Large Space Scales Research Articles

A class of germs arising from homogenization in traffic flow on junctions

We consider traffic flows described by conservation laws. We mainly study a 2:1 junction (with two incoming roads and one outgoing road). At the mesoscopic level, the priority law at the junction is given by traffic lights, which are periodic in time; the traffic can also be slowed down by periodic in time flux-limiters. Looking at long-time behavior and on large space scale, we intuitively expect an effective junction condition to emerge, thus deriving a macroscopic model from the mesoscopic one. At the limit of the rescaling, we show rigorous homogenization of the problem and identify the effective junction condition, which belongs to a general class of germs (in the terminology of [B. Andreianov, K. H. Karlsen and N. H. Risebro, A theory of [Formula: see text]-dissipative solvers for scalar conservation laws with discontinuous flux, Arch. Ration. Mech. Anal. 201 (2011) 27–86; U. S. Fjordholm, M. Musch and N. H. Risebro, Well-posedness and convergence of a finite volume method for conservation laws on networks, SIAM J. Numer. Anal. 60(2) (2022) 606–630; M. Musch, U. S. Fjordholm and N. H. Risebro, Well-posedness theory for nonlinear scalar conservation laws on networks, Netw. Heterog. Media 17 (2022) 101–128]). The proof of homogenization requires two steps: our first key result is the identification of this germ and of a characteristic subgerm which determines the whole germ. The second key result is the construction of a family of correctors whose values at infinity are related to each element of the characteristic subgerm. This construction is indeed explicit at the level of some mixed Hamilton–Jacobi equations for concave Hamiltonians (i.e. fluxes). The solutions are found in the spirit of representation formulas for optimal control problems.

Isotope diffusive exchange experiments for deriving porewater isotope composition in low-permeability rocks – Improvements in experimental procedure and data processing

Over the last decades, several methods have been developed for determining the porewater stable isotope composition (δ2H, δ18O) in low-permeability, argillaceous rocks and pertinent to the acquisition of spatially highly-resolved tracer profiles for investigating subsurface transport processes over large scales of time and space. One of these methods is the so-called isotope diffusive exchange technique (IDE) where the porewater of the rock equilibrates via the vapour phase with a test water of known isotope composition. In this study we aim for 1) identifying and assessing important parameters and artefacts these experiments are sensitive and prone to, respectively, 2) evaluating their impact on the porewater isotope composition derived from such experiments and 3) testing the reproducibility and accuracy of the method. For this, the experimental data and the calculated porewater isotope composition of 752 isotope diffusive exchange experiments, performed on drillcore samples from variable lithologies, were examined under these aspects. The investigations are complemented by comparison between porewater and groundwater isotope values in regions of water-conducting zones and an interlaboratory comparison. Ultimately, this allowed defining a stringent procedure for the evaluation of the experimental data and classifying experiments as ‘reliable’, less reliable’ and ‘failed’. For calculating the porewater isotope composition, a new approach was developed that accounts for sample-scale heterogeneity of the water content. This procedure of data evaluation and processing resulted in smooth isotope profiles with only little scatter across largely different lithologies. The interlaboratory comparison attests the method a very good reproducibility. The comparison with groundwater isotope data reveals slightly enriched δ18O and δ2H signatures by 0.3–0.6 and 1.7–2.7‰ VSMOW, respectively, for some samples investigated by the IDE method. No stringent explanation exists at this stage for these differences, but it must be emphasized that these deviations are small compared to the typical natural variations observed in profiles of these tracers. This demonstrates that porewater isotope data obtained by the IDE method represent the conditions in the in situ porewater reasonably well when strictly following the proposed procedures of the experimental setup, the evaluation of experimental data and the calculation of porewater isotope compositions.

Experimental investigation on spray and flame characteristics of a marine diesel engine with single and double injection

Multiple injection is one of the advanced technologies employed in modern diesel engines to improve combustion efficiency, reduce pollutant emissions, and minimize combustion noise. The application of multiple injection in marine diesel engines differs from its use in vehicles or heavy-duty engines, as it is not commonly combined with Exhaust Gas Recirculation (EGR). However, there is a scarcity of studies specifically examining the combustion characteristics of medium-speed marine diesel engines utilizing multiple injection. Given the large space scale of marine diesel engine, a constant volume chamber with a visible diameter of 240 mm was used, and an injector with a nozzle diameter of 0.465 mm was employed in the experiment. The spray development and combustion process were recorded by Mie-scattering and flame natural luminosity imaging respectively. Both conventional and double injection combustion processes were analyzed in detail. The results show that although the liquid phase spray does not fully penetrate to the cylinder wall in marine diesel engines, the flame penetrates to the cylinder wall rapidly, the flame burns near the wall almost throughout the entire combustion duration. The combustion characteristics of the double injection are significantly different, the flame propagation speed of the pilot and main injection fuel is one-third to one-half of that of a single injection with a long duration. For single injection spray with long injection duration, the flame penetration velocity is determined by the sequential ignition velocity of the fuel. While the flame penetration velocity for sprays with short injection duration mainly depends on the jet penetration velocity. The investigation on the impact of dwell time, fuel distribution, and injection pressure on the combustion process of double injection also provides valuable insights for optimizing multiple injection strategies.

A Graphic Processing Unit–High-Order Spectral (GPU-HOS) Numerical Wave Tank for the Simulation of Directional Wave Field Evolution over a Long Time

Existing numerical models for direct simulations of stochastically directional waves are limited by their computational burden, and only a few of them can be applied to modeling directional waves on account of nonlinear evolutions on large time scales. In response to these drawbacks, this paper proposes a modified rectangular numerical wave tank based on the high-order spectral (HOS) method. Three main arrangements are responsible for the model improvement. Firstly, the relaxation technique is applied on the four sides of the tank for generating and attenuating waves, with an enhancement in the total computational efforts required of less than 5% being achieved. Secondly, for this paper, the HOS method for solving the nonlinear evolution of waves was modified to a GPU-speedup version for the first time, and the speedup increases dramatically (up to 16-fold) when the grid number is O(106). Thirdly, the higher-order Runge–Kutta method with order 8 is adopted for the purpose of suppressing cumulative temporal errors. Furthermore, several numerical results are presented for the validation of the model. With our modified numerical wave tank, the nonlinear evolutions of random directional waves can be efficiently studied over a large time and space scale.

Accelerating Thermal Simulations in Additive Manufacturing by Training Physics-Informed Neural Networks With Randomly Synthesized Data

Abstract The temperature history of an additively manufactured part plays a critical role in determining process–structure–property relationships in fusion-based additive manufacturing (AM) processes. Therefore, fast thermal simulation methods are needed for a variety of AM tasks, from temperature history prediction for part design and process planning to in situ temperature monitoring and control during manufacturing. However, conventional numerical simulation methods fall short in satisfying the strict requirements of time efficiency in these applications due to the large space and time scales of the required multiscale simulation. While data-driven surrogate models are of interest for their rapid computation capabilities, the performance of these models relies on the size and quality of the training data, which is often prohibitively expensive to create. Physics-informed neural networks (PINNs) mitigate the need for large datasets by imposing physical principles during the training process. This work investigates the use of a PINN to predict the time-varying temperature distribution in a part during manufacturing with laser powder bed fusion (L-PBF). Notably, the use of the PINN in this study enables the model to be trained solely on randomly synthesized data. These training data are both inexpensive to obtain, and the presence of stochasticity in the dataset improves the generalizability of the trained model. Results show that the PINN model achieves higher accuracy than a comparable artificial neural network trained on labeled data. Further, the PINN model trained in this work maintains high accuracy in predicting temperature for laser path scanning strategies unseen in the training data.

Emergence of Hydrodynamic Spatial Long-Range Correlations in Nonequilibrium Many-Body Systems.

At large scales of space and time, the nonequilibrium dynamics of local observables in extensive many-body systems is well described by hydrodynamics. At the Euler scale, one assumes that each mesoscopic region independently reaches a state of maximal entropy under the constraints given by the available conservation laws. Away from phase transitions, maximal entropy states show exponential correlation decay, and independence of fluid cells might be assumed to subsist during the course of time evolution. We show that this picture is incorrect: under ballistic scaling, regions separated by macroscopic distances "develop long-range correlations as time passes." These correlations take a universal form that only depends on the Euler hydrodynamics of the model. They are rooted in the large-scale motion of interacting fluid modes and are the dominant long-range correlations developing in time from long-wavelength, entropy-maximized states. They require "the presence of interaction" and "at least two different fluid modes" and are of a fundamentally different nature from well-known long-range correlations occurring from diffusive spreading or from quasiparticle excitations produced in far-from-equilibrium quenches. We provide a universal theoretical framework to exactly evaluate them, an adaptation of the macroscopic fluctuation theory to the Euler scale. We verify our exact predictions in the hard-rod gas, by comparing with numerical simulations and finding excellent agreement.

Figuring Out Gas & Galaxies in Enzo (FOGGIE). VI. The Circumgalactic Medium of L ∗ Galaxies Is Supported in an Emergent, Nonhydrostatic Equilibrium

The circumgalactic medium (CGM) is often assumed to exist in or near hydrostatic equilibrium, with the regulation of accretion and the effects of feedback treated as perturbations to a stable balance between gravity and thermal pressure. We investigate global hydrostatic equilibrium in the CGM using four highly resolved L * galaxies from the Figuring Out Gas & Galaxies in Enzo (FOGGIE) project. The FOGGIE simulations were specifically targeted at fine spatial and mass resolution in the CGM (Δx ≲ 1 kpc h −1 and M ≃ 200M ⊙). We develop a new analysis framework that calculates the forces provided by thermal pressure gradients, turbulent pressure gradients, ram pressure gradients of large-scale radial bulk flows, centrifugal rotation, and gravity acting on the gas in the CGM. Thermal and turbulent pressure gradients vary strongly on scales of ≲5 kpc throughout the CGM. Thermal pressure gradients provide the main supporting force only beyond ∼0.25R 200, or ∼50 kpc at z = 0. Within ∼0.25R 200, turbulent pressure gradients and rotational support provide stronger forces than thermal pressure. More generally, we find that global equilibrium models are neither appropriate nor predictive for the small scales probed by absorption line observations of the CGM. Local conditions generally cannot be derived by assuming a global equilibrium, but an emergent global equilibrium balancing radially inward and outward forces is obtained when averaging over the nonequilibrium local conditions on large scales in space and time. Approximate hydrostatic equilibrium holds only at large distances from galaxies, even when averaging out small-scale variations.

Continuous mapping of aboveground biomass using Landsat time series

Aboveground biomass (AGB) is an essential variable in the study of the carbon cycle, and remote sensing provides the only viable means for mapping and monitoring biomass at large scales in time and space. Still, inconsistencies in biomass estimates are large which necessitates methods to achieve consistent mapping of biomass over time and space. In this study, we combine Lidar-derived biomass-estimates from GLAS measurements, time series analysis of 20 years of Landsat data, and machine learning algorithms to map biomass for a study area in the Amazon basin. The results show that we are able to map AGB consistently over space and time at annual intervals between 1999 and 2019, with a root-mean-square error (RMSE) of 64 to 92 Mg AGB ha−1 (depending on the evaluation methodology used) for the best performing models, with AGB estimates ranging between 0 to 600 Mg AGB ha−1. Models run with the Extreme gradient boosting (XGBoost) resulted in the lowest errors. The presented methodological approach makes it possible to map biomass over time in large areas with wide biomass ranges, and without saturation below 400 Mg AGB ha−1.

Scaling‐up the biodiversity–ecosystem functioning relationship: the effect of environmental heterogeneity on transgressive overyielding

Knowledge of how biodiversity sustains ecosystem function comes predominantly from studies focused on small spatial scales. Thus, we know relatively little about the role of biodiversity at larger scales of space and time where habitats become increasingly heterogeneous. Efforts to upscale the relationship between biodiversity and function have yielded inconclusive results. Given that increasing habitat heterogeneity is a ubiquitous consequence of increasing spatial scale, we asked: as habitat heterogeneity increases, can single species continue to maintain ecosystem function? Or, does transgressive overyielding (functioning of species mixture divided by the functioning of the highest functioning single species) change with habitat heterogeneity? We addressed this using a combination of computer simulations, an experiment and a meta‐analysis. The three parts followed the same rationale: habitat heterogeneity was increased by aggregating local habitats with different conditions into larger and more heterogeneous landscapes. The computer simulations showed that, on average, transgressive overyielding increased with habitat heterogeneity because monoculture functioning decreased with habitat heterogeneity. We tested this expectation experimentally by varying the strain richness from one to five species across 10800 bacterial communities in five different habitats defined by sub‐inhibitory concentrations of antibiotics. On average, the experimental results concurred with the simulations. We tested the generality of this result using a meta‐analysis of 26 published experiments that manipulated habitat conditions and species richness. This confirmed that transgressive overyielding tended to increase with habitat heterogeneity but only when species were specialised to different habitats and were not inhibited in mixtures by negative species interactions. This was not the case in several experiments used in our meta‐analysis where one species maximised functioning across all habitats, contrary to the assumptions of many ecological models. Our results illustrate the importance of biodiversity at larger spatial scales with more heterogeneity but also highlights contingencies that this pattern depends on.

Modelling site response at regional scale for the 2020 European Seismic Risk Model (ESRM20)

Quantitative estimation of seismic risk over a region requires both an underlying probabilistic seismic hazard model and a means to characterise shallow site response over a large scale. The 2020 European Seismic Risk Model (ESRM20) builds on the 2020 European Seismic Hazard Model (ESHM20), requiring additional information to firstly parameterise the local site condition across all of Europe, and subsequently determine its influence on the prediction of seismic ground motion. Initially, a harmonised digital geological database for Europe is compiled, alongside a model of topographic/bathymetric elevation and a database of 30 m averaged shearwave velocity measurements (V_{S30}), in order to produce separate 30 arc-second maps of inferred V_{S30} based on topography and on geology. We then capitalise on a large database of seismic recording stations in Europe for which site-to-site ground motion residuals (delta S2S_{S}) have been determined with respect to the shallow crustal ground motion model used in the ESHM20. These residuals allow us to incorporate site amplification functions into the European GMM calibrated upon either observed or inferred V_{S30}, or on the European geology and topography models. We present the resulting pan-European seismic site amplification model and assess its impact on seismic hazard and risk compared against other approaches. The new site amplification model fulfils the requirements of the ESRM20 and, providing uncertainty is fully propagated, yields estimates of seismic hazard and risk at a large space scale that may be comparable to other methods often applied at local/urban scale where better-constrained site information is available.

Uncertainty and sensitivity analysis of radionuclide migration through fractured granite aquifer

The radionuclide migration in the high-level radioactive waste (HLW) disposal is usually predicted by numerical simulations for risk analysis of radionuclide contamination in a large scale of time and space. However, the uncertainties in radionuclide migration models and their associated parameters significantly affect the simulation results. In the present study, we first selected certain parameters and output data as independent parameters and risk metrics and performed a series of radionuclide transport models at a research site in Northwestern China. The models considered radionuclide migration in the equivalent porous medium with the mechanism of nuclide decay in an arbitrary-length decay chain, adsorption, advection, diffusion, and dispersion. Then 3000 Monte Carlo (MC) simulations were performed to carry out a set of uncertainty and global sensitivity analysis by coupling an uncertainty quantification tool with a radionuclide migration simulator. The results indicated that both hydraulic gradient and hydraulic conductivity significantly influenced the risk metrics. Thus, it is critical to obtain hydraulic gradient and hydraulic conductivity data under the same economic conditions. We applied the multivariate adaptive regression spline (MARS) method to generate response surface models representing the relationships among independent parameters and risk metrics. Calculations of the risk metric distribution ranges revealed that the peak release doses would appear at 0.40 and 0.79 million years, and their values will be in the range of 4.7 × 10−7–1.93 × 10−6 Sv/a. Uncertainty and sensitivity analysis results of radionuclide contamination in the fractured granite upon which HLW is disposed can improve simulation and prediction accuracy for radionuclide migration.

Mapping the most heavily reclaimed shorelines of the Yangtze River delta urban agglomerations

Objectively understanding the characteristics and evolution of coastal geomorphology, and predicting the growth potential of intertidal flats are the prerequisites for the effective conservation and development of shoreline resources. However, the vulnerability of shorelines in the long term and large space scale needs to be assessed since human intervention in recent decades has intensified the double oppression of river delta system transformation and land reclamation. The Yangtze River Delta Urban Agglomerations (YRDUA) is a highly developed global economy, therefore, the YRDUA with the most intense reclamation, and their dynamic shoreline changes before and after the sharply decreasing sediment supply were detected based on 4,596 remote sensing images and corresponding hydrodynamic data. We found that the sediment replenishment from the radial sand ridges on the middle Jiangsu Coast made the shoreline expansion rate reach 4–5 times that of other Jiangsu coasts. Specifically, a close correlation between the shoreline accretion rate and the amount of sediment supply was found on the eastern Chongming Wetland. Generally, there were still sufficient sediments on the Yangtze River Estuary and Hangzhou Bay interface to support the shoreline expansion despite the upstream sediment reduction. The longshore sediment transport from the delta-front erosion and the land reclamation including vegetation ecological responses were the main factors promoting the shoreline advance. Human interventions, dominated mainly by reclamation, formed positive feedback with local hydrodynamic processes and promoted continuous shoreline accretion. This study focused on the external and internal drivers and their interactions of long-term shoreline evolution with very intensive human activities, which can provide the decision-making reference for the regional coastal zone management and conservation.

Emergence of dynamic contractile patterns in slime mold confined in a ring geometry

Coordination of cytoplasmic flows on large scales in space and time are at the root of many cellular processes, including growth, migration or division. These flows are driven by organized contractions of the actomyosin cortex. In order to elucidate the basic mechanisms at work in the self-organization of contractile activity, we investigate the dynamic patterns of cortex contraction in true slime mold Physarum polycephalum confined in ring-shaped chambers of controlled geometrical dimensions. We make an exhaustive inventory of the different stable contractile patterns in the absence of migration and growth. We show that the primary frequency of the oscillations is independent of the ring perimeter, while the wavelength scales linearly with it. We discuss the consistence of these results with the existing models, shedding light on the possible feedback mechanisms leading to coordinated contractile activity.

Entanglement dynamics of thermofield double states in integrable models

We study the entanglement dynamics of thermofield double (TFD) states in integrable spin chains and quantum field theories. We show that, for a natural choice of the Hamiltonian eigenbasis, the TFD evolution may be interpreted as a quantum quench from an initial state which is low-entangled in the real-space representation and displays a simple quasiparticle structure. Based on a semiclassical picture analogous to the one developed for standard quantum quenches, we conjecture a formula for the entanglement dynamics, which is valid for both discrete and continuous integrable field theories, and expected to be exact in the scaling limit of large space and time scales. We test our conjecture in two prototypical examples of integrable spin chains, where numerical tests are possible. First, in the XY-model, we compare our predictions with exact results obtained by mapping the system to free fermions, finding excellent agreement. Second, we test our conjecture in the interacting XXZ Heisenberg model, against numerical iTEBD calculations. For the latter, we generally find good agreement, although, for some range of the system parameters and within the accessible simulation times, some small discrepancies are visible, which we attribute to finite-time effects.

BSR-TC: Adaptively Sampling for Accurate Triangle Counting over Evolving Graph Streams

Triangle counting is a fundamental graph mining problem, widely employed in various real-world application scenarios. Given the large scale of graph streams and limited memory space, it is feasible to achieve the estimation of global and local triangles by sampling. Existing streaming algorithms for triangle counting can be generalized into two categories: Reservoir-based methods and Bernoulli-based methods. The former use a fixed memory budget, whose size is difficult to set for accurate estimation without any prior knowledge about graph streams. The latter sample edges by a specified probability, but memory budget is uncontrollable for following a binomial distribution. In this work, we propose a novel and bounded-sampling-ratio algorithm for both global and local triangle counting, called BSR-TC, by adaptively resizing memory budget upwards over evolving graph streams. Specifically, our proposed single-pass BSR-TC can gain more advantage than the state-of-the-art algorithms over the continuous growth of graph streams. Experimental results show that BSR-TC achieves accuracy of at least 99.8% for global triangles, when the ratio of initial memory budget against whole graph streams [Formula: see text] and given [Formula: see text], respectively.

Analysis for magnetic field disturbance of hybrid DC circuit breaker during breaking

The high current of hybrid DC circuit breaker (HCB) in the process of breaking generates strong transient magnetic field (MF), which may interfere with the normal operation of driver control units (DCUs). Therefore, the analysis for transient MF disturbance is of great significance. Due to the large space scale of HCB, with the large number of power electronic devices, the numerical calculation method has the disadvantages of large consumption of resources and slow calculation speed in solving the transient MF inside the HCB. In this study, the current generation mechanism of a 500 kV HCB is analysed, and the equivalent current path is obtained by considering the skin effect. Combined with the temporal and spatial distribution of transient current, the multi-process transient equivalent model of transient MF calculation is established, and the model has the advantages of high precision and high speed. Then, the breaking experiment of HCB is carried out, and the transient MF near the DCU is measured. The experiment results verify the validity of the model. Furthermore, the disturbance of transient MF at the DCU of the transfer branch during breaking 25 kA current is analysed.

Co-occurrence of planktonic bacteria and archaea affects their biogeographic patterns in China\u2019s coastal wetlands

Planktonic bacteria and archaea play a key role in maintaining ecological functions in aquatic ecosystems; however, their biogeographic patterns and underlying mechanisms have not been well known in coastal wetlands including multiple types and at a large space scale. Therefore, planktonic bacteria and archaea and related environmental factors were investigated in twenty-one wetlands along China’s coast to understand the above concerns. The results indicated that planktonic bacteria had different biogeographic pattern from planktonic archaea, and both patterns were not dependent on the wetland's types. Deterministic selection shapes the former’s community structure, whereas stochastic processes regulate the latter’s, being consistent with the fact that planktonic archaea have a larger niche breadth than planktonic bacteria. Planktonic bacteria and archaea co-occur, and their co-occurrence rather than salinity is more important in shaping their community structure although salinity is found to be a main environmental deterministic factor in the coastal wetland waters. This study highlights the role of planktonic bacteria-archaea co-occurrence on their biogeographic patterns, and thus provides a new insight into studying underlying mechanisms of microbial biogeography in coastal wetlands.

ETKDS: An efficient algorithm of Top-K high utility itemsets mining over data streams under sliding window model

The researcher proposed the concept of Top-K high-utility itemsets mining over data streams. Users directly specify the number K of high-utility itemsets they wish to obtain for mining with no need to set a minimum utility threshold. There exist some problems in current Top-K high-utility itemsets mining algorithms over data streams including the complex construction process of the storage structure, the inefficiency of threshold raising strategies and utility pruning strategies, and large scale of the search space, etc., which still can not meet the requirement of real-time processing over data streams with limited time and memory constraints. To solve this problem, this paper proposes an efficient algorithm based on dataset projection for mining Top-K high-utility itemsets from a data stream. A data structure CIUDataListSW is also proposed, which stores the position of the item in the transaction to effectively obtain the initial projected dataset of the item. In order to improve the projection efficiency, this paper innovates a new reorganization technology for projected transactions in common batches to maintain the sort order of transactions in the process of dataset projection. Dual pruning strategy and transaction merging mechanism are also used to further reduce search space and dataset scanning costs. In addition, based on the proposed CUDHSW structure, an efficient threshold raising strategy CUD is used, and a new threshold raising strategy CUDCB is designed to further shorten the mining time. Experimental results show that the algorithm has great advantages in running time and memory consumption, and it is especially suitable for the mining of high-utility itemsets of dense datasets.

Large-scale simulations of biological cell sorting driven by differential adhesion follow diffusion-limited domain coalescence regime.

Cell sorting, whereby a heterogeneous cell mixture segregates and forms distinct homogeneous tissues, is one of the main collective cell behaviors at work during development. Although differences in interfacial energies are recognized to be a possible driving source for cell sorting, no clear consensus has emerged on the kinetic law of cell sorting driven by differential adhesion. Using a modified Cellular Potts Model algorithm that allows for efficient simulations while preserving the connectivity of cells, we numerically explore cell-sorting dynamics over very large scales in space and time. For a binary mixture of cells surrounded by a medium, increase of domain size follows a power-law with exponent n = 1/4 independently of the mixture ratio, revealing that the kinetics is dominated by the diffusion and coalescence of rounded domains. We compare these results with recent numerical studies on cell sorting, and discuss the importance of algorithmic differences as well as boundary conditions on the observed scaling.

Energy Efficient Dynamic Offloading in Mobile Edge Computing for Internet of Things

With proliferation of computation-intensive Internet of Things (IoT) applications, the limited capacity of end devices can deteriorate service performance. To address this issue, computation tasks can be offloaded to the Mobile Edge Computing (MEC) for processing. However, it consumes considerable energy to transmit and process these tasks. In this paper, we study the energy efficient task offloading in MEC. Specifically, we formulate it as a stochastic optimization problem, with the objective of minimizing the energy consumption of task offloading while guaranteeing the average queue length. Solving this offloading optimization problem faces many technical challenges due to the uncertainty and dynamics of wireless channel state and task arrival process, and the large scale of solution space. To tackle these challenges, we apply stochastic optimization techniques to transform the original stochastic problem into a deterministic optimization problem, and propose an energy efficient dynamic offloading algorithm called EEDOA. EEDOA can be implemented in an online manner to make the task offloading decisions with polynomial time complexity. Theoretical analysis is provided to demonstrate that EEDOA can approximate the minimal transmission energy consumption while still bounding the queue length. Experiment results are presented which show the EEDOA’s effectiveness.