Exponential Decay Law Research Articles

Experimental studies on the influence of smoke acceleration effect feedback to the flame behavior in the U shaped shaft of a high-rise building

This paper presents an experimental investigation of the feedback effect with smoke acceleration on flame behaviors in the U shaped shaft of a high-rise building. Heat release rate of the fire, depths and widths of the U shaped shaft are changed. The flame height, vertical maximum temperature in the open shaft and the heat flux distribution on the façade are studied. Results show that the flame height is elongated by the smoke acceleration effect in the U shaped shaft and larger than that in the open space. Correlations for the flame height are established by taking into account the geometries of the U shaped shaft. The vertical maximum temperature in the U shaped shaft first decreases rapidly then keeps room temperature, which are compared with that under stack effect in the staircase. The exponential decay law between the vertical maximum temperature and height is modified. The total heat flux is mainly affected by the width and heat release rate. Radiation heat transfer fraction is larger than 80 % in the continuous and intermittent flame regions, of which the flame emissivity is about 0.53.

Acoustoelectric Effect due to an In-Depth Inhomogeneous Conductivity Change in ZnO/Fused Silica Substrates

The acoustoelectric (AE) effect induced by the absorption of ultraviolet (UV) light at 365 nm in piezoelectric ZnO films was theoretically and experimentally studied. c-ZnO films 4.0 µm thick were grown by the RF reactive magnetron sputtering technique onto fused silica substrates at 200 °C. A surface acoustic wave (SAW) delay line was fabricated with two split-finger Al interdigital transducers (IDTs) photolithographically implemented onto the ZnO-free surface to excite and reveal the propagation of the fundamental Rayleigh wave and its third harmonic at about 39 and 104 MHz. A small area of a few square millimeters on the surface of the ZnO layer, in between the two IDTs, was illuminated by UV light at different light power values (from about 10 mW up to 1.2 W) through the back surface of the SiO2 substrate, which is optically transparent. The UV absorption caused a change of the ZnO electrical conductivity, which in turn affected the velocity and insertion loss (IL) of the two waves. It was experimentally observed that the phase velocity of the fundamental and third harmonic waves decreased with an increase in the UV power, while the IL vs. UV power behavior differed at large UV power values: the Rayleigh wave underwent a single peak in attenuation, while its third harmonic underwent a further peak. A two-dimensional finite element study was performed to simulate the waves IL and phase velocity vs. the ZnO electrical conductivity, under the assumption that the ZnO layer conductivity undergoes an in-depth inhomogeneous change according to an exponential decay law, with a penetration depth of 325 nm. The theoretical results predicted single- and double-peak IL behavior for the fundamental and harmonic wave due to volume conductivity changes, as opposed to the AE effect induced by surface conductivity changes for which a single-peak IL behavior is expected. The phenomena predicted by the theoretical models were confirmed by the experimental results.

Study of Effect of Radiation Hazards in Human Life

In this paper, we have investigated the effect of radiations on human life by expressing the exponential decay law curve, dose curve, shielding effectiveness curve and radiation exposure simulation curve. Also this research investigates the impact of radiation hazards on human health, focusing on both quantitative data and qualitative case studies. Utilizing a comprehensive analysis of radiation exposure levels and their associated health outcomes, we plotted various graphs to illustrate the correlation between radiation dose and adverse health effects. Our research combines empirical data with in-depth case studies to assess how different levels and types of radiation influence human life. The findings reveal a significant relationship between radiation exposure and increased risks of several health conditions, including cancer and radiation sickness. By analyzing the plotted data and case studies, this paper provides a detailed understanding of the short-term and long-term effects of radiation hazards. The results underscore the importance of effective radiation safety measures and informed public health policies to mitigate these risks.

A theoretical model for wave attenuation by vegetation considering current effects

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).

Measurement of the 22Na half-life and evidence supporting the exponential-decay law

The half-life of 22Na has been determined through 523 activity measurements over 14.5 years with a re-entrant ionisation chamber in a temperature-stabilised room. The data were selected and aggregated from in total 127 830 ionisation current measurements with a reproducibility of the order of 0.065% standard deviation. The ionisation current was collected over an air capacitor and measured as a change of voltage over time, which warrants excellent linearity with activity throughout the experiment. The residuals to an exponential decay curve show a distinct annual cycle of 0.0055 (5)% amplitude, which reduces to 0.0012 (5)% after compensation for a correlation with ambient humidity. The data confirm the validity of the exponential-decay law, in absence of cyclic perturbations at daily, monthly, and multi-annual scale at the level of 0.0005% standard deviation. The 22Na half-life value obtained in this study is 950.68 (12) d or 2.60290 (34) a, with a relative standard uncertainty of 0.013%. This value is consistent with the mean value of other measurement results in the literature, although the latter have an issue with incomplete uncertainty budgets. Owing to the high statistical accuracy and conservative uncertainty estimate of systematic errors, the result obtained in this work can be recommended as a reliable reference value.

Analytical solutions for a class of variable-order fractional Liu system under time-dependent variable coefficients

In this article, we present a nonlinear model of the Liu system that includes fractional derivatives of variable-order. Due to the nonlocality of the dynamical system, we introduce the fractional derivative with power laws, exponential decay laws, and generalized Mittag-Leffler functions as kernels. We provide a detailed analysis of the existence and uniqueness of the proposed model, as well as the stability of these equations. Due to the existence of time-varying fractional derivatives, the proposed variable-order fractional system exhibits more complex characteristics and more degrees of freedom than an integer or conventional constant fractional-order chaotic Liu oscillator. Different chaotic behaviors can be obtained by using different smooth functions defined within the interval (0,1] as variable orders for fractional derivatives in the simulations. Furthermore, simulations demonstrate that fractional chaotic systems with variable orders can be synchronized.

Tuning exponential decay factor in oligophenylene molecular junctions with graphene nanoribbon electrodes

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.

Ambient humidity, the overlooked influencer of radioactivity measurements

When verifying the validity of the exponential-decay law through 137 precise decay rate measurement series at various nuclear laboratories, minor violations have been observed in the shape of annual cycles in the residuals with different amplitudes and phase shifts. The timing and amplitude of these deviations have been compared with local weather data and it appears that ambient humidity is highly correlated with the observed instabilities in these radioactivity measurements. In fact, when compensating the residuals for a linear relationship with absolute humidity in air, most of the annual cycles are no longer statistically significant. As a result, the validity of the exponential-decay law can now be demonstrated with even higher fidelity.

Understanding recreational ecosystem service supply-demand mismatch and social groups’ preferences: Implications for urban–rural 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.

Accelerating Quantum Decay by Multiple Tunneling Barriers.

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.

Noise induced dynamics of two-qubit entangled Bell’s states

The stability of different types two-qubit entangled states was analyzed by a direct calculations of the time dependent probability to find the system in its initial state in the presence of Gaussian noise. The entangled states time evolution was studied in the presence of both classical and quantum noise. It was demonstrated that one pair of Bell’s states is robust to the Gaussian fluctuations, while the another one decays. The decay law of unstable entangled states is determined by the noise correlation function. The developed general formalism was applied for analysis the dynamics of entangled states in the presence of fluctuations produced by the electron–phonon interaction. It was revealed that unstable entangled states interacting with phonon bath can demonstrate the crossover between short time exponential decay law and long time power law decay. Obtained results can be effectively exploited for quantum computation, in which it is essential to be able to retrieve information about the initial quantum state even in the presence of interaction with the environment.

ПРЕДВАРИТЕЛЬНЫЕ РЕЗУЛЬТАТЫ ЛАБОРАТОРНЫХ ИССЛЕДОВАНИЙ ЭВОЛЮЦИИ НЕФРОНТАЛЬНЫХ ВИХРЕЙ В ДВУСЛОЙНОЙ ВРАЩАЮЩЕЙСЯ ЖИДКОСТИ

In this work, by means of laboratory modeling, the patterns of evolution (baroclinic instability and/or viscous degeneration) of mesoscale non-frontal baroclinic eddies, or open ocean eddies (without a core with the water of different density) were revealed. The experiment was provided in a two-layer salinity-stratified aquatic environment in a cylindrical tank located on a rotating platform. Using the original application of the “cylinder method”, single axisymmetric cyclonic and anticyclonic eddies were produced in the upper layer, and their evolution was traced over 100 or more platform rotation periods (laboratory days). It has been established that the vortices lose their stability if the value of the defining parameter representing the ratio of the Burger and Froude numbers is less than the critical one. In this case, eddies either fall apart into two or more secondary vortices (strong instability) or acquire an elongated shape (weak instability). The slope of the bottom and its roughness increase the stability of eddies. For values of the determining parameter greater than the critical one, the vortices are stable and gradually degenerate due to viscous friction. In the case of a large difference in salinity (density) between the layers, the bottom roughness does not have a significant effect on the rate of upper layer eddy damping, which, apparently, is determined by the friction in this layer. A parametrization is proposed that describes the exponential law of eddy decay, which is tested on the example of the Black Sea mesoscale eddy.

Effective description of sub-maximal chaos: stringy effects for SYK scrambling

It has been proposed that the exponential decay and subsequent power law saturation of out-of-time-order correlation functions can be universally described by collective ‘scramblon’ modes. We develop this idea from a path integral perspective in several examples, thereby establishing a general formalism. After reformulating previous work on the Schwarzian theory and identity conformal blocks in two-dimensional CFTs relevant for systems in the infinite coupling limit with maximal quantum Lyapunov exponent, we focus on theories with sub-maximal chaos: we study the large-q limit of the SYK quantum dot and chain, both of which are amenable to analytical treatment at finite coupling. In both cases we identify the relevant scramblon modes, derive their effective action, and find bilocal vertex functions, thus constructing an effective description of chaos. The final results can be matched in detail to stringy corrections to the gravitational eikonal S-matrix in holographic CFTs, including a stringy Regge trajectory, bulk to boundary propagators, and multi-string effects that are unexplored holographically.

A novel numerical dynamics of fractional derivatives involving singular and nonsingular kernels: designing a stochastic cholera epidemic model

<abstract><p>In this research, we investigate the direct interaction acquisition method to create a stochastic computational formula of cholera infection evolution via the fractional calculus theory. Susceptible people, infected individuals, medicated individuals, and restored individuals are all included in the framework. Besides that, we transformed the mathematical approach into a stochastic model since it neglected the randomization mechanism and external influences. The descriptive behaviours of systems are then investigated, including the global positivity of the solution, ergodicity and stationary distribution are carried out. Furthermore, the stochastic reproductive number for the system is determined while for the case $ \mathbb{R}_{0}^{s} > 1, $ some sufficient condition for the existence of stationary distribution is obtained. To test the complexity of the proposed scheme, various fractional derivative operators such as power law, exponential decay law and the generalized Mittag-Leffler kernel were used. We included a stochastic factor in every case and employed linear growth and Lipschitz criteria to illustrate the existence and uniqueness of solutions. So every case was numerically investigated, utilizing the newest numerical technique. According to simulation data, the main significant aspects of eradicating cholera infection from society are reduced interaction incidence, improved therapeutic rate, and hygiene facilities.</p></abstract>

A Discrete Elements Study of the Frictional Behavior of Fault Gouges.

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.

Analysis of quantum decay law: is quantum tunneling really exponential?

The exponential decay law is well established since its first derivation in 1928; however, it is not exact but only an approximate description. In recent years some experimental and theoretical indications for non-exponential decay have been documented. First we solve analytically the time-dependent Schrödinger equation in one dimension for a potential consisting of an infinite wall plus a rectangular barrier with finite width and also a cut harmonic oscillator potential by considering it as a sequence of square potentials. Then using the staggered Leap-Frog method, we solve the time-dependent Schrödinger equation for the cut harmonic oscillator potential. In both methods, time dependence of the survival probability of the particle and the decay parameter \( \lambda \) are analyzed. The results exhibit non-exponential behavior for survival probability at short and intermediate times.

Physics‐based model to predict the acoustic detection distance of terrestrial autonomous recording units over the diel cycle and across seasons: Insights from an Alpine and a Neotropical forest

Abstract 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.

Study on smoke temperature induced by two fires in a naturally ventilated tunnel

The temperature of smoke flow beneath the tunnel ceiling induced by two fires in a naturally ventilated tunnel is studied. The two fires are located in the lateral direction of the tunnel, and the distance between two fires is varied. Both the maximum temperature rise and the temperature distribution beneath the tunnel ceiling are investigated. For temperature distribution in the tunnel longitudinal direction, there is decrease in temperature with the increasing burner separation distance at the near fire region, while at the region far away from the fire location, the smoke temperature gets very close. Results show that the longitudinal temperature distribution exhibits an exponential decay law along the tunnel ceiling. A formula is established to predict the longitudinal temperature distribution and results show that there is good agreement between the numerical data and formula calculations. Comparison of temperature distribution in the tunnel longitudinal direction and transverse direction shows that at separation distance ofL=0m, there is obvious decrease in temperature with the increasing distance from the zero point both in the tunnel longitudinal direction and transverse direction, while at separation distance ofL=6m, there is obvious increase in temperature at the near fire location in the transverse direction, and at other regions, the temperature is very close in both directions. The maximum temperature rise in the tunnel longitudinal direction decreases with the increasing burner separation distance. A model by considering the fire heat release rateQ̇, the effective tunnel height Hef and the burner separation distance L is proposed to express the maximum temperature rise, and results show that the model can well predict the numerical data. The findings obtained in this work could provide reference for the design of tunnel fire safety with two fire sources.

CHAOTIC BEHAVIOR OF MODIFIED STRETCH–TWIST–FOLD FLOW UNDER FRACTAL-FRACTIONAL DERIVATIVES

The application of the recently proposed integral and differential operators known as the fractal-fractional derivatives and integrals has opened doors to ongoing research in different fields of science, engineering, and technology. These operators are a convolution of the fractal derivative with the generalized Mittag-Leffler function with Delta-Dirac property, the power law, and the exponential decay law with Delta-Dirac property. In this paper, we aim to extend the work in the literature by applying these operators to a modified stretch–twist–fold (STF) flow based on the STF flow related to the motion of particles in fluids that naturally occur in the dynamo theorem. We want to capture the dynamical behavior of the modified STF flow under these operators. We will present the numerical schemes that can be used to solve these nonlinear systems of differential equations. We will also consider numerical simulations for different values of fractional order and fractal dimension.

Quantum dots as a probe of fundamental physics: deviation from exponential decay law

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.