Exponential Law Research Articles

Static bending and buckling of FG sandwich nanobeams with auxetic honeycomb core

This study is the first of its kind to apply an analytical technique to offer an accurate solution for the static buckling and static bending of functionally graded (FG) sandwich nanobeams, in which the core layer is an auxetic honeycomb. One notable aspect of this work is the use of third-order shear deformation theory for the computations. It is worth noting that the displacement field of the nanobeam is contingent upon a single parameter. This approach enables the resolution of stability and static bending issues encountered in nanobeams including auxetic honeycomb cores, while also providing a realistic depiction of the beam's mechanical behavior. The two surface layers are composed of different materials, each of which has mechanical characteristics that change in accordance with the exponential function law. The precise solution described in this work is very adaptable and may be used to investigate the mechanical behavior of beams with different boundary constraints, taking into consideration the effect of the nonlocal parameter. When the angle α of the cell varies, the honeycomb core's mechanical characteristics, such as Poisson's coefficient and elastic modulus E, vary continually. This results in static bending and buckling responses that are distinct from those of other auxetics. This study also found it intriguing that the wall angle α has a value of around 90° and that sandwich nanobeams have the highest load capacity. In addition, numerical calculations have been performed to demonstrate the influence of certain geometrical parameters, materials, and boundary constraints on the critical buckling load and maximum deflection of the nanobeam.

Sensorless HSPMSM Control of an Improved SMC and EKF Based on Immune PSO

Here, for controlling a high-speed flywheel permanent magnet synchronous motor (HSPMSM), a position sensorless control method for estimation of motor rotor position and speed is proposed to address the problems faced by mechanical position sensors of high cost, large size, and poor interference immunity. The extended Kalman filter (EKF) has difficulty obtaining the optimal covariance matrix when performing state estimation. Therefore, the particle swarm algorithm (PSO) with an immune mechanism is used to optimize the covariance matrix of the EKF. However, the EKF algorithm makes the system less robust due to its delay effect. Based on the traditional sliding mode control rate, the exponential convergence law is improved, and the continuous function sat(s) is used instead of the symbolic function sgn(s). This improves the convergence law and proves the asymptotic stability of the designed sliding mode variable structure controller based on Lyapunov’s stability theorem. Then, the novel control law is applied to the sliding mode surface (SMS). An ordinary sliding mode controller (OSMC) using a linear sliding mode controller (LSMC), a global sliding mode controller (GSMC) using a global sliding mode surface (GSMS), and an integral sliding mode controller (ISMC) using an integral sliding mode surface (ISMS) are designed for improving control. Joint simulation in MATLAB and Simulink verifies that the optimized EKF based on the immune PSO can improve precision and accuracy for controlling the electronic rotor position and speed. Comparing the new sliding mode controller with a traditional PI controller reveals that the proposed system has stronger resistance to load disturbance and better robustness.

Prediction of landslide velocity and displacement from groundwater level changes considering the shear rate-dependent friction of sliding zone soil

In reactivated slow-moving landslides, the prediction of velocity and displacement is a crucial issue for understanding landslide kinematics and realizing warning systems. A variety of data-based numerical models have been used to predict landslide displacement; however, kinematics-based models, which consider the shear behaviors of soils within the sliding zone that fundamentally control landslide movement, have been relatively limited. In the present research, the Tangjiao landslide in the Three Gorges Reservoir (TGR) in China was taken as a case study. The monitored ground displacement from March 2007 to September 2016 and deformation signs observed in the field survey show that the Tangjiao landslide experienced slow movement with the ground displacement increasing stepwise in response to seasonal rainfall and periodic fluctuation of the reservoir water level. We performed a rate-stepped continuous ring shear test on two specimens remolded from the sliding zone soil at shear rates ranging from 0.01 to 10 mm/s. The test results show that the residual strengths of both specimens show a nonmonotonic shear rate dependency, i.e., a weak negative shear rate dependency (fitted by an exponential law) followed by a significant positive dependency (fitted by a linear law). The transition from a negative shear rate dependency to a positive shear rate dependency may be attributed to the change in shear mode when the shear rate exceeds a critical value. This complex shear rate-dependent residual behavior regulates the movement of the Tangjiao landslide in the reactivated state. On this basis, a kinematics-based model for predicting landslide velocity and displacement was proposed by taking into account the shear rate-dependent friction of the sliding zone soil. This model can reproduce the velocity and displacement of the Tangjiao landslide from the change in groundwater level (i.e., stress perturbations in this paper). The results suggest that by using this model, the well-investigated material parameters can enhance the prediction reliability and accuracy of landslide behavior. Our proposed approach, with the ability to reliably predict landslide velocity and displacement, such as the Tangjiao landslide in this work, has important implications for predicting movement trends and developing early warning systems for reactivated slow-moving landslides, especially translational landslides under similar geological conditions.

Contribution of viscous shear to friction in cold rolling of low-carbon steel

This work shows that for temperatures, pressures and shear rates that are common in cold rolling of low-carbon steel, viscous shear stress significantly contributes to the total friction force. Experiments were carried out to validate the theory on lubricant film formation and elasto-hydrodynamic lubrication, both with laboratory scale tribometers and a semi-industrial pilot mill facility. These experiments showed that at high shear rates, that are common in cold rolling, the lubricant does not behave as a Newtonian fluid anymore; moreover the viscosity at high pressure cannot accurately be described by a simple exponential law. With the correct relations implemented in a rolling model, both rolling force and forward slip are predicted with good accuracy for hydrodynamically lubricated cold rolling experiments.

Turbulent flow modification in the atmospheric surface layer over a dense city

Winds in the atmospheric surface layer (ASL) over distinctive urban morphology are investigated by building-resolved large-eddy simulation (LES). The exponential law is applied to urban canopy layers (UCLs) unprecedentedly to parameterize vertical profiles of mean-wind-speed u¯z and examine the influence of morphological factors. The skewness of streamwise velocity Su is peaked at the zero-plane displacement d (drag center) where flows decelerate mostly. The dynamics and intermittency in roughness sublayers (RSLs) are further contrasted. It helps determine the critical strength of the organized structures (ejection, Q2 and sweep Q4) in their contributions to the average momentum transport (i.e., 3<u”w”> to 5<u”w”>). Two key factors of the local-scale dynamics are revealed - building heterogeneity and upstream giant wakes that could amplify turbulence kinetic energy (TKE) and energetic intermittent Q4 by different mechanisms. The former is conductive for large-eddy generation that promotes vertical fluctuating velocity w”, stimulating intermittent, energetic Q2 and Q4. The latter, whose footprints are identified by the two-point correlation of streamwise velocity Ruu with specific size and inclination, facilitates intermittent, fast streamwise fluctuating velocity u”, forming vigorous Q4. Nevertheless, excessive planar density λp (≈ 0.7) is detrimental to both transport processes. These findings contribute to the theoretical and empirical wall models of large-scale roughness that help urban planners and policymakers to improve air quality.

Hair relaxation after shaping - A kinetic approach.

Hair fibres have been shaped via either a thermal route or via a chemical route. The time-relaxation transients of the shaped hairs in air, and in water, respectively, were evaluated. The collected data were kinetically modelled in order to reveal information about the rate controlling mechanism of the recovery process. Hair fibres were thermally shaped at different temperatures between heated plates and left to relax in an environment of controlled humidity and temperature. Different hair fibres were chemically shaped and left to relax in water of different controlled temperatures. Relaxation data were used for modelling the kinetics of the recovery processes by using exponential and logarithmic kinetic laws. The fitting of the models to the two sets of data has been checked by using the residual sum of squares for matching the proper model to each set of data. The processes of shaping and recovery were assimilated with a sequence of two successive quasi-chemical reactions, occurring at the used temperatures. Based on chemical and physical assumptions, the two groups of experiments were modelled by two different laws: an exponential law, suggesting a first-order process as the rate-determining step of the relaxation of thermally shaped fibres, and a logarithmic law, suggesting a slow relaxation, based on percolation theory, for the chemically shaped fibres. This allowed use of chemical kinetics tools for calculating the values of the activation energy in each case. The evaluated values of activation energy of the relaxation processes for both thermal and chemical shaping were found to be close to each other, in spite of the different methods of shaping. The kinetic analysis suggests that despite different reaction sequences occurring during the different shaping-relaxation processes, the rate-controlling mechanism that manages the recovery process is the same in all cases; and this process is proposed to be the thiol-disulphide reformation of intra-protein bonds inside hair.

A dynamic model of the packed dehumidifier

Liquid desiccant dehumidification, a clean energy technique for creating comfortable environments has received a lot of interest. Several dynamic models have been proposed to predict the outlet air humidity ratio and temperature, however, a study on presenting variations of heat and mass transfer coefficients and thermal mass of desiccant during the dynamic dehumidification process was not encountered according to authors’ best knowledge. This gap is primarily due to the complex nature of the coupled heat and mass transfer processes, which make it challenging to capture the evolution of heat and mass transfer coefficients over time. In this study, variations of these parameters are analyzed at first. A theoretical study is conducted to show the thermal mass of the desiccant can be considered constant when changing the inlet air humidity ratio or desiccant temperature, simplifying the dynamic modeling process. While the variation of heat and mass transfer coefficients show significant impact in such conditions. Subsequently, a new method based on mass conservation is provided to determine the thermal mass of desiccant. By examining the cause-and-effect relationships between heat and mass transfer coefficients and outlet air humidity ratio, the evolution of heat and mass transfer coefficients following exponential laws is deduced by inversion. Then a dynamic model of packed dehumidifiers can be completed easily based on above derivations, and its viability is confirmed by experimental results. Compared to the existing method, the prediction accuracy can improve by 50% based on the proposed methods. This study characterizes evolution rules of heat and mass transfer coefficients over time, and with this, evolutions of outlet air parameters during the dynamic dehumidification process can be acquired conveniently based on the existing steady dehumidification model.

The use of bio-oil from biodiesel production for enhancing the bitumen healing

Road pavements are exposed to traffic and temperature effects that produce distress, mainly cracking that leads to pavement failure, after which rehabilitation actions are necessary to extend pavement life. Bio-rejuvenators have been used to recover the bitumen properties lost due to fatigue of the asphalt mixtures and ageing due to temperature variations and oxidation. Thus, this paper investigates the healing of bitumen modified with bio-oil derived from biodiesel production. One base bitumen in three different ageing stages (unaged, short and long-term ageing) was used for adding up to 3% of bio-oil to the bitumen. In addition to consistency and rheological tests to characterise the modified bitumen, fatigue resistance tests with and without rest periods were performed to assess the healing through three indexes, relating the complex shear modulus, the number of cycles to failure and the amount of damage, after a rest period. It was verified that the healing follows an exponential law with the rest period, but the number of cycles in each loading period decreases compared to the previous period. For a 15-minute rest period, the healing was limited to 26.9%, but the bio-oil contributed significantly to that restoration.

Statistical regulations of the occurrence of fires in cities during marital state

The process of the occurrence of fires in cities located near the demarcation line during martial law was studied. The subject of the study is statistical regularities that allow us to describe the process of fire occurrence in cities during martial law. Data on fires that occurred in seventeen urban settlements of Ukraine, which are in the immediate vicinity of the demarcation line for the period of 2022, were processed. Statistical hypotheses that allow describing the flow of fires that periodically occurred in cities during the studied period, as well as the time intervals between the moments of their occurrence, have been verified. It has been established that the number of fires that periodically occur on the territory of cities during martial law cannot be described by the Poisson distribution law. Instead, for 59 % of the studied cities, the hypothesis about the geometric law of distribution was confirmed. For some cities in which the number of fires was less than 50 during the period of 2022, it was not possible to obtain any results. It was established that for 35 % of the total number of analyzed cities, the statistical hypothesis about the possibility of describing the time intervals between the occurrence of fires by the exponential law of distribution was confirmed. A much worse result was obtained when testing the possibility of describing the time intervals between the occurrence of fires by other distribution laws. Therefore, if it is necessary to describe the process of the occurrence of fires in urban settlements during martial law, it is necessary to study each individual case by probabilistic laws. The research results can be used to build information systems to support decision-making by management involved in the elimination of the consequences of dangerous events and emergency situations related to fires.

Winds and eddy dynamics in the urban canopy layer over a city: A parameterization based on the mixing-layer analogy

Urban atmospheric flows are vital to the global ecology. This study characterizes urban canopy layer (UCL) dynamics and parameterizes the flows in the atmospheric surface layer (ASL) over heterogeneous urban surfaces. Large-eddy simulations (LESs) are used to transiently calculate the winds over a real, dense city. A linear function of eddy diffusivity of momentum KM is applied to the lower UCL. Analogous to its mixing-layer counterpart, the strong UCL top shear manifests an inflected mean wind speed profile which aligns well with the exponential law. The solutions to the mixing length lm and the turbulent momentum flux are analytically derived by consolidating the mixing-layer type shear and the form drag from the explicitly resolved roughness elements. The behavior of lm in the lower UCL, especially its peaked level, is captured well. Based on the balance between shear and form drag, an aerodynamic effective roof level Hae is designated where the ground effect is alleviated under shear dominance. Results reveal that a rougher urban surface generates eddies with a larger shear length scale, thus enhancing momentum transport. In-canopy turbulence mixing, which slows down wind decay, is also enhanced, resulting in stronger street-level breezes. The newly developed ASL flow model will be beneficial to urban planning by offering reliable predictions, effectuating the management of urban sustainability.

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.

An exponential-potential description for the guest–host interactions in rattler-containing cage materials

Anomalous low-energy excitations (ALEs) associated with the vibrations of atoms accommodated in a space with large freedom of motion are frequently observed in cage materials. Such ALEs have been of great interest for their important roles in large electron–phonon coupling targeting high-TC superconductivity as well as phonon–phonon scattering giving rise to low thermal conductivity to achieve high thermoelectric performance. In our previous work, we showed that van der Waals-like repulsive interactions between the atoms forming the host cage and the atoms accommodated inside the cage (rattler) play a crucial role in giving small force constants and consequently nearly dispersionless low-energy phonons. In the present work, we show that the exponential law derived from the revised Morse potential model that we used previously could provide a universal trend for the ALEs of three typical cage materials: clathrates, skutterudites, and pyrochlores. This not only confirms the effectiveness of the potential model but also provides a clear description for different types of rattler vibrational modes based on the deduced parameters from the potential model. In addition to the free space in which a rattler can move and the mass of the rattler, which we considered in our previous work, structural anisotropy, electronegativity of the component cage atoms, and the coordination number of the rattler are shown to be important factors for description of an ALE.

Hierarchical perturbation compensation system with ERL sliding mode controller in a quadrotor

This article addresses the problem of perturbation in Unmanned Air Vehicle (UAV) quadrotors. Three subsystems are designed to provide a continuous and precise estimation of perturbation and residual perturbation. The three subsystems form a Hierarchical Perturbation Compensator (HPC), which is built to compensate for system dynamics uncertainties, non-modeled dynamics, and external disturbances. The nonlinear control Exponential Reaching Law Sliding Mode (ERLSM) is utilized with the HPC. Lyapunov stability analysis proves the stability of the entire compensator-controller system. This system has the ability to decrease unknown perturbation either external or internal. It also has the ability to maintain full control of the six-degree-of-freedom quadrotor. The system performance for position, altitude, and attitude control is demonstrated by analysis, simulation, and experiments.

Parallel adaptive event-triggered asynchronous control for two-time-scale fuzzy semi-Markov jump systems under deception attacks

In this brief, the parallel adaptive event-triggered (PAET) asynchronous control issue for a category of two-time-scale fuzzy semi-Markov jump systems (TTS-FSMJSs) is investigated. To save limited network resources, a novel PAET strategy is designed to process the data from slow and fast channels of TTS-FSMJSs separately. Meanwhile, the mode-dependent exponential decay adaptive law effectively avoids Zeno behavior. In addition, in order to reduce the influence of the attack signal in the communication network, an attack strategy with norm-bounded uncertainty is constructed. Based on the proposed PAET strategy, a composite asynchronous controller with time-varying mode emission probabilities (EPs) is designed. When the singular perturbation parameter is not greater than the given upper bound, the system is stable. The sufficient conditions for the closed-loop system is exponentially stable with H∞ performance are ensured by utilizing the integral inequalities. Ultimately, the validity of the proposed approach is illustrated through the DC motor model.

Aging measurement and empirical modeling of BTI on FPGA using 16 nm FinFETs for static and dynamic stresses

This article presents an empirical modeling of BTI on 16 nm FinFET technology. This model is based on a 5000 h aging test and measurements on Zynq UltraScale+ FPGAs with nine temperature and voltage stresses and 21 different stress signals. The aging time, acceleration factor in temperature (Arrhenius law) and in voltage (exponential law) are considered in this model. The comparison between the model and the measurements of degradation under dynamic stress shows the presence of recovery. After modeling recovery we finally obtain an empirical BTI model for static and dynamic stresses.

Investigation of the time dependent gate dielectric stability in SiC MOSFETs with planar and trench gate structures

In this work, the time-dependent dielectric breakdown (TDDB) analysis is performed to understand the gate oxide reliability in SiC MOSFETs with two different structures, i.e., planar and trench gate structures. We have discovered different gate leakage current behaviors between the SiC MOSFETs with planar gate (Sample A) and trench gate (Sample B) during the forward gate bias stress. Notably, the slight increase of the gate current during the stress and the negative activation energy (Ea = −0.07 eV) observed in Sample A suggest that the hole generation caused by the impact ionization can be occurred during the forward gate TDDB tests. Furthermore, the SiC MOSFETs with trench gate structure (Sample B) exhibit the operation voltage of 55.7 V (exponential law) and 57.3 V (power law) for the 0.001 % failure of 30 years under 175 °C, indicating that SiC trench gate MOSFETs with enough thick gate dielectric (87.1 nm (bottom) and 77.9 nm (sidewall)) can have the promising forward gate TDDB stability.

Double-hierarchical fuzzy exponential convergence law fractional-order sliding mode control for PMSM drive control in EV

In the vector control of permanent magnet synchronous motor (PMSM), the speed overshoot and torque pulsation phenomena need to be solved. There are two prerequisites for the drive control of PMSM in electric vehicle (EV). The first is that the vehicle control has to be ensured as a whole. The second is, to ensure the economy of the vehicle control while ensuring the stable control of the motor. Therefore, this paper first proposes the fuzzy exponential convergence law fractional-order sliding mode control (F-CFSMC), it is constructed with the purpose of online correction of the exponential convergence law of the fractional-order sliding mode surface. It is expressing the arrival time and convergence speed of the fractional-order sliding mode surface explicitly with parameters. The stability of the F-CFSMC is proved to be derived using the Lyapunov equation. The F-CFSMC is applicable to PMSMs with different parameters. Next, the fuzzy controller that considers the battery parameter factor in EV is introduced to combine the lithium battery and PMSM to enhance energy utilization. At this point, the double-hierarchical fuzzy exponential convergence law fractional-order sliding mode control (DF-CFSMC) build is complete. Moreover, comparative simulations and experiments using the DF-CFSMC and the conventional PMSM control are conducted, and the results are performed in PMSM hierarchical. Simulations are also performed in the EV hierarchical application to show the universality, repeatability and advantages of DF-CFSMC.

Oxidation behavior of Si-C-O-(Ti) fibers from 450° to 1140°C: Comparing the kinetic of oxide scale growth to the slow crack growth

The oxidation behavior of Tyranno® Grade-S SiC-tows was investigated under ambient air in the 450–1140 °C range. Below 650 °C, a linear oxidation rate was identified for oxide scale thicknesses up to 1.2 µm, attributed to the hydroxyl (Si-OH) groups degrading the silica structure as shown by 1H and 1H–29Si CP/MAS NMR. Above this temperature, the classical parabolic oxidation rate (diffusion controlled) was identified with a dehydroxylated silica scale. These results bring new insights to interpret the slow crack growth (SCG) transition observed at 650 °C. Above 650 °C the activation energies (Ea) for oxidation and SCG are close to 50 kJ mol−1 indicating the diffusion might be the rate limiting factor; whereas for lower temperatures EaSCG < Eaoxidation as a consequence of the stress-enhanced chemical reactivity. The oxide thicknesses at failure time (predicted with power or exponential laws) were assessed and highlight some incoherencies in the lifetime projection to lower stresses.

IMPACT OF THE GLUE LAYER PROPERTIES ON THE STRESS-STRAIN STATE OF THE GLUE ANCHOR FOR THE STEEL ROD IN CONCRETE

The article deals with the distribution of stresses and displacements along a steel anchor fixed in concrete with a polymer binder - an acrylic compound. It was established that the maximum values of tangential, radial, and circular stresses, which more fully characterize the operation of the connection, change depending on the strength characteristics of the adhesive layer and its thickness according to the exponential law. The obtained results of stress at any point of the adhesive joint allow us to propose a methodology for the design of steel rods in concrete fixed with polymers. As a result of solving the problem of the stressed-strained state of the anchor connection on acrylic adhesives, equations were obtained for determining stresses and strains at any point. As a result of the analysis of the obtained dependencies, the following conclusions can be drawn. When calculating the strength of anchor joins on acrylic adhesives, it is necessary to take into account the maximum values of tangential, radial, and circular stresses. In order to calculate the strength of the join, it is necessary to know the strength limit at uniform separation of the glue from the metal surface, as well as at shear for the glue-metal contact. Tangential and normal stresses in the adhesive cylinder and at the adhesive-concrete interface decrease with an increase in the modulus of elasticity of the acrylic adhesive. But this leads to an increase in normal axial stresses in the part of the anchor embedded in concrete and radial stresses at the glue-anchor and glue-concrete contacts. The elasticity modulus of the glue layer is smaller than the elasticity modulus of concrete and metal. Therefore, the adhesive distributes the stresses that arise from the application of the pull-out force between the anchor and the concrete massif. This is explained by the fact that the pull-out stresses from the anchor are completely transferred to the adhesive layer and then to the concrete. The main vector of tangential stresses does not depend on the ratios of the elasticity modulus of the materials which form the anchor join. The thickness of the adhesive layer has a slight effect on the stress in the glue-anchor contact, but significantly on the stress in the glue-concrete contact.

Free vibration response of rotating pretwisted porous exponential and sigmoid functionally graded conical shells in thermal environment

A finite element method is used to analyze the free vibration of rotating functionally graded (FG) porous conical shell in thermal environment. Exponential and sigmoid laws are used for grading the FG conical shell in the presence of even and uneven porosity distributions. The one-dimensional Fourier heat conduction equation is used to calculate the nonlinear temperature distribution across the thickness of the shell. The parametric studies reveal that the porosity volume fraction has a significant impact on natural frequency. Centrifugal stiffening, which manifests as a geometrical stiffness matrix, causes rotational speed to enhance the natural frequency of the FG shell.