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This paper was to present a mathematical model of non-integer order and demonstrated the detrimental consequences of lumpy skin disease (LSD). The LSD model included primarily affected cattle and other animals, particularly buffalo and cows. Given the significant drop in the number of livestock and dairy products, it was essential to use mathematical models to raise awareness of this issue. We examined the suggested LSD model to understand as well as every possible avenue that could result in the illness spreading throughout the community. Ulam-Hyers stability made it easier to analyze the stability of the LSD model, and fixed-point theory was a valuable tool for finding the existence and uniqueness of the solution to the suggested model. We have used new versions of power law and exponential decay fractional numerical methods. Numerical calculations were showing the influence of various fractional orders on the spread of disease and provided more informations than integer orders for the sensitive parameters of the proposed model. The graphical depiction is showed an understanding of the proposed LSD model. [ABSTRACT FROM AUTHOR]

This Article investigates the decay of precedents in state supreme courts—the speed at which judicial opinions lose precedential force as measured by the rates of subsequent citation. Prior literature has documented the existence of this effect, but to date researchers have not systematically investigated the phenomenon. This Article performs that analysis by examining three unique databases, each consisting of more than a hundred thousand relevant citations. We fnd that the frequency of citation drops off by a roughly constant ratio with each passing year—a pattern that fts an exponential curve with remarkable precision. The large scale and extended time period of our study suggest that this pattern must result from underlying forces unrelated to circumstances of time or place. The main takeaway is the extraordinary persistence of exponential decay across all of the data. Citations age at different rates across different cuts of the data, but in every case the deterioration of precedents displays an exponential pattern. In addition to documenting the exponential pattern of precedential decay, we explore the determinants of that process across case types. We fnd that opinions with dissents tend to cite older opinions and longer decisions tend to be cited more often and faster. As compared to constitutional law cases, criminal law opinions tend to cite more recent precedents, while trust and estate opinions tend to cite older precedents. We offer some conjectures about possible reasons for the observed differences in decay rates. [ABSTRACT FROM AUTHOR]

A prototype cleanroom for hazardous testing and handling of satellites prior to launcher encapsulation, satisfying the ISO8 standard has been designed and analyzed in terms of performances. Unsteady Reynolds Averaged Navier-Stokes (URANS) models have been used to study the related flow field and particulate matter (PM) dispersion. The outcomes of the URANS models have been validated through comparison with equivalent large-eddy simulations. Special attention has been paid to the location and shape of the air intakes and their orientation in space, in order to balance the PM convection and diffusion inside the cleanroom. Forming a cyclone-type flow pattern inside the cleanroom is a key to maintaining a high ventilation efficiency. [ABSTRACT FROM AUTHOR]

Nowadays, the complete world is suffering from untreated infectious epidemic disease COVID‐19 due to coronavirus, which is a very dangerous and deadly viral infection. So, the major desire of this task is to propose some new mathematical models for the coronavirus pandemic (COVID‐19) outbreak through fractional derivatives. The adoption of modified mathematical techniques and some basic explanation in this research field will have a strong effect on progressive society fitness by controlling some diseases. The main objective of this work is to investigate the dynamics and numerical approximations for the recommended arbitrary‐order coronavirus disease system. This system illustrating the probability of spread within a given general population. In this work, we considered a system of a novel COVID‐19 with the three various arbitrary‐order derivative operators: Caputo derivative having the power law, Caputo–Fabrizio derivative having exponential decay law and Atangana–Baleanu‐derivative with generalized Mittag–Leffler function. The existence and uniqueness of the arbitrary‐order system is investigated through fixed‐point theory. We investigate the numerical solutions of the non‐linear arbitrary‐order COVID‐19 system with three various numerical techniques. For study, the impact of arbitrary‐order on the behavior of dynamics the numerical simulation is presented for distinct values of the arbitrary power β. [ABSTRACT FROM AUTHOR]

We explore the transport properties of oligophenylene molecular junctions, where the center molecule containing 1, 2, or 3 phenyls is sand-wiched between two graphene nanoribbons (GNR) with different edge shapes. According to the obtained results of the first-principles calculations combined with non-equilibrium Green's function method, we find that the molecular length-dependent resistance of all examined oligophenylene molecular junctions follows well the exponential decay law with different slopes, and the exponential decay factor is sensitive to the edge shape of GNRs and the molecule-electrode connecting configuration. These observations indicate that the current through the oligophenylene molecular junction can be effectively tuned by changing the edge shape of GNRs, the molecular length, and the molecular contacting configuration. These findings provide theoretical insight into the design of molecular devices using GNRs as electrodes. [ABSTRACT FROM AUTHOR]

A quantum particle constrained between two high potential barriers provides a paradigmatic example of a system sustaining quasi-bound (or resonance) states. When the system is prepared in one of such quasi-bound states, the wave function approximately maintains its shape but decays in time in a nearly exponential manner radiating into the surrounding space, the lifetime being of the order of the reciprocal of the width of the resonance peak in the transmission spectrum. Naively, one could think that adding more lateral barriers would preferentially slow down or prevent the quantum decay since tunneling is expected to become less probable and due to quantum backflow induced by multiple scattering processes. However, this is not always the case and in the early stage of the dynamics quantum decay can be accelerated (rather than decelerated) by additional lateral barriers, even when the barrier heights are arbitrarily large. The decay acceleration originates from resonant tunneling effects and is associated to large deviations from an exponential decay law. We discuss such a counterintuitive phenomenon by considering the hopping dynamics of a quantum particle on a tight-binding lattice with on-site potential barriers. [ABSTRACT FROM AUTHOR]

Using logging data and samples collected by the four expeditions of the International Ocean Discovery Program NanTroSEIZE drilling campaign that occupied Site C0002 in the Nankai margin located southwest of Japan, we determined effective porosity and sonic velocity profiles down to 3 km below the seafloor in the accretionary prism, above the seismogenic plate interface. We measured cation exchange capacity to differentiate clay‐bound water content from effective porosity, which is representative of compaction. The decrease in effective porosity with depth is fitted with a single exponential decay, which suggests hydrostatic conditions for most of the borehole. The Erickson‐Jarrard template was adapted to account for the actual clay‐bearing nature of the sediments. We used this improved P‐wave velocity–effective porosity relationship to fill shipboard data gaps and predict P‐ and S‐wave velocity profiles at Site C0002. Plain Language Summary: Effective porosity reflects the network of pores that affects the transport properties and the history of sediment compaction. However, evaluating this property is not straightforward given that standard methods provide total porosity, which also includes clay‐bound water. We can estimate the effective porosity using cation exchange capacity of the rocks. This method was used at Site C0002, the deepest hole in history of the International Ocean Discovery Program, drilled down to the heart of the Nankai accretionary prism, located southwest of Japan. We show that the effective porosity follows a simple exponential decay law with depth. We also demonstrate that there is a single relationship between effective porosity and P‐wave velocity. We use this relationship to fill the data gaps in the P‐ and S‐wave velocity profiles at Site C0002. Conversely, this provides a direct method to estimate effective porosity, and hence, the compaction state, from seismic profiles acquired across the Nankai accretionary prism. Key Points: Effective porosity was derived from cation exchange capacity analysis on samples from Site C0002, the deepest International Ocean Discovery Program borehole ever drilledTotal and effective porosities decay exponentially all along Site C0002, down to the heart of the Nankai accretionary prism (3,000 mbsf)Modifying the parameters of the Erickson‐Jarrard model using effective porosity and clay content improves the P‐wave velocity prediction [ABSTRACT FROM AUTHOR]

Passive acoustic monitoring of biodiversity is growing fast, as it offers an alternative to traditional aural point count surveys, with the possibility to deploy long‐term acoustic surveys in large and complex natural environments. However, there is still a clear need to evaluate how the frequency‐ and distance‐dependent attenuation of sound as well as the ambient sound level impact the acoustic detection distance of the soniferous species in natural environments over the diel cycles and across seasons. This is of great importance to avoid pseudoreplication and to provide relevant biodiversity indicators, including species richness, species abundance and species density.To address the issue of detection distance, we tested a field‐based protocol in a Neotropical rainforest (French Guiana, France) and in an Alpine coniferous forest (Jura, France). This standardized and repeatable method consists in a recording session of the ambient sound directly followed by an experiment using a calibrated white noise sound broadcast at different positions along a 100 m linear transect. We then used acoustic laws to reveal the basic physics behind sound propagation attenuation.We demonstrate that habitat attenuation in two different kinds of forests can be modelled by an exponential decay law with a linear dependence on frequency and distance. We also report that habitat attenuation, as first approximation, can be summarized by a single value, the coefficient of attenuation of the habitat.Finally, we show that the detection distance can be predicted knowing the contribution of each attenuation factor, the coefficient of attenuation of the habitat, the ambient sound pressure level and the amplitude and frequency bandwidth characteristics of the transmitted sound. We show that the detection distance mostly depends on the ambient sound and may vary by a factor of up to 5 over the diel cycle and across seasons. These results reinforce the need to take into account the variation of the detection distance when performing passive acoustic surveys and producing reliable biodiversity indicators. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the semi-analytical solution of Kaup-Kupershmidt equations with the help of a modified method known as the new iteration transformation technique. This method combines the Yang transform and the new iteration technique. The nonlinear terms can be calculated straightforwardly by a new iteration method. The numerical simulation results have been presented to demonstrate the reliability and validity of the proposed approach. The result confirms that the suggested technique is the best tool for dealing with any nonlinear problems arising in technology and science. In addition, in terms of figures for varying fractional order, the physical behavior of new iteration transformation technique solutions has been shown and the numerical simulation is also exhibited. The solutions of the new iteration transformation technique reveal that the projected technique is reliable, competitive and powerful for studying complex nonlinear fractional type models. [ABSTRACT FROM AUTHOR]

A series of discrete elements simulations is presented for the study of fault gouges' frictional response. The gouge is considered to have previously undergone ultra‐cataclastic flow and long‐time consolidation loading. We explore the effect of different particle characteristics such as size, polydispersity, and also shearing velocities on gouge's response under the conditions met in the seismogenic zone. Monte‐Carlo analyses suggest that the local stick‐slip events disappear when averaging over a large number of numerical samples. Moreover, the apparent material frictional response remains almost unaffected by the spatial randomness of particles' position and by the particle's size distribution. On the contrary, the mean particle size controls the formation and thickness of the observed shear bands, which appear after the peak friction is met. Furthermore, the apparent friction evolution fits well to an exponential decay law with slip, which involves a particle size dependent critical slip distance. For the studied conditions and depth, the shearing velocity is found to play a secondary role on the apparent frictional response of the gouge, which highlights the importance of analyses involving multiphysics for studying the rheology of fault gouges. Besides improving the understanding of the underlying physics of the problem, the above findings are also useful for deriving pertinent constitutive models in the case of modeling with continuum theories. Plain Language Summary: Understanding the response of a fault gouge, the granular material at the core of fault zones, can shed light on the way earthquakes are nucleated. For this purpose, in this paper, a series of particle‐based simulations of a fault gouge, under conditions similar to the ones expected at deep down at the seismogenic zone, are conducted. A full‐scale fault with dimensions of the order of kilometers is almost impossible to be simulated at the grain‐scale. In order to capture the inhomogeneities at this level, the response of several, small samples is combined in a stochastic‐ensemble manner. The results suggest that local stick‐slip events are vanishing with increasing number of tests thus, they are not critical for the macroscopic, global, material's response. Contrary to this, the amount of slip needed to promote earthquake instabilities is shown to vary with respect to the mean particle size of the material. Finally, the granular polydispersity and the slip velocity do not seem to affect the system's behavior. The later highlights possible important role of multiphysics on the rheology of fault gouges and provides evidence for the constitutive assumptions used in continuum models. Key Points: The local stick‐slip motion vanishes for multiple, averaged tests and does not affect the expected value of the apparent frictional responseBoth the thickness of the principal slip zone and the critical slip distance scale with the mean particle diameterParticle size distribution and shearing velocity exerts a second order control on global friction [ABSTRACT FROM AUTHOR]

In this study, a heat transfer problem defined by the Caputo–Fabrizio derivative, which is known to behave by the exponential decaying law, is addressed in an axially symmetric cylindrical region. Thus, the fundamental solutions of the heat diffusion process and the associated thermal stresses are aimed to find. For this purpose, Laplace and finite Hankel integral transforms are applied according to the geometry of the region. To obtain the thermal stresses, constitutive relations of the classical thermoelasticity theory are used. The effects of fractional orders on the diffusion process are illustrated graphically using MATLAB. [ABSTRACT FROM AUTHOR]

The double-exponential formula is a quadrature formula that applies the trapezoidal formula to the infinite integral of double-exponentially decaying functions. Its high efficiency has been recognized since the 1970s, and in 1997, it was demonstrated that the formula is optimal in some sense. To achieve its best performance, its mesh size and truncation numbers are optimally selected depending on a given positive integer. However, existing selection formulas are not optimal. In this paper, we propose optimal selection formulas for the mesh size and truncation numbers, giving a far better error bound than the existing one. [ABSTRACT FROM AUTHOR]

The Sinc approximation is known to yield quite accurate results for double-exponentially decaying functions. To date, this approximation has been successfully applied to derivatives, initial value problems, boundary value problems, and so forth. However, an error analysis of the approximation of the m-th derivatives has not been explicitly given, except in the case of m = 1. This study provides an error analysis for all positive integers m. [ABSTRACT FROM AUTHOR]

This paper treats a water flow regularization problem by means of local boundary conditions for the two-dimensional viscous shallow water equations. Using an a-priori energy estimate of the perturbation state and the Faedo–Galerkin method, we build a stabilizing boundary feedback control law for the volumetric flow in a finite time that is prescribed by the solvability of the associated Cauchy problem. We iterate the same approach to build by cascade a stabilizing feedback control law for infinite time. Thanks to a positive arbitrary time-dependent stabilization function, the control law provides an exponential decay of the energy. [ABSTRACT FROM AUTHOR]

We investigated the leptospirosis epidemic model by using Caputo and Fabrizio fractional derivatives. Picard's successive iterative method and Sumudu transform are taken into consideration for developing the iterative solutions for the leptospirosis disease. Employing nonlinear functional analysis, the stability and uniqueness of the proposed model are established. Sensitivity analysis is taken into account to highlight the most sensitive parameters corresponding to the basic reproductive number. Various solutions to the proposed system have been interpolated by graphs with the application of Matlab software.

A unified treatment of oscillatory and monotonic exponential decays of interactions in electrolytes is displayed, which highlights the role of dielectric response of the fluid in terms of renormalized (effective) dielectric permittivity and charges. An exact, but physically transparent statistical mechanical formalism is thereby used, which is presented in a systematic, pedagogical manner. Both the oscillatory and monotonic behaviors are given by an equation for the decay length of screened electrostatic interactions that is very similar to the classical expression for the Debye length. The renormalized dielectric permittivities, which have similar roles for electrolytes as the dielectric constant has for pure polar fluids, consist in general of several entities with different physical meanings. They are connected to dielectric response of the fluid on the same length scale as the decay length of the screened interactions. Only in cases where the decay length is very long, these permittivities correspond approximately to a dielectric response in the long-wavelength limit, like the dielectric constant for polar fluids. Experimentally observed long-range exponentially decaying surface forces are analyzed as well as the oscillatory forces observed for short to intermediate surface separations. Both occur in some ionic liquids and in concentrated as well as very dilute electrolyte solutions. The coexisting modes of decay are in general determined by the bulk properties of the fluid and not by the solvation of the surfaces; in the present cases, they are given by the behavior of the screened Coulomb interaction of the bulk fluid. The surface-fluid interactions influence the amplitudes and signs or phases of the different modes of the decay, but not their decay lengths and wavelengths. The similarities between some ionic liquids and very dilute electrolyte solutions as regards both the long-range monotonic and the oscillatory decays are analyzed. [ABSTRACT FROM AUTHOR]

Carbon quantum dots are widely used in various fields owing to excellent optical properties and outstanding biocompatibility. We synthesize rare super body-centered cubic (C8) structured carbon quantum dots by using cheap source materials and simple preparation method. They exhibit one shifting blue emission band and two close immobile green bands. They have large Stokes shifts ranging from 0.68 to 1.01 eV and large quantum yields as high as 60%. The three types of emissions are competitive and their intensities vary sensitively and differently with pH. Moreover, their emission intensity versus excitation power curves follow I (P) ∝ P k with k values significantly smaller than unity. The blue emission follows the stretched exponential decay law with an intermediate lifetime of ∼3.9 ns and a lifetime-dispersion factor of ∼0.85 whereas the two green emissions exhibit faster and slower decays with respective lifetimes of around 2.0 and 13.0 ns. The results reveal that the blue emission originates from an ensemble of emission sites exhibiting quantum confinement-like effect and two green emissions stem from pH-sensitive surface functional groups-associated fluorophores. [ABSTRACT FROM AUTHOR]

Information needs constant reliable protection. Protection against unauthorized access and distribution, accidental deletion or modification. All developed European countries are concerned about the problem of information security, as well as the protection of personal data of the country's citizens. Social networks are one of the main methods of communication, finding connections and sharing both public and personal information. Social networks make up a constantly growing share among general networks. The network itself acquires new properties, acting as an independent factor. Therefore, it is constantly necessary to develop an information protection system, especially the protection of personal data in social networks. The paper analyzes the parameters of social networks. The parameters of the social network are the transfer of information to other users, traffic density, the probability of building a secure network, and others. A mathematical model for determining the security of personal data from trust and the amount of information in social networks has been developed. Mathematical modeling was carried out in the MatLab environment, the simulation proved that, based on the conditions of the dissipation ratio and the natural frequency of fluctuations of the quantity, the decay of the latter to a certain value is carried out periodically, with a decaying amplitude, or according to an exponential decay law. That is, the protection of personal data increases due to the growth of information trust factors. Mathematical modeling of the proposed model, a model that determines the dependence of personal data protection on trust and the amount of information, confirmed the adequacy of the developed model and proved that personal data protection is proportional to trust. The protection of personal data increases with the growth of trust parameters. But the protection of personal data diminishes slightly as the amount of information to be protected grows. This fully corresponds to the real situation and confirms the adequacy of the developed model. [ABSTRACT FROM AUTHOR]

This paper deals with the initial boundary value problem for a higher-order parabolic equation with logarithmic source term ... . By employing the potential wells technique we show the global existence of the weak solution. Also, we obtain the exponential decay for the weak solutions. [ABSTRACT FROM AUTHOR]

We explore a possibility of measuring deviation from the exponential decay law in pure quantum systems. The power law behavior at late times of decay time profile is predicted in quantum mechanics and has been experimentally attempted to detect, but with failures except a claim in an open system. It is found that electron tunneling from resonance state confined in man-made atoms, quantum dots, has a good chance of detecting the deviation and testing theoretical predictions. How initial unstable state is prepared influences greatly the time profile of decay law, and this can be used to set the onset time of the power law at earlier times. Comparison with similar process of nuclear alpha decay to discover the deviation is discussed, to explain why there exists a difficulty in this case. [ABSTRACT FROM AUTHOR]

Elucidating layer-resolved charge distribution in van der Waals stacked crystals is crucial for electronic applications based on 2D materials. Here, we use CVD-grown few-layer graphene (FLG) labeled by carbon isotopes as a prototype, in which Raman features of two isotope components identify distinct layers. Electrical transfer characteristics of graphene field-effect transistors (GFETs) are employed to quantitatively calibrate the correspondence of Fermi level and G-phonon frequency that shifts with the charge-carrier concentration (n) variation. The isotope-assisted spectroscopy reveals previously unprobed characteristics that the n value of both top and bottom layers in FLG is close rather than following an exponential decay law. This negligible gradient likely benefits from the π − π interaction that favors the interlayer diffusion of charges. In addition, each extra layer reduces the degree of charge exchange at the graphene/dopant interface. These results have important implications for FLG nanoelectronics and provide a robust framework by which one can further investigate the critical properties of other 2D systems. [Display omitted] [ABSTRACT FROM AUTHOR]

Multivariate monitoring of industrial or clinical procedures often involves more than three correlated quality characteristics and the status of the process is judged using a sample of size one. Majority of existing control charts for monitoring process variability for individual observations are capable of monitoring up to three characteristics. One of the hurdles in designing optimal control charts for large dimension data is the enormous computing resources and time that is required by simulation algorithm to estimate the charts parameters. This paper proposes a novel algorithm based on Parallelised Monte Carlo simulation to improve the ability of the Multivariate Exponentially Weighted Mean Squared Deviation and Multivariate Exponentially Weighted Moving Variance charts to monitor process variability for high dimensions in a computationally efficient way. Different techniques have been deployed to reduce computing space and execution time. The optimal control limits (L) to detect small, medium and large shifts in the covariance matrix of up to 15 characteristics are provided. Furthermore, utilising the large number of optimalLvalues generated by the algorithm enabled authors to develop exponential decay functions to predictLvalues. This eliminates the need for further execution of the parallelised Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

A new theoretical model is derived to predict wave attenuation in an emerged vegetation domain under current influences by considering the current effects on changing both wave group velocity and energy dissipation rate. Considering the current effect on changing wave group velocity, the theory predicts an asymmetric behavior of wave decay in following and opposing currents, different from the earlier theory that predicts a symmetry decay behavior by ignoring the current effect on wave group velocity. The new theory dictates that as the current speed increases, the rate of wave decay changes from the traditionally reciprocal law to the exponential law, where the mixed exponential and reciprocal decay law exists under intermediate current conditions. Furthermore, the present theory can be reduced to an explicit expression of the drag coefficient for weak and strong current conditions. In addition, the theory shows that the decay rate depends on both incident wave amplitude and current velocity when the current velocity is relatively small to wave orbital velocity, whereas it is independent of incident wave amplitude when the current is strong. All of these wave decaying characteristics predicted by the theory have been confirmed by the available experimental data and the numerical results from a 2D RANS model (NEWFLUME). • A theoretical model is developed to predict wave attenuation by the vegetation under wave-current conditions and validated by the available experiments and numerical results. • For the same magnitude of current velocity, opposing current induces greater wave attenuation. • As the current velocity increases, the decaying law of wave height will change from reciprocal decay to exponential decay. • The wave attenuation rate is independent of the incident wave amplitude when the current is strong. [ABSTRACT FROM AUTHOR]

Galaxy ybys, interactions where two independent halos inter-penetrate but detach at a later time and do not merge, occur frequently at lower redshifts. These interactions can significantly impact the evolution of individual galaxies - from the mass loss and shape transformation to the emergence of tidal features and formation of morphological disc structures. The main focus of this paper is on the dark matter mass loss of the secondary, intruder galaxy, with the goal of determining a functional relationship between the impact parameter and dark matter mass loss. Series of N-body simulations of typical galaxy ybys (10:1 mass ratio) with differing impact parameters show that the dark matter halo leftover mass of the intruder galaxy follows a logarithmic growth law with impact parameter, regardless of the way the total halo mass is estimated. The lost mass then, clearly, follows the exponential decay law. The stellar component stretches faster as the impact parameter decreases, following the exponential decay law with impact parameter. Functional dependence on impact parameter in all cases seems universal, but the fitting parameters are likely sensitive to the interaction parameters and initial conditions (e.g. the mass ratio of interacting galaxies, initial relative velocity of the intruder galaxy, interaction duration). While typical ybys, investigated here, could not be the sole culprit behind the formation of ultra-diffuse or dark matter deficient galaxies, they can still contribute significantly. Rare, atypical and stronger ybys are worth further exploring. [ABSTRACT FROM AUTHOR]

The aim of the article is to analyze the dynamics of Rubella disease model with fractal-fractional exponential decay kernel. Different fractal dimensions and fractional-orders are used to investigate various aspects of the model. It is observed that the considered operator is very effective for the proposed model. The existence and uniqueness of the model is obtained using Banach fixed point theorems. The stability of the system is verified by Ulam–Hyers stability analysis. A numerical technique is established based on the Adam–Bashforth scheme and Lagrange piecewise interpolation. The numerical illustrations are graphically displayed, reflecting great behavior of every class in the model. The behavior of infected people is reported to be largely influenced by recovery and transmission rates. This demonstrates that quarantining Rubella-infected patients for a week or two reduces the virus transmission. It is revealed that the fractal dimensions has significant impact on the system’s dynamics.

In this paper, we investigate the implementations of newly introduced nonlocal differential operators as convolution of power law, exponential decay law, and the generalized Mittag-Leffler law with fractal derivative in fluid dynamics. The new operators are referred as fractal-fractional differential operators. The governing equations for the problem are constructed with the fractal-fractional differential operators. We present the stability analysis and the error analysis. [ABSTRACT FROM AUTHOR]

Screened electrostatic interactions in ionic liquids are investigated by means of exact statistical mechanical analysis combined with physical arguments that enhance the transparency and conceptual accessibility of the analysis and results. The constituent ions and immersed particles in the liquid can have arbitrary shapes and any internal charge distributions. The decay of the screened electrostatic potential and the free energy of interaction in ionic liquids can be exponentially damped oscillatory (like in molten simple salts) as well as plain exponential and long-ranged (like in dilute electrolyte solutions). Both behaviors are in agreement with the exact statistical mechanical analysis and reasons for their appearances are investigated. Exact but surprisingly simple expressions for the decay parameter k of the screened electrostatics are obtained, which replace the classical expression for the Debye-Hückel parameter kDH (the reciprocal Debye length). The expressions are applicable both for cases with plain exponential and oscillatory behaviors. The key importance of nonlocal electrostatics is thereby demonstrated explicitly. Dielectric properties of ionic liquids and other electrolytes are investigated, in particular the static dielectric function ∊(k) and some effective relative permittivities (εreff and εr*), which take roles that the dielectric constant εr has for polar liquids consisting of electroneutral molecules. The dielectric constant in the latter case, which is the limit of ∊(k) when the wave number k → 0, can be expressed solely in terms of dipolar features of the molecules. In contrast to this, the effective dielectric permittivities of ionic liquids have contributions also from quadrupolar, octupolar, and higher multipolar features of the constituent ions. The "dielectric constant" of electrolytes does not exist since ∊(k) → ∞ when k → 0, a well-known effect of perfect screening. The effective relative permittivities, εreff, and εr* of ionic liquids are obtained from the non-diverging part of ∊(k), but not as a k → 0 limit. Influences of ion associations, especially pairing, are investigated for screened electrostatics and these permittivities. A general, multipolar expansion of ∊(k) is derived and used to analyze dielectric properties of ionic liquids and other electrolytes. [ABSTRACT FROM AUTHOR]

Based on first-principles calculations, we studied the coupling of topological interface states at the interface of Bi2Se3/Bi2Se3 and TlSe/TlSe junctions. From our calculations, the coupling leads to an energy gap at the Dirac point of topological interface states and the energy gap is an exponential decay function of interface spacing when the interface spacing is large enough. The law of exponential decay may be used to identify the formation of interface states from interface-bulk mixed states. It also suggests that the coupling is caused by quantum tunneling. The coupling of the interface states in TlSe/TlSe can be greatly enhanced by intercalating hexagonal BN, although hexagonal BN is often used as a 2D substrate or insulator. The intercalation of bilayer BN or single atomic Au layer can further enhance the interfacial coupling. Our calculations may be helpful for the application of junctions composed of topological insulators. [ABSTRACT FROM AUTHOR]

Decoherence of Rabi oscillation in a two-level quantum system consists of two components, a simple exponential decay and a damped oscillation. In dense-ensemble spin systems like negatively charged nitrogen-vacancy (NV−) centers in diamond, fast quantum state decoherence often obscures clear observation of the Rabi nutation. On the other hand, the simple exponential decay (or baseline decay) of the oscillation in such spin systems can be readily detected but has not been thoroughly explored in the past. This study investigates in depth the baseline decay of dense spin ensembles in diamond under continuously driving microwave (MW). It is found that the baseline decay times of NV− spins decrease with the increasing MW field strength and the MW detuning dependence of the decay times shows a Lorentzian-like spectrum. The experimental findings are in good agreement with simulations based on the Bloch formalism for a simple two-level system in the low MW power region after taking into account the effect of inhomogeneous broadening. This combined investigation provides new insight into fundamental spin relaxation processes under continuous driving electromagnetic fields and paves ways to better understanding of this underexplored phenomena using single NV− centers, which have shown promising applications in quantum computing and quantum metrology. [ABSTRACT FROM AUTHOR]

In this paper, we explore the dynamics of tuberculosis (TB) epidemic model that includes the recruitment rate in both susceptible and infected population. Stability and sensitivity analysis of the classical TB model is carried out. Caputo-Fabrizio (CF) operator is then used to explain the dynamics of the TB model. The concept of fixed point theory is employed to obtain the existence and uniqueness of the solution of the TB model in the light of CF operator. Numerical simulations based on Homotopy Analysis Transform Method (HATM) and padé approximations are performed to obtain qualitative information on the model. Numerical solutions depict that the order of the fractional derivative has great dynamics of the TB model. [ABSTRACT FROM AUTHOR]

Accurate prediction of the angular and spatial distributions of radiative intensity is a very important and challenging issue for the coupled radiation and conduction problem with nonlinear anisotropic scattering medium. Different with the traditional hybrid spectral methods, spectral collocation method associated with discrete ordinate method (SCM-DOM), the spectral collocation method is extended to discretized both angular and spatial domains of governing equations in concentric cylinders. The angular and spatial derivative terms of governing equations in the cylindrical coordinate system are approximated by high order Chebyshev polynomials instead of the low order finite difference schemes. The performance of SCM is evaluated by comparing with available data in literature. Numerical results show that convergence rates of angular and spatial nodes approximately follow the exponential decaying law. In addition, for nonlinear anisotropic scattering medium, the SCM provides smoother results and mitigates the ray effect. The SCM is a successful and efficient method to deal with coupled radiative and conductive heat transfer in concentric cylinders. Furthermore, the effects of various geometric and thermal physical parameters on dimensionless temperature and heat flux are comprehensively investigated. [ABSTRACT FROM AUTHOR]

• Transferable model is adapted to spatially explicit recreational ecosystem service (RES). • RES supply increase, while demand decrease exponentially from urban to rural areas. • Females, older, and local groups show higher natural landscape preferences. • High-income, younger, and non-local people pursued longer travel distances. • Urban–rural and social groups' preferences facilitate multiscale landscape planning. Recreational ecosystem service (RES) supply and demand are fundamentally influenced by urbanization and are closely related to residents' well-being. Nevertheless, how socio-economic attributes affect spatial RES demand and preferences and can be integrated into urban–rural planning is still unclear. Taking the Beijing-Tianjin-Hebei urban agglomeration region of China as an example, based on survey and spatial data, we applied the Recreation Opportunity Spectrum and a new transferable Quasi-Poisson regression model to examine spatial RES supply and demand. Then, a scaling approach was adopted to interpret the urban–rural spatial patterns of RES. The results showed that the RES supply values exhibited either quadratic relationships or no particular patterns in most cities along urban–rural gradients, while the RES demand values monotonically decreased with an exponential decay or power law. The RES imbalance with higher demand (43%) in urban areas, the supply–demand balance (37%) in urban–rural fringes, and the supply sufficiency (64%) in rural areas were dominant. Divergent RES demand and preferences were identified across genders, ages, income, city scales, and household statuses. Females showed higher preferences for water, grassland, and agricultural landscapes than males; older groups showed higher preferences for natural landscapes but traveled less distance for RES; and high-income groups showed a lower frequency of visits but pursued longer travel distances. We suggest that at both the regional-city and local-community levels, more adaptive and elaborate landscape planning and design should be implemented by integrating urban–rural heterogeneity and the specific population's preferences into RES management. [ABSTRACT FROM AUTHOR]

Approximate formulas of the phosphorescence decay kinetics have been obtained for the statistical distribution of molecules over the rate constants of radiative and non-radiative deactivations of triplet excitations. It is shown that the characters of the phosphorescence decay differ for these two cases. The obtained difference in the kinetics has been used to establish a reason for the deviation from the exponential law and a faster decay of the sensitized phosphorescence of naphthalene and diphenyl in n-paraffin matrices (at T = 77 K) in the presence of heavy dibromo-diphenylene sulfide atoms in the donor. [ABSTRACT FROM AUTHOR]

The analysis of interpersonal relationships has started to become popular in the last few decades. Interpersonal relationships exist in many ways, including family, friendship, job, and clubs. In this manuscript, we have implemented the homotopy perturbation Elzaki transform method to obtain the solutions of romantic and interpersonal relationships model involving time‐fractional‐order derivatives with non‐singular kernels. The present method is the combination of the classical homotopy perturbation method and the Elzaki transform. This method offers a rapidly convergent series of solutions. The present approach explores the dynamics of love between couples. Validation and usefulness of the method are incorporated with new fractional‐order derivatives with exponential decay law and with general Mittag–Leffler law. Obtained results are compared with the established solution defined in the Caputo sense. Further, a comparative study among Caputo and newly defined fractional derivatives are discussed. [ABSTRACT FROM AUTHOR]

In this note, we studied the asymptotic behaviour of the length of the longest common substring for run-length encoded sequences. When the original sequences are generated by an α-mixing process with exponential decay (or - mixing with polynomial decay), we proved that this length grows logarithmically with a coefficient depending on the Rényi entropy of the pushforward measure. For Bernoulli processes and Markov chains, this coefficient is computed explicitly. [ABSTRACT FROM AUTHOR]

A simple model of alpha decay with the Dirac delta potential is studied. The model leads to breakdown of the exponential decay and to the power law behavior at asymptotic times. Time dependence of the survival probability of the particle in the potential well is analyzed numerically with two methods: integration of the Green's function representation and numerical solution of the time-dependent Schrödinger equation. The numerical results confirm power law with exponent n = 3 after the turnover into the non-exponential decay regime. Moreover, oscillations of non-escape probability are observed in the intermediate stage of the process. The simple alpha-decay model is compared to the results of the Rothe-Hintschich- Monkman experiment which was the first experimental proof of violation of the exponential law. [ABSTRACT FROM AUTHOR]

As the Riemann–Liouville derivative is a derivative of a convolution of a function and the power law, the fractal–fractional derivative of a function is the fractal derivative of a convolution of that function with the power law or exponential decay. In order to further open new doors on ongoing investigations with field of partial differential equations with non-conventional differential operators, we introduce in this paper new Cauchy problems with fractal–fractional differential operators. We consider two cases, when the operator is constructed with power law and when it is constructed with exponential decay law with Delta-Dirac property. For each case, we present the conditions under which the exact solution exists and is unique. We suggest a suitable and accurate numerical scheme that can be used to solve such differential equation numerically. We present illustrative examples where an application to a partial differential equation and to a model of groundwater flow within the confined aquifer are done with numerical simulations provided. The clear variation of water level shows the impact of the fractal–fractional derivative on the dynamics. [ABSTRACT FROM AUTHOR]

In this paper, the malaria transmission (MT) model under control strategies is considered using the Liouville–Caputo fractional order (FO) derivatives with exponential decay law and power-law. For the solutions we are using an iterative technique involving Laplace transform. We examined the uniqueness and existence (UE) of the solutions by applying the fixed-point theory. Also, fractal–fractional operators that include power-law and exponential decay law are considered. Numerical results of the MT model are obtained for the particular values of the FO derivatives ς and ρ. [ABSTRACT FROM AUTHOR]

In this paper the stretch function resulting from solving the fractional-order Bloch equations using fractional calculus was discussed. This function has promising results to represent diffusion signal decay from MRI images. Conventional analyses of (DWI) measurements resolve the normalized magnetization decay profiles in terms of discrete and mono-exponential components with distinct lifetimes. In complex, heterogeneous biological and biophysical samples such as tissue, multi-exponential decay functions can appear to provide truer representation to normalized magnetization decay profile than the assumption of a mono-exponential decay, but the assumption of multiple discrete components is arbitrary and is often erroneous. Moreover, interactions, between both normalized magnetization and with their environment, can result in complex normalized magnetization decay profiles that represent a continuous distribution of lifetimes. The purpose in this paper is to study different factors that influence the stretch function strength, clarity, and contrast of MRI magnetization signal relaxation by manipulating the anomalous diffusion parameters Δ, δ, Gz, β and μ. of Bloch equations. Through this study, it was found that complex normalized magnetization decay profiles behave like stretch exponential function inside power law. Further developments of this study may be useful in optimizing anomalous diffusion in tissues with neurodegenerative, and ischemic diseases. [ABSTRACT FROM AUTHOR]

In this paper, an extension is paid to an idea of fractal and fractional derivatives which has been applied to a number of ordinary differential equations to model a system of partial differential equations. As a case study, the fractal fractional Schnakenberg system is formulated with the Caputo operator (in terms of the power law), the Caputo-Fabrizio operator (with exponential decay law) and the Atangana-Baleanu fractional derivative (based on the Mittag-Liffler law). We design some algorithms for the Schnakenberg model by using the newly proposed numerical methods. In such schemes, it worth mentioning that the classical cases are recovered whenever α = 1 and β = 1. Numerical results obtained for different fractal-order (β ∈ (0 , 1)) and fractional-order (α ∈ (0 , 1)) are also given to address any point and query that may arise. [ABSTRACT FROM AUTHOR]

Nonlocal differential and integral operators with fractional order and fractal dimension have been recently introduced and appear to be powerful mathematical tools to model complex real world problems that could not be modeled with classical and nonlocal differential and integral operators with single order. To stress further possible application of such operators, we consider in this work an advection-dispersion model, where the velocity is considered to be 1. We consider three cases of the models, when the kernels are power law, exponential decay law and the generalized Mittag-Leffler kernel. For each case, we present a detailed analysis including, numerical solution, stability analysis and error analysis. We present some numerical simulation. [ABSTRACT FROM AUTHOR]

Sutherland, T.F. and Amos, C.L., 2020. An in situ assessment of seabed stability in Baynes Sound, British Columbia, Canada. Journal of Coastal Research, 36(3), 472–486. Coconut Creek (Florida), ISSN 0749-0208. The Sea Carousel, an annular flume, was deployed to examine (in situ) fundamental parameters of seabed stability in Baynes Sound, British Columbia, Canada. Sediment grain size, water and organic contents, and chlorophyll and phaeopigment concentrations were collected to establish a hierarchy of factors associated with seabed stability. Sediment stability increased toward the Sound entrance in concert with decreases in water, organic, and silt–clay contents and a transition from cohesive to noncohesive properties. Bed-stress estimates, based on the quadratic stress law and turbulent kinetic energy (TKE) methods, showed a decrease in the drag coefficient from the inner (0.04) to the outer (0.0015) Sound. Surface erosion thresholds ranged between 0.04 to 0.28 Pa, whereas the friction coefficients (e.g., the failure envelop) were on average 12°, representing normally consolidated sediments. Type I (floc) erosion occurred at low shear stresses, whereas type II (mass) erosion happened at higher values. Erosion rates (E, for type I erosion) fitted a power function of excess shear stress (Em = τ0 – τcrit,z)m with zero offset, where 0.81 < m < 2.32. The lowest and highest values for a given excess-shear stress occurred in the inner Sound and outer Sound, respectively. Settling of (resuspended) sediment after an exponential decay law [d(SSC)/dt] = SSC0 (exp–kt), where k fell within that of published values (3 < k < 539). Higher values of k (fastest settling) were observed in the inner Sound relative to the outer Sound. The sedimentation diameter (ds) fell in a coarse–silt to fine-sand range and was larger in the outer Sound, reflecting a coarsening of bed sediments. [ABSTRACT FROM AUTHOR]

It is shown that, in the melts of linear macromolecules, the effects of dynamic heterogeneity associated with the presence of end segments are not vanishingly small in the limit , where is the number of Kuhn segments in the macromolecule. The effect has a frequency nature, i.e., the division of the segments into "end" ones, more mobile in comparison with the "median" ones, mainly depends on the observation time. With the increase in the observation time, symmetrical growth of the "end" regions of the polymer chain occurs from both ends of the macromolecule which covers the entire macromolecule at times on the order of the terminal relaxation time. The effect generates nontrivial experimentally observed consequences. For example, the free induction decay of deuterons in monodisperse polymer melts of macromolecules should have an extended region with the exponential decay law , where for the reptation model and for isotropic renormalized Rouse models: is the exponent of the molecular weight dependence of the terminal relaxation time of macromolecules. At , the influence of the effects of dynamic heterogeneity on the shape of free induction decay is weaker, although it is observable at sufficient accuracy of the measurements. [ABSTRACT FROM AUTHOR]

We describe and validate a Monte Carlo model to track photons over the full range of solar wavelengths as they travel into optically thick Antarctic blue ice. The model considers both reflection and transmission of radiation at the surface of blue ice, scattering by air bubbles within it, and spectral absorption due to the ice. The ice surface is treated as planar whilst bubbles are considered to be spherical scattering centres using the Henyey–Greenstein approximation. Using bubble radii and number concentrations that are representative of Antarctic blue ice, we calculate spectral albedos and spectrally integrated downwelling and upwelling radiative fluxes as functions of depth and find that, relative to the incident irradiance, there is a marked subsurface enhancement in the downwelling flux and accordingly also in the mean irradiance. This is due to the interaction between the refractive air–ice interface and the scattering interior and is particularly notable at blue and UV wavelengths which correspond to the minimum of the absorption spectrum of ice. In contrast the absorption path length at IR wavelengths is short and consequently the attenuation is more complex than can be described by a simple Lambert–Beer style exponential decay law – instead we present a triple-exponential fit to the net irradiance against depth. We find that there is a moderate dependence on the solar zenith angle and surface conditions such as altitude and cloud optical depth. Representative broadband albedos for blue ice are calculated in the range from 0.585 to 0.621. For macroscopic absorbing inclusions we observe both geometry- and size-dependent self-shadowing that reduces the fractional irradiance incident on an inclusion's surface. Despite this, the inclusions act as local photon sinks and are subject to fluxes that are several times the magnitude of the single-scattering contribution. Such enhancement may have consequences for the energy budget in regions of the cryosphere where particulates are present near the surface. These results also have particular relevance to measurements of the internal radiation field: account must be taken of both self-shadowing and the optical effect of introducing the detector. Turning to the particular example of englacial meteorites, our modelling predicts iron meteorites to reside at much reduced depths than previously suggested in the literature (< 10 cm vs. ∼ 40 cm) and further shows a size dependency that may explain the observed bias in their Antarctic size distribution. [ABSTRACT FROM AUTHOR]