Nonmonotonic Behavior Research Articles

Development of a Generalized Partition Curve Model for Hydrocyclones

ABSTRACT Partition curves associated with hydrocyclone classification processes have been known to deviate from the typical S-shape by exhibiting asymmetric and non-monotonic behaviors, making their mathematical modeling challenging. In addition to the well-documented phenomenon of fish-hooks at the finer end, the partition curves can also sometimes exhibit fat-tailed behavior at the coarser end of the size spectrum, which has not been extensively highlighted in the literature. This study aimed to develop a parametric model for the partition curves which can systematically and effectively accommodate both these irregularities at the coarser and finer ends. Instead of adopting a piece-wise modeling approach for the task, a continuous model was successfully developed in the form of the addition of three component functions, each affecting different regions and features of the partition curve with a total of 7 fitting parameters. Two of the component functions were modified versions of the cumulative density functions of the Weibull distribution while the third was the modified solution of a single hyperbolic branch having a horizontal and a slant asymptote to accommodate the observed fat-tailed behavior. The model exhibited remarkable fitting performance for both experimentally generated and literature data. An alternative method of defining the separation cut size has also been proposed in this study to overcome the limitations of the classical concept of the d50. It was also shown how the developed model can be utilized for quantitative analysis of the critical aspects of the partition curve such as the cut size, bypass, and the dip point.

Desorption kinetics of indium adlayers on GaN(0001): Fractional order and non-monotonic behavior

Epitaxial growth is a dynamic process and, to the first order, is governed by the nature and the rates of elementary surface kinetic mechanisms, such as adatom desorption. In compound-type growing surfaces, particularly in III-nitride molecular beam epitaxy, where the presence of a metallic surface bilayer has a catalytic role, desorption also affects the rates of other elementary mechanisms. In this study, we investigated the desorption of an indium (In) adlayer from GaN(0001) surfaces, a critical kinetic process in the epitaxy of In-containing alloys, using reflection high-energy electron diffraction, density functional theory calculations, and quasi-continuous modeling methods to reveal the underlying physical mechanisms. Our results demonstrate that while the indium bilayer desorbs in a layer-by-layer mode, the desorption mechanisms from the bottom and top monolayers differ significantly. The bottom follows a 3/4 order Polanyi–Wigner relation, attributed to contributions from two different adlayer phases. The top monolayer desorption exhibits a non-monotonic dependence on coverage. This is associated with the liquidus status of this monolayer and its continuous restructuring during desorption. These findings clarify and quantify indium desorption processes from GaN(0001) surfaces, offering insights into analogous mechanisms in other compound-type material systems.

Role of obstacle softness in the diffusive behavior of active particles.

We numerically investigate the diffusive behavior of active Brownian particles in a two-dimensional confined channel filled with soft obstacles, whose softness is controlled by a parameter K. Here, active particles are subjected to an external bias F. Particle diffusion is influenced by entropic barriers that arise due to variations in the shape of the chosen channel geometry. We observed that the interplay between obstacle softness, entropic barriers, and external bias leads to striking transport characteristics of the active particles. For instance, with increasing F, the non-linear mobility exhibits a non-monotonic behavior, and effective diffusion is greatly enhanced, showing multiple peaks in the presence of soft obstacles. Furthermore, as a function of K and F, particles exhibit various diffusive behaviors, e.g., normal diffusion-where the role of obstacles is insignificant, and subdiffusion or superdiffusion-where the particles are partially trapped by the obstacles, and the particles are ultimately caged by the obstacles. These findings help understand the physical situations wherein active agents diffuse in crowded environments.

Role of clustering in the anomalous properties of supercritical fluids

We propose that the anomalous (non-monotonic) behavior of physical properties of supercritical fluids (SCF) in the Widom delta is attributed to the formation of medium-sized clusters. This hypothesis is experimentally verified for carbon dioxide using both experimental methods and molecular dynamics simulations. From a microscopic point of view, the non-monotonic behavior of the nonlinear refractive index, speed of sound, and Raman scattering efficiency is caused by the formation of quasi-linear clusters of medium size (5–200 molecules per cluster). Within the clusters, the molecule concentration is close to that of the liquid phase, while outside the clusters, it resembles the gas phase, leading to experimentally observed high (∼15 %) density fluctuations. Isolated linear clusters exhibit high second-order hyperpolarizability, resulting in an increase in the molecular contribution to the nonlinear refractive index and the intensity of Raman scattering. The appearance of multiple Widom lines on the pressure–temperature (p-T) diagram, each associated with unique physical properties, arises from the combined effects of cluster-specific and density-related factors. This interplay results in the divergence of Widom lines and the formation of the characteristic feature known as the Widom delta.

An overlapping-generations model with data-driven equilibrium behavior

We propose a class of overlapping generations models that can serve as a workhorse for policy analysis. Recent literature identifies several features of key observable economic variables in Europe and the U.S.: the life-cycle path of earnings is hump-shaped, while the aggregate variables — per-capita consumption and labor hours — exhibit a clear time trend. Our class generates non-monotonic life-cycle behavior of labor supply and the desired aggregate trends in all its balanced-growth equilibria (BGE). There is a finite number of these equilibria and at least one of them exists provided a single-generation consumer problem has a solution. The model has a constant-returns-to-scale production, non-trivial depreciation of capital, exogenous labor-saving growth and an arbitrary individual life-cycle productivity. The necessary restrictions imposed on preferences are consistent with those generating the aggregate trends in a representative-agent economy, while ruling out popular specifications such as Cobb–Douglas or CES. We characterize BGE with MaCurdy preferences and solve a parametrized model that yields at least two stationary equilibria with reasonable interest rates. The hump-shaped life-cycle consumption profile can be generated with an additional parameter interpreted as reflecting family structure or a desire for immediate gratification that peaks at mid-life.

Detonation flows of explosives containing compressible inert particles

The present study employs a combination of numerical and analytical techniques to examine the detonation flows of explosives containing compressible inert particles. A two-phase numerical model incorporating the compressibility of the particles is developed, and the two-phase detonation process is simulated under the Lagrangian framework, where the explosive and the particles are treated as a fluid and discrete spheres, respectively. For small velocity difference between phases, a perturbation method is utilized for the analysis of the dynamics of the detonation front, the detonation product, and the particles. The effects of the particles' compressibility and material density are examined in detail. The results show that the material density of the particles exerts a linear influence on the detonation flow of the explosive, while the effects of the particle compressibility are much more complex. An increase in the particle's material density or compressibility can reduce the velocities of both the detonation front and the flowing-stagnant boundary. The jump of the particle volume fraction across the detonation front relies on the particle compressibility. For more compressible particles, the particle volume fraction exhibits a non-monotonic behavior in the flowing region. A concise scaling law is also obtained for the velocity difference between phases. The present research provides a quantitative prediction to the effects of compressible particles on the detonation flows of explosives.

Ground Motion Characteristics of Subshear and Supershear Ruptures in the Presence of Sediment Layers

Summary We investigate the impact of sediment layers on ground motion characteristics during subshear and supershear rupture growth. Our findings suggest that sediment layers may lead to local supershear propagation, affecting ground motion, especially in the fault parallel (FP) direction. In contrast to homogeneous material models, we find that in the presence of sediment layers, a larger fault normal (FN) compared to fault parallel (FP) particle velocity jump, reflects shear propagation at depth but does not rule out shallow supershear propagation. Conversely, a large fault parallel (FP) compared to fault normal (FN) particle velocity jump indicates supershear propagation at depth. In the presence of a shallow layer, we also uncover a non-monotonic behavior in the sediment’s influence on supershear transition and ground motion characteristics. During supershear propagation at depth we observe that sediment layers contribute to enhancing FP velocity pulses while minimally affecting the FN component. Furthermore, in the limit of global supershear propagation we identify local supersonic propagation within the sediment layers that significantly alters the velocity field around the rupture tip as observed on the free surface, creating both dilatational and shear Mach cones. In all our models with sediments we also find a significant enhancement in the fault vertical component of ground velocity. This could have particular implications for hazard assessments, such as in applications related to linear infrastructure, or a higher propensity to tsunami wave generation. Our research unravels the importance of considering heterogeneous subsurface material distribution in our physical models as they can have drastic implications on earthquake source physics.

The dynamics of pinned charge density wave in NbSe3 nanoribbons revealed by noise spectroscopy

Abstract Systematic nonlinear transport and broadband noise (BBN) measurements are performed on single nanoribbon devices of the charge density wave (CDW) conductor NbSe$_{3}$ over a wide range of excitation levels and temperatures. The nonlinear voltage-current characteristics elucidate the depinning process of the two CDWs and the temperature dependence of their threshold electric fields. Within the temperature and electric field range where the CDW is anticipated to be entirely pinned by residual impurities, a non-monotonic behavior in the noise magnitude versus electric field is observed. This phenomenon is attributed to the proliferation of thermally activated phase slip events, enhanced by the size effect in nanodevices. The idea is corroborated by the observation of a smeared activated behavior described by the Dutta-Horn relation. Certain aspects of the temperature dependence of the noise magnitude deviate from a simple activated behavior, suggesting a multifaceted origin of the resistance fluctuations in CDW systems at the nanometer scale. These findings provide valuable insights into the dynamics of CDW in nanodevices.

Field Driven Polymer Translocation Through a Nanochannel

In this paper, we used Monte Carlo simulations in two dimension (2D) to investigate field driven polymer translocation through a nanochannel with Bond Fluctuation Method. Accordingly, we studied the static properties of a polymer chain by calculating the mean-squared end-to-end distance 〈 R 2 〉 and the average squared radius of gyration 〈 R g 2 〉 of the polymer. In addition, the scaling behavior of radius of gyration and end-to-end distance with respect to chain length N has been investigated. And we got non-universal and non-monotonic scaling behavior. Moreover, we investigated the probability distribution of the escape time of the chain in the presence of an external field, and the most probable escape times were calculated.The influences of the external force F and the chain length N on the escape time has been also studied in terms of the scaling exponent α and δ ( τ ∼ F − δ and τ ∼ N α ). We found that the scaling exponents α = 2.1 for weak force and 1.80 for strong force; while δ = 0.97 for N = 31 and 0.74 for N = 71. Finally, the effect of the channel size on the translocation time of the polymer has been investigated. Our result indicates that escape times decreases rapidly with increasing channel width and the escape time τ increases with increasing channel length.

Transport Properties of Liquid Pentaerythritol Tetranitrate (PETN) from Molecular Dynamics Simulations.

We have used molecular dynamics simulations to determine the transport properties of liquid pentaerythritol tetranitrate (PETN), an important energetic material. The density, ρ, self-diffusion coefficient, D, thermal conductivity, κ, and shear viscosity, μ, have been computed over pressures and temperatures relevant to the subshock regime (up to 1000 K and a few GPa), where PETN is known to melt prior to initiation. We find that the thermal conductivity κ(P, T) can be represented by a simple analytical function that fits the data points with very good accuracy, even beyond the subshock regime, up to 2000 K and 20 GPa. The self-diffusion coefficient, D, exhibits nonmonotonic behavior, with notably the temperature-independent prefactor decreasing by several orders of magnitude between 0 and 2 GPa before remaining nearly constant after, and the activation energy varying little in the subshock regime before increasing linearly beyond. Lastly, the viscosity, μ, is well described by Nahme's law, which is fitted to the MD results and allows us to predict μ(P, T) for temperatures and pressures corresponding to the subshock regime. These results can be used to model the response of PETN to low-velocity impacts, where the material melts prior to the first reactions, and thermal conduction and viscosity play a crucial role.

Toroidal torques due to n=1 magnetic perturbations in ITER baseline scenario

Abstract Toroidal torques, generated by the resonant magnetic perturbation (RMP) and acting on the plasma column, are numerically systematically investigated for an ITER baseline scenario. The neoclassical toroidal viscosity (NTV), in particular the resonant portion, is found to provide the dominant contribution to the total toroidal torque under the slow plasma flow regime in ITER. While the electromagnetic torque always opposes the plasma flow, the toroidal torque associated with the Reynolds stress enhances the plasma flow independent of the flow direction. A peculiar double-peak structure for the net NTV torque is robustly computed for ITER, as the toroidal rotation frequency is scanned near the zero value. This structure is found to be ultimately due to a non-monotonic behavior of the wave-particle resonance integral (over the particle pitch angle) in the superbanana plateau NTV regime in ITER. These findings are qualitatively insensitive to variations of a range of factors including the wall resistivity, the plasma pedestal flow and the assumed frequency of the rotating RMP field.

A computer simulation study of a chiral active ring polymer.

We investigate a ring polymer under the influence of chiral active Brownian forces in two dimensions using coarse-grained computer simulations. We observe a non-monotonic behavior of the radius of gyration of an active Brownian ring as a function of active force. However, the shrinkage of the ring in the intermediate strength of active forces becomes more pronounced in the presence of chiral active forces, and the shrinkage is monotonic at a given activity level as a function of the angular frequency controlling the direction of the active force. The distribution of radius of gyration, inter-monomer distance, and radial distribution suggest that the monomers come close to each other, eventually leading to the shrinkage of the ring. Moreover, the bond-correlation suggests that the chirality introduces a local folding of the monomers. Furthermore, using the diameter correlation function, we show that the ring performs tank-treading motion with a frequency following power-law relation with active force with exponent 3/2. The mean squared displacement of the monomers further assists the tank-treading dynamics by exhibiting oscillatory behavior.

Charge State of Weak Polyelectrolyte Brushes Determines Salt-Dependent Swelling and Hysteretic Behavior.

We investigate the combined effects of ionizable monomer fraction f, pH, and monovalent salt concentration Cs on the swelling of weak polyelectrolyte brushes (PEBs) by using in situ ellipsometry. Our system consists of random copolymers of basic (2-(dimethylamino)ethyl acrylate, DMAEA) and neutral (2-hydroxyethyl acrylate, HEA) monomers at varying fractions of ionizable monomer. Swelling of the brushes qualitatively follows the trends predicted by scaling laws for PEBs under different charge states but quantitatively deviates at specific ionic strengths and pH values. We posit these deviations stem from the lack of excluded volume effects and assumptions of strong chain stretching in current theoretical models. Most notably, we uncover a salt-dependent, nonmonotonic hysteretic behavior as weak PEB brushes are cycled from protonated to deprotonated and back. The nonmonotonic trend of hysteresis with salt can be explained by an interplay between the protonation facilitating effects of salt in the osmotic regime and the charge screening effects in the salted regime, which make charge distribution along weak PEBs more uniform. Our results provide insight into the mechanisms that determine whether polyelectrolytes exhibit weak versus strong polyelectrolyte behavior in various environmental conditions.

Shear-driven diffusion with stochastic resetting

External flows, such as shear flow, add directional biases to particle motion, introducing anisotropic behavior into the system. Here, we explore the non-equilibrium dynamics that emerge from the interplay between linear shear flow and stochastic resetting. The particle diffuses with a constant diffusion coefficient while simultaneously experiencing linear shear and being stochastically returned to its initial position at a constant rate. We perturbatively derive the steady-state probability distribution that captures the effects of shear-induced anisotropy on the spatial structure of the distribution. We show that the dynamics, which initially spread diffusively, will at late times reach a steady state due to resetting. At intermediate timescales, the system approaches this steady state either by passing through a superdiffusive regime (in the shear-dominated case) or by exhibiting purely sub-diffusive behavior (in the resetting-dominated case). The steady state also gains cross correlations, a feature absent in simpler resetting systems. We also show that the skewness has a non-monotonic behavior when one passes from the shear-dominated to the resetting-dominated regime. We demonstrate that at small resetting rates, the energetic cost of maintaining the steady state becomes significantly higher due to the displacement caused by shear, a unique scaling not seen without shear. Surprisingly, if only the x-position is reset, the system can maintain a Brownian yet non-Gaussian diffusion pattern with non-trivial tails in the distribution.

Nonmonotone Spectral Analysis for Variational Inclusions

Gradient descent algorithms perform well in convex optimization but can get tied for finding local minima in non-convex optimization. A robust method that combines a spectral approach with nonmonotone line search strategy for solving variational inclusion problems is proposed. Spectral properties using eigenvalues information are used for accelerating the convergence. Nonmonotonic behaviour is exhibited to relax descent property and escape local minima. Nonmonotone spectral conditions leverage adaptive search directions and global convergence for the proposed spectral subgradient algorithm.

Unveiling non-monochromatic modes and nonlinearity in Piet Hein quantum semiconductor waveguides

We investigate the propagation characteristics of transverse electric (TE) and transverse magnetic (TM) modes in a semiconductor quantum plasma-filled coaxial waveguide with a Piet Hein cross-section. The unique geometry of the Piet Hein cross-section offers intriguing possibilities for tailoring modal properties and exploiting novel nonlinear phenomena. Using analytical and numerical methods, we unveil the non-monochromatic behaviour of TE and TM modes, characterized by distinct peaks and troughs in their field components. The Ez\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_{z}$$\\end{document} component of the TM mode exhibits a suppressed field within the central core and higher concentration in the cladding region, potentially minimizing energy loss within the waveguide. The Eρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_{\\rho }$$\\end{document} component exhibits pronounced oscillations near the waveguide boundaries, suggesting constructive and destructive interference patterns. The Eξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_{\\xi }$$\\end{document} component displays a non-monotonic behaviour with multiple pits and bumps, highlighting the interplay between the TE mode, the Piet Hein geometry, and the semiconductor quantum plasma properties. The Bρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{\\rho }$$\\end{document} component of the TM mode exhibits a non-monochromatic behaviour with multiple maxima and minima, attributed to the complex interactions between propagating waves with different phase shifts. The Bξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{\\xi }$$\\end{document} component exhibits a non-uniform distribution with distinct pits and bumps, with a resurgence towards the waveguide edges potentially due to higher-order mode contributions and local field enhancement effects. Our findings pave the way for the development of novel photonic devices with enhanced functionalities based on Piet Hein semiconductor quantum plasma waveguides.

Effects of frequency mixing on Shapiro-step formations in sliding charge-density-waves

A one-dimensional charge-density wave (CDW) is driven to slide by a dc electric field, carrying an electric current. In an additional ac field with frequency ωex, it is known that the sliding CDW can be synchronized to ωex, leading to the occurrence of Shapiro steps in the I–V characteristics. Motivated by a recent experiment where ac fields with two frequencies ωex and ωex′ are simultaneously applied, we theoretically investigate the effects of frequency mixing on the Shapiro-step formation. Based on the Fukuyama–Lee–Rice model, we show that in addition to the main steps induced by ωex, satellite steps characterized by ωex′ emerge. It is also found that with increasing the ac-field strength for ωex′, each step width first exhibits a damped oscillation as in the one-frequency case and then exhibits a non-monotonic behavior. The origin of these behaviors and the relevance to the associated experiment are also discussed.

Study of net-baryon higher moments in PNJL model and their expectation for net-proton using the subensemble acceptance method for the search of QCD critical point

The critical point is one of the most important aspects of the QCD phase diagram of strongly interacting matter. The nonmonotonic behavior of the higher-order moments of conserved quantities like net-baryon (ΔB), net-charge (ΔQ), and net-strangeness (ΔS) are believed to be the signatures of the QCD critical point as a function of energy. We study the effect of the QCD critical point on moments of net-baryon in the Polyakov loop enhanced Nambu-Jona-Lasinio (PNJL) model of QCD with six-quark and eight-quark interactions for finite and infinite volume systems. The study is performed at energies similar to Relativistic Heavy-Ion Collider beam energy scan. Experimentally measuring conserved quantities is difficult due to systematic limitations. Therefore, net-proton, net-pion, and net-kaon are measured as the proxy of ΔB, ΔQ, and ΔS. Recent studies in the subensemble acceptance method on the hadron resonance gas (HRG) model show the dependency of the measured higher-order moment on the experimental acceptance. We applied the subensemble acceptance method to analyze the behavior of κσ2 of net-baryon distribution within the subvolume system for various acceptance fractions. These results can be directly mapped to the subvolume (particle) percentage of the total volume (conserved quantities). Our findings are compared to the solenoidal tracker at RHIC (STAR) net-proton and proton data with different energies to investigate the presence of the critical point. Additionally, these results are also compared with the ultrarelativistic quantum molecular dynamics (UrQMD), HRG model, and available lattice data. Published by the American Physical Society 2024

Influence of bed temperature on the final properties of PLA parts manufactured by material extrusion

Purpose This paper aims to study the influence of bed temperature on the properties of printed parts and their structural stability. Design/methodology/approach Material extrusion is a manufacturing technique in which a part is completed layer by layer with molten filament. The first layer is deposited on a build platform called bed, which is usually at a controlled temperature above room temperature. The density, coefficient of thermal expansion and Young’s modulus were determined as a function of the bed temperature. The complex permittivity was determined at different temperatures, with the aim of analyzing the influence of the bed temperature and isothermal treatments on the characteristics of the amorphous phase. Findings The Young’s modulus presented a non-monotonic behavior, while the coefficient of thermal expansion did not present a clear dependence on the bed temperature. However, a contraction of the dimensions of the parts was observed after heating at temperatures above the glass transition. With treatments at temperatures lower than the glass transition temperature, no changes were observed. However, with treatments at temperatures higher than this, changes in the mobile amorphous region were inferred. Originality/value Issues related to the use of parts manufactured by 3D printing after a posterior heating were analyzed: an improvement in the Young’s modulus and a slight variation of the coefficient of thermal expansion were observed. However, a significant variation in dimensions was detected, mainly for the lowest bed temperatures. This is important for possible applications at temperatures above 60°C.

Convection flow of NE-phase change material-water mixture in evacuated tube solar collector manifold: Numerical analysis of MHD double-diffusive convection and exothermic reaction

This study investigates the convection flow of nano-encapsulated phase change material (NEPCM)-water mixture in an evacuated tube solar collector manifold, focusing on the effects of magnetohydrodynamic (MHD) double-diffusive convection and exothermic reaction. Computational fluid dynamics simulations using the Galerkin finite element method were employed to analyze temperature and concentration distributions, fluid flow, melting zone of PCM nanocapsules, Nusselt number, Sherwood number, entropy generation, and thermal performance. The numerical analysis considers a range of dimensionless parameters, including Rayleigh number (Ra=103−105), Lewis number (Le=0.1−10), buoyancy ratio (Nz=1−5), nanoparticle concentration (ϕ=0.01−0.035), fusion temperature (ϴf=0.1−0.9), Stefan number (Ste=0.1−0.9), Hartmann number (Ha=0−50), magnetic field inclination angle (γ=0°−90°), and Frank-Kamenetskii number (FK=0−2.5). Results show that increasing Ra enhances the average Nusselt number (Nuav) by up to 156.1 % and the average Sherwood number (Shav) by up to 104.5 %, while increasing the total entropy generation by up to 13,155 %. Increasing FK reduces Nuav by up to 42.2 % but increases Shav by up to 13.1 %. The Lewis number and buoyancy ratio significantly influence the hydrothermal performance, with Nuav exhibiting non-monotonic behavior and Shav increasing by up to 240.9 % as Le increases. The nanoparticle concentration enhances Nuav by up to 49.7 %. Interestingly, the magnetic field effects are less pronounced than in previous studies, with Ha having a minor impact on Nuav and Shav. These findings have significant implications for the design and optimization of evacuated tube solar collectors and other thermal energy storage systems, potentially leading to improved efficiency and performance in real-world applications.