Relaxation Approximation Research Articles

Flexibility-Oriented AC/DC Hybrid Grid Optimization Using Distributionally Robust Chance-Constrained Method

With the increasing integration of stochastic sources and loads, ensuring the flexibility of AC/DC hybrid distribution networks has become a pressing challenge. This paper aims to enhance the operational flexibility of AC/DC hybrid distribution networks by proposing a flexibility-oriented optimization framework that addresses the growing uncertainties. Notably, a comprehensive evaluation method for operational flexibility assessment is first established. Based on this, this paper further proposes a flexibility-oriented operation optimization model using the distributionally robust chance-constrained (DRCC) method. A customized solution method utilizing second-order cone relaxation and sample average approximation (SAA) is also introduced. The results of case studies indicate that the flexibility of AC/DC hybrid distribution networks is enhanced through sharing energy storage among multiple feeders, adaptive reactive power regulation using soft open points (SOPs) and static var compensators (SVCs), and power transfer between feeders via SOPs.

Power-Efficient Resource Allocation for Active STAR-RIS-Aided SWIPT Communication Systems

Simultaneous wireless information and power transfer (SWIPT) has emerged as a pivotal technology in 6G, offering an efficient means of delivering energy to a large quantity of low-power devices while transmitting data concurrently. To address the challenges of obstructions, high path loss, and significant energy consumption associated with long-distance communication, this work introduces a novel alternating iterative optimization strategy. The proposed approach combines active simultaneous transmission and reflection of reconfigurable intelligent surfaces (STAR-RIS) with SWIPT to maximize spectrum efficiency and reduce overall system energy consumption. This method addresses the considerable energy demands inherent in SWIPT systems by focusing on reducing the power output from the base station (BS) while meeting key constraints: the communication rate for information receivers (IRs) and minimum energy levels for energy receivers (ERs). Given complex interactions between variables, the solution involves an alternating iterative optimization process. In the first stage of this approach, the passive beamforming variables are kept constant, enabling the use of semi-definite relaxation (SDR) and successive convex approximation (SCA) algorithms to optimize active beamforming variables. In the next stage, with active beamforming variables fixed, penalty-based algorithms are applied to fine-tune the passive beamforming variables. This iterative process continues, alternating between active and passive beamforming optimization, until the system converges on a stable solution. The simulation results indicated that the proposed system configuration, which leverages active STAR-RIS, achieves lower energy consumption and demonstrates improved performance compared to configurations utilizing passive RIS, active RIS, and passive STAR-RIS. This evidence suggests that the proposed approach can significantly contribute to advancing energy efficiency in 6G systems.

Rate splitting multiple access for UAV Secure Communication Systems with Friendly Jamming

A rate splitting multiple access (RSMA)-based dual-unmanned aerial vehicle (UAV) secure communication system is proposed in this paper, where one UAV is deployed to communicate with ground users, while the other UAV is dispatched to transmit the jamming signal to a ground eavesdropper. Considering the limited energy of UAV batteries, the minimum secrecy rate is maximized via optimizing RSMA precoding matrix and trajectories of UAVs under the constraint of UAV energy consumption. To address the complexity arising from coupled variables, the optimization problem is decomposed into two equivalent subproblems: precoding matrix optimization and UAV trajectory design. This decomposition is achieved using the block coordinate descent method. Next, the subproblems are transformed into convex forms by using semidefinite relaxation and successive convex approximation techniques, which are iteratively solved until convergence. Simulation results show that the secrecy performance of RSMA scheme is superior to that of the benchmark schemes, Specifically, the average secrecy rate of the RSMA scheme is approximately 22% and 10.8% higher than that of the NOMA and TDMA schemes, respectively.

Gradient-Based Monte Carlo Methods for Relaxation Approximations of Hyperbolic Conservation Laws

Particle methods based on evolving the spatial derivatives of the solution were originally introduced to simulate reaction-diffusion processes, inspired by vortex methods for the Navier–Stokes equations. Such methods, referred to as gradient random walk methods, were extensively studied in the ’90s and have several interesting features, such as being grid-free, automatically adapting to the solution by concentrating elements where the gradient is large, and significantly reducing the variance of the standard random walk approach. In this work, we revive these ideas by showing how to generalize the approach to a larger class of partial differential equations, including hyperbolic systems of conservation laws. To achieve this goal, we first extend the classical Monte Carlo method to relaxation approximation of systems of conservation laws, and subsequently consider a novel particle dynamics based on the spatial derivatives of the solution. The methodology, combined with asymptotic-preserving splitting discretization, yields a way to construct a new class of gradient-based Monte Carlo methods for hyperbolic systems of conservation laws. Several results in one spatial dimension for scalar equations and systems of conservation laws show that the new methods are very promising and yield remarkable improvements compared to standard Monte Carlo approaches, either in terms of variance reduction as well as in describing the shock structure.

Active Reconfigurable Intelligent Surface Enhanced Internet of Medical Things.

The incredible potentiality of reconfigurable intelligent surface (RIS) in addressing power supply and obstacle environment of Internet of Medical Things (IoMT) has been capturing our interest. Considering the nettlesome "double-fading" effect introduced by passive RIS, we investigate an active RIS-enhanced IoMT system in this article, where the wireless power transfer (WPT) from power station (PS) to IoMT devices and the wireless information transfer (WIT) from IoMT devices to the access point (AP) are both implemented with the assistance of active RIS. Aiming to maximize the sum throughput of the considered IoMT system, a joint design of time schedules and reflecting coefficient matrices of the active RIS is proposed. Trapped by the non-convex and obstinate optimization problem, we explore the semi-definite programming (SDP) relaxation and successive convex approximation (SCA) techniques based on alternating optimization (AO) algorithm. Simulation results verify our solution approach to the intractable optimization problem and showcase the boosted spectrum and energy efficiency of the active RIS-enhanced IoMT system.

Probing the structural, magneto-electronic, thermophysical, and thermoelectric properties of vanadium-based V2MnZ (Z = As, Ga) Heusler alloy: a computational assessment

The structural, magneto-electronic, thermophysical and thermoelectric properties of vanadium-based V2MnZ (Z = As, Ga) alloys have been investigated using density functional theory simulation scheme and semiclassical Boltzmann transport methods. First of all, the structural characterization has been performed in ferromagnetic and non-magnetic states which signifies that both the alloys crystallized in C1b type structure with space group F-43m. We also computed the various thermodynamical parameters such as heat capacity (Cv), Debye temperature (θ D), and grüneisen parameter (γ) of these materials, with the help of quasi-harmonic approximation (QHA) at pressures ranging from 0 to 20 GPa and temperatures ranging from 0 to 900 K. We have used the Boltzmann transport theory with the constant relaxation approximation as a basis for calculating various thermoelectric coefficients such as the Seebeck coefficient, power factor, total thermal conductivity and figure of merit. The efficient half-metallicity and thermoelectric responses contribute to spintronics and green energy harvesting technology.

Complex unstructured-grid groundwater modeling using centroidal Voronoi tessellation refinement and curve fitting

An unstructured grid is a powerful data structure for a proper depiction of various geological features such as faults and pinch-outs and for groundwater simulation in a complex aquifer system. This study presents a mesh generation methodology based on 2.5D centroidal Voronoi tessellations (CVTs), which provides a great flexibility in specifying grid connections in 3D, matching irregular geometries, and adding high levels of refinement in areas of interest. Lloyd relaxation approximation is introduced to effectively guarantee the generation of centroidal Voronoi grids. A curve-fitting Voronoi gridding approach is developed to construct Voronoi cell edges conforming to intricated geological traces in the horizontal 2D projection with unstructured vertical discretization. A controlled refinement in spatial grid resolution has been demonstrated to prevent adverse impacts on groundwater flow simulations. The methodology is applied to the Southern Hills aquifer system in the Capital Area of Louisiana, USA. Significant groundwater depletion has occurred due to continuous and excessive withdrawals over decades for public supplies and industries. The Baton Rouge fault and the Denham-Springs Scotlandville fault are leaky barriers and have a significant influence on groundwater flow. A curve-fitting centroidal Voronoi grid is developed to simulate the effects of the two faults as leaky barriers. CVT-based high-fidelity unstructured multi-model groundwater modeling is conducted using MODFLOW 6 to allow more flexibility in model design. Complex groundwater flow in the Southern Hills aquifer system was revealed through the centroidal Voronoi unstructured grid.

On a relaxation approximation of the 2-D incompressible magnetohydrodynamic equations

We study the Cauchy problem of a 2-D hyperbolic relaxation system for the incompressible magnetohydrodynamic (MHD) equations, which is related with the scientific computational aspects. We prove that this relaxed problem possesses a global strong solution, provided that the relaxation parameter is small and the appropriate norm of the initial data is not very large. We also show that such global solution converges to the one of the original incompressible MHD equations, as the relaxation parameter goes to zero.

A 0–1 linear relaxation and stochastic approximation method for real-time pricing in a smart grid with non-convex constraints

In this article, real-time pricing (RTP) for a smart grid with complicated non-convex and/or non-smooth constraints is explored. First, piecewise linear functions are adopted to approximate any kinds of utility function and RTP is formulated into bilevel non-convex programming. Then, a 0–1 relaxation method is used to linearize sparse constraints and piecewise linear utility functions, to obtain mixed integer linear programming. Finally, a distributed simultaneous perturbation stochastic approximation (DSPSA) method is designed to solve the bilevel non-convex programming. The RTP strategy is generalizable because sparse constraints and non-differentiable and/or non-concave utility functions are widespread in practice, and the piecewise linear functions approximation method is applicable to all kinds of utility function, not just to non-smooth and/or non-concave utility functions. In addition, the 0–1 linear relaxation and stochastic approximation method make the bilevel non-convex programming easily solvable by DSPSA, which converges rapidly while maintaining the high accuracy of solutions.

A classical firewall transformation as a canonical transformation

The firewall transformation put forward by ’t Hooft in recent years has made ambitious claims of solving the firewall problem and the black hole information paradox while maintaining unitary evolution. However, the theory has received limited attention from the community, especially in regards to its foundations in purely classical gravitational physics. This paper investigates the underlying assumptions of ’t Hooft’s firewall transformation before quantization. We find that the limiting procedure used by ’t Hooft in order to obtain an identification of the quantum operators for ingoing and outgoing particles near a black hole is not consistent. We propose a correction, which involves a more relaxed approximation regime. In the new approximation regime, we find a new classical analog for the firewall transformation for spherical shells, which allows evolving the spherical shells’ dynamics past their point of collision. In the classical theory, no firewall is removed, as both ingoing and outgoing matter is present on every spacelike hypersurface, and it does not appear that any firewalls will be removed after a canonical quantization.

Relaxation Approximation and Asymptotic Stability of Stratified Solutions to the IPM Equation

Relaxation Approximation and Asymptotic Stability of Stratified Solutions to the IPM Equation

Energy Consumption Minimization in Secure Multi-Antenna UAV-Assisted MEC Networks With Channel Uncertainty

This paper investigates the robust and secure task transmission and computation scheme in multi-antenna unmanned aerial vehicle (UAV)-assisted mobile edge computing (MEC) networks, where the UAV is dual-function, i.e., aerial MEC and aerial relay. The channel uncertainty is considered during information offloading and downloading. An energy consumption minimization problem is formulated under some constraints including users’ quality of service and information security requirements and the UAV’s trajectory’s causality, by jointly optimizing the CPU frequency, the offloading time, the beamforming vectors, the artificial noise and the trajectory of the UAV, as well as the CPU frequency, the offloading time and the transmit power of each user. To solve the non-convex problem, a reformulated problem is first derived by a series of convex reformation methods, i.e., semi-definite relaxation, S-Procedure and first-order approximation, and then, solved by a proposed successive convex approximation (SCA)-based algorithm. The convergence performance and computational complexity of the proposed algorithm are analyzed. Numerical results demonstrate that the proposed scheme outperforms existing benchmark schemes. Besides, the proposed SCA-based algorithm is superior to traditional alternative optimization-based algorithm.

Cooperative Beamforming for RIS-Aided Cell-Free Massive MIMO Networks

The combination of cell-free massive multiple-input multiple-output (CF-mMIMO) and reconfigurable intelligent surface (RIS) is envisioned as a promising paradigm to improve network capacity and enhance coverage capability. However, to reap full benefits of RIS-aided CF-mMIMO, the main challenge is to efficiently design cooperative beamforming (CBF) at base stations (BSs), RISs, and users. Firstly, we investigate the fractional programing to convert the weighted sum-rate (WSR) maximization problem into a tractable optimization problem. Then, the alternating optimization framework is employed to decompose the transformed problem into a sequence of subproblems, i.e., hybrid BF (HBF) at BSs, passive BF at RISs, and combining at users. In particular, the alternating direction method of multipliers algorithm is utilized to solve the HBF subproblem at BSs. Concretely, the analog BF design with unit-modulus constraints is solved by the manifold optimization (MO) while we obtain a closed-form solution to the digital BF design that is essentially a convex least-square problem. Additionally, the passive BF at RISs and the analog combining at users are designed by primal-dual subgradient and MO methods. Moreover, considering heavy communication costs in conventional CF-mMIMO systems, we propose a partially-connected CF-mMIMO (P-CF-mMIMO) framework to decrease the number of connections among BSs and users. To better compromise WSR performance and network costs, we formulate the BS selection problem in the P-CF-mMIMO system as a binary integer quadratic programming (BIQP) problem, and develop a relaxed linear approximation algorithm to handle this BIQP problem. Finally, numerical results demonstrate superiorities of our proposed algorithms over baseline counterparts.

Recasting an operator splitting solver into a standard finite volume flux-based algorithm. The case of a Lagrange-projection-type method for gas dynamics

In this paper, we propose a modification of an acoustic-transport operator splitting Lagrange-projection method for simulating compressible flows with gravity. The original method involves two steps that respectively account for acoustic and transport effects. Our work proposes a simple modification of the transport step, and the resulting modified scheme turns out to be a flux-splitting method. This new numerical method is less computationally expensive in the low-Mach regime, more memory efficient, and easier to implement than the original one. We prove stability properties for this new scheme by showing that under classical CFL conditions, the method is positivity preserving for mass, energy and entropy satisfying. The flexible flux-splitting structure of the method enables straightforward extensions of the method to multi-dimensional problems (with respect to space) and high-order discretizations that are presented in this work. We also propose an interpretation of the flux-splitting solver as a relaxation approximation. Both the stability and the accuracy of the new method are tested against one-dimensional and two-dimensional numerical experiments that involve highly compressible flows and low-Mach regimes.

Energy-Efficient Optimization in Distributed Massive MIMO Systems for Slicing eMBB and URLLC Services

The fifth generation (5G) communication system aims to support diverse services such as enhanced mobile broadband (eMBB) and ultra-reliable and low-latency communication (URLLC). In order to enable the coexistence of eMBB and URLLC services on a common physical infrastructure, network slicing incorporated in the distributed massive multiple-input multiple-output (DM-MIMO) system is regarded as a promising solution. In this paper, a non-orthogonal slicing scheme is proposed to improve the spectral efficiency, and the short packet transmission is adopted for URLLC to meet the low latency requirement. Through a joint optimization of beamforming and remote radio unit (RRU) selection, we investigate the energy efficiency (EE) maximization problem for the downlink DM-MIMO system. The formulated problem is a mixed integer nonlinear program (MINLP) that we solve by applying some efficient approaches, such as the Dinkelbach method, the reweighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{1}$</tex-math></inline-formula> -norm and difference of convex (DC) programming. By combining these approaches in one iteration, a double-loop procedure based on semi-definite relaxation (SDR) and successive convex approximation (SCA) is employed to find the suboptimal solution of the problem. Simulation results show that the proposed scheme significantly improves the EE of the DM-MIMO system and efficiently manages resource allocation.

Intelligent Reconfigurable Surface enhanced Ambient Backscatter Communication enabled Wireless Body Area Network

This paper considers an Intelligent Reconfigurable Surface (IRS)-enhanced Ambient Backscatter Communication (AmBC)-enabled Wireless Body Area Network (WBAN) system. We study the Base Station (BS) transmit power minimization problem, where the BS’s transmit beamforming vector and IRS’s reflecting coefficients are jointly optimized, subjected to the Signal-to-Noise Ratio (SNR) requirements of intra-WABN communication and throughput requirement of primary communication. To solve the non-convex problem, a near-optimal algorithm based on Semi-Definite Relaxation (SDR) and Successive Convex Approximation (SCA), and a low complexity algorithm based on IRS elements partition are proposed. Numerical results show that the two proposed algorithms considerably outperform the baseline schemes.

Structure Relaxation Approximation (SRA) for Elucidation of Protein Structures from Ion Mobility Measurements (II). Protein Complexes.

Characterizing structures of protein complexes and their disease-related aberrations is essential to understanding molecular mechanisms of many biological processes. Electrospray ionization coupled with hybrid ion mobility/mass spectrometry (ESI-IM/MS) methods offer sufficient sensitivity, sample throughput, and dynamic range to enable systematic structural characterization of proteomes. However, because ESI-IM/MS characterizes ionized protein systems in the gas phase, it generally remains unclear to what extent the protein ions characterized by IM/MS have retained their solution structures. Here, we discuss the first application of our computational structure relaxation approximation [Bleiholder, C.; et al. J. Phys. Chem. B 2019, 123 (13), 2756-2769] to assign structures of protein complexes in the range from ∼16 to ∼60 kDa from their "native" IM/MS spectra. Our analysis shows that the computed IM/MS spectra agree with the experimental spectra within the errors of the methods. The structure relaxation approximation (SRA) indicates that native backbone contacts appear largely retained in the absence of solvent for the investigated protein complexes and charge states. Native contacts between polypeptide chains of the protein complex appear to be retained to a comparable extent as contacts within a folded polypeptide chain. Our computations also indicate that the hallmark "compaction" often observed for protein systems in native IM/MS measurements appears to be a poor indicator of the extent to which native residue-residue interactions are lost in the absence of solvent. Further, the SRA indicates that structural reorganization of the protein systems in IM/MS measurements appears driven largely by remodeling of the protein surface that increases its hydrophobic content by approximately 10%. For the systems studied here, this remodeling of the protein surface appears to occur mainly by structural reorganization of surface-associated hydrophilic amino acid residues not associated with β-strand secondary structure elements. Properties related to the internal protein structure, as assessed by void volume or packing density, appear unaffected by remodeling of the surface. Taken together, the structural reorganization of the protein surface appears to be generic in nature and to sufficiently stabilize protein structures to render them metastable on the time scale of IM/MS measurements.

Joint carrier allocation and precoding optimization for interference-limited GEO satellite

The rise of flexible payloads on satellites opens a door for controlling satellite resources according to the user demand, user location, and satellite position. In addition to resource management, applying precoding on flexible payloads is essential to obtain high spectral efficiency. However, these cannot be achieved using a conventional resource allocation algorithm that does not consider the user demand. In this paper, we propose a demand-aware algorithm based on multiobjective optimization to jointly design the carrier allocation and precoding for better spectral efficiency and demand matching with proper management of the satellite resources. The optimization problem is non-convex, and we solve it using convex relaxation and successive convex approximation. Then, we evaluate the performance of the proposed algorithm through numerical results. It is shown that the proposed method outperforms the benchmark schemes in terms of resource utilization and demand satisfaction.

Sum of Age-of-Information Minimization in Aerial IRSs Assisted Wireless Networks

In this letter, we investigate a blocked wireless network in which multiple aerial intelligent reconfigurable surfaces (IRSs) mounted on unmanned aerial vehicles (UAVs) are deployed to assist devices in communication with one base station (BS). To improve the freshness of information received at the BS, we formulate a sum of age-of-information (AoI) minimization problem by optimizing the device scheduling, IRS phase shift, and deployment positions of aerial IRSs. The formulated problem is mixed-integer non-convex due to the existence of binary variables and the coupling among variables. To solve it, we commence by applying the clustering algorithm to reduce the complexity of global scheduling. Then, we decouple the optimization variables and propose an iterative algorithm based on binary variable relaxation and successive convex approximation (SCA) approach to deal with the non-linear relations among variables. Simulation results demonstrate that the proposed algorithm outperforms the benchmarks in improving the information freshness.

Secure Transmission by Leveraging Multiple Intelligent Reflecting Surfaces in MISO Systems

Recent advance of Intelligent Reflecting Surface (IRS) introduces a new dimension for secure communications by reconfiguring the transmission environments. In this paper, we devise a secure transmission scheme for multi-user MISO systems by leveraging multiple collaborative IRSs. Specifically, to guarantee the worst-case achievable secrecy rate among multiple legitimate users, we formulate a max-min problem that can be solved by an alternating optimization method to decouple it into multiple sub-problems. Based on semidefinite relaxation and successive convex approximation, each sub-problem can be further converted into convex problem and easily solved. Extensive experimental results demonstrate that our proposed scheme can adapt to complex scenarios for multiple users and achieve significant gain in terms of achievable secrecy rate. Compared to the traditional single IRS scheme, the proposed scheme can achieve better performance at the range of 2.4-6.4 bps/Hz with the increase in the number of reflecting elements in the multi-user scenarios. We also evaluate the gap between the secrecy rate for our proposed scheme under continuous phase shift/amplitude control and discrete phase shift/amplitude control, and our results show that the secrecy rate obtained from discrete approximation method converges to that achieved from the proposed scheme when increasing the discretization granularity.