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This article is concerned with the problem of determining an unknown source of non-potential, external time-dependent perturbations of an incompressible fluid from large-scale observations on the flow field. A relaxation-based approach is proposed for accomplishing this, which leverages a nonlinear property of the equations of motions to asymptotically enslave small scales to large scales. In particular, an algorithm is introduced that systematically produces approximations of the flow field on the unobserved scales in order to generate an approximation to the unknown force; the process is then repeated to generate an improved approximation of the unobserved scales, and so on. A mathematical proof of convergence of this algorithm is established in the context of the two-dimensional Navier-Stokes equations with periodic boundary conditions under the assumption that the force belongs to the observational subspace of phase space; at each stage in the algorithm, it is shown that the model error, represented as the difference between the approximating and true force, asymptotically decrements to zero in a geometric fashion provided that sufficiently many scales are observed and certain parameters of the algorithm are appropriately tuned; the issue of the sharpness of the assumptions, among other practical considerations such as the transient periods between updates, are also discussed., Comment: 17 pages, introduction and appendix expanded, main results reworded for clarity, additional remarks and references added, accepted to Proc. R. Soc. Edinb. A: Math

A new backward compatible WiFi amendment is under development by the IEEE bd Task Group towards the so-called IEEE 802.11bd, which includes the possibility to transmit up to three repetitions of the same packet. This feature increases time diversity and enables the use of maximum ratio combining (MRC) at the receiver to improve the probability of correct decoding. In this work, we first investigate the packet repetition feature and analyze how it looses its efficacy increasing the traffic as an higher number of transmissions may augment the channel load and collision probability. Then, we propose two strategies for adaptively selecting the number of transmissions leveraging on an adapted version of the channel busy ratio (CBR), which is measured at the transmitter and is an indicator of the channel load. The proposed strategies are validated through network-level simulations that account for both the acquisition and decoding processes. Results show that the proposed strategies ensure that devices use optimal settings under variable traffic conditions.

Recent advancements in V2X communications have greatly increased the flexibility of the physical and medium access control (MAC) layers. This increases the complexity when investigating the system from a network perspective to evaluate the performance of the supported applications. Such flexibility needs in fact to be taken into account through a cross-layer approach, which might lead to challenging evaluation processes. As an accurate simulation of the signals appears unfeasible, a typical solution is to rely on simple models for incorporating the physical layer of the supported technologies, based on off-line measurements or accurate link-level simulations. Such data is however limited to a subset of possible configurations and extending them to others is costly when not even impossible. The goal of this paper is to develop a new approach for modelling the physical layer of vehicle-to-everything (V2X) communications that can be extended to a wide range of configurations without leading to extensive measurement or simulation campaign at the link layer. In particular, given a scenario and starting from results in terms of packet error rate (PER) vs. signal-to-interference-plus-noise ratio (SINR) related to a subset of possible configurations, we derive one parameter, called implementation loss, that is then used to evaluate the network performance under any configuration in the same scenario. The proposed methodology, leading to a good trade-off among complexity, generality, and accuracy of the performance evaluation process, has been validated through extensive simulations with both IEEE 802.11p and LTE-V2X sidelink technologies in various scenarios.

Spectrum scarcity is one of the main challenges of future wireless technologies. When looking at vehicle-to-everything (V2X), this is amplified as spectrum sharing could impact road safety and traffic efficiency. It is therefore of particular importance to study solutions that allow the coexistence, in the same geographical area and in the same channels, of what are today the main V2X access technologies, namely IEEE 802.11p and sidelink LTE-V2X Mode 4. In this work, in addition to investigating the impact of the reciprocal interference, which we demonstrate to have a strong impact especially on the first and in congested channel conditions, a mitigation solution is extensively studied, which is based on the insertion of the IEEE 802.11p preamble at the beginning of the LTE-V2X sidelink transmission. The proposal, which is also under discussion within the standardization bodies, requires no modifications to the IEEE 802.11p protocol stack and minor changes to LTE-V2X sidelink. This solution is directly applicable to upcoming IEEE 802.11bd and extendable to NR-V2X sidelink. The paper shows, through analysis and simulations in free-flow and dense scenarios, that the proposal allows for a mitigation of collisions caused by co-channel coexistence under low to high-load channel conditions and that the improvement is also granted in congested cases when combined with additional countermeasures. Regarding the latter aspect, in particular, different approaches are compared, demonstrating that acting on the congestion control mechanisms is a simple but effective solution.

Most V2X (Vehicle-to-Everything) applications rely on broadcasting awareness messages known as CAM (Cooperative Awareness Messages) in ETSI or BSM (Basic Safety Message) in SAE standards. A large number of studies have been devoted to guarantee their reliable transmission. However, to date, the studies are generally based on simplified data traffic models that generate awareness messages at periodic intervals or with a constant message size. These models do not accurately represent the real generation of CAM messages that follow specific mobility-based rules. Using simplified and unrealistic traffic models can significantly impact the results and validity of the studies, and hence accurate models for the generation of awareness messages are necessary. This paper proposes the first set of models that can realistically generate CAM messages. The models have been created from real traces collected by two car manufacturers in urban, sub-urban and highway test drives. The models are based on mth order Markov sources, and model the size of CAMs and the time interval between CAMs. The models are openly provided to the community and can be easily integrated into any simulator.

In the last few years, two technologies have been developed to enable direct exchange of information between vehicles. These technologies, currently seen as alternatives, are ITS-G5, as commonly referred in Europe, and sidelink LTE-vehicle-to-everything (LTE-V2X) (one of the solutions of the so-called cellular-V2X, C-V2X). For this reason, the attention has been mostly concentrated on comparing them and remarking their strengths and weaknesses to motivate a choice. Differently, in this work we focus on a scenario where both are used in the same area and using the same frequency channels, without the assistance from any infrastructure. Our results show that under co-channel coexistence the range of ITS-G5 is severely degraded, while impact on LTE-V2X is marginal. Additionally, a mitigation method where the CAM data generation is constrained to periodical intervals is shown to reduce the impact of co-channel coexistence, with less degradation on ITS-G5 performance and even improvement for LTE-V2X.

An intrinsic property of almost any physical measuring device is that it makes observations which are slightly blurred in time. We consider a nudging-based approach for data assimilation that constructs an approximate solution based on a feedback control mechanism that is designed to account for observations that have been blurred by a moving time average. Analysis of this nudging model in the context of the subcritical surface quasi-geostrophic equation shows, provided the time-averaging window is sufficiently small and the resolution of the observations sufficiently fine, that the approximating solution converges exponentially fast to the observed solution over time. In particular, we demonstrate that observational data with a small blur in time possess no significant obstructions to data assimilation provided that the nudging properly takes the time averaging into account. Two key ingredients in our analysis are additional boundedness properties for the relevant interpolant observation operators and a non-local Gronwall inequality.

We construct a determining form for the surface quasi-geostrophic (SQG) equation with subcritical dissipation. In particular, we show that the global attractor for this equation can be embedded in the long-time dynamics of an ordinary differential equation (ODE) called a determining form. Indeed, there is a one-to-one correspondence between the trajectories in the global attractor of the SQG equation and the steady state solutions of the determining form. The determining form is a true ODE in the sense that its vector field is Lipschitz. This is shown by combining De Giorgi techniques and elementary harmonic analysis. Finally, we provide elementary proofs of the existence of time-periodic solutions, steady state solutions, as well as the existence of finitely many determining parameters for the SQG equation.

Understanding and controlling the surface adhesion of pathogenic bacteria is of urgent biomedical importance. However, many aspects of this process remain unclear (for example, microscopic details of the initial adhesion and possible variations between individual cells). Using a new high-throughput method, we identify and follow many single cells within a clonal population of Escherichia coli near a glass surface. We find strong phenotypic heterogeneities: A fraction of the cells remain in the free (planktonic) state, whereas others adhere with an adhesion strength that itself exhibits phenotypic heterogeneity. We explain our observations using a patchy colloid model; cells bind with localized, adhesive patches, and the strength of adhesion is determined by the number of patches: Nonadherers have no patches, weak adherers bind with a single patch only, and strong adherers bind via a single or multiple patches. We discuss possible implications of our results for controlling bacterial adhesion in biomedical and other applications.

Most bacteria swim in liquid environments by rotating one or several flagella. The long external filament of the flagellum is connected to a membrane-embedded basal body by a flexible universal joint, the hook, which allows the transmission of motor torque to the filament. The length of the hook is controlled on a nanometer scale by a sophisticated molecular ruler mechanism. However, why its length is stringently controlled has remained elusive. We engineered and studied a diverse set of hook- length variants of Salmonella enterica. Measurements of plate-assay motility, single- cell swimming speed, and directional persistence in quasi-2D and population- averaged swimming speed and body angular velocity in 3D revealed that the motility performance is optimal around the wild-type hook length. We conclude that too-short hooks may be too stiff to function as a junction and too-long hooks may buckle and create instability in the flagellar bundle. Accordingly, peritrichously flagellated bacteria move most efficiently as the distance travelled per body rotation is maximal and body wobbling is minimized. Thus, our results suggest that the molecular ruler mechanism evolved to control flagellar hook growth to the optimal length consistent with efficient bundle formation. The hook-length control mechanism is therefore a prime example of how bacteria evolved elegant but robust mechanisms to maximize their fitness under specific environmental constraints.

Most bacteria swim in liquid environments by rotating one or several flagella. The long external filament of the flagellum is connected to a membrane-embedded basal body by a flexible universal joint, the hook, which allows the transmission of motor torque to the filament. The length of the hook is controlled on a nanometer scale by a sophisticated molecular ruler mechanism. However, why its length is stringently controlled has remained elusive. We engineered and studied a diverse set of hook- length variants of Salmonella enterica. Measurements of plate-assay motility, single- cell swimming speed, and directional persistence in quasi-2D and population- averaged swimming speed and body angular velocity in 3D revealed that the motility performance is optimal around the wild-type hook length. We conclude that too-short hooks may be too stiff to function as a junction and too-long hooks may buckle and create instability in the flagellar bundle. Accordingly, peritrichously flagellated bacteria move most efficiently as the distance travelled per body rotation is maximal and body wobbling is minimized. Thus, our results suggest that the molecular ruler mechanism evolved to control flagellar hook growth to the optimal length consistent with efficient bundle formation. The hook-length control mechanism is therefore a prime example of how bacteria evolved elegant but robust mechanisms to maximize their fitness under specific environmental constraints.