Array Layout Research Articles

Hydrodynamic Interactions and Enhanced Energy Harnessing amongst Many WEC Units in Large-Size Wave Parks

Interactions between wave energy converters (WECs) can significantly affect the overall energy-harnessing performance of a wave park. Although large-size wave parks with many WEC units are commonly considered in practical applications, it is challenging to simulate such parks due to huge computational costs. This paper presents a numerical model that uses the boundary element method (BEM) to simulate wave parks. Each wave energy converter (WEC) was modelled as a comprehensive system, including WEC buoys, power take-off, and mooring systems, with hydrodynamic interactions included. Two classical layouts for arranging 16 units were simulated using this numerical model. The energy-harnessing performance of these array layouts was analyzed for both regular waves and a selection of irregular sea state conditions with different wave directions, wave heights, wave periods and water depths. For each layout, three WEC separation distances were studied. An increase of up to 16% in the power performance of the WEC under regular waves was observed, which highlights the importance of interaction effects.

Wave excitation force prediction for arrays of wave energy converters in directional waves

The implementation of advanced control strategies is an effective means of maximizing the energy production of wave energy converters (WECs), and most of them require future wave excitation forces to determine the optimal control sequence. The WECs deployed in arrays can enable a significant reduction in the cost of wave energy and improve prediction performance by incorporating excitation forces from the array. In this paper, a critical comparison of the excitation prediction methods, including the time series, machine learning, and neural network, for a two-body heaving point absorber WEC is presented. Considering the symmetry of the WEC and arrays, the directional spectrum is utilized to determine the reference measurement of wave excitation. The prediction methods are applied to isolated WEC and different array layouts. Moreover, additional sensitivity analyses are performed to evaluate the performance. The results show that the autoregressive with extra input (ARX) model has the best performance in short-term wave excitation force prediction. In most cases, the ARX model is weakly influenced by the sampling period and can adapt well to changes in the directional distribution and sea states of irregular waves, and the ARX model requires the least amount of computational time in the simulations.

Three-row MRI receive array with remote circuitry to preserve radiation transparency

Objective. Up to this point, 1.5 T linac-compatible coil array layouts have been restricted to one or two rows of coils because of the desire to place radiation-opaque circuitry adjacent to the coils and outside the window through which the linac beam travels. Such layouts can limit parallel imaging performance. The purpose of this work was to design and build a three-row array in which remotely located circuits permitted a central row of coils while preserving the radiolucent window. Approach. The remote circuits consisted of a phase shifter to cancel the phase introduced by the coaxial link between the circuit and coil, followed by standard components for tuning, matching, detuning, and preamplifier decoupling. Tests were performed to compare prototype single-channel coils with remote or local circuits, which were followed by tests comparing two and three-row arrays . Main results. The single-channel coil with the remote circuit maintained 85% SNR at depths of 30 mm or more as compared to a coil with local circuit. The three-row array provided similar SNR as the two-row array, along with geometry factor advantages for parallel imaging acceleration in the head–foot direction. Significance. The remote circuit strategy could potentially support future MR-linac arrays by allowing greater flexibility in array layout compared to those confined by local circuits, which can be leveraged for parallel imaging acceleration.

Control co-design for wave energy farms: Optimisation of array layout and mooring configuration in a realistic wave climate

This paper presents a novel Control Co-Design (CCD) methodology aimed at economically optimising the layout of wave energy converter (WEC) arrays. CCD ensures the synergy of optimised WEC and array parameters with the final control strategy, resulting in a comprehensive and efficient design of the array. By integrating a spectral-based control strategy into the array layout design, this study pursues the twin objectives of maximising energy absorption while reducing costs. To prove the performance of the proposed CCD methodology, an application case is proposed where the inter-device distance, alignment, and mooring configuration of a five-device array, considering realistic wave scenarios, are optimised. Energy capture and system cost evaluations are conducted, with results emphasising the significance of incorporating advanced control strategies in the design phase to improve energy absorption and reduce costs. With the application case, the study demonstrates that the optimal layout of a WEC array considering economic factors may differ from the optimal from purely technical factors, such as energy absorption, in the analysed case.

Wireless strain-field monitoring system for motion recognition via direct-ink-writing sensor-array

Large-area strain-monitoring is highly desired in various engineering applications. Despite the fact that the commercial strain gauges have been successfully used for strain measurement, there is still big challenge for this manually-pasting based solution especially for large-area monitoring. First, the wires of multiple commercial strain gauges for large-area monitoring will exhibit remarkably abundant and complex, and eventually reduce the reliability and convenience of the measurement system. Second, the commercial terminal instrument is usually function-redundant with complicated electronic configuration to match the low-sensitive metal-foil strain gauge. Meanwhile, the wire-based signal acquisition and processing system substantially limit the compatibility for moving objects. Here we take the advantages of direct-ink-writing (DIW) 3D printed sensor array, thereby propose a wireless-based solution for large-area strain field measurement, data transmission and processing. The sensitivity of the printed sensing unit is one order of magnitude higher than that of traditional strain gauges, while the sensor array layout is optimized for compatibility to the strain orientation and detecting domain. A high-frequency signal acquisitor is designed and assembled with a wireless transmitter for rapid multi-point strain detection and real-time data transmission. A remote data receiver and processing terminal are developed and integrated for twin-visualization of the detected strain field. In particular, the detected strain data are processed to construct a cascaded support-vector-machine (SVM) classifier, that successfully identify motion states of moving vehicles in high precision. This study provides insight into exploring the advantages of DIW printed sensor arrays combined with specifically-designed wireless system and strain-based dynamic recognition.

Numerical Simulation of the Influencing Factors of Array Jet Shock Cooling

Array jet impingement cooling is a significant technology of enhanced heat dissipation which is fit for high heat flux flow with large area. It is gradually applied to the cooling of electronic devices. However, The researches on the nozzle array mode and the uniformity of cooling surface still have deficiencies. Therefore, the influence of heat flux, inlet temperature, jet height, array mode and diversion structure on jet impingement cooling performance and temperature distribution uniformity is analyzed by means of numerical calculation. The results show that the heat transfer coefficient of jet impingement cooling increases linearly with the increment of heat flux and inlet temperature. With the increment of the ratio of jet height to nozzle diameter (H/d), the heat transfer coefficient increases first and then decreases, that is, there is an optimal H/d, which makes the heat transfer performance of the array jet impact cooling best. The temperature uniformity of array jet impact cooling is greatly affected by array mode. The improvement effect of nozzle array mode on temperature uniformity is ranked as sequential > staggered > shield > elliptical array. The overall temperature uniformity and heat transfer coefficient are increased by 5.88% and 7.29% compared with elliptical array. The heat transfer performance can be further improved by adding a flow channel to the in-line array layout, in which the heat transfer coefficient is increased by 6.53% and the overall temperature uniformity is increased by 1.45%.

Layout of Detection Array Based on Multi-Strategy Fusion Improved Adaptive Mayfly Algorithm in Bearing-Only Sensor Network.

The various applications of bearing-only sensor networks for detection and localization are becoming increasingly widespread and important. The array layout of the bearing-only sensor network seriously impacts the detection performance. This paper proposes a multi-strategy fusion improved adaptive mayfly algorithm (MIAMA) in a bearing-only sensor network to perform layout planning on the geometric configuration of the optimal detection. Firstly, the system model of a bearing-only sensor network was constructed, and the observability of the system was analyzed based on the Cramer-Rao Lower Bound and Fisher Information Matrix. Then, in view of the limitations of the traditional mayfly algorithm, which has a single initial population and no adaptability and poor global search capabilities, multi-strategy fusion improvements were carried out by introducing Tent chaos mapping, the adaptive inertia weight factor, and Random Opposition-based Learning. Finally, three simulation experiments were conducted. Through comparison with the Particle Swarm Optimization (PSO) algorithm, Mayfly Algorithm (MA), and Genetic Algorithm (GA), the effectiveness and superiority of the proposed MIAMA were validated.

Extended Kalman Filter-Based Vehicle Tracking Using Uniform Planar Array for Vehicle Platoon Systems.

We develop an extended Kalman filter-based vehicle tracking algorithm, specifically designed for uniform planar array layouts and vehicle platoon scenarios. We first propose an antenna placement strategy to design the optimal antenna array configuration for precise vehicle tracking in vehicle-to-infrastructure networks. Furthermore, a vehicle tracking algorithm is proposed to improve the position estimation performance by specifically considering the characteristics of the state evolution model for vehicles in the platoon. The proposed algorithm enables the sharing of corrected error transition vectors among platoon vehicles, for the purpose of enhancing the tracking performance for vehicles in unfavorable positions. Lastly, we propose an array partitioning algorithm that effectively divides the entire antenna array into sub-arrays for vehicles in the platoon, aiming to maximize the average tracking performance. Numerical studies verify that the proposed tracking and array partitioning algorithms improve the position estimation performance.

Structural behaviour of asymptotic geodesic hybrid timber gridshells

Asymptotic geodesic gridshells are a novel structural system that is fabricated from straight and flat planks. The planks are elastically bent and twisted around their slender dimension to achieve the desired geometry, while the tall dimension creates structural stiffness. This system combines the geometric features of asymptotic and geodesic curves to create a hybrid tri-hex network on doubly curved surfaces, and provides a stable grid to resist its self-weight and external loads. To comprehensively explore the structural capabilities of asymptotic geodesic gridshells, a full-scale timber gridshell prototype was designed and built. Loading tests, including local and one shell asymmetrical loading, were carried out to examine the structural behaviour of the gridshell. A nonlinear finite-element model was developed and subsequently validated using experimental data. The evaluation of the timber gridshell revealed its high performance under uniformly distributed loads, and the simulation indicated a viable live load capacity of 7.0 kN/m². In a parametric study, the influence of the polar array layout, the joint rotation stiffness, and the support condition on the structural performance of the hybrid gridshell are analysed. Parameters influencing the achievable span are discussed regarding strength, stiffness and buckling behaviour for future design considerations.

Pruning: a tool to optimize the layout of large scale arrays for ultra-high-energy air-shower detection

The deployment of several large scale arrays is envisioned to study astroparticles at ultra-high energies. In order to circumvent the heavy computational costs of exploring and optimizing their layouts, we have developed a pruning method. It consists in i) running a set of microscopic simulations and interpolate them over a dense, regularly spaced array of detection units, and ii) pruning the unnecessary units out of the layout, in order to obtain the shower footprint on a newly shaped layout. This method offers flexibility to test various layout parameters, instrumental constraints, and physical inputs, with a drastic reduction in the required CPU time. The method can be universally applied to optimize arrays of any size, and using any detection techniques. For demonstration, we apply the pruning tool to radio antenna layouts, which allows us to discuss the interplay between the energy and inclination of air-showers on the size of the radio footprint and the intensity of the signal on the ground. Some rule-of-thumb conclusions that can be drawn for this specific case are: i) a hexagonal geometry is more efficient than a triangular geometry, ii) the detection efficiency of the array is stable to changes in the spacing between radio antennas around 1000 m step size, iii) for a given number of antennas, adding a granular infill on top of a coarse hexagonal array is more efficient than instrumenting the full array with a less dense spacing.

Abstract 5808: Designing arrays for delivering tumor treating fields (TTFields) to the mouse head

Abstract Introduction: Tumor Treating Fields (TTFields) therapy is an approved treatment for glioblastoma (GBM), the most abundant malignant brain tumor. TTFields therapy is delivered to patients suffering from GBM continuously by two array pairs placed on their scalp. Since arrays for TTFields application to the mouse head are lacking, and as most GBM animal models are based on mice, in vivo studies of GBM treatment with TTFields are limited. The development of such arrays is challenging due to the small dimensions and specific geometries of the mouse head, but is needed to allow continued preclinical studies to broaden the understanding of the effects of TTFields on GBM. Methods: We tested various array layouts to identify one that will be suited to the specific geometries of the mouse head. For animal well-being, the selected array was required to minimally restrict head movement. Additionally, we investigated adhesive tapes to allow on one hand good adherence of the arrays to the skin, and on the other hand easy array removal. To examine the feasibility of treating mice with these arrays, they were applied to mice for 11 days, while recording the electric currents and the actual treatment time (from which the percent usage could be calculated). To validate that the selected array layout delivers meaningful field intensity to the desired region, we performed field measurements using a floating scope. Results: To tackle the limitation of the small head size, we developed an array layout in which only two arrays were situated on the head, while the opposing arrays were located on the mouse torso. Additionally, the arrays on the head were divided into two smaller disks. We also identified a thin and transparent adhesive tape (facilitating correct arrays positioning), that offered good tackiness and allowed easy removal without leaving residual adhesive on the skin. The arrays met the minimum treatment requirements: current ≥50 mA, usage ≥75%, field intensity ≥1 V/cm RMS. At the posterior side of the mouse head, at a location more directly underneath the arrays, field intensity was higher than at the anterior position. Conclusion: TTFields could be delivered at sufficient intensities to mice heads by utilizing specifically engineered arrays. Our newly developed arrays are flexible and strongly adhering to enable efficient electric field delivery. By allowing TTFields delivery to mice heads, we will facilitate further advancing this research field. Citation Format: Sewar Zbidat, Roni Blatt, Mariell Sellevoll, Martin Gabay, Inbar Schlachet, Shay Cahal, Shiri Davidi, Itai Tzchori, Adi Haber, Moshe Giladi, Yoram Palti. Designing arrays for delivering tumor treating fields (TTFields) to the mouse head [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 5808.

Numerical study on the sensitivity of photovoltaic panels to wind load on array layout

Offshore floating photovoltaics began to gradually enter people's vision due to the limitation of inland land resources. However, the offshore environment is harsh, and wind load is an essential factor in floating photovoltaic design. At the same time, the photovoltaic panel will be subjected to a large wind load in strong typhoon weather, which may cause a drag-driven or lift-driven instability for offshore floating photovoltaics. In this work, the effects of wind loads on six PV array structure configurations installed on offshore floating PV platforms at high Reynolds numbers are investigated by using the computational fluid dynamics numerical method. The differences in wind load on photovoltaic panels under different layout structures are analyzed and explained, including analysis of velocity and pressure distribution, turbulence field, and lift and drag coefficient of photovoltaic panels. The results showed array b with symmetrically staggered has less sensitivity to wind direction, less lifting torque, and relatively small pressure on the surface of the photovoltaic panel, which is a potential arrangement.

Optimal Design of Sparse Matrix Phased Array Using Simulated Annealing for Volumetric Ultrasonic Imaging with Total Focusing Method.

The total focusing method (TFM) is often considered to be the 'gold standard' for ultrasonic imaging in the field of nondestructive testing. The use of matrix phased arrays as probes allows for high-resolution volumetric TFM imaging. Conventional TFM imaging involves the use of full matrix capture (FMC) for ultrasonic signals acquisition, but in the case of a matrix phased array, this approach is associated with a huge volume of data to be acquired and processed. This severely limits the frame rate of volumetric imaging with 2D probes and necessitates the use of high-end equipment. Thus, the aim of this research was to develop a novel design method for determining the optimal sparse 2D probe configuration for specific conditions of ultrasonic imaging. The developed approach is based on simulated annealing and involves implementing the solution of the sparse matrix phased array layout optimization problem. In order to implement simulated annealing for the aforementioned task, its parameters were set, the acceptance function was introduced, and the approaches were proposed to compute beam directivity diagrams of sparse matrix phased arrays in TFM imaging. Experimental studies have shown that the proposed approach provides high-quality volumetric imaging with a decrease in data volume of up to 84% compared to that obtained using the FMC data acquisition method.

Abstract B032: Designing arrays for the mouse head to facilitate in vivo studies of Tumor Treating Fields (TTFields) treatment of glioblastoma

Abstract Background: Tumor Treating Fields (TTFields) therapy is a noninvasive, anticancer treatment delivered by two pairs of arrays placed on the skin surrounding the tumor location. Based on efficacy and safety data from phase 3 global clinical studies, TTFields therapy is FDA-approved and CE marked for treatment of glioblastoma (GBM), the most common malignant brain tumor. In vivo studies of TTFields in GBM models, which are mostly based on mice, are complicated by the relatively small size of the mouse head and corresponding limited surface area to apply the arrays. This challenge has thus far limited in vivo research on TTFields treatment in GBM. Materials and Methods: To identify a method for efficient delivery of TTFields to the mouse brain, we examined the ability of different array layouts to accommodate the geometries of the mouse head while minimally impacting head movement, taking into account that it may not be feasible to place two pairs of arrays on the head. The properties of different adhesive tapes, specifically their ability to attach to the skin, was also investigated. Finally, the ability of array layouts to deliver therapeutic intensities to the desired region was validated using simulations and direct electric field measurements. Results: Assessments showed an optimal layout consisted of arrays such that one of the pair was on the mouse head, and the other on the mouse torso; and the arrays for placement on the head divided into two smaller disks, A thin, transparent adhesive tape was identified that allowed the arrays to be securely attached to the skin, but was easily removed without leaving residues. Validation studies using simulations demonstrated that the array layout met the minimum treatment requirements (field intensity ≥1 V/cm RMS; current ≥50 mA), and facilitated TTFields usage for ≥75% of each day. Conclusions: These data show that TTFields treatment can be effectively delivered to the heads of mice by utilizing carefully designed arrays. Our newly developed mouse head arrays are a flexible construct, that adheres strongly to the skin, and enables efficient electric field delivery to the mouse brain. These improvements in the delivery of TTFields treatment to mice will facilitate research of TTFields as a therapy for GBM. Citation Format: Sewar Zbidat, Roni Blatt, Mariell Sellevoll, Martin Gabay, Inbar Schlachet, Shay Cahal, Shiri Davidi, Itai Tzchori, Amal El-Mabhouh, Adi Haber, Moshe Giladi, Yoram Palti. Designing arrays for the mouse head to facilitate in vivo studies of Tumor Treating Fields (TTFields) treatment of glioblastoma [abstract]. In: Proceedings of the AACR Special Conference on Brain Cancer; 2023 Oct 19-22; Minneapolis, Minnesota. Philadelphia (PA): AACR; Cancer Res 2024;84(5 Suppl_1):Abstract nr B032.

Low-latency equal optical path difference sampling for multi-field VLWIR interference signals

The spaceborne Fourier Transform Spectrometer has been utilized for vertical atmospheric soundings with a HgCdTe infrared focal plane arrays (FPAs) detector. However, the VLWIR FPA Fourier spectrometer system faces the difficulty of poor sensitivity due to the major contribution of the system sampling error. In this work, low-latency data acquisition of multi-field VLWIR interference signals based on VLWIR FPA Fourier spectrometer system is realized with an optimized field programmable gate array (FPGA) timing driver scheme and layout algorithm. This scheme can effectively reduce routing delay and constrain critical timing paths, and thus leads to a significant decrease in the deviation of equal optical path difference sampling time from 10.27μs to 0.10μs. Interferograms and spectrograms are efficiently obtained. Furthermore, the average value of noise equivalent spectral radiance (NESR) in VLWIR FPA Fourier spectrometer system, is reduced by 1.75% by timing optimization. In particular, the decay of the NESR can be as high as 15% for some of the pixels. These results illustrate that the proposed scheme will acquire hyperspectral data accurately with VLWIR FPA and meet the needs of rapid soundings development of the Geostationary Interferometric Infrared Sounder (GIIRS) availing a rapid prediction of the appearance of an extreme weather event.

Research on the 3D indoor positioning technology based on feature light source

Nowadays, positioning technologies mainly consist of three methods: positioning based on satellites, positioning based on RF and positioning based on self-contained sensors. However, due to the complex propagation characteristics of wireless signals in indoor environments, the existing positioning technologies widely used in outdoor environments cannot meet the requirements of indoor applications. Compared to outdoor environments, indoor environments are more complex, and wireless signals are affected by various factors, making it difficult for existing indoor positioning systems to meet the requirements of high accuracy and low cost. Thus, a three-dimensional indoor positioning technology based on a characteristic light source and a spherical lighting device is proposed in this paper to solve the problems. The technology measures the angle of the optical signal through a spherical lighting device, which can receive light in all directions and obtain height information compared with flat mode. Pseudo-source interference caused by the wave nature of light will not be introduced with the use of the particle nature of light. Array layout and optimization algorithms can further improve positioning accuracy. A simulation experiment in Matlab is conducted. The experimental results and the analysis of accuracy confirmed that the positioning accuracy can be controlled within a small error. Three-dimensional indoor positioning technology can achieve high accuracy at a low cost.

Investigation of Electrical Configuration Topologies for Enhancing the Performance of Solar Photovoltaic Water Pumping System

The numerous solar energies provide humans with clean, environmentally friendly, and abundant energy resources. Electricity shortages and high diesel prices have an impact on rural water irrigation systems and drinking water supplies. Solar energy for water pumping could be an alternative to standard electric and diesel pumping systems. The rising importance of solar photovoltaic water pumping systems (SPVWPS) as a feasible power source in rural, inaccessible, and unconnected areas drives the study. These locations, often in poor nations like India, lack conventional power. Solar energy is converted into electrical energy via photovoltaic (PV) technology, which is then used to power a DC or AC submersible or surface water pump. PV module configurations are crucial in improving a PV system’s performance. Many researchers have studied the solar water pumping design on series parallel combination and acquired the best system efficiency, but the other configurations, Total Cross Tied (TCT) and Bridge Link (BL) have never been employed in a solar water pumping system. This research aims to investigate the experimental comparison of different PV configurations for better system efficiency on different operating parameters. These PV array layouts were considered in a uniform situation. The result shows that power increases with increase in radiation and the flow rate provided by (6Sx2P) configuration is 18,956 l/day of water and calculated the best average pump efficiency.

Performance analysis of two generations of heaving point absorber WECs in farms of hexagon-shaped array layouts

ABSTRACT Numerical analyses are presented for two generations of a floating heaving point absorber wave energy converter (WEC) installed with different farm array layouts. The wave farm configurations are based on WECs developed by Waves4Power. The numerical models are developed in the DNV software package, Sesam. Parametric studies of the isolated WEC configurations and farm array layouts are conducted under typical environmental conditions and various incident wave directions to understand the hydrodynamic power performance and the levelised cost of energy (LCoE). Hexagonal layouts are proposed for deploying the WEC units and compared with a 10-unit layout termed StarBuoy, which has been reported in previous work. The results of the present study confirm that the interactions between arrayed units in a farm can have either positive or negative effects on the LCoE, which is dependent on the array layout and environmental conditions. The hexagonal array layouts lead to lower LCoE owing to constructive interaction effects.

Extracted power optimization of hybrid wind-wave energy converters array layout via enhanced snake optimizer

In recent years, wind energy and wave energy are widely concerned as highly developmental clean energy alternatives to traditional energy sources. From the perspective of cost reduction and power output enhancement, in this study, a V27-225 kW wind turbine and wave energy converter are combined to construct a hybrid wind-wave energy converters (HWWEC), which greatly improves the power generation and operation stability. The optimization of wind-wave energy layout that involves strategically placing wave energy devices can directly influence the energy output of the whole system. To enhance the overall power generation efficiency, the optimal array configuration becomes a challenging but also promising solution regarding this concern. To optimize the array configuration that is composed of multiple HWWECS, this study develops an enhanced snake optimizer (ESO) based optimization scheme including chaotic initialization, asynchronous learning factors, and levy flight, which shows strong optimum searching ability while avoiding falling into local optimums. Simulation results under various case studies of three-line WECs consisting of three, six, and twelve buoys indicate that the ESO achieves the highest absorption power compared to other algorithms, particularly, the output power achieved by ESO is 144.337 kW higher than that obtained by the original SO.

An efficient unused integrated circuits detection algorithm for parallel scan architecture

In recent days, many integrated circuits (ICs) are operated parallelly to increase switching operations in on-chip static random access memory (SRAM) array, due to more complex tasks and parallel operations being executed in many digital systems. Hence, it is important to efficiently identify the long-duration unused ICs in the on-chip SRAM memory array layout and to effectively distribute the task to unused ICs in SRAM memory array. In the present globalization, semiconductor supply chain detection of unused SRAM in large memory arrays is a very difficult task. This also results in reduced lifetime and more power dissipation. To overcome the above-mentioned drawbacks, an efficient unused integrated circuits detection algorithm (ICDA) for parallel scan architecture is proposed to differentiate the ‘0’ and ‘1’ in a larger SRAM memory array. The proposed architecture avoids the unbalancing of ‘0’ and ‘1’ concentrations in the on-chip SRAM memory array and also optimizes the area required for the memory array. As per simulation results, the proposed method is more efficient in terms of reliability, the detection rate in both used and unused ICs and reduction of power dissipation in comparison to conventional methods such as backscattering side-channel analysis (BSCA) and network attached storage (NAS) algorithm.