Robot-assisted therapy affords effective advantages to the rehabilitation training of patients with motion impairment problems. To meet the challenge of integrating the active participation of a patient in robotic training, this study presents an admittance-based patient-active control scheme for real-time intention-driven control of a powered upper limb exoskeleton. A comprehensive overview is proposed to introduce the major mechanical structure and the real-time control system of the developed therapeutic robot, which provides seven actuated degrees of freedom and achieves the natural ranges of human arm movement. Moreover, the dynamic characteristics of the human-exoskeleton system are studied via a Lagrangian method. The patient-active control strategy consisting of an admittance module and a virtual environment module is developed to regulate the robot configurations and interaction forces during rehabilitation training. An audiovisual game-like interface is integrated into the therapeutic system to encourage the voluntary efforts of the patient and recover the neural plasticity of the brain. Further experimental investigation, involving a position tracking experiment, a free arm training experiment, and a virtual airplane-game operation experiment, is conducted with three healthy subjects and eight hemiplegic patients with different motor abilities. Experimental results validate the feasibility of the proposed scheme in providing patient-active rehabilitation training. Stroke is a severe neurological disease caused by the blockages or rupture of cerebral blood vessels, leading to significant physical disability and cognitive impairment , 2. The In recent decades, robot-assisted rehabilitation therapies have attracted increasing attention because of their unique advantages and promising applications , 13. ComThe control strategies applied in therapeutic robots are important to ensure the effectiveness of rehabilitation training. So far, according to the training requirement of patients with different impairment severities, many control schemes have been developed to perform therapy and accelerate recovery. Early rehabilitation robot systems implemented patient-passive control algorithms to imitate the manual therapeutic actions of therapists. These training schemes are suitable for patients with severe paralysis to passively execute repetitive reaching tasks along predefined trajectories. Primary clinical results indicate that patient-passive training contributes to motivating muscle contraction and preventing deterioration of arm functions. The control of the human–robot interaction system is a great challenge due to its highly nonlinear characteristics. Many control algorithms have been proposed to enhance the tracking accuracy of passive training, such as the robust adaptive neural controller , fuzzy aThe major disadvantage of patient-passive training is that the active participation of patients is neglected during therapeutic treatment . SeveralTaking the above issues into consideration, the main contribution of this paper is to develop a control strategy for an upper limb exoskeleton to assist disabled patients in performing active rehabilitation training in a virtual scenario based on their own active motion intentions. Firstly, the overall structure design and the real-time control system of the exoskeleton system are briefly introduced. A dynamic model of the human–robot interaction system is then established using the Lagrangian approach. After that, an admittance-based patient-active controller combined with an audiovisual therapy interface is proposed to induce the active participation of patients during training. Existing commercial virtual games without a specific predetermined training trajectory can be integrated into the controller via a virtual keyboard unit. Finally, three types of experiments, namely the position tracking experiment without interaction force, the free arm movement experiment, and the virtual airplane-game operation experiment, are conducted with healthy and disabled subjects. The experimental results demonstrate the feasibility of the proposed exoskeleton and control strategy.The architecture of the proposed exoskeleton is shown in Figure The lengths of the upper arm and the forearm as well as the shoulder height of the exoskeleton can be adjusted to satisfy the dimensions of patients with body heights in the range of 1.6 m to 1.9 m. The revolute robot joints at the shoulder and the elbow are actuated by the flexible Bowden-cable actuation systems located on the remote support frame . The schA passive gravity-compensation mechanism made up of two zero free-length springs and two auxiliary parallel links is integrated into the exoskeleton to balance the gravity of the entire system [detailed description can be found in ]. The coThe closed-loop real-time control system of the therapeutic exoskeleton is built in the MATLAB/Real-Time-Workshop (RTW) environment with a hierarchical architecture, as shown in Figure It is important to analyze the dynamic characteristics of the exoskeleton equipped on the right arm of the operator to improve the control system performance. The overall dynamic model of the exoskeleton with human–robot interaction forces can be established based on the Lagrangian approach as follows:M(θ) represents the symmetric positive-defined system inertia matrix. Du represents the lumped effects of uncertainties. Γ2 represent the Cartesian interaction forces acting on the upper arm and the end-effector of the exoskeleton, respectively. Jacobian matrixes, J1(θ) and J2(θ), provide the mapping from the interaction forces to the torques at robot joints, and they can be derived from the kinematics model of the exoskeleton , as the proposed exoskeleton robot is kept in a static balanced state during the operation . Note thThe friction existing in the exoskeleton system can be basically subdivided into three parts: the friction from Bowden-cable transmission systems ith proximal pulley, i.e., τin, i, and the output torque acting on the ith robot joint, i.e., τout, i, can be described using the following equation:The friction of the Bowden-cable transmission can be derived from the torque transmission model presented in our previous research . The relTi and λi are the cable pretension and the bending angle of the ith Bowden-cable unit. The term μi represents the Coulomb friction coefficient. r1 and r2 denote the radiuses of the proximal pulley and the distal pulley. Note that the values of r1 and r2 of the presented exoskeleton are equal to 25 mm. Thus, Equation (3) can be refined aswhere b, i is the friction torque from the ith Bowden-cable transmission unit.where τAccording to the existing research results , the frir, i and τj, i represent the friction torques from the ith reducer and robot joint. bi is the coefficient of viscosity. τc, i denotes the Coulomb friction torque.where τith element of the integrated system friction vector can be obtained and expressed asTherefore, by inserting Equations  into Equation (2), the e, i represents the equivalent parameter for the Coulomb friction torque.Here, τRobot-assisted rehabilitation training with games played in virtual reality environments has positive effects on inducing active patient participation and encouraging the neural plasticity of the brain . Thus, iThe real-time information about robot configuration and human–robot interaction, which are acquired from F/T sensors, position sensors, as well as the switches and pushbuttons mounted at the end-effector, are transmitted into a virtual keyboard unit to handle the virtual game process. The virtual keyboard unit was developed in the Microsoft Visual C++ programming environment and used as the interface between the operator and the virtual environment, allowing patient-active training during rehabilitation. In other words, the disabled patient can play the virtual game by actively manipulating the exoskeleton, and this is beneficial to the recovery of motor function and mental confidence. Communication between the RTW control system and the virtual environment was established via the transmission control protocol/internet protocol (TCP/IP).Fe(t), measured by the distal F/T sensor are transformed into the actual forces in basic Cartesian space, F(t), through coordinate conversion. The force errors, ΔF(t), between the desired interaction forces, Fd(t), and the actual interaction forces at the end-effector are transmitted into an admittance filter to compute the value of position regulation, ΔP(t). The desired impedance characteristic describing the relationship between interaction force and end-effector position can be expressed asThe admittance control module is developed to regulate the robot configurations and human–robot interaction forces at the end-effector while executing patient-active training. The fed-back forces from the end-effector, wherePd (t) denotes the desired inertial training position of the end-effector predefined according to the virtual game scenes; Pc (t) denotes the corresponding control position of the end-effector in Cartesian space; Md, Bd, and Kd are the objective inertia, damping, and stiffness of the admittance filter.Here Thus, in the frequency domain, Equation (7) can be represented asPc (t), which depends on the distal interaction forces and admittance parameters, can be converted to the angular position in joint coordinates, θc (t), via the inverse kinematics of the robot. A detailed description of the analytical inverse kinematic resolution of the proposed redundant exoskeleton has been analyzed in , we havec (t). The position control was realized by using a fuzzy sliding mode control (FSMC) scheme developed based on the system dynamics model, and it was proposed in our previous research (where Inv (·) denotes the inverse kinematic calculation. The inner position controller is implemented to move the robot to the desired position expressed by θresearch .According to Equation (1), since the inertia matrix is symmetric and positive definite, the dynamic model is refined asS(t) can be defined asThe switching function of sliding surface e(t) = θc(t) − θ(t) denotes the position tracking error. λ and η represent the positive diagonal matrixes of proportional gain and derivative gain.where Combining Equations , the deviation of the sliding variable can be calculated asAnd then, the control law can be designed aswhere sgn (·) means the sign function. ε represents a positive switching gain computed by a fuzzy controller .For the purpose of demonstrating the stability of the proposed patient-active control algorithm, a positive definite Lyapunov function candidate is defined ast and combining Equations (10) with Equation (13) yields Equation (15) as follows.Differentiating Equation (14) with respect to time Du are supposed to satisfy the following assumption.Here, the lumped effects of uncertainties Assumption 1: The boundary of the uncertainty term can be given as (given as If the positive switching gain is selected asthen (16) can be rewritten asS(t) = 0 in finite time.Here, it can be observed that Upon completing the hardware design, dynamic modeling, and controller development, three typical experiments were conducted on the exoskeleton to validate the feasibility of the proposed patient-active admittance control strategy. In the first case, the position tracking experiment without the operator and external interactions was carried out to analyze the control performance of the inner fuzzy sliding mode position controller. In the second case, the free arm movement training experiment with different admittance parameters was conducted with three healthy subjects. In the third case, the virtual airplane-game operation training with graphical guidance was carried out with two healthy subjects and eight stroke patients with different Fugl-Meyer assessment (FMA) scores . The ethAccording to the control diagram illustrated in Figure The position tracking experiment without the participation of the subject was carried out to evaluate the position control performance. The desired position trajectory of the end-effector, which is defined in the base robot coordinate frame of the exoskeleton and parallel to the coronal plane, is shown in Figure The experimental performance of the proposed FSMC algorithm was compared to that of a conventional PID controller. The selected control parameters of the PID controller  were estimated via the Ziegler–Nichols method and carefully optimized by trial and error. The control parameters of the FSMC algorithm were optimally adjusted by intensive tests to improve control accuracy and ensure system stability. The results of trajectory tracking experiments with different control strategies are compared in Figure The fundamental purpose of developing the patient-active control framework is to encourage the voluntary efforts and active participations of patients during rehabilitation training. The basic function of the admittance control module, as the core component of the patient-active controller, is to modulate the configuration of the exoskeleton according to the detected real-time human–robot interaction force and the desired mechanical admittance characteristic. Hence, the second experiment was conducted to evaluate the feasibility of the admittance controller in free arm operation training.x, calculated from the positions of the robot's joints and inverse kinematics, reflects the corresponding training difficulty and intensity. The range of position deviation was generally restricted within the interval of .In this experiment, three healthy neurologically intact volunteers with various anthropometric parameters and ages  were asked to undergo free arm movement trainings with different admittance parameters. The volunteers were comfortably positioned in the therapeutic system with their right arms wearing the exoskeleton. The limb lengths and the joint axes of the upper arm and the forearm of the exoskeleton were adjusted in accordance with the anthropometric parameters of wearers. Next, the subjects grasped the end-effector of the exoskeleton and actively performed horizontal reciprocating movements along the x-axis of the base coordinate system. The relation between the interaction force, measured by the distal F/T sensor of the end-effector, and the position deviation ΔTo compare and investigate the training performance with different admittance parameters, three different groups of parameters  were implemented to the admittance filter during the free arm movement experiments, as shown in Table Existing study results indicate that the EMG signals provide information on the scale of muscular power and activation patterns . BesidesAs shown in Figure Moreover, the experimental results  of the RMS EMG values from the bicipital muscle of different subjects and admittance parameters are compared in Figure The purpose of the third experiment was to evaluate the practical feasibility by applying the proposed admittance-based patient-active controller to rehabilitation training in a virtual reality environment. Figure During the trial, the participants were required to actively manipulate the exoskeleton system and control the virtual airplane prototype displayed on the screen to accomplish the requested actions along the predesigned trajectory, including the taking-off operation, landing operation, and free-flight operation. To modulate the sensitivity of game control and improve the maneuverability of virtual training, the predefined thresholds of position variation (100 mm) and interaction force (10 N) were integrated into the virtual keyboard program. Only if the position variation and detected force exceed the respective threshold simultaneously, the virtual keyboard unit will trigger the corresponding keys to regulate the game process. In this way, the virtual keyboard acts as the interface that maps the human–robot interaction force and the robot configuration to the operations in the airplane game.Md = diag  Ns2/mm, Bd = diag  Ns/mm, Kd = diag  N/mm. All the subjects were required to make their best efforts to complete the airplane operation task six times. Figure In this experiment, the admittance parameters were set as follows: The execution time required to finish the airplane operation task reflects the difficulty of the game for a specific participant. The execution times for the subjects with different FMA scores were recorded and compared Figure . The aveFrom the results of three different experiments—the position tracking experiment, the free arm training experiment, and the virtual airplane-game operation experiment—it can be observed that the proposed FSMC-based admittance control strategy is capable of providing patient-active mode training during rehabilitation. More specifically, from the results of position tracking tests, it can be seen that the inner FSMC position controller is capable of achieving smaller tracking errors and better control performance when compared with the conventional PID controller, and can ensure the modulation accuracy of robot configuration based on the output value of the admittance filter. From the results of the free arm training experiment conducted with three healthy participants with different admittance parameters, it can be observed that the developed FSMC-based admittance controller can assist the patient actively undergo the free arm movement trainings with desired training difficulty and intensity. Moreover, it is able to encourage the voluntary efforts and active participations of patients during rehabilitation training. The increase of the admittance parameters of patient-active controller leads to the increase of motion resistance and the EMG activity levels of the bicipital muscle. According to the results of virtual airplane-game operation experiment conducted with two healthy volunteers and eight post-stroke chronic patients with various FMA scores, it can be found that, with the developed admittance-based patient-active control strategy, the volunteer wearing the exoskeleton system is able to actively handle the motion of virtual airplane during rehabilitation training. The rehabilitation training integrated with commercial virtual games without a specific predefined trajectory has valid impact on enhancing the interestingness of physical therapy and, furthermore, contributes to neurological rehabilitation and psychotherapy. The experimental results for different disabled patients indicate that the required execution time of the same operation task increases with the decrease of motor functions of patients. Besides, the feasibility in encouraging active participation has been proved from the statements of volunteers. In the actual performance, the protocol for each patient should be selected based on several factors, such as the detailed FMA scores of patient, the desired rehabilitation training programs, the quantitatively statistical training reports from the evaluation system, and the experience of physiotherapists.There are several limitations in the proposed exoskeleton and control strategy. Firstly, the proposed patient-active controller can be used with patients with good cognitive function, fair sitting balance, and good upper limb motor performance; it cannot be applied to severely paralyzed subjects without any motor functions. The resistance from the exoskeleton needs to be overcome during patient-active training. Secondly, the proposed exoskeleton can be used only for patients with right-sided weakness, thus limiting the range of applicability. An extension of this research will be to improve the control strategy to be suitable for severely paralyzed patients. The mechanical structure will be further optimized to realize the switch between right arm training and left arm training. The effectiveness of the proposed rehabilitation exoskeleton system and control strategy will be tested and demonstrated via a more substantial trial in future works. Besides, the perceived value and motivation of patient will be qualitatively evaluated by using electroencephalography (EEG) sensor. A rational rehabilitation evaluation system will be developed to estimate recovery progress. The controller parameters, such as the admittance filter, should be optimized based on the evaluation of patients to improve treatment efficiency. In addition, the therapeutic training of the human hand will be integrated into the rehabilitation system.This paper dealt with the development and validation of an upper limb exoskeleton and a patient-active admittance control strategy, which can be applied to assist the patients with affected arm motor functions in performing active training in virtual environments. Firstly, the major hardware of the wearable exoskeleton system, including the gravity-balanced mechanical structure with 7 + 2 DOFs and the MATLAB/RTW real-time control system, was briefly introduced. Then, the system dynamic model was established using the Lagrangian method. To encourage the active participation of patients during rehabilitation training, a patient-active controller was proposed based on the dynamic model. A patient wearing the exoskeleton can undergo active rehabilitation training with the guidance of a graphical interface, and the training trajectory is not constrained to a specific predetermined trajectory. Different kinds of existing commercial virtual games, which are far more realistic and interesting than the simple self-designed ones, can be integrated into the proposed control strategy via a virtual keyboard unit. The feasibilities of the proposed therapeutic system and control strategy were verified via three pilot tests. A position tracking experiment was carried out to evaluate the performance of the inner fuzzy sliding mode position control strategy. A free arm training experiment was conducted with three healthy subjects to study the functionality of the admittance module during free arm operation. To verify the practical feasibility of applying the patient-active control strategy to the training within virtual environments, a virtual airplane-game operation experiment was conducted with ten volunteers with different FMA scores.QW and XW participated in the design of this study. QW and BC carried out the experiments and analyzed the experimental data. HW contributed in the exoskeleton development and maintenance. QW wrote and modified the manuscript. All authors read and approved the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Two main spatial cues that can be exploited for dual microphone voice activity detection (VAD) are the interchannel time difference (ITD) and the interchannel level difference (ILD). While both ITD and ILD provide information on the location of audio sources, they may be impaired in different manners by background noises and reverberation and therefore can have complementary information. Conventional approaches utilize the statistics from all frequencies with fixed weight, although the information from some time–frequency bins may degrade the performance of VAD. In this letter, we propose a dual microphone VAD scheme based on the spatial cues in reliable frequency bins only, considering the sparsity of the speech signal in the time–frequency domain. The reliability of each time–frequency bin is determined by three conditions on signal energy, ILD, and ITD. ITD-based and ILD-based VADs and statistics are evaluated using the information from selected frequency bins and then combined to produce the final VAD results. Experimental results show that the proposed frequency selective approach enhances the performances of VAD in realistic environments. Voice activity detection (VAD) which decides if the speech signal is present in the current frame of the input signal has become a crucial part of the speech enhancement, noise estimation, pitch extraction, and the variable rate speech codecs ,30,31,32Like the human binaural perception, two main cues that capture the spatial information may be the differences of the arrival times and signal levels in the microphones. These statistics, which are called interchannel time difference (ITD) and interchannel level difference (ILD), can be exploited for dual microphone VAD. When the range of the direction-of-arrival (DoA) of the desired signal is known in advance as in the case of the handset mode of the mobile phone, the VAD can be constructed based on the estimated DoAs. There have been several approaches to the DoA estimation and the VAD based on ITD. The generalized cross correlation with phase transform (GCC-PHAT)  may be tAs speech signal is sparse in the time–frequency (TF) domain in nature, there are always TF bins with SNRs in which the ILD or ITD information are more reliable and those with low SNRs where the ILD or ITD information may not be useful at all in noisy environments. In this letter, we propose a VAD based on both ITD and ILD information from reliable frequency bins only. The reliability is determined for each TF bin by three conditions on signal energy, ILD, and ITD. ITD-based and ILD-based VADs or statistics evaluated using only the reliable frequency bins are combined together to construct final voice activity decision. The long term spectral divergence  and the The dual microphone VAD can perform better if prior knowledge on the location of the desired speaker is available. One example of the scenarios in which the range of the locations of the desired signal source is known in advance is the handset mode of the mobile phone, where user’s mouth is much closer to the primary microphone.K-point short-time Fourier transform (STFT) coefficients of the signals from the primary and secondary microphones for the kth frequency bin at the lth frame, respectively. The test statistics for the NDPSD-based VAD [Let ased VAD  are the It is noted that each frequency bin contributes to the final test statistic equally, although the absolute values of a posteriori probabilities of speech presence, and then thresholded to determine voice activity. Like NDPSD, PLDRs can also be strongly affected by the presence of the interfering source near the secondary microphone.The two step PLDR method  also takU overlapped sectors of which the width are equal. LTIPD is then defined asi denotes the indices of the sectors, k-th frequency bin indicates the ith sector among the last L frames, and Another important source of information about the location of the sound sources is ITD. Ref.  proposedIt is noted that the LTIPD-based VAD includes the reliable frequency selection, but the selection criterion is based only on the ITD information.The performance of VAD may be improved by utilizing both ITD and ILD information simultaneously, as two statistics provide different information on the spatial diversity. In , the VADthe best . Anotherthe best  is to buectively , is usedAs for the input of the SVM, it is reported that features . HoweverThe performance of each VAD can be significantly enhanced by introducing the hangover scheme, which requires several consecutive frames with instantaneous VAD of 0 to make the final VAD to be 0. The number of hangover frames remains as a tunable parameter along with the thresholds for each VAD. For As speech components are sparsely distributed in the TF domain, the spatial cues in some of the TF bins are useful while those from other TF bins are not reliable. In this paper, we propose a dual microphone VAD based on the spatial information from the selected frequency bins with high reliability, which is determined in each frame by signal energies, ILDs, and ITDs for the corresponding frequency bins. After we determine the reliability of information from each TF bin, the test statistics for conventional VAD approaches are modified to consider reliable TF bins only.k-th frequency bin at the l-th frame as Let us denote the spectral mask to select reliable frequency bins for the The second and third conditions determine the reliability in each bin with ILD and ITD information, respectively. The second sub-mask The proposed frequency selective approach using the spectral masks a posteriori probability computed from the output of the SVM with masked input vectors.Similarly, the Equation  for the Equation . It is n3 and the reverberation time of the room was approximately 120 ms. In the center of the room, one of the two male and two female speakers stood holding the mobile phone with the right hand in the handset mode. The desired near-end speech was spoken by those speakers in English. The distance between the microphones was about 140 mm. The diffuse noise field was generated by playing back white, babble, or car noises from NOISEX-92 database [L and U, were set to 12 and 10, respectively. To demonstrate the performance of the proposed algorithm, we have recorded the desired speech, directional interferences, and diffuse noises with two microphones located on a commercial mobile phone, Samsung Galaxy S7. The placement of the user and the loudspeakers are illustrated in database  with fouα was set to 0.8 as the false rejection may be more critical for variable rate speech codecs or speech enhancement. Experimental results in a more reverberant environment are also available at the demo page .The performances of the various ILD- and ITD-based VAD methods with and without the proposed reliable frequency bin selection for the whole test data are shown in ge as in , possibl1−α)×FAR , in whicIn this letter, we have proposed a dual microphone VAD scheme based on the spatial information from reliable TF bins only. The frequency selection masks are constructed based on three criteria on signal energy, ILD, and ITD. Conventional ITD- and ILD-based VADs and the combination of them are modified to consider the spatial information from the reliable spectral bins only. Experimental results with a commercial smartphone showed that the frequency selective approach can enhance the performance of the ILD- and ITD-based VADs, the logical combination of them, and the SVM-based VAD in various noise environments.


A class of bipolar electrostatically actuated micro-resonators is presented in this paper. Two parametric equations are proposed for changing the microbeam shape of the upper and lower sections. The mechanical properties of a micro-resonator can be enhanced by optimizing the two section parameters. The electrostatic force nonlinearity, neutral surface tension, and neutral surface bending are considered in the model. First, the theoretical results are verified with finite element results from COMSOL Multiphysics simulations. The influence of section variation on the electrostatic force, pull-in behaviors and safe working area of the micro-resonator are studied. Moreover, the impact of residual stress on pull-in voltage is discussed. The multi-scale method (MMS) is used to further study the vibration of the microbeam near equilibrium, and the relationship between the two section parameters of the microbeam under linear vibration was determined. The vibration amplitude and resonance frequency are investigated when the two section parameters satisfy the linear vibration. In order to research dynamic analysis under the case of large amplitude. The Simulink dynamics simulation was used to study the influence of section variation on the response frequency. It is found that electrostatic softening increases as the vibration amplitude increases. If the nonlinearity initially shows hardening behavior, the frequency response will shift from hardening to softening as the amplitude increases. The position of softening-hardening transition point decreases with the increase of residual stress. The relationship between DC voltage, section parameters, and softening-hardening transition points is presented. The accuracy of the results is verified using theoretical, numerical, and finite element methods. Nowadays, micro electromechanical system (MEMS) devices are attracting attention due to their small size, low weight, and low energy consumption. Among them, microbeams are a popular micro-component and are widely used in MEMS devices, e.g., as a microswitch ,2, sensoElectrostatic actuation is one of the most common actuation methods in microstructures . HoweverIn addition to studying the pull-in behavior, vibration of the micro-resonator should also be analyzed. Nonlinearity can lead to multiple solutions, leading to jump instability. The relationship between the system’s equivalent natural frequency and DC voltage depends on the strong nonlinearity and electrostatic softening. Moreover, the ideal working condition of the micro-resonator is linear vibration, thus the nonlinearity in the design should be eliminated to the greatest possible extent. Li et al.  studied As research has deepened, many scholars have found that the mechanical properties of a micro-resonator can be improved by adjusting the microbeam geometry when using the same raw materials. Joglekar and Trivedi ,20 studiSo far, research on microbeam optimization primarily focuses on adjusting the microbeam size , using tThe structure of this paper is as follows. The mathematical model  for electrostatic actuation of a microbeam resonator considering neutral stretching and bending is established in A schematic of an electrically actuated microbeam is shown in Changes in the microbeam shape will produce an uneven electrostatic force between the upper and lower parts of the microbeam. The distance between the microbeam section at the fixed end and electrode plate is The total energy stored by two capacitors isThe electrostatic force isThe equation of motion considers changes in the cross-sectional area and the electrostatic force on the bipolar plate, the equation is therefore rewritten as follows :(4)∂2∂x2The boundary conditions areIn Equation (4), For the convenience of calculation, consider following dimensionless:Substituting Equation (6) into (4) and (5) yields the dimensionless bending vibration equation:The corresponding boundary condition becomesIn the following figure, the “The fringing fields of electrostatic force are not taken into account in the above calculation. In order to observe the accuracy of electrostatic force, the electrostatic force in Equation (7) is compared with the electrostatic force considering edge effect. The results are shown in The deflection of the microbeam is defined as follows:The boundary conditions arei-th modal coordinate amplitude, and i-th order undamped linear orthogonal mode function. According to results from the literature [terature , a modelic force . The firThe static equilibrium equation can be written as follows:Without considering damping and AC disturbances, the following Hamiltonian system corresponding to the dimensionless dynamic equation can be obtained:The potential energy function isOne should note here that the maximum lateral displacement of the microbeam is at the midpoint viz., First, a static analysis of the system is conducted. The safe region of the micro-resonator can be obtained from static analysis. Only by guaranteeing that the device can operate safely under the selected parameters can the research presented here be meaningful. Here, the accuracy of the electrostatic force obtained from theoretical analysis is verified. All possible microbeam cases are selected. The capacitance the between plates and microbeam was simulated using COMSOL Multiphysics, and the simulation model is shown in The results from two methods are compared in The theoretical results shown in Next, the influence of the section parameters on static pull-in behaviors will be studied. In order to facilitate observation, the special case of a rectangular microbeam is added as a comparison, where the pull-in behavior is indicated with the black curve in In addition, static displacement jump will occur in the asymmetric microbeam. One can see from the case where In order to discuss this phenomenon more intuitively, Assume Therefore, reducing Residual stress may occur in the process of fabrication or operation of devices and the mechanical properties will be influenced. In order to accurately predict the safe working area of the device, the influence of residual stress on pull-in voltage and secondary pull-in will be discussed below. As shown in It is very important to conduct dynamic analysis of MEMS devices. The influence of section variation on the frequency response and bifurcation behavior can be observed through dynamic analysis, so as to optimize micro-resonator. MMS is used in the following to calculate small amplitude vibrations of the micro-resonator in the stable region. Here, we define First, The meaning of each coefficient is shown in Because In order to describe the primary resonance accurately, a tuning parameter The approximate solution to Equation (17) is expressed as follows:Substituting Equations (18) and (19) into (17) and gathering like powers of The general solution to Equation (20) can be written asSubstituting Equation (23) into (21) yields:To eliminate the secular term, one needsThe solution Substituting Equations (23) and (27) into Equation (22) yields the secular termsAt this point, it is convenient to express Substituting Equation (29) into Equation (28) and separating the imaginary and real parts yields:The steady-state response can be obtained by imposing the condition The peak vibration amplitude and backbone curve are terature ,31.In the previous section, the stable region of the micro-resonator is optimized by static analysis, followed by conducting dynamic analysis. Previous research  has showThe coordinates of these special points listed in Next, points A, B, C, and F in The equivalent frequency and amplitude of the microbeam in different conditions are also important for studying the micro-resonator. The variation in the resonance frequency and amplitude with the sectional parameters Since traditional MMS is only suitable for small vibrations, the traditional MMS will produce incorrect results when vibration amplitude exceeds a certain value . In ordeIt is assumed that the final vibration frequency is equal to the excitation frequency. A scaling parameters The approximate solution to Equation (33) is expressed as follows:Substituting Equation (34) into (33) and equating coefficients of like powers of The general solution to Equation (35) can be written in the following form:The secular term derived from MMS is expressed as:Substituting Equation (37) into Equation (38) and separating the imaginary and real parts yields:The steady-state response can be obtained by applying the condition The micro-resonator vibration amplitude increases as the AC voltage amplitude increases. The physical parameters of the microbeam are terature .Two kinds of motion can occur at the transition point: dynamic pull-in and jump to a higher stable branch. The energy output is higher in the second case. Changes in the softening-hardening transition point can be observed as the vibration amplitude increases from According to previous studies, the location of the transition point is related to the microbeam thickness and DC voltage. The location of the transition point can be obtained by calculating softening-hardening transition. Next, the relationship between the DC voltage, microbeam thickness, and transition point position is verified. The microbeam resonator was explored and optimized using theoretical and numerical analysis. The finite element method will be used to simulate the optimization results using COMSOL Multiphysics software.A, B, C, D, and G in In COMSOL, the “solid mechanics” interface and “electrostatic” interface are combined with a dynamic grid function. First, the steady state of the model and the eigenfrequency in the steady state are studied. Here, finite element simulations are performed for the aforementioned seven cases, and the calculated simulation results are shown in The seven cases correspond to linear vibration when The simulated equivalent natural frequency contains some error, although the error between the finite element solution and the theoretical solution is relatively small. More simulated frequency response curves are presented in this section. The physical parameters of the microbeam are One can see that the amplitude response is linear when the amplitude is small, while hardening appears at higher amplitude. The red asterisk shows the results obtained from the frequency response analysis in COMSOL. One can see that the simulated amplitude is consistent with the theoretical amplitude when the AC voltage varies. When Static and dynamic analyses of electrostatically-driven microbeam resonators are presented in this paper. Two parametric equations describing control over the upper and lower sections of microbeam were introduced. The mechanical properties of the micro-resonator are strengthened by optimizing the parameters in these equations. The neutral plane tension, neutral plane bending, and electrostatic nonlinearity are considered in the mathematical model. First, the model is reduced and simplified by Galerkin discretization. Then the relationship between two section parameters under linear vibration is obtained by a Newton iteration. Finally, the vibration at small and large amplitudes were obtained using MMS and NMMS. The results were verified with the Runge-Kutta method, Simulink dynamic simulation and finite element method.The potential energy and electrostatic force are greater when the microbeam intermediate thickness is thinner for a given applied voltage. Decreasing the thickness at the midpoint of the microbeam will increase the pull-in voltage and increase the likelihood of secondary pull-in. The pull-in position is biased toward the larger of y = x symmetric point in When the micro-resonator vibrates linearly, the relationship between The MMS should not be used as the amplitude increases. The frequency response obtained with MMS will exhibit weaker nonlinear softening. If the initial vibration exhibits hardening, the transition between hardening and softening will occur at a certain time as the vibration amplitude increases. The position of the transition point does not change as the amplitude continues to increase. At the transition point, the micro-resonator can jump to a higher stable branch and output more energy.The key conclusions are as follows.It is found that the static and dynamic behaviors of micro-resonator can be changed by adjusting the microbeam shape. Determining the appropriate geometry can improve the mechanical properties for given raw materials.


Interaction between light and matter results in new quantum states whose energetics can modify chemical kinetics. In the regime of ensemble vibrational strong coupling (VSC), a macroscopic number  Strong coupling of molecular vibrations to an optical cavity may catalyze thermally activated reactions, showcasing the potential of polariton chemistry. Here, the authors provide a theoretical framework explaining the chemical kinetics deriving from transit through polaritonic and dark states. Recent studies of molecular polaritons have revealed new phenomena and features that are appealing for applications in chemistry and materials science. These discoveries opened the doors to the emerging field of polariton chemistry11. Of particular interest are recent observations of chemoselective suppression and enhancement of reactive pathways for molecules whose high-frequency vibrational modes are strongly coupled to infrared optical cavities15. These effects of vibrational strong coupling (VSC) are noteworthy in that they occur in the absence of external photon pumping, implying that they involve thermally activated (TA) processes and potentially paving the road for a radically new synthetic chemistry strategy that involves injecting microfluidic solutions in suitable optical cavities 20, unless the temperature is low enough for the lower polariton to overtake the predominant population second to that of the ground state. It is thus puzzling and remarkable that differences in the chemical kinetics can be detected in macroscopic systems under VSC at room temperature. This study provides a possible rationale for these observations. By studying a VSC version of the well-established Marcus–Levich–Jortner (MLJ) TA electron transfer model23, we find a parameter range where, even if the number of dark-state channels massively outweigh the few polaritonic ones, the latter dictate the kinetics of the reaction given their smaller activation energies. The present model does not feature the complexity of the experimentally studied systems; however, it provides a minimalistic conceptual framework to develop qualitative insights on general TA VSC processes. We believe that this mechanism of polaritonic activation barrier reduction might be a widespread feature among such processes.Of the population of vibrationally excited states at thermal equilibrium, a tiny fraction would be allocated to the polariton modes, with the overwhelming majority residing in the dark-state reservoir23According to the MLJ theory, the rate coefficient of charge transfer from a reactant (R) to a product (P) electronic state, at constant temperature 25. The Hamiltonian for such system is26 with single-molecule coupling 26 , we note that they were considered in the electronic strong coupling regime; as we shall see, the vibrational counterpart demands a different formalism and offers conceptually different phenomenology.To gauge the effects of VSC, we consider the interaction between a single microcavity mode and an ensemble of mentclass2pt{minim29P state at a given stage in the reaction. These operators correspond to the upper and lower polaritons (UP and LP), and dark (D) modes, respectively. It is noteworthy that the operators 32). This effect is negligible for the phenomena considered in this work given that the density of molecular excitations is much larger than that of the photon modes.)As a consequence of VSC, the system is best described in terms of collective normal modes defined by the operators33 took advantage of the massive degeneracy of the dark modes to introduce a judicious basis34,35 of these. Explicitly, for the reactants we have33. Here, 36. Using the notation from Eq. . In this model, there is a range of molecular features where the shrinkage of the activation energy of the lower polariton channel can outcompete the rate associated with the massive number of dark-state channels. This model describes a mechanism suitable to be present in a wide variety of thermally activated non-adiabatic reactions, e.g., electron, proton, and methyl transfer, among others. We have found a range of molecular parameters where the shrinkage of the activation energy of the lower polariton channel can outcompete the rate associated with the massive number of dark-state channels. We determined that these effects are most prominent under resonant conditions. This finding is relevant, as such is the behavior observed in experimental reactions performed under VSC. We must remark, however, that the latter are presumably vibrationally adiabatic reactions and the involvement of the present mechanism is not obvious . Although a thorough understanding of the reaction pathways involved in these observations is beyond the scope of this article, we believe that the tug-of-war between the activation energy reduction from few polariton channels against the numerical advantage of the dark states could be a ubiquitous mechanism of TA polariton chemistry under VSC, independently of whether it occurs with reactants or products. Even though there might be other subtle physical mechanisms underlying VSC TA reactions, we conclude with three important observations regarding the presently proposed catalytic mechanism. First, it does not offer a reduction of reaction rate coefficients for a broad range of parameters; after all, if the polariton channels do not provide incentives for their utilization, the dark states will still be accessible, leading to virtually unaffected reaction rates as compared with the bare case. However, an experimental suppression of reactions by VSC under TA conditions (as in refs. 13) could correspond, microscopically, to the polaritonic modification of elementary step rates in the network of reaction pathways that comprises the mechanism. Second, it is not evident whether the conclusions associated with this mechanism are relevant in photochemical processes where non-equilibrium initialization of polariton populations is allowed. Finally, it is important to emphasize that this VSC mechanism is not guaranteed to yield changes in TA reactivity, given that particular geometric molecular conditions need to be fulfilled. Regardless, it is remarkable that TA reactions under VSC can be modified at all given the entropic limitations imposed by the dark states. It is of much interest to the chemistry community to unravel the broader class of reactions and the VSC conditions for which this mechanism is operative; this will be part of our future work.We have shown that VSC can result in catalysis of TA reactions. We have presented an MLJ model to study charge transfer processes under VSC (in passing, these results suggest a VSC alternative to enhance charge conduction, which has so far been only considered in the electronic strong coupling regime51, in agreement with recent studies of mean-field solutions to polariton problems in the ensemble regime52. The rate coefficient To calculate the consumption of the reactant as the polaritonic ensemble grows, we performed a finite-difference numerical integration of Eq. . As the n of Eq.  with limfrom Eq.  truncatimentclasspt{minimafrom Eq.  by settiSupplementary InformationPeer Review File


Slum rehabilitation policies in India is observed to have a rebound effect on the occupants, where rehabilitated occupants move back to the horizontal slums. In this study, we investigate the cause behind this rebound phenomenon based on a theory of homeostasis, where the loss of homeostasis refers to occupants' heightened discomfort and distress in their built environment. A novel methodological framework was developed to investigate it based on the principles of participatory backcasting approach and the theory of homeostasis. Thirty households in Mumbai's slum rehabilitation housing were interviewed to determine the social, economic and environmental cause of distress and discomfort. Granular information was obtained by further investigating the factors that influence occupants' attitude, emotions, health, control and habits in their built environment that regulates their holistic comfort and lack of stress. The causal linkages among these factors were established using a qualitative fault tree. Results show two primary cause of distress and discomfort in the study area owing to economic distress and built environment related discomfort. Economic distress was from low-income and high electricity bills due to higher household appliance ownership, and built environment discomfort was due to lack of social spaces and poor design of the slum rehabilitation housing. This study showed that mitigating such non-income drivers of distress and discomfort can prevent rebound phenomenon and improve the sustainability of the slum rehabilitation process. BetweenIt is well understood in the policy sphere that the slum life has a significant adverse effect on health, education, labour and women. It is also widely discussed in the current policy discourses that improving the living conditions of the slums must include concerned-efforts of all the stakeholders . Policierebound phenomenon’ of this slum rehabilitation process. It might seem that poverty is the primary cause of the rebound behaviour as the occupants cannot cope-up with the increased cost of living and low-income, as suggested by Restrepo . It is responsible for the evaluation and approval of slum redevelopment proposals submitted by developers. In the entire rehabilitation process, the developers have full discretion on the quality of rehabilitated buildings, which affects the living standards, so much so that, these rehabilitation buildings are transformed into ‘vertical slums’ , Debnat. It forcRestrepo . HoweverRestrepo . We arguWhile the actual cause of this rebound phenomenon is yet unknown, it is often discussed in the literature that the horizontal slums help to maintain the informal economy which creates job opportunities for the occupants. Furthermore, the design of the current rehabilitation housing restricts them from accessing communal spaces which are an integral part of their lives in slums. Occupants' discomfort is further exaggerated by the poor quality of the housing units, which are often characterised by the lack of ventilation, thermal discomfort, lack of daylight and poor indoor air quality in the living spaces , Bardha, Yardle. In econHere, we make a generalised assumption that the rebound phenomenon is caused due to occupants' economic, social and environmental discomfort and distress in their built environment. While low-income remains a constant source of distress and distress, we investigate the influence of non-income factors that contribute to it. The non-income factors comprises of physical, social, behavioural and psychological elements that regulate the attitudes, habits and emotions of the occupants towards maintaining a balanced state of comfort and lack of stress in their built environment, as per Ortiz et al.‘s theory of homeostasis  discuss. This thWhat causes discomfort and distress in the slum rehabilitation housing?’, and the second, ‘How can the community help in reducing their discomfort and distress?’.We extend this theory of homeostasis  by develTo address these research questions, we designed an innovative methodology to derive a proof-of-concept to support our assumptions regarding the non-income drivers of the rebound phenomenon. It consisted of designing a conceptual framework that can logically accommodate the non-income drivers of discomfort and distress based on the theory of homeostasis of Ortiz et al.  see sec. It was Backcasting approach is ‘working backwards’ from a future end-point to the present, and is widely used in policy modelling . Our met22.1The urbanisation process in Mumbai has been coherent with the housing crisis and urban informality for over 150 years. At present, more than 50% of the population lives in slum areas . The proafter-effects of these policies on the occupants’ overall well-being. Market forces regarding land and finance drive the entire slum rehabilitation process that creates intense competition for the slumlands among the private developers  has revealed that occupants tend to seek more healthcare visits due to lack of ventilation and fresh air exchanges . Thermal2.2The slum rehabilitation process is an institutional change that involves shifting of an entire informal built environment to a formal housing structure . The conenergy use is a consequence of trying to attain homeostasis ’ ’ . While dstress)’ . Our stuAccording to the theory of homeostasis, discomfort and distress of an individual are due to a disbalance in their physical, psychological, social and behavioural elements of lives that contribute to better well-being by influencing attitudes, emotions, health, controls and habits . We adop3A systems-of-systems approach was adopted in designing the conceptual framework for estimating the indicators of occupants' discomfort and distress in their built environment. Systems-of-systems approach refers to a multi-system organisation where a broader system is made up of several sub-systems that have inherent interdependencies within them . The conThe physical, social, behavioural and psychological systems represent the sub-systems that affect homeostasis at an individual level, significantly influencing their attitude, emotions, health, control and habits, as mentioned above. Assessment of these sub-systems can derive critical routes of assessing the causes of discomfort and distress in slum rehabilitation housing, which can be essential policymaking variables for a sustainable slum rehabilitation process. In this manner, we expand the application of the theory of homeostasis in assessing the sustainability of a slum rehabilitation process through the lens of occupants’ holistic comfort and lack of stress in their built environment.4Household surveys were conducted to assess the determinants of discomfort and distress based on the conceptual framework illustrated in The basic structure of our version of the participatory backcasting method consists of four steps. These steps guide the intent of the surveys; in this case, it is to investigate the causes of discomfort and distress in the study area to prevent rebound phenomenon see . The fouWhat would you do if the living conditions here worsen in the future?‘; ‘If the concerned authorities do not take any action in improving the SRHs, will you contribute towards community development or you move back to slums?‘; ‘What are the major causes of discomfort and distress in your current housing as compared to the horizontal slums?’ These questions set the backcasting theme of the interviews as these questions probed probable future scenarios. Following this, specific questions were asked to understand occupants' attitude, emotions, health, control and habits of the occupants, as per Ortiz et al. (The step (2) involved assessment of the causes of discomfort and distress along the attributes of attitudes, habits, controls and emotions to understand occupants' implications with the loss of homeostasis  involved interviews concerning a future ‘research question 1 through step (1) and step (2) and create a way forward for research question 2 through step (3) and step (4)  involved post-processing of the interview data using a qualitative fault tree analysis (FTA) (4) see .4.1Thirty household surveys were conducted in the slum rehabilitation site of Natvar Parekh Compound (NPC) Mumbai, India see . The NPCThe surveys occupants were selected based on stratified random sampling. Only the head of the households was surveyed, in case the head was absent, the available adult household member was interviewed. The language of the interview was in Hindi or Marathi. As mentioned in the previous section, unstructured interviews were the primary medium of the surveys as it provided the flexibility of adapting the questionnaire based on the responses of Step (1), (2) and (3) of the methodology see . Owing t55.1we have to work indoors all the time” which has drastically reduced their socialising time. They emphasised that “no common private space” is available which is a primary discomfort in living in the SRH. According to them, shifting of their activities indoors from outdoors  affected their social life. Almost every interviewee reported “children do not have enough open spaces to play in front of our eyes … we fear they will wander off in the vertical maze”. This lack of outdoor and social spaces for cooking and socialising is a social-distress in the SRH.Narratives were collected through informal conversations using survey the execution method presented in Their perception of thermal comfort is closely related to the amount they had to spend on electricity bills that closely modulated their behaviour and control of the devices. The female respondents said that they refrain from using electrical appliances for their comfort during the day due to high electric bills. They usually operate them when children and male members were present indoors, mostly during the nigh-time. This observation was also reported in the work of Sunikka-Blank et al. . While ithese problems are trivial when we have a permanent house in Mumbai”. However, given a better house “with more space” to accommodate the larger household size.During the collapse state discussions (Step 2), most of the respondents said that even if the situation in SRH worsens, they will continue to stay because “not in our control because the house design restricts airflow”. However, they were not interested in investing in the exhaust fan in fear of burdening the electric bills. They revealed that lack of daylight promoted them to switch on the lights during the day, and even cannot use the corridors for socialising as its “too dark to even see”. Social isolation or ‘feel lonely and want to go back to horizontal slums” was consistently reported as a primary cause of distress. Visiting family and neighbours were considered as “hassle and cannot do it regularly”.While few respondents had a definite idea about an improved situation and said that cleaning the neighbourhood is very important as it could free up some spaces for social activities. Unmistakably, lack of ventilation in their living spaces was a problem for which was reported as “5.2The demographic descriptive of the survey is illustrated in 5.2.1As mentioned in section having a permanent home’. Horizontal slums were always treated as a temporary place of stay, and these SRHs gave them a permanent identity. However, this aspiration-driven appliance purchase increased its monthly electricity bill by 40%. It was found that in horizontal slums the average monthly electricity bill was around Rs. 300 (∼4 USD) which rose to around Rs. 500 (∼7 USD) in the study area. It was a significant economic burden on the surveyed households.Through narratives, it was found that occupants tend to purchase more appliance as they feel the fulfilment of their aspiration of ‘aspirations and not out of their income-driven capabilities. The same logic applies for the group 500–600 which have more appliances than the higher billed 1000–1100 group  devices like TV and smartphones for entertainment purpose. It can be interpreted than social isolation has a stronger influence than economic factor on appliance usage, as the respondents had always lived a ‘community-life’ in the slums but the vertical structures altered it to an ‘individualistic-life’.Additionally, as mentioned in section In step (3) of the survey see , most of5.2.2The general feeling regarding thermal comfort is neutral among the respondents see . While eCommon attitudes and practices involved keeping windows closed throughout the night-time due to the entry of insects/dust and a higher risk of burglary . Informmmunity’ . These ammunity’ .Fig. 7SoAdditionally, as discussed earlier in section During the step (3) of the survey, see  occupant5.2.4As a part of the homeostatic theory, the well-being of the occupants was investigated. The multivariate PERMA methodology of community-feeling and it was the major cause of psychological distress among the occupants.The interviewees scored higher on positive well-being indices like feeling joyful , contended , and while scored significantly low when asked about their general focussed-at-work  see . When asfeeling lonely’, ‘feeling anxious’ and ‘feeling angry’ were inversely scored, i.e., lower scores on these feelings indicate higher weight. For example, in feel very lonely, as ‘0 = very lonely’ and ‘10 = not lonely at all’. Similarly, for feeling anxious, the mode score is 0, whereas the mean score is 3.6 indicating a higher occurrence of anxiety among the surveyed occupants. Occupants have scored feeling angry with a mean value of 3.9 and a mode value of 0  in such low-income settlements , Sunikk, Ranade.6.1The occupant-led recommendations are presented in the fault tree illustration in Most of the occupants, and especially female suggested community-based microfinancing and neighbourhood maintenance co-operatives as they improve accountability of the occupants in improving their built environment. Thus, enhancing their homeostasis (i.e. holistic comfort and lack of stress) in the SRH. The female respondents said that they spend most of their time indoors and engaging in a self-help group would connect them for subsistence activities and generate income. We build on these suggestions to propose a possible community-led co-operative based model for the Natvar Parekh Compound (NPC), shown in We mention a woman-led self-help group (SHG) driven cooperative model see  for mitiIn return, the part of the revenue generated through these subsistence activities can be used to fund the SHG and create a micro-financing body. It can further provide the needed personal loans for buying a household appliance, without the loan-driven economic distress . The need was identified based on the current pattern of occupants' behaviour in the SRHs in Mumbai, where they are abandoning these vertical houses and moving back to the horizontal slums, presenting a rebound effect from these state-provided houses. The low-income and poverty remain a critical source of distress among the rehabilitated occupants, but there were underlying causal factors for such a rebound phenomenon. Therefore, we adopted an occupant driven investigation pathway for examining the multi-layered causes of the rebound effect of the SRH in Mumbai. The methodology consisted of two key segments: first was the conceptualisation of a bottom-up sustainability assessment method that centred around the notion of homeostasis, i.e. holistic comfort and lack of stress in the built environment. The second was the planning and design of a field survey based on the principle of participatory backcasting technique to record the dynamism of occupants’ attitudes, emotions, control, health and habits in their transitioning built environment.It was found that the interconnected causes of discomfort and distress in the study area were due to two primary reasons, first was due to economic distress owing to low-income status coupled with higher appliance ownership and usage implicating higher monthly electricity bills. The second reason was due to poor design and planning of the SRH that altered occupants’ social structure from a community-living to an individualistic life. The poor design of the SRH prevented the respondents from using the social spaces which had changed their household practices, attitudes and emotions. These findings act a proof-of-concept for our proposed sustainability assessment framework based on the theory of homeostasis (i.e. holistic comfort and lack of stress).In doing so, we expanded the application of the theory of homeostasis in sustainability assessment and policymaking of low-income settlements where understanding the local socio-cultural context becomes critical for the success of the project. There are three key contributions of this study, first is setting up the scope for non-income drivers of discomfort and distress in low-income housing like the slum rehabilitation housing in Mumbai that can influence the occupants to move out of such house to horizontal slums. The current literature on sustainable slum rehabilitation policies is heavily centred around ‘low-income’ specific dialogues where poverty is identified as the pivotal cause of failures. This study opens the discourse towards the causal factors that remain invisible in current literature. The proposed methodology contributes to the perspective development on sustainability and slum upgradation through an occupant-led policy development route. It provides a structure to the current bottom-up approach in slum rehabilitation policy. Critically this study contributes towards avenues of incorporating context of space in policy making rather than impulsively adopting the approach of verticalization and the control of sprawl.The second contribution of this paper is towards the development of a reproducible and defensible method that can broadly collect and interpret causes of occupants' discomfort and distress in transitioning low-income built environment. It fills an important literature gap in low-income sustainability planning of the Global South as most of the planning methods are often borrowed and reiterated from the Global North which misses the granular aspect of socio-cultural dynamics of occupants living in poverty. The theoretical framework presented in this study can be further developed into a web-based sustainability assessment tool that can provide valuable information concerning occupants’ socio-economic and environmental needs for better well-being in low-income housing sites. It can prevent similar rebound effects of the future affordable and low-income building stocks that Global South will accommodate over the economic growth phase.The third contribution of this study is on the development of the backcasting methodology for sustainable development of the slum rehabilitation houses. This study demonstrated for the first time that working backwards can reveal granular details on the cause of occupants’ distress and discomfort in their built environment. We anticipate that involving such backcasting methodologies in the broader policy-making framework of urban poverty alleviation will improve the robustness of the policies by introducing a feedback loop in the linear policy frameworks like the slum rehabilitation process in Mumbai. The introduction of such feedback loops and their inclusion in the current policy framework can amend the informality persistent in the Indian planning and planning institutions by improving the accountability of stakeholders from policy making to the delivery process.This study also recognised that investigating the well-being of such low-income settlements based on a standardised set of indicators, like PERMA method, reveal counter-intuitive results. Well-being has always been a developed country notion, and it cannot be adequately investigated with those indices for the cities of the Global South. A newer method is needed to understand and explore the notion of well-being in such complex urban systems where built environmental and socio-economic factors dominate the well-being of an individual. Discomfort and distress assessment-based methods like the theory of homeostasis can fill in this gap, provided it is developed with significant empirical evidence from a multi-disciplinary perspective.This study is limited by its small sample size, and the findings are restricted to the socio-cultural context of the study area (NPC). However, the results can be considered as a representation of the rehabilitated population in Mumbai as SRH is restricted to a similar socio-economic class which shows the possible generalisability of the conceptual framework. The methodology remains replicable and reproducible to other slum rehabilitation sites as well. The assumption of distress and discomfort causing rebound phenomenon is limited by our attribute selection which can be further refined through a larger sample size across the slum rehabilitation sites in India and the Global South. The theory of homeostasis needs to be tested and developed over a large population set, which remains a significant gap in the current literature.


Lenticular lenses are widely used in the three-dimensional display industry. Conventional lenticular lens components are made of plastics that have low thermal stability. An alternative is to use glass to replace plastic as the lenticular lens component material. Single crystal silicon is often used as the mold material in the precision glass molding process. It is, however, difficult to fabricate a lenticular lens silicon mold that has a large feature size compared to the critical depth of cut of silicon. In order to solve the problems of machining lenticular lens silicon molds using the conventional diamond cutting method, such as low machining efficiency and severe tool wear, a hybrid machining method that combined laser ablation and diamond cutting was proposed. A feasibility study was performed to investigate the possibility of using this method to fabricate a lenticular lens silicon mold. The influence of the laser parameters and machining parameters on the machining performance was investigated systematically. The experimental results indicated that this hybrid machining method could be a possible method for manufacturing lenticular lens silicon molds or other similar microstructures. Autostereoscopic display technology is a glass-free, three-dimensional (3D) technology that allows people to acquire a 3D perception of images without wearing specialized headgear or glasses. There are mainly two types of autostereoscopic display techniques: the parallax barrier type and the lenticular lens type . With thPrecision glass molding is a promising method in the large-scale industrial production of lenticular lenses. Single crystal silicon is an important mold material used in the precision glass molding industry due to its high thermal stability and available processing methods ,4,5. HowThe poor machinability of silicon leads to low machining efficiency. There are several approaches to improve the machinability of silicon, such as increasing the critical depth of cut through modifying the material property of the cutting region with the ion implantation method ,16, or u2 laser polishing. They could achieve a surface roughness of less than 10 nm after the laser polishing process. However, the limitation of this method is that it is difficult to predict the exact profile of the output surface, since the subsequent laser polishing process will change the topography of the surface created by femtosecond laser milling in an uncertain way. Thus, to obtain a designed surface texture within a reasonable form error, extensive trial and error is needed. Other examples of combined machining methods that follow the paradigm of the rough-finish sequential process are laser ablation followed by electrical discharge machining (EDM) [Nonconventional machining, or hybrid machining methods, are also possible alternatives to the diamond cutting method in generating large feature sized microstructures on brittle materials. Youn et al.  demonstrng (EDM) , femtoseng (EDM) , and eleng (EDM) . To the In order to improve the machining efficiency, as well as reduce diamond tool wear in fabricating lenticular lens silicon mold inserts, a new hybrid machining method combining laser ablation and diamond cutting was proposed in this research. This hybrid method also followed the paradigm of the rough-finish process. The laser ablation served as a rough machining process to remove the majority of the material, and the diamond cutting was the finishing process to shape the grooves, created by laser ablation, to their final status.The flow chart of the hybrid machining process is shown in The laser ablation experiment was conducted on the homemade laser micro-machining setup developed by the authors, which is shown in There are several methods to produce a groove of a given depth, such as changing laser power, scan speed or defocus depth. It is relatively easier to adjust the defocus depth by a numerically controlled 3-degree of freedom (DOF) motion platform than it is to adjust the laser power and scan speed. Therefore, in this experiment, different depths of laser ablation grooves was realized by changing the defocus depth.nD, was calculated. Then according to the relationship between the laser ablation depth and defocus depth obtained from the experimental result, the defocus depth, nd, was calculated. The interval between two laser scanning paths was set to be 5 µm.After the laser ablation process, grooves with a rough shape were obtained on a silicon workpiece surface. However, the surface quality of the laser-generated grooves was very unsatisfactory. In laser ablation, instead of directly removing it from the workpiece surface, the melt-off material piled up on the workpiece surface and subsequently needed to be removed by the diamond cutting process. Since the laser ablation experiment was performed on the laser micro-machining equipment, when the workpiece was moved to the diamond cutting machine, tool alignment was needed to make the groove axis comply with the diamond tool travel axis. Subsequently, diamond cutting with different finish depths of cuts was conducted to investigate the influence of the depth of cut on the surface quality of the machined grooves.The diamond cutting experiment was performed on a Nanoform 200 ultra-precision lathe. It can be seen from this image that the depths of these laser-generated grooves were almost the same, which means the repeatability of the laser ablation process was reliable, and thus acceptable for our purpose. Laser ablation experiments with changing laser power and scan speed were conducted. The cross-sectional profile of the lenticular lens groove was an arc. In this experiment, two grooves with different depths were generated in the laser ablation process. The design arc radius of the grooves was 0.5 mm, and the depths of the grooves were 50 µm and 80 µm. The width of the grooves were calculated to be 0.436 mm and 0.543 mm, respectively. The width of a single laser ablated groove was around 5 µm, which could be estimated from The optical microscopic images of the cross-sectional profiles of the laser-ablated grooves are shown in The main focus of this paper is on the feasibility of using this hybrid method to machine lenticular lens microstructures on a silicon workpiece surface. Since most of the material is removed in the laser ablation step, which is a relatively fast and low cost process, this machining method is expected to be highly efficient, as well as cost effective, compared to the conventional diamond cutting method. In this research, a preliminary experimental approach was successfully performed. The surface quality of the machined grooves was evaluated to demonstrate the feasibility of using this hybrid method to machine lenticular lens silicon mold inserts in terms of improving machining efficiency, as well as reducing tool wear.However, there are limitations of this research. For example, even though the machined surface quality could be improved significantly by reducing the finish depth of the cut, the best surface roughness of the machined groove, which was in the order of 100 nm, still could not fulfill the requirement of a practically useful high quality lenticular lens mold insert. There are several potential methods to further improve the machining performance of this hybrid method, such as using a negative rake angle diamond tool, or further reducing the finish depth of the cut to below the critical depth of cut of single crystal silicon. Another limitation of this method is that, at present, the two machining steps were conducted separately on two independent machine systems, which brings about the problem of re-alignment before the second machining step was conducted. In the future, this can be solved by combining the two steps into one machine system.Machining highly brittle materials using conventional methods is a long-term challenge. This work was a pilot research study of using hybrid methods to machine highly brittle materials. Further work is still required to make this method more applicable for the fabrication of lenticular lenses.In this research, a hybrid machining method that combined laser ablation and diamond cutting was proposed to machine a lenticular lens silicon mold. A feasibility study was performed to investigate the feasibility of using this method to fabricate a lenticular lens silicon mold. The influence of laser power, laser scan speed and defocus depth on the laser ablation depth was investigated. It was found that there was a linear relationship between laser power and laser ablation depth, and between laser scan speed and laser ablation depth, whereas, the influence of defocus depth on laser ablation depth was a non-linear effect. In the diamond cutting process, the machined surface quality was able to be improved significantly by reducing the finish depth of the cut. The experimental results indicate that this could be a feasible method of manufacturing lenticular lens silicon molds or other similar microstructures with improved machining efficiency, as well as reduced tool wear.


Electric field-based smart wetting manipulation is one of the extensively used techniques in modern surface science and engineering, especially in microfluidics and optofluidics applications. Liquid dielectrophoresis (LDEP) is a technique involving the manipulation of dielectric liquid motion via the polarization effect using a non-homogeneous electric field. The LDEP technique was mainly dedicated to the actuation of dielectric and aqueous liquids in microfluidics systems. Recently, a new concept called dielectrowetting was demonstrated by which the wettability of a dielectric liquid droplet can be reversibly manipulated via a highly localized LDEP force at the three-phase contact line of the droplet. Although dielectrowetting is principally very different from electrowetting on dielectrics (EWOD), it has the capability to spread a dielectric droplet into a thin liquid film with the application of sufficiently high voltage, overcoming the contact-angle saturation encountered in EWOD. The strength of dielectrowetting depends on the ratio of the penetration depth of the electric field inside the dielectric liquid and the difference between the dielectric constants of the liquid and its ambient medium. Since the introduction of the dielectrowetting technique, significant progress in the field encompassing various real-life applications was demonstrated in recent decades. In this paper, we review and discuss the governing forces and basic principles of LDEP, the mechanism of interface localization of LDEP for dielectrowetting, related phenomenon, and their recent applications, with an outlook on the future research.  S, L, and V, which are the abbreviations of the corresponding media as solid, liquid, and vapor, respectively. However, in reality, there exists no ideally homogeneous surface, as every solid surface possesses small inhomogeneity in the form of roughness or chemical impurity or both, which often reflects in the measurement of the contact-angle hysteresis . F. FD and Dielectrophoresis (DEP), as the name suggests, is a commonly observed phenomenon with dielectrics, involving the translation motion of neutral matter in a non-uniform electric field caused by the polarization effect. The electrohydrodynamic (EHD) motion and the change of the liquid–vapor interface shape of an insulating liquid actuated by the DEP force is known as liquid dielectrophoresis (LDEP). To understand the LDEP effect, we need to analyze the electrostatic interaction with the liquid molecules. In a uniform electric field, the electron cloud of a neutral molecule is slightly displaced toward the positive polarity of the field due to the electrostatic attraction giving rise to the induced dipole moment  depicts the strength of the force on a dielectric material in ambient air medium that depends on the polarizability, the volume of the attracted medium, and the field intensity squared. However, the Kelvin polarization force density only demonstrates the interaction between the dipole moments present in the dielectric material, whether permanent or induced by the electric field. In reality, the liquid could contain free charges in the form of ions and impurity and, upon that, the interaction among the dipoles could lead to a contribution to the exerted force and the electric field. All the effects can be summarized in one equation by writing the electrostatic force density, which originates when an electric field is exposed to an electrically linear and incompressible liquid medium .(5)f→e=V can be calculated by a simple surface integral of the Maxwell stress tensor over the surface S bounding the volume ass.For the complete electrohydrodynamics (EHD) force, the Navier–Stokes equations governing the hydrodynamics need to be coupled with the electrostatics via deriving the Maxwell stress tensor Jones and his co-workers also demonstrated that, in addition to the actuation of ideally dielectric liquids, the LDEP force can also be applied to actuate aqueous liquids which are partially conducting or leaky dielectric ,29,30. TThe closed surface for the integral was chosen in such a way that it must enclose the liquid–air interface, as the LDEP force acts only at the interface; however, the top and bottom faces should be far enough apart to avoid distortions near the corners at the three-phase contact point  due to the fringe electric field, as shown in =σ1D see B.The expressions for the electric fields are as follows:The time average of the vertical force of electrical origin can be calculated substituting Equations (9)–(12) in Equation (8) asIn mechanical equilibrium, the vertical force of electrical origin is equal to the downward pulling gravitational force due to the weight of the liquid column.The critical frequency, −4–10−2 S/m) for a wide range of frequencies using a modified version of Pellat’s experimental set-up [Jones et al. also verified these theoretical predictions by measuring the height rise of three different aqueous liquids with varying conductivity (10l set-up . They fo2 or glass). Upon application of an AC voltage around 200 V root mean square (rms) at 60 Hz, a highly insulating liquid , the wettability of a dielectric liquid drop can be manipulated reversibly if the LDEP force is localized at the solid–liquid interface, using a substrate with an interdigitated electrode (IDE) pattern. Recently demonstrated by McHale et al., this new mechanism for the manipulation of the contact angle of a dielectric liquid drop is called dielectrowetting . In dielMcHale et al. derived the equation for manipulation of the apparent contact angle of dielectric liquid as a function of voltage, which is very similar to the famous Young–Lippmann equation for the electrowetting phenomenon . The eneFor dielectrowetting, typically, linear IDEs with the same electrode width and gap e number ,38. TherIn typical experimental conditions, the liquid thickness is very high compared to the penetration depth of the electric field cosθrinkling ,38. In two-liquid systems, the contact angle of the droplet is, typically, determined by the interfacial tension of the liquid–liquid (medium). The liquid medium plays a very important role in LDEP-based wettability manipulation, as, contrary to the case in air medium, the contact angle could increase upon the application of voltage if the ambient has higher polarizability than the droplet liquid, i.e., ectively . The larconstant . They al follows :(19)h2(VEquation (19) was experimentally verified using droplets of six different test liquids in six different liquid media. They also showed that dielectrowetting in the liquid–liquid system could be an effective method of determining material properties such as interfacial tension or permittivity from the ratio of In dielectrowetting, the spreading direction of the dielectric liquid drop is dictated by the geometry of the interdigitated electrodes, as the drop prefers to spread in the parallel direction of the electrodes, resulting in huge modulation of apparent contact angle along one direction only . The liqWith the huge advancement in science and technology in the 21st century, a natural trend in modern technology is to manufacture miniaturized, cheap, and easy-to-handle devices. The emerging microfabrication technology made it possible to integrate many biological and chemical analysis processes into a miniaturized chip, known as the micro total analysis system (μTAS) or lab-on-a-chip (LoC) technology. In recent decades, the modern medical diagnostic, bio technology, and microfluidic research greatly benefited from these technologies due to their various advantages, such as portability, versatility, high speed, and high throughput with extremely small volumes of samples and reagents ,49,50,51A classical spherical lens, typically made from solid materials such as glass or plastic material, refracts the light passing the interface depending on the contrast of the refractive indices of the media. Although solid lenses are highly scalable in size, they lack the flexibility to adapt the variable focal lengths. On the contrary, liquid lenses are highly flexible, as the focal length can be tuned by two mechanisms; one involves controlling the spatial distribution of the refractive index of the anisotropic optical medium  and another involves tuning the curvature of the liquid–vapor interface of a droplet. The controlled tuning of the focal length of a liquid crystal (LC) lens can be achieved by a non-uniform electric field via spatial distribution of the refractive index in the nematic LCs ,57,58,59The electrical tuning of focal length was also demonstrated by electrowetting and dielectric force via controlled deformation of the interface profile of a droplet . ObviousIn 2011, the first optical switch based on the dielectrowetting mechanism was developed by Ren et al. . The autIn recent years, dielectrowetting gained huge popularity as an active and alternative tool for manipulation of the wetting property of a non-conducting droplet, which is reflected in the modern literature, as scientists came up with various ideas to explore the technique in novel applications in real life. Recently, a couple of research groups demonstrated a liquid iris based on the dielectrowetting phenomenon ,72. TsaiThis paper provided a brief overview of the LDEP phenomenon for liquid manipulation and its latest version of the dielectrowetting phenomenon, in which the contact angle of a dielectric liquid droplet can be modified reversibly though the localization of the LDEP force at the solid–liquid interface. LDEP is a bulk force of electrical origin which penetrates into the bulk of the dielectric liquid through the polarization of liquid molecules to produce a movement toward the higher-intensity direction of a non-homogeneous electric field. The RC-equivalent circuit analysis of the LDEP system predicts that the actuation of aqueous liquids by the LDEP force using high frequency, much higher than the critical frequency, can be achieved. The fundamental concept of dielectrowetting is the reversible modification of the apparent contact angle through localizing the LDEP force at the three-phase contact line to deform the liquid–vapor interface. Apparently, the contact-angle change behavior has similarity with the electrowetting on dielectrics, but the electrode design (co-planar linear interdigitated electrodes instead of planar electrodes) and the basic mechanism are very different from the latter. The main advantage of dielectrowetting is that a dielectric liquid drop can easily be spread into a thin film at sufficiently high voltage, overcoming the limitation of the contact-angle saturation encountered in EWOD. With the capability of super spreading a dielectric liquid drop, dielectrowetting was applied to microfluidics and optofluidics devices. Although dielectrowetting is in its early stage, many problems such as axis-asymmetric spreading of the liquid droplet with an advanced engineered electrode pattern and contact-angle hysteresis using a slippery surface were solved. However, the actuation voltage for contact-angle manipulation by dielectrowetting is quite high compared to the EWOD technique, which restricts it from application in devices with a low power requirement. This issue could be solved by the combination of better electrode design and a high-dielectric-constant liquid. One possible future research direction for the principle of dielectrowetting could be the investigation of the physics of contact line pinning during spreading at virtual pinning sites created by the periodic potential in the perpendicular direction of the linear interdigitated electrodes.