Mixed reality technology can give humans an intuitive visual experience, and combined with the multi-source information of the human body, it can provide a comfortable human–robot interaction experience. This paper applies a mixed reality device (Hololens2) to provide interactive communication between the wearer and the wearable robotic limb . Hololens2 can obtain human body information, including eye gaze, hand gestures, voice input, etc. It can also provide feedback information to the wearer through augmented reality and audio output, which is the communication bridge needed in human–robot interaction. Implementing a wearable robotic arm integrated with HoloLens2 is proposed to augment the wearer’s capabilities. Taking two typical practical tasks of cable installation and electrical connector soldering in aircraft manufacturing as examples, the task models and interaction scheme are designed. Finally, human augmentation is evaluated in terms of task completion time statistics. The supernumerary robotic limb (SRL) is a new type of wearable robot that is different from prosthetic and exoskeleton robots. It improves the human body’s ability to move, perceive, and operate through mechanical and human limbs’ integration, mutual assistance, and cooperation ,2,3. AccIt is also imperative to design appropriate interaction methods to make SRLs not affect the wearer’s operation ability and rationally use human body information. Ref.  divided The use of collaborative robots in the industry has grown over the past few years. Augmented Reality (AR), as a prominent and promising tool to support human operators in understanding and interacting with robots, has been applied in many human–robot collaboration and cooperative industrial applications. Research on the human–robot collaboration of head-mounted displays (HMDs) and projectors has attracted more attention . CompareThe structure of this paper is as follows. First, the research work related to this paper is introduced. Then, the composition of the system and the interaction framework combined with HoloLens2 multi-source information are explained to realize the interaction with SRL. Aiming at cable installation and electrical connector soldering tasks, the task models and interaction methods are constructed. Finally, through comparative experiments, the feasibility of the system and the enhanced performance on the human body are evaluated.Unlike traditional collaborative robots, SRLs have a closer human–computer interaction mode and a cooperative mode of moving with the human body. Therefore, the current human–robot interaction methods for SRLs focus on researching natural interaction methods that do not affect the wearer’s ability to operate. Refs. ,13 have Advances in display and vision technologies create new interaction methods that enable information-rich, real-time communication in shared workspaces. The visualization methods applied by AR in human–computer collaboration mainly include HMDs, spatial augmented reality projectors, fixed screens, and hand-held displays (HHDs) . The curThe wearable robotic arm system comprises a 6-degree-of-freedom (6 DOF) SRL previously introduced in our prior work , which lTo reduce weight and enhance structural strength, the arms are fabricated from standard carbon fiber tubes with inner diameters of 26 mm and outer diameters of 30 mm. Most other components are constructed from aluminum alloy (AL6061-T6). The total weight of one robotic arm, including its structure, motors, and sensors, amounts to 3.45 kg. The HoloLens2 headset weighs 566 g, while additional components such as the backplate, controller, and battery contribute an extra 2.2 kg. Consequently, the overall system weight totals about 9.67 kg.To ensure wearer comfort, we designed a backplate that conforms closely to the wearer’s back and secured it with flexible fabric straps. We simplified the wearing process by carrying the SRL robot on the back like a backpack, with adjustable buckles for tension control. The HoloLens headset is worn directly on the head and can be adjusted for fit using a rear-mounted knob. Safety measures have been implemented in the SRL, including mechanical limits and software-based safeguards, enhancing the wearer’s security to a certain extent. The overall system’s wearing configuration is convenient, but its weight, though not excessive, may potentially cause some discomfort during extended use.The working mode of the wearable robotic arm is to move with the body and cooperate closely with the wearer. Therefore, we want to manipulate the robot and obtain effective feedback without affecting the human’s ability to operate. As a head-mounted display, HoloLens2 is easy to wear and intuitive to use. HoloLens2 can more conveniently obtain multi-modal information about the human body and provide rich feedback to realize an efficient and natural interaction mode. In this process, HoloLens2 is a communication medium between the wearer and the SRLs, as shown in The program construction of HoloLens2 and the integration method of SRL are shown in Building an application through which the wearer interacts with the SRL is a complex process based on Mixed Reality. This mainly depends on the interactive information that the wearer can express in the working situation. To propose a complete interaction framework, the way of information transfer and fusion in the process of SRL augmentation assisting the wearer needs to be analyzed. The role of HoloLens2 mainly includes the transmission of the wearer’s intention (task information), the working mode of SRLs and the feedback of sensor information, the operation guidance and assistance of the wearer’s operation, and the safety protection of the wearer. Specifically, the transmission of human intentions can also be decomposed into the target location, task content (specified task operation), and task trigger timing. The trigger timing of the task is critical, which involves the rationality of the SRL movement timing. For example, Leader–Follower ,30 is a The interaction architecture focuses on effectively combining the human body’s multimodal information with the functional modules of Mixed Reality, as shown in To construct the interaction method between HoloLens2 and the SRL and share the virtual space data, we propose a method to establish the relationship between the virtual space coordinate system and the actual space coordinate system. Regarding tracking methods, there are mainly marker-based and markerless approaches, which are gradually increasing. Because of the projection system, the feature extraction software focuses more on tracking the target. However, the markerless approach generally has higher requirements on the performance of the equipment and a large amount of calculation. Thus, we use a marker-based method for tracking. Although some may use the markers for the first calibration, once completed, they require little recalibration since they are not removable. The device moves with the body for a wearable robotic arm, so a real-time tracking method is needed. To establish the relationship between the virtual space coordinate system and the robot real space coordinate system, we designed a coordinate transfer method using the Vuforia QR code recognition technology and the position and attitude of the “virtual object” presented by AR as an intermediate medium. Since the position of the SRL moves with the wearer, the T265 tracking camera is used to obtain the pose change in the robotic limb base, and the relationship between the origin of the virtual space coordinate system and the robotic limb real space coordinate system is corrected in real time. The specific calculation method is constructed as follows.The variables determined by the installation position are defined as follows: the transformation matrix of the QR code relative to the SRL is Therefore, through the above coordinate system relationship construction method, we can communicate the AR object information in HoloLens with the SRL to realize the application of multimodal communication.The wearer’s collaboration with the SRL can be divided into different task phases. The task model includes task state, parameters, and switching conditions. The task model can also be fine-tuned to adapt to similar process tasks. We first build task models for the cable installation and electrical connector soldering tasks.In the aircraft manufacturing process, workers need to install many cables in the cabin, and the problems they face are the neat arrangement of cables and the bundling of multi-strand cables. Workers need to grasp and tension the cables with both hands to complete the bundling task, which is complex and cumbersome for both hands. The task of soldering cables and electrical connectors is equally challenging. It involves the manipulation of two soldering objects, a soldering tin and a soldering iron: a total of four things. If the SRL can assist workers in completing these tasks, it will improve the worker’s operational efficiency and comfort.The process of SRL assisting the operator to complete the cable installation task can be expressed as follows: (i) the operator organizes the cables and places them near the installation location; (ii) the SRL helps the operator grasp the cables and apply a specific force to keep the tension of the cables; (iii) the operator concentrates on installing and fixing the cables; (iv) after the cables are installed, the SRL returns to the initial position. The process of the SRL assisting the operator to complete the soldering task is similar but more complicated: (i) the SRL grabs the electrical connector delivered by the operator; (ii) the operator drags the end of the SRL to the vicinity of the position to be soldered; (iii) the SRL adjusts the posture of the electrical connector according to the posture of the soldering iron, giving the operator a comfortable soldering angle; (iv) the operator completes the soldering of the electrical connector and cable; (v) after the task is completed, the SRL returns to the initial position.FSM can be expressed as a tuple containing the following: task state space S, state switching condition T, SRLs motion mode set M, and state transition function Different task states can be divided according to the flow of the task. The cable installation task and electrical connector soldering task model based on PS), “cooperation state” (CS), “installation state” (IS), and “end state” (ES). The operation process of the soldering task includes five states: “preparation state” (PS), “drag state” (DS), “cooperation state” (CS), “soldering state” (SS), and “end state” (ES). The state space of the cable installation task , and after finishing the arrangement, the switching condition CS. The SRL triggers IS). The operator triggers ES), and the next cycle operation can be performed.In the cable installation task, the mode of cooperation between SRL and the operator is as follows. (i) The operator arranges the cables (PS) and triggers the switching condition DS) and triggers CS). The SRL maintains the spatial position and pose of the tip (SS). The operator triggers the switching condition ES).The cooperation mode of the electrical connector soldering task is as follows. (i) The operator prepares the soldering tools  in the task completion time between the two conditions. The task completion time under the condition of wearing the device  was significantly shorter than that under the condition of not wearing the device . Similarly, we conducted a correlation analysis and a paired-sample t-test on the electrical connector welding task experiment data. The results demonstrated a significant correlation in the data  and a statistically significant difference in task completion time between the two conditions (t(49) = 11.114; p < 0.001). The task completion time was significantly shorter when wearing the equipment  compared to when not wearing the equipment .The average time for the ten participants to complete the task is shown in The results show that in two typical industrial tasks, the proposed system reduces the task completion time and improves the operator’s efficiency. The reduction in task time was more pronounced in soldering tasks. It may have something to do with how necessary the task requires a third arm. But its completion time is more unstable, and there is a phenomenon in which the task completion time after wearing the system exceeds that of completing the task alone. This may be related to different subjects’ soldering skills and equipment adaptability. The mean completion time of tasks shows that the system can improve the efficiency of human operations. It also demonstrates the usability of the equipment.After completing the testing phase, we gathered qualitative feedback from participants regarding their subjective experiences. Participants reported experiencing heightened physical strain and indicated potential limitations in their capacity to utilize the system over prolonged durations. Some participants conveyed feelings of nervousness and apprehension stemming from their initial interactions and concerns regarding the safety implications associated with close proximity to the robotic arm. Furthermore, participants noted that the AR display obstructed their vision field, leading to operational task disruptions. The field of view provided by the HoloLens was found to be somewhat restricted, necessitating substantial head movements to adjust the viewing angle. Moreover, the calibration procedures carried out before the experiment were observed to be intricate and demanding in terms of effort.These negative findings underscore the system’s limitations, encompassing physical and cognitive burdens, safety concerns, issues with obstructed line of sight, and operational complexities. We posit that alleviating psychological stress and enhancing safety could be achieved by incorporating additional holographic displays to provide prompt guidance for operations. Addressing the line-of-sight obstruction challenge entails combining gaze and spatial perception data to jointly optimize the positioning of holographic images, thus minimizing occlusions. Furthermore, simplification of the system calibration procedures is warranted.(1)FSM-based task models. The task model is adaptable and can be used for similar tasks. Although the method based on Mixed Reality has an intuitive feedback function, its visual occlusion is also a problem that needs to be considered in future work.This paper proposes an SRL interaction method based on Mixed Reality, which has the characteristics of intuitive display and easy development. This will provide new research ideas for the interaction of wearable robotic limbs. This paper also proposes an AR-based coordinate-tracking method and (2)The average task time under different experimental conditions was tested. The results indicate the possibility of system availability and enhanced human manipulation capabilities. But there is also some increased body load. This factor needs to be considered in designing both the structure of wearable robotic arms and interaction methods. The differences in the three-hand tasks will also affect the system’s ability to enhance the human body and the load index.(3)In the experiments of the cable installation task, the operation mode of replacing the human hand to hold the cable with the SRL and installing the cable is selected. Of course, it is also feasible to install cables on wearable robotic limbs and keep the cables by hand, but the task of cable installation has more subjective factors, and the operation is more complicated. Thus, this paper adopts a more straightforward collaboration strategy. We found that the ability of the wearable robotic limb to maintain the force and position of the end is essential, and it is used to ensure the tension and neatness of the cable, which can be used as a follow-up research direction.(4)In the experiments of the soldering task, a suitable angle was adopted to constrain the soldering angle between the electrical connector on the SRL and the end of the soldering iron to improve soldering comfort. The interaction research of wearable robotic limbs can pay more attention to the information of the human hand and the tools operated by the human hand. The wearable robotic limbs combine this information to construct strategies for interacting and collaborating with the wearer.FSM and interaction methods have been designed for two aircraft manufacturing tasks: cable installation and an electrical connector welding task. The results from the experiment involving ten participants suggest that the system enhances the operators’ task completion efficiency. However, some participants also reported experiencing physical and psychological burdens, obstructed vision, and operational complexity. This shows that the system has certain limitations. These negative aspects merit consideration in future work. The approach presented in this paper attempts to apply mixed reality to wearable robotic limbs, demonstrating initial potential for improving wearer efficiency. This paper proposes a novel human–robot interaction approach for wearable robotic limbs based on Mixed Reality and multimodal human information. We have constructed an interactive framework and a real-time tracking method for the system comprised of HoloLens and SRL. Task models based on


Owing to their complex structural design and control system, musculoskeletal robots struggle to execute complicated tasks such as turning with their limited range of motion. This study investigates the utilization of passive toe joints in the foot slip-turning motion of a musculoskeletal robot to turn on its toes with minimum movements to reach the desired angle while increasing the turning angle and its range of mobility. The different conditions of plantar intrinsic muscles (PIM) were also studied in the experiment to investigate the effect of actively controlling the stiffness of toe joints. The results show that the usage of toe joints reduced frictional torque and improved rotational angle. Meanwhile, the results of the toe-lifting angle show that the usage of PIM could contribute to preventing over-dorsiflexion of toes and possibly improving postural stability. Lastly, the results of ground reaction force show that the foot with different stiffness can affect the curve pattern. These findings contribute to the implementations of biological features and utilize them in bipedal robots to simplify their motions, and improve adaptability, regardless of their complex structure. Musculoskeletal robots are designed to imitate the structure and movement of actual beings  to utiliSlip-turning is a turning mechanic that is said to overcome the physical limitations of robots . PreviouIn this paper, we propose an experimental investigation of the foot slip-turning motion of the musculoskeletal robot equipped with toe joints and PIM. The objective is to improve the musculoskeletal robot’s slip-turning capabilities. According to our hypothesis, implementing slip-turning on toe joints in a musculoskeletal robot is expected to yield increased body rotational angle, regardless of whether there are joints in the yaw axis or the vertical axis of the human. Additionally, we propose that the activation of the PIM during motion can affect foot stiffness, which can influence the robot’s postural stability and capability to perform quick movements.A series of experiments were conducted to assess the effectiveness of toe joints in enabling foot slip-turning. The first experiment aimed to compare slip-turning performance between a foot equipped with toe joints and a foot without toe joints. The second experiment focused on demonstrating the role of the PIM in preventing over-dorsiflexion of the toes, thus improving the robot’s postural stability. In the final experiment, the active utilization of the PIM was investigated to determine its impact on motion propulsion.The findings of this study could contribute to the advancement of musculoskeletal robot locomotion by introducing a novel approach using the foot structure to improve slip-turning capabilities. The flexibility of the joints combined with the active control of the PIM could provide a versatile solution for achieving agile and efficient movements, enhancing the robot’s adaptability in various real-world scenarios. Future research can focus on further optimizing the design and control of the toe joints, exploring their potential applications in more complex locomotion tasks, and investigating the integration of similar mechanisms in other robotic systems or implementations for medical purposes such as gait training or rehabilitation.The remainder of this paper is organized as follows: For imitation of the movements of biological beings, applying the musculoskeletal structure to a robot is a viable approach to mimic the biomechanical characteristics of living systems. This approach allows robots to replicate the biological features that motor-driven robots cannot achieve with their mechanical design alone. On the other hand, the entire musculoskeletal structure could be challenging to implement in a robot due to its complexity and sophistication. To address this problem, a simplified version of the design is adopted, focusing on the key components necessary for realizing the desired robot motion to alleviate the complexities associated with control architecture.The number of muscles required for the robot’s turning motion was chosen based on the biomechanical studies on human turning gait  and muscAs a result, the structure of the bipedal robot consists of four joints and seven muscles in each leg, eight DoFs in total. The bipedal musculoskeletal robot named “PneuTurn‐T” see  was deveThe musculoskeletal robot is driven by pneumatic actuators called pneumatic artificial muscles (PAMs) or the McKibben artificial muscles. The PAMs are capable of acting as muscles of the biological being by contracting and stretching themselves, pulling tendons, and driving the joints. Pneumatic actuators offer some advantages over hydraulic or electric actuators, other than their elasticity. They provide a simple and cost-effective solution with a high power-to-weight ratio, making them suitable for building light-weighted robots. The PAMs offer quick and responsive operation, allowing for rapid changes in direction with a wide range of motions, and can be easily replaced to change the parameter. Our McKibben muscles are made of an 8-mm-diameter rubber tube with 1 mm thickness, with both ends plugged using pneumatic fittings; one closed-end and one open-end connected to an air tube and covered with polyester braided sleeves. The length of each PAM and its contraction ratio is calculated before the fabrication of the PAMs and then measured and tested before being implemented in the robot to accomplish the desired range of motion, referring to the average human range of motion see .The control system of the robot is depicted in The slip-turning motion of the robot is achieved by providing a muscle activation pattern to the controller. The muscle activation pattern was created to actuate all 14 PAMs simultaneously in the correct sequence to realize the motion.The slip-turn was previously demonstrated by some motor-driven robots: WABIAN-2 , HRP-4C The control method for the bipedal robot is a joint control method that directly controls the angle of each joint through the activation of PAMs. To realize the slip-turning motion, the muscle activation pattern was specifically generated to replicate the joint movements observed during human spin turns. Each muscle was activated for a comparable duration and speed as indicated by the reference EMG pattern and joint angle measurements. The EMG pattern was used for generating the activation timing, as the signal provided explicit indications of muscle activation without any delay caused by signal transmission. In contrast to an electroencephalogram (EEG), the EMG pattern allowed for more accurate and immediate detection of muscle activation, making it a suitable choice for generating precise activation timings in the control process. By studying the EMG pattern, we can roughly estimate the activation time of the muscles. When the graph indicates muscle activation, the corresponding valve connected to the PAM represents that the muscle will undergo a change in its state. This change may involve supplying air, exhausting air, or closing the air supply, depending on the specific requirements of the muscle’s activation. Previous studies have highlighted that determining the timing of muscle activation alone does not provide sufficient information . Once thThe activation time of the PAMs is controlled through the microcontroller, changing the valve state while causing some delays between each phase. The angular speed of each joint is a fixed value, manually adjusted by using flow control valves (SMC AS2002F-06) connected to the supplying air tube. In comparison to their experiments , our robThe experiments were conducted to investigate the impact of utilizing toe joints and the PIM in the slip-turning motion. The realization of the slip-turning motion, implemented in our robot “PneuTurn‐T” using the muscle activation pattern, is shown in The experimental setup for data collection is illustrated in The objective of the experiments was to investigate the effects of slip-turning on different types of feet. Four distinct foot configurations were utilized in the experiments, each contributing to the study as shown in The first experiment aimed to compare the turning behavior of a foot with a fixed toe to a foot with a passive toe, demonstrating the advantages of utilizing toe joints in slip-turning motion. In the second experiment, the toe-lifting angle was compared between a foot with an unrestricted toe and a foot with a passive toe, highlighting the role of foot stiffness provided by the PIM. Lastly, an experiment was conducted to compare the ground reaction forces among all foot types, investigating propulsion and postural stability during similar robot movements. The summary of all three experiments is shown in In the first experiment, the contribution of using the toe joint in the slip-turning motion was examined by comparing the foot with a fixed toe to the foot with a passive toe. The results of frictional torque revealed a noticeable change in frictional torque at 0.2 s, as depicted in The second results show the rotational angle of the robot’s body measured by the 9-axis IMU installed on the robot’s body during slip-turning motion, as shown in θL was measured to analyze the results. In the experiment comparing slip-turning on the foot with and without foot stiffness from the PIM, restraining the motion, the toe-lifting angle The occurrence of toe over-dorsiflexion can lead to a loss of postural balance in the robot due to reduced foot contact area in an unstable state, similar to individuals with floating toes .The final experiment aimed to compare the ground reaction force (GRF) among all types of feet to assess the impact of the changing foot stiffness on the motion. The GRF pattern provided insights into the contributions of foot stiffness see . The resOn the other hand, following the initial propulsion at 0.2 s, a noticeable decrease in ground reaction force (GRF) was observed in all types of feet, suggesting a potential disruption or an enhancement in postural stability during the robot’s motion. A higher GRF value indicated a greater weight transfer toward the left foot in the front, shifting the COM position closer to the anterior direction, which is favorable for maintaining the robot’s posture at the end of the motion.As our robot was designed with a human-like musculoskeletal structure, the position of the COM of the body was supposed to be placed in a similar manner. In humans, the support polygon aligns with the direction of the toes, pointing toward the anterior side of the body. During the neutral stance of a human, the COM tilts slightly forward in favor of balancing the whole-body stability, where the shifting of the COM is possible within the area of the support polygon. However, our robot, lacking an upper body, exhibits a posterior inclination of the COM, making it challenging to achieve a proper positioning of the COM for maintaining postural stability. Moreover, during rapid motions, although the foot structure aids in stabilizing the body, the absence of a balanced body weight amplifies the robot’s backward tendency, further compromising postural stability. Nonetheless, this characteristic of the robot could be utilized to further investigate the body stability in the absence of upper extremities, offering potential applications in medical practices for patients with upper-limb paralysis.Due to the compressibility of air, the robots driven by the PAMs provide lower accuracy of joint control and unstable velocity , which mAs previous studies have mentioned, the PIMs are more likely to contribute to foot stabilization than to balance control during postural challenges , such asThis paper demonstrated a turning motion of the musculoskeletal robot, which is usually unfavorable to execute due to its limited range of motion and complex controls. The bipedal robot could realize the slip-turning motion on toe joints about its yaw axis, while all eight joints of the robot were placed on the pitch axis. The foot with toe joints has enabled the heel-off motion of the musculoskeletal robot and could reduce the foot contact area during the turning motion compared to the rigid foot with a fixed toe, resulting in a reduction of frictional torque, minimizing its power, and an increase in the rotational angle. The second experiment proved that by using the PIM to restrain the toe joint, the robot could prevent the over-dorsiflexion of the toe, which can contribute to the improvement of static postural stability in the anterior–posterior direction. Meanwhile, the active toe could generate an even stronger propulsion, which can be useful in a quick motion. The unique structure of the human foot needs to be studied further to understand its contributions to the intrinsic tension force and the stability of the foot in a quick motion. Our findings contribute to the advancement of robotic systems that mimic biological structures and movements and widen the possibilities for future research in the field of robotics.Future works include studies for optimizing control strategies for the PIM, exploring the adaptability of the foot, enhancing the motion, and integrating sensory feedback into the control system. These advancements will contribute to the development of more versatile and capable robots with improved locomotion abilities, enabling applications in various fields such as search and rescue, exploration, medical practice, and human-assistive robotics.


Light scattering spectroscopy is a powerful tool for studying various media, but interpretation of its results requires a detailed knowledge of how media excitations are coupled to electromagnetic waves. In electrically conducting media, an accurate description of propagating electromagnetic waves is a non-trivial problem because of non-local light-matter interactions. Among other consequences, the non-locality gives rise to the anomalous (ASE) and superanomalous (SASE) skin effects. As is well known, ASE is related to an increase in the electromagnetic field absorption in the radio frequency domain. This work demonstrates that the Landau damping underlying SASE gives rise to another absorption peak at optical frequencies. In contrast to ASE, SASE suppresses only the longitudinal field component, and this difference results in the strong polarization dependence of the absorption. The mechanism behind the suppression is generic and is observed also in plasma. Neither SASE, nor the corresponding light absorption increase can be described using popular simplified models for the non-local dielectric response. Two types of the skin effect are commonly distinguished: the normal (NSE) one with the exponential spatial decay of the field, and the anomalous (ASE) skin effect with the power law decay. The field profile inside the media is not directly accessible in experiment, but the skin effect determines the penetration interval, where the field interacts with the media and loses its energy. This changes the surface impedance and, thus, the light scattering.Propagation and scattering of electromagnetic (EM) wave in conductive media, e.g. in metals, is a physical problem of fundamental importance. Delocalized charged carriers in such media screen the EM field modifying both reflection and absorption. The screening is referred to as 5. This leads to the normal skin effect with the exponential field decay z is the distance from the metal surface, and a is the characteristic decay length7. In this regime, the frequency dependence of the surface impedance follows the law In the Hagen-Rubens regime of lower frequencies 12. The frequency dependence for the surface impedance becomes 12.At higher frequencies of 13, which is usually connected to the ASE as well14. However, in the interval of frequencies and wave vectors that corresponds to the scattered light, the dielectric response of the metal is practically local, and the skin effect is normal6. Also, unlike the absorption increase at lower frequencies, the higher frequency second peak depends strongly on the field polarization and on the scattering angle. It disappears for the normal angle scattering.When the frequency increases further, to the optical range in normal metals, the absorption demonstrates another peaked enhancement16. However, the SASE takes place only for large wave vectors q and c is the speed of light).It has been recently shown that in the optical frequency range a metal can demonstrate the so-called superanomalous skin effect (SASE), where the field decays as In this work we revisit the classical problem of scattering of EM waves on a metallic surface using an exact solution of the EM problem with the non-local Lindhard-Reuter-Sondheimer permittivity. We demonstrate that despite the mismatch of the wave vectors, the second absorption peak is directly connected to the SASE not ASE. It is shown that the two absorption peaks are facilitated by different loss mechanisms that depend on the field polarization. While the ASE losses affect the transverse field component, the SASE suppresses the longitudinal one, similarly to the conventional Landau damping. This explains the polarization dependence of the second absorption peak and the fact it disappears for the normal scattering.22, fail to capture the SASE absorption peak and one needs more advanced models that take into account kinetic properties of metallic electrons23. This fact is very important for modelling optical properties of conductive media when the non-locality in the dielectric response plays a significant role24, e.g. to study propagation of plasmons in nanostructures28, near-field radiative heat transfer29, thermal and zero-point EM energy and forces on curved metallic boundaries30, losses in EM emitters placed near a metallic surface31, and propagation of EM waves in plasma14.It is also shown that popular approximations for the non-local dielectric response, such as hydrodynamic and single-pole modelsThe results are presented as follows. We first outline the solution for the light scattering problem for a metallic surface with an arbitrary dielectric response of the metal. Then, using this solution, we calculate the absorptivity frequency spectrum, introduce the SASE and ASE and discuss their relation to the scattering characteristics. We demonstrate that a popular single-pole approximation fails to describe the SASE and its contribution to the absorption. A generic nature of the SASE- as well as ASE-related loss mechanisms is illustrated by considering a classical Maxwellian plasma. Finally, we summarize the results and discuss their significance.1.The absorption spectrum is obtained by solving the scattering problem for an EM wave reflected from a metal-dielectric interface as shown in Fig. 3233. A model where weakly interacting metallic electrons are described by the Boltzman equation with the SRM for the scattering at the interface13 is also referred to as the semiclassical model (SCM) in the literature23 Although the adopted model appears simplified, it captures essential physics of the the SASE for as long as the characteristic skin length much exceeds the actual width of the interface. In normal metals the microscopic width of the interface is estimated as the inverse of the Fermi wave number 34, which much smaller than other pertinent characteristic lengths in the problem, including the skin width, estimated as The dielectric response of the metal will be taken into account by using results for the kinetic model that describes metal electrons. Further, we assume the metal-vacuum interface is infinitely thin. Thereby, we neglect the finite-width effects such as depletion of the electron density in the vicinity of the interface. We also consider a specular reflection model (SRM) for metal electrons scattering at the interface )diffusion parameter35, where the Maxwell equations are complemented with the additional boundary condition [see 36). The consistency of this approach requires the boundary conditions for the polarization correspond to the kinetic model for metallic electrons. It is ensured for the SCM model, for which one obtains an exact solution of the EM problem. However, in many other situations, in particular, for semiconductors with excitons, the validity of the ABC is debated41.The adopted model for the electrons and the interface means the normal component of the electrical current at the interface vanishes, which implies a certain boundary condition for the respective polarization component ˙⊥=0 see . The scation see . The sol42. For TM (p) polarized waves, the magnetic field is parallel to the interface, while for TE (s) polarized waves, the electric field is parallel. The reflection coefficient for both cases is given as s-wave polazrization: p-wave polarization: Here we use notations x-component only, and other quantities are related to the incoming wave as Solving Maxwell equations on each side of the interface and matching the solutions at it is relatively straightforward albeit tedious. An interested reader can find details of the calculations in the 21 and transverse (Reuter & Sondheimer)10 components given as 43, and does not reduce to a simple substitution The dielectric response of a normal metal is a sum of ion polarization and a contribution of freely moving charge carriers (electrons). The latter comprises the part due to interband electronic transitions and the part induced by electrons moving within the same conduction band - intraband scattering. In this work, we are interested in the latter because it yields the non-local dielectric response. It is well described using the model of weakly interacting particles with a quadratic energy dispersion and a spherical Fermi surface. This model gives a permittivity tensor with the longitudinal (Lindhard)k is not too large, and need to be changed to the full expressions when k becomes comparable to the Fermi wave number k corrections introduce only relatively small quantitative changes (less than  20%) to the results and do not modify the conclusions.The LRS model contains three material parameters, entclass1pt{minimaThe non-locality of the dielectric response is manifested by the 45.In our numerical calculations below, we consider silver as the prototype metal with the following parameters  and S . In A approximation, we assume RS model , and forpression . The surIn S approximation, we take, respectively, the LRS model  for \docWe now use A and S approximations are to calculate the relative absorptivity 21. This model takes a non-local nature of the metal dielectric response into account by amending the Drude expression with an additional k-dependent terms into the denominator one obtains the transverse permittivity ask’s. This expression can be also obtained using a popular hydrodynamic model for the dielectric response34, which, however, yields different coefficients k48 It is commonly assumed that the single-pole approximation describes all physically relevant effects due to non-locality in the dielectric response22. However, as we will demonstrate it is not the case with the SASE and the related absorption peak at higher frequencies.Qualitative differences between the two peaks can be also clearly demonstrated by adopting a popular Silin-Klimontovich-Lindhard model for the permittivityThe relative absorptivity le model  is shownle model  is definn in Eq.  and takiwith Eq.  obtainedentclass1pt{minimafrom Eq. . NevetheIn contrast, the SASE contribution to the impedance  and the enhanced absorption of light scattered on a surface of a conductive medium. The analysis is done by using an exact scattering solution for the chosen model for the dielectric response of the medium. We use the solution to extract both the SASE and the light scattering spectrum, and demonstrate that the SASE manifests itself in the additional enhancement of the light absorption in the optical frequency range The origin of both peaks is related to the non-locality of the dielectric response and collisionless damping of EM waves in an electrically conductive medium. However, the loss mechanisms due to SASE and ASE differ: the ASE suppresses the transverse field component, whereas the SASE affects the longitudinal one. This difference gives rise to strong dependence of the absorption spectrum on the polarization and incident angle of scattered light waves.It is important to note that the SASE increases the energy loss even though the domain of frequencies and wave lengths where the SASE is observed is well outside those of the scattered light. The reason is that the light scattering generates a continuum of surface plasmons modes including those lying in the frequency/wave number interval where the SASE takes place. The generation of surface plasmons in the SASE domain leads to a deeper field penetration and, therefore, larger energy losses of the scattered light. The loss mechanism is related to the Landau damping where the energy of the longitudinal plasmon wave is transferred collisionlessly to the kinetic energy of charge carriers. The mechanism takes place in any electrically conductive medium. It requires the Landau damping and the longitudinal component of the electric field in the propagating EM wave. The latter is ensured by the scattering geometry when the light is scattered at a non-normal angle.k. These factors enhance a generation of surface plasmons leading to a larger energy loss. It is known that the light-plasmon coupling can be increased by scratching the metal surface or by placing small light scatterers in its vicinity. Also, numerical calculations using phenomenological models for the diffusive electron scattering on imperfect surfaces demonstrated only quantitative but not qualitative changes in the absorptivity spectrum33. However, further analysis is needed as the SASE-related effects are not accounted in those models.A generic origin of the loss mechanism leads us to a conclusion that the same or even larger SASE absorptivity enhancement is expected when the metal surface is not perfect. Surface irregularities randomize the scattering angle for both the EM wave and electrons in the metal. This results in a larger contribution of the longitudinal field component of ab EM wave propagating inside the metal and in a larger contribution of the waves with large Finally, we note that the visibility of the SASE peak in experiments depends on many factors, in particular, the decay rate of the carrier states. The calculations for silver demonstrate that interband transitions in the optical frequency range do not suppress the SASE peak, which remains visible at intermediate incident angles. The SASE-induced effects should, thus, reveal themselves by comparing absorption spectra for different polarization and scattering angle of the incoming light. These differences cannot be described using popular hydrodynamic models or single-pole approximations for the dielectric permittivity function.Supplementary Information.


Cell-to-cell variability in protein concentrations is strongly affected by extrinsic noise, especially for highly expressed genes. Extrinsic noise can be due to fluctuations of several possible cellular factors connected to cell physiology and to the level of key enzymes in the expression process. However, how to identify the predominant sources of extrinsic noise in a biological system is still an open question. This work considers a general stochastic model of gene expression with extrinsic noise represented as fluctuations of the different model rates, and focuses on the out-of-equilibrium expression dynamics. Combining analytical calculations with stochastic simulations, we characterize how extrinsic noise shapes the protein variability during gene activation or inactivation, depending on the prevailing source of extrinsic variability, on its intensity and timescale. In particular, we show that qualitatively different noise profiles can be identified depending on which are the fluctuating parameters. This indicates an experimentally accessible way to pinpoint the dominant sources of extrinsic noise using time-coarse experiments. These fluctuations (or noise) can lead to phenotypic differences even in genetically identical cells sharing the same history and environment.Noise can often be detrimental for the cell since it affects the precision and reliability of several processes, for example related to signalling. Indeed, a high noise level has been associated to partial or complete loss of cellular functions –3, and tFocusing specifically on the gene expression process, two possible sources of fluctuations can be defined, i.e. intrinsic and extrinsic noise. Intrinsic noise arises from the inherently stochastic nature of the molecular reactions involved in the transcription, translation, and degradation of messenger RNAs (mRNAs) and proteins. Extrinsic noise is instead the result of fluctuations in global cellular factors such as the concentration of key macromolecules (e.g. ribosomes and polymerases) involved in the process performing catalytic/enzymatic activity , 22. TheE. coli [Noise propagation through gene regulation is another key source of gene expression noise. In fact, the number of regulatory inputs of a gene is correlated with its expression variability in E. coli  and eukaE. coli , 38, andE. coli , 40.A large amount of theoretical and experimental work has focused on disentangling the contributions to protein fluctuations from intrinsic and extrinsic sources (see for example –43). On The specific definition of what is considered extrinsic noise depends on the system one wants to explicitly model . We focus on a single gene and, from a modelling standpoint, extrinsic noise can be defined as fluctuations of the parameters of the expression process such as degradation and production rates. All the possible biological sources of extrinsic noise listed above can affect in complex ways one or more parameters. For example, growth rate fluctuations directly impact the dilution rate of proteins through volume fluctuations, but at the same time can change the protein production rates by affecting the concentration of key enzymes, such as ribosomes, that are closely coupled with cell growth . The proThis work focuses on this problem by looking at the consequences of extrinsic noise on the out-of-equilibrium dynamics of gene expression. This regime represents the dynamical approach to a steady state, during which the reactions of molecule production and degradation are not yet balanced. Specifically, we will provide analytical expressions supported by simulations that characterize how the protein level and its fluctuations evolve during gene activation and inactivation in the presence of extrinsic fluctuations on different parameters. On top of the theoretical interest of this analysis, the results have immediate practical applications. In fact, the different dynamic profiles of protein noise that we characterized naturally provide an experimentally accessible method to distinguish between different extrinsic-noise scenarios.2.2.1.The ‘standard model’ of stochastic gene expression takes into account messenger RNA and protein production and degradation as first-order chemical reactions –50. AfteThe degradation rate of mRNA molecules sets their average lifetime  minutes . On the division , 50–52, n(2)/γp .The master equation describing this simple two-step model of gene expression  can be s is zero . In partFor stable proteins, the timescale separation between the dynamics of mRNAs and proteins ic noise , 54 and E. coli and yeast have suggested that this is the typical case for highly expressed genes by looking at the scaling of protein noise with the average protein level [in level , 44. Intin level .We will also consider the dynamics of a gene at steady state that is inactivated at the transcriptional level. In this case, the average protein evolution in time is given bySo far we have only included intrinsic fluctuations since all the rates were constant. To include extrinsic fluctuations, we introduce a generic cellular factor on rates . For exaExtrinsic fluctuations often have a lifetime that is not negligible and can be comparable to the cell cycle and to protein half-life , 44, 56.To explore the role of both extrinsic fluctuations strength and timescale, we model the dynamics of the cellular factor as a bursty birth-and-death process with constant production and degradation rates  lead to higher protein noise, as the comparison between their analytical expressions in The Taylor expansion of the extrinsic contribution for small on rates .On the other hand, the protein noise dynamics The contribution of The generalization of this simple argument allows us to roughly quantify the impact of extrinsic fluctuations at any time through the factorization explained in the This approximation is displayed as a dashed blue line in In the case of fluctuations of The minimum values of A relevant implication of this analysis is that the simple observation of the dynamics of protein noise, which is experimentally accessible, can clearly distinguish between alternative sources of gene-expression variability, even if the parameter values are not known.3.3.E. coli. This section explores in detail the role of the strength of extrinsic fluctuations in shaping the single-cell expression dynamics. To model the biologically relevant range of extrinsic fluctuations orted in  about thThe dashed lines in 3.4.The specific timescale of extrinsic fluctuations crucially depends on their biological origin and can be slow or fast with respect to the relevant timescale of protein halflife. For instance, slow fluctuations of a transcription factor level would imply extrinsic fluctuations acting on the transcription rate with a relatively long timescale In the opposite setting (i.e. As mentioned before, at the beginning of the dynamics At the steady state (However, while the analytical expression seem generally accurate, the noise exceeds the prediction in simulations with The sigmoidal dependence of protein fluctuations on the extrinsic noise timescale suggests the presence of an effective noise filter. To survive the filtering, the effective frequency of extrinsic fluctuations must be of the same order or lower than the frequency of intrinsic fluctuations. In fact, the possible behavior of simple genetic circuits as low-pass filters was previously investigated using frequency domain analysis ,64. Spec3.5.The analysis has focused so far on the gene activation dynamics. This section studies the time-evolution of protein noise in the case of a sudden transcriptional repression. We consider a gene expressed at steady-state level whose transcription rate goes to zero at time zero, and we analyze the following protein dynamics when extrinsic noise affects different parameters. Again a mathematically controlled comparison (defined in the As the expression level progressively approaches zero, the intrinsic contribution grows exponentially, following the grey continuous line in the inset of Our theoretical predictions for To determine the role of The trend of The fluctuation trends in the gene deactivation dynamics do not have qualitatively different behaviors as in the case of gene activation, there is a general increase in protein noise . HoweverAs the inset of 3.6.One single parameter could be predominantly affected by extrinsic fluctuations as we have assumed so far. For example, if fluctuations in ribosome concentration are the main source of extrinsic noise, as it has been hypothesized in fast-growing bacteria , the traPrevious studies have shown that extrinsic fluctuations can combine constructively or destructively at the steady state depending on their action on parameters , 43. HerMore specifically, a single extrinsic factor When two sources of noise independently affect the transcription and degradation rates, a simple additive combination can be observed. In other words, the total extrinsic noise is well described by the sum of the extrinsic contributions we previously calculated with a single fluctuating parameter. Therefore, the total protein noise can be simple written asWhen a single extrinsic factor This expression is plotted as a continuous purple line in On the contrary, when a single source of stochasticity affects The non-monotonous trend of protein noise, which is the hallmark of dominant extrinsic fluctuations in 4.The analysis of noise has always played a crucial role in our quantitative understanding of basic biological processes –69. MoreThe observation that equilibrium distributions could not be sufficient to characterize the noise sources was previously recognized in an analysis on the role of RNA degradation fluctuations . AnalogoWe used a simple and general modelling framework to keep it amenable of analytical calculations and applicable to different biological systems. The actual cellular mechanisms giving rise to extrinsic noise are only phenomenologically captured by a generic ‘cellular factor’ ll cycle , 78 and ll cycle , 79, 80 ll cycle . Along tll cycle –35. It wWhile this work focuses on the dynamics of an isolated gene, a natural extension will be to consider more complex regulatory interactions, such as the ubiquitous circuits of auto-regulation, feed-forward loops and regulatory cascades. Noise propagation through transcriptional regulation is a known substantial source of extrinsic noise , 37, andIn the framework of synthetic biology, genetic circuits can be designed using different types of regulators, thus introducing controlled modulations of specific rates, from transcription rates to degradation rates –84. The Finally, the presence of extrinsic noise can have relevant consequences on the timing precision of genetic circuits. Models of stochastic timing in gene expression have typically focused on the consequences of intrinsic noise –87. Howe


Textile-based sensors fabricated using the direct-coating method are the appropriate choice to meet the aspects of flexibility, non-invasiveness, and lightness for continuous monitoring of the human body. The characteristics of the sensor substrate are directly influenced by factors such as the type of weave, thread fineness, fabric density, and the type of polymeric constituent fibers. The fabric used as the sensor substrate, fabricated using the direct-coating method, must be capable of retaining the electrode paste solution, which has higher viscosity, on one surface of the fabric to avoid short circuits during the fabrication process. However, during its application, this fabric should allow the easy passage of analyte solutions with low viscosity as much as possible. Hence, an appropriate fabric construction is required to serve as the substrate for textile-based sensors to ensure the success of the fabrication process and the effectiveness of the resulting sensor’s performance. The development of the structural design of the fabric to be used as a substrate for non-invasive biosensors with a multilayer concept is carried out by weaving and sewing processes utilizing polyester-viscose fibers. During the production process, variations are applied, such as weft yarn density, the characterization of wetting time, absorption rate, maximum wetted radius, spreading speed, and accumulative one-way transport index. The most suitable fabric for use as a substrate for non-invasive biosensors with a multilayer concept, such as in this research, is a fabric with a weft thread density of 70 strands per inch, along with the addition of an analyte transfer thread configuration. Health measurement devices, including those for glucose, lactic acid, and cholesterol monitoring, are anticipated to exhibit excellent performance throughout their usage . These dTextile-based sensors created through the direct-coating method are a suitable choice for fulfilling the criteria of flexibility, ease of transportation, non-invasiveness, and lightness. These sensors heavily rely on the design and structure of their substrate, which includes the arrangement of layers and electrode positions. The positioning of the electrodes must be carefully arranged to prevent any contact between them prior to the introduction of the analyte. This precaution is essential to prevent short circuits during the fabrication process. Simultaneously, the sensor should facilitate the easy penetration of low viscosity analyte solutions. This enables the analyte to access all surfaces of the working electrode, counter electrode, and reference electrode. This, in turn, has a direct impact on the minimum amount of analyte required to initiate reduction and oxidation reactions on the sensor, as well as the initial detection time during measurements. Therefore, a well-designed sensor structure is imperative to achieve optimal performance in textile-based sensors employing the multilayer concept. Double-faced woven fabric offers the advantage of a thicker structural design, which serves as a barrier against short circuits during the electrode paste coating process. This fabric has a layered structure composed of two groups of warp threads, causing the upper and lower surfaces of the fabric to be more separated compared to typical fabrics. The configuration of this layered structure on the substrate establishes a moisture barrier that significantly influences the movement of both liquid and vapor between the two fabric surfaces ,5. This Polyester–viscose (65: 35) was used as the warp yarn, which was procured from Dhanar Mas Concern in Bandung, Indonesia, while 100% polyester was employed as the weft yarn, sourced from Elephant Star, also in Bandung, Indonesia. The substrate material in this context comprised a blend of polyester and rayon viscose fibers, strategically chosen to attain the utmost spreading radius and wetting speed ,16. The Double-faced woven fabric has a thick structural formation, which can prevent short circuits during the coating process in the sensor fabrication. The substrate employed in this sensor exhibits a layered design structure meticulously arranged to provide optimal permeability. The arrangement of this stratified structure on the substrate creates a moisture barrier that has a substantial impact on the transfer of both liquids and vapors between the two fabric layers . The thrOne method employed to regulate permeability involves the incorporation of additional threads oriented perpendicularly to both the warp and weft yarn axes, connecting the upper surface to the lower surface of the fabric (interlacing thread). This method is commonly referred to as the multistitched fabric structure . The intThe production of the double-faced fabric in this research was accomplished using a Picanol GT-Max (rapier) 12 Dobby Weaving loom, with the motor operating at a set speed of 400 RPM d. The adThe fabrication process involved the utilization of 6600 warp threads, with a density of 98 warp threads per inch. The adjustment of variations in the number of weft yarn was determined by gradually reducing them by 10 strands, resulting in densities of 90 strands per inch, 80 strands per inch, and 70 strands per inch e. A low A woven fabric with a weft yarn count of 90 strands per inch exhibits a higher density compared to fabrics with 80 and 70 weft strands per inch. The density of the fabric is directly proportional to its weight but inversely proportional to its permeability . FabricsThe results of the measurement of wetting time characteristics can be observed in The porosity of the double-faced fabric with a weft density of 70 strands per inch decreases after the addition of the analyte transfer threads (ATT), as demonstrated in According to the terminology defined by AATCC (American Association of Textile Chemists and Colorists), the absorption rate is the average value of a fabric’s absorption capacity over a period of 20 s. The results of measuring the characteristics of the absorption rate are presented in The measurement results indicate that the fabric with a weft thread density of 70 strands per inch achieves the highest maximum wetted radius on its surface, specifically with a value of 20 mm. The maximum wetted radius values for fabrics with weft thread densities of 90 and 80 strands per inch, respectively, fall within the ranges of 6–9 mm and 7.5–10 mm, as depicted in Based on measurements of wetting time characteristics, fluid spreading rate on the fabric surface, absorption rate, and maximum horizontal wetted radius of the fabric surface, it can be generally concluded that fabrics with a weft thread density of 70 strands per inch and the fabrics with a weft thread density of 70 strands per inch with ATT are the most suitable variation in this research. However, it is necessary to analyze the fabric’s ability to vertically diffuse fluid from one fabric surface to another (Axis—Z), as depicted in The measurements of the accumulative one-way transport index indicate that fabrics with a weft thread density of 70 strands per inch have the lowest values compared to fabrics with weft thread densities of 90 and 80 strands per inch, as shown in 2R groups. This condition facilitates transient hydrogen bonding with water molecules, thereby initiating the diffusion mechanism within the analyte transfer threads’ configuration [The addition of an analytical configuration of transfer threads to a fabric with a weft thread density of 70 threads per inch results in a cumulative increase of 16.8% in the one-way fluid flow index. This enhancement is attributed to the ability of fluid to diffuse through the hydrophilic constituent fibers of the analytical transfer thread, which contains -OH, C=O, and -COguration . Within guration . The mecguration .All quantitative data obtained from prior measurements underwent analysis in accordance with the AATCC Test Method 195-2009 . SubsequAccording to the analysis using the AATCC method, it has been determined that fabrics manufactured with a specific structural design, utilizing polyester-viscose fibres material and a weft thread density of 70 strands per inch are capable of meeting the classification of moisture management fabric. In the context of this research, the most suitable fabric to serve as a substrate for a non-invasive sensor with a multilayer concept is the one with a weft thread density of 70 strands per inch, supplemented with an analyte transfer thread configuration. It is essential to note that the fluid requires a certain amount of time to reach the peak of wetting and absorption of the fabric during the biosensor application process.Therefore, further investigation is warranted to determine the specific duration required for this process. This can be accomplished by analyzing the data obtained from measuring the relationship between the moisture content in the fabric and time, utilizing fabric substrates with a weft thread density of 70 strands per inch and an additional analyte transfer thread configuration. This analysis will provide valuable insights into the kinetics of fluid interaction with the fabric, which are crucial for optimizing the performance of the non-invasive biosensor.


Heat exchangers (HXs) play a critical role in maintaining human thermal comfort and ensuring product safety and quality in various industries. However, the formation of frost on HX surfaces during cooling operations can significantly impact their performance and energy efficiency. Traditional defrosting methods primarily rely on time-based control of heaters or HX operation, overlooking the actual frost formation pattern across the surface. This pattern is influenced by ambient air conditions (humidity and temperature) and surface temperature variations. To address this issue, frost formation sensors can be strategically placed within the HX. However, the non-uniform frost pattern poses challenges in sensor placement. This study proposes an optimized sensor placement approach using computer vision and image processing techniques to analyze the frost formation pattern. Through creating a frost formation map and evaluating various sensor locations, frost detection can be optimized to control defrosting operations with higher accuracy, thereby enhancing the thermal performance and energy efficiency of HXs. The results demonstrate the effectiveness of the proposed method in accurately detecting and monitoring frost formation, providing valuable insights for sensor placement optimization. This approach presents significant potential in enhancing the overall performance and sustainability of the operation of HXs. Frost formation remains a significant challenge to the efficiency of air conditioning and refrigeration systems. In light commercial systems, heat exchangers (HXs) with a large area-to-volume ratio are particularly susceptible to frost accumulation on fin surfaces under subfreezing temperature conditions ,2,3. TheVarious defrosting methods have been developed to address frost formation ; howeverDemand defrost aims to address the frost formation issue through predicting its occurrence via the calculation of influencing parameters, detection of accumulation symptoms, or direct frost measurement . VariousGe et al.  developeTo assess the accuracy of these sensors, an accurate frost detection method must be employed to cross-check sensor measurements with actual frost formation.Computer vision techniques have been employed to detect frost formation in HXs ,23. ThesIn a mainstream application, the use of computer vision methods for frost detection in the HX of refrigeration systems can provide accurate results, but the need for specialized equipment, complex setups, and processing power can present challenges in terms of cost, space, and practicality. A small low-cost sensor, such as those developed in previous works , could pPrior research  developeThis study introduces a novel application of computer vision in analyzing frost formation in HXs for the optimization of sensor placement. Unlike previous approaches that primarily focused on using computer vision for frost detection or to control defrosting operations, our research explores the usage of computer vision as a tool for the optimization of the placement of frost-measuring sensors. This method is an improvement on previous works . ThroughThe experimental setup involves an HX located in a tunnel with air flow forced through a fan. The HX is cooled using a refrigerant below the freezing point of water. When the air encounters the cooled HX surface, below the dew point, water condenses and forms frost. This setup is illustrated in A resistive sensor was utilized to detect moisture, frost, or a dry surface within the HX through absorbing condensation. A camera was placed directly above the center of the HX at a perpendicular and level angle to minimize image distortion. Additionally, a fixed light source was aimed at the HX to eliminate any noise resulting from external lighting fluctuations. Two crucial aspects of the experiment setup require emphasis: firstly, the sensor used to detect frost formation and the experimental design utilized for conducting the tests, and secondly, the steps involved in capturing the images and analyzing the resultant data.In previous studies , a low-c2] represents the cross-sectional area of the connection between the electrodes. As water condenses on the HX surface, it is assimilated by the cotton string of the sensor, causing a decrease in fabric resistivity, and resulting in a reduction in the voltage drop across the sensor terminals. Conversely, when frost is formed, resistivity increases, leading to a rise in the voltage drop, which is then detected as frost. During the defrosting process, water is once again detected until the HX is dry. The sensor, depicted in The sensor’s overall resistance, denoted by R [Ω], experiences fluctuations based on the resistivity ρ [Ω.m] of the material between the electrodes. This variance arises due to the dissimilar electrical resistivity values of air, water, and ice. L [m] represents the length of the material or the distance between the electrodes, while A [mThe voltage drop between the electrodes is gauged using an 8-bit analog-to-digital converter (ADC) linked via a voltage divider. The ADC provides a reading ranging from 0 to 1023, which can be transformed into voltage drop. However, to simplify analysis and comparison, the reading is left unconverted.To ensure the veracity of the sensor measurements, a Logitech C920 webcam was placed in front of the HX, and MATLAB version R2018b was employed for capturing and processing images using the approach illustrated in the diagram depicted in The process of capturing and analyzing images of the HX commences with MATLAB creating a webcam object and defining fixed capture properties to maintain uniformity. Illumination is provided via two 12 V DC white LED strips with 9 SMD 5050 LEDs each to assure constant lighting conditions. A static image is then captured and cropped to display solely the HX, as illustrated in Following the capture of a static image of the HX, the image is converted into a black and white (B&W) binary image using a threshold. The threshold was calibrated so that a fully frosted HX appears predominantly white, while a completely dry HX appears almost entirely black. Notably, a binary image differs from a grayscale image in that each pixel in a grayscale image ranges in value from 0 to 255, while each pixel in a binary image has only a value of 1 or 0. For the current camera settings and illumination parameters, the threshold is set to 50%. This means that a gray pixel with a value between 0 and 127 is considered 0, which translates to black, and a gray pixel with a value between 129 and 255 is considered 1, which translates to white. Subsequently, the number of black pixels is tallied, and the ratio of black to white pixels is calculated to fall between 0 (fully black) and 1023 (fully white), thereby ensuring that the camera-based frost measurements fall within the same range as those measured with the sensor’s ADC.To accommodate the rapid frost and defrost cycles characteristic of the experimental setup, an image sample is captured, processed, and saved in RGB and B&W binary formats every three seconds. Although a three-second data acquisition rate may be considered high, it provides sufficient time to collect and process the data effectively, allowing for comprehensive analysis of dynamic phenomena, including the faster transitions observed during defrosting processes, such as frost melting. To gain a more comprehensive understanding of the frost formation in different regions of the HX, it was essential to divide it into smaller sections encompassing both the fins and refrigerant tubing. This is particularly crucial since the tubing is among the first parts of the HX to experience frost formation. Through creating 144 tiles that include both fins and refrigerant tubing, the HX is divided into 12 × 12 sections, ensuring that the resulting map provides an accurate representation of frost formation. This prevents any biases that may arise from irregular slicing, which could result in either the tubing or the fins being missed. This study utilizes specific grid labels shown in The black and white binary image is loaded into MATLAB, and the program determines the image’s division based on its resolution, resulting in the creation of 144 square tiles. For each tile, the number of white pixels, representing frost, is counted, and the percentage of white pixels is recorded in a three-dimensional matrix. This 3D matrix comprises 12 × 12 2D matrices, with each element representing the percentage of frost in its corresponding tile. Two types of information can be extracted from the 3D matrix, which is better illustrated in Following the execution of the experiments using the methods described in this section, the results of the study are presented herein. In the following section, the findings will be analyzed, and the collected data will be interpreted. The aim is to identify any patterns and trends in the data and highlight any limitations or challenges encountered during the experimental process.Prior to presenting the results of the current study, it is important to examine the outcomes of previous research. In order to compare the sensor readings to the camera readings, it is essential to interpret the sensor data. The sensor initially detects air, which has high resistivity, and as moisture accumulates, the resistivity decreases. When the water freezes, the resistivity increases, and the sensor detects the frost. Upon initiation of a defrosting cycle, the frost melts, and the water’s resistivity decreases again until the water dries, and the resistivity increases, marking the end of the defrosting cycle and the start of a new cycle (as represented by the vertical bars in Before analyzing the variations in frost detection across different tiles, it is relevant to examine the frost formation map to identify the most interesting tiles to focus on. Based on the frost formation map presented in Upon analyzing two tiles arbitrarily, it becomes evident that the sensitivity of frost detection can vary depending on the tile’s location. This observation is critical, as it highlights how the frost detection method can improve accuracy while reducing its effectiveness. Two undamaged tiles, c1 and g3, with different brightness in the frost formation map, were analyzed for their sensitivity to frost detection. The analysis indicated that areas that appear brighter in the frost formation map are likely to have a higher sensitivity to frost detection. Tile c2, where the frost measurement sensor was primarily placed, is expected to provide more accurate results compared to the sensor readings, assuming the sensor is functioning properly. The comparison between tile c2 and the sensor readings is presented in The analysis of frost in tile c2 highlights the effectiveness of this method in verifying frost sensing measurements. However, it is crucial to note that the method has limitations in differentiating between a wet and dry HX, which results in the graphs showing the resistive sensor’s detection of water drying. Additionally, the tile lags behind the sensor readings in detecting frost, especially in the case of black ice, which is virtually invisible to the camera. Despite this, the tile detects frost before the overall average method in all the frost–defrost cycles, proving to be a superior method, as demonstrated in Analyzing the frost formation in tile c2 has demonstrated the method’s effectiveness in verifying frost sensing measurements. However, it is important to acknowledge the method’s limitations in distinguishing between a wet and dry HX, as the resistive sensor’s detection of water drying is shown in the graphs. Furthermore, the tile’s ability to detect frost lags behind the sensor readings, particularly in the case of black ice, which is difficult to detect with the camera. Nonetheless, the tile detects frost before the overall average method in all the frost–defrost cycles, indicating its superiority as demonstrated in The method of detecting frost using individual tiles results in more irregular curves due to the smaller sample size, as opposed to the overall average method which produces smoother curves.In the current study, the tiles represent only 1/144th of the original image area, which accentuates the irregularities in frost formation within each tile. Smaller tiles will result in more irregular curves, while larger tiles will yield smoother curves but may compromise the accuracy of frost detection in a specific area. It is essential to strike a balance between tile size and computational power to obtain accurate and representative results, especially for real-time monitoring.Tile c2 consistently detects more frost than the overall average method, as demonstrated by the lighter color of the tile in the frost formation map. The curves from individual tiles and the frost formation map can also be used to diagnose issues in the HX, such as blockages, inefficient defrosting, poor HX performance, or damage. Unexpected behavior in certain tiles, such as c4, f6, g5, and a9, can be seen in Tile c4 exhibits abnormally high values due to its location in a damaged area of the HX that reflects more light—whiter in the picture. Tile g5 is not possible to analyze due to being obscured by a white temperature and humidity sensor. Despite appearing normal, tiles f6 and a9 have suffered performance degradation due to the fins becoming disconnected from the refrigerant tubing.The main goal of this study is to determine the best location for placing a frost detection sensor. As discussed in the previous chapter, there is significant variability in frost formation across the HX over time. The shaded area in Several methods are proposed for selecting the best tile to place the sensor, given the high disparity in frost formation across the HX. Different methods may have distinct applications and should be selected accordingly.The aim of this approach is to identify the tiles that best represent the average frost formation pattern. To achieve this, all the tiles are plotted along with the camera average curve. The tiles that have curves closest to the camera average plot are then selected. An accurate representation of the average frost formation can be seen in tile g2, as shown in Through comparing the frost formation curve in tile g2 to those shown in The proposed early warning trigger method suggests placing the frost detection sensor in the tiles where frost formation occurs first. These tiles are not only the most critical and prone to blockage but also allow for early detection of frost before it becomes problematic. This approach can be used to provide timely and sensitive warnings, particularly in cases where even a small amount of frost formation can significantly affect the system’s performance. To accomplish this, the frost formation map displayed in Frost detection in tile d1 is rapid and highly sensitive, as shown in the plot of its frost detection in The late warning trigger method suggests monitoring the tiles where frost formation occurs last. This approach could prevent unnecessary defrosting operations, which come with performance costs and undesired thermal loads. To implement this method, one can consult the frost formation map presented in Upon initial inspection, the measurements may seem unreliable and inaccurate. However, this is not the case, as in cycles 1, 3, and 4, the frost accumulation was insufficient for this method of frost sensing to trigger a defrosting operation. In contrast, during frost–defrost cycle number 2 and the end of frost–defrost cycle 5, the severity of the frost accumulation was sufficient for the tile to detect the presence of frost with clarity, as evidenced by the high values of frost detection shown in the shaded area in To effectively sense frost in a HX with uneven frost distribution, consideration must be given to the frost formation map and the area in which the frost sensor is placed. To compare frost formation in tiles with varying sensitivities, Choosing the ideal tile for placing the frost detection sensor depends on the application’s frost sensitivity requirement and the number of sensors that can be installed. A method that could result in the most precise understanding of frost formation in the HX is placing three sensors in tiles with different frost formation behaviors. The first sensor is placed in a tile with behavior similar to the average to measure overall frost formation, the second in a highly sensitive tile to provide immediate frost formation warning, and the third in a low frost formation tile to indicate a critical moment in frost formation. However, using three sensors could add complexity to the system, which should be as resilient and reliable as possible throughout many cycles. Therefore, a better application could be a single sensor placed in a tile chosen based on the information from the frost formation map and system requirements.One possible approach with two sensors would be to use both the highly sensitive and low-sensitivity tiles and analyze the data from both to determine the optimal time for defrosting operations. Alternatively, two tiles that are representative of the average frost formation can be selected, and the data from both can be used to confirm each other, thereby increasing reliability and resilience.Finally, if only one sensor is used, it is recommended to place it in a tile in which the sensitivity better suits the application, to increase the efficiency of the system and the stability of the temperature of the refrigerated goods. It is important to keep in mind that the chosen tile does not necessarily have to be one with extreme readings, but rather one of the most suitable results. The selection of the appropriate method is not a clear-cut decision and involves a spectrum of sensitivities.The objective of this investigation was to measure frost formation across an HX using an image analysis technique in order to corroborate data measured from a resistive sensor and optimize its placement within the HX. The findings emphasized the significance of initially examining the pattern of frost formation in order to gain a better understanding of the process before installing the frost-measuring sensor.Creating a frost formation map can serve as a crucial tool in analyzing the frost formation pattern, aiding in the placement of a frost detection sensor in a spot with ideal sensitivity for the specific application.Furthermore, the irregular frost formation patterns in specific tiles can be utilized to identify potential issues in the HX, including blockages or damage to the fins.The method demonstrated has the capacity to complement or enhance current frost sensing techniques.A higher tile resolution requires more computational power to process the data, which is not an issue when developing a frost map with previously gathered data. However, it can become critical when conducting real-time measurements with high sample rates.While the image analysis method for frost detection in HXs shows potential for improving sensor placement and reliability of defrosting operations, practical methods for obtaining a frost formation map must be developed, as each HX is unique.This study emphasizes the intricacies of frost sensing in HX and the significance of monitoring frost formation to achieve optimal performance and energy efficiency.The sensitivity of frost detection using this image analysis method can be adjusted through manipulating camera settings, such as exposure time, to achieve the desired level of sensitivity. This flexibility allows for customization of the frost detection system to meet the specific requirements of different applications.Future research should focus on enhancing the automation and intelligence of frost-sensing systems. This could involve the integration of machine learning algorithms or artificial intelligence techniques to improve the accuracy and reliability of frost detection and prediction. Through analyzing large datasets of sensor readings and operation conditions, advanced algorithms can learn patterns and optimize the timing and control of defrosting operations.


The molecular mechanisms controlling the adaptation of viruses to host cells are generally poorly documented. An essential issue to resolve is whether host membranes, and especially lipid rafts, which are usually considered passive gateways for many enveloped viruses, also encode informational guidelines that could determine virus evolution. Due to their enrichment in gangliosides which confer an electronegative surface potential, lipid rafts impose a first control level favoring the selection of viruses with enhanced cationic areas, as illustrated by SARS-CoV-2 variants. Ganglioside clusters attract viral particles in a dynamic electrostatic funnel, the more cationic viruses of a viral population winning the race. However, electrostatic forces account for only a small part of the energy of raft-virus interaction, which depends mainly on the ability of viruses to form a network of hydrogen bonds with raft gangliosides. This fine tuning of virus-ganglioside interactions, which is essential to stabilize the virus on the host membrane, generates a second level of selection pressure driven by a typical induced-fit mechanism. Gangliosides play an active role in this process, wrapping around the virus spikes through a dynamic quicksand-like mechanism. Viruses are thus in an endless race for access to lipid rafts, and they are bound to evolve perpetually, combining speed  and precision (fine tuning of amino acids) under the selective pressure of the immune system. Deciphering the host membrane guidelines controlling virus evolution mechanisms may open new avenues for the design of innovative antivirals. To introduce their genetic material inside the target cells, enveloped viruses first cross the barrier constituted by the plasma membrane . Two strFrom a biochemical point of view, lipid rafts are microdomains consisting of an assembly of cholesterol and sphingolipids in the outer leaflet of the plasma membrane . One of Lipid rafts are dynamic membrane entities that can fuse and modify their shape just like “a myriad of mercury sheets perpetually moving on the surface of a mirror” . Indeed,The problem of the size of the rafts in relation to the size of the spikes of SARS-CoV-2 is illustrated in 2 which can be compared to the size of a tennis court [Lipid rafts of respiratory epithelial cells play a critical role in respiratory infections. The alveolar epithelium is the largest epithelial surface of the host exposed to the external environment. Its surface has been estimated to be 140 mis court ,35. The is court , which pis court . Such a is court  and SARSis court .Figure Most—if not all—enveloped viruses use lipid rafts as privileged attachment sites on the plasma membrane of host cells ,42. ThisSeen from the outside, the plasma membrane of the host cell is studded with slightly protruding plates that display a high electronegative potential . At firsThe electronegative charges of lipid rafts are due to the sialic acid units of gangliosides which bear an anionic carboxylate at physiological pH. The binding to sialic acids has been demonstrated for several coronaviruses ,59,60,61The analysis of the surface potential of the successive variants of SARS-CoV-2 perfectly illustrates the peremptory nature of this selection pressure. As shown in Yet it would be too simple to believe that virus evolution would only consist of a gradual enrichment of cationic amino acids. For instance, the N-terminal domain (NTD) of the Delta variants was already highly electropositive ; therefoIf the surface electrostatic potential of the spike trimers was sufficient to explain the evolution of SARS-CoV-2 and the emergence of new variants, one could expect that spike-ganglioside interactions mainly involve cationic amino acids, i.e., arginine and lysine. In fact, analysis of amino acid residues directly involved in virus-raft interactions shows that cationic residues contribute less than 15% to the overall energy of the interaction .This analysis shows that the ganglioside-spike interaction chiefly involves amino acids able to form hydrogen bonds ,89, suchAccording to these data, the electrostatic surface potential of the spike protein appears to be totally independent of its hydrogen bond forming capacity. The evolution of the surface potential of trimeric spikes has been compared among SARS-CoV-2 variants from the original Wuhan strain to Omicron BA.1 . It appeThis can be viewed as a compensation mechanism in which above a critical level of electropositivity, the NTD transfers the electrostatic guideline given by the host membrane to the RBD. The advantage of this transfer is double: (i) the NTD does not stick too strongly to the raft by nonproductive electrostatic interactions and thus retains the conformational flexibility required for the formation of the hydrogen bond network between the trimeric spike and the raft; (ii) the increased electropositivity of the RBD is fully compatible with the highly electronegative surface of the ACE2 receptor , a propeAn illustration of hydrogen bonds in the NTD-ganglioside complex of the Wuhan and XBB 1.5 strains is presented in Overall, mutated spike proteins combine speed and precision to interact optimally with lipid rafts and trigger the fusion (or endocytosis) process leading to the penetration of the virus RNA in the host cell. Speed and precision are governed by lipid rafts and can be considered as mandatory membrane guidelines of virus evolution.The induced fit mechanism that controls the functional interaction of the NTD of a given variant with raft gangliosides can be visualized by molecular modeling approaches . As discOverall, it can be hypothesized that the host membrane exerts a selective pressure governing both the kinetics  and precMutations that are not compatible with this two-step mechanism are likely forbidden because they will lead to variants that are either too slow  or unable to lock the complex (if not compatible with the stabilizing hydrogen bond network). For instance, the substitution of anionic (Asp or Glu) by cationic (Arg or Lys) residues is generally favored because it will render the virus more electropositive. A similar effect is obtained when an anionic residue is replaced by a neutral one, or when a glycosylation site is eliminated, as observed for the V3 loop of the HIV-1 surface envelope glycoprotein .However, these possibilities remain limited, at least for the domains of attachment to rafts. Indeed, the positive charges of the Lys or Arg residues are not the most suitable for forming hydrogen bonds with ganglioside sugars because they can also be involved in electrostatic and/or cation-Pi interactions with proximal amino acid residues of the protein . Their lThe establishment of this network of hydrogen bonds requires an adaptation of the raft which appears to play an active role in the formation of the virus-cell complex. It is therefore essential that the raft is not a rigid structure but on the contrary, a malleable entity capable of offering the hydrogen bond-forming residues of the NTD many possibilities to reach the donor or acceptor atoms and form high energy hydrogen bonds. This conformational plasticity of lipid rafts has been shown by molecular modeling in the case of amyloid proteins . Our teaThe problematic of reconciling two selection pressures which do not always go in the same direction is perplexing. Only a high mutational potential can solve such an equation, and this is probably what happened with SARS-CoV-2 . Since its emergence at the end of 2019, SARS-CoV-2 has evolved into a myriad of variants constituting several successive lineages. Yet, for all these variants, the interactions of the viral particle with the host membrane remain a speed/precision affair, mixing immediate electrostatic attraction (love at first sight) and fine tuning (formation of a lasting couple). In this scenario, the lipid raft plays the matchmaker who sets the rules of the game. In parallel, immune evasion together with a greater potential to adhere to primary nasal epithelial tissue probably allowed the emergence and success of the Omicron lineage , given tFinally, the membrane guidelines also apply to animal reservoirs, and to the back and forth of the virus from man to animals and from animals to man ,97,115. In this review, we reconsider the role of lipid rafts in virus infection and evolution. These membrane microdomains are not just passive gateways through which viruses penetrate the cells, but rather, they play a more active role than generally admitted. Their unique biochemical composition confers them a series of emergent properties driving virus infection and evolution. These emergent properties are generated by the coalescence and conformational adaptability of ganglioside-cholesterol complexes, which are the molecular unit of lipid rafts.Correspondingly, there is a permanent race that favors viruses with an increased surface electrostatic potential together with the capability of forming a network of hydrogen bonds with raft gangliosides. The immune system of the host also contributes to the selection of such virus variants. Identifying membrane guidelines governing the evolution of viruses is not only of an academic interest but also has prophylactic and therapeutic implications. In the case of SARS-CoV-2, both the NTD and RBD display neutralizing epitopes, which are generally located on the trimeric spike surface that faces the host cell membrane. Indeed, there is a significant overlapping between these neutralizing epitopes and the ganglioside and ACE2 binding domain ,93. The Neutralizing antibodies directed against HIV-1  and the Deciphering the host membrane guidelines controlling virus evolution mechanisms may open new avenues for optimizing vaccine formulations and designing new antivirals.