Logarithmic Rate Research Articles

Inactivation effect and kinetic analysis of multi-band ultraviolet LED combined with Ag/N modified magnetic TiO2 on microorganisms in ballast water

The invasion of harmful aquatic organisms from ship ballast water is a serious threat to the marine ecosystem. However, the existing treatment technology has the defects of high energy consumption, secondary pollution and easy revival of organisms, etc. How to inactivate the microorganisms in ballast water efficiently is always a difficult challenge. In this study, the inactivation of Karenia mikimotoi and Escherichia coli under UVA/UVCLED photocatalytic system (UVA/UVCLED + Ag/N-Fe3O4-SiO2-TiO2) was investigated using Ag-modified and N-modified magnetic TiO2 nanomaterials. The results showed that the ability of 1.5 % Ag with 3 % N dual-modified TiO2 to enhance the system's biologically logarithmic inactivation rate was 4–5 times higher than that of conventional unmodified TiO2. The Ag/N-modified magnetic TiO2 had the best photocatalytic activity at a dosage of 500 mg/L. After 6 cycles of use, the inactivation efficiency in combination with UVA/UVCLED only decreased by 8.76 % compared with the initial use, and the recycling rate was still up to 95.75 %. Meanwhile, the scanning electron microscope showed that the photocatalyst itself only had some minor changes after 6 cycles, which confirmed the fact that the photocatalytic removal rate (higher than 91.24 %) could still be maintained at a high level. The UVA/UVCLED photocatalytic system significantly inhibited the scavenging ability of superoxide dismutase (SOD) on reactive oxygen species (ROS), enhanced the toxic effect of ROS on cells, and ultimately accelerated the process of apoptosis and inhibited biological resurrection. In addition, this study verified the inactivation kinetics of the target microorganisms using Chick-Watson, Hom and Biphasic models, and found that all individuals in the same population differed in their tolerance to UV radiation, and some of them absorbed more than a threshold dose of UV radiation before showing inactivation responses. The Biphasic model (R2: 0.99571–0.99926) can better simulate the nonlinear changes exhibited during the inactivation process and is more applicable to the actual disinfection situation of UVA/UVCLED photocatalytic systems. The UVA/UVCLED + Ag/N-Fe3O4-SiO2-TiO2 photocatalytic technology developed in this study, as a novel oxidation process, reduces energy consumption while effectively inhibiting the reanimation of organisms, and exhibits a strong potential for application in the fields of restoring the environment of water bodies and blocking the spread of pathogens.

Research on the Dynamic Characteristics of Cantilever Rotor System With ISFD

Aiming at the common vibration problem of the cantilever rotor system and the nonlinear problem of traditional squeeze film damper (SFD), an integral squeeze film damper (ISFD) for the cantilever rotor system was proposed based on the traditional SFD. In order to investigate the effect of the ISFD on the dynamic characteristics of the cantilever rotor system, the vibration reduction experiment of the rotor system was carried out. The mechanical model and finite element model of the cantilever rotor system were established. The first‐order critical speed, strain energy, stability, and steady‐state response of the cantilever rotor system were numerically analyzed. Experimental research on the vibration reduction of the cantilever rotor system by the ISFD under different unbalance conditions and different rotational speed conditions was carried out on the test rig of the cantilever rotor system. The results showed that the ISFD has remarkable performance, which can reduce the bending deformation and strain energy of the rotating shaft, increase the logarithmic decay rate, and improve the overall stability of the system. Under various working conditions, the ISFD can effectively suppress the unbalanced vibration of the rotor and the shaft center displacement of the rotor, and the amplitude of the rotor system at the working frequency (1X) is greatly reduced.

Thermally activated intermittent flow in amorphous solids.

Using mean field theory and a mesoscale elastoplastic model, we analyze the steady state shear rheology of thermally activated amorphous solids. At sufficiently high temperature and driving rates, flow is continuous and described by well-established rheological flow laws such as Herschel-Bulkley and logarithmic rate dependence. However, we find that these flow laws change in the regime of intermittent flow, where collective events no longer overlap and serrated flow becomes pronounced. In this regime, we identify a thermal activation stress scale, xa(T,), that wholly captures the effect of driving rate  and temperature T on average flow stress, stress drop (avalanche) size and correlation lengths. Different rheological regimes are summarized in a dynamic phase diagram for the amorphous yielding transition. Theoretical predictions call for a need to re-examine the rheology of very slowly sheared amorphous matter much below the glass transition.

High-Temperature Oxidation and Microstructural Changes of Al0.75CoCrFeNi High-Entropy Alloy at 900 and 1100 °C

The development of high-entropy alloys (HEAs) for high-temperature applications has been driven by the limitation of nickel-based superalloys in achieving optimal efficiency at higher temperatures for higher efficiency in power generation engines. The alloys must have high oxidation resistance and microstructural stability at high temperatures. Relatively equimolar multi elements involved in HEAs produce microstructure containing a single solid solution or multiphase that improves the mechanical properties and oxidation resistance resulting from sluggish diffusion and core effects. In this study, the oxidation behavior and microstructural changes of Al0.75CoCrFeNi HEA at 900, 1000, and 1100 °C in air atmosphere were investigated. Based on the XRD and SEM-EDS analysis, the mechanism of oxide scale formation and microstructural changes of the substrate are proposed. The results show that the oxidation behavior of the alloy follows a logarithmic rate law. Different oxide compounds of CoO, NiO, Cr2O3, and CrO3, θ-Al2O3, α-Al2O3, and Ni(Cr,Al)2O4 with semicontinuous oxides of Al2O3 with Cr2O3 subscale and an oxide mixture consisting of spinel of Ni(Cr,Al)2O4 and Co(Cr,Al)2O4 were found. During oxidation, Widmanstätten of FCC-A1 and BCC-B2/A2 phases in the substrate have changed. Spheroidization of B2 and a reduction in volume fraction decrease the hardness of the substrates.

Exploring mechanical properties and failure mechanisms of aramid and PBO crystals through molecular dynamics simulations

Molecular dynamics simulations were used to analyze the mechanical properties and failure processes of poly(p-phenylene-terephthalamide) (PPTA), poly(p-phenylene-benzimidazole-terephthalamide) (PBIA), PBIA–PPTA (formed by 1:1 copolymerization of PPTA and PBIA), and poly(p-phenylene-benzobisoxazole) (PBO) crystals at different strain rates and temperatures. The failure stress and strain were found to be linear with the temperature and logarithmic strain rate. Moreover, based on the kinetic theory of fracture and the comprehensive simulation results, we formulated a model that describes the failure stress of the aforementioned crystals under varying strain rates and temperatures. Through the analysis of the failure process, we found that in PPTA, PBIA, and PBIA–PPTA crystals, the bond failure probability is correlated with the strain rate and temperature. The examination of bond lengths and angles unveiled that bonds with larger initial aligning angles are more susceptible to failure during the strain process. Intriguingly, the stretching process induced a conformational change in the PBO molecular chain, leading to a deviation from the linear relation in its stress–strain curve.

Application of Synthetic Taxonomic Measures to Assess the Investment Attractiveness of the Selected Companies in the Construction Materials Industry Listed on the Warsaw Stock Exchange

The study used the synthetic taxonomic measure TMAI and BZW to determine whether the fundamental strength of 17 companies from the construction material industry listed on the Warsaw Stock Exchange affects their investment performance. Companies whose operations are conducted mainly in Poland and whose profit and loss account is prepared in the calculation system were selected for the study. It was checked how the use of different methods of aggregation of the same diagnostic variables (with and without a pattern) affects the classification results. Investment efficiency was measured with the annual, logarithmic rate of return and the created rankings of companies for the years 2016-2021 were compared with it.

Forecasting stock index return and volatility based on GAVMD- Carbon-BiLSTM: How important is carbon emission trading?

This paper proposes a new forecast method of stock price return and volatility by GAVMD-Carbon-BiLSTM. First, based on the data from eight carbon markets in China, the logarithmic rate of return of carbon emission rights price is constructed. Second, the TVP-VAR model is used to investigate the impact effect of carbon emission rights trading, stock price return, and volatility. It is used as a predictor of return and volatility rationality. Third, the genetic algorithm is used to optimize the parameters of the variational mode decomposition. Fourth, the return and volatility of stock price are decomposed into multiple intrinsic modes, effectively reducing the data’s complexity. Finally, GAVMD is combined with BiLSTM, and the logarithmic return of carbon emission trading price is used as input to predict the stock price return and volatility. The results show that carbon emissions trading impacts the rate of return and volatility at different lead times and time points. Therefore, using it to predict stock price return and volatility can improve prediction accuracy. At the same time, combining GAVMD with BiLSTM, the prediction performance of carbon emission trading price logarithmic return rate as input is much better than other machine learning models.

The asymptotic behavior of solutions for stochastic evolution equations with pantograph delay

The polynomial stability problem of stochastic delay differential equations has been studied in recent years. In contrast, there are relatively few works on stochastic partial differential equations with pantograph delay. The present paper is devoted to investigating large-time asymptotic properties of solutions for stochastic pantograph delay evolution equations with nonlinear multiplicative noise. We first show that the mild solutions of stochastic pantograph delay evolution equations with nonlinear multiplicative noise tend to zero with general decay rate (including both polynomial and logarithmic rates) in the [Formula: see text]th moment and almost sure senses. The analysis is based on the Banach fixed point theorem and various estimates involving the gamma function. Moreover, by using a generalized version of the factorization formula and exploiting an approximation technique and a convergence analysis, we construct the nontrivial equilibrium solution, defined for [Formula: see text], for stochastic pantograph delay evolution equations with nonlinear multiplicative noise. In particular, the uniqueness, Hölder regularity in time and general stability, in the [Formula: see text]th moment and almost sure senses, of the nontrivial equilibrium solution are established.

Hydrogen addition effect on cellularization and intrinsic instability of ethyl acetate spherical expanding flame

The cellularization and intrinsic instability of ethyl acetate (EA) spherical expanding flame with different proportions of hydrogen (4%, 8%, 12%) were studied through experiments and theoretical analysis. The high-speed schlieren imaging technique combined with the image processing method was used in the constant volume combustion chamber to quantify the development of flame surface cracks and saturation time, crack length, number of cellular units, and average cellular area. The results show that the evolution of flame cracks can be mainly classified into two periods. In the first period, several initial cracks are generated on the flame surface. In the second period, cracks rapidly expand while forming a large number of small cellular units, and the surface areas also increase rapidly. The increase in the proportion of hydrogen led to an increase in minor cellular cracks and a more moderate structural evolution of flame cells during the second period. Afterwards, the involved thermodynamic parameters, including the thermal expansion ratio, flame thickness, effective Lewis number, critical Peclet number, and perturbation logarithmic growth rate of unstable flames, were quantitatively analyzed. The results show that an increase in initial pressure significantly reduces the flame thickness, leading to more unstable flame. In contrast, the proportion of hydrogen has less impact on the involved thermodynamic parameters, while the equivalence ratio is the primary factor influencing instability parameters. Additionally, the study examined the flame's self-acceleration characteristics and found that increasing the proportion of hydrogen reduces the tendency for ethyl acetate self-acceleration.

Hydrometallurgical recycling of lithium-titanate anode batteries: Leaching kinetics and mechanisms, and life cycle impact assessment

Since the inception of Li-ion batteries, the chemistry of cathode and anode materials has changed time-to-time. In recent times, the lithium-titanate (LTO) anode material has gained attention due to a higher surface area (100 m2/g) than the usual graphite-made anode (3 m2/g). The development of a new recycling strategy, in particular, to deal with spent LTO batteries, is therefore urgently needed as plenty of batteries deployed in electric vehicles are near to completing their lifespan. Herein, we demonstrate the recycling of spent LTO batteries by optimizing the parametric influence of H2SO4 concentration, H2O2 dosage, agitation speed, temperature, and time for lithium and titanium leaching from the anode material. About 92% titanium and 98% lithium were efficiently leached from the anode powder using a 3.5 mol/L H2SO4 solution with 25 vol% H2O2 at a pulp density of 5 wt./vol.%, temperature 120 °C, and time 120 min. The leaching examined in the temperature range between 60 °C and 120 °C with respect to time showed the best fits to the kinetic model governed by the logarithmic rate law. The apparent activation energies of titanium (78.9 kJ/mole) and lithium (11.3 kJ/mole) indicated two different mechanisms governed by chemically controlled and diffusion-controlled reactions, respectively. It indicated that both metals’ leaching proceeded through lixiviant diffusion on the LTO surface, which was corroborated by the instrumental analyses of the untreated LTO sample and the leached residues. A life-cycle assessment suggests the need for discharge acid for recycling within the system due to a terrestrial ecotoxicity of 97.09 kg DCB-eq; however, the ionizing radiation and eutrophication potential are found to be negligible.

Use of Logarithmic Rates in Multi-Armed Bandit-Based Transmission Rate Control Embracing Frame Aggregations in Wireless Networks

Herein, we propose the use of the logarithmic values of data transmission rates for multi-armed bandit (MAB) algorithms that adjust the modulation and coding scheme (MCS) levels of data packets in carrier-sensing multiple access/collision avoidance (CSMA/CA) wireless networks. We argue that the utilities of the data transmission rates of the MCS levels may not be proportional to their nominal values and suggest using their logarithmic values instead of directly using their data transmission rates when MAB algorithms compute the expected throughputs of the MCS levels. To demonstrate the effectiveness of the proposal, we introduce two MAB algorithms that adopt the logarithmic rates of the transmission rates. The proposed MAB algorithms also support frame aggregations available in wireless network standards that aim for a high throughput. In addition, the proposed MAB algorithms use a sliding window over time to adapt to rapidly changing wireless channel environments. To evaluate the performance of the proposed MAB algorithms, we used the event-driven network simulator, ns-3. We evaluated their performance using various scenarios of stationary and non-stationary wireless network environments including multiple spatial streams and frame aggregations. The experiment results show that the proposed MAB algorithms outperform the MAB algorithms that do not adopt the logarithmic transmission rates in both the stationary and non-stationary scenarios.

Approximation of smooth functionals using deep ReLU networks

In recent years, deep neural networks have been employed to approximate nonlinear continuous functionals F defined on Lp([−1,1]s) for 1≤p≤∞. However, the existing theoretical analysis in the literature either is unsatisfactory due to the poor approximation results, or does not apply to the rectified linear unit (ReLU) activation function. This paper aims to investigate the approximation power of functional deep ReLU networks in two settings: F is continuous with restrictions on the modulus of continuity, and F has higher order Fréchet derivatives. A novel functional network structure is proposed to extract features of higher order smoothness harbored by the target functional F. Quantitative rates of approximation in terms of the depth, width and total number of weights of neural networks are derived for both settings. We give logarithmic rates when measuring the approximation error on the unit ball of a Hölder space. In addition, we establish nearly polynomial rates (i.e., rates of the form exp−a(logM)b with a>0,0<b<1) when measuring the approximation error on a space of analytic functions.

Development and Verification of Wireless Vibration Sensors

Structural vibration testing is an effective guarantee for the Structural Health Monitoring (SHM) of large-scale civil engineering. Traditional vibration testing has drawbacks such as difficulties in wiring and picking up low-frequency signals, low communication speed, and susceptibility to testing site conditions. In order to improve the universality of wireless vibration sensors, this article develops a wireless vibration sensor, introduces the module composition and basic principles of the sensor, and conducts standard vibration table performance comparison tests between wired acceleration sensors and wireless vibration sensors, verifying the accuracy of wireless vibration sensors. In order to further explore the feasibility of wireless vibration sensor applications, the wired acceleration sensor and wireless vibration sensor were used to analyze the structural dynamic characteristics of the four-layer steel frame structure model in the laboratory, and the comparison was made based on ABAQUS finite element simulation. Finally, the field vibration test was carried out outdoors. The results show that the natural frequency identification results of the wireless vibration sensor and the wired acceleration sensor for the four-story steel frame structure through fast Fourier transform, short-time Fourier transform, and wavelet transform are basically the same, the half-power bandwidth method and logarithmic decrement rate method are used to identify the damping, and wavelet transform is used to identify the vibration mode with minimal error and high accuracy. It shows that the wireless vibration sensor is feasible in practical engineering, has stable and reliable transmission capacity, and can provide certain reference values for earthquake monitoring, building Structural Health Monitoring, etc.

A new constitutive model and hot processing map of 5A06 aluminum alloy based on high-temperature rheological behavior and higher-order gradients

To develop a high-precision constitutive model and hot processing map for 5A06 aluminum alloy, the hot deformation behavior of the alloy was investigated through isothermal compression experiments and microstructure analysis experiments, which were conducted at temperatures ranging from 573 K to 773 K and at strain rates ranging from 0.01 to 10 s−1. Firstly, a new constitutive model, which is based on the partial derivatives of the experimental flow data and does not significantly increase the material parameters, was proposed. Secondly, a comparison and analysis of the predictive accuracies of both the new model and the classic model were conducted. Finally, the new constitutive model was used to construct the hot processing maps of the 5A06 aluminum alloy, and the optimal hot processing parameters were validated through metallographic experiments. The results show that a high-precision constitutive model can be constructed with a small number of material parameters by considering the second-order approximation between logarithmic stress and temperature, as well as the third-order approximation between logarithmic stress and logarithmic strain rate. The mean square errors of the new model were significantly lower than those of the Arrhenius model and Hense-Spittle model for all strain rates and temperatures. There were significant differences in the prediction accuracy of the AH and HS models at different temperatures and strain rates, indicating their accuracy was dependent on temperature and strain rate. The coefficients of the new model were significantly higher than those of the AH and HS models. Moreover, the proximity of predicted values to experimental values was ranked in descending order as follows: new model, AH model, and HS model. The energy dissipation rate is relatively high when the strain rate is lower than 10 s-1 and the temperature is higher than 623 K. The instability factor is larger than zero for all conditions except when the strain rate is equal to 10 s−1. The optimal hot working temperature range for 5A06 aluminum alloy is 623–700 K, and the strain rate should be in the range of 0.01 s−1 to 1 s−1. The microstructure analysis matches the predicted results from hot processing maps, which can guide the hot working process of 5A06 aluminum alloy.

Evaluation of biogas production rate and leachate treatment in Landfill through a water-energy nexus framework for integrated waste management

The aim of this study was to investigate the simultaneous biogas generation and leachate treatment using municipal waste and its polluted leachate at Mashhad landfill in northeast Iran. The research focused on examining the kinetic model of CH4, CO2, CO, H2S and O2 production with and without leachate recirculation (LR) through control/test wells. The findings from both wells showed an increase in logarithmic CH4 production rate, with the coefficient related to the rate of increase in methane concentration ranging from 0/52-0/64 in the control well and 0/47-0/55 in the test well, respectively. Under LR conditions, it was observed that the CH4 production rate was slower, taking an average of 120 minutes to reach 50% concentration, compared to just 15 minutes without LR. Using first-order equations, the CH4 production coefficients were measured to be 2/17 h−1 and 0/9 h−1 for the control and test wells, respectively. The analysis of recirculated leachate revealed a significant decrease (∼30%) in the total volume of leachate with 72% COD removal, which could help manage overloaded leachate problems in the landfill. The COD removal coefficient was found to be 0/036 day−1 in the control well, whereas the test well with leachate recirculation showed a more rapid decrease from 50 g.l−1 to about 14 g.l−1 with a removal coefficient of 0/012 day−1, three times higher than the control well. Additionally, nitrogen content analysis indicated that although the amount of ammonia content increased with LR, the increase was relatively low in comparison to conditions without LR, equivalent to 1394 ppm and 1000 ppm in control and test wells, respectively. This study aligns with the water-energy-nexus concept by offering a sustainable solution for waste management and energy generation, while also addressing water management challenges associated with landfill operations.

The Impact of Psychological Factors on the Asymmetry of Stock Market Volatility in China—An Empirical Study Based on EGARCH Model

The asymmetry of stock market volatility has existed for a long time. Most of the early scholars’ research on this phenomenon is based on the assumption of efficient market. In recent years, with the development and deepening of behavioral finance theory, psychological factors have been added to the research process as an important variable to better explain the asymmetry of stock market volatility. Therefore, on the basis of this analysis, this paper uses the basic theories of overconfidence, disposal effect, herding effect and framing effect of behavioral finance to analyze the impact of different psychological conditions on stock market volatility. This paper collects all the closing price data of the Shanghai and Shenzhen 300 index, and processes the logarithmic rate of return, then introduces the proxy variable turnover rate of psychological factors into the mean equation of EGARCH model, establishes a modified EGARCH model, and obtains the empirical results that psychological factors do have an impact on the asymmetry of volatility in China’s stock market. It is concluded that: first, there is asymmetry of volatility in China’s stock market, Investors will respond significantly more to bad news than to good news. Second, when investors are hit by bad news, their expectations for the future become worse, which will increase the turnover rate and finally obtain a lower yield; When investors are hit by good news, their expectations for the future become better, which will reduce the turnover rate and finally obtain a higher yield. Finally, according to these two conclusions, positive and feasible suggestions are given.

Women Will Drive the Demand for EVs in the Middle East over the Next 10 Years—Lessons from Today’s Kuwait and 1960s USA

The Middle East, Gulf Cooperation Council Countries (GCC), and Kuwait, in particular, are currently experiencing a similar transition as the USA in the 1970s regarding the empowerment and independence of women, fueled by a declining birth rate from four per women to less than two. In addition, the percentage of women with university degrees has been increasing at a logarithmic rate every decade since the 1960s in the USA and since 1990 in Kuwait, resulting in women comprising well over half of all university graduates. This has led to women obtaining better jobs and enjoying greater independence to make their own decisions. In the 1960s, Toyota and other Japanese car manufactures used this phenomenon to penetrate the US market, with significant success. Their selling points were lower maintenance requirements, higher reliability, safety, better environment friendliness and slicker interior designs, the last being especially adapted to women’s tastes. We believe that Chinese and Korean electric vehicle (EV) manufacturers will employ the same playbook with similar success, as the Middle East accelerates its readiness for the EV mainstream market. In this study, this prediction was supported by a quantitative questionnaire of 234 educated female Kuwaiti drivers from the ages of 18 to 40 in Kuwait regarding their preferences regarding EVs. The findings indicate that potential female buyers favor EVs for their environmental benefits, regardless of their demographics. Moreover, potential female consumers are highly willing to purchase EVs in the future under three conditions: infrastructure availability, environmental development, and affordability. We believe that this group, in particular, will present the greatest opportunity to EV manufacturers over the next 10 years.

A New, Precise Constitutive Model and Thermal Processing Map Based on the Hot Deformation Behavior of 2219 Aluminum Alloy

To study the hot deformation behavior of and obtain the optimal hot processing parameters for 2219 aluminum alloy, a new, precise constitutive model based on the partial derivative of flow data was constructed and hot processing maps were constructed based on the new model. First, isothermal compression experiments were conducted at strain rates of 0.01–10 s−1 and temperatures of 573–773 K, and the high-order differences of the logarithmic stress with respect to the temperature and logarithmic strain rate were calculated. Second, a new, precise constitutive model based on the high-order differences was constructed, and the predictive accuracies of the new model and the Arrhenius model were compared. Finally, the hot processing maps of 2219 aluminum alloy were constructed using the new model, and its optimal hot processing parameters were validated with metallographic experiments. The results showed that a first-order approximation between logarithmic stress and temperature and a third-order approximation between logarithmic stress and the logarithmic strain rate need to be considered to construct a high-precision constitutive model without significantly increasing material parameters. The new model exhibited a significantly higher prediction accuracy than the Arrhenius model at a high strain rate and low temperature levels. With an increase in temperature, the energy dissipation increased at a constant strain rate, and with an increase in the strain rate, the energy dissipation first increased and then decreased at constant temperature. The best region for hot processing was located in the temperature range of 673–773 K and the strain rate range of 0.1–1 s−1. The results of microstructure analysis were in good agreement with the prediction results of hot processing maps. Hot processing maps can be used to guide the hot working process formulation of 2219 aluminum alloy.

Energy dissipation and notch sensitivity of mild steel at different strain rates and temperatures

Understanding of energy dissipation process of the selected material for a crashworthy structure is essential for its safety and reliability. Critical stress analysis for notched components of the structure is important to determine stress concentration factor. Commonly used mild steels are the primary choice of design engineers as the structural materials due to their good combination of mechanical properties, low cost and availability. Therefore, this paper presents the study of the flow behaviour of a mild steel with its energy dissipation capacity and notch sensitivity at strain rates 0.0001–0.1 s−1 and temperatures 25–500 °C under tensile, compressive and flexural loads. Several tests are conducted on electromechanical universal testing machine (Zwick/Roell, 250 kN) with the suitable fixtures. High temperature (300–500 °C; heating rate 8 °C/min, soaking time 15 min) deformation behaviour is studied and, the phenomenon of “blue brittle” is observed. Heat treatment (400–700 °C) effects on the steel behaviour are considered for heating rate 12 °C/min and soaking/holding time 1–3 h. Fractography analysis is done to know the nature of fracture surfaces. Influence of different notch profiles (C, U and V) on tensile behaviour of the steel is observed and, notch sensitivity ratio (NSR) is determined for their varying dimensions. It is found that the energy dissipation increases with increasing radius/angle in notched (C, U and V) specimens of the steel. Steel properties are found dependent on specimen geometry. Flexural/three-point bending behaviour (0.0001–0.01 s−1) is studied for 120–160 mm span lengths. Linear relationships of yield strength, ultimate strength and toughness/energy dissipation of the steel with logarithmic strain rate are presented. Finally, the Cowper-Symonds and Johnson-Cook material models are calibrated at different loading conditions.

The dynamical behavior of a class of stochastic vegetation models

We investigate the influence of random fluctuations in environmental parameters (e.g. rainfall and grazing rate) on the dynamical behavior of a class of ecological models for vegetation biomass in semi-arid regions. Firstly, we show the global existence and uniqueness of positive solutions for the number of vegetation biomass B(t). Then some sufficient conditions are presented for extinction and persistence of B(t) by using the stochastic linearization technique, the Hurwitz criterion and the Lyapunov function method. In particular, a threshold value R0s for the stochastic vegetation model is established in order to illustrate extinction and persistence of B(t). We also find that R0s=1 can be a warning signal for the emergence of desertification. In the case of R0s>1, we show that the stochastic vegetation system has a unique stationary distribution. Finally, we present conditions for persistence of B(t), and prove the pth moment stability and almost sure stability of the null solution in a general decay rate sense (including the exponential, polynomial and logarithmic rates) where the parameters in the stochastic vegetation system can also be dependent on time. These results are illustrated by numerical simulations.