Short-range Forces Research Articles

Curved GaAs cantilever waveguides for the vertical coupling to photonic integrated circuits.

We report the nanofabrication and characterization of optical spot-size converter couplers based on curved GaAs cantilever waveguides. Using the stress mismatch between the GaAs substrate and deposited Cr-Ni-Au strips, single-mode waveguides can be bent out-of-plane in a controllable manner. A stable and vertical orientation of the out-coupler is achieved by locking the spot-size converter at a fixed 90 ∘ angle via short-range forces. The optical transmission is characterized as a function of temperature and polarization, resulting in a broad-band chip-to-fiber coupling extending over 150 nm wavelength bandwidth at cryogenic temperatures, with the lower bound for the coupling efficiency into the TE mode being 16±2% in the interval 900-1050 nm. The methods reported here are fully compatible with quantum photonic integrated circuit technology with quantum dot emitters, and open opportunities to design novel photonic devices with enhanced functionality.

Mechanism of long-range hydrophobic force based on cavitation of metastable liquid film

Hydrophobic force, a key driving force in colloid physicochemical system and biological macromolecular system, exhibits a distinct multi-scale effect. The prevailing scholarly consensus attributes long-range hydrophobic force to bubble bridging, facilitated by unstable liquid film cavitation, while short-range force is thought to arise from the reorganization of water molecules at the solid-liquid interface. However, a comprehensive theoretical study remains elusive. To further elucidate the mechanism of the long-range hydrophobic force based on unstable liquid film cavitation, we carry out systematic research on the long-range hydrophobic force between perfluorooctyl trichlorosilane hydrophobic particles and the surface, by utilizing atomic force microscopy (AFM) and molecular dynamics simulations. According to AFM force tests, the long-range hydrophobic force escalates incrementally with subsequent close contacts before reaching a plateau. On the tenth contact, the penetration curve exhibits a sudden jump to an adhesion distance of 502.01 nm. A distinct step in the retraction curve suggests the rupture of the cavitation bubble capillary bridge. Importantly, the classical capillary force mathematical model provides an effective fit for the penetration curve. Our calculations estimate the volume of the capillary bridge at 0.30 μm³, offering direct theoretical evidence of the unstable liquid film cavitation bubble capillary bridge. Further insights are gained from large-scale tensile molecular dynamics simulations by using GROningen MAchine for Chemical Simulations (GROMACS). The inherent correlation mechanism of the formation, evolution, and mechanical behavior of the cavitation bubble capillary bridge in the separation process of hydrophobic particles are further explored from a molecular perspective. The results demonstrate that the local pressure drop occurring at the moment of “jump-out” separation of the hydrophobic particles attracts nitrogen molecules to diffuse into the liquid film, thereby forming a cavitation bubble capillary bridge. Simultaneously, a jumping behavior is observed in the calculated spring potential curve at the moment of capillary bridge rupture. Finally, the influence of solution gas content on long-range hydrophobic force is investigated. There is a positive correlation between gas molecule content and both the growth rate of cavitation bubble capillary bridge volume and the length of capillary bridge stretch-rupture, further demonstrating the gas concentration dependence of long-range hydrophobic forces. In a word, revealing the long-range hydrophobic force mechanism based on the cavitation of unstable liquid film can enhance our understanding of the interaction between colloid physical chemistry and biological macromolecules. Meanwhile, hydrophobic force is the fundamental driving force of particle-bubble adhesion in mineral flotation system, and the revelation of its action mechanism has important guiding significance for regulating the actual mineral flotation process.

Effect of hydrostatic pressure on the supramolecular assembly of surfactant-cyclodextrin inclusion complexes.

The supramolecular assembly of simple colloids into complex, hierarchical structures arises from a delicate interplay of short-range directional and isotropic long-range forces. These assemblies are highly sensitive to environmental changes, such as temperature variations and the presence of specific molecules, making them promising candidates for nanomachine design. In this study, we investigate the effect of hydrostatic pressure, up to 1800 bar, on the supramolecular assemblies of cyclodextrin/surfactant complexes. Using small-angle neutron scattering, we demonstrate that while the overall structure of the supramolecular aggregates remains largely stable under pressure, the stiffness of the planar lattice formed by the inclusion complexes, the basic structural unit of the supramolecular assemblies, shows a fourfold increase between 250 and 1000 bar. These findings suggest that high-pressure studies can be exploited to better understand the mechanisms of supramolecular assembly processes, thereby aiding in the design of more robust and functional systems.

Enhancing non-Newtonian gravity constraint using a levitated pendulum in vacuum

The detection of non-Newtonian gravity is crucial for fundamental physics research and our understanding of dark energy. However, conducting an experiment that provides explicit evidence of its existence remains an endeavour. We propose an experiment utilizing a diamagnetically levitated pendulum in vacuum to detect non-Newtonian gravity on a micrometer scale. The pendulum configuration effectively helps to shield electromagnetic force fluctuations in the vacuum levitation system. The structural parameters of the pendulum are intentionally optimized to enhance the constraint on the non-Newtonian gravity strength α. The designed pendulum can be stably levitated in the diamagnetic trap thanks to its passive levitation mechanism. By conducting resonance force measurements at room temperature for a duration of 104 s, we anticipate a significant improvement in the constraint on the non-Newtonian gravity strength (α≥28) within the force range of λ=7.6 µm. This represents an enhancement of over three orders of magnitude compared to the current limit. This study presents a promising tool for investigating short-range forces and exploring frontier physics in tabletop laboratory.

Force-Directed Graph Layouts Revisited: A New Force Based on the T-Distribution.

In this article, we propose the t-FDP model, a force-directed placement method based on a novel bounded short-range force (t-force) defined by Student's t-distribution. Our formulation is flexible, exerts limited repulsive forces for nearby nodes and can be adapted separately in its short- and long-range effects. Using such forces in force-directed graph layouts yields better neighborhood preservation than current methods, while maintaining low stress errors. Our efficient implementation using a Fast Fourier Transform is one order of magnitude faster than state-of-the-art methods and two orders faster on the GPU, enabling us to perform parameter tuning by globally and locally adjusting the t-force in real-time for complex graphs. We demonstrate the quality of our approach by numerical evaluation against state-of-the-art approaches and extensions for interactive exploration.

Atomic‐scale insights into electronic, structural, dielectric, and ferroelectric properties of Ba(Zr, Ti)O3 perovskites

Ba(Zr, Ti)O3 perovskites are promising lead-free piezoelectric and relaxor ferroelectric materials for energy storage and harvest devices, of which the ferroelectric mechanism has long been ambiguous. We theoretically investigated the ferroelectric mechanism from the electronic and atomic scale using first-principles calculation based on density functional theory and density functional perturbation theory. With increasing zirconium content, it is obtained a lattice expansion and a decrease in the ferroelectric polarization in agreement with experiment. An unstable zone-center phonon mode is observed in the polar ferroelectric phase, which tends to stabilizein the nonpolar paraelectric phase, which is associated with the engineering of the relative displacement of the B-site ions that alters the short-range force. The newly formed Ti/Zr (dzx,dyz)-O (2px,2py) π-type bonds are discovered to be the origin of the Ba(Zr, Ti)O3ferroelectric instability and polarization. Local relaxation strains caused by lattice misalignment of the ionic displacements of Ti ions and Zr ions suppress the polarization of Ba(Zr, Ti)O3 by counteracting the off-centering of Ti ions and adjacent Zr ions in certain directions.

Peridynamic modelling of dynamic damage and fragmentation of cracked solids during impact contact

Dynamics damage of solids exhibit unique characteristics that are absent in static analysis. The presence of pre-existing cracks further increases the complications. To address this issue, the present study focuses on modelling dynamic damage of cracked solids during impact contact. The model is formulated based on the state-based peridynamics. It incorporates a modified damage model and employs the short-range force approach to capture the impact damage. The damping force is introduced to eliminate numerical oscillation around cracks. Then, the adaptive explicit time integration is introduced to efficiently solve the peridynamic equations. Model performance is evaluated through benchmark tests. Next, we simulate impact between two spheres with pre-existing cracks. Our focus lies in comprehending the mechanisms by which material properties and crack patterns affect damage. Further sensitivity analysis reveals that the kinetic energy of the impact system is significantly affected by the pre-existing cracks and geometric parameters of the cracks, including their number, length, angle, and distribution. The interplay of crack interaction and the gradual connection of the damaged region plays a vital role in the phenomena. The presented study offers insights into damage evolution during impact contact and provides guidelines for assessing impact damage in structures with pre-existing defects.

Universal Pairwise Interatomic van der Waals Potentials Based on Quantum Drude Oscillators.

Repulsive short-range and attractive long-range van der Waals (vdW) forces play an appreciable role in the behavior of extended molecular systems. When using empirical force fields, the most popular computational methods applied to such systems, vdW forces are typically described by Lennard-Jones-like potentials, which unfortunately have a limited predictive power. Here, we present a universal parameterization of a quantum-mechanical vdW potential, which requires only two free-atom properties─the static dipole polarizability α1 and the dipole-dipole C6 dispersion coefficient. This is achieved by deriving the functional form of the potential from the quantum Drude oscillator (QDO) model, employing scaling laws for the equilibrium distance and the binding energy, and applying the microscopic law of corresponding states. The vdW-QDO potential is shown to be accurate for vdW binding energy curves, as demonstrated by comparing to the ab initio binding curves of 21 noble-gas dimers. The functional form of the vdW-QDO potential has the correct asymptotic behavior at both zero and infinite distances. In addition, it is shown that the damped vdW-QDO potential can accurately describe vdW interactions in dimers consisting of group II elements. Finally, we demonstrate the applicability of the atom-in-molecule vdW-QDO model for predicting accurate dispersion energies for molecular systems. The present work makes an important step toward constructing universal vdW potentials, which could benefit (bio)molecular computational studies.

Surface Phase Diagrams for Wetting with Long-Ranged Forces.

Recent density functional theory and simulation studies of wetting and drying transitions in systems with long-ranged, dispersionlike forces, away from the near vicinity of the bulk critical temperature T_{c}, have questioned the generality of the global surface phase diagrams for wetting, due to Nakanishi and Fisher, pertinent to systems with short-ranged forces. We extend these studies deriving fully analytic results which determine the surface phase diagrams over the whole temperature range up to T_{c}. The phase boundaries, order of, and asymmetry between the lines of wetting and drying transitions are determined exactly showing that they always converge to an ordinary surface critical point. We highlight the importance of lines of maximally multicritical wetting and drying transitions, for which we determine the exact critical singularities.

Ab-initio investigation of structural, opto-electronic, and thermodynamic properties of ZnAl2Se4 for photovoltaic applications

In this manuscript, the structural, opto-electronic, and thermodynamic properties of ZnAl2Se4 chalcogenide compounds were studied in detail using the full potential linearized augmented plane wave method. The exchange and correlation potentials used in density functional theory were calculated using local density approximation, the generalized gradient approximation (GGA) method, and the modified Becke–Johnson (mBJ) potential using Wien2k code. The obtained results were compared with each other as well as with available experimental data. At ambient conditions, ZnAl2Se4 is a direct wide bandgap (Г–Г) semiconductor with a bandgap of 2.1 and 3.3 eV with GGA and mBJ potentials, respectively. Density of states (DOS; total DOS and Partial Density Of States (PDOS)) and electron density contour plots were in similar accordance with bandgap, showing semiconductive behavior and covalent bonding nature. The optical properties like the real and imaginary parts of the dielectric constant, the energy loss function L( ω), and the conductivity σ( ω) were calculated. Optical aspects show interaction among phonon and electron in terms of long-range and short-range forces. The studied compound is very useful for various linear–nonlinear optical devices, so this compound is very valuable for several linear–nonlinear optical devices. So this manuscript represents a comprehensive approach for calculating the complete set of useful properties of the ZnAl2Se4 compound, which can provide support for understanding various device phenomena such as electrochemical sensing, photovoltaics, and nonvolatile electronic memories.

A mathematical model-based investigation of liquid film dewetting over porous solid substrates

Thin liquid films resting on solid surfaces are susceptible to dewetting when physical inhomogeneities like surface roughness, textured patterns, and porosities are present on the substrate surface. These inhomogeneities affect liquid transport phenomena through dynamic wetting behavior and imbibition. They can render the liquid film unstable, thereby resulting in rupture and dewetting. Here, we mathematically model and simulate the dynamics of a thin liquid film with passive air above it, dewetting a porous solid substrate that bounds the liquid from below. The solid is modeled as a surface with regions of equally spaced pores, with a partial slip condition for the lateral velocity component of the liquid film, a spatially varying long-range attractive force parameter, as well as short-range repulsive interaction force parameters between the liquid–air interface and liquid–solid interface. Our results explain how the size and spacing of pore regions on the substrate, slip length of the liquid, and intermolecular force potentials influence the formation of morphological patterns and dewetting time scales of the liquid film.

The structure of low-lying 1− states in 90,94Zr from (α,α′γ) and (p,p′γ) reactions

The low-lying dipole strength was investigated in 90,94 Zr via the (p,p′γ) reaction at 80 MeV and via the (α,α′γ) reaction at 130 MeV. These experiments were performed at the Research Center for Nuclear Physics (Osaka University) and made combined use of the high-resolution magnetic spectrometer Grand Raiden and the CAGRA HPGe gamma array. The comparison of our results with existing (γ,γ′) reaction data shows differences in the excitation patterns. In the present experimental conditions, in fact, both α and p probes are exciting the investigated 1− states mainly through the short-range nuclear force, expected to favour the population of surface excitations. Distorted Wave Born Approximation (DWBA) calculations were made using form factors built assuming specific transition densities, characterized by a strong neutron component at the nuclear surface and based on Random Phase Approximation (RPA). A combined analysis of the (α,α′γ) and (p,p′γ) data was performed to investigate the isoscalar character of the 1− states in 90,94Zr. Although an overall general consistency was obtained in the studied energy intervals, not all (p,p′γ) cross sections were well reproduced using the isoscalar strength deduced from (α,α′γ) data. This might suggest that the mixing of isoscalar and isovector components and the degree of collectivity are not the same for all the 1− states studied.

Toughening colloidal gels using rough building blocks

Colloidal gels, commonly used as mesoporous intermediates or functional materials, suffer from brittleness, often showing small yield strains on the order of 1% or less for gelled colloidal suspensions. The short-range adhesive forces in most such gels are central forces—combined with the smooth morphology of particles, the resistance to yielding and shear-induced restructuring is limited. In this study, we propose an innovative approach to improve colloidal gels by introducing surface roughness to the particles to change the yield strain, giving rise to non-central interactions. To elucidate the effects of particle roughness on gel properties, we prepared thermoreversible gels made from rough or smooth silica particles using a reliable click-like-chemistry-based surface grafting technique. Rheological and optical characterization revealed that rough particle gels exhibit enhanced toughness and self-healing properties. These remarkable properties can be utilized in various applications, such as xerogel fabrication and high-fidelity extrusion 3D-printing, as we demonstrate in this study.

Maximum entropy distributions of dark matter in ΛCDM cosmology

Context. Small-scale challenges to ΛCDM cosmology require a deeper understanding of dark matter physics. Aims. This paper aims to develop the maximum entropy distributions for dark matter particle velocity (denoted by X), speed (denoted by Z), and energy (denoted by E) that are especially relevant on small scales where system approaches full virialization. Methods. For systems involving long-range interactions, a spectrum of halos of different sizes is required to form to maximize system entropy. While the velocity in halos can be Gaussian, the velocity distribution throughout the entire system, involving all halos of different sizes, is non-Gaussian. With the virial theorem for mechanical equilibrium, we applied the maximum entropy principle to the statistical equilibrium of entire system, such that the maximum entropy distribution of velocity (the X distribution) could be analytically derived. The halo mass function was not required in this formulation, but it did indeed result from the maximum entropy. Results. The predicted X distribution involves a shape parameter α and a velocity scale, v0. The shape parameter α reflects the nature of force (α → 0 for long-range force or α → ∞ for short-range force). Therefore, the distribution approaches Laplacian with α → 0 and Gaussian with α → ∞. For an intermediate value of α, the distribution naturally exhibits a Gaussian core for v ≪ v0 and exponential wings for v ≫ v0, as confirmed by N-body simulations. From this distribution, the mean particle energy of all dark matter particles with a given speed, v, follows a parabolic scaling for low speeds (∝v2 for v ≪ v0 in halo core region, i.e., “Newtonian”) and a linear scaling for high speeds (∝v for v ≫ v0 in halo outskirt, i.e., exhibiting “non-Newtonian” behavior due to long-range gravity). We compared our results against N-body simulations and found a good agreement.

Unveiling the role of long-range and short-range forces in the non-productive adsorption between lignin and cellulases at different temperatures

Quantitatively understanding of interaction mechanism between lignin and cellulases is essential for the efficient improvement of lignocellulose enzymatic hydrolysis. However, the individual contribution of multiple forces between lignin and cellulases to the non-productive adsorption of enzymes still remains deeply ambiguous, especially in situations of near enzymatic hydrolysis temperatures. Herein, atomic force microscopy (AFM) and computational simulations were utilized to quantitatively analyze the intermolecular forces between lignin and enzyme at 25 °C and 40 °C. Our results unveiled that an increase in temperature obviously improved adsorption capacity and total intermolecular forces between lignin and cellulases. This positive relationship mainly comes from the increase in the decay length of hydrophobic forces for lignin-cellulases when temperature increases. Different from the hydrophobic interaction which provides long-range part of attractions, van der Waals forces dominate the intermolecular force only at approaches < 2 nm. On the other hand, electrostatic forces exhibited repulsive effects, and its intensity and distance were limited due to the low surface potential of cellulases. Short-range forces including hydrogen bonding (main) and π-π stacking (minor) stabilize the non-specific binding of enzymes to lignin, but increasing temperature reduces hydrogen bond number. Therefore, the relative contribution of long-range forces increased markedly at higher temperatures, which benefits protein capture and brings lignin and cellulase close together. Finally, the structure–activity relationships between lignin physicochemical properties and its inhibitory effect to enzymes indicated that hydrophobic interactions, hydrogen bonding, and steric effects drive the final adsorption capacity and glucose yields. This work provides quantitative and basic insights into the mechanism of lignin-cellulase interfacial interactions and guides design of saccharification enhancement approaches.

Hybrid PD-DEM approach for modeling surface erosion by particles impact

Peridynamics (PD) theory is a promising technique for modeling solids with discontinuities. Short-range repulsive force models are commonly employed in PD impact event simulations. Despite their extensive usage, short-range force models do not take damping, friction, and tangential force components into account and hence are unable to effectively describe energy dissipation, leading to uncertainty in the calculation of contact forces. However, the accuracy of impact simulations using alternate contact models has not been extensively investigated in the context of PD impact simulations. The Discrete Element Method (DEM) has been proven to be the most reliable and effective approach to model collision processes between distinct solid objects. This work presents, a particle-based hybrid PD-DEM model to accurately predict the particle impact forces and the resulting damage to the target material. The present model brings together the unique capabilities of PD and DEM and has the potential to make use of the various DEM contact laws, which allow the development and adjustment of relevant contact forces in the normal and tangential directions. Furthermore, damping effects, friction, and intra-particle stiffness are incorporated into the simulations through DEM. The proposed method has been used for modeling material failure after being validated and verified for the contact parameters during the impact process. The predicted damage patterns and resulting material loss demonstrate good agreement with the experimental results reported in the literature.

Water in the Electrical Double Layer of Ionic Liquids on Graphene

The performance of electrochemical devices using ionic liquids (ILs) as electrolytes can be impaired by water uptake. This work investigates the influence of water on the behavior of hydrophilic and hydrophobic ILs─with ethylsulfate and tris(perfluoroalkyl)trifluorophosphate or bis(trifluoromethyl sulfonyl)imide (TFSI) anions, respectively─on electrified graphene, a promising electrode material. The results show that water uptake slightly reduces the IL electrochemical stability and significantly influences graphene's potential of zero charge, which is justified by the extent of anion depletion from the surface. Experiments confirm the dominant contribution of graphene's quantum capacitance (CQ) to the total interfacial capacitance (Cint) near the PZC, as expected from theory. Combining theory and experiments reveals that the hydrophilic IL efficiently screens surface charge and exhibits the largest double layer capacitance (CIL ∼ 80 μF cm-2), so that CQ governs the charge stored. The hydrophobic ILs are less efficient in charge screening and thus exhibit a smaller capacitance (CIL ∼ 6-9 μF cm-2), which governs Cint already at small potentials. An increase in the total interfacial capacitance is observed at positive voltages for humid TFSI-ILs relative to dry ones, consistent with the presence of a satellite peak. Short-range surface forces reveal the change of the interfacial layering with potential and water uptake owing to reorientation of counterions, counterion binding, co-ion repulsion, and water enrichment. These results are consistent with the charge being mainly stored in a ∼2 nm-thick double layer, which implies that ILs behave as highly concentrated electrolytes. This knowledge will advance the design of IL-graphene-based electrochemical devices.

Normal coordinate analysis to study the optical phonons in B-site cation disordered Ruddlesden-Popper Sr3B2O7 (B = V, Cr, Fe, Co) crystals

The Raman and infrared (IR) phonons for the Ruddlesden-Popper Srn+1BnO3n+1 (B = V, Cr, Fe, Co) bilayered tetragonal compounds with n = 2 of symmetry D174h and phase I4/mmm (Z = 2) have been analyzed with Wilson's GF-Matrix Method. Theoretical assignments for the optical wavenumbers have been reported first time for the bilayered tetragonal Sr3V2O7, Sr3Cr2O7, and Sr3Co2O7 compounds by using ten short-range force constants. The appropriate optical vibrational modes have been assigned to the bilayered tetragonal Sr3Fe2O7 compound. The theoretically calculated Raman modes found in the literature are not satisfactorily matched with the experimentally observed frequencies for the bilayered tetragonal Sr3Fe2O7 compound. Using the available data of the isostructural compounds Sr3Ti2O7 and Sr3Mn2O7, we have tried to calculate and report better results for the Raman vibrational modes of the Sr3Fe2O7 compound. Also, we have compared all these three compounds together in terms of frequencies and force constants. The impact of cation-B (B = V, Cr, Fe, Co) exchange on the lattice dynamics of the tetragonal bilayered Sr3B2O7 (B = V, Cr, Fe, Co) isostructural compounds has been analyzed by comparison of the Zone centre vibrational modes, force constants, and bond lengths. For understanding the structure more clearly an attempt is also made to analyze the effect of B-cations (B = V, Cr, Fe, Co) on the affected apical bonds. For each normal mode of the bilayered tetragonal Sr3B2O7 (B = V, Cr, Fe, Co) Ruddlesden-Popper phase, the potential energy distribution (PED) has been analyzed for the significant impact of short-range force constants on different vibrational modes.

Code modernization strategies for short-range non-bonded molecular dynamics simulations

Modern HPC systems are increasingly relying on greater core counts and wider vector registers. Thus, applications need to be adapted to fully utilize these hardware capabilities. One class of applications that can benefit from this increase in parallelism are molecular dynamics simulations. In this paper, we describe our efforts at modernizing the ESPResSo++ simulation package for molecular dynamics by restructuring its particle data layout for efficient memory accesses and applying vectorization techniques to benefit the calculation of short-range non-bonded forces, which results in an overall three times speedup and serves as a baseline for further optimizations. We also implement fine-grained parallelism for multi-core CPUs through HPX, a C++ runtime system which uses lightweight threads and an asynchronous many-task approach to maximize concurrency. Our goal is to evaluate the performance of an HPX-based approach compared to the bulk-synchronous MPI-based implementation. This requires the introduction of an additional layer to the domain decomposition scheme that defines the task granularity. On spatially inhomogeneous systems, which impose a corresponding load-imbalance in traditional MPI-based approaches, we demonstrate that by choosing an optimal task size, the efficient work-stealing mechanisms of HPX can overcome the overhead of communication resulting in an overall 1.4 times speedup compared to the baseline MPI version.

Numerical discreteness errors in multispecies cosmological N-body simulations

ABSTRACT We present a detailed analysis of numerical discreteness errors in two-species, gravity-only, cosmological simulations using the density power spectrum as a diagnostic probe. In a simple set-up where both species are initialized with the same total matter transfer function, biased growth of power forms on small scales when the solver force resolution is finer than the mean interparticle separation. The artificial bias is more severe when individual density and velocity transfer functions are applied. In particular, significant large-scale offsets in power are measured between simulations with conventional offset grid initial conditions when compared against converged high-resolution results where the force resolution scale is matched to the interparticle separation. These offsets persist even when the cosmology is chosen so that the two particle species have the same mass, indicating that the error is sourced from discreteness in the total matter field as opposed to unequal particle mass. We further investigate two mitigation strategies to address discreteness errors: the frozen potential method and softened interspecies short-range forces. The former evolves particles under the approximately ‘frozen’ total matter potential in linear theory at early times, while the latter filters cross-species gravitational interactions on small scales in low-density regions. By modelling closer to the continuum limit, both mitigation strategies demonstrate considerable reductions in large-scale power spectrum offsets.