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This paper considers a Problem of Periodic Routing of Vehicles Platoons (PRVPP), which is a novel extension of the Periodic Vehicle Routing Problem (PVRP). The PRVPP boils down to scheduling of the fleet of vehicles travelling in a convoy while constituting the timetable for the passage of individual vehicles along the planned routes. The imprecise nature of transport/service operation times means there is a need to take into account the fact that the accumulating uncertainty of previously performed operations results in increased uncertainty of timely execution of subsequent operations. This raises the question as to the method required to avoid additional uncertainty introduced during aggregating uncertain operation execution deadlines. Due to the above fact, an algebraic model for calculating fuzzy schedules for individual vehicles, and for planning time buffers enabling the adjustment of the currently calculated fuzzy schedules, is developed. The model uses Ordered Fuzzy Numbers (OFNs) to reflect the uncertainty of times. The conducted research demonstrated that the proposed model allows us to develop conditions following the calculability of arithmetic operations of OFNs and guarantee the interpretability of the results obtained.

The various combinations of factors that form an interannual variability of ice coveren in the western, northeastern and southeastern parts of the Barents Sea were analysed for the period 1950 ̶ 2022. The co-phased cyclic fluctuations between the Barents Sea ice coveren and atmospheric circulation indices (5 ̶ 7 and 8 ̶ 14 years), Atlantic multidecadal oscillation (5 ̶ 9 years), solar activity (10 years), parameters of the Earth’s rotation axis and other astrogeophysical characteristics (6, 9 and 10 years) were reported. Multiple regression equations for the winter and summer seasons for each part of the Barents Sea were formed. The connecting of each predictor with ice coveren variability and their contribution to the ice coveren total dispersion were evaluated. It was shown that the set of factors forming interannual variability of the Barents Sea ice coveren is differs depending on the area and season. It appears that previous state of the ice coveren has the greatest impact at the ice coveren variability in the western and the northeastern parts of the Barents Sea (78 % and 74 % of total dispersion respectively). And in the southeastern part of the Barents Sea the highest impact at the ice coveren volatility has the atmosphere temperature variability − 45 % of total dispersion..

This paper considers a Problem of Periodic Routing of Vehicles Platoons (PRVPP), which is a novel extension of the Periodic Vehicle Routing Problem (PVRP). The PRVPP boils down to scheduling of the fleet of vehicles travelling in a convoy while constituting the timetable for the passage of individual vehicles along the planned routes. The imprecise nature of transport/service operation times means there is a need to take into account the fact that the accumulating uncertainty of previously performed operations results in increased uncertainty of timely execution of subsequent operations. This raises the question as to the method required to avoid additional uncertainty introduced during aggregating uncertain operation execution deadlines. Due to the above fact, an algebraic model for calculating fuzzy schedules for individual vehicles, and for planning time buffers enabling the adjustment of the currently calculated fuzzy schedules, is developed. The model uses Ordered Fuzzy Numbers (OFNs) to reflect the uncertainty of times. The conducted research demonstrated that the proposed model allows us to develop conditions following the calculability of arithmetic operations of OFNs and guarantee the interpretability of the results obtained. [ABSTRACT FROM AUTHOR]

Many processes in living organisms are subject to periodic oscillations at different hierarchical levels of their organization: from molecular-genetic to population and ecological. Oscillatory processes are responsible for cell cycles in both prokaryotes and eukaryotes, for circadian rhythms, for synchronous coupling of respiration with cardiac contractions, etc. Fluctuations in the numbers of organisms in natural populations can be caused by the populations’ own properties, their age structure, and ecological relationships with other species. Along with experimental approaches, mathematical and computer modeling is widely used to study oscillating biological systems. This paper presents classical mathematical models that describe oscillatory behavior in biological systems. Methods for the search for oscillatory molecular-genetic systems are presented by the example of their special case – oscillatory enzymatic systems. Factors influencing the cyclic dynamics in living systems, typical not only of the molecular-genetic level, but of higher levels of organization as well, are considered. Application of different ways to describe gene networks for modeling oscillatory molecular-genetic systems is considered, where the most important factor for the emergence of cyclic behavior is the presence of feedback. Techniques for finding potentially oscillatory enzymatic systems are presented. Using the method described in the article, we present and analyze, in a step-by-step manner, first the structural models (graphs) of gene networks and then the reconstruction of the mathematical models and computational experiments with them. Structural models are ideally suited for the tasks of an automatic search for potential oscillating contours (linked subgraphs), whose structure can correspond to the mathematical model of the molecular-genetic system that demonstrates oscillatory behavior in dynamics. At the same time, it is the numerical study of mathematical models for the selected contours that makes it possible to confirm the presence of stable limit cycles in them. As an example of application of the technology, a network of 300 metabolic reactions of the bacterium Escherichia coli was analyzed using mathematical and computer modeling tools. In particular, oscillatory behavior was shown for a loop whose reactions are part of the tryptophan biosynthesis pathway.

In the article, on the basis of the theory of thermodynamic potentials, a study was made of the quasistatic Phillips and Carnot heat engines in which a comparative analysis was made of their work both for cycles with a working body, an ideal gas, and for cycles with a working body, real gas. On the basis of the conducted research, it was established that the existing formulation of the Carnot theorem is valid only for the working fluid “ideal gas”. In general, based on the above calculations, the Carnot theorem can be formulated, for example, like this: “The efficiency of a reversible heat engine is maximum, does not depend on the properties of the heat engine and is a function of the temperatures of only hot and cold tanks: η=1-ƒ(t1,t2), where ƒ(t1,t2) is a function only of the temperatures t1 and t2 of the hot and cold tanks. This formulation is valid only for working fluid ideal gas. In the case of using real gas as a working fluid, the efficiency of a heat engine, in addition to dependence on the temperatures of hot and cold tanks, is a function of the thermodynamic characteristics of the working fluid and the type of heat engine, and reaches its maximum value for this type of working fluid and engine type if there is reversibility the system under consideration».

A study has been made of the Philips and Carnot cycles based on the modernized physicochemical model of "ideal gas", which utilizes the theory of thermodynamic potentials and assumes the presence of chemical energy. The feasibility study of the Phillips and Carnot heat engines using the thermodynamic potential method is substantiated by plotting the diagrams of the dependence of the internal energy and Helmholtz energy on the absolute temperature and their comparison with the usual pressure-volume diagrams. This method is compared with traditional approach to analysis of cyclic processes. Based on the analysis carried out, the results are similar to those obtained in the study of these processes in the traditional way. On the other hand, the use of new research methods has a significant advantage, since it allows direct use of the activity of the substance (gas) and the entire arsenal of chemical thermodynamics for the analysis of cyclic processes, for example, in the thermal machines of Philips and Carnot.

The dynamics of global flows of matter in the biosphere has been studied. The general law of redistribution of average elemental compositions in the biosphere between the solid and liquid phases (lithosphere–hydrosphere) is established. In these processes, the main role is played by "living matter." The most active processes of redistribution of mean elemental compositions in the biosphere take place in the places of "life thickening" (biogeochemical barriers) such as ocean–atmosphere, river–sea and hydrosphere–lithosphere. The result of these processes is a general relative increase in the concentrations of trace elements in the environment of living organisms. A new methodological approach is proposed to study the role of the transfer of trace elements in the ocean–atmosphere–continent system as a factor in the formation of the elemental composition of the Earth's soil cover. [ABSTRACT FROM AUTHOR]

Recently, we have proposed a new formulation approach for control degree of freedom (CDOF) analysis of process systems. This formula interrelates the CDOF and elements of a process flow diagram (PFD). The formulation is accurate, easily applicable by process engineers, and needs little prior knowledge of the process under study. This paper describes further about this new formulation and its advantages by applying it to batch and cyclic processes. The results demonstrate the correctness of the method in determining CDOF for all case studies at both steady state and dynamic conditions. The CDOF for "reheat regenerative Rankine" and "vapor absorption refrigeration" cycles have been determined to be 9 and 8, respectively. The steady state CDOF values for the Rankine and refrigeration cycles have been calculated as 8 and 4, respectivley. Also the CDOF for the process of "heat pump integrated with batch distillation column" is 4 that verifies the suggested formula of CDOF. The method also gives beneficial insights about the manipulated variables (MVs) in a control system. [ABSTRACT FROM AUTHOR]

Mathematical models are developed to simulate the behaviour of high pressure processing systems (single- and multi-cycle processes of different pulse-shapes) and predict the effects of processing parameters on their energy consumption. The validity of the models is established by comparing simulation results with experimental measurements from published works and the present study. Specific energy consumption is shown to depend mainly on holding pressure, pressure medium compressibility, equipment scale and vessel filling efficiency. Inlet temperature, compression and decompression times show negligible effects as do cycle pressure shapes. Longer compression times, however, reduce power capacity requirements, if all other conditions remain constant. The holding time has negligible effects on energy consumption, save for leakages and standby power, hence, extending it does not incur significant energy penalties. On the other hand, a drop in holding pressure leads to a more than proportionate drop in energy consumption. Hence, lower-pressure, longer-time processes are more advantageous from an energy standpoint, provided they satisfy product quality, safety and throughput requirements. Lower-compressibility fluids enable higher pressures to be established with lower energy losses. Higher equipment scales and vessel filling efficiencies reduce the proportion of wasted energy. These conditions are therefore beneficial for energy-efficient operation. Industrial relevance The production of clean-label, minimally-processed and microbial-safe food products with excellent nutritional, organoleptic properties and extended shelf life is becoming increasingly important. High-pressure processing HPP is a promising technology in this regard, increasingly being deployed at commercial scale. To reduce per-unit HPP product costs, which are currently higher than those of traditional thermal systems, it is important to reduce energy usage, which constitutes a significant proportion of operating costs. The modelling scheme developed in this work would help process designers and operators determine optimal processing conditions with respect to energy consumption, while satisfying product quality and safety constraints; providing a basis for improved process automation. [ABSTRACT FROM AUTHOR]

The solution of nonlinear structural problems by means of a space-time model order reduction approach is investigated. The main target is the prediction of the long-term response while reducing both the computation time and the storage requirements considerably. A nonstandard discretization approach is used which treats the internal degrees of freedom as additional unknowns. The resulting nonlinear problem is formulated in a variational setting. The proposed reduced basis represents the behavior of the structure in a complete time interval, e.g. during one load cycle (for cyclic processes). The reduced variables are obtained by a projection of the time-local stationary conditions onto appropriate test functions defined in space-time. This leads to a low-dimensional nonlinear system of equations. Details regarding the theoretical derivation, the discretization and the numerical treatment of the nonlinearity are presented. In the numerical examples the reduced model is compared to FEM reference solutions. Different choices for the test functions are discussed and the postprocessing abilities offered by the reduced model are illustrated. [ABSTRACT FROM AUTHOR]

The operation of lithium ion batteries in discharge and charge processes is addressed. A simple phenomenological model is developed to predict all variables values. A set of algebraic and differential equations is derived taking into account salt and lithium balances in electrodes, in the separator, and in particles. Balances are developed for finite volumes and appropriate average values of several variables such as concentrations, current densities, and electrochemical reaction rates are introduced. Definitions of current densities as volume fraction functions are critical issues in the computations. Experimental values taken from the literature for discharge processes are predicted very accurately. Constant salt concentration in the separator can be assumed and consequently, the model can be analytically solved. Charge and discharge times, initial cell capacity, lost capacity, and relaxation times are easily estimated from simple equations and cell parameters. The limiting processes taking place during cell discharge can be determined. Energy efficiency and capacity usage are quantified for cycles. © 2014 American Institute of Chemical Engineers AIChE J, 61: 90-102, 2015 [ABSTRACT FROM AUTHOR]

In recent literature, a utopia-tracking strategy has been proposed for multi-objective model predictive control. This strategy tracks a vector of independently minimized objectives, evaluated at steady-state operation (the utopia point). The approach in the present work is based on the premise that cyclic process operation may in some cases outperform, on average, steady-state operation. We therefore concern ourselves with optimizing average performance for one cyclic period of operation. A dynamic utopia-tracking strategy is proposed, which generalizes steady-state utopia-tracking to systems which are optimally operated cyclically. The proposed control law minimizes the distance of its cost vector to a vector of independently minimized objectives, evaluating average cyclic performance (the dynamic utopia point). Recursive feasibility is established for a cyclic terminal state constraint formulation, however, conditions for stability are not given. The theoretical concepts are illustrated for a simple acetylene hydrogenation case, and a more complex oil production optimization case. The simulation study indicates novel operational insight for the oil production optimization case, by illustrating how simultaneous optimization of two objectives results in cyclic operation with improved performance. [ABSTRACT FROM AUTHOR]

Problems of cyclic scheduling are usually observed in flexible manufacturing systems which produce multitype parts where the automated guided vehicle system plays the role of a material handling system, as well as in various other multimodal transportation systems where goods and/or passenger itinerary planning plays a pivotal role. The schedulability analysis of the processes executed in the so-called systems of concurrent cyclic processes (SCCPs) can be executed within a declarative modeling framework. Consequently, the considered SCCP scheduling problem can be seen as a constraint satisfaction problem. Such a representation provides a unified way for evaluating the performance of local cyclic processes as well as of multimodal processes supported by them. Here, the crucial issue is that of a control procedure (e.g., a set of dispatching rules), which would guarantee the cyclic behavior of the SCCP. In this context, we discuss the sufficient conditions guaranteeing the schedulability of both local and multimodal cyclic processes, and we propose a recursive approach in designing them. [ABSTRACT FROM AUTHOR]

Abstract: Nonlinear model predictive control (NMPC) with economic objective attracts growing interest. In our previous work , nominal stability of economically oriented NMPC for cyclic processes was proved by introducing a transformed system, and an infinite horizon NMPC formulation with discount factors was proposed. Moreover, the nominal stability property for economically oriented NMPC was analyzed in for a class of systems satisfying strong duality. In this study, we extend the previous stability analysis in to a general infinite horizon NMPC formulation with economic objectives. Instead of the strong duality assumption, we require the stage cost to be strongly convex, which is easier to check for a general nonlinear system. In addition, robust stability of this NMPC controller is also analyzed based on the Input-to-State Stability (ISS) framework. A simulated nonlinear double tank system subject to periodic change in electricity price is presented to illustrate the stability property. Finally, an industrial size air separation unit case study with periodic electricity cost is presented. [Copyright &y& Elsevier]

A new apparatus for the chromatographic separation of liquid mixtures is investigated. The apparatus contains a number of vertical columns connected in a serpentine shape and consisting of cells placed on top of each other. The cells in the columns are separated by perforated septa. A special dosing unit is used to provide a discrete (cyclic) mobile-phase feed [flow?] into the apparatus and a pulsed cyclic mode of phase contact in column cells. Studies on a single column and on an apparatus consisting of four columns have been performed to assess the efficiency of the pulsed cyclic device. The results of experimental investigations have confirmed the potential of the newly developed topic in the area of liquid mixture separation processes. [ABSTRACT FROM AUTHOR]

Abstract: Several applications in process industries, such as simulated moving bed (SMB) separation and pressure swing adsorption (PSA), exhibit cyclic steady state behavior. Moreover, it is of economic interest to require energy intensive applications to take advantage of the periodically varying electricity price by changing the operating point frequently. Because traditional two-layer optimization methods are difficult to apply to these systems, we consider instead an economically oriented nonlinear model predictive control (NMPC) that directly considers system’s economic performance subject to the dynamic model. On the other hand, the commonly used Lyapunov framework to analyze the stability for the economically oriented NMPC cannot be applied directly. This work proposes two economically oriented NMPC formulations and proves nominal stability for both. We introduce transformed systems by subtracting the optimal cyclic steady state from the original system, for which the Lyapunov function can easily be established. Moreover, we show that the asymptotical stability of the transformed system is equivalent to that of the original system. Hence, the original systems are also nominally stable at the cyclic optimal solution. Finally, an industrial size air separation unit case study with periodic electricity cost is presented. [Copyright &y& Elsevier]

Abstract: We investigated two lignite quarries in northern Greece for orbital and suborbital climate variability. Sections Lava and Vegora are located at the southern and northern boundaries of the Ptolemais Basin, a northwest southeast elongated intramontane basin that contains Upper Miocene to Lower Pliocene lacustrine sediments. Sediments show cyclic alterations of marl-rich (light), and coal-rich or clay-rich (dark) strata on a decimeter to meter scale. First, we established low-resolution ground-truth stratigraphy based on paleomagnetics and biostratigraphy. Accordingly, the lower 67m and 65m that were investigated in both sections Vegora and Lava, respectively, belong to the Upper Miocene and cover a time period of 6.85 to 6.57 and 6.46 to 5.98Ma at sedimentation rates of roughly 14 and 22cm/ka. In order to obtain a robust and high-resolution chronology, we then tuned carbonate minima (low L* values; high magnetic susceptibility values) to insolation minima. Besides the known dominance of orbital precession and eccentricity, we detected a robust hemi-precessional cycle in most parameters, most likely indicative for monsoonal influence on climate. Moreover, the insolation-forced time series indicate a number of millennial-scale frequencies that are statistically significant with dominant periods of 1.5–8kyr. Evolutionary spectral analysis indicates that millennial-scale climate variability documented for the Ptolemais Basin resembles the one that is preserved in ice-core records of Greenland. Most cycles show durations of several tens of thousands of years before they diminish or cease. This is surprising because the generally argued cause for Late Quaternary millennial-scale variability is associated with the presence of large ice sheets, which cannot be the case for the Upper Miocene. Possible explanations maybe a direct response to solar forcing, an influence on the formation of North Atlantic Deep Water through the outflow of high-salinity water, or an atmospheric link to the North Atlantic Oscillation. [Copyright &y& Elsevier]

We have investigated the fabric and the deformational processes of an exhumed subduction zone thrust active at seismogenic depths. The Rodeo Cove thrust zone, which outcrops north of the Golden Gate Bridge of San Francisco, imbricates two basalt-chertsandstone sequences belonging to the Marin Headlands terrane (Franciscan Complex). The thrust outcrop is a 200-m-thick complex zone that displays a range of stratal disruption from incipient deformation to a broken formation in the central part of the outcrop, dominated by basaltic lithologies, where zones of concentration of deformation have been mapped. Disruption is made by variably dense discrete fault systems synthetic to the main thrust (R and P fractures). These faults are marked by cataclasites with a shaly matrix that shows a scaly foliation defined by chlorite and pumpellyite, which also constrain the depth of faulting (8-10 km, T = 200-250 °C) within the seismogenic zone. The central part of the fault also features the densest system of carbonate-filled veins. Veins occur in the broken formation matrix and fragments, in both cases parallel to the foliation. The veins are either folded, truncated, or pressure-solved along the cleavage. Cementation and hardening of shear surfaces of the fault core may have caused the distribution, as opposed to localization, of subsequent slip events. The fault core may have developed in basaltic rocks because of their inherently high permeability and propensity to transmit overpressure from deeper levels of the subduction zone. Our analysis has shown that accretionary deformation is strongly controlled by injection of overpressured fluids occurring through systems of multiple dilatant fractures grossly parallel to the décollement zone. The crosscutting relationships between veining and foliation suggest that fluid injection is cyclic and, consequently, that large transient variations in permeability and cohesion may occur. The repeated injection of veins parallel to the fault zone may be explained by cyclic changes of the stress, or by difference in tensional strength parallel to and perpendicular to the foliation, both of which would require extremely high fluid pressure. We interpret the features of the Rodeo Cove thrust zone as evidence of the seismic cycle and hypothesize a compressional stress field in the interseismic phase and an extensional stress field in the immediately postseismic phase. [ABSTRACT FROM AUTHOR]

Organic biomarker and nannofossil assemblages are used in combination with sedimentary petrology to identify the role of diagenesis for the formation of a rhythmic calcareous succession. A record from the Early Pliocene of the Maldives (Ocean Drilling Program, ODP Leg 115) is presented containing precession and eccentricity cycles expressed as variable aragonite content. Additional sub-Milankovitch cycles are caused by rhythmic precipitation of calcite cement in the lower part of the interval. Comparison with palaeo-productivity indicators (nannofossils, chlorin, total organic carbon) suggests that cementation occurs preferentially in intervals characterized by increasing or decreasing productivity. The coupled variability in productivity and carbonate diagenesis is attributed to the effect of organic matter degradation in the sediment. The observed combination of primary and diagenetic factors hampers the interpretation of the cyclicity on Milankovitch and sub-Milankovitch scales. Diagenetically stable proxies for palaeo-productivity, such as nannofossil assemblage data, were used to distinguish between palaeoclimate and diagenetic influences. [ABSTRACT FROM AUTHOR]

Redox processes affect many aspects of geological systems. It is therefore useful to distinguish between chemical processes that result in changes in the capacities of reservoirs to oxidize or reduce from those that do not. Two terms are proposed to make this distinction. The first is redox decoupling: the transport of redox- sensitive elements (e.g., H, C, S, Fe) such that reservoirs experience a change in their capacity to oxidize or reduce other material. The second is electrochemical differentiation: the effect of one or more redox decoupling processes that change existing gradients in redox potential. Recognition of redox decoupling requires the use of an extensive rather than an intensive redox variable, because intensive variables do not provide information on fluxes. Redox budget, defined as the number of moles of negative charge that must be added to a sample to reach a reference state, is such a variable. Construction of redox budgets for mid-oceanic-ridge basalt (MORB) lavas and glasses reveals that redox decoupling occurs during crystallization at the Mid-Atlantic, Pacific, and Red Sea ridges, with net oxidation of the crystallized lava. The concepts of electrochemical differentiation, redox decoupling, and redox budget may be useful for researchers studying global cycling, the formation of ore deposits, volcanism, evolution of the mantle, crust and core, redox-related environmental problems, and biotic systems. [ABSTRACT FROM AUTHOR]

A cyclic marl-limestone succession of Middle-Late Campanian age has been investigated with respect to a Milankovitch-controlled origin of geochemical data. In general, the major element geochemistry of the marl-limestone rhythmites can be explained by a simple two-component mixing model with the end-members calcium carbonate and 'average shale'-like material. Carbonate content varies from 55 to 90%. Non-carbonate components are clay minerals (illite, smectite) and biogenic silica from sponge spicules, as well as authigenically formed zeolites (strontian heulandite) and quartz. The redox potential suggests oxidizing conditions throughout the section. Trace element and stable isotopic data as well as SEM investigations show that the carbonate mud is mostly composed of low-magnesium calcitic tests of planktic coccolithophorids and calcareous dinoflagellate cysts (calcispheres). Diagenetic overprint results in a decrease of 2‰ δ18 and an increase in Mn of up to 250 ppm. However, the sediment seems to preserve most of its high Sr content compared to the primary low-magnesium calcite of co-occurring belemnite rostra. The periodicity of geochemical cycles is dominated by 413 ka and weak signals between 51 and 22.5 ka, attributable to orbital forcing. Accumulation rates within these cycles vary between 40 and 50 m/Ma. The resulting cyclic sedimentary sequence is the product of (a) changes in primary production of low-magnesium calcitic biogenic material in surface waters within the long eccentricity and the precession, demonstrated by the CaCO3 content and the Mg/Al, Mn/Al and St/Al ratios, and (b) fluctuations in climate and continental weathering, which changed the quality of supplied clay minerals (the illite/smectite ratio), demonstrated by the K/Al ratio. High carbonate productivity correlates with smectite-favouring weathering (semiarid conditions, conspicuously dry and moist seasonal changes in warmer climates). Ti as the proxy... [ABSTRACT FROM AUTHOR]

An efficient version of a numerical gradient optimization procedure for the computation of solutions to periodic optimal control problems is presented. This procedure consists of a first order gradient method in combination with the Newton–Picard shooting method. The first order gradient method is able to compute the optimal control of a periodic process under one or more nonlocal constraints, such as a minimum purity constraint. The Newton–Picard method computes very efficiently periodic solutions to the state and adjoint equations. The presented numerical procedure is used to optimize a rapid pressure swing reactor and a rapid pressure swing adsorber. It is shown that the optimal cycle scheme consists of four steps: a no-inflow pre-pressurization step, a pressurization step, a no-inflow post-pressurization step, and a depressurization step. [Copyright &y& Elsevier]

Enclosed bodies of water such as lakes or harbours often experience large-scale oscillatory motions (seiching). As a simple model of such flow, we investigate exact solutions to the shallow-water equations which represent oscillatory flow in an elliptical basin with parabolic cross section. Specifically, we consider two fundamental modes of oscillation, in one of which the flow is parallel to the axis of the ellipse, while in the other it is radial. We obtain periodic analytical solutions for sediment transport, including erosion, deposition and advection, under either mode of oscillation, and present a method for obtaining such solutions for a more general class of flow fields and sediment transport models.Our solutions provide estimates of the morphodynamical importance of seiching motions and also reveal a characteristic pattern of net erosion and deposition associated with each mode. In particular, we find that a net flux of suspended sediment can be transported from the deeper to the shallower regions of the basin. These transport patterns, which are driven essentially by settling lag, are highly robust to the formulation of the sediment transport relation and appear not to be substantially affected by the omission of frictional terms in the hydrodynamics: they should thus provide considerable insight into sediment transport in less-idealised systems. [Copyright &y& Elsevier]

The determination of periodic states of cyclic chemical processes by standard simulation techniques is computationally inefficient due to the long transient phase. We introduce the Newton–Picard method, a hybrid convergence acceleration method and compare its performance to the performance of existing convergence accelerating techniques. The comparison is made with respect to the number of function evaluations, robustness and dependence on initial conditions. We also discuss, depending on the characteristics of the chemical process, which acceleration method has the best performance. [Copyright &y& Elsevier]

We present two novel algorithm features for the transient simulation of cyclic processes that exhibit cyclic steady state (CSS). In principle, the algorithm could be used for many cyclic process. Air separation using rapid pressure swing adsorption (RPSA) is used as an illustration. The first feature of the algorithm is an a priori rational stopping criterion to determine the CSS unambiguously. The stopping criterion ensures that neither is progress towards CSS truncated prematurely nor is computer time wasted by simulating an unnecessarily large number of cycles. The second feature of the algorithm is a reduction of the number of cycles required to reach the CSS while ensuring that the CSS is certainly determined. The conditions where these two novel algorithm features are applicable have been clearly identified. These two features could be employed regardless of the numerical methods used to solve the mathematical models, and regardless of the process in question, as long as certain desired conditions are fulfilled. [Copyright &y& Elsevier]