Nonmonotonic Dependence Research Articles

Search for the Critical Point via Intermittency Analysis in NA61/SHINE

The existence and location of the QCD critical point are objects of both experimental and theoretical studies. The comprehensive data collected by NA61/SHINE during a two-dimensional scan in beam momentum and system size allows for a systematic search for the critical point – a search for a non-monotonic dependence of various correlation and fluctuation observables on collision energy and size of colliding nuclei. Intermittency analysis is a statistical tool used in heavy ion collisions that includes the study of scaled factorial moments (SFMs) of multiplicity distributions in the 2D transverse momentum space to detect power-law fluctuations and explore different aspects of the QCD phase diagram. In particular, proton intermittency has been used to locate the critical point of strongly interacting matter, and, more recently, intermittency of negatively charged hadrons have also been used to study the properties of QCD interactions.

Impact of mixing and configurational entropies on the entropy-driven potential of mean force

Using classical density functional theory (cDFT) with the fundamental measure functional (FMF) approximation, we examine how the entropic force and its integration, the potential of mean force (PMF), between two hard walls in a polydisperse hard-body solvent vary with monomer size polydispersity (whether the solvent consists of spherical monomers or chain molecules formed by freely linked monomers) or the number of monomers in the chain solvent. Molecular dynamics simulations validate the FMF's accuracy in predicting density distributions for five- and seven-component hard sphere fluids in slit geometries, though improvements are possible at high packing fractions. The PMF calculations reveal that increasing monomer size polydispersity or the number of monomers in a chain molecule reduce entropic attraction strength at contact and lower the main potential barrier height. This reduction is due to the system's limited capacity to further increase entropy when both mixing and conformational entropies are already high. For monomer or dimer solvent, the main potential barrier position shows either monotonic or non-monotonic dependence on monomer size polydispersity, depending on bulk packing fractions, while the PMF range shortens with increasing monomer size polydispersity or chain molecule monomer number. These findings could inform the design of tunable materials.

Verification of radical pair mechanism predictions for weak magnetic field effects on superoxide in planarians.

Superoxide concentration and tissue regeneration in planarians exhibit a complex non-monotonic dependence on the strength of an applied weak magnetic field. While this is difficult to understand based on classical physics, a recently proposed quantum model based on a flavinsuperoxide radical pair mechanism could replicate the previously observed superoxide concentrations. However, this model also predicts increased superoxide concentrations for both lower and higher fields. This seemed to conflict with earlier experimental observations on blastema sizes, which were correlated with superoxide in the previously observed regime but were known not to follow the predicted trends for lower and higher fields. Motivated by this apparent contradiction, we here directly experimentally tested the predictions of the quantum model for superoxide for lower and higher fields. To our own surprise, our experiments confirmed the predictions of the radical pair model for superoxide, and incorporating interactions with multiple nuclei further improved the model's agreement with the experimental data. While open questions remain regarding the exact relationship between blastema sizes and superoxide, which is revealed to be more complex than previously observed, and the detailed properties of the underlying radical pair, our results significantly support a quantum biological explanation for the observed magnetic field effects.

A dynamical systems model for the total fission rate in Drp1-dependent mitochondrial fission.

Mitochondrial hyperfission in response to cellular insult is associated with reduced energy production and programmed cell death. Thus, there is a critical need to understand the molecular mechanisms coordinating and regulating the complex process of mitochondrial fission. We develop a nonlinear dynamical systems model of dynamin related protein one (Drp1)-dependent mitochondrial fission and use it to identify parameters which can regulate the total fission rate (TFR) as a function of time. The TFR defined from a nondimensionalization of the model undergoes a Hopf bifurcation with bifurcation parameter [Formula: see text] where [Formula: see text] is the total concentration of mitochondrial fission factor (Mff) and k+ and k- are the association and dissociation rate constants between oligomers on the outer mitochondrial membrane. The variable μ can be thought of as the maximum build rate over the disassembling rate of oligomers. Though the nondimensionalization of the system results in four dimensionless parameters, we found the TFR and the cumulative total fission (TF) depend strongly on only one, μ. Interestingly, the cumulative TF does not monotonically increase as μ increases. Instead it increases with μ to a certain point and then begins to decrease as μ continues to increase. This non-monotone dependence on μ suggests interventions targeting k+, k-, or [Formula: see text] may have a non-intuitive impact on the fission mechanism. Thus understanding the impact of regulatory parameters, such as μ, may assist future therapeutic target selection.

Interface evolution induced by two successive shocks under diverse reshock conditions

The effects of reshock conditions, including the interface evolution state before reshock and the second shock intensity, on interface instability induced by two successive shocks propagating in the same direction are investigated via shock-tube experiments. It is observed that the reshock promotes the interface instability, and the post-reshock perturbation evolution relates to both the pre-reshock interface evolution state and second shock intensity. For the linear evolution of the twice-shocked interface, existing models perform poorly when either the pre-reshock interface shape effect or the secondary compression effect is pronounced, as current reduction factors fail to accurately describe these effects. Besides, the reshock-induced linear amplitude growth rate shows a non-monotonic dependence on the scaled pre-reshock amplitude, primarily due to the shape effect of the pre-reshock interface. For the post-reshock nonlinear evolution, the model proposed by Zhang & Guo (J. Fluid Mech., vol. 786, 2016, pp. 47–61) offers reasonable predictions when the second shock is weak. However, when the second shock is moderately strong, the model overestimates the bubble growth and underestimates the spike evolution under the influence of the significant secondary compression effect. Furthermore, empirical linear and nonlinear models capable of describing the dependence of the post-reshock evolution on reshock conditions are proposed based on the present experimental results and existing models.

Microscopic Origin of Twist-Dependent Electron Transfer Rate in Bilayer Graphene.

Using molecular simulation and continuum dielectric theory, we consider how electrochemical kinetics are modulated by the twist angle in bilayer graphene electrodes. By establishing a connection between the twist angle and the screening length of charge carriers within the electrode, we investigate how tunable metallicity modifies the statistics of the electron transfer energy gap. Constant potential molecular simulations show that the activation free energy for electron transfer increases with screening length, leading to a non-monotonic dependence on the twist angle. The twist angle alters the density of states, tuning the number of thermally accessible channels for electron transfer and the reorganization energy by affecting the stability of the vertically excited state through attenuated image charge interactions. Understanding these effects allows us to express the Marcus rate of interfacial electron transfer as a function of the twist angle in a manner consistent with experimental observations.

A Monte Carlo study on a 3-dimensional comb polymer translocation through a nanopore driven by an electric field

Abstract A lattice Monte Carlo simulation study of the translocation of comb polymers through a nanopore subjected to an electric field is presented. The translocation dynamics was extensively studied in terms of the applied electric field strength, the pore size, and the comb polymer topology. The variations of the most probable translocation time $\tau_p$ and the mean translocation time \mt\ as a function of the applied electric field strength show distinct features, the latter exhibiting a nonmonotonic dependence on the electric field. We were able to show the existence of a critical field strength $\delta \epsilon_c$ defined by the narrowest distribution of the translocation time, which is closely related to the size of the nanopore. In addition, we have found that the critical field strength also defines a transition point between two regimes of translocation: a smooth translocation for a field strength below $\delta \epsilon_c$ and a chaotic translocation for a field strength above $\delta \epsilon_c$. Moreover, for the smallest pore size ($r_p = 1$), monomers can only cross the nanopore in a single file, while for larger pores different modes of polymer translocation are identified. Finally, the dependence of the mean translocation time on the backbone length is governed by a power law relationship $\left < \tau \right > \sim {N_B}^{\alpha}$, where the scaling exponent $\alpha$ is found to be in the range of 1.3--1.7 for the set of side chain lengths and nanopore sizes investigated. As for the side chain length $N_S$, the mean translocation time is found to follow a linear dependence $\left < \tau \right > \sim {N_S}$.

Wave Function Localization Reduces the Bandgap of Disordered Double Perovskite Cs2AgBiBr6.

Double perovskite Cs2AgBiBr6 is a promising alternative to lead-based perovskites with excellent stability and attractive optoelectronic properties. However, a relatively large bandgap severely limits its performance in many applications such as solar cells and photodetectors. It has been reported that a random distribution of Ag and Bi atoms in Cs2AgBiBr6 effectively reduces its bandgap without introducing dopants or impurities, while the mechanism remains unclear. Here, using density functional theory calculations, we demonstrate that the Ag-Bi disorder in Cs2AgBiBr6 generates localized electronic states as band edges to regulate the bandgap. The disordered structures segregate Ag and Bi atoms in the lattice, and the formed homoatomic clusters lead to wave function localization. Moreover, the bandgap decrease exhibits a non-monotonic dependence on the degree of disorder. Our results are comparable with experimental observations and provide crucial insights into understanding the order-disorder transition in double perovskites.

Evolution of critical current density in CaKFe4As4 with La-doping

Abstract Single crystals of (Ca1-xLax)KFe4As4 (0 ≤ x ≤0.16) have been grown by using the self-flux method, and the evolution of physical properties including the critical current density (Jc) with La-doping has been investigated. Tc decreases monotonically with increasing x, while Jc at the same temperature and magnetic field increases initially and reach its maximum at x = 0.082. The increase in Jc is more obvious at low temperatures and high fields. At T = 5 K and H = 40 kOe, Jc reaches 0.34 MA/cm2, which is ~4 times larger than that for pure crystals. It is also found that anomalous temperature dependence of Jc in CaKFe4As4 is wiped away as the La content is increased. However, Jc shows non-monotonic field dependence (peak effect) at high fields in crystals with large x. In addition, we found that despite weak anisotropy of Hc2, there is extremely large anisotropy of Jc up to ~15, which is most likely caused by novel planar defects in the crystal, similar to CaKFe4As4. Jc characteristics in (Ca1-xLax)KFe4As4 with disorder outside FeAs planes is compared with that in CaK(Fe1-xCox)4As4 with disorder within FeAs planes.

Non-Amontons frictional behaviors of grain boundaries at layered material interfaces

Against conventional wisdom, corrugated grain boundaries in polycrystalline graphene, grown on Pt(111) surfaces, are shown to exhibit negative friction coefficients and non-monotonic velocity dependence. Using combined experimental, simulation, and modeling efforts, the underlying energy dissipation mechanism is found to be dominated by dynamic buckling of grain boundary dislocation protrusions. The revealed mechanism is expected to appear in a wide range of polycrystalline two-dimensional material interfaces, thus supporting the design of large-scale dry superlubric contacts.

Reinforcement Learning for Submodel Assignment in Adaptive Modeling of Turbulent Flames

Reinforcement learning (RL), an unsupervised machine learning approach, is innovatively introduced to turbulent combustion modeling and demonstrated through the automated construction of submodel assignment criteria within the framework of zone-adaptive combustion modeling (AdaCM). In AdaCM, the appropriate combustion submodel—whether the cost-effective species transport model or the advanced transported probability density function (TPDF) method—is adaptively assigned to different regions based on a criterion crucial for performance. The use of RL avoids the extensive manual optimization that involves repetitive calculations and struggles to account for multiple factors. Specifically, RL agents observe local variables as the state and determine the appropriate submodel through a policy. The policy is refined to maximize a reward measuring both accuracy and efficiency through the interaction between RL agents and the AdaCM solver. The methodology is demonstrated for a turbulent non-premixed jet flame, and a sophisticated RL criterion exhibiting a nonlinear and nonmonotonic dependency on the two-dimensional state of mixture fraction and Damköhler number is learned. The AdaCM with the trained criterion provides predictions that are nearly indistinguishable from those obtained using the TPDF method for the whole computational domain, while substantially reducing the computational cost with the speedup of 3.4 and only 22% of cells for TPDF.

Revealing membrane integrity and cell size from diffusion kurtosis time dependence.

The nonmonotonic dependence of diffusion kurtosis on diffusion time has been observed in biological tissues, yet its relation to membrane integrity and cellular geometry remains to be clarified. Here we establish and explain the characteristic asymmetric shape of the kurtosis peak. We also derive the relation between the peak time , when kurtosis reaches its maximum, and tissue parameters. The peak shape and its position qualitatively follow from the adiabatic extension of the Kärger model onto the case of intra-cellular diffusivity time-dependence. This intuition is corroborated by the effective medium theory-based calculation, as well as by Monte Carlo simulations of diffusion and exchange in randomly and densely packed spheres for various values of permeability, cell fractions and sizes, and intrinsic diffusivity. We establish that is proportional to the geometric mean of two characteristic time scales: extra-cellular correlation time (determined by cell size) and intra-cellular residence time (determined by membrane permeability). When exchange is barrier-limited, the peak shape approaches a universal scaling form determined by the ratio . Numerical simulations and theory provide an interpretation of a specific feature of kurtosis time-dependence, offering a potential biomarker for in vivo evaluation of pathology by disentangling the functional (permeability) and structural (cell size) integrity in tissues. This is relevant as the time-dependent diffusion cumulants are sensitive to pathological changes in membrane integrity and cellular structure in diseases, such as ischemic stroke, tumors, and Alzheimer's disease.

Non-monotonic dynamic correlation explored via active microrheology

Abstract In the study of local and heterogeneous structures in supercooled liquids, microrheology plays a crucial role, offering a closer examination of the mechanical properties at a local level. We concentrate on active microrheology, where an external force drives a probe particle. This technique is employed in the study of a Kob–Andersen mixture, using extensive molecular dynamics simulations. Through active microrheology, we analyze the positional dependence of viscosity, observing how probe particles respond to activation velocity. Utilizing advanced stochastic analysis, we disentangle the deterministic and stochastic components of the local viscosity time series, characterizing its nonlinear and intermittent properties, which indicate heterogeneity. We construct a Langevin equation to model the dynamics of local viscosity and derive its drift and diffusion coefficients from simulation data. Additionally, we investigate the temperature-dependent variations of viscosity dynamics, unveiling their multiplicative and nonlinear nature. We elaborate on how the existence of multiplicative dynamics in viscosity results in the characteristic emergence of heterogeneity within viscosity dynamics. We derive a dynamic correlation length from local viscosity. Moreover, this correlation length shows a non-monotonic dependence on temperature with a maximum at about the Kauzmann temperature.

An Increase in The Cross-Section of Two-Photon Absorption of Styrene Dye in Supramolecular Complexes with Cucurbituriles

Two-photon absorption cross sections of aqueous solutions of the styryl dye trans-4-[4-(dimethylamino)styryl]-1-methylpyridinium iodide (DASPI) and its inclusion complexes with cucurbit[n]urils (CB[n] n = 6–8) were measured using fluorescence spectroscopy. A nonmonotonic dependence of the cross-section size on the excitation wavelength and on the cavitand cavity size was found. Compared with a free dye, a sevenfold increase in the two-photon absorption cross section was observed in DASPI inclusion complexes with CB[8] at an excitation wavelength of 980 nm.

Mechanisms and models of interface trap annealing in positively-biased MOS devices

Abstract We propose a hydrogen anion (H$^-$) passivation mechanism of the interface trap annealing (ITA) in positively-biased metal-oxide-semiconductor (MOS) devices. It is demonstrated that, the protons (H$^+$) released in SiO$_2$ due to H$_2$ cracking on oxide traps can migrate into Si at relatively high temperature, therefore passivating the interfacial $P_b$ centers by capturing two electrons provided by the positive bias. This new mechanism explains the elimination temperature of about 100$^\circ$C in experiments, which is much lower than temperature above 220$^\circ$C predicted by the traditional H$_2$ passivation mechanism. We also derive analytic models of the ITA, based on the coupling transformation dynamics of oxide and interface traps, as well as the concept of hierarchically constrained dynamics in glassy materials. These models can universally describe a generation-to-elimination transition of $P_b$, and predict the enhanced elimination of $E'_\gamma$ as the annealing temperature is elevated. Moreover, we demonstrate that, the defect annealing models can be applied to analysis the nonmonotonic temperature dependence of the annealing of threshold voltage shift in nMOS devices. Our findings provide a theoretical basis for achieving the low temperature elimination of interface traps, and for setting the high temperature stages of accelerated aging and damage evaluations of MOS devices.

Exchange-enhanced spin-orbit splitting and its density dependence for electrons in monolayer transition metal dichalcogenides

We show that spin-orbit splitting (SOS) in monolayers of semiconducting transition metal dichalcogenides (TMDs) is substantially enhanced by an electron-electron interaction. This effect, similar to the exchange enhancement of the electron g factor, is most pronounced for conduction band electrons (in particular, in MoS2), and it has a nonmonotonic dependence on the carrier sheet density n. That is, the SOS enhancement is peaked at the onset of filling of the higher-energy spin-split band by electrons, n*, which also separates the regimes of slow (at n<n*) and fast (for n>n*) spin and valley relaxation of charge carriers. Moreover, this density itself is determined by the enhanced SOS value, making the account of exchange renormalization important for the analysis of the spintronic performance of field-effect transistors based on two-dimensional TMDs. Published by the American Physical Society 2024

Stokes drift and particle trajectories induced by surface waves atop a shear flow

Surface waves and currents are crucial to the mass transfer in the air-sea interaction as they can drive a variety of dynamical processes. How mass can be transported by surface waves and current coupling is addressed through a study of their induced motions of fluid parcels. To this end, a weakly nonlinear wavetrain is imposed on the background flow whose direction and magnitude are permitted to vary with water depth and second-order features of this configuration are investigated. A leading-order approximation to the Stokes drift is derived, correct to the second order in wave steepness, and applicable to an arbitrarily depth-dependent background flow. The reduced forms of the approximate Stokes drift are provided in a few limiting cases such as a current with an exponential profile or propagating in an orthogonal direction to the wave propagation. Novel features related to the Stokes drift and particle trajectories have been reported for the first time as a result of the rotation induced by the wave and current coupling. A non-vanishing component of the Stokes drift velocity and net-mean displacement of fluid parcels in the span-wise direction to the wave propagation are observed in the cases where a shear current propagates obliquely to the waves direction. A non-monotonic dependence on water depth of the stream-wise component of the Stokes drift is shown, and thereby the largest mass transport induced no longer occurs on the still water surface but some depth beneath. The non-monotonic behavior occurs beyond the regime of the near-irrotational assumption of wave-induced motions. It can also lead to the change of the signs for the stream-wise Stokes drift throughout the water column, and thus an overall cancellation of the integrated mass transport by waves over the water column, indicating that the depth-integrated models can likely lead to underestimated effects of the mass transport which is non-trivial at a local depth. The results from this study have far-reaching impact. The Stokes drift profile is a direct input to the parametrization of the surface waves forcing in ocean circulations and the obliquely propagating Stokes drift can be plausibly responsible for the formation of oblique Langmuir rolls to wave propagation in the open ocean.

Dynamic permittivity of confined water under a static background field.

Molecular and collective reorientations in interfacial water are by-and-large decelerated near surfaces subjected to outgoing electric fields (pointing from surface to liquid, i.e., when the surface carries positive charge). In incoming fields at negatively charged surfaces, these rates show a nonmonotonic dependence on field strength where fastest reorientations are observed when the field alignment barely offsets the polarizing effects due to interfacial hydrogen bonding. This extremum coincides with a peak of local static permittivity. We use molecular dynamics simulations to explore the impact of background static field on high frequency AC permittivity in hydration water under an electric field mimicking the conditions inside a capacitor where one of the confinement walls is subject to an outgoing field and the other one to an incoming field. At strong static fields, the absorption peak undergoes a monotonic blue shift upon increasing field strength in both hydration layers. At intermediate fields, however, the hydration region at the wall under an incoming field (the negative capacitor plate) features a red shift coinciding with maximal static-permittivity and reorientation-rate. The shift is mostly determined by the variation of the inverse static dielectric constant as proposed for mono-exponentially decaying polarization correlations. Conversely, hydration water at the opposite (positively charged) surface features a monotonic blue shift consistent with conventional saturation. The sensitivity of absorption peaks on the field suggests that surface charge densities could be deduced from sub-THz dielectric spectroscopy experiments in porous materials when interfaces accommodate a major fraction of water contained in the system.

Surface acoustic wave amplification by drifting electrons in semiconducting epitaxial graphene on silicon carbide

Abstract A theory is presented for the amplification of a surface acoustic wave (SAW) due to its interaction with conduction electrons in gate-controlled epitaxial graphene (epigraphene) on a SiC substrate. It is assumed that the SAW is launched onto the substrate in the direction of an external dc electric field applied to the graphene sample and causing the conduction electrons to drift at a speed greater than the speed of the SAW. The wavelength of the SAW is assumed to be shorter than the mean free path of the electrons, so that the quantum regime of interaction of those electrons with the SAW is realized. The Green’s function method is used to calculate the SAW gain as a function of the electron concentration in epigraphene and the external dc electric field strength. It is shown that the substrate-induced band gap in the electronic spectrum of epigraphene leads to a significant (at least an order of magnitude) increase in the SAW gain as compared to the case of gapless graphene. In addition, the opening of the band gap results in a non-monotonic dependence of the SAW gain on the electron concentration, controlled by the gate voltage applied to the graphene sample. This dependence is characterized by the presence of a distinct maximum at a certain value of electron concentration (of about 2 × 10 12 cm−2 for typical values of the other parameters involved), which distinguishes it from the monotonic concentration dependence of the SAW gain in gapless graphene.

Transport of non-equilibrium quasiparticle excitations in superconducting aluminum

The electron transport of non-equilibrium quasiparticles injected into superconducting aluminum from a normal metal has been experimentally studied at ultralow temperatures. We studied hybrid nanostructures in the form of a T-shaped normal metal electrode (copper) – a dielectric tunnel layer (aluminum oxide) – a superconducting fork (aluminum), which can be considered as a solid-state analogues of a two-beam optical interferometer. At fixed bias voltages larger than the superconducting gap, a non-monotonic dependence of the tunnel current on perpendicular magnetic field is observed. The effect is interpreted as the presence of a coherent component of the quasiparticle current.