Isolators, or optical diodes, are devices enabling unidirectional light propagation by using non-reciprocal optical materials, namely materials able to break Lorentz reciprocity. The realization of isolators at terahertz frequencies is a very important open challenge made difficult by the intrinsically lossy propagation of terahertz radiation in current non-reciprocal materials. Here we report the design, fabrication and measurement of a terahertz non-reciprocal isolator for circularly polarized waves based on magnetostatically biased monolayer graphene, operating in reflection. The device exploits the non-reciprocal optical conductivity of graphene and, in spite of its simple design, it exhibits almost 20 dB of isolation and only 7.5 dB of insertion loss at 2.9 THz. Operation with linearly polarized light can be achieved using quarter-wave plates as polarization converters. These results demonstrate the superiority of graphene with respect to currently used terahertz non-reciprocal materials and pave the way to a novel class of optimal non-reciprocal devices. Optical isolators, or optical diodes, allow electromagnetic radiation to travel in one direction but not the other. Here, the authors achieve unidirectional propagation of terahertz waves by taking advantage of the non-reciprocal nature of optical conductivity in magnetostatically biased graphene. The potential applications of graphene for terahertz passive and active devices have received considerable attention in recent scientific literature123456789101112131415161718192016819Apart from ferrite and graphene, alternative materials have also been proposed to achieve efficient terahertz non-reciprocity, and several works have been recently published presenting experimental characterization of the properties of these materials. One example is given by other free carrier based materials such as doped silicon27In the following we aim to exploit the non-reciprocity of magnetically biased monolayer graphene using a reflection configuration to achieve isolation for circularly polarized waves. The concept of isolator for circularly polarized light has been presented theoretically in a transmission configuration for graphene and other magneto-optical materials19N of graphene sheets are placed on a back-metallized thin silicon layer of 10 μm thickness (for our device N=3). The sheets are separated by thin poly methyl methacrylate (PMMA) layers (∼60 nm), while the thickness of the metallization (chromium and platinum) is 200 nm. The whole structure is bonded to a pyrex wafer, which has solely the function of mechanical support. A magnetostatic field B is applied orthogonally to graphene.A non-reciprocal isolator is a device possessing at least one electromagnetic mode showing unilateral propagation, that is, it allows the transmission of an electromagnetic wave in a given direction while strongly attenuating it in the other one The device operation is based on reflecting incident left hand circularly polarized (LHCP) plane waves as right hand circularly polarized (RHCP) ones, while absorbing RHCP incident waves. The device thus achieves non-reciprocal unidirectional propagation and isolation for circularly polarized waves1923η of free space , causing total absorption  rotating waves (incident RHCP or reflected LHCP) a total surface impedance equal to the impedance rization , taking σCW=σd+jσo and σCCW=σd−jσo for circularly polarized waves.which has two eigenvalues B=7 T the real part of σCW is very close to (3η)−1 and thus the total impedance of the three monolayers stack is very close to η. The role of the metallized silicon reflector is to cancel the imaginary part of σCW at the working frequency in order to enable full impedance matching in the CW case. Additional details can be found in the full design procedure provided in The yellow region in θ between the two polarizers. The magnetostatic field is normal to the sample surface, while the light k vector is close to normal. B=0 T. One can see that the normalized reflection shows strong absorption dips. These strong absorption features have a periodicity of 4.65 THz, corresponding to Fabry–Perot oscillation in a silicon layer of 9.43 μm in very good agreement with the nominal value. B=7 T. This is also shown better by the polarization diagrams in ϕ goes up to 90° and continues from −90° to 0°.The fabricated device has been measured using a Fourier transform infrared spectrometer connected to a split-coil superconducting magnet. A polarizer is used to create a linearly polarized incident light, while an analyser  is used in front of the detector see . The refThe isolation (ISO) and insertion loss (IL) of the device are defined as:Even though our measurement setup is equipped only with linear polarizers, both these quantities can be computed accurately from the measured polarization parameters . The sought isolation and insertion loss can then be retrieved as:Emax and Emin are the major and minor axis of the mapped elliptical polarization of the reflected electric field and Einc is the linearly polarized incident electric field. The full algorithm is actually more complex and it enables the compensation of polarizer imperfections  is a device figure of merit of the isolator, which depends on the isolation and on the insertion loss, and it defines the shape of the forbidden region. Notably, it forbids points having at the same time high isolation and low insertion loss, which represent the target for any isolator design.The right member For the fitted parameters, it can be shown that the forbidden region is frequency-independent in the band from 0 THz to 20  THz. The performance of the device is just 1 dB below the theoretical upper bound, which means that the device is near optimal.While the presented isolator operates with circularly polarized light, it is clear that most terahertz applications need components able to handle linearly polarized waves. It is however, quite simple to adapt our isolator to linear polarization operation using one or two quarter-wave plates as polarization converters, as shown in In this work we demonstrated the possibility of designing and implementing close to optimal terahertz isolators based on graphene. To achieve this goal, we proposed a reflection structure that exploits the Fabry–Perot resonances in a thin layer of silicon to obtain isolation using just three graphene monolayers. The operation of the device can be fully understood in the framework of Maxwell's equations using a 2D linear conductivity tensor to model carrier dynamics in magnetostatically biased graphene. One of the most significant aspects of this design is its ability to be very close to the optimal performances available with the used graphene45k vectors at the same time. Electric field effect in gated graphene could be used to fine tune the device to virtually infinite isolation, as demonstrated also at microwave frequenciesIn addition, it is worth mentioning some additional advantages related to this particular device geometry. First, due to the fact that the device is planar , it works for incident waves having different Because the device exploits Fabry–Perot resonances, it is relatively narrowband; however, the absolute bandwidth is in the order of 50 GHz, which is an excellent value for telecommunications and for continuous wave applications. This value can possibly be increased using more complex designs including patterned graphene, added metal patterns and more complex multilayer structuresFinally, the reflection configuration of the device eliminates completely the input impedance mismatch (return loss) issue, which is instead a concern for any device operating in a transmission configuration. For waves with a non-zero incidence angle  this fact is evident considering that the device is invariant to translation and hence it operates with a single diffraction order. This implies that the wave cannot possibly be reflected to the receiver. For normally incident waves, this is due to the fact that an incident left hand wave can only be reflected as right hand and vice versa, because the device is invariant to rotation.B biasing field is to use graphene with higher mobility2 V−1 s−1. With a mobility of 40,000 cm2 V−1 s−1 and a biasing field of 1 T (easily generated by rare earths permanent magnets) the insertion loss for perfect isolation would be as low as 0.3 dB according to the upper boundThe main drawbacks of our device are the need of high magnetic field (7 T) and an insertion loss of more than 7 dB. Both these issues cannot be solved by improving the design, since it is already quasi-optimum in this sense. Hence, the only way to lower the insertion loss and reduce the required 2 box layer of 4 μm. Platinum (200 nm) was evaporated on the top side of the silicon on insulator wafer and then it was bonded using parylene to a support pyrex wafer. The handle and box layers were then ground and etched leaving the device layer exposed. Three layers of graphene were subsequently transferred on the substrate keeping the PMMA support film between each layer. More details about fabrication and measurements are available in the The reflective substrate has been fabricated starting with an silicon on insulator wafer having a high resistivity silicon device layer with thickness 10 μm a handle layer of 500 μm separated by an SiOReflection coefficients and derived quantities (insertion loss and modulation depth) are defined in terms of electric fields, and consequently the corresponding decibel unit is defined as How to cite this article: Tamagnone, M. et al. Near optimal graphene terahertz non-reciprocal isolator. Nat. Commun. 7:11216 doi: 10.1038/ncomms11216 (2016).Supplementary Figures 1-5, Supplementary Notes 1-4 and Supplementary References


We show that electron charge is transferred across the interface and magnetization is induced in the graphene sheet due to the strong interaction between C and Mn. Depending on the relative orientation of graphene and BaMnO3, a quasi-half-metal or a magnetic semiconductor can be obtained. A remarkably large proximity induced spin splitting of the Dirac cones (~300 meV) is achieved. We also show how doping with acceptors can make the high-mobility region of the electronic bands experimentally accessible. This suggests a series of possible applications in spintronics  for hybrid organic-multiferroic materials and reveals hybrid organic-multiferroics as a new class of materials that may exhibit exotic phenomena such as the quantum anomalous Hall effect and a Rashba spin-orbit induced topological gap.Graphene and magnetoelectric multiferroics are promising materials for spintronic devices with high performance and low energy consumption. A very long spin diffusion length and high carrier mobility make graphene attractive for spintronics. The coupling between ferroelectricity and magnetism, which characterises magnetoelectrics, opens the way towards unique device architectures. In this work, we combine the features of both materials by investigating the interface between graphene and BaMnO Conventional III–V semiconductors were originally proposed as channel materials due to their high SOC and long spin lifetime. However, since the mean velocity of the carriers is quite small, the corresponding spin diffusion length is relatively short and results in weak magnetoresistance signalsμm) spin diffusion lengths57via an external applied field. In addition, to achieve graphene-based transistors one needs to open its vanishing electronic gap. Isolated pristine graphene is not optimal for spintronics applications: it is necessary to combine it with a material with high SOC, and either cut it into nanoribbons3O4proximity interaction)13magnetoelectric (ME) multiferroic material as substrate can satisfy all these points. ME materials are characterised by a coupling between ferroelectricity and magnetization, hence allowing one to control the magnetization via an electric fieldSpintronicsd electrons carry a strong spin polarization. First-principles calculations have shown that Mn adatoms interact strongly with carbon π orbitals inducing Rashba SOC and quantum anomalous Hall effect in graphene3 has been chosen as representative of this class of materials since it is ME203 is the same as for the class of RMnO3 hexagonal manganites (where R is a rare earth element). We find that the graphene–BaMnO3 (g–BMO) hybrid system is spin polarized with magnetization and charge transfer induced in the carbon atoms due to the strong interaction with the surface Mn atoms. The most stable reconstruction is quasi-half-metallic and acts as an injector of 100% spin polarized carriers. The electronic properties at the Fermi energy (EF) are governed by the details of the interface. The graphene Dirac cones for majority and minority carriers present a huge splitting of about 300 meV. Furthermore, we show that both the energy at which the band crossing occurs and the splitting of spin-up/spin-down bands can be tuned by doping of the graphene monolayer.This paper reports on the first principles investigation of the electronic and magnetic properties of the interface between graphene and ME multiferroics. We focus on manganite-based MEs, since the Mn 3, which is crucial in order not to short-circuit the graphene layer, ensure that electron transport will only occur through graphene and correctly model the spin polarization induced on the C network  with respect to the middle of the slab . The electrons at the surface give rise to the spin-polarized bands below EF  surface of BaMnOtion see . The slation see , charactbelow EF . A slighthe bulk .3, we can now address those of its interface with graphene. The g–BMO slab is constructed by placing a 4 × 4 graphene supercell on either side of the strained BMO slab. Atomic relaxations with different graphene offsets lead to the most stable structure shown in fat bands).Having clarified the electronic and magnetic properties of BaMnO5 m/s for the band crossing EF: only minority carriers can propagate at the interface. The majority band edge lies slightly above EF (78 meV), such that by applying a small gating potential, an injector of 100% spin polarised carriers is achieved (spin filter). The band contribution coming from each atom and orbital has been identified with projected bands. This technique  than that in the centre of the slab , as shown in 3 compounds as substrate. The magnetic moment on individual C atoms is at most As a consequence of this strong interfacial interaction, the surface Mn atoms induce spin polarization and charge transfer in graphene. The hybrid system is magnetic. As for the bare BaMnOolarized . These rF and, hence, the position of the Dirac cones. Several structures with one and two B substitutional dopants per graphene layer have been relaxed and analysed. The most likely site for a single dopant (3% p-type doping concentration) is sublattice “3”  is close to pristine graphene (8.5 × 105 m/s). Velocities up to 4.2 × 105 m/s (majority) and 6.6 × 105 m/s (minority) are reached for 2 Boron dopants.An important feature of the electronic structure is that the graphene Dirac cones are found at the K and K’ points of the 4 × 4 supercell. The latter are mostly contributed by C and, to a minor extent, by Mn and O. There is a remarkably large splitting of ~290 meV between spin up and down Dirac points. However, these high mobility regions occur at energies which are difficult to reach in experiments. Doping graphene with acceptors can shift Etice “3” . When a tice “3” . Inspecttice “3”  shows th3 interfaces have been checked. A metastable configuration is reached when one Mn lies in the middle of a C hexagon and two Mn are vertically aligned with C in the unit cell. This system is a magnetic semiconductor  effect and Rashba spin orbit splitting, analogously to graphene doped with Mn adatomsSince the electronic band structures exhibit quite different features for majority and minority spins, very different electronic transport properties are expected as well. A possible device exploiting these results is a spin–FET in which spin injection is obtained by graphene-BaMnO3. The strong interaction between graphene π electrons and the magnetic Mn d states induces a significant spin polarization in graphene. This interaction breaks the carbon network in six sublattices with different magnetic and charge transfer properties. The ground-state structure is a quasi-half-metal that allows for injection of 100% spin polarised carriers. Depending on the relative orientation of graphene and substrate, a magnetic semiconducting metastable state is also found. In each case, the graphene Dirac cones present a remarkably large spin splitting (300 meV). This high-mobility region (similar to suspended graphene) can be made accessible to experiment via substitutional doping of graphene with acceptors. The main features of the electronic structure do not depend on the Ba atom, and are expected to hold also for other hexagonal manganites RMnO3 or any magnetic insulator.In conclusion, first-principles calculations have been used to investigate the interfaces between graphene and a magnetoelectric multiferroic material, BaMnO3 is achieved for a real space grid cutoff of 1200 Ry, a shifted 6 × 6 × 12 k-point sampling of the Brillouin zone and a Fermi-Dirac smearing of 100 K in a 30-atom cell which is primitive for the ground state phase (space group P63cm).All calculations have been performed using the SIESTA implementationHow to cite this article: Zanolli, Z. Graphene-multiferroic interfaces for spintronics applications. Sci. Rep. 6, 31346; doi: 10.1038/srep31346 (2016).


An optimization method for condition based maintenance (CBM) of aircraft fleet considering prognostics uncertainty is proposed. The CBM and dispatch process of aircraft fleet is analyzed first, and the alternative strategy sets for single aircraft are given. Then, the optimization problem of fleet CBM with lower maintenance cost and dispatch risk is translated to the combinatorial optimization problem of single aircraft strategy. Remain useful life (RUL) distribution of the key line replaceable Module (LRM) has been transformed into the failure probability of the aircraft and the fleet health status matrix is established. And the calculation method of the costs and risks for mission based on health status matrix and maintenance matrix is given. Further, an optimization method for fleet dispatch and CBM under acceptable risk is proposed based on an improved genetic algorithm. Finally, a fleet of 10 aircrafts is studied to verify the proposed method. The results shows that it could realize optimization and control of the aircraft fleet oriented to mission success. Prognostic and health management (PHM) technology has a rapid development and been widely used in aeronautical equipment in recent years. The failure position and remain useful life (RUL) of equipment could be predicted by PHM. Further, it can be used in aircraft condition based maintenance (CBM) . HoweverThe aircraft usually performs mission in fleet manner and shares limited support resource. So, there will be a tradeoff range for fleet CBM. This means each aircraft can choose strategy among dispatching strategy, standby strategy, and maintenance strategy or their combination when the RUL has been obtained, and the synthetic strategy for fleet (combination of each aircraft's strategy) should meet the mission requirement.There are three forms of RUL in PHM, and each form includes some uncertainty. First is the point value of the time of potential failure. Second is the interval value of the time of potential failure –7. ThirdTwo methods can be used in reducing the impact of prognostics uncertainty on CBM decision. One is to reduce the uncertainty of failure prediction directly so that the decision risk will decrease –15. The Most research about RUL for CBM is about the life cycle maintenance optimization decisions on single aircraft and researchers would rather consider the maintenance decisions than think about the mission requirements and the dispatched strategy. The research on fleet CBM oriented to mission successes is few. Agent technology and the heuristic algorithm are used to fleet CBM in article , 23, butAn optimal aircraft fleet CBM method for aviation unit maintenance is proposed in the paper considering dispatch, mission, and resource constraints. Moreover, the RUL distribution of the key LRM has been transformed into the failure probability of the aircraft, and the calculation method of the costs and risks for mission is given. Then, an optimization decision making method for fleet dispatch and CBM under acceptable risk is proposed based on an improved genetic algorithm.m aircrafts and k integrated support stations (ISS) facing continuous combat missions (k < m), in which a single mission requires l aircrafts (l ≤ m). Each aircraft contains p LRMs of which RUL can be estimated. The mission preparation period starts at time t0, while the mission period is from time t1 to t2. The basic process of the fleet CBM decisions, which is mission success oriented, is given in Consider an aircraft fleet containing The aircraft fails when any key LRM fails.t0 is F(t) of which probability density function is f(t).The RUL distribution of LRM which is given at the time Assume the maintenance method of the LRM is renew, which means the LRM will be as good as new after maintenance, considering the field maintenance of aviation unit maintenance.t0 to t1.Only one aircraft can be repaired in each ISS simultaneously. But the total number of the aircraft maintenance may be more than one from the time Different LRM in the same aircraft can be replaced at the same time for renew is served as a maintenance method.j class is Cj.The maintenance cost of the different LRM varied while the same LRM cost is the same. The maintenance cost of the LRM on Each aircraft malfunction will cause the mission to fail when the fleet is on mission. The consequences of the economic loss will not be taken into consideration.Spare parts are plentiful.The basic assumptions of the problem are listed below in order to define the problem.The main work of the optimization decision making method for fleet CBM considering prognostics uncertainty includes the following steps: (1) the definition of the fleet initial health status based on the RUL prognostic, (2) maintenance program generating, (3) maintenance time and cost estimation, and (4) mission risk assessment. Based on the objects above, the optimal CBM and maintenance program through the rational optimization algorithm is obtained in the paper. The modeling framework is given in jth key LRUij on the ith aircraft is Fij(t). In the mission period (t1-t2), the probability of failure can be got byfij(t) is the probability density function of the Fij(t).Assume the distribution of the m aircrafts and each include n LRMs, the initial health status matrix of all LRM is P(a) that is given byConsidering an aircraft fleet containing Maintenance program considers whether a certain LRM should be maintained and the selection of the ISSs.U of fleet can be described asuij = 1 means that the jth LRM of the ith aircraft needs to be repaired; otherwise, uij = 0.The maintenance matrix S of the fleet is shown assiq = 1 means that the ith aircraft should be maintained at the qth ISS; otherwise, uij = 0.According to the assumption (4), the LRM can be maintained at the same place; however, many the LRMs fails. Therefore, the ISS matrix jth LRM spends time Tj and needs cost Cj. According to the assumption (5), the total maintenance time Tmi of the ith aircraft is given asAssume repairing the q, so the total maintenance time of all aircrafts can be calcluated asThere may be more than one aircraft that should be repaired at ISS The total maintenance cost of all aircrafts can be got asP(b) of the fleet can be built according to the Assumption (3). Consider pij(b) = 0 after the LRMij on the ith aircraft was renewed; otherwise, pij(b) = pij(a) without renew. The elements in the matrix can be obtained byWhether the aircraft is “dispatching” or “dispatching after maintenance” should be taken into consideration when calculating the mission risk of the fleet. The status of the aircraft should be updated if the single strategy of the fleet is “dispatching after maintenance.” Then, the modified health status matrix Pi(a) of the ith aircraft can be given asThe failure probability of the single aircraft could be estimated after modifying the health matrix of the fleet. According to the first assumption, “the aircraft fails when any key LRM fails”; the failure probability Formula  can be oi) = 1,2,…, m can be obtained by sorting the failure probability of single aircraft in ascending order. The ordered failure probability of the aircraft is given asThen, Pro(P2(a) is the smallest Pro(i). Then, set Pro(2) = 1, and let P1(b) = P2(a) after reordering. Pick up aircrafts of which Pro(i) = 1,2,…, l when the mission needs dispatch l aircrafts.Suppose PF is the mission risk.Assume the serious consequences of the mission that failed are similar without taking the economic losses into account. The failure probability of the fleet mission can be calculated by the following according to :(12)PF=The optimization problem in the paper is to find a fleet CBM strategy with acceptable risk and lowest cost considering prognostics uncertainty.MinC = ∑i=1m∑j=1n[uij × Cj].Thus, describe the objective of the optimization as RA of the site, the time constraint RB, the security risk constraint RC, the mission risk constraint RD, and the variable constraint RE.The constraints that should be considered about involve the maintenance ability constraint RA, set siq = 0   and uij = 0   if none of LRMs need maintenance. Else if any LRMij requires maintenance, then uij = 1 and the corresponding siq = 1 while the other siq = 0. Thus, the RA can be described asFor first constraint q should be finished before the mission starts. Thus, the RB can be given asAll maintenance of site q is ∑i=1msiq = x > 1 . If ∑i=1x−1siq × Tmi ≤ t1 − t0 < ∑i=1xsiq × Tmi, which means the maintenance for the xth aircraft could not be finished before the mission start time, this aircraft will not be taken into account when the maintenance decisions is “dispatching after maintenance.”Assume that the total number of the aircraft which maintained at site l aircrafts, and the RC can be described as  conditions, and the dimension of decision making variables which can be written as m × n + m × k is relatively large. So an improved genetic algorithm was proposed in this paper for the problem instead of traditional mathematical methods.The optimization problem cannot meet the KKT  = 1, the aircraft i need not be repaired and all siq  = 0; otherwise, the aircraft i needs to be repaired. Then, the determining condition is described as ∑q=1ksiq = 1 and siq ∈ {0,1}.According to formula , an inity aircrafts need not be repaired. Remove y rows which stand for these aircrafts. Then, a new (m − y) × k matrix S′ which represents the new relationship between the ISS and the aircraft that needs to be repaired can be built as the reduced cycle matrix of S.Consider that there areTmi of the aircraft needs to be repaired in matrix S′ which can be obtained by formula (i=1m−yTmi/k. It can be determined not meet the time constrain if max(Tmi) > t1 − t0 or AMT > t1 − t0, then turn to The maintenance time  formula . Then, tS′, and set siq = 0 .Initialize the matrix S′ from the first row to the kth row. The method of the qth is described as follows.Tmi − AMT|  . If the aircraft z makes the |Tmz − AMT | = min|Tmi − AMT|, then szq = 1. Furthermore, the aircraft can be selected in random if there is more than one aircraft that meets this formula.Calculate the value of |z is in to build a new reduced cycle matrix S′. Update the remaining maintenance time TGq = t1 − t0 − Tmz of the site q.Remove the line in which the aircraft TGq and the Tmi for the S′. If the formula “min(Tmi) | i = o ≤ TGq” can be met by a parameter o, form a new reduced cycle matrix and set soq = 1. Moreover, the remaining available reference time should be updated as TGq = TGq(b) − Tmo. This work should be repeated until the min (Tmi) > TGq; then, turn to the (q + 1)th row.Compare the Set the value of the matrix U should be adjusted if the constraints of resource maintenance cannot be met. Consider that the maintenance cost should be as low as possible and the requirement of the mission risk should be satisfied; the elements which uij = 1 should find pij(a) corresponded and the min{pij(a)}; then, set uij = 0. Return to U until meeting constrains RA and RB.The matrix U which is initial or got by adjusting, crossover, and mutation may not meet the requirement of the mission risk constrain. The penalty method can be used in the method followed to solve this problem.Some matrix U can be written asF is the vector of the penalty function and the Fi = max{0, gi}, while M, which is the penalty factor vector, is a large positive number.The energy function for every Emax and Emin are the maximum and the minimum values of the energy function in the population.The fitness function is given as follows in order to minimize the objective function:Proportional selection, single-point crossover, and the basic alleles can be used in solving this problem.This problem can be dealt with by some method written in the article –26 in orN is the size of the population and g is the genetic algebra, while T0 is the initial temperature and fi is the fitness of the ith individual.Simulate the annealing stretching for fitness before selecting the operator as follows:Pe and Pf can be defined as , and the mean μ and the variance σ2 are given in Consider a fleet containing 10 aircrafts and each aircraft includes 4 LRM  of which life can be predicted. Assume the RUL following Gaussian distributions Psl should be below the 10−8 while Psl should be below 10−6.The mission requires dispatch 8 aircrafts one hour later and lasting two hours. Assume there are 3 ISSs, of which ability of the maintenance are the same, being in charge of all aircrafts' maintenance. The maintenance time and cost of each LRM is given in Consider that there are 100 individuals in populations, and one of these individuals is described as follows:k1 = k2 = 0.97, k3 = k4 = 0.02. The result is described in Set up the −07 which meet the requirement.The total cost of the maintenance is 14439.3 and the mission risk is 8.95 ∗ 10Then, optimal maintenance program can be written as B/D are the LRMs that need to be repaired. There are six aircrafts and eight LRMs that need to be repaired, and the numbers of the aircrafts that need dispatch are 1, 3, 4, 5, 6, 7, 8, and 10.Then, the optimal scheme of aircraft CBM and dispatching are described completely in This paper researches optimization decision method for aircraft fleet CBM oriented to mission success considering prognostics uncertainty and the resource constrain. The CBM and dispatch process of fleet is analyzed; the modeling method and an improved genetic algorithm for the problem are given, and the method is verified by case about fleet with 10 aircrafts.The alternative strategy sets for single aircraft are defined; then, the optimization problem of fleet CBM is translated to the combinatorial optimization problem of single aircraft strategy. The relationship between maintenance strategy and mission risk is established, and the problem becomes easier to solve.This paper used the RUL distribution, which has the maximum information and the highest in prognostics. It has more accurate description of the uncertainty compared with others.The optimization decision with risk for fleet CBM is realized. The fleet mission risk is quantitatively assessed, and the optimal CBM strategy for fleet could satisfy the requirement of lowest maintenance cost and acceptable risk.The main advantages of this method are shown as follows.This paper presents a theoretical approach for fleet CBM considering prognostics uncertainty. Some factors have been simplified, such as the cost of risk, the consequences of risk mission, the effect of the CBM process form ability of maintenance personnel, and the effect of random failures. The focus of further work is a more detailed and comprehensive model considering all above factors.


Median U-turn intersection treatment (MUTIT) has been considered an alternative measure to reduce congestion and traffic conflict at intersection areas. The MUTIT is sometimes difficult to implement in the field because it requires wide median on arterials for U-turn vehicles. The objective of this study is to introduce an unconventional U-turn treatment (UUT) for intersections which requires less median space but is also effective. The UUT has a dual-bay design with different turning radiuses for small and large vehicles. The VISSIM simulation model was developed to evaluate the operational features of the UUT. The model was calibrated using data collected from intersections in China. The capacity, delay and number of stops were evaluated and compared with the direct-left-turn (DLT) for the same intersections. The results showed that the UUT significantly improved the operations at intersection areas, especially when volume/capacity ratio is small, and ratio of left-turn to through traffic is small. With the UUT, the capacity is increased by 9.81% to 10.38%, vehicle delay is decreased by 18.5% to 40.1%, and number of stops is decreased by 23.19% to 36.62%, when volume/capacity ratio is less than 0.50. The study also found that traffic efficiency could be further improved when the UUT is designed in conjunction with signal control. In the case, the UUT plus signalized control increases the capacity by 25% to 26.02%, decreases vehicle delay by 50.5% to 55.8%, and reduces number of stops by 69.5%, compared with the traditional DLT. Signal design for left-turn traffic at intersection has been long considered as a dilemma. Providing protected left-turn signal for left-turn vehicles could increase delay to through traffic , 2. Non-During the past decades, various indirect left-turn designs have been used on urban or suburban multilane arterials to eliminate problems associated with direct left-turn movements at intersections. Using non-traversable medians and/or directional median openings, direct left-turn movements from collector streets or local streets are prohibited. Left-turning vehicles will be redirected to a preselected downstream U-turn location to make U-turns. The median U-turn intersections (MUTI), superstreet intersections, crossover displaced left-turn intersections, the upstream signalized crossover schemes are common U-turn designs –15.The median U-turn intersection treatment (MUTIT), also known as the Michigan U-turn, is the most common design for U-turn vehicles. The geometric configuration of the MUTIT is shown in The MUTIT has several limitations which restrict its application around the world. One of the limitations is that the MUTIT requires sufficient median width to accommodate the design of U-turn lane. For intersections with narrow median on arterials in both directions, it is very difficult to implement the MUTIT for the U-turn design. In addition, the small vehicles and the large vehicles  have different turning radius which should be considered when designing the U-turn on arterials with narrow median and large volume of heavy vehicles.In this study, a modified MUTIT design named the unconventional U-turn treatment (UUT) was proposed to relax the unconventional of narrow median. The configuration of the UUT is shown in In the UUT, the median width of each upstream segment is enlarged only locally in a short distance in order to create an adequate turning radius for the U-turn vehicles. Though some median space is still needed for the UUT design, it is considered much less as compared to that for the MUTIT design. In each intersection arm, the UUT is designed with two U-turn bays: the inner bay (close to the intersection approach) is exclusively prepared for small vehicles, and the outer one is an exclusive U-turn of heavy vehicles, as shown in The primary objective of this study is to evaluate the operational effects of the UUT at intersections. The capacity, delay and number of stops with the UUT were evaluated for various traffic situations. For comparison purpose, the traffic operations with the direct left turn (DLT) for the same intersection were evaluated. In the following section, a review of previous studies is provided. In section 3, the model development is introduced. In section 4, data collection and model calibration are introduced. The simulation results are discussed in section 5. The paper ends with brief concluding remarks and future work in section 6.Definitions of traffic variables at UUT and their calculations are introduced in this section. The variables used in the study are summarized in C is determined by the green phases and the clearance time for both directions, which is:In the study, the green phase of one intersection arm and its opposite arm is assumed to be symmetric. The cycle length i is the sum of the demand flow of the following three movements:The demand flow in arm Besides, the demand flow of U-turn movement and through movement at median crossover is identical with the demand flow at intersection approach:P(xj) denotes the probability of a driver j selecting the former type; As stated before, left-turn vehicles can make two types of U-turns at the UUT. The selection of U-turn type where both “straight → U-turn → right-turn” and “turn right → U-turn → straight” roundabouts are determined by the binary logit model , which ii is as follows:ξi is determined as left-turn vehicles divided by total traffic volume , which is calculated byConsequently, the demand flow of each approach lane in arm Li should be large enough to prevent vehicle spillback at intersections. In this study, Li should be greater than the vehicle queue length at the intersection approach, which is calculated as:The spacing between median crossover and intersection Li could also be determined by the AASHTO Green Book  which recommends that the minimum spacing between a median crossover and the MUTIT intersection could be between 122m (400ft) and 183m (600ft), if no traffic data are available for calculating Li. Furthermore, the median width for U-turn maneuvers under UUT should be larger than the lower bound value w, as shown in In practical applications, the value of Theoretically, a before—after study in field applications is preferred to compare the operational features of the UUT and DLT design. However, in reality it is very hard to obtain the data before and after the UUT taking place on the same intersection. Thus, simulation technique was used in the study to evaluate the operations of traffic at intersections. Previously, traffic problems have been studied by models such as continuous flow models , car folTo ensure that the geometric elements of intersections are precisely modeled, the CAD layouts of typical intersections on four-lane and six-lane divided streets were imported into VISSIM. When UUT is executed without U-turn signal control, the priority rule for through and U-turn movements should be defined in VISSIM simulation. In this study, U-turning vehicles must yield to the through traffic which is also confirmed by field observations. U-turn drivers need to wait at the bay area until there is an acceptable headway gap in traffic stream . The gapThe turning radius of U-turn vehicles at the bay area can be determined by the median nose width and receiving lane width. Vehicle movements are decided for the simulation model according to field observations. The inner bay is exclusively prepared for small vehicles, and the outer one is an exclusive U-turn of heavy vehicles. In practical applications, the U-turn median width should be large enough to make sure that the vehicle turning speed is consistent to field observations for conventional U-turns, as shown in Three measures are calculated to evaluate the operational features of the U-turn design, including the delay, number of stops and capacity of intersections. Those measures are commonly used in previous studies for the evaluation of intersection performances ,28–30.DiU denotes the total delay of left-turn vehicles at intersection approach i with UUT; diU1 denotes the average stopped delay of U-turn vehicles from the entrance lanes to the target exit lanes, and diU2 denotes the average travel delay of U-turn vehicles from the entrance lanes to the target exit lanes.DiC denotes the total delay of left-turn movement vehicles at intersection approach i with DLT; diC1 denotes the average stopped delay of left-turn vehicles conventional signalized treatment vehicles from the entrance lanes to the target exit lanes, and diC2 denotes the average travel delay of left-turn vehicles operating under conventional signalized treatment from the entrance lanes to the target exit lanes. More details on the calculation of the above parameters can be found in [Delay is measure by the difference of actual travel time and desired travel time without stop. With travel time information, vehicle delay is the combination of average stop delay and travel delay . Averagefound in .SiU denotes the average count of stops of left-turn movements at intersection approach i with UUT; sijU denotes the count of stops for left-turn vehicle j at intersection approach i with UUT; Qi2 denotes total number of left-turn vehicles at intersection approach i with UUT.SiC denotes the average count of stops of left-turn movements at intersection approach i with DLT; sijC denotes the count of stops for left-turn vehicle j at intersection approach i with DLT; Qi2 denotes total number of left-turn vehicles at intersection approach i with DLT.The number of stops per vehicle is calculated by the total stop counts divided by the number of vehicles crossing the intersection, which is:i, the capacity is calculated as:CiU denotes the whole capacity at intersection approach arm i with UUT; cikU denotes the capacity of vehicles from left-turn, through and right-turn movement respectively. Note that U-turn capacity constitutes the capacity of left-turn movements at approach i with UUT.The capacity is the sum of vehicle count from all movements at intersection area with UUT. For the intersection arm i with DLT is as follows:CiC denotes the whole capacity at intersection approach arm i with DLT; cikC denotes the capacity of vehicles from left-turn, through and right-turn movement respectively. The detailed calculation of vehicles capacity of each movement is also referred to [The whole vehicle capacity at intersection approach arm erred to .Field data collection was conducted to obtain the data for model calibration. There is no specific permission required for these locations. Field data were collected from six intersections in the urban public area of Nanchang, China, other than private lands. Video cameras were used in the data collection at intersections. The field studies did not involve endangered or protected species. The city for data collection has a population of 5.6 million and an area of 7,402 square kilometers by 2013.Firstly, two intersections were selected for data collection in order to calibrate the simulation model. Because that the UUT has not been implemented in the field, our study selected intersections with geometric features similar to the UUT to calibrate the vehicle maneuver parameters in the VISSIM simulation model. The selected sites are located at intersections of Beijing East Rd—Shanghai North Rd , and Beijing East Rd—Qingshanhu Rd .Secondly, four other intersections were selected for data collection during weekdays including both peak and off-peak periods. Those sites were used to evaluate the performance of the UUT compared with the DLT. The geometric features and traffic information at each site are shown in Tables The VISSIM model was calibrated and validated against field data to ensure that it simulates accurate traffic operation. To calibrate the selected parameters in the simulation model, field data were collected including traffic data, geometric features, and drivers’ behavioral information.Initially, the logit model for predicting driver’s choice of two U-turns was calibrated. A total of 316 U-turn behaviors were identified in the field observation. The percentages of the two U-turns are 52.6% and 47.4% respectively. The green signal for the through and right-turn movement was 40 s and 30 s respectively.Some data gathered in the field were considered as the inputs in the VISSIM: 1) The percentage of private vehicles and heavy vehicles are 96% and 4% respectively; 2) The headway of private vehicles ranges from 4.0 s to 14.0 s which an average of 6.9 s; 3) The headway of heavy vehicles ranges from 7.4 s to 11.0 s with an average of 9.8 s; 4) The turning speed of private vehicles is 12.3 km/h, and the speed ranges from 7.1 km/h to 18.7 km/h; and 5) The turning speed of heavy vehicles is 9.7 km/h and the speed ranges from 7.2 km/h to 10.8 km/h.Several parameters in the VISSIM model needs to be calibrated which are the parameters in the gap-accepting model, the car-following model, and the lane-changing model. Considering that the capacity is one of the most important factors in the evaluation of U-turn movements, the capacity was considered as the measurement of goodness of fit to calibrate the predictions in the VISSIM model. This study used the Kyte’s method  to measucf denotes the capacity of U-turn movement measured in the field (veh/h); ts denotes the average service delay for each U-turning vehicle (s), which is defined as delay occurs at the first position of the U-turn queue; and tmv denotes average move-up time for each U-turning vehicle (s), which is the amount of time from when the previous U-turning vehicle exits the stop line until the subsequent queued vehicle reaches the stop line.The method proposed by Kyte in 1991 was to measure field capacity in an under-saturated condition, which is described in the following equation:n denotes the number of video sections, csi is the capacity of U-turn movement estimated by the VISSIM simulation model (veh/h), and cfi is the field capacity of U-turn movement at time interval (veh/h).Besides, capacity was selected as the goodness of fit measure for validation of the calibrated simulation model. The index used for measuring simulation error is the mean absolute percent error (MAPE), which can be estimated as:The VISSIM simulation models are developed for the same intersections to evaluate the traffic operational features, including capacity, delay, and number of stops. Actual traffic parameters such as flow and traffic components collected in the field are inputted in the simulation model.The simulation results for four intersections with both UUT and DLT design, according to traffic demands in The above results show that the UUT design has the better potential to effectively improve the operational performance at intersections than the DLT design. The UUT is more suitable for designing intersection with small the value of ratio between volume and capacity and low ratio of left-turn to through traffic volume.Field data collection does not cover all possible traffic situations which restricts the full evaluation of operational effects of the UUT design. In this section, different traffic situations are specified in the VISSIM simulation model to further investigate the differences between the UUT and DLT design. The intersection used for simulation is crossed by an arterial (6 legs) and a collector (4 legs) and the whole capacity for the intersection is 5800 pcu/h. At first, sensitivity analysis of delay and number of stops are calculated for different traffic situations. The traffic volume on the arterial street is specified to range from 600 to 2400 pcu/h, with an increase of 600 pcu/h. The traffic volume on the collector increases from 100 to 1500 pcu/h, with an increase of 200 pcu/h.Vehicle delay under different traffic situations are shown in The number of stops is also analyzed for different traffic situations. The results are shown in In summary, according to the results from sensitivity analyses, it is can be found that the intersection operates fluently if traffic demand is less than 1700 pcu/h. Furthermore, when the volume/capacity ratio of the intersections is less than 0.58, the UUT is a good design.A comparison of operational effect between UUT and DLT was also conducted. When the intersection operates with the ratio of left-turn to through traffic volume less than 0.33:1, UUT has better performance than DLT in terms of higher capacity, less delay and number of stops. The sensitivity analysis shows that when the ratio of left-turn to through traffic volume is close to or larger than 1, the advantage of the UUT design is not quite obvious as compared to the DLT. The reason for this is that as the increase of flow and decrease of headway, traffic conflicts are more severe because: (1) the U-turn vehicles cannot merge into the mainstream traffic stream easily; and (2) the right-turn vehicles cannot merge into the mainstream traffic stream easily. To further improve the operational performance, two advanced signal control strategies in conjunction with UUT are proposed.The first strategy is the UUT plus signalized control at the intersection approach (denotes as UUT plus A), as shown in The second strategy is to use the UUT pluses an integrated signalized control at both the U-turn bay and the intersection approach (denotes as UUT plus B), as show in Four intersections, as shown in UUT plus A can effectively improve the capacity of intersections and reduce the delay when compared with UUT only, especially for the intersections of large volume/capacity ratio. Capacities of intersections from site1 to 4 are increased by 13%, 9%, 13% and 19%, and delay of each site is decreased by 11%, 24%, 79% and 78%, respectively. However, the average number of stops at site1 and 2 is increased by 34% and 17% respectively, where the volume/capacity ratio was small. Actually, the average number of stops of left-turn vehicles increased due to signal control. Meanwhile, the average number of stops of site 3 and 4 significantly decreased where the volume/capacity ratio was large. In addition, the design of UUT plus B further increased the capacity and reduced the delay and number of stops at intersection areas. For example, with the UUT plus B, the capacity is increased by more than 8%, the delay is decreased by over 7%, and the average number of stops is decreased by more than 9% for the same intersections.The results showed that the UUT design with integrated signal control can effectively increase the capacity and reduce the delay and vehicle stops at intersections, as compared with either UUT only or DLT. The UUT plus B has the best operational performance. In addition, the simulation results also showed that with the integrated signal control, the UUT can still effectively improve intersection operations in the traffic situations with large volume/capacity ratio.Traditional MUTIT has the limitation in the requirement of large median width to accommodate the U-turn lane. In this study, a new U-turn design, named the unconventional U-turn treatment (UUT) is proposed. The core design of UUT is that the median is enlarged only locally to accommodate larger turning radius for U-turn vehicles but doesn’t occupy large median space. The UUT is designed with two U-turn bays with different radiuses for small vehicles and large vehicles respectively. The VISSIM simulation model is developed and calibrated to evaluate the operational features at intersections with UUT. Traditional DLT design is also evaluated for comparison.The results show that when the intersection operates with small volume/capacity ratio and low ratio of left-turn to through traffic volume, UUT has an obviously better performance than the DLT. In the case, the capacity is increased by 9.81% to 10.38%, vehicle delay is decreased by 18.5% to 40.1%, and number of stops is decreased by 23.19% to 36.62% when the volume/capacity ratio is less than 0.50. When the traffic volume of through and left-turn traffic is large, UUT has very little improvement as compared to DLT, but UUT with signal control (UUT plus A) presents obvious advantage over UUT only. Compared with DLT, the capacity is increased by 25% to 26.02%, vehicle delay is decreased by 50.5% to 55.8%, and number of stops is decreased down to 69.5% when the volume/capacity ratio is more than 1. Furthermore, the UUT in conjunction with signal control at both U-turn bay and intersection approach (UUT plus B) is the most appropriate measure to cope with high left-turn and through traffic volume, because it effectively reduced delay and number of stops.The findings of this study can provide useful information in understanding the applicability of UUT under different traffic conditions. It can be utilized as a guideline for transport policy makers and planners to determine when and where the UUT should be used. Before the UUT being used in practical applications, some issues can be further studied in the future. First, the distance between two U-turn bays in one intersection arm is fixed in this study, which can be relaxed to consider its effect on UUT. Second, this study only investigates an isolate intersection. The study scope could be extended to a broader spectrum for simulating a larger network to more precisely estimate the operational effects of UUT. In addition, the performance of DLT could be further improved by optimization of signal control. It would be interesting to compare the UUT and DLT design when both are integrated with advanced signal control techniques. The authors recommend that future studies could focus on these issues.


The honeycomb lattice structure of graphene gives rise to its exceptional electronic properties of linear dispersion relation and its chiral nature of charge carriers. The exceptional electronic properties of graphene stem from linear dispersion relation and chiral nature of charge carries, originating from its honeycomb lattice structure. Here, we address the quantum Hall effect in artificially stacked graphene bilayers and single layer graphene grown by chemical vapor deposition. The quantum Hall plateaus started to appear more than 3 T and became clearer at higher magnetic fields up to 9 T. Shubnikov-de Hass oscillations were manifestly observed in graphene bilayers texture. These unusual plateaus may have been due to the layers interaction in artificially stacked graphene bilayers. Our study initiates the understanding of interactions between artificially stacked graphene layers. The robust electronic properties of graphene stem from linear dispersion relation, containing massless Dirac fermions and chiral nature of charge carriers. This behavior of graphene originats from its honeycomb lattice structure. Bernal stacked bilayers graphene consists of massive Dirac fermions spectrum, which is demonstrated by two pairs of parabolic bands1246810111213141718The electrical transport such as quantum Hall effect in single and Bernal stacked bilayers graphene has been explored to a large extent. However, it is interesting to investigate the electronic transport properties of artificially stacked graphene layers. Here we report the electronic transport properties of artificially stacked chemical vapor deposition grown graphene bilayers. We have observed that the quantum Hall effect consisting of various plateaus with non-integer quantized values at 4.2 K, however a typical massless Dirac fermions spectrum has observed in a single layer graphene. The clear quantum Hall plateaus started to appear from 3 T in graphene bilayers and became more prominent at higher magnetic fields. The Shubnikov-de Hass (SdH) oscillations were observed as well in graphene bilayers texture.2/Si substrate. 2/Si substrate as displayed in 2/Vs, respectively; while the field effect hole and electron mobility values of the double-layer region of graphene device at 0 T appeared to be about 2058 and 1625 cm2/Vs at temperature of 4.2 K, respectively. 2D/IG) value is ~3.66 for the case of SLG and ~2.77 for ASGBL as shown in the et al.−1, respectively as shown in The optical micrograph image of complete Hall bar device structure with Au electrodes has shown in xx) and Hall conductivity (σxy) of SLG as a function of applied back-gate voltage (Vg), with magnetic field (B) of 9 T at 4.2 K. The result showed a strong evidence of quantum Hall effect (QHE) with conductivity plateaus appeared at ±2, ±6, ±10, ±14, +18, together with resistivity minima, consistent with the Landau level spectrum expected for SLG graphene2g(Vg − VDirac)/e, where Cg/e = 7.19 × 1010 cm−2V−1 and VDirac = +10 V is the offset voltage to reach charge neutralityxx) and the Hall resistivity (ρxy) as a function of magnetic field at local back gate voltage of −40 V. Interestingly, this complex system of artificially stacked graphene bilayers shows the Shubnikov-de Haas oscillation. The resulting data (ρxx vs. B) reveal SdH oscillations which starts from magnetic fields as low as B ~3 T and it is consistent with g and B data which follows the quantum Hall states randomly as a monolayer  or bilayers . The contour plot of longitudinal resistivity (ρxx) as a function of Vg and B is shown in 2526et al.et al.et al.In summary, we have studied the structural and electrical transport properties of chemical vapor deposition grown single layer graphene and artificially stacked graphene bilayers. The typical massless Dirac fermions spectrum is observed in the quantum transport of single layer graphene, however artificially stacked graphene bilayers texture follows the quantum Hall states randomly as a monolayer or bilayers at 4.2 K. The hierarchy of Dirac fermions are significantly related to charge transport due to the combination of massive and massless fermions. The unusual Dirac fermion spectrum may have possibly caused by the layers interaction in artificially stacked graphene bilayers.–4 Torr, and the temperature rose to 1010 °C with H2 gas flow (~10–2 Torr). After the temperature stabilized at 1010 °C, CH4 and H2  were injected into the furnace to synthesize the graphene for 8 min, after which the sample was cooled at a rate of 50 °C/min to room temperature4)2S2O8), and the PMMA membrane was washed with deionized water. Next, the graphene film with the PMMA membrane was transferred to the p-doped Si substrate having a top 300 nm-thick layer of SiO2. The graphene layers transferred onto the Si/SiO2 substrate were heated at 80 °C for 10 min to dry and then put in acetone for one day to completely dissolve the PMMA layer30Graphene film was grown on 25-μm-thick copper foils from Alfa Aesar (99.8% pure) via thermal CVD. A mechanically polished and electropolished copper foil was inserted into the CVD furnace. The furnace was evacuated to ~10–1, with a laser wavelength of 514.5 nm. The spot size was 1 μm and the power was kept at 1.0 mW to avoid local heating. The electrical and magneto-transport properties of graphene junctions were measured using ac lock-in techniques at frequency of 11.7 Hz with the root-mean-square current amplitude of 50 μA. Low temperature measurements were carried out in liquid helium cryostat (down to 4.2 K) with magnetic field up to 9 T. Lake Shore 331 temperature controller was utilized to modulate and control the temperature range.Raman spectra were measured with a Renishaw microspectrometer over a wavenumber range from 1100 to 3200 cmHow to cite this article: Iqbal, M. Z. et al. Interaction driven quantum Hall effect in artificially stacked graphene bilayers. Sci. Rep.6, 24815; doi: 10.1038/srep24815 (2016).


Arabidopsis thaliana. We show that it is additionally involved in splicing and facilitates the excision of two cis-spliced group II introns, nad1 intron 2 and nad2 intron 1, in Arabidopsis mitochondria. odb1 mutants lacking detectable amounts of ODB1 protein over-accumulated incompletely spliced nad1 and nad2 transcripts. The two ODB1-dependent introns were both found to splice via first-step hydrolysis and to be released as linear or circular molecules instead of lariats. Our systematic analysis of the structures of excised introns in Arabidopsis mitochondria revealed several other hydrolytically spliced group II introns in addition to nad1 intron 2 and nad2 intron 1, indicating that ODB1 is not a general determinant of the hydrolytic splicing pathway.Transcript splicing in plant mitochondria involves numerous nucleus-encoded factors, most of which are of eukaryotic origin. Some of these belong to protein families initially characterised to perform unrelated functions. The RAD52-like ODB1 protein has been reported to have roles in homologous recombination-dependent DNA repair in the nuclear and mitochondrial compartments in  Higher plant organelle genomes contain several group-II introns originating from mobile ribozymes that invaded these genomes during evolution –3. PlantArabidopsis thaliana. They can be assigned to two categories: (i) Intron-encoded RNA maturases and related maturase enzymes encoded by nuclear genes, and (ii) splicing factors proposed to have originated from host proteins and to have been recruited to additionally function in mitochondrial transcript processing  domain protein WTF9, which is specifically required for intron excision from the rpl2 and ccmFc pre-mRNAs (chloroplast RNA splicing and ribosome maturation) domain protein mCSF1 involved in the splicing of multiple mitochondrial introns (RCC1/UVR8/guanine exchange factor-like 3)  family protein mTERF15  . This pr mTERF15 . Excepti mTERF15 –26.in vitro  extending from a central hub; tertiary interactions between these domains mediate productive intron folding -dependent DNA repair in the nuclear and mitochondrial compartments; it co-localised with mitochondrial high-molecular weight complexes in a DNA- and RNA dependent manner , T-DNA insertion lines odb1–1 (Sail_25_H08) and odb1–2 (SALK_089362)  and supplemented with 1% w/v sucrose, stratified at 4°C for 3 days in the dark and then exposed to a light intensity of 100 μmol quanta m−2 s−1 in a 16-h photoperiod at 23°C._089362)  and compGenomic DNA was isolated from seedlings or flowers as previously described . RNA wasODB1 promoter, coding region and untranslated regions was amplified using Phusion DNA polymerase (Finnzymes) and primers 5′- GGGGACAAGTTTGTACAAAAAAGCAGGCTTGTTATTAAGTAACGTCCTGCCA-3′ and 5′- GGGGACCACTTTGTACAAGAAAGCTGGGTTGTTTGTTAAGTCGAATAACCACC-3′ and transferred into binary vectors pKWG (complemented line C1) or pGWB40 (complemented line C2) using gateway cloning procedures (Life Technologies). The resulting plasmids were used to transform odb1–1 plants via Agrobacterium-mediated floral dip transformation. Resulting seeds were sown on soil and transformants selected using kanamycin (pKWG) or hygromycin (pGWB40). odb1–1 plants carrying the ODB1 transgene were identified by PCR using primers amplifying the vector-insert junctions.A genomic DNA fragment comprising the Total RNA (3 μg) extracted from Arabidopsis seedlings was resolved on 1.2% w/v agarose/formaldehyde gels and transferred onto positively charged nylon membranes (Roche Applied Science), followed by membrane staining with methylene blue (0.04% (w/v) in 0.5M sodium acetate, pH 5.2). DIG-labelled DNA probes were generated using Arabidopsis genomic DNA or cDNA as template, the PCR DIG probe synthesis kit (Roche Applied Science), and primer pairs listed in Supplementary Table S1. Hybridisations were performed in DIG Easy Hyb solution (Roche Applied Science) according to the manufacturer's instructions; chemiluminescent detection of signals was performed using anti-digoxigenin-alkaline phosphatase conjugates and CSPD reagent (Roche Applied Science).18S rRNA (At3g41768) and ACT genes  were used for data normalisation.Quantitative RT-PCR (qRT-PCR) for measuring mitochondrial intron splicing efficiencies was performed using SYBR Green I Master Mix (Roche Applied Science) and primer pairs listed in Supplementary Table S2 as previously described  on a Lignad2 intron 1-specific primer (5′-GAAAGCCCGGCCAGAAC-3′) and SuperScript III Reverse Transcriptase (Life Technologies). The resulting cDNAs served as template in subsequent PCR reactions set up with primers 5′-GGACTCATGTGCCTTCCAGAAC-3′ and 5′-ATGAACCAATGGATCGTAATAAGTC-3′ and DyNAzyme DNA polymerase (Finnzymes) in order to amplify head-to-tail-ligated intron 1-containing nad2 transcripts. PCR reactions were analysed on 3% (w/v) agarose gels, and products of interest were excised, purified over NucleoSpin columns (Macherey-Nagel), and ligated into pGEM-T (Promega) for cloning and sequencing.RNA (1 μg) was incubated with 2.5 units of tobacco acid pyrophosphatase  as previously described ; controlnad5 intron 3-derived products were amplified with Phusion DNA polymerase (Finnzymes). PCR reactions were analysed on 3% (w/v) agarose gels. Products of interest were excised, purified over NucleoSpin columns (Macherey-Nagel) and ligated into pGEM-T (Promega) for cloning and sequencing. Several clones were sequenced per intron. A list of all gene-specific primers used in reverse transcription and PCR reactions is provided in Supplementary Table S3.RNA (1 μg) was treated with T4 RNA ligase (New England Biolabs) or mock-treated, extracted and precipitated as detailed above and dissolved in water. The RNA was then reverse-transcribed using gene-specific primers and SuperScript II Reverse Transcriptase (Life Technologies). The products of reverse transcription were again extracted and precipitated and subsequently amplified by PCR, using 1/10 of the RT reaction as template, intron-specifc forward and reverse primers and DyNAzyme DNA polymerase (Finnzymes). nad2 transcript that over-accumulated in odb1–1 mutant plants but was barely seen in the wild type or in odb1–2  regions. Maturation of its mRNA requires one trans- and three cis-splicing events -dependent DNA repair in mitochondria of Arabidopsis . When su2 Figure . odb1–2  of ODB1 . nad2 ing events  for both odb1–1 and wild-type seedlings. We ensured that a potential alternative primary nad2 transcript for nad2 would also be ligated by pre-treating RNA samples with tobacco acid pyrophosphatase (TAP). TAP converts primary, 5′-triphosphorylated mitochondrial transcripts into 5′-monophosphorylated transcripts  excision of this intron may proceed via first-step hydrolysis rather than lariat formation in Arabidopsis.We assumed that the nscripts . Only thnscripts . A cRT-Pe Figure . Amplifi2 3′ end  fused to1 Figure . We thuscox2, ccmFc, rpl2 and rps3 each contain a single intron, nad4 contains three introns and nad1, nad2, nad5 and nad7 each contain four introns . Introduction of an ODB1 wild-type gene copy into odb1–1 plants restored ODB1 protein expression and efficient excision of both nad2 intron 1 and nad1 intron 2 , confirming that reduced splicing of these introns in odb1–1 plants was due to ODB1 loss. ODB1 is thus required for efficient splicing of two mitochondrial introns, nad1 intron 2 and nad2 intron 1, in vivo.We performed RNA gel blot hybridisations with probes for most other mitochondrial introns and found that in agreement with qRT-PCR data, splicing of mitochondrial introns other than odb1 mutants. Both introns are classified as group II introns (http://blast.ncbi.nlm.nih.gov). Sequence identity between nad1 intron 2 and nad2 intron 1 in domains dV and dVI as well as in other domains and the intron structural core has been previously noted in the genus Oenothera, and a common evolutionary origin of the two introns has been proposed .For s Figure  or intros Figure . The strs Figure . In the nad1 intron 2, nad4 intron 2 and nad1 intron 1 lack an unpaired adenosine whereas this potential lariat branching point is present in all other Arabidopsis mitochondrial introns (Figure We subsequently applied the cRT-PCR/RT-PCR strategy to all mitochondrial introns in order to systematically determine splicing pathways used in Arabidopsis mitochondria (Figure s Figure .nad1 intron 2 and nad2 intron 1, two other introns, nad4 intron 2 and nad7 intron 1, did not yield lariat-derived RT-PCR products and appear to exclusively use a hydrolytic pathway. For nad1 intron 3, nad4 intron 1 and the single rpl2 intron, hydrolytically released molecules as well as lariats were detected; all other introns showed lariat-derived products. According to these results, ODB1 is not generally required for efficient release of hydrolytically spliced introns but has a specific role in the excision of nad1 intron 2 and nad2 intron 1. Combining our analysis of splicing pathways with current data on the specificities of known mitochondrial splicing factors shows that none of these factors is common and exclusive to introns released via a hydrolytic pathway (Figure In addition to y Figure .nad2 mRNA in Arabidopsis mitochondria (Transcript splicing in higher plant organelles involves numerous ancillary factors most of which can be classified as intron maturases, RNA helicases or members of various RNA-binding protein families ,5. A numchondria . The maichondria ,47 as wechondria  belong tchondria –50. The chondria  and showchondria ,53 incluchondria . This prchondria .nad1 intron 2 and nad2 intron 1, both of which were found to splice via a hydrolytic pathway. ODB1 is distantly related to RAD52 (Results presented here demonstrate a role for the protein ODB1 in group-II intron splicing in mitochondria of Arabidopsis. ODB1-deficient plants displayed reduced splicing efficiencies for to RAD52 , a proteto RAD52 . Accordito RAD52 . Howeverto RAD52 ,38, and to RAD52 . The duaodb1–1 plants which completely lacked ODB1 displayed defects in both HR-dependent DNA repair and nad1 and nad2 splicing, odb1–2 plants with strongly reduced but detectable amounts of ODB1 protein were impaired in DNA repair to a degree that was comparable to odb1–1 but showed no splicing defect for nad2 intron 1 and accumulated significantly less incompletely spliced nad1 transcripts than odb1–1 (nad1 and nad2 in odb1–1 shows that ODB1 is not strictly required for the splicing of these transcripts but has an accessory role. Participation of ODB1 in splicing may be more crucial under conditions that reduce splicing efficiencies, e.g. during growth in the cold (nad1 intron 2 and nad2 intron 1 in domains dV and dVI, which are highly similar between the two introns, either through interaction with other components of the splicing machinery or by direct intron binding. Organellar proteins that bind both RNA and DNA have been previously described (ODB1 is assumed to be rather abundant in Arabidopsis mitochondria . Interesthe cold . ODB1 coescribed ,57.nad1 intron 2 and nad2 intron 1 depends on first-step hydrolysis it is unlikely that ODB1 is a general determinant of the hydrolytic pathway. Two other introns, nad4 intron 2 and nad7 intron 1, were identified that spliced exclusively via a hydrolytic pathway in Arabidopsis but did not depend on ODB1. In addition, nad1 intron 1 is likely hydrolytically released (ODB1 gene inactivation. It is nevertheless expected that trans-acting factors impact on the biochemistry of mitochondrial group-II intron splicing. nad7 intron 1, which in dVI is predicted to have a bulged A flanked by G:C pairs and was thus expected to be released as lariat, appears to exclusively splice via first-step hydrolysis. On the other hand, nad2 intron 3 and nad7 intron 2 which have predicted dVI configurations similar to nad2 intron 1 were found to strictly use the lariat pathway. It thus seems that intron folding and the presence/absence of a dVI unpaired adenosine do not exclusively define the group II intron splicing pathway in higher plant mitochondria, and other factors probably influence whether intron excision proceeds via first-step transesterification or hydrolysis. As yet there is no candidate splice factor that could potentially determine the biochemistry of intron release as none of the mitochondrial splice factors identified to date is common and exclusive to introns that splice via a hydrolytic pathway.In the course of this study we performed the first systematic analysis of mitochondrial group II intron splicing pathways, which underscored unusual aspects of splicing in plant mitochondria. Although excision of both released  but its Supplementary Data are available at NAR Online.


Acute exacerbation of idiopathic pulmonary fibrosis (AE-IPF) is associated with high mortality. However, few studies have so far reviewed analyses of autopsy findings in patients with AE-IPF.We retrospectively reviewed 52 consecutive patients with AE-IPF who underwent autopsies at five university hospitals and one municipal hospital between 1999 and 2013. The following variables were abstracted from the medical records: demographic and clinical data, autopsy findings and complications during the clinical course until death.The median age at autopsy was 71 years (range 47–86 years), and the subjects included 38 (73.1%) males. High-dose corticosteroid therapy was initiated in 45 (86.5%) patients after AE-IPF. The underling fibrotic lesion was classified as having the usual interstitial pneumonia (UIP) pattern in all cases. Furthermore, 41 (78.8%) patients had diffuse alveolar damage (DAD), 15 (28.8%) exhibited pulmonary hemorrhage, nine (17.3%) developed pulmonary thromboembolism and six (11.5%) were diagnosed with lung carcinoma. In addition, six (11.5%) patients developed pneumothorax prior to death and 26 (53.1%) developed diabetes that required insulin treatment after the administration of high-dose corticosteroid therapy. In addition, 15 (28.8%) patients presented with bronchopneumonia during their clinical course and/or until death, including fungal , cytomegalovirus  and bacterial  infections.The pathological findings in patients with AE-IPF represent not only DAD, but also a variety of pathological conditions. Therefore, making a diagnosis of AE-IPF is often difficult, and the use of cautious diagnostic approaches is required for appropriate treatment. Idiopathic pulmonary fibrosis (IPF) is a chronic, progressive, fibrosing form of interstitial pneumonia with a median survival after diagnosis of three to five years -4. AcuteLung tissue derived from patients with IPF shows a characteristic histopathological pattern known as usual interstitial pneumonia (UIP), which includes the presence of fibroblastic foci. The pathological findings of AE-IPF comprise diffuse alveolar damage (DAD) superimposed on underlying UIP; this is the most commonly described finding on surgical lung biopsies ,11,12. OThe current study is a retrospective review of an autopsy series designed to describe and evaluate the pathological findings, including concomitant and infectious diseases, observed during the clinical course until death in patients with AE-IPF.A total of 52 patients with AE-IPF who underwent autopsies at five university hospitals and one municipal hospital between January 1, 1999 and December 31, 2013 were identified based on medical records. The Ethics Committee of University of Occupational and Environmental Health in Kitakyushu, Japan approved this study , with a waiver for informed consent due to the retrospective study design. AE-IPF was defined according to a previous report [All autopsied lung materials were fixed in 10% formalin for more than seven days. At least one tissue block was prepared from the gross AE-IPF lesions in each lobe, and the tissue blocks were embedded in paraffin. Sections (4 μm thick) were cut and stained with hematoxylin and eosin (H&E) using standard procedures. The pathological diagnosis of UIP was made according to the current guidelines . We also2O2 in 100 ml of Tris–HCl . After counterstaining with Meyer’s hematoxylin, the sections were observed under a light microscope.Four-micrometer-thick sections were cut from the lung tissue blocks and stained with H&E for the histopathological examinations in addition to Periodic acid-Schiff (PAS) stain, Grocott's methenamine silver stain and Gram stain to identify any infectious pathogens in the presence of bronchopneumonia. Bronchopneumonia  was conclusively diagnosed based on histopathological evidence, such as neutrophil infiltration, fibrinopurulent exudate accumulation or abscess formation in the broncho-bronchioloalveolar space. For immunohistochemical detection of cytomegalovirus (CMV) antigens, the sections were incubated with a mouse monoclonal anti-CMV antibody  for 30 minutes. Secondary antibody peroxidase-linked polymers were then applied, and the sections were incubated with a solution consisting of 20 mg of 3.3’-diaminobenzidine tetrahydrochloride, 65 mg of sodium azide and 20 ml of 30% HA total of 52 patients with AE-IPF underwent autopsies during the study period. The demographics of the patients are reported in Table Nearly half of the patients had received corticosteroid therapy before AE-IPF. The therapeutic regimens for AE-IPF are shown in Table The mean duration between death and autopsy was 286 minutes (range: 60 to 990 minutes). Overall, the median weights of the right and left lungs were 658 g  and 552 g , respectively. These median weights were remarkably heavier than the standard lung weights reported for Japanese males  . The undThe pathological findings in the 11 patients with AE-IPF who met the 2007 criteria but did not have DAD were indicative of UIP alone (n = 5), alveolar hemorrhage n = 3), pulmonary thromboembolism (n = 1), OP (n = 1) and lung adenocarcinoma (n = 1)  patients Table . In thesIn this study, we retrospectively analyzed the autopsy findings of AE-IPF and clarified that AE-IPF exhibits a variety of pathological findings in addition to DAD. Moreover, the AE-IPF patients were diagnosed with various infectious diseases and complications during their clinical course after AE-IPF.DAD has been reported to be the focal pathological finding of AE-IPF . DAD alsRegarding acute respiratory distress syndrome (ARDS), in which the diagnostic criteria are based on clinical findings, in the same manner as AE-IPF, Patel S.R. et al. reported that they investigated the pathological findings of 57 cases satisfying the diagnostic criteria for ARDS via open-lung biopsy, with DAD observed in 23 patients (40.3%) . On the Although there is no established standard therapy for AE-IPF , high-doThere are several limitations associated with this study. First, only patients who died and underwent autopsy were included; therefore, the results may differ based on the status of onset of AE-IPF. In other words, no patients who survived after AE-IPF were included, and the present findings thus do not reflect all aspects of the entity of AE-IPF. Second, we did not perform endotracheal aspiration or bronchoalveolar lavage due to the presence of severe hypoxemia in all cases. However, we carefully excluded patients based on the findings of sputum, laboratory and physical examinations. In addition, a previous study reported that the features of clinically suspected acute exacerbation diagnosed based on the radiological and clinical course are similar to those of acute exacerbation diagnosed based on the results of several intensive examinations, including BAL . Third, The pathological findings of AE-IPF include DAD as well as a variety of pathological conditions, and making a definitive diagnosis of AE-IPF is difficult. Patients with AE-IPF therefore are at risk of death due to the occurrence of several complications during their clinical course, including the effects of treatment with high-dose corticosteroid therapy. In patients with AE-IPF, it is very important to treat the disease by monitoring the patient’s condition and timely intervening with appropriate treatment.


Interestingly, iso-height lines of other rough surfaces are not necessarily conformally invariant even if they have the same Hurst exponent, e.g. random Gaussian surfaces. We have found that the distribution of the modulus of the Fourier coefficients plays an important role on this property. Our results not only introduce a new universality class and place the study of suspended graphene membranes within the theory of critical phenomena, but also provide hints on the long-standing question about the origin of conformal invariance in iso-height lines of rough surfaces.Suspended graphene sheets exhibit correlated random deformations that can be studied under the framework of rough surfaces with a Hurst (roughness) exponent 0.72 ± 0.01. Here, we show that, independent of the temperature, the iso-height lines at the percolation threshold have a well-defined fractal dimension and are conformally invariant, sharing the same statistical properties as Schramm-Loewner evolution (SLE Rough surfaces are very common in nature and can be found, for instance, in real landscapes445679Graphene, consisting of literally a single carbon monolayer, represents the first instance of a truly two-dimensional material see 111213. I1112Since previous numerical studies have shown that the structure of graphene possesses self-affine propertiesL × L graphene membranes to the inner area x-y plane having small random perturbations in z-direction (to break the symmetry) and zero initial velocity (zero temperature). For each temperature and system size, we perform three independent simulations with different initial perturbations. We use an equilibration time of 0.2 ns to reach the desired temperature and verify that the respective Maxwell-Boltzmann distribution for the velocities is recovered  potentialered see . From eaS(q) determines the Hurst exponent α via the relation In order to compare graphene membranes with RGS, we generate the latter ones by using the so-called Fourier Filtering Method (FFM). In contrary to graphene sheets, where simulations are performed in real space expressing physical interactions between atoms, RGS are constructed in Fourier space, and can be designed to have a desired Hurst exponent. In the FFM method, the Fourier coefficients of RGS are constructed using the decomposition h is the height profile of the surface defined by the z component of the atoms. For self-affine rough surfaces, the function α characterises the roughness of the surface. We take the statistical averages α = 0.72 ± 0.01 is independent of both, system size and temperature, and is in agreement with the previous work by Abedpour et al.α < 0.74, even though they used different boundary conditions. The existence of a Hurst exponent confirms the self-affinity property of graphene membranes and thus sets our graphene sheets in the context of rough surfaces . This provides a strong numerical evidence that the RGS are not SLE.Therefore to test the consistency of the iso-height contour lines with SLE, one solves numerically the Loewner differential equation that describes the conformal mapping220.02 see . From th0.02 see . On the  0.8 see , which cθ between two points of the curve separated by a distance L is defined as the oriented angle between the tangential vector of the curve at the first point and the vector connecting the two points. The winding angle distribution is expected to be Gaussian of mean In order to further explore the conformal invariance of these iso-height contour lines, we study the winding angle of the curves. The winding angle df is the fractal dimension of the curves, and a a constant24df = 1.23 ± 0.03 for the fractal dimension of the curves using L, the distribution of the winding angle displays the expected Gaussian behaviour . However, by performing the same measurement in graphene, we find a distribution that can be fitted with As we have observed, not all rough self-affine surfaces satisfy SLE statistics. Therefore, we are interested in understanding the origin of this discrepancy. Since graphene sheets and RGS possess the same Hurst exponent, we have extended our study to Fourier space to seek for further information. We have taken the Fourier transform of the graphene membranes and also of the RGS. By construction, the modulus of the Fourier coefficients, ith  see . Additioith  see  and uncoith  see , which fThus, one can conclude that the distribution of the modulus of the Fourier coefficients in rough self-affine surfaces might play an important role in the conformal invariance of their iso-height lines at the percolation threshold, although it does not affect the fractal dimension. A similar connection between the distribution of the phase of the Fourier coefficients and conformal invariance has already been observed for contour lines of zero-vorticity in 2D turbulenceκ with Summarising, we have shown that the iso-height lines of graphene sheets at the percolation threshold are scale invariant and provided evidence that they might also be conformally invariant. These properties are independent of temperature (within the range of 100–600 K). Additionally, they can be described by SLEThis result provides insights on the long-standing question on which are the responsible properties for conformal invariance in self-affine surfaces, and can be used to construct self-affine surfaces with conformal invariance properties. Additionally, the fact that iso-height lines in graphene are conformally invariant place the study of graphene within the theory of critical phenomena, belonging to a new universality class.227For an experimental verification of our findings we need the height profile of suspended graphene membranes. However, it is still challenging to measure the height profile of suspended graphene with an accuracy in the sub-angstrom regime with current methods, because they are generally not well applicable to suspended regions of a two-dimensional crystal (due to its low binding rigidity). In the past few years, it has been possible to obtain the height profile of graphene grown on many different substrates, most commonly on SiOFinally, one can also explore if the scale and conformal invariance properties are typical for graphene or are present in other two-dimensional crystals. We have made tests on suspended silicene, a membrane made with silicon atoms, and unfortunately, we have found that it crumples see , preventHow to cite this article: Giordanelli, I. et al. Conformal Invariance of Graphene Sheets. Sci. Rep.6, 22949; doi: 10.1038/srep22949 (2016).


As the thinnest conductive and elastic material, graphene is expected to play a crucial role in post-Moore era. Besides applications on electronic devices, graphene has shown great potential for nano-electromechanical systems. While interlayer interactions play a key role in modifying the electronic structures of layered materials, no attention has been given to their impact on electromechanical properties. Here we report the positive piezoconductive effect observed in suspended bi- and multi-layer graphene. The effect is highly layer number dependent and shows the most pronounced response for tri-layer graphene. The effect, and its dependence on the layer number, can be understood as resulting from the strain-induced competition between interlayer coupling and intralayer transport, as confirmed by the numerical calculations based on the non-equilibrium Green's function method. Our results enrich the understanding of graphene and point to layer number as a powerful tool for tuning the electromechanical properties of graphene for future applications. The thinness and elastic properties of graphene make it an ideal candidate for nanoelectromechanical systems. Here, the authors demonstrate the positive piezoconductive effect in suspended bi- and multi-layer graphene, showing the most pronounced response for three layer samples. Graphene1238101116In situ piezoconductive measurements on graphene provide an effective approach to study the correlations between electrical properties and mechanical strains. So far, studies have been focused on mono-layer graphene, and the negative piezoconductive effect has been widely reported, independent of the differences in graphene film synthesis, transfer methods and sample substrates1819202122in situ stress with a scanning probe. We observe positive piezoconductance in bi- and multi-layer graphene, with tri-layer graphene showing the most pronounced response. This intriguing phenomenon can be explained by the model of strain-induced competition between electronic interlayer coupling and intralayer transport, and further confirmed by numerical calculations based on non-equilibrium Green's function method.Here we investigate the piezoconductive effect of suspended graphene membranes with various layer numbers by applying 2 wafers with pre-etched trenches. The number of the graphene layers is identified via colour interference, and confirmed by Raman spectroscopy. Metal electrodes (5 nm Ti/50 nm Au) are deposited through home-made shadow masks, which effectively avoid wet process-induced device performance degradationin situ piezoconductive measurements, we introduce pressure-modulated conductance microscopy25Suspended graphene membranes are mechanically exfoliated and deposited on Si/SiOg. Here g(x) is defined byG(x) is the device conductance at AFM tip position x  and G0 is the undisturbed conductance value. For mono-layer suspended graphene, the device conductance drops upon local pressure applied  with different strains (up to 1‰). The detailed results are shown in gmax . According to the geometry of our devices, the strain ɛ can be calculated by the equationTo further study the observed layer number-dependent piezoconductive effect, we perform the same measurement on various suspended graphene devices . Here h has been corrected by subtracting the height of the tip at which the force begins to rise  device shows much larger gmax than the other multi-layer devices .where The positive piezoconductive effect is difficult to explain in terms of strain-induced decrease of Fermi velocity, the model that has been applied to strained mono-layer graphene19π-orbital tight-binding model Hamiltonian, which is written as428To understand the observed positive piezoconductive effect, we numerically calculate the transport properties of strained multi-layer graphene devices, which can be calculated by applying non-equilibrium Green's function technique and using two-terminal Landauer–Büttiker formula, with details described in the Methods section. To numerically study the piezoconductive effect in the multi-layer graphene systems in the presence of an external pressure, we consider a ci are the creation and annihilation operators on the site i. The first term H0 describes the pristine multi-layer graphene sheets, with μ being the chemical potential and tintra,inter denoting the intra- and interlayer nearest-neighbour hopping strength, respectively. In our consideration, we take tintra =2.60 eV and tinter =0.34 eV, respectively. The second term HD describes the influences of external disorders and the dephasing effect that is used to recover the macroscopic behaviour from a finite-sized quantum system and can be modelled by attaching individual virtual leads at each site i. Here ɛi is the on-site Anderson disorder strength that is uniformly distributed in the interval of  with W characterizing the strength of disorder and aik are the creation and annihilation operators for the virtual lead attached at the i-th site. In our consideration, we set the disorder strength to be 0.1 eV, because the prepared multi-layer graphene sheets are rather clean and it can better smear off the room temperature-induced thermal fluctuation. The last term HS represents the applied strain-induced effects including the induced site potentials and the variation of the intra- and interlayer nearest-neighbour hopping energies in the lattice-deformed region. The AFM tip-contacted lattices should experience noticeable lattice deformations, while the lattice deformation farther away from the AFM tip gradually decreases. Thus it is reasonable to assume that the variation of the intra- and interlayer hopping energy due to the lattice deformation takes the form of r0 is the centre of deformed region and L is the system length of the disordered scattering region, and the varying site potential takes the similar form of where gmax is determined by the strain-induced competition between the intralayer hopping and interlayer interactions. In the presence of an applied pressure from the AFM tip, the direct consequences on the multi-layer graphene include: (1) the extension of the lattice constant in the lattice-deformed area that correspondingly decreases the intralayer nearest-neighbour hopping; and (2) the local compression of the interlayer separation in the lattice-deformed area that effectively modulates the interlayer interactions, that is, increasing the interlayer hopping and inducing the local site energies. By applying the non-equilibrium Green's function technique and Landauer–Büttiker formula (see details in the Methods section) on a tri-layer graphene ribbon with length of 100 nm and width of 13 nm, we theoretically study the relation between the maximum relative conductance change gmax and the applied strain ɛ for tri-layer graphene. It is noteworthy to mention that all our obtained data are used to qualitatively explain and understand the underlying physical origin of the positive piezoconductive effect, and for the better presentation we have chosen certain parameters to compare with the experimental observations. Our numerical results show that gmax is always positive and increases with increasing strain, as plotted in the blue cycles in gmax increases slower, and suggests the relative contribution from interlayer modulation becomes less dominant. This model also explains why the piezoconductive property of bi- and multi-layer graphene is distinct from mono-layer graphene. For strained mono-layer graphene, negative peizoconductance is observed because no interlayer modulation but only intralayer contribution is present.We first focus on the tri-layer graphene that shows the most pronounced positive piezoconductive effect. As illustrated in Vienna ab initio simulation packaged between the nearest two layers as a function of the layer number n in To further understand the intriguing phenomenon that tri-layer graphene shows the most pronounced positive piezoconductive effect, we have performed first-principle calculations to study the lattice configuration of different multi-layer graphene devices under strain. Our first-principle calculations are performed using the projected-augmented-wave method as implemented in the γ, to describe the piezoconductive properties of bi- and multi-layer graphene devices:We can now introduce a characteristic factor, the piezoconductive factor γ has the same sign as piezoconductive effect. The square root dependence on strain is phenomenological but describes the experimental and theoretical data well and allows us to parameterize each gmax(ɛ) curve by a single-value γ. By applying the same non-equilibrium Green's function technique as used in studying the tri-layer graphene, we calculate the gmax–ɛ relation for graphene with various layer number n (n=2 to 6)  and find they are consistent with theoretical results. For bi- and tri-layer graphene, γ increases with n, suggesting the enhancement of the contribution from strain-induced interlayer modulation. But while n increases further, γ decreases, suggesting the interlayer modulation is dominated by the top three layers and additional parallel conduction paths from the extra layers suppress the positive piezoconductive effect. Here we note that, the roles of external effects  system, where CH4 and CHF3 are used as etching gases. The typical width of the trenches is 3 μm and the depth is around 250 nm. The number of layers of graphene membranes is first identified by an optical microscopy and further confirmed by Raman spectroscopy. To avoid common wet process-induced device performance degradation and yield loss, the electronic devices are fabricated by using a home-made shadow mask methodThe suspended graphene membranes are obtained by using mechanical exfoliation method on the pre-defined trenches on 300-nm thick SiO−1. The detailed experimental setup is schematically shown in A Bruker Multimode 8 AFM is used to build up the pressure-modulated conductance microscopy setup. A non-conducting AFM tip is used to apply adjustable local pressure on the top of the suspended graphene, yielding topography/height image of the strained graphene. The conductance/resistance of the device is measured via lock-in technique and monitored simultaneously as an external input of the AFM. The comparison of the conductance/resistance image and topography image offers detailed piezoconductive information of the suspended graphene membranes. The scanning procedure is done in contact mode with a Bruker NP-S10 tip, of which the Young's modulus is 0.24 N mp  can be expressed as:Using multi-probe Landauer–Büttiker formula, the current in the lead Vp/q is the spin-independent bias in the lead p/q. The electronic transmission coefficient from lead q to lead p is calculated as Tpq = Tr[ΓpGrΓqGa], in which the line-width function Γp is defined as I is the unit matrix with the same dimension as that of H. The retarded and advanced self-energy due to the coupling to all the real leads can be obtained numericallyd is fixed to 0.01 eV. In our simulations, a small external bias is applied between the left and right lead with VL=−VR=0.5 V. For dephasing effect, electrons lose the phase memory by entering and leaving the virtual leads. Thus, for each virtual lead i, the current has the constraint that Ji=0, which ensures the current conservation. Combining the above equation of Jp together with all boundary conditions for the real and virtual leads, the voltage Vp and current Jp in each real lead can be obtained.where −1. The first Brillouin-zone integration is carried out by using the 3 × 3 × 1 Gamma-centred grids. A vacuum buffer space of 20 Å is set to prevent the interaction between adjacent slabs.The generalized gradient approximation combined the Vander Waals correction with the DFT-D2 method of Grimme is used. The kinetic energy cutoff is set to be 500 eV. During the structure relaxation, the edge atoms and the probed atoms are not allowed to relax while the others are. All parameters are chosen to converge the forces to be <0.01 eV ÅHow to cite this article: Xu, K. et al. The positive piezoconductive effect in graphene. Nat. Commun. 6:8119 doi: 10.1038/ncomms9119 (2015).Supplementary Figures 1-11, Supplementary Table 1, Supplementary Notes 1-5 and Supplementary References