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This study explores our ability to simulate the atmospheric chemistry stemming from isoprene emissions in pristine and polluted regions of the Amazon basin. We confront two atmospheric chemistry models – a global, Eulerian chemistry-climate model (UM-UKCA) and a trajectory-based Lagrangian model (CiTTyCAT) – with recent airborne measurements of atmospheric composition above the Amazon made during the SAMBBA campaign of 2012. The simulations with the two models prove relatively insensitive to the chemical mechanism employed; we explore one based on the Mainz Isoprene Mechanism, and an updated one that includes changes to the chemistry of first generation isoprene nitrates (ISON) and the regeneration of hydroxyl radicals via the formation of hydroperoxy-aldehydes (HPALDS) from hydroperoxy radicals (ISO2). In the Lagrangian model, the impact of increasing the spatial resolution of trace gas emissions employed from 3.75° × 2.5° to 0.1° × 0.1° varies from one flight to another, and from one chemical species to another. What consistently proves highly influential on our simulations, however, is the model framework itself – how the treatment of transport, and consequently mixing, differs between the two models. The lack of explicit mixing in the Lagrangian model yields variability in atmospheric composition more reminiscent of that exhibited by the measurements. In contrast, the combination of explicit (and implicit) mixing in the Eulerian model removes much of this variability but yields better agreement with the measurements overall. We therefore explore a simple treatment of mixing in the Lagrangian model that, drawing on output from the Eulerian model, offers a compromise between the two models. We use this Lagrangian/Eulerian combination, in addition to the separate Eulerian and Lagrangian models, to simulate ozone at a site in the boundary layer downwind of Manaus, Brazil. The Lagrangian/Eulerian combination predicts a value for an AOT40-like accumulated exposure metric of around 1000 ppbv h, compared to just 20 ppbv h with the Eulerian model. The model framework therefore has considerable bearing on our understanding of the frequency at which, and the duration for which, the rainforest is exposed to damaging ground-level ozone concentrations.

We introduce a natural temporal analogue of Eulerian circuits and prove that, in contrast with the static case, it is NP-hard to determine whether a given temporal graph is temporally Eulerian even if strong restrictions are placed on the structure of the underlying graph and each edge is active at only three times. However, we do obtain an FPT-algorithm with respect to a new parameter called interval-membership-width which restricts the times assigned to different edges; we believe that this parameter will be of independent interest for other temporal graph problems. Our techniques also allow us to resolve two open question of Akrida, Mertzios and Spirakis [CIAC 2019] concerning a related problem of exploring temporal stars. Furthermore, we introduce a vertex-variant of interval-membership-width (which can be arbitrarily larger than its edge-counterpart) and use it to obtain an FPT-time algorithm for a natural vertex-exploration problem that remains hard even when interval-membership-width is bounded., Extended abstract of this paper appeared in IWOCA 2021: Combinatorial Algorithms pp 107-121 (doi: https://doi.org/10.1007/978-3-030-79987-8_8 )

Advection of trace species (tracers), also called tracer transport, in models of the atmosphere and other physical domains is an important and potentially computationally expensive part of a model's dynamical core (dycore). Semi-Lagrangian (SL) advection methods are efficient because they permit a time step much larger than the advective stability limit for explicit Eulerian methods. Thus, to reduce the computational expense of tracer transport, dycores often use SL methods to advect passive tracers. The class of interpolation semi-Lagrangian (ISL) methods contains potentially extremely efficient SL methods. We describe a set of ISL bases for element-based transport, such as for use with atmosphere models discretized using the spectral element (SE) method. An ISL method that uses the natural polynomial interpolant on Gauss-Legendre-Lobatto (GLL) SE nodes of degree at least three is unstable on the test problem of periodic translational flow on a uniform element grid. We derive new alternative bases of up to order of accuracy nine that are stable on this test problem; we call these the Islet bases. Then we describe an atmosphere tracer transport method, the Islet method, that uses three grids that share an element grid: a dynamics grid supporting, for example, the GLL basis of degree three; a physics grid with a configurable number of finite-volume subcells per element; and a tracer grid supporting use of our Islet bases, with particular basis again configurable. This method provides extremely accurate tracer transport and excellent diagnostic values in a number of validation problems. We conclude with performance results that use up to 27,600 NVIDIA V100 GPUs on the Summit supercomputer.

A Direct Numerical Simulation (DNS) scheme for solving the temporal-spatial multiscale problem of sympathetic detonation is proposed. According to the physical and chemical properties, the SD process is divided into two stages in the numerical simulation. Two different grid sizes are used in the two stages to improve calculation accuracy and efficiency. The local Level Set Method is used to accurately track the multi-material interface, and the Harten Lax and van Leer Contact (HLLC) method is used to solve local Riemann problem. Based on the computing method mentioned above, choosing the high evolution Weighted Essentially Non-Oscillatory (WENO) scheme for the spatial discretization of governing equations in alliance with Total Variation Diminishing (TVD) Runge-Kutta for time discretization, the Eulerian code of SD is developed. It solves the data interaction between the two solvers with variable grid size and time step, and realizes the three-dimensional parallel computing of SD. Composition B is taken as the research object. The processes of SD in different stand-off distances are analyzed. The transmission and safety distances of Composition B are given. The test under the same conditions is designed to verify the numerical simulation. The numerical simulation results are in good agreement with the experiment, which proves the accuracy and feasibility of the numerical method.

The fluidized bed is an essential and standard equipment in the field of process development. It has a wide application in various areas and has been extensively studied. This review paper aims to discuss computational modeling of a fluidized bed with a focus on pharmaceutical applications. Eulerian, Lagrangian, and combined Eulerian-Lagrangian models have been studied for fluid bed applications with the rise of modeling capabilities. Such models assist in optimizing the process parameters and expedite the process development cycle. This paper discusses the background of modeling and then summarizes research papers relevant to pharmaceutical unit operations.

The Eulerian multifluid mathematical model is developed to describe the marine atmospheric boundary layer laden with sea spray under the high-wind condition of a hurricane. The model considers spray and air as separate continuous interacting turbulent media and employs the multifluid E–ϵ closure. Each phase is described by its own set of coupled conservation equations and characterized by its own velocity. Such an approach enables us to accurately quantify the interaction between spray and air and pinpoint the effect of spray on the vertical momentum transport much more precisely than could be done with traditional mixture-type approaches. The model consistently quantifies the effect of spray inertia and the suppression of air turbulence due to two different mechanisms: the turbulence attenuation, which results from the inability of spray droplets to fully follow turbulent fluctuations, and the vertical transport of spray against the gravity by turbulent eddies. The results of numerical and asymptotic analyses show that the turbulence suppression by spray overpowers its inertia several meters above wave crests, resulting in a noticeable wind acceleration and the corresponding reduction of the drag coefficient from the reference values for a spray-free atmosphere. This occurs at much lower than predicted previously spray volume fraction values of ∼10−5. The falloff of the drag coefficient from its reference values is more strongly pronounced at higher altitudes. The drag coefficient reaches its maximum at spray volume fraction values of ∼10−4, which is several times smaller than predicted by mixture-type models.

We compare the computational performance of two modeling approaches for the flow of dilute cavitation bubbles in a liquid. The first approach is a deterministic model, for which bubbles are represented in a Lagrangian framework as advected features, each sampled from a distribution of equilibrium bubble sizes. The dynamic coupling to the liquid phase is modeled through local volume averaging. The second approach is stochastic; ensemble-phase averaging is used to derive mixture-averaged equations and field equations for the associated bubble properties are evolved in an Eulerian reference frame. For polydisperse mixtures, the probability density function of the equilibrium bubble radii is discretized and bubble properties are solved for each representative bin. In both cases, the equations are closed by solving Rayleigh-Plesset-like equations for the bubble dynamics as forced by the local or mixture-averaged pressure, respectively. An acoustically excited dilute bubble screen is used as a case study for comparisons. We show that observables of ensemble- and volume-averaged simulations match closely and that their convergence is first order under grid refinement. Guidelines are established for phase-averaged simulations by comparing the computational costs of methods. The primary costs are shown to be associated with stochastic closure; polydisperse ensemble-averaging requires many samples of the underlying PDF and volume-averaging requires repeated, randomized simulations to accurately represent a homogeneous bubble population. The relative sensitivities of these costs to spatial resolution and bubble void fraction are presented.

Carsten Thomassen and I proved that in any graph G , the number of cycles containing a specified edge as well as all the vertices of odd degree is odd if and only if G is eulerian. Where all vertices have even degree this is a theorem of Shunichi Toida and where all vertices have odd degree it is Andrew Thomason’s extension of Smith’s Theorem. Our proof was not algorithmic. In this paper, I extend Thomason’s algorithm to one which, in a non-eulerian graph, finds a second cycle containing a specified edge and all the odd-degree vertices. Kenneth Berman extended Thomason’s Theorem to spanning trees: he proved that if T is a spanning tree such that the degree of every vertex in G − E ( T ) is odd, then there is an even number of spanning trees of G with the same degree as T at each vertex. In this paper, I give a common generalization of all of these theorems to a parity theorem about “good” trees in general graphs. My proof provides an algorithm for finding a second “good” tree.

Background: The control and manipulation of the hydrodynamics of droplets primarily relate to flow governing and geometrical parameters. This study has explored the influences of capillary number ( 10 − 4 ≤ C a c ≤ 1 ) and flow rate ratio ( 0.1 ≤ Q r ≤ 10 ) on the hydrodynamics of droplet generation in two-phase flow through T-junction cross-flow microfluidic device. Methods: The finite element method is used to solve the Eulerian framework of a mathematical model based on mass continuity, Navier-Stokes, and conservative level set equations at fixed flow ( R e c = 0.1 ). Significant findings: Results are presented in terms of the instantaneous phase flow field, droplet size, droplet detachment time, and generation frequency as a function of governing parameters ( C a c and Q r ). The flow regimes namely squeezing, first transition, dripping, second transition, parallel, and jet flow are marked. In contrast to reported value of threshold C a c ≈ 10 − 2 , squeezing regime exists for all C a c and 2 ≤ Q r ≤ 10 . The flow regimes are also mapped into droplets and non-droplet zones by using threshold C a r which scales quadratically with Q r . The droplet length varies linearly with Q r in the squeezing regime. Both droplet size and frequency show the power-law relations with C a c and Q r in the droplet zone. Finally, predictive correlations are presented to guide the engineering and design of droplet microfluidics devices.

Total Lagrangian - Smoothed Particle Hydrodynamics (TL-SPH) is a classical algorithm to improve the tensile instability encountered in the conventional Eulerian kernel-based SPH method for solid mechanics. Meanwhile, the gradient correction usually is employed in TL-SPH to enhance the consistency of approximation, which would generate unavoidable time costs. Therefore, a simplified gradient correction under the initial configuration is derived. Aiming at different particle configurations, the corresponding selection modes are provided and verified. Then the simplified gradient correction is introduced into TL-SPH, which is the Improved TL-SPH (ITL-SPH) method. Firstly, a classical example – elastic rubber collision is simulated to verify ITL-SPH has the same ability as TL-SPH to improve tensile instability. Then, the convergence and high efficiency of ITL-SPH is demonstrated via the uniaxial tension of a plate. Moreover, the plate with square and triangle holes also is simulated to show the adaptation and stability of ITL-SPH for the extreme boundary. Under the Total Lagrangian frame, the treatment to model the crack is necessary. So, this paper proposes a damage model and combines it with the ITL-SPH method for crack initiation and propagation, which is verified by the plate with holes and the notched beam examples.

The application of the Eulerian based computational solid mechanic (CSM) models in numerical modeling of friction stir welding (FSW) is not deeply studied, because implementing a complicated friction model in an Eulerian based CSM model is challenging. To overcome this, the literature used Eulerian based computational fluid dynamics (CFD) models. On the other hand, due to the usage of finite element methods (FEMs) instead of finite volume methods (FVMs), the accuracy of CSM is higher than CFD. In this paper, for the first time, a modified friction model is implemented in an Eulerian based CSM model. To investigate the influence of the friction model on the stress, material flow, equivalent plastic strain and temperature, a comparison between the modified friction model and the Coulomb friction model is done. Developing the modified friction model results in achieving four phases for the relationship between the relative velocity and ratio between the shear stress and pressure. The comparisons of FE models show that, the modified friction model has been successful in simulating the partial sliding/sticking condition, because of achieving a uniform pattern for the stress with the maximum values of 150 MPa. Moreover, a successful prediction the material flow, heat flux, equivalent plastic strain and temperature is also obtained. Maximum values of the equivalent plastic strain is found to be 14. A “M” shape form, shifted to the advancing side with the peak temperature of 413 °C (5 mm far from the welding center) is also found. Finally, the results of the model in which the modified friction model is employed are found to be in correlation with experiments and the literature.

Eulerian computational fluid dynamics (CFD) models that can predict bubbling behavior accurately are important to predict solids mixing, transport processes, and reactions in fluidized beds. In the...

Accretion and ablation, i.e., the addition and removal of mass at the surface, are important in a wide range of physical processes, including solidification, growth of biological tissues, environmental processes, and additive manufacturing. The description of accretion requires the addition of new continuum particles to the body, and is therefore challenging for standard continuum formulations for solids that require a reference configuration. Recent work has proposed an Eulerian approach to this problem, enabling side-stepping of the issue of constructing the reference configuration. However, this raises the complementary challenge of determining the stress response of the solid, which typically requires the deformation gradient that is not immediately available in the Eulerian formulation. To resolve this, the approach introduced the elastic deformation as an additional kinematic descriptor of the added material, and its evolution has been shown to be governed by a transport equation. In this work, the method of characteristics is applied to solve concrete simplified problems motivated by biomechanics and manufacturing. Specifically, (1) for a problem with both ablation and accretion in a fixed domain and (2) for a problem with a time-varying domain, the closed-form solution is obtained in the Eulerian framework using the method of characteristics without explicit construction of the reference configuration.

Gas-particle flows in circulating fluidized beds (CFB) with wide particle size distributions were simulated using the Eulerian-Eulerian approach to analyze the effects of the particle phase division and the applicability of the particle-particle drag model. The results indicate that the simulation is not accurate by just using a single average particle diameter when the particle size distribution includes a critical particle diameter. A binary particle phase division criterion was then developed to establish two particle phases representing two types of particles with different flow patterns. Coupling the Eulerian-Eulerian approach with the new criterion enabled accurate predictions of the pressures, particle volume fractions, and particle mass circulation rates that were in agreement with experimental data. The influences of different particle-particle drag models were also investigated to show that the simulation using the Syamlal model was not accurate due to the overestimated particle-particle drag, while the results without particle-particle drag and with the Manger model were similar and much more accurate. Moreover, the flow mechanism for the non-uniformity of particle circulation rates in the parallel circulating loops of the CFB boiler was revealed. This study improves the Eulerian-Eulerian simulations of fluidization with wide particle size distributions and further deepens the understanding of flow characteristics in CFB.

The motion of a body can be expressed relative to the present configuration of the body, known as the relative motion description, besides the classical Lagrangian and the Eulerian descriptions. When the time increment from the present state is small enough, the nonlinear constitutive equations can be linearized relative to the present state so that the resulting system of boundary value problems becomes linear. This formulation is based on the well-known ``small-on-large'' idea, and can be implemented for solving problems with large deformation in successive incremental manner. In fact, the proposed method is a process of repeated applications of the well-known “small deformation superposed on finite deformation” in the literature. This article presents these ideas applied to thermoelastic materials with a brief comment on the exploitation of entropy principle in general. Some applications of such a formulation in numerical simulations are briefly reviewed and a numerical result is shown.

‘Long-duration’ blast waves can exert damaging drag loads on finite structural columns that are complex to characterise. In the absence of suitable drag coefficients, computational fluid dynamics c...

In this study, a Eulerian Wall Film (EWF) model and a discrete phase model (DPM) are applied to simulate the phenomenon of droplet re-entrainment in a baffle demister. The primary objective was to ...

This paper aims to present several approaches for fluid–solid coupling applied in landslide river blocking simulations based on the Abaqus software. These approaches include the coupled Eulerian Lagrangian (CEL) model and the finite element method-smoothed particle hydrodynamics (FEM-SPH) model, which use discrete finite element meshed blocks to simulate landslides, and use continuum models of Eulerian material and SPH material for river simulations, respectively. Another approach is to use the Eulerian model with Eulerian material to simulate landslides and river at the same time. A physical model of an elastic plate subjected to time-dependent water pressure was applied to validate the selected methods in the fluid–solid coupling. The process was recorded and corresponding numerical simulations were performed. The results show that the simulated plate and water behavior is consistent with the physical model in all simulations. Afterwards, the methods were applied to a real-scale rock avalanche river blocking simulation and the processes of sliding mass movement, impulse wave behavior, and the formation of landslide dams were described and analyzed. Applied Eulerian materials and discrete finite element meshed blocks were used to simulate the sliding mass and similar sliding movement characteristics were obtained. However, discrete blocks have shown better potential for simulating more complex situations and processes leading to better mass movement and deposition results. In addition, discrete finite element meshed blocks and other similar discontinuum models can better reflect the structural characteristics of the source rock in the simulation. As for the impulse wave, the use of Eulerian model for simulating the sliding mass will lead to an abnormally high wave height. Whether to consider a water effect and how to consider it affect the shape of the landslide dams and the simulation results show the importance of fluid–solid coupling in the landslide river blocking simulation. Similar and accurate results can be obtained using the Eulerian method and the SPH method for water simulation. However, it is worth noting that the existence of the Eulerian boundary makes the Eulerian method a better option for simulating more complex flow conditions compared to the SPH method. The meshless characteristics of the SPH method make it more computational efficient provided the fluid volume is constant and the final scale of the model is uncertain.

The main aim of this research is to simulate a compression test of semi-solid A380 aluminium alloy in numerical software. In order to achieve a more realistic model, 2D image-based modelling is used. The first step of this method is to obtain appropriate microstructural images. As the semi-solid material consists of non-dendritic solid phase and liquid channels, ECAP tool is used to apply a high plastic strain to casted samples. In order to observe desirable (non-dendritic) microstructure, microstructure image is taken from water quench ECAPed sample heated at semi-solid range. After the binarizing image data, the data are imported to appropriate software. A coupled Eulerian–Lagrangian (CEL) approach is used to obtain macro-scale mechanical behaviour. This approach is used to take advantages of both main formulations: Eulerian formulation and Lagrangian formulation. In CEL approach, material moves through an Eulerian mesh that is fixed in space while Lagrangian mesh is attached to the material points and is used to set boundary conditions. The simulations results show a strong dependence of mechanical behaviour on strain rate. This informations can be used for prediction of semi-solid forming, as well.

In this paper, smoothed bond-based peridynamics (SBBPD) is proposed to simulate the large deformation. The governing equation of smoothed bond-based PD is obtained by incorporating the observed changes in the density field and long-range force reaction in Eulerian form. The Hencky stretch is introduced into smoothed bond-based PD to calculate the true strain because of the change in density (volume). The proposed method can achieve a more accurate result in solid mechanics compared with SPH and can well handle extremely large deformation problems compared with traditional bond-based PD. Numerical experiments are launched to test these modifies of smoothed bond-based PD method in solid mechanics.

Let be a commutative ring with unity. The essential ideal graph of , denoted by , is a graph with vertex set consisting of all nonzero proper ideals of A and two vertices and are adjacent whenever is an essential ideal. An essential ideal of a ring is an ideal of ( ), having nonzero intersection with every other ideal of . The set contains all the maximal ideals of . The Jacobson radical of , , is the set of intersection of all maximal ideals of . The comaximal ideal graph of , denoted by , is a simple graph with vertices as proper ideals of A not contained in and the vertices and are associated with an edge whenever . In this paper, we study the structural properties of the graph by using the ring theoretic concepts. We obtain a characterization for to be isomorphic to the comaximal ideal graph . Moreover, we derive the structure theorem of and determine graph parameters like clique number, chromatic number and independence number. Also, we characterize the perfectness of and determine the values of for which is split and claw-free, Eulerian and Hamiltonian. In addition, we show that the finite essential ideal graph of any non-local ring is isomorphic to for some .

Erosion occurs in many industrial processes which results in economic losses and environmental issues. Having a more confident prediction method has always been the goal of the erosion community. Numerous studies have investigated erosion prediction utilizing Computational Fluid Dynamics (CFD) and many have obtained seemingly good agreement with experimental data. However, the uncertainties resulting from the grid size on erosion representation has not been investigated thoroughly. In this paper, one-way coupled discrete phase and Eulerian flow models are utilized to examine the effect of cell size on erosion calculated by CFD. It is found that both erosion pattern and magnitude can be easily affected by the grid size. Thus, an appropriate cell size range used to represent local erosion magnitude and the full erosion profile is proposed. The study provides guidelines for engineers to predict erosion in gas pipelines and quantify the uncertainties in a more deterministic fashion.

High-accuracy numerical algorithms are proposed and justified for the simulation of cold plasma oscillations in both nonrelativistic and relativistic cases. A specific feature of the given approach is that Lagrangian variables are used for the approximate solution of the problem formulated in Eulerian variables. The main results are stated as convergence theorems for the proposed algorithms with respect to small discretization parameters of independent Eulerian variables. The theoretical results are illustrated by numerical experiments. Specifically, the breaking of plasma oscillations is modeled and this effect is confirmed to have the form of a gradient catastrophe.

In this work, the cluster dynamics in the riser of a pilot-scale circulating fluidized bed with the presence of wide particle size distribution (PSD) are numerically simulated via the multiphase particle-in-cell (MP-PIC) approach. Specifically, the gas and solid motions are tracked in the Eulerian and Lagrangian frameworks, respectively. The gas-solid numerical model is firstly validated with the experimental data. Then, the spatial distribution of particle clusters together with the cluster dynamics (velocity, length, aspect ratio) in the bed operating with different parameters are explored. The results demonstrate the ability of the MP-PIC model on predicting the important features of the cluster in the riser. Clusters mainly distribute in the lower part of the riser. The closer of the cluster to the riser wall, the larger vertical length, and larger aspect ratio appear. Moreover, the presence of riser outlet and solid inlet slightly affects the spatial distribution, the size and aspect ratio of clusters in the riser. The superficial gas velocity has an obvious impact on the cluster volume and the cluster vertical length, while the PSD width significantly affects the horizontal length and the aspect ratio. The results obtained in this work provide meaningful insights regarding the cluster dynamics in the riser, which will be beneficial to the deep understanding of this specific structure in the practical operation.

A 2-edge-coloured graph G is supereulerian if G contains a spanning closed trail in which the edges alternate in colours. We show that for general 2-edge-coloured graphs it is NP-complete to decide whether the graph is supereulerian. An eulerian factor of a 2-edge-coloured graph is a collection of vertex-disjoint induced subgraphs which cover all the vertices of G such that each of these subgraphs is supereulerian. We give a polynomial algorithm to test whether a 2-edge-coloured graph has an eulerian factor and to produce one when it exists. A 2-edge-coloured graph is (trail-)colour-connected if it contains a pair of alternating (u, v)-paths ((u, v)-trails) whose union is an alternating closed walk for every pair of distinct vertices u, v. We prove that a 2-edge-coloured complete bipartite graph is supereulerian if and only if it is colour-connected and has an eulerian factor. A 2-edge-coloured graph is M-closed if xz is an edge of G whenever some vertex u is joined to both x and z by edges of the same colour. M-closed 2-edge-coloured graphs, introduced in Contreras-Balbuena et al. (Discret Math Theoret Comput Sci 21:1, 2019), form a rich generalization of 2-edge-coloured complete graphs. We show that if G is obtained from an M-closed 2-edge-coloured graph H by substituting independent sets for the vertices of H, then G is supereulerian if and only if G is trail-colour-connected and has an eulerian factor. Finally we discuss 2-edge-coloured complete multipartite graphs and show that such a graph may not be supereulerian even if it is trail-colour-connected and has an eulerian factor.

The present work deals with the numerical prediction of the particle flow within a three-way nozzle in Laser Metal Deposition (LMD) technology adopted during additive manufacturing processes. In particular, the paper focuses on CFD (Computational Fluid Dynamics) simulations of the particle flow problem, regarding the coupling between a fluid phase, i.e., the carrier gas, and a solid phase, i.e., a metallic material powder that is delivered through the nozzle of the LMD machine. Two different numerical approaches are investigated, both implemented in a in-house code using OpenFOAM open source C++ toolbox. The former is based on a mixed formulation, combining an Eulerian description of the carrier gas flow with a Lagrangian description of the particle flow. The latter on a pure Eulerian formulation of both carrier gas and particles. In agreement with the experimental evidences, the present work compares the two approaches in terms of capability of simulating some key physical features of the LMD process, i.e., the geometrical properties of the powder cone formed out from the nozzle.

The well-known Lighthill–Whitham–Richards (LWR) theory is the fundamental pillar for most macroscopic traffic models. In the past, many methods were developed to numerically derive solutions for LWR problems. Examples for such numerical solution schemes are the cell transmission model, the link transmission model, and the variational theory (VT) of traffic flow. So far, the eulerian formulation of VT found applications in the fields of traffic modelling, macroscopic fundamental diagram estimation, multi-modal traffic analyses, and data fusion. However, these studies apply VT only at the link or corridor level. To the best of our knowledge, there is no methodology yet to apply VT at the network level. We address this gap by developing a VT-based framework applicable to networks. Our model allows us to account for source terms (e.g. inflows and outflows at intersections) and the propagation of spillbacks between adjacent corridors consistent with kinematic wave theory (KWT). We show that the trajectories extracted from a microscopic simulation fit the predicted traffic states from our model for a simple intersection with both source terms and spillbacks. We also use this simple example to illustrate the accuracy of the proposed model, and the ability to model complex bottlenecks. Additionally, we apply our model to the Sioux Falls network and again compare the results to those from a microscopic KWT simulation. Our results indicate a close fit of traffic states, but with substantially lower computational cost. The developed methodology is useful for extending existing VT applications to the network level, for network-wide traffic state estimations in real-time, or other applications within a model-based optimization framework.

A numerical scheme to perform data assimilation of concentration measurements in Lagrangian models is presented, along with its first implementation called Ocean Plastic Assimilator, which aims to improve predictions of the distributions of plastics over the oceans. This scheme uses an ensemble method over a set of particle dispersion simulations. At each step, concentration observations are assimilated across the ensemble members by switching back and forth between Eulerian and Lagrangian representations. We design two experiments to assess the scheme efficacy and efficiency when assimilating simulated data in a simple double-gyre model. Analysis convergence is observed with higher accuracy when lowering observation variance or using a circulation model closer to the real circulation. Results show that the distribution of the mass of plastics in an area can effectively be improved with this simple assimilation scheme. Direct application to a real ocean dispersion model of the Great Pacific Garbage Patch is presented with simulated observations, which gives similarly encouraging results. Thus, this method is considered a suitable candidate for creating a tool to assimilate plastic concentration observations in real-world applications to estimate and forecast plastic distributions in the oceans. Finally, several improvements that could further enhance the method efficiency are identified.

In this paper, we are concerned with the Riemann problem for the generalized pressureless Euler equations with a composite source term, which covers the important Eulerian droplet model associated ...

The alternating descent statistic on permutations was introduced by Chebikin as a variant of the descent statistic. We show that the alternating descent polynomials on permutations, called alternating Eulerian polynomials, are unimodal via a five-term recurrence relation. We also find a quadratic recursion for the alternating major index q-analog of the alternating Eulerian polynomials. As an interesting application of this quadratic recursion, we show that $$(1+q)^{\lfloor n/2\rfloor }$$ divides $$\sum _{\pi \in {{\mathfrak {S}}}_n}q^{\mathrm{altmaj}(\pi )}$$ , where $${{\mathfrak {S}}}_n$$ is the set of all permutations of $$\{1,2,\ldots ,n\}$$ and $$\mathrm{altmaj}(\pi )$$ is the alternating major index of $$\pi $$ . This leads us to discover a q-analog of $$n!=2^{\ell }m$$ , m odd, using the statistic of alternating major index. Moreover, we study the $$\gamma $$ -vectors of the alternating Eulerian polynomials by using these two recursions and the cd-index. Further intriguing conjectures are formulated, which indicate that the alternating descent statistic deserves more work.

Parabolic trough solar collector (PTSC) is an effective solar harvesting system that can be combined to various systems with different working fluids. This research presents a novel investigation o...

One of the most widely used components in industrial rotary machines is the plain journal bearings. These components consist of a rotating shaft, which is separated from the outer sheath by a thin layer of lubricant and rotated in it. In this research, the journal bearings are investigated numerically in three dimensions using ANSYS-FLUENT software. To have a more realistic analysis, the cavitation, which is a common event in bearings, is simulated. The Eulerian two-phase model along with Zwart–Gerber–Belarmi method is used to simulate the cavitation phenomena. In addition, the changes in fluid viscosity due to the temperature and pressure have been considered in calculations. Moreover, the effect of the viscous dissipation term is considered that leads to a change in fluid temperature. Simulations are conducted for two angular velocities of 48 and 68 [rad/s] as well as two eccentricity ratios of 0.6 and 0.8. The comparison of the results with other numerical and experimental data shows the accuracy of the two-phase model and conducted settings in the software. The results show that the consideration of cavitation along with the viscosity changes have a significant impact on the pressure distribution, cavity volume, and load-bearing capacity.

Combinatorial techniques are outlined through generalization Sheehan’s version of Pόlya’s theorem extended to all irreducible representations of the dihedral point group aimed at applications to na...

Multiple identical paths are usually connected to form circulating loops in many industrial reactors including chemical looping combustion (CLC), however the flow pattern may be highly nonuniform in these identical paths, compromising the stable operation. In this study, by using the Eulerian multifluid model, the nonuniformity in a CLC apparatus is studied. First, the symmetry of computational domain is verified by simulation and the model setting is validated by experimental data. Then the typical nonuniformity phenomenon is discussed and evaluated in terms of bed inventory evolution and gas-solid distribution in symmetrical parts. The effects of key operating parameters including total bed inventory, gas aeration rate, and wall roughness on nonuniformity degree are then studied. The simulating results show that the nonuniformity degree between the two symmetrical parts increases with the increase of total bed inventory and gas aeration rate and this trend will be intensified in the predictable short-term future. And through the analysis of pressure fluctuation, the instability of the system is aggravated. However, wall roughness shows an indefinite influence and tendency. This work provides an insightful understanding of nonuniformity and will help further optimise symmetrical CLC systems.