Decay Term Research Articles

The Optimal Determination of the Truncation Time of Non-Exponential Sound Decays

The noise effects in the room impulse response (RIR) make the decay range of the integrated impulse response insufficient for reliable determination of reverberation time (RT). One of the preferred techniques to minimize noise effects is based on noise subtraction, RIR truncation, and correction for the truncation. The success of RT estimation through the method depends critically on the accurate estimation of the truncation time (TT). However, noise fluctuation and RIR irregularities can lead to discrepancies in the determined TT from the optimal value. The general goal of this paper is to improve RT estimates. An iterative procedure based on a non-exponential decay model consisting of a double-slope decay term and a noise term is presented to estimate the TT accurately. The model parameters are generated until the iterative procedure converges to a minimum difference between the energy decay curve (EDC) generated by the model and the Schroeder decay function. The decay rates of the EDCs with added pink noise levels are compared to those of the EDCs with low background noise. In addition, the detected TTs and the corresponding RTs are compared with the existing method and the noise compensation method (subtraction–truncation–correction method).

Weak and strong convergence analysis of Elman neural networks via weight decay regularization

In this paper, we propose a novel variant of the algorithm to improve the generalization performance for Elman neural networks (ENN). Here, the weight decay term, also called regularization, which can effectively control the value of weights excessive growth, also over-fitting phenomenon can be effectively prevented. The main contribution of this work lies in that we have conducted a rigorous theoretical analysis of the proposed approach, i.e. the weak and strong convergence results are obtained. The comparison experiments to the problems of function approximation and classification on the real-world data have been performed to verify the theoretical results.

Nelson–Siegel decay factor and term premia in Japan

This study examines the low–interest rate environment in Japan from mid-1990 to the end of 2020, using a dynamic Nelson–Siegel framework emphasizing the role of the decay factor. A regime-switching model estimates that the regime with low decay factor and bond yield volatility (“low” regime) has persisted since the early years of Bank of Japan's quantitative and qualitative monetary easing (QQE) policy. A shift away from the low regime can instantly increase the 10-year government bond yield by over 50 basis points by increasing the term premiums with little changes in the expected short rate.

Ultrahard BC5 – An efficient nanoscale heat conductor through dominant contribution of optical phonons

In this work, we study lattice thermal conductivity (k) of BC5, an diamondlike ultra-hard material, using first-principles computations and analyze the effect of both isotopic disorder as well as length scale dependence. k of isotopically pure BC5 is computed to be 169 Wm−1 K−1 (along a-axis) at 300 K; this high k is found to be due to the high frequencies and phonon group velocities of both acoustic and optical phonons owing to the light atomic mass of Carbon (C) and Boron (B) atoms and strong C-C and B-C bonds. We also observe a dominance of optical phonons (∼54%) over acoustic phonons in heat conduction at higher temperatures (∼500 K). This unusually high contribution of optical phonons is found to be due to a unique effect in BC5 related to a weaker temperature dependence of optical phonon scattering rates relative to acoustic phonons. The effect is explained in terms of high frequencies of optical phonons causing decay into other high frequency phonons, where low phonon populations cause the decay term to become insensitive to temperature. The effect further leads to high nanoscale thermal conductivity of 77 Wm−1 K−1 at 100 nm length scale due to optical phonon meanfreepaths being in nanometer regime. These results provide avenues for application of BC5 in nanoscale thermal management.

Models of the water activity effect on microbial growth rate and initiation.

The role water activity, aw, plays in microbial growth by itself or in conjunction with other factors, notably temperature and pH, has been described mathematically by different algebraic models obtained by fitting experimental growth rate vs. aw relationships. Many of these models have one, two, or all three cardinal parameters, namely the minimal, optimal, and maximal aw, in their formulation. Although they all have good fit as judged by statistical criteria, their different mathematical structures have different ramifications concerning the threshold aw for growth initiation, and the growth pattern around and beyond the optimal aw level where it exists. The focus of this review is on the biological implications of the different growth rate vs. aw models inferred exclusively from their mathematical properties, leaving out any statistical fit considerations. It also describes a recently proposed single-parameter model of monotonic or the monotonic part of experimental growth rate vs. aw curves, which can be combined with a decay term to produce a general conceptual model of peaked and monotonic microbial growth rate vs. aw relationships over the entire aw range. KEY POINTS: • Traditional and new growth rate vs. aw models are presented and their implications compared. • Analogy between aw and the temperature or pH effect on microbial growth rate is reassessed. • Cardinal parameters alone do not establish a unique growth rate vs. aw relationship.

Best Operating Conditions for Biogas Production in Some Simple Anaerobic Digestion Models

We consider one-step and two-step simple models of anaerobic digestion that are able to adequately capture the main dynamical behaviour of the full anaerobic digestion model ADM1. We do not consider specific growth functions. We only require them to satisfy certain qualitative assumptions. These assumptions are satisfied for concave growth functions, but they are also satisfied for a large class of growth functions found in many applications. We consider the maximisation of the biogas production with respect to the operating parameters of the model, which are the dilution rate and the substrate input concentration. We give the best operating conditions and we describe them as a subset of the set of operating parameters. Our models incorporate biomass decay terms, corresponding to maintenance. Numerical plots with specified growth functions and biological parameters illustrate the obtained results.

Tensor PDE model of biological network formation

We study an elliptic-parabolic system of partial differential equations describing formation of biological network structures. The model takes into consideration the evolution of the permeability tensor under the influence of a diffusion term, representing randomness in the material structure, a decay term describing metabolic cost and a pressure force. A Darcy's law type equation describes the pressure field. In the spatially two-dimensional setting, we present a constructive, formal derivation of the PDE system from the discrete network formation model in the refinement limit of a sequence of unstructured triangulations. Moreover, we show that the PDE system is a formal $L^2$-gradient flow of an energy functional with biological interpretation, and study its convexity properties. For the case when the energy functional is convex, we construct unique global weak solutions of the PDE system. Finally, we construct steady state solutions in one- and multi-dimensional settings and discuss their stability properties.

A semi-quantum approach for modelling the accelerated test data

The traditional models for the analysis of the accelerated test data cannot physically explains how the environment affects lifetime and its uncertainty. To solve this problem, this paper utilizes the theory of open quantum system, the theory about random behaviour of microparticles under the external environment, to describe the effects of stresses on lifetime uncertainty. The interaction between the system and environments motivates us to describe the accelerated test data from a quantum perspective. A quantum master equation is used as the reliability dynamics, which can be separated into a conservation term and a decay term. Then, the acceleration model is further incorporated into the decay term of the dynamic and forms a semi-quantum model. A practical procedure is proposed to obtain the initial guesses of parameters and do a graphic check on the assumption. Applications on two sets of real accelerated life test data show the proposed model outperforms the existing ones and hence verify its validity. This paper makes the first attempt to quantify the uncertainty under different environments from a quantum perspective and shows that it is feasible to utilize quantum theory to make a further exploration.

Kinetic modeling of aquathermolysis for upgrading of heavy oils

The growing energy demand and reduction of conventional oil reservoirs have prompted the investigation of technologies to recover unconventional heavy oils. Steam injection is the most widely used thermal method for heavy oil recovery. However, this process presents some challenges due to the high viscosity and content of heavy components such as resins and asphaltenes in this type of oil. Additionally, the mechanisms of the different chemical reactions that take place during steam injection are not fully understood. Aquathermolysis is another approach that can be used not only for heavy oil recovery but also for heavy oil upgrading. An analysis and discussion of the kinetic models focused on the aquathermolysis reaction reported up to date is performed. Different aspects of reaction mechanisms, operating conditions, reaction rate equations, kinetic parameter values, and catalytic decay terms are reviewed. It has been concluded that kinetic modeling studies for aquathermolysis are scarce in the literature and that the reported models are simple in nature, which indicates the need for more research in this area for proper evaluation of technologies for in situ upgrading of heavy oils, either catalytic or non-catalytic.

Analytical solutions of advection-dispersion-reaction equation with first decay under constant and time-dependent boundary conditions: Mass transfer shape factor effects

To describe the combined dispersion and convection mechanisms of solute transport through porous media, one may typically refer to the advection-dispersion equation (ADE). In this study, a generalized analytical solution to the ADE combined with first order decay term is derived for the problem of solute transport through porous media in one-dimensional finite region considering transient boundary conditions. First, the addressed convection-dispersion-reaction equation is simplified into a diffusion equation. Subsequently, an analytical solution is generated for a general fractured porous medium for a case where a fracture is viewed as the transient boundary condition. To verify the proposed analytical solution, experimental data acquired from literature as well as numerical techniques of finite difference and element are utilized. Previous studies have utilized fixed values for mass transfer shaper factor which is deployed in dual porosity modeling approach of fractured reservoirs, while in reality this parameter changes over time. In this regard, an attempt is made to attain mass transfer shape factor while considering the impacts of important parameters such as Péclet number, and decay coefficient during both pseudo steady state (PSS) and transient periods. Moreover, for two circumstances of linearly ascending and constant concentration boundary conditions, a correlation is developed to compute PSS mass transfer shape factor as a function of Péclet number, dimensionless time, and decay coefficient. The results illustrated the dependency of PSS shape factor on the decay coefficient, Péclet number, and time while transient shape factor solely depended on time. In addition, the findings showed that the larger the Péclet number, the larger the PSS matrix-fracture mass transfer shape factor. The obtained analytical solution is helpful when validating the numerical simulation results and for performing fast sensitivity analysis. The developed mass transfer shape factor can be applied in the dual porosity modeling part of the commercial reservoir simulation software packages for more accurately modeling the solute transport in the fractured reservoirs.

Prescribed signal concentration on the boundary: Weak solvability in a chemotaxis-Stokes system with proliferation

We study a chemotaxis-Stokes system with signal consumption and logistic source terms of the form where kappa ge 0, mu >0 and, in contrast to the commonly investigated variants of chemotaxis-fluid systems, the signal concentration on the boundary of the domain Omega subset mathbb {R}^N with Nin {2,3} is a prescribed time-independent nonnegative function c_*in C^{2}!left( {{,mathrm{overline{Omega }},}}right) . Making use of the boundedness information entailed by the quadratic decay term of the first equation, we will show that the system above has at least one global weak solution for any suitably regular triplet of initial data.

Evaluation and application of chlorine decay models for humanitarian emergency water supply contexts

ABSTRACT Chlorine is a widely used water disinfectant in humanitarian emergency water supply. However, its effective application can be limited by the uncertainty in initial dose determination. The target free chlorine residual in water should achieve both health objectives and aesthetic considerations, but the varying field conditions and changing source water quality may affect the performance of chlorination strategies. A chlorine dose predictive tool could assist in initial dose determination. To this end, an accurate chlorine decay kinetic model can serve as a strong foundation for developing such a tool. In this study, a literature search identified 7 basic chlorine decay kinetic models that were subsequently tested with 610 different chlorine decay test data (from a semi-systematic literature search and laboratory-generated results). The models were then ranked based on their goodness of fit (R 2) and root mean square error. An empirical model, power models and parallel models were found able to fit most decay data with more than half of the regressions resulting in R 2 value over 0.97. First order models can achieve R 2 value above 0.95 when the data points in the rapid phase are excluded from the model fitting. The power models and parallel models can form a strong basis for developing a chlorine dose predictive tool if the power term and the ratio term (model parameters) can be controlled. An essential next step is to evaluate the relationships between easily obtainable water parameters in the field and the decay term in the models to allow rapid model calibration.

Hydrodynamic Approach to Electronic Transport in Graphene: Energy Relaxation

In nearly compensated graphene, disorder-assisted electron-phonon scattering or “supercollisions” are responsible for both quasiparticle recombination and energy relaxation. Within the hydrodynamic approach, these processes contribute weak decay terms to the continuity equations at local equilibrium, i.e., at the level of “ideal” hydrodynamics. Here we report the derivation of the decay term due to weak violation of energy conservation. Such terms have to be considered on equal footing with the well-known recombination terms due to nonconservation of the number of particles in each band. At high enough temperatures in the “hydrodynamic regime” supercollisions dominate both types of the decay terms (as compared to the leading-order electron-phonon interaction). We also discuss the contribution of supercollisions to the heat transfer equation (generalizing the continuity equation for the energy density in viscous hydrodynamics).

Analytical solution of two-dimensional conservative solute transport in a heterogeneous porous medium for varying input point source

In the present study, an analytical solution is obtained for two-dimensional advection–dispersion equation with variable coefficients in a semi-infinite heterogeneous porous medium. Dispersion coefficient and groundwater velocity are assumed to vary temporally as well as spatially while the retardation factor varies spatially only. The first-order decay and zero-order production terms are also considered into account. The variations in parameters along both longitudinal and transverse directions are of exponentially decreasing nature. Initially the geological formation is considered not solute free. The nature of pollutant is considered of conservative and is assumed to be originating from time-dependent varying point source. New time and space variables are introduced to convert the variable coefficients of the advection–dispersion equation into constant coefficients. Analytical solution of the proposed model is obtained by employing Laplace integral transformation technique (LITT). The proposed analytical solution is illustrated graphically to study the effects of various parameters on the solute transport for temporally exponentially decreasing and sinusoidal nature velocities.

Energetics of stochastic BCM type synaptic plasticity and storing of accurate information

Excitatory synaptic signaling in cortical circuits is thought to be metabolically expensive. Two fundamental brain functions, learning and memory, are associated with long-term synaptic plasticity, but we know very little about energetics of these slow biophysical processes. This study investigates the energy requirement of information storing in plastic synapses for an extended version of BCM plasticity with a decay term, stochastic noise, and nonlinear dependence of neuron’s firing rate on synaptic current (adaptation). It is shown that synaptic weights in this model exhibit bistability. In order to analyze the system analytically, it is reduced to a simple dynamic mean-field for a population averaged plastic synaptic current. Next, using the concepts of nonequilibrium thermodynamics, we derive the energy rate (entropy production rate) for plastic synapses and a corresponding Fisher information for coding presynaptic input. That energy, which is of chemical origin, is primarily used for battling fluctuations in the synaptic weights and presynaptic firing rates, and it increases steeply with synaptic weights, and more uniformly though nonlinearly with presynaptic firing. At the onset of synaptic bistability, Fisher information and memory lifetime both increase sharply, by a few orders of magnitude, but the plasticity energy rate changes only mildly. This implies that a huge gain in the precision of stored information does not have to cost large amounts of metabolic energy, which suggests that synaptic information is not directly limited by energy consumption. Interestingly, for very weak synaptic noise, such a limit on synaptic coding accuracy is imposed instead by a derivative of the plasticity energy rate with respect to the mean presynaptic firing, and this relationship has a general character that is independent of the plasticity type. An estimate for primate neocortex reveals that a relative metabolic cost of BCM type synaptic plasticity, as a fraction of neuronal cost related to fast synaptic transmission and spiking, can vary from negligible to substantial, depending on the synaptic noise level and presynaptic firing.

Modelling one-dimensional reactive transport of toxic contaminants in natural rivers

Solute transport models are widely employed to the predict spatio-temporal fate of contaminants in rivers. However, most previous studies have assumed that contaminants spilled are unreactive; they disregard the inherent reactivity of contaminants in water. The Reactive Solute Transport Model (RSTM) (Gooseff et al., 2005) includes lumped decay terms to reflect the decayability of the chemicals, but its applicability was still poor due to dependence on an optimization method. The purpose of this study is to perform reactive transport modelling considering chemicals’ reactivities for sorption, volatilization, and biodegradation. To this end, we manipulated the governing equations of the RSTM and suggested theoretical and empirical methods of estimating the key parameters of the reaction terms. The results showed, for example, that benzene lost 57.7% of its primary mass after being transported 4.54 km downstream due to its high volatility. Also, the arrival time of toluene was delayed by 10.4% due to adsorption.

Impact of Program/Erase Cycling Interval on the Transconductance Distribution of NAND Flash Memory Devices

This study comprehensively investigates the impact of the time interval (t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">wait</sub> ) between program/erase (P/E) cycles on the oxide quality of NAND Flash memory devices. It is observed that, at room temperature, P/E cycles with a shorter t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">wait</sub> yield a better oxide quality than those with a longer t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">wait</sub> . The oxide charge (Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> ) evolution by distributed P/E cycles can be well described by an analytical equation through the extension of our previous statistical transconductance reduction (G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m,max</sub> ) method. This equation is characterized by a power of the number of P/E cycles multiplied by an exponential decay term of t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">wait</sub> . The former term is related to the Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> generation, whereas the latter is related to the Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> emission during t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">wait</sub> between cycles. This model allows to evaluate the activation energy for both Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> generation (E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A,G</sub> ) and recovery (E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A,R</sub> ). E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A,G</sub> is revealed to be a function of the logarithmic scale of t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">wait</sub> , decreasing from 100 to 85 meV for t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">wait</sub> varying from 0.1 to 4 s. Moreover, E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A,R</sub> is approximately 0.4 eV, which is consistent with the value of electron thermal emission from traps in SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> .

Hybrid Event-Based Leader-Following Consensus of Nonlinear Multiagent Systems With Semi-Markov Jump Parameters

This article aims to systematically address the leader-following consensus issue for continuous-time multiagent systems with semi-Markov jump parameters. A more universal random process, semi-Markov process, is utilized to model the variations of parameters which may result from the complexity of environment. The innovative hybrid event-triggered strategy associated with an improved threshold function is employed for economizing the network bandwidth resources. It presents an exponential decay term in the threshold function for decreasing the transmission frequency of superfluous data packets, ulteriorly reducing triggering times. The dominating core concentrates on the design of a controller interrelated with the hybrid event-triggered condition, which can be implemented to ensure the leader-following consensus of the considered systems. On the strength of time-dependent and piecewise Lyapunov–Krasovskii functional, several criteria, which are capable of ensuring the leader-following consensus of the multiagent systems, are derived. Ultimately, two suitable numerical examples and a meaningful practical one are utilized to demonstrate the validity and potential of the derived results.

Variable-sampling-period dependent global stabilization of delayed memristive neural networks based on refined switching event-triggered control

This paper studies the stabilization problem of delayed memristive neural networks under event-triggered control. A refined switching event-trigger scheme that switches between variable sampling and continuous event-trigger can be designed by introducing an exponential decay term into the threshold function. Compared with the existing mechanisms, the proposed scheme can enlarge the interval between two successively triggered events and therefore can reduce the amount of triggering times. By constructing a time-dependent and piecewise-defined Lyapunov functional, a less-conservative criterion can be derived to ensure global stability of the closed-loop system. Based on matrix decomposition, equivalent conditions in linear matrix inequalities form of the above stability criterion can be established for the co-design of both the trigger matrix and the feedback gain. A numerical example is provided to demonstrate the effectiveness of the theoretical analysis and the advantages of the refined switching event-trigger scheme.

Study of multispecies convection-dispersion transport equation with variable parameters

Multispecies pollutant migration is most natural phenomenon, frequently occurring in the polluted groundwater system and also evidently occurs in the nuclear repositories and sites having radioactive substances and chemical solvent. Modeling pollutant migration of reactive multispecies problem with variable transport parameters is quite a challenging issue, necessary for better sightedness of fate and transport of reactive solutes and their geochemical growth in the geological formations. At present most of the solutions for multispecies problem are corresponding to the constant parameters affecting the concentration distribution, not for variable transport parameters, because of the complexity of the modelled equation. This paper dealt with the comparative study of multispecies pollutant transport problem in porous structure to analyse the effect of spatially and temporally varying hydrodynamic dispersion coefficient and transport velocity terms in more general form. For mathematical elaboration, two-species transport problem is considered subjected to the concept of linear isotherm with both the parent and daughter species without using identical retardation factor and model is also incorporated with the first-order decay term under spatially varying initial conditions. Homotopy analysis method (HAM) is adopted to develop the series solution for the concentration segmentation of each species of the model. The advantage of this method is that it is capable to overcome the limitation of existing transform methods for some cases of complex modelled problems. The zeroth order deformation equation is derived by using HAM to generate the semi-analytical solution of the model under certain auxiliary linear operator. The impact of distinct retardation factor for different species and effect of diversity in dependency of modelled parameters over space and time are graphically depicted for both the species and illustrated that it has a valuable impact over multispecies pollutant migration. As there exist no analytical or numerical solution for such complex variable dependency of migration parameters over transport phenomenon, these solutions may be helpful to deliver a better significant about the concentration variation due to space and time dependent transport parameters, responsible for reactive multispecies migration, in more natural way.