Short Time Delay Research Articles

Numerical Studies of Coal Devolatilization Characteristics with Gas Temperature Fluctuation

In the present work, coal devolatilization characteristics in a hot gaseous environment with gas temperature fluctuation are investigated numerically with the chemical percolation devolatilization (CPD) model and the two-step (TS) model in a zero-dimensional configuration. The numerical results are first validated against the experimental data, showing that the CPD model can reproduce the coal devolatilization process well. The effects of mean gas temperature, gas temperature fluctuation amplitude, and coal particle size on coal devolatilization are then explored. The particle temperature is found to fluctuate with the gas temperature fluctuation at the same frequency. However, the particle temperature shows a delay in responding to the gas temperature fluctuation, with smaller particles having a shorter delay time. It is also found that the gas temperature fluctuation facilitates coal devolatilization. In particular, higher mean gas temperature and fluctuation amplitude values reduce the start time of th...

A Mathematical Model for Processes in Coal–Water Slurries Containing Petrochemicals under Heating

One of the promising directions for improving the environmental, technical, and economic efficiency of coal-fired thermal power plants is the use of the multicomponent fuels based on coal and combustible liquids. Such fuels, as a rule, are called coal–water slurries containing petrochemicals (CWSPs). The typical wastes of coal enrichment, low-grade coals, oil production, and oil refining wastes as well as used flammable liquids, for example oils, can be included in the fuel composition. To date, mathematical models have not been developed for predicting the effective conditions for the ignition of promising CWSPs at minimum ambient temperatures and with short ignition delay times. This problem was solved in the present work. On the basis of the experimental results, three modes of physical and chemical transformations were established when heating single particles of the composite fuel. The first one is the intensive thermal decomposition of the coal component after evaporation of the liquid components of...

Crustal seismic anisotropy and compressive stress in the eastern margin of the Tibetan Plateau and the influence of the <italic>M</italic><sub>S</sub>8.0 Wenchuan earthquake

Spatial distribution and temporal changes of seismic anisotropy in the upper crust are revealed in the eastern margin of the Tibetan Plateau, including the Longmenshan fault zone, where the M S8.0 Wenchuan earthquake occurred on May 12, 2008, by analyzing seismic data recorded by long-running seismic stations in national permanent and regional portable seismic networks, with a recording period of up to 18 years. The resulting shear-wave splitting parameters, including the fast shear-wave polarization orientation (i.e., fast orientation) and the slow shear-wave time delay (i.e., time delay, also named splitting time) are measured to characterize the spatial distribution of crustal anisotropy and its variation before and after the Wenchuan earthquake in different subzones. The splitting parameters are influenced by both the stress field and fault structure, and consequently, some subzones show two predominant fast orientations. In addition, relative to the interior of tectonic blocks, more complicated polarization characteristics are observed along the margins of the subzones and in the vicinity of the faults. Changes in both the fast orientation and the splitting time in some subzones or at some stations are observed before and after the Wenchuan earthquake. Stations demonstrating such changes are either located near the epicenter, or are adjacent to faults or tectonic boundaries. The results suggest that relative to the surrounding area, the Longmenshan fault zone shows a greater reduction in the observed time delay after the earthquake. The reduction in time delay is the greatest in the northern section of the fault zone and reduces toward the south, and the smallest reduction is found in the southern end of the Longmenshan fault where the Xianshuihe and Anninghe faults join, reflecting lateral variations in crustal stress and physical properties. The splitting parameters are used to infer the distribution of the principal compressive stress in the Longmenshan fault zone and surrounding areas. Changes of the splitting parameters after the M S7.0 Lushan earthquake are also analyzed in this study. This study suggests two important phenomena. (1) The time delays before a large earthquake can be statistically larger than those after the earthquake, indicating a decrease in stress after the earthquake or an increase prior to the earthquake. (2) After a large earthquake, the splitting parameters show different patterns in different subzones, and changes of time delays along the seismogenic fault are more significant than the other areas. Shorter time delays indicate lower stress levels. Because the splitting parameters are sensitive to stress change, the latter can be monitored by the characteristics of seismic shear-wave splitting, a technique that can be further applied to the research on earthquake stress-forecasting. Note, different tectonic position is differently response to the stress change.

Ignition and combustion of a single aluminum particle in hot gas flow

For simulating the aggregated aluminum bulks on the burning surface of solid propellants, large aluminum particles (40–160 µm) are used in this work. The isolated aluminum particles are ignited in hot oxidizing gas. Based on the bright-spot diameter profiles and the known respective reaction mechanisms, the total ignition and combustion process of aluminum particle can be divided into three stages, namely, pre-heating, ignition and combustion. The initial and bright-spot diameters of the aluminum particle are measured directly from the images by using the in-house automated data processing routines. Ignition delay time, ti, and combustion time, tc, are also obtained by post-processing the sequential images and can be associated with the particle diameters, D, in the form of ti = aD + b and tc = αD, respectively. The changing trends of ignition delay time and combustion time with the effective oxidizer mole fraction in the range of 22.8%–49.1% are distinctly different. The oxidizing environments with a high effective oxidizer mole fraction can result in short combustion time but long ignition delay time. For small particles (40–110 µm), the environmental effective oxidizer mole fraction exerts a limited effect on the sum of ignition delay time and combustion time, which indicates total time. By considering the effects of particle sizes and effective oxidizer mole fractions of environments, the percentages of ignition delay time in the total time are analyzed. These results suggest that with the goal of decreasing the total time, suitable methods can be employed for different conditions. Furthermore, we observe and discuss the phenomenon of aluminum particle microexplosion in an environment with high effective oxidizer mole fraction, which decreases particle combustion time by a large margin.

Rational Design and Facile Synthesis of Boranophosphate Ionic Liquids as Hypergolic Rocket Fuels.

The design and synthesis of new hypergolic ionic liquids (HILs) as replacements for toxic hydrazine derivatives have been the focus of current academic research in the field of liquid bipropellant fuels. In most cases, however, the requirements of excellent ignition performances, good hydrolytic stabilities, and low synthetic costs are often contradictory, which makes the development of high-performance HILs an enormous challenge. Here, we show how a fuel-rich boranophosphate ion was rationally designed and used to synthesize a series of high-performance HILs with excellent comprehensive properties. In the design strategy, we introduced the {BH3 } moiety into the boranophosphate ion for improving the self-ignition property, whereas the complexation of boron and phosphite was used to improve the hydrolytic activity of the borohydride species. As a result, these boranophosphate HILs exhibited wide liquid operating ranges (>220 °C), high densities (1.00-1.10 g cm-3 ), good hydrolytic stabilities, and short ignition delay times (2.3-9.7 milliseconds) with white fuming nitric acid (WFNA) as the oxidizer. More importantly, these boranophosphate HILs could be readily prepared in high yields from commercial phosphite esters, avoiding complex and time-consuming synthetic routes. This work offers an effective strategy of designing boranophosphate HILs towards safer and greener hypergolic fuels for liquid bipropellant applications.

Selectivity of Electronic Coherence and Attosecond Ionization Delays in Strong-Field Double Ionization.

Experiments are presented on real-time probing of coherent electron dynamics in xenon initiated by strong-field double ionization. Attosecond transient absorption measurements allow for characterization of electronic coherences as well as relative ionization timings in multiple electronic states of Xe^{+} and Xe^{2+}. A high degree of coherence g=0.4 is observed between ^{3}P_{2}^{0}-^{3}P_{0}^{0} of Xe^{2+}, whereas for other possible pairs of states the coherences are below the detection limits of the experiments. A comparison of the experimental results with numerical simulations based on an uncorrelated electron-emission model shows that the coherences produced by strong-field double ionization are more selective than predicted. Surprisingly short ionization time delays, 0.85fs, 0.64fs, and 0.75fs relative to Xe^{+} formation, are also measured for the ^{3}P_{2}, ^{3}P_{0}, and ^{3}P_{1} states of Xe^{2+}, respectively. Both the unpredicted selectivity in the formation of coherence and the subfemtosecond time delays of specific states provide new insight into correlated electron dynamics in strong-field double ionization.

Coherence resonance in an autaptic Hodgkin–Huxley neuron with time delay

Autapses, synapses between a neuron and itself, are believed to serve as a regulator of information processing in the nervous system. Noise, as random or unpredictable fluctuations, affects nearly all aspects of nervous function. In this work, we studied the regulatory ability of an autapse on firing behaviors of a Hodgkin–Huxley neuron in response to synaptic-like signals in the presence of noise. For weak subthreshold synaptic input, the autaptic neuron produced the similar firing behavior governed by the noise in case of either determinate or random synaptic input. The critical noise intensity necessary to trigger the spike train slightly was decreased with determinate low-frequency input. Under a strong suprathreshold synaptic current, noise-induced frequency resonance and precise responses mostly occured with a high-frequency determinate input. With a random strong synaptic input, an increase in the autaptic delay led to a resonance-like response, but had no observable effects in cases with a short delay time under a low-frequency input.

A combined monitoring scheme with fuzzy logic filter for plant-wide Tennessee Eastman Process fault detection

Principal Component Analysis (PCA) is the most common Multivariate Statistical Process Control (MSPC) method that is widely used for Fault Detection and Diagnosis (FDD). Since early abnormality detection with high accuracy is required for safe and reliable process operation, False Alarms Rate (FAR), Missed Detection Rate (MDR) and the detection time delay are the major factors that must be taken into consideration when developing any process monitoring scheme. Unfortunately, the PCA performance, with fixed limits, is weak in terms of the stated factors. In contrast, conventional Moving Window PCA (MWPCA) is an adaptive technique which updates both the PCA model and the thresholds once a new normal observation is available. Yet, MWPCA methodology still does not reduce the MDR and the detection delay. In this paper, a Modified MWPCA (MMWPCA) with Fuzzy Logic Filter (FLF) is proposed to enhance the monitoring performance of PCA. It is an adaptive approach with a fixed model that combines both aforementioned techniques. The aim of using FLF is to ensure robustness to false alarms without affecting the Fault Detection (FD) performance. The application of the proposed method has been carried out on the Tennessee Eastman Process (TEP). Hold-one and hold-five MMWPCA with FLF are applied and compared to recent FDD work in the literature. The obtained results demonstrate the superiority of the proposed technique in detecting different types of faults with high accuracy and with shorter time delay.

Trap-controlled mechanoluminescence in Pr3+-activated M2Nb2O7 (M = Sr, Ca) isomorphic perovskites

Isomorphic materials tend to exhibit differentiated performance due to the small differences between the constituent atoms and the crystal structures. Inspired by the isomorphic strategy, herein we developed a novel trap-controlled mechanoluminescent (TC-ML) material, Pr3+-activated Sr2Nb2O7, that shows mechanoluminescence (ML) under the mechanical actions of compression and friction. Compared to the isomorphic Ca2Nb2O7:Pr3+ which requires a long-time delay to achieve high-contrast ML due to the strong long-lasting afterglow, Sr2Nb2O7:Pr3+ enables the obtaining of high-contrast ML in a short-time delay because of the weak short-lasting afterglow, which greatly simplifies the imaging process to facilitate the further application of ML. The investigations of structural and optical characteristics between Sr2Nb2O7:Pr3+ and Ca2Nb2O7:Pr3+ reveal that the unique ML of Sr2Nb2O7:Pr3+ should result from its lower trap concentration and shallower trap depth relative to Ca2Nb2O7:Pr3+. Our results are expected to deepen our understanding on the behavioral diversity of isomorphic phosphors and thereby broaden the horizon of designing and regulating TC-ML materials.

Role of scan strategies on thermal gradient and solidification rate in electron beam powder bed fusion

Local microstructure control in electron beam powder bed fusion (EB-PBF) is of great interest to the additive manufacturing community to realize complex part geometry with targeted performance. The local microstructure control relies on having a detailed understanding of local melt pool physics (e.g., 3-D melt pool shape as well as spatial and temporal variations of thermal gradient (G) and solidification rate (R)). In this research, a new scan strategy referred to as ghost beam is numerically evaluated as a candidate to achieve the targeted G and R of IN718 alloy. The boundary conditions for simulations, including the speed (490 mm/s) and spatial locations of the beam within a given layer, are obtained by using series of snapshot images, recorded at 12,000 frames per second, using a high-speed camera. The heat transfer simulations were performed using TRUCHAS an open-source software deployed within a high-performance computational infrastructure. The simulation results showed that reheating at short beam on-time and time delay decreases both G and R. Local variation of R at the center of the melt pool trailing edge showed periodic temporal fluctuations. Finally, the ghost beam scan strategy was compared to other existing raster and spot scan strategies.

WordDriver-1: evaluating the efficacy of an app-supported decoding intervention for children with reading impairment.

Fluent word reading is a key characteristic of skilled reading, yet most children with reading disorders have impaired word-reading skills. Previous research has demonstrated that multi-component interventions targeting phonemic awareness and the alphabetic principle are effective for children with reading disorders. However, about 25% of children fail to respond to these interventions. While it has been difficult to isolate the active ingredient, the findings of some studies suggest that tasks targeting phonological recoding and orthographic processing are essential elements in improving decoding. To develop and evaluate an intervention that specifically targets phonological recoding and orthographic processing (a decoding intervention) for children with persistent word-reading impairment. A single-subject crossover design with multiple treatments was used to examine the efficacy of the decoding intervention (15 × 20-min sessions) compared with a language intervention that controlled for individual therapy time. Eight children (aged 7:6-8:11 years) with persistent word-reading impairment were randomly assigned to one of two intervention sequences. The effect of the decoding intervention was evaluated by (1) changes in decoding accuracy measured by performance on researcher-developed non-word lists; and (2) generalization to other standardized measures of reading. The results showed that all participants demonstrated significant gains in non-word reading on researcher-developed non-word lists and standardized measures of non-word-reading accuracy and efficiency. Trends for improvement on standardized measures of word-reading efficiency, text-reading accuracy and reading comprehension were observed. This decoding intervention significantly improved non-word decoding skills in all participants who had not responded to previous reading interventions. As such, it may be an efficient adjunct to the first stage of reading interventions for this population. The relative lack of generalization to other word-reading skills may have been due to the nature of the outcome measures, the short intervention time and/or additional delays in participant orthographic processing skills.

Determining the embedding parameters governing long-term dynamics of copper prices

Mineral extraction activities and the commercialisation of mineral-based products in later stages are fundamental for economic, technological and social development, so understanding their long-term market behaviour in order to forecast prices is crucial for governments, companies and society. Mineral commodity markets are multidimensional as they are driven by the dynamic evolution of financial, technological, psychological and geopolitical factors. Thus, identifying the key features governing mineral commodity prices and modelling their long-term behaviour is an intricate problem that becomes even more complex when the relationship with time is also considered. Although several techniques are available to represent the behaviour and reduce the dimensionality of data sets, these techniques often neglect the temporal relationship and evolution of variables. In many cases, the selection of key variables is solely based on the correlation with each other, relevance and degree of variance, and the cause and effect behaviour of the time-relation of variables, is neglected. This is a critical issue in assessing dynamic systems, especially those involving human behaviour such as social sciences and biology where learning and cognition capacities evolve through time. In this sense, before any attempt to forecast mineral commodity prices, a proper understanding of the embedding dimension and time delay of the variables governing the system is fundamental to determining the number of key features driving the system and the extension of the delayed effects of changes in the initial conditions, respectively. Determining these parameters may become even more complicated because of data scarcity, since the high cost, technical or temporal limitations often hamper obtaining large data sets related to complex dynamic systems that occur in nature and the social sciences. Daily and monthly quotations have been commonly used to represent the dynamics of mineral commodity markets and predict prices, yet they are not sufficient to capture and understand the dynamic evolution of prices in the long-term. These quotations are too short as the delayed effects that reflect on the entire economy and arises from changes in macroeconomic variables can normally be perceived about a year ahead, and may last for up to six years. However, chaos theory has provided valuable tools to assess the dynamics of complex systems allowing the proper determination of the embedding parameters (dimension and time delay), even when using small data sets. This paper examines the long-term dynamics of mineral commodity prices via chaos theory based on a short data set of annual copper prices observed between 1900 and 2015. Copper was used as a study case because it is one of the most competitive markets and representative of mineral commodities traded worldwide. It was found that the dynamic-deterministic behaviour of annual copper prices is embedded in a high-dimensional space that fluctuates between five and seven, and a relatively short time delay between two and three periods. Our finding argues for the use of chaos theory as an important technique to assess the long-term behaviour of mineral commodity prices using short data sets because it improves the understanding of those complex dynamic systems and provides important guidelines that remarkably simplifies the forecasting task.

Mode Selection Rules for a Two-Delay System with Positive and Negative Feedback Loops

The mode selection rules for a two-delay system, which has negative feedback with a short delay time t1 and positive feedback with a long delay time t2, are studied numerically and theoretically. We find two types of mode selection rules depending on the strength of the negative feedback. When the strength of the negative feedback |α1| (α1 0), 2m + 1-th harmonic oscillation is well sustained in a neighborhood of t1/t2 = even/odd, i.e., relevant condition. In a neighborhood of the irrelevant condition given by t1/t2 = odd/even or t1/t2 = odd/odd, higher harmonic oscillations are observed. However, if |α1| is slightly less than α2, a different mode selection rule works, where the condition t1/t2 = odd/even is relevant and the conditions t1/t2 = odd/odd and t1/t2 = even/odd are irrelevant. These mode selection rules are different from the mode selection rule of the normal two-delay system with two positive feedback loops, where t1/t...

A Modified Moving Window dynamic PCA with Fuzzy Logic Filter and application to fault detection

Principal Component Analysis (PCA) model is constructed from measured data and used to monitor new testing samples. In fact, the statistical independency assumption between observations is true only for long sampling intervals. Nowadays, industrial systems are sophisticated and fast for which this assumption becomes no longer valid and the current observation becomes highly dependent on the past observations. In another hand, Dynamic PCA (DPCA) is a PCA extension to deal with the aforementioned problem, but monitoring process using this method with fixed control limits showed a high False Alarms Rate (FAR), high Missed Detection Rate (MDR) and long Detection Time Delay (DTD). In this paper, a Modified Moving Window DPCA (MMW-DPCA) with Fuzzy Logic Filter (FLF) is proposed to address the above issue. The developed monitoring scheme continually updates control limits throughout an obtained DPCA-based model. The adaptive thresholds are established by moving a fixed size window over the data. The dynamic behavior of the data is handled by DPCA, whereas the sensitivity enhancement and the FAR reduction are handled by the developed adaptive thresholds for which the FLF is employed to ensure robustness to outliers and noise without affecting the fault detection performances. The proposed technique has been tested on Tennessee Eastman Process (TEP). It has been compared to other well-known fault detection methods. The obtained results demonstrate that the MMW-DPCA with FLF detects different types of faults with high accuracy and in a short time delay. The experimental application of the MMW-DPCA with FLF has been carried out on cement rotary kiln. The obtained results illustrate that the proposed method has successfully detected a real fault.

Resolving the Singlet Excited State Manifold of Benzophenone by First-Principles Simulations and Ultrafast Spectroscopy.

Accurate characterization of the high-lying excited state manifolds of organic molecules is of fundamental importance for the interpretation of the rich response detected in time-resolved nonlinear electronic spectroscopies. Here, we have characterized the singlet excited state manifold of benzophenone (BP), a versatile organic photoinitiator and a well-known DNA photosensitizer. Benchmarks of various multiconfigurational/multireference (RASSCF/PT2) and time-dependent density functional theory (TD-DFT) approaches allowed assignments of experimental linear absorption signals of BP in the ultraviolet (UV) region, with unprecedented characterization of ground state absorptions in the far UV. Experimental transient absorption spectra obtained by UV-vis pump-probe spectroscopy at very short time delays are shown to be directly comparable to theoretical estimates of excited state absorptions (from the low-lying nOπ* and ππ* singlet states) in the Franck-Condon region. Multireference computations provided reliable interpretation of the PP spectra, with TD-DFT results yielding a fair agreement as long as electronic transitions featuring double excitations contributions are not involved. These results lay the groundwork for further computational studies and interpretation of experimental nonlinear electronic spectra of benzophenone in more complex systems, such as BP/DNA adducts.

Stochastic resonance in a time-delayed feedback tristable system and its application in fault diagnosis

Stochastic resonance (SR) phenomena in a time-delayed feedback tristable system driven by Gaussian white noise are investigated by simulating the potential function, mean first-passage time (MFPT), and signal-to-noise ratio (SNR) of the system. Through the use of a short delay time, the generalized potential function and stationary probability density function (PDF) are obtained. The delay feedback term has a significant effect on both equations, and that the parameters b, c, and d have different effects on the three wells of the potential function. The MFPT is calculated, which plays an extremely important role in research on particles escape rates. We find that the delay feedback term can affect the noise enhanced stability (NES). In addition, the SR characteristics are studied by the index of SNR. The simulation demonstrates that SNR is a non-monotonic distributed and that the peak SNR value can be attained by adjusting the appropriate parameters. Finally, the proposed theory is combined with a variable step method and applied to the detection of high frequencies in experiments. The result indicates that the fault frequency can be identified, and that the energy of the fault signal can be enhanced under suitable delay feedback parameters.

Sampled fiber gratings for picosecond time delay signal processing

Sampled fiber grating for high-resolution time-domain signal processing is investigated. Sampled fiber grating is useful to introduce precise time delays in picosecond (ps) across many wavelength channels. We analyze and simulate for Sinc2 sampled fiber grating, and show that a large number linear sub-ps time delays can be achieved by the grating. We present that Gaussian sampled fiber gratings can be fabricated by inscribing optical fiber by Gaussian laser beam, and can realize short time delays over a number of wavelength channels with a required time delay profile. For a Gaussian sampled fiber grating fabricated, an average time delay step of 4.49 ps with 10% linearity for 8 wavelength channels, and an average delay step of 2.5 ps with 8% linearity if for 4 channels, are realized. A physical model of cascaded equivalent Fabry-Perot cavities together with rectangular truncation of the inscription laser beam for the Gaussian sampled refractive index is suggested, and used to explain the grating spectra. A technique for time delay step tunability of the grating is presented. Some issues are discussed with conclusions given. We demonstrate that the sampled fiber gratings have capability to provide a large number of picosecond time delays with good linearity. This offers a simple technique for ps-high-resolution signal processing in time-domain and THz signal generation.

Spectroscopic characteristics of Hα/OI atomic lines generated by nanosecond pulsed corona-like discharge in deionized water

Basic emission fingerprints of nanosecond discharges produced in deionized water by fast rise-time positive high-voltage pulses (duration of 6 ns and amplitude of +100 kV) in a point-to-plane electrode geometry were investigated by means of time-resolved intensified charge-coupled device (ICCD) spectroscopy. Time-resolved emission spectra were measured via ICCD kinetic series during the discharge ignition and later phases over the 350–850 nm spectral range with fixed, either 3 ns or 30 ns, acquisition time and with 3 ns or 30 ns time resolution, respectively. The luminous phase of the initial discharge expansion and its subsequent collapse was characterized by a broadband vis-NIR continuum emission evolving during the first few nanoseconds which shifted more toward the UV with further increase of time. After ~30 ns from the discharge onset, the continuum gradually disappeared followed by the emission of Hα and OI atomic lines. The electron densities calculated from the Hα profile fit were estimated to be of the order of 1018–1019 cm−3. It is unknown if the Hα and OI atomic lines are generated even in earlier times (before ~30 ns) because such signals were not detectable due to the superposition with the strong continuum. However, subsequent events caused by the reflected HV pulses were observed to have significant effects on the emission spectra profiles of the nanosecond discharge. By varying the time delay of the reflected pulse from 45 to 90 ns after the primary pulse, the intensities of the Hα/OI atomic lines in the emission spectra of the secondary discharges were clearly visible and their intensities were greater with shorter time delay between primary and reflected pulses. These results indicate that the discharges generated due to the reflected pulses were very likely generated in the non-relaxed environment.

Design and realization of high performance logarithmic converters using non-uniform multi-regions constant adder correction schemes

This paper proposes high performance logarithmic converters that use non-uniform multi-regions constant adder correction schemes. Instead of a conventional shift-and-add method, the novel hardware structure presented in this paper uses a constant adder correction circuit that only uses adders. The proposed logarithmic converters can achieve lower approximation error range, smaller hardware area and shorter delay time, which are superior to those of methods previously reported in the literature. The approximation error ranges of the proposed logarithmic converters were 0.0548, 0.0446, 0.032 and 0.0249 for the 3-region, 5-region, 7-region and 9-region constant adder correction logarithmic conversion, respectively. Meanwhile, the proposed converters could achieve 25.63%, 42.47%, 64.43% and 53.23% area delay product savings for the 3-region, 5-region, 7-region and 9-region constant adder correction circuit, respectively. All very large scale integration (VLSI) realization is synthesized using the TSMC 0.18 μm CMOS technology. In addition, the hardware structure of the proposed logarithmic converters is quite simple, with a lower approximation error, fast enough and ROM-free due to the proposed converters only using adders compared to the previously reported shift-and-add based methods. The proposed work can easily realize VLSI digital circuits and is fit for use in embedded digital signal processing and cloud computing.

Determining the chaotic behaviour of copper prices in the long-term using annual price data

Mineral commodity prices are influenced by economic, technological, psychological, and geopolitical factors. Stochastic approaches, and time series and econometric techniques have been used to represent the dynamics of mineral commodity markets and predict prices. However, these techniques cannot provide a comprehensive representation of market dynamics because they do not recognise the relationship between these factors over time, and they are unable to capture both the evolution and the cumulative effects of these factors on prices. Stability of motion and chaos theories can detect sensitivity to initial conditions, and therefore the evolutionary patterns allowing a proper understanding and representation of mineral commodity market dynamics. Most of the techniques used to assess chaos require a colossal amount of data, so the use of small data sets to assess chaos has been largely criticised. Nevertheless, by definition, the dynamics of a chaotic system remain at different scales owing to its self-organisation features that exhibit ordered patterns in the absence of codes or rules. Therefore, any deterministic chaotic behaviour of mineral commodity prices can be captured by using small data sets if a detailed qualitative and quantitative analysis are carried out. This paper examines the chaotic behaviour of annual copper prices between 1900 and 2015. To do so, we combine chaos theory, stability of motion and statistical techniques to reconstruct the long-term dynamics of copper prices. First, we examine the time dependency and the presence of a strange attractor by a visual analysis of the time series and phase space reconstruction based on Takens’ theorem and determine embedding parameters. Then we examine the dynamic characteristics of the system which assesses its complexity and regularity patterns to measure the system’s entropy. Finally, we calculate the largest Lyapunov exponent λ to assess the sensitivity to initial conditions and determine chaotic behaviour supported by a surrogate test. We find that annual copper prices have a chaotic behaviour embedded in a high-dimensional space and short time delay. The study suggests that copper prices exhibit only a single state of low prices, which fluctuate through transitional periods of high prices. It challenges the assertion that metal markets have fluctuated over four major super cycles and debate the adequacy of stochastic and econometric models for representing mineral commodity market behaviour.This study recommends that the use of chaotic behaviour improves our understanding of mineral commodity markets and narrows the data searching, processing and monitoring requirements for forecasting. Therefore, it improves the performance of traditional techniques for selecting key factors that influence the market dynamics, and may also be used to select the most suitable algorithm for forecasting prices.