Exponential Decay Research Articles

Tunable topological phases in nanographene-based spin-1/2 alternating-exchange Heisenberg chains.

Unlocking the potential of topological order in many-body spin systems has been a key goal in quantum materials research. Despite extensive efforts, the quest for a versatile platform enabling site-selective spin manipulation, essential for tuning and probing diverse topological phases, has persisted. Here we utilize on-surface synthesis to construct spin-1/2 alternating-exchange Heisenberg chains by covalently linking Clar's goblets-nanographenes each hosting two antiferromagnetically coupled spins. Using scanning tunnelling microscopy, we exert atomic-scale control over chain lengths, parities and exchange-coupling terminations, and probe their magnetic response via inelastic tunnelling spectroscopy. Our investigation confirms the gapped nature of bulk excitations in the chains, known as triplons. Their dispersion relation is extracted from the spatial variation of tunnelling spectral amplitudes. Depending on the parity and termination of chains, we observe varying numbers of in-gap spin-1/2 edge excitations, reflecting the degeneracy of distinct topological ground states in the thermodynamic limit. By monitoring interactions between these edge spins, we identify the exponential decay of spin correlations. Our findings present a phase-controlled many-body platform, opening avenues toward spin-based quantum devices.

Contribution of Protonation to the Dielectric Relaxation Arising from Bacteriopheophytin Reductions in the Photosynthetic Reaction Centers of Rhodobacter sphaeroides

The pH dependence of the free energy level of the flash-induced primary charge pair P+IA− was determined by a combination of the results from the indirect charge recombination of P+QA− and from the delayed fluorescence of the excited dimer (P*) in the reaction center of the photosynthetic bacterium Rhodobacter sphaeroides, where the native ubiquinone at the primary quinone binding site QA was replaced by low-potential anthraquinone (AQ) derivatives. The following observations were made: (1) The free energy state of P+IA− was pH independent below pH 10 (–370 ± 10 meV relative to that of the excited dimer P*) and showed a remarkable decrease (about 20 meV/pH unit) above pH 10. A part of the dielectric relaxation of the P+IA− charge pair that is not insignificant (about 120 meV) should come from protonation-related changes. (2) The single exponential decay character of the kinetics proves that the protonated/unprotonated P+IA− and P+QA− states are in equilibria and the rate constants of protonation konH +koffH are much larger than those of the charge back reaction kback ~103 s−1. (3) Highly similar pH profiles were measured to determine the free energy states of P+QA− and P+IA−, indicating that the same acidic cluster at around QB should respond to both anionic species. This was supported by model calculations based on anticooperative proton distribution in the cluster with key residues of GluL212, AspL213, AspM17, and GluH173, and the effect of the polarization of the aqueous phase on electrostatic interactions. The larger distance of IA− from the cluster (25.2 Å) compared to that of QA− (14.5 Å) is compensated by a smaller effective dielectric constant (6.5 ± 0.5 and 10.0 ± 0.5, respectively). (4) The P* → P+QA− and IA−QA → IAQA− electron transfers are enthalpy-driven reactions with the exemption of very large (>60%) or negligible entropic contributions in cases of substitution by 2,3-dimethyl-AQ or 1-chloro-AQ, respectively. The possible structural consequences are discussed.

Exponential Stability of a Kirchhoff Plate Equation with Structural Damping and Internal Time Delay

In this manuscript, we investigate the exponential stability of a Kirchhoff plate equation with free boundary conditions in a bounded domain of R2. First, we consider the case where the model is subjected only to structural damping and, using the energy method, we prove the exponential decay of the energy associated with this model. Second, we consider the case where structural damping with a linear internal time delay term is applied, and we use the same technique to derive the exponential stability of the new model. Finally, we examine the scenario where the model is governed by structural damping with an added fractional time delay term and, by constructing an appropriate Lyapunov function, we show that the energy associated with the system is exponentially stable. This work improves upon prior results concerning the Kirchhoff plate equation with frictional damping, where exponential stability could not be achieved.

Evaluation of reliability and characteristics measure using exponential decay distribution of non‐series parallel network

AbstractThe purpose of this paper is to analyze the reliability and characteristics of the non‐series‐parallel network. The illustrative non‐series parallel networks, that is, the Twin T‐Network and the network with six components of resistor and capacitor, have been converted into a series of parallel network combinations by use of the minimal path technique. The stochastic variables related to component failure rate have been demonstrated using exponential decay distribution. We obtain the reliability, mean time to failure, and sensitivity with the use of the exponential decay distribution. The reliability and its attributes are examined by assuming different values of scale and shape parameters at different points of time. Using Owen's methodology, we obtained minimal signature, tail signature, expected time, expected cost, and Barlow‐Proschan index were determined. The performance of all reliability characteristics has been observed graphically for arbitrary values of parameters. A real‐world example is used to introduce the point.

Optimal decay of the Boltzmann equation

The Boltzmann equation is a typical example of partially dissipative equations, where the linearized collision operator is positive definite with respect to the microscopic part and the dissipation of the hydrodynamic part is discovered from the coupling structure between the transport operator and the linearized collision operator. Guo and Wang (Comm. Partial Differential Equations, 37, 2012) developed a general energy method for proving the optimal time decay rates of the solution to such type of equations in the whole space; however, the decay rate of the highest order spatial derivatives of the solution is not optimal. In this paper, by incorporating the high‐low frequency decomposition in the energy estimates, both linearly and nonlinearly, we prove the optimal decay rates of any high order spatial derivatives of the low frequency part of the solution to the Boltzmann equation and the almost exponential decay rate of the high frequency part, which imply in particular the optimal decay rate of the highest order spatial derivatives of the solution. Moreover, the velocity‐weighted assumption of the initial data required in Guo and Wang (Comm. Partial Differential Equations, 37, 2012) is removed by capturing the time‐weighted dissipation estimates via the time‐weighted energy method. The method can be applied to the compressible Navier–Stokes equations and many partially dissipative equations in kinetic theory and fluid dynamics.

Numerical Insights Into Gobi Wind‐Blown Sand: Deriving a Saltation Flux Scheme

AbstractDust emissions from land‐air interaction in arid and semi‐arid regions are crucial for predicting the global dust cycle. However, a comprehensive understanding of the complex physical mechanisms contributing to dust emissions from Gobi surfaces remains elusive. The expansive Gobi Desert, spanning northern China and Mongolia, significantly intensifies sandstorms in East Asia. Although researchers use models to study global dust transport, current models primarily depend on the aerodynamic roughness of the Gobi Desert. They often overlook the particle‐bed collision processes unique to the Gobi bed surface, which differ significantly from those of desert surfaces, thus compromising the accuracy of global dust cycle simulations. In this article, we establish a numerical model for drift sand in the Gobi based on existing theoretical and experimental studies. The model accurately simulates the wind‐blown sand in the Gobi and been used to investigate the saltation structure of sand transport. Simulations reveal an exponential decay of mass concentration with height, with an average attenuation rate of 0.00385 in the Gobi compared to 0.00806 in sandy deserts. The horizontal velocity of saltating particles increases with height following a power law. Through quantitative analysis of this structure, we present a saltation flux formula suitable for the Gobi.

Anomalous frozen evanescent phonons

Evanescent Bloch waves are eigensolutions of spatially periodic problems for complex-valued wavenumbers at finite frequencies, corresponding to solutions that oscillate in time and space and that exponentially decay in space. Such evanescent waves are ubiquitous in optics, plasmonics, elasticity, and acoustics. In the limit of zero frequency, the wave “freezes” in time. We introduce frozen evanescent waves as the eigensolutions of the Bloch periodic problem at zero eigenfrequency. Elastic waves, i.e., phonons, in metamaterials serve as an example. We show that, in the complex plane, the Cauchy-Riemann equations for analytical functions connect the minima of the phonon band structure to frozen evanescent phonons. Their exponential decay length becomes unusually large if a minimum in the band structure tends to zero and thereby approaches a soft mode. This connection between unusual static and dynamic behaviors allows to engineer large characteristic decay lengths in static elasticity. For finite-size samples, the static solutions for given boundary conditions are linear combinations of frozen evanescent phonons, leading to interference effects. Theory and experiment are in excellent agreement. Anomalous behavior includes the violation of Saint Venant’s principle, which means that large decay-length frozen evanescent phonons can potentially be applied in terms of remote mechanical sensing.

Metabolite T2 relaxation times decrease across the adult lifespan in a large multi-site cohort.

Relaxation correction is crucial for accurately estimating metabolite concentrations measured using in vivo MRS. However, the majority of MRS quantification routines assume that relaxation values remain constant across the lifespan, despite prior evidence of T2 changes with aging for multiple of the major metabolites. Here, we comprehensively investigate correlations between T2 and age in a large, multi-site cohort. We recruited approximately 10 male and 10 female participants from each decade of life: 18-29, 30-39, 40-49, 50-59, and 60+ y old (n = 101 total). We collected PRESS data at eight TEs (30, 50, 74, 101, 135, 179, 241, and 350 ms) from voxels placed in white-matter-rich centrum semiovale (CSO) and gray-matter-rich posterior cingulate cortex (PCC). We quantified metabolite amplitudes using Osprey and fit exponential decay curves to estimate T2. Older age was correlated with shorter T2 for tNAA2.0, tCr3.0, tCr3.9, tCho, and tissue water (CSO and PCC), as well as mI and Glx (PCC only); rs = -0.22 to -0.63, all p < 0.05, false discovery rate (FDR)-corrected. These associations largely remained statistically significant when controlling for cortical atrophy. By region, T2 values were longer in the CSO for tNAA2.0, tCr3.9, Glx, and tissue water and longer in the PCC for tCho and mI. T2 did not differ by region for tCr3.0. These findings underscore the importance of considering metabolite T2 differences with aging in MRS quantification. We suggest that future 3T work utilize the equations presented here to estimate age-specific T2 values instead of relying on uniform default values.

Identification of a double decay length ([formula omitted]) heat flux deposition shape with embedded thermal measurement and neural network

The estimation of the heat flux density distribution profiles in tokamak devices is a very important research topic for edge plasma physics purposes and also to ensure the safety of the machine. In the radial direction, the heat flux exhibits an exponential decay that could be captured by thermal sensors distributed in the plasma facing components. Radially distributed thermal sensors based on Fiber Bragg grating technology have been embedded in the WEST lower divertor to study the heat flux deposition profiles during plasma operation. The comparison between embedded measurements and a 3D finite element model shows a small decay length (5 – 10 mm) on top of a wider heat flux with a decay length around 30 to 50 mm. A tool using neural network has been developed in order to predict the values of the different parameters describing the deposited heat flux from embedded temperature measurements in steady state. A large span of deposited heat fluxes with maximum heat flux ranging from 1 to 9 MW/m2 and decay length from 5 to 50 mm were characterized using this tool over a database of more than 250 experimental L-mode pulses performed in WEST in attached divertor configuration. The comparison of the predicted heat flux parameters values with macroscopic plasma parameters have revealed the appearance of the narrow component with the increase of the divertor power load (Pdiv) with a threshold dependant of the plasma current (IP).

Bubble plume effects on the flotation kinetics of nonmetallic inclusions based on experimental observations

AbstractSteelmaking has shown an increasing concern toward nonmetallic inclusions, leading to new technologies in the secondary metallurgy of steel. Although the typical inclusion removal procedure is by injecting inert gas into the ladle, this vessel does not fulfill all the requirements to accept a porous structure tailored to produce “clean steels.” Consequently, the spotlight has moved to the tundish, the last vessel before solidification, in which gas injection can continuously operate. Therefore, this work focuses on understanding the influence of typical gas flow rates (10–60 NL/min) on the kinetics of inclusion flotation, considering two bubble diameters (0.6 and 1.1 mm). For this purpose, experimental measurements were conducted in a water model, where glass hollow spheres played the role of inclusions, and their concentration was fitted by an exponential decay. In general, injecting bubbles into the system contributed positively to a faster and greater flotation of particles. The smaller bubbles led to a higher maximum efficiency, whereas the larger ones allowed a shorter time scale (i.e., a faster removal), defining a trade‐off to tune the bubble size. Regarding the gas flow rate, the results indicate an optimum range to decrease the time scale, and suggestions for bubble curtains in tundishes are drawn.

Numerical analyses of spherical indenter intrusion into sandstone: From laboratory tests to numerical simulations

To explore the mechanical mechanisms of rock fracturing under compression during ball milling. The study investigates the effects of intrusion depth and indenter diameter on the evolution of stresses and plastic strains, integrating laboratory tests and numerical predictions. The results reveal a reduction in both axial and radial stresses with increasing intrusion depth into the rock. Shear stress experiences an initial rise followed by a decline, while circumferential stress demonstrates an initial increase followed by a rapid decrease in the radial direction. As the intrusion deepens, the predominant influence on plastic strain of rock shifts from shear stress dominance to a combined dominance of shear and circumferential stresses. The influence of the indenter diameter on the stress field diminishes following an exponential decay pattern. In terms of the plastic strain field, smaller indenters are more likely to induce plastic failure due to shear and circumferential stresses, larger indenters are more prone to plastic failure induced solely by shear stresses. As the number of indenters increases, the integration of the stress and plastic strain fields is enhanced. This implies that introducing more spherical indenters amplifies the collaborative effect, leading to a more cohesive fracturing of the rock.

Revisiting Brownian SYK and its possible relations to de Sitter

We revisit Brownian Sachdev-Ye-Kitaev model and argue that it has emergent energy conservation overlooked in the literature before. We solve this model in the double-scaled regime and demonstrate hyperfast scrambling, exponential decay of correlation functions, bounded spectrum and unexpected factorization of higher-point functions. We comment on how these results are related to de Sitter holography.

Time-Dependent Resistance of Sol–Gel HfO2 Films to In Situ High-Temperature Laser Damage

Laser damage in films under long-term high-temperature conditions is a significant concern for advancing laser applications. This study focused on HfO2 films prepared using the sol–gel method with HfCl4 as a precursor. It examined the effects of temperature on various properties of the films, including their optical properties, microstructure, surface morphology, absorption, and laser-induced damage threshold (LIDT). The prepared film demonstrated desirable characteristics at the high temperature of 423 K, such as high transmittance, low absorption, and high LIDT. As the duration of its high-temperature exposure increased, the LIDT of the films gradually decreased. An intriguing finding was that the film’s LIDT exhibited an exponential decay pattern with prolonged heating time. This observation could be attributed to the power-law increase in defects on both the internal and surface areas of the film as the duration of high-temperature exposure lengthened. Moreover, even after a 15-day heating period at 423 K, the film maintained an LIDT of 12.9 J/cm2, indicating its potential applicability in practical high-temperature environments. This study provided a general pattern and a universal formula for understanding the laser damage of sol–gel films at high temperatures over time. Furthermore, it opened possibilities for future developments of laser films suitable for extreme environments.

Quantum geometrical properties of topological materials

The momentum space of topological insulators and topological superconductors is equipped with a quantum metric defined from the overlap of neighboring valence band states or quasihole states. We investigate the quantum geometrical properties of these materials within the framework of Dirac models and differential geometry. Their momentum space is found to be always a maximally symmetric space with a constant Ricci scalar, and the vacuum Einstein equation is satisfied in 3D with a finite cosmological constant. For linear Dirac models, several geometrical properties are found to be independent of the band gap, including a peculiar straight line geodesic, constant volume of the curved momentum space, and the exponential decay form of the nonlocal topological marker, indicating the peculiar yet universal quantum geometrical properties of these models.

Effects of multiple reflections on nonlinear absorption measurements

Accurate measurement of nonlinear absorption coefficients by transmission-based techniques, such as Z-scan and its modifications, remains challenging due to high measurement errors. In this Letter, we claim that one of the reasons for that could lie in ignoring multiple reflections of light in plane-parallel samples in the presence of multi-photon excitation. Closed-form formulations for transmittance and reflectance coefficients, considering both linear and multiphoton absorption, are obtained in the geometrical optics approximation. The contributions of multiple reflections to the total transmittance are calculated for several II–VI materials reported in the literature. The results show a nonlinear dependence on incident intensity, ranging from 15.7% down to 7.9% for CdS, from 10.3% down to 5.8% for CdSe, and from 18.1% down to 9.1% for ZnSe. The dependence of the contribution of multiple reflections on the sample thickness is shown to exhibit a near exponential decay.

Unveiling Anomalies in Terrain Elevation Products from Spaceborne Full-Waveform LiDAR over Forested Areas

Anomalies displaying significant deviations between terrain elevation products acquired from spaceborne full-waveform LiDAR and reference elevations are frequently observed in assessment studies. While the predominant focus is on “normal” data, recognizing anomalies within datasets obtained from the Geoscience Laser Altimeter System (GLAS) and the Global Ecosystem Dynamics Investigation (GEDI) is essential for a comprehensive understanding of widely used spaceborne full-waveform data, which not only facilitates optimal data utilization but also enhances the exploration of potential applications. Nevertheless, our comprehension of anomalies remains limited as they have received scant specific attention. Diverging from prevalent practices of directly eliminating outliers, we conducted a targeted exploration of anomalies in forested areas using both transmitted and return waveforms from the GLAS and the GEDI in conjunction with airborne LiDAR point cloud data. We unveiled that elevation anomalies stem not from the transmitted pulses or product algorithms, but rather from scattering sources. We further observed similarities between the GLAS and the GEDI despite their considerable disparities in sensor parameters, with the waveforms characterized by a low signal-to-noise ratio and a near exponential decay in return energy; specifically, return signals of anomalies originated from clouds rather than the land surface. This discovery underscores the potential of deriving cloud-top height from spaceborne full-waveform LiDAR missions, particularly the GEDI, suggesting promising prospects for applying GEDI data in atmospheric science—an area that has received scant attention thus far. To mitigate the impact of abnormal return waveforms on diverse land surface studies, we strongly recommend incorporating spaceborne LiDAR-offered terrain elevation in data filtering by establishing an elevation-difference threshold against a reference elevation. This is especially vital for studies concerning forest parameters due to potential cloud interference, yet a consensus has not been reached within the community.

Speedy Component Resolution Using Spatially Encoded Diffusion NMR Data.

Diffusion-ordered NMR spectroscopy (DOSY) is a powerful tool to analyse mixtures. Spatially encoded (SPEN) DOSY enables recording a full DOSY dataset in just one scan by performing spatial parallelisation of the gradient dimension. The simplest and most widely used approach to processing DOSY data is to fit each peak in the spectrum with a single or multiple exponential decay. However, when there is peak overlap, and/or when the diffusion decays of the contributing components are too similar, this method has limitations. Multivariate analysis of DOSY data, which is an attractive alternative, consists of decomposing the experimental data, into compound-specific diffusion decays and 1D NMR spectra. Multivariate analysis has been very successfully used for conventional DOSY data, but its use for SPEN DOSY data has only recently been reported. Here, we present a comparison, for SPEN DOSY data, of two widely used algorithms, SCORE and OUTSCORE, that aim at unmixing the spectra of overlapped species through a least square fit or a cross-talk minimisation, respectively. Data processing was performed with the General NMR Analysis Toolbox (GNAT), with custom-written code elements that now expands the capabilities, and makes it possible to import and process SPEN DOSY data. This comparison is demonstrated on three different two-component mixtures, each with different characteristics in terms of signal overlap, diffusion coefficient similarity, and component concentration.

Longitudinal one-dimensional mechanical topological insulator

Abstract We present a study of a longitudinal one-dimensional mechanical topological insulator based on a slinky spring in the Su–Schrieffer–Heeger (SSH) configuration. The system demonstrates key characteristics of topological insulators, including the existence of edge states in the bandgap, exponential decay of amplitude, and a winding number of 1 for topological phases. By manipulating the stiffness of the spring through the placement of masses, we transition between trivial, metallic, and topological phases. Our findings also show that the edge states are robust against perturbations, and we observe a critical phase transition where the coherence length follows a critical exponent of -1, as predicted by theory. This simple mechanical system provides an accessible platform for studying the special properties of topological insulators and opens up new possibilities for exploring topological phenomena in classical systems.

How Fast do Rumours Spread?

We study a rumour propagation model along the lines of Lebensztayn and Rodriguez (Stat Probab Lett 78(14):2130–2136, 2008) as a long-range percolation model on Z\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {Z}$$\\end{document}. We begin by showing a sharp phase transition-type behaviour in the sense of exponential decay of the survival time of the rumour cluster in the sub-critical phase. In the super-critical phase, under the assumption that radius of influence r.v. has 2+ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2+\\epsilon $$\\end{document} moment finite (for some ϵ>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon >0$$\\end{document}), we show that the rightmost vertex in the rumour cluster has a deterministic speed in the sense that after appropriate scaling, the location of the rightmost vertex converges a.s. to a deterministic positive constant. Under the assumption that radius of influence r.v. has 4+ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4+\\epsilon $$\\end{document} moment finite, we obtain a central limit theorem for appropriately scaled and centered rightmost vertex. Later, we introduce a rumour propagation model with reactivation. For this section, we work with a family of exponentially decaying i.i.d. radius of influence r.v.’s, and we obtain the speed result for the scaled rightmost position of the rumour cluster. Each of these results is novel, in the sense that such properties have never been established before in the context of the rumour propagation model on Z\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {Z}$$\\end{document}, to the best of our knowledge.

Spin relaxation dynamics with a continuous spin environment: The dissipaton equation of motion approach.

We investigate the quantum dynamics of a spin coupling to a bath of independent spins via the dissipaton equation of motion (DEOM) approach. The bath, characterized by a continuous spectral density function, is composed of spins that are independent level systems described by the su(2) Lie algebra, representing an environment with a large magnitude of anharmonicity. Based on the previous work by Suarez and Silbey [J. Chem. Phys. 95, 9115 (1991)] and by Makri [J. Chem. Phys. 111, 6164 (1999)] that the spin bath can be mapped to a Gaussian environment under its linear response limit, we use the time-domain Prony fitting decomposition scheme to the bare-bath time correlation function (TCF) given by the bosonic fluctuation-dissipation theorem to generate the exponential decay basis (or pseudo modes) for DEOM construction. The accuracy and efficiency of this strategy have been explored by a variety of numerical results. We envision that this work provides new insights into extending the hierarchical equations of motion and DEOM approach to certain types of anharmonic environments with arbitrary TCF or spectral density.