Numerical Experiments Research Articles

Impacts of Local and Remote SST Warming on Summer Circulation Changes in the Western North Pacific

Abstract This study explores how future SST warming in remote ocean basins may affect the western North Pacific (WNP) wet season climate by applying a high-resolution atmospheric general circulation model to conduct a series of numerical experiments. A marked precipitation and tropical cyclone (TC) activity reduction, as well as enhanced anticyclonic circulation, in the WNP is projected in AMIP experiments forced by SST change in a future warming scenario. The sensitivity experiments reveal that various SST warming phenomena (e.g., in the global SST warming pattern, the tropical ocean belt, the Indian Ocean, the tropical Atlantic, and the subtropical northeast Pacific) and the increase in greenhouse gas concentration could weaken the precipitation, TC activity, and circulation. By contrast, the SST warming in the WNP and eastern equatorial Pacific has opposite and mixed effects, respectively, and tends to weakly offset the dominant influences of remote ocean warming. These results indicate that the WNP, being the epicenter of the global teleconnection of divergent and rotational flow, is susceptible to the influence of the SST warming in remote ocean basins. The remote forcing as projected in future scenarios would overwhelm the enhancing effect of local SST warming and weaken the circulation, convection, and TC activity in the WNP. These findings further the understanding of how the decreased precipitation and enhanced subtropical high in the WNP may be easily triggered by remote SST warming as revealed in the AMIP-type simulations. How this effect would be affected by air–sea coupling needs further investigation.

Double-loop importance sampling for McKean–Vlasov stochastic differential equation

This paper investigates Monte Carlo (MC) methods to estimate probabilities of rare events associated with the solution to the d-dimensional McKean–Vlasov stochastic differential equation (MV-SDE). MV-SDEs are usually approximated using a stochastic interacting P-particle system, which is a set of P coupled d-dimensional stochastic differential equations (SDEs). Importance sampling (IS) is a common technique for reducing high relative variance of MC estimators of rare-event probabilities. We first derive a zero-variance IS change of measure for the quantity of interest by using stochastic optimal control theory. However, when this change of measure is applied to stochastic particle systems, it yields a P×d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P \ imes d$$\\end{document}-dimensional partial differential control equation (PDE), which is computationally expensive to solve. To address this issue, we use the decoupling approach introduced in (dos Reis et al. 2023), generating a d-dimensional control PDE for a zero-variance estimator of the decoupled SDE. Based on this approach, we develop a computationally efficient double loop MC (DLMC) estimator. We conduct a comprehensive numerical error and work analysis of the DLMC estimator. As a result, we show optimal complexity of OTOLr-4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}\\left( \ extrm{TOL}_{\ extrm{r}}^{-4}\\right) $$\\end{document} with a significantly reduced constant to achieve a prescribed relative error tolerance TOLr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{TOL}_{\ extrm{r}}$$\\end{document}. Subsequently, we propose an adaptive DLMC method combined with IS to numerically estimate rare-event probabilities, substantially reducing relative variance and computational runtimes required to achieve a given TOLr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{TOL}_{\ extrm{r}}$$\\end{document} compared with standard MC estimators in the absence of IS. Numerical experiments are performed on the Kuramoto model from statistical physics.

Configuration and multistep switching of machines in dynamic hybrid MTS/MTO production systems

This study proposes the configuration of MTS-/MTO-dedicated and hybrid (switchable) machines under a multistep switching policy where each hybrid machine can be switched stepwise and compares it to the existing model with MTS-dedicated and hybrid machines under a group switching policy that makes all hybrid machines switch together. Since companies have been required to satisfy wide varieties of customers' needs in recent years, the dynamic hybrid make-to-stock (MTS) / make-to-order (MTO) production system–one of the flexible production strategies with superior efficiency and productivity–is widely adopted in the garment industry. This system contains MTS and MTO streams in a shared facility and holds dedicated and hybrid machines that can be switched between MTS and MTO production. The machine configuration and switching policy are essential factors to increase the effectiveness of this system; hence, the features of such components must be investigated. Numerical experiments demonstrate that the cost and the number of MTO customers waiting can be reduced by appropriately setting the multistep switching policy and the machine configuration. Effective operating rules can also be achieved using our proposed search heuristics. These results contribute to the improvement of the existing dynamic hybrid system and the expansion of its possible applications.

Nonlinear Regularized HSS Iteration Method for a Class of Nonlinear Saddle-Point Systems with Applications to Image Deblurring Problems

In this paper, we construct a nonlinear regularized Hermitian and skew-Hermitian splitting (NRHSS) iteration method for a class of nonlinear saddle-point systems. The NRHSS iteration method can be seen as a generalization of the Peaceman-Rachford splitting method with monotone plus skew-symmetric splitting (PRSM/MSS). Besides, if the nonlinear operator reduces to the linear case, the NRHSS iteration method reduces to the regularized Hermitian and skew-Hermitian splitting (RHSS) iteration method. Hence, the NRHSS iteration method can also be seen as a generalization of the RHSS iteration method. To overcome the heavy workload when direct solution methods are used, we also propose an inexact version of the NRHSS iteration method. Detailed theoretical analysis regarding the convergence properties is given. Numerical experiments on image deblurring problems are carried out to illustrate the feasibility and efficiency of the NRHSS iteration method.

On a posteriori error estimation for Runge–Kutta discontinuous Galerkin methods for linear hyperbolic problems

AbstractA posteriori bounds for the error measured in various norms for a standard second‐order explicit‐in‐time Runge–Kutta discontinuous Galerkin (RKDG) discretization of a one‐dimensional (in space) linear transport problem are derived. The proof is based on a novel space‐time polynomial reconstruction, hinging on high‐order temporal reconstructions for continuous and discontinuous Galerkin time‐stepping methods. Of particular interest is the question of error estimation under dynamic mesh modification. The theoretical findings are tested by numerical experiments.

Exact Solutions and Bounds for the Thermal Conductivity Coefficient of a Dispersed Medium

Exact solutions for the thermal conductivity coefficient of a two-phase dispersed medium are obtained using the most general physical principles of locality and symmetry. Two solutions define the well-known Hashin–Shtrikman bounds. The third solution, invariant under the phase inversion transformation, significantly narrows the Hashin–Shtrikman boundaries; this is confirmed by comparison with numerous experiments by other authors. It has been shown that taking into account the remote interaction of dispersed particles at their increased concentration only slightly (less than 3%) affects the result.

Policies for Selecting the Advance Selling Mode in a Supply Chain Considering Network Externalities

ABSTRACTThe marketing strategy of advance selling new products through e‐commerce channels is becoming increasingly popular among merchants and users. In advance selling on e‐commerce platforms, network externalities and the probability of consumer satisfaction with products are important factors affecting consumers' strategic behavior. This study considers network externalities and the probability of consumer satisfaction with products in the advance selling decision‐making problem in the supply chain. Using game theory and prospect theory, three scenario models—advance selling considering network externalities, advance selling without considering network externalities, and nonadvance selling—are designed to construct theoretical models for supply chain decision‐making. The optimal decision‐making problem of supply chain members is discussed. Furthermore, through a comparison of pricing, demand and profits, the impacts of advance selling with or without considering network externalities on the decisions of retailers and manufacturers are analyzed. By comparing the differences in decision‐making between manufacturers and retailers, the feasible area for advance selling under network externalities is obtained. Furthermore, through numerical experiments, the impacts of the strength of network externalities, and the probability of consumer satisfaction with products on the decision‐making of supply chains are analyzed.

Learning quantum properties from short-range correlations using multi-task networks

Characterizing multipartite quantum systems is crucial for quantum computing and many-body physics. The problem, however, becomes challenging when the system size is large and the properties of interest involve correlations among a large number of particles. Here we introduce a neural network model that can predict various quantum properties of many-body quantum states with constant correlation length, using only measurement data from a small number of neighboring sites. The model is based on the technique of multi-task learning, which we show to offer several advantages over traditional single-task approaches. Through numerical experiments, we show that multi-task learning can be applied to sufficiently regular states to predict global properties, like string order parameters, from the observation of short-range correlations, and to distinguish between quantum phases that cannot be distinguished by single-task networks. Remarkably, our model appears to be able to transfer information learnt from lower dimensional quantum systems to higher dimensional ones, and to make accurate predictions for Hamiltonians that were not seen in the training.

A distributed end-to-end fair bandwidth allocation algorithm for multi-path networks

Multi-path transmission significantly improves network performance, yet it complicates the problem of fair resource allocation. While traditional fair bandwidth allocation schemes thrive in single-path settings, they often falter when applied to multi-path environments, highlighting the challenge of achieving fair bandwidth sharing in such networks. To tackle this issue, the concept of "max-min similarity" of queuing delays has been introduced based on insight into the intrinsic interactions between queuing packets, delays, and bandwidth allocation, which leads to a formal definition of max-min fair bandwidth allocation for multi-path environments. Theoretical analysis shows that the max-min similarity of queuing delays is a sufficient condition for max-min fair bandwidth allocation in single bottleneck environments. A novel distributed end-to-end fair bandwidth allocation algorithm, named DMFBA, is then proposed, which separates the control into flow-level and transmission path-level. In achieving max-min similarity in queuing delays by dynamically adjusting the distribution of flows’ queuing packet quotas across paths it achieves the goal of max-min fair bandwidth allocation. Two sets of numerical simulation experiments were conducted and the results show that DMFBA has less overhead and faster convergence than the traditional utility fair algorithms.

Critical Lengths of Steklov Eigenvalues of Hypersurfaces of Revolution in Euclidean Space

We study the Steklov problem on hypersurfaces of revolution with two boundary components in Euclidean space and focus on the phenomenon of critical length, at which a Steklov eigenvalue is maximized. In this article, we conjecture that, in any dimension, there is a finite number of infinite critical length. To investigate this, we develop an algorithm to efficiently perform numerical experiments, providing support to our conjecture. Furthermore, we prove the conjecture in dimension n = 3 and n = 4.

Blind prediction and post-experimental analysis of RC core wall’s cyclic flexural response using MVLEM-FD

AbstractBlind prediction and post-experimental studies of the flexural cyclic response of a U-shaped core wall, tested at UCLouvain, Belgium, are presented. The tested specimen (referred to as UW1) was modelled using a relatively simple 3D force–displacement-based version of the beam–column multiple-vertical-line-element (MVLEM-FD), developed at the University of Ljubljana (UL), using standard element parameters. The blind prediction accurately identified critical failure points within the specimen. However, the predicted type of failure, attributed to the rupture of longitudinal bars in the boundary region of flanges was somewhat different from that observed in the experiment. These bars were indeed ruptured, but their rupture was preceded by their buckling and the spalling of the surrounding concrete core. Moreover, the predicted force–displacement hysteretic loop exhibited a slight shift compared to experimental observations. Post-experimental studies revealed that this discrepancy was primarily due to the modelling of the loading at the top of the wall rather than the modelling of the wall itself. Specifically, an additional bending moment induced by the eccentricity of the vertical load applied using three actuators, which was overlooked in the blind prediction. Upon correcting the loading, the agreement between the numerical studies and experiment was considerably improved in terms of both the global and local response quantities. Additionally, minor improvements in modelling the boundary regions of the wall’s flanges, considering the relatively large unconfined concrete cover, were introduced, leading to enhanced estimations of near-collapse response.

Expected coordinate improvement for high-dimensional Bayesian optimization

Bayesian optimization (BO) algorithm is very popular for solving low-dimensional expensive optimization problems. Extending Bayesian optimization to high dimension is a meaningful but challenging task. One of the major challenges is that it is difficult to find good infill solutions as the acquisition functions are also high-dimensional. In this work, we propose the expected coordinate improvement (ECI) criterion for high-dimensional Bayesian optimization. The proposed ECI criterion measures the potential improvement we can get by moving the current best solution along one coordinate. The proposed approach selects the coordinate with the highest ECI value to refine in each iteration and covers all the coordinates gradually by iterating over the coordinates. The greatest advantage of the proposed ECI-BO (expected coordinate improvement based Bayesian optimization) algorithm over the standard BO algorithm is that the infill selection problem of the proposed algorithm is always a one-dimensional problem thus can be easily solved. Numerical experiments show that the proposed algorithm can achieve significantly better results than the standard BO algorithm and competitive results when compared with five high-dimensional BOs and six surrogate-assisted evolutionary algorithms. This work provides a simple but efficient approach for high-dimensional Bayesian optimization. A Matlab implementation of our ECI-BO is available at https://github.com/zhandawei/Expected_Coordinate_Improvement.

Mixed finite element analysis for a modified Poisson–Fermi interface problem accounting for electrostatic correlations

The Bazant–Storey–Kornyshev (BSK) theory [1–3] recently developed an important continuum framework to expound the nonlocal dielectric permittivity of ionic liquids due to electrostatic correlations, leading to a fourth-order modified Poisson–Fermi equation to model the electrostatic potential field in the solvent (e.g., the electrolyte), while the standard second-order Poisson–Fermi equation is still valid in modeling the electrostatic potential field in the solute. Thus an interface problem is formed between the fourth-order and second-order Poisson–Fermi equations through the interface of solvent and solute with jump coefficients, which has exerted tremendous impacts on applications of electrokinetics, electrochemistry, biophysics, and etc. In this paper, a type of mixed finite element method is developed to solve the proposed interface problem once for all variables: the electrostatic potential, electric field, electric displacement field, electrostatic stress as well as interactional force in the electrolyte in an accurate fashion, and its optimal convergence properties are analyzed for all variables in their respective norms. Numerical experiments are carried out through self-defined mathematical examples to validate all attained theoretical results. Furthermore, as a part of modeling verification for the presented interface problem that models the BSK theory, a practically physical example is investigated to validate the necessity of introducing the fourth-order modified Poisson–Fermi equation to describe the electrostatic correlation effects due to charge reversal phenomenon.

Deep reinforcement learning driven trajectory-based meta-heuristic for distributed heterogeneous flexible job shop scheduling problem

As the production environment evolves, distributed manufacturing exhibits heterogeneous characteristics, including diverse machines, workers, and production processes. This paper examines a distributed heterogeneous flexible job shop scheduling problem (DHFJSP) with varying processing times. A mixed integer linear programming (MILP) model of the DHFJSP is formulated with the objective of minimizing the makespan. To solve the DHFJSP, we propose a deep Q network-aided automatic design of a variable neighborhood search algorithm (DQN-VNS). By analyzing schedules, sixty-one types of scheduling features are extracted. These features, along with six shaking strategies, are used as states and actions. A DHFJSP environment simulator is developed to train the deep Q network. The well-trained DQN then generates the shaking procedure for VNS. Additionally, a greedy initialization method is proposed to enhance the quality of the initial solution. Seven efficient critical path-based neighborhood structures with three-vector encoding scheme are introduced to improve local search. Numerical experiments on various scales of instances validate the effectiveness of the MILP model and the DQN-VNS algorithm. The results show that the DQN-VNS algorithm achieves an average relative percentage deviation (ARPD) of 3.2%, which represents an approximately 88.45% reduction compared to the best-performing algorithm among the six compared, with an ARPD of 27.7%. This significant reduction in ARPD highlights the superior stability and performance of the proposed DQN-VNS algorithm.

Cuts and semidefinite liftings for the complex cut polytope

AbstractWe consider the complex cut polytope: the convex hull of Hermitian rank 1 matrices $$xx^\textrm{H}$$ x x H , where the elements of $$x \in \mathbb {C}^n$$ x ∈ C n are mth unit roots. These polytopes have applications in MAX-3-CUT, digital communication technology, angular synchronization and more generally, complex quadratic programming. For $$m=2$$ m = 2 , the complex cut polytope corresponds to the well-known cut polytope. We generalize valid cuts for this polytope to cuts for any complex cut polytope with finite $$m>2$$ m > 2 and provide a framework to compare them. Further, we consider a second semidefinite lifting of the complex cut polytope for $$m=\infty $$ m = ∞ . This lifting is proven to be equivalent to other complex Lasserre-type liftings of the same order proposed in the literature, while being of smaller size. Our theoretical findings are supported by numerical experiments on various optimization problems.

Dynamic collaborative truck-drone delivery with en-route synchronization and random requests

Coordinated truck and drone delivery is gaining popularity in logistics as it can greatly reduce operation costs. However, existing studies on related operations management problems typically ignore the following important features: (i) the random appearance of requests, which require operators to dynamically respond to the requests; and (ii) the decisions of optimal launch and retrieval locations for trucks and drones instead of fixed to customer locations, which can significantly impact the overall time costs. To tackle these challenges, this study investigates the dynamic collaborative truck-drone routing problem with randomly arriving requests and synchronization on routes. We model the problem as a Markov Decision Process (MDP) and solve the MDP via a reinforcement learning (RL) approach. The proposed RL approach determines: (i) whether each request should be serviced upon arrival, (ii) which truck or drone should be assigned for the request, and (iii) the optimal en-route take-off and landing positions for paired trucks and drones. We further employ a framework of decentralized learning and centralized dispatching in RL to increase performance. Numerical experiments are conducted to assess the proposed solution approach on instances generated based on both the Solomon dataset and real-world operational data of a logistics operator in Singapore over several benchmark algorithms under various battery endurance levels of drones and distinct transportation scenarios including node-based dynamic collaborative truck-drone routing problem, dynamic non-collaborative truck and drone routing problem, and dynamic vehicle routing problem. The results show that our RL solution outperforms the benchmark algorithm in total profit by an average of 28.03 %, and our en-route takeoff and landing scenario outperforms the benchmark scenarios in total profit by an average of 8.43 % in multi-day instances. Additionally, compared to the traditional node-based landing scenario, employing our en-route takeoff and landing strategy can save 0.9 h/(drone*day) of waiting time on average.

A Model-Free Adaptive Positioning Control Method for Underactuated Unmanned Surface Vessels in Unknown Ocean Currents

Aiming to address the problem of underactuated unmanned surface vehicles (USVs) performing fixed-point operations at sea without dynamic positioning control systems, this paper introduces an original approach to positioning control: the virtual anchor control method. This method is applicable in environments with currents that change slowly and does not require prior knowledge of current information or vessel motion model parameters, thus offering convenient usability. This method comprises four steps. First, a concise linear motion model with unknown disturbances is proposed. Then, a motion planning law is designed by imitating underlying principles of ship anchoring. Next, an adaptive disturbance observer is proposed to estimate uncertainties in the motion model. In the last step, based on the observer, a sliding-mode method is used to design a heading control law, and a thrust control law is also designed by applying the Lyapunov method. Numerical simulation experiments with significant disturbances and tidal current variations are conducted, which demonstrate that the proposed method has a good control effect and is robust.

Periodic and Quasi-Periodic Orbits in the Collinear Four-Body Problem: A Variational Analysis

This paper investigated the periodic and quasi-periodic orbits in the symmetric collinear four-body problem through a variational approach. We analyze the conditions under which homographic solutions minimize the action functional. We compute the minimal value of the action functional for these solutions and show that, for four equal masses organized in a linear configuration, these solutions are the minimizers of the action functional. Additionally, we employ numerical experiments using Poincaré sections to explore the existence and stability of periodic and quasi-periodic solutions within this dynamical system. Our results provide a deeper understanding of the variational principles in celestial mechanics and reveal complex dynamical behaviors, crucial for further studies in multi-body problems.

Analytic computation for stationary distributions of D-BMAP/D-MSP(a,b )/1 queueing system

This paper analyses single server correlated batch arrival and correlated batch service queue with innumerable waiting space in discrete-time. The arrival and service processes are governed by discrete batch Markovian arrival process and discrete Markovian service process with general bulk service rule, respectively. Observing two consecutive random epochs, we construct general structure transition probability matrix and it is then reblocked to the desired M/G/1 structure. The UL-type RG-factorization approach combined with spectral expansion method is adopted to unravel the queue length distribution at random epoch. The relationships are undertaken to obtain the queue length distributions at pre-arrival, outside observer's, intermediate and post-departure epochs. Our most challenging effort is to derive the probability mass functions of waiting time and service batch size for arbitrary customer in an arriving batch. We address the warehouse management process for finished products from dealer to retailer as a potential practical use of our batch queue with correlation in both arrival and service, and provide the effect of our queueing behaviour in this application based on our analytical and computational investigation. Based on the implementation of parametrized numeric experiments with numerous categories, we impart our computational results to validate the analytical findings reported in this investigation.

Modelling an emission trading scheme based on a dual-market mechanism in multimode networks with customised bus services

ABSTRACT The transport-related emissions are one of the main contributors to air pollution. In this paper, we construct an efficient and stable emission trading scheme (ETS) to reduce emissions. We build a dual-market mechanism for carbon emission permit (CEP) in the transportation system to control emissions at source, where CEPs are issued in a paid way in the primary market and traded freely in the secondary market. At the same time, we include customised bus (CB) and describe the competitive relationship between CB and private car (PC) in a multimode network. The market trading process and travel choice behaviours are formulated as a variational inequality problem (VIP). The VIP is solved using a relaxation algorithm, and the multi-round iteration strategy is used for updating permit volumes. Finally, we conduct numerical experiments based on Braess and Sioux Falls networks to demonstrate the merits of the ETS based on a dual-market mechanism.