the heating circuit. Through mathematical transformations, essential parameters such as complex impedance, frequency function, and vibration frequency characteristics are derived, providing valuable insights into the dynamic behavior of the system. Culminating this investigation, the paper constructs the frequency response of the circuit, offering a comprehensive understanding of its dynamic behavior across varying frequencies. This synthesis of theoretical frameworks and practical applications advances our understanding of pulse mode hot water heating technology, paving the way for enhanced efficiency and performance in heating systems.