These electrically erasable/rewritable channels show currents of tens of nanoamperes (200 to 400 nA/μm) at voltages ≤2 V and metallic-like non thermally-activated transport properties down to 4 K, as confirmed by nanoscopic mapping. The domain structure analysis and phase-field simulations reveal complex switching dynamics, in which the extraordinary conductivity in strained PbO3 films is explained by an interplay between ferroelastic a- and c-domains. This work demonstrates the potential of accessible and stable arrangements of nominally uncharged and electrically switchable domain walls for nanoelectronics.Conductive domain walls in ferroelectrics offer a promising concept of nanoelectronic circuits with 2D domain-wall channels playing roles of memristors or synoptic interconnections. However, domain wall conduction remains challenging to control and pA-range currents typically measured on individual walls are too low for single-channel devices. Charged domain walls show higher conductivity, but are generally unstable and difficult to create. Here, we show highly conductive and stable channels on ubiquitous 180° domain walls in the archetypical ferroelectric, tetragonal PbO Conductive domain walls are envisioned for future nanoelectronics and computational hardware. Here, the authors investigate an approach to use rewriteable arrangements of highly conductive channels based on nominally neutral 180°-domain walls. The ability of domain walls to form nonvolatile conductive channels, which can be moved, erased and recreated via electrical stimuli, and their plasticity hold promise for a variety of applications from memories to neuromorphic circuits. Since the first report of electrical transport properties of domain walls in BiFeO3 (BFO) films5 an impressive progress has been made in exploring different materials with domain wall conduction, demonstrating their functionalities10 and advancing their technological relevance11. A nonvolatile ferroelectric domain wall memory has been proposed based on the formation of domain walls bridging two planar electrodes on a BFO film with insulating bottom interface12. In an alternative concept, temporary-formed domain wall channels were used for nondestructive readout of persistent polarization states13. Beyond BFO systems, multi-level DW-based memristor functionalities have been demonstrated on thin slabs of LiNbO3, an uniaxial ferroelectric with conically shaped domains15. In a number of other materials including PbO3 (PZT)16, BaTiO317 and ErMnO318, domain wall conduction has been reported, however its relevance for logic and memory devices remains to be validated.Conductive domain walls (DWs) in ferroelectrics attract a lot of attention as potential basic elements for novel paradigms of electronics19. However, the physics of domain wall conduction becomes more complex if strain and other factors, resulting in domain distortion, are taken into account. In particular, it was shown that nominally neutral ferroelastic 90°-DWs could become bent and hence partially charged due to an interplay between the lattice tetragonality and mismatch with the substrate. Consequently, the 90°-DWs in such PZT films exhibited an intrinsic conductivity with metallic-like non thermally-activated transport characteristics20. Despite the significant advancements in understanding the mechanisms of domain wall conduction and proofs of concepts of DW-based devices, important issues still impede progress in the field. A relatively low level of current sustained by individual domain walls  is too low for domain wall based electronics. A possible way to address this problem is using multiple domain walls22, but in this case the scaling potential is compromised. Charged domain walls can provide much higher currents24, however they are generally unstable and form transiently under voltage13, or require a special poling procedure26, which complicates their practical use. In Supplementary Table The physical origin of domain wall conduction involves either intrinsic or extrinsic mechanisms. The former implies a change of the energy band structure occurring at the domain boundary due to a polarization discontinuity (charged DWs), while the latter is associated with defect accumulation such as oxygen vacancies within the domain wall region. Generally, the extrinsic mechanism is applicable to neutral domain walls such as 180°-DWs in tetragonal PZT, where the role of oxygen vacancies in the DW-transport properties was experimentally proven3 (PZT), one of the archetypical ferroelectrics offering well-studied domain structures and mature processing technologies. We demonstrate that high-magnitude switchable non thermally-activated domain wall conduction can be achieved in nominally neutral 180°-DWs. The transport properties of the domain walls are revealed by scanning probe characterizations, which combine atomic force microscopy (AFM) topography imaging, piezoelectric force microscopy (PFM), conductive AFM (cAFM) and cryogenic scanning probe experiments down to 4 K. The on-demand created domain walls were utilized to show basic memristive device functionalities by controlling their position through electrical stimuli. A large degree of control, good stability and high magnitude of conductance of such single domain walls hold promise for readily accessible tunable multi-resistive state devices for neuromorphic applications.Here, in the quest for robust, accessible and controllable DW-based conductors we focus on tetragonal PbO3 (DSO) substrate with a 20 nm SrRuO3 (SRO) bottom electrode by pulsed laser deposition (PLD) (details in “Methods”). The PZT film showed predominantly downward-oriented c-domains interrupted by thin 10 nm wide ferroelastic a-domains formed due to the specific strain conditions as described in ref. 20. I–V characteristics of the 90°-DWs revealed a strong asymmetric behavior with no current detectable under negative sample biases  formalism provides an adequate description of this mechanism, which is supported by the FN-fit of the I–V curve (black dotted line) in Fig. 60 nm PZT Zr/Ti = 10:90) layers were epitaxially grown on a DyScO0:90 layeUpon complete removal of the switched domains by backpoling to the initial state Fig. k–m, the 2 were used for contacting/controlling the individual 180°-DWs. Figure I–V curves .To further investigate the relevance of the conductive channels for device applications, domain wall contacting and conduction measurements with a parallel-plate capacitor geometry were performed. The acquired data were consistent with the data collected on the bare PZT surface and basic device functionalities could be demonstrated based on controlling the presence and position of the domain walls by electrical stimuli. Cr/Au (5/20 nm thick) electrodes with a size of 250 × 250 nmves Fig. . Figure 20  were observed. The conductive traces could be completely erased by removing the switched domains through backpoling with a sample bias of ≤−5 V.To further analyze the nature of conduction at the 180°-DWs, a series of scanning probe measurements have been carried out at cryogenic temperatures in ultra-high vacuum (UHV) Fig. . The ent2 K Fig. k. Analys2 K Fig. l, m - haThese results of cryogenic scanning probe microscopy provide a valuable insight into the physical origin of the observed 180°-DW conduction. In particular, they imply an intrinsic nature associated with the domain walls’ electronic properties rather than an extrinsic defect-driven mechanism. The formation of a 2D electron gas, characterized by its metallic-like conduction is consistent with the non thermally-activated conduction observed at the 180°-DWs, which supports remarkably high current levels down to 4 K. With at least 1 nA at 4 V measured by a scanning diamond probe in a cryogenic environment, this illustrates the potential for applications in a wide temperature range.A possible interplay between the ferroelastic a-domain and c-domain boundaries is another issue essential for illucidation of the domain wall conduction mechanism. Indeed, prior to poling, conductive 90°-DWs were already observed in the pristine PZT. The data in Fig. Another type of domain wall formation is shown in Fig. um = 0.35%. The pristine state is prepared from the paraelectric phase by field-cooling. Interaction of free carriers with the charged domain walls is accounted for by the introduction of the Thomas-Fermi-Debye-Hückel screening term into the electrostatic Poisson equation. The carriers’ concentration is accounted for by the screening length δ. The details of the simulations are given in Methods.To gain further insights into the origin of the 180°-DW conductivity and the interplay between the a- and c-domain boundaries, we performed quantitative phase-field simulations of the poling dynamics. For this, we model the part of a 50 nm PZT film, with lateral dimensions of 500 × 500 nm, strained by the substrate with a tensile strain of Figure In compliance with experimental observations, the pristine sample presents a uniform grid of downward polarized c-domains separated by a rectangular crosshatch pattern of thin a-domains. The internal structure of the system reveals a complex intertwined network of nearly 45° inclined 90°-DWs, that minimizes the interplay of elastic and electrostatic energies of the system.The biased tip polarizes the sample locally with visible demolition of the a-domains at the film surface Fig. b. The seMore details on the dynamics of the formation of the poled state are presented in the 2D cross-section simulation of Fig. These poling dynamics give a hint for understanding the conductive traces at the poled region boundaries. Importantly, the boundary between poled and pristine regions, which looks from the surface as a single 180°-DW, has in fact a more complex internal structure. As shown in Fig. 20 to originate from the progressive bending of the domain walls from the charge-neutral head-to-tail (HT) or tail-to-head (TH) 45° orientation. The domain wall bending breaks the polarization continuity, resulting in the emergence of bound charges at the domain wall. The now charged domain walls attract the carriers from the bulk of the film, which partially screens the bound charges. The bulk carriers are normally localized at the impurities energy levels, for instance at oxygen vacancies. Importantly, the potential drop at charged domain walls ∼0.8 eV is below the defect level (located at ∼−0.6 eV with respect to the bulk conduction band), thus pushing the conduction band at the domain wall region below the Fermi-level and providing the metallic-like conductivity of a 2D electron gas.The origin of the conductivity of the 90°-DWs on DSO-deposited PZT films was shownFigure 3. Phase-field simulations reveal rather complex domain arrangements behind the apparent single 180°-DWs detected by the surface-based AFM-techniques. The analysis of poling dynamics suggests the formation of interconnected structures of 90°-domains emerging from the 180°-DW. The deviation from the neutral 45° angle of these a-domain networks, entails the formation of partially charged domain walls. This results in a 2D electron gas formation responsible for the extraordinary transport properties observed at the 180°-DWs. This mechanism is different from the previously reported defect-assisted conduction in 180°-DWs in PZT and leads to fundamentally different conduction properties. Thus, the longstanding issues of domain wall electronics relating to low current densities and high operation voltages can be overcome by using highly stable 180°-DWs through accessible domain reconfigurations in one of the most used ferroelectrics, PZT.In conclusion, we report controllable 2D conductive channels with a remarkably high current density of 200–400 nA/μm at voltages ≤2 V, associated with 180°-DWs in tetragonal PZT. These channels exhibit a metallic-like behavior with non thermally-activated conduction persisting down to 4 K. Individual domain walls could reproducibly be contacted by nanometer-size electrodes forming single-DW-based memristors with time- and readout-stable conductance states characterized by on-state currents of 50 nA and on/off ratios up to 100.1Ti0.9)O3 (PZT) was grown on a (110) DyScO3 (DSO) substrate by pulsed laser deposition (PLD). The DSO substrates with a miscut angle of 0.1° towards the [1-10] direction were acquired from CrysTec GmbH. A thin layer of 20 nm SrRuO3 (SRO) was deposited by PLD before the PZT growth and served as a bottom electrode. The PLD deposition parameters were the following: a 248 nm laser was used with an energy density of 1 J/cm2. For SRO and PZT deposition, the substrate temperature/oxygen pressure were 625°C/0.145 mbar and 575°C/0.25 mbar, respectively. The cooling after the film deposition was performed at the controlled rate of 15°C/min with 1 mbar oxygen pressure. XRD-analysis yielded an epitaxial structure and previously performed TEM analysis of similar 60 nm PZT films revealed the bent 45° narrow ferroelastic a-domains of 10–12 nm widths. These a-domains form due to the film/substrate lattice mismatch to minimize the mechanical energy29. Their width and density depends on the exact lattice mismatch and results in the formation of a crosshatch pattern30 clearly visible in the topography AFM  and vertical PFM images . The polarization in all as-grown c-domains was oriented from the top to bottom interface, as confirmed by the switching dynamics through piezo-force microscopy measurements.For this study, highly tetragonal Pb(Zr2 flux (5–10 mbarg) and were preceded by a 15 min exposure to 200°C in order to eliminate adsorbed water from the surface. For all RT-experiments stiff (40 N/m) conductive boron doped diamond coated tips from ADAMA Innovations were used: AD-40-AS with standard sharpness (tip radius: 10 ± 5 nm) and AD-40-SS for high resolution images (tip radius: <5 nm). For the PFM as well as cAFM measurements, a Cypher Dual Gain ORCA Holder (capable of measuring between 1 pA and 10 μA) was used. Because of the circuitry of the ORCA holder all biases to the sample are applied with respect to the bottom SRO electrode and the tip (top electrode) was kept at virtual 0 V. All electrical characterizations (I–V curves and pulse measurements) were performed with the AFM by using the tip (or through contacting the top electrode with the tip). For cAFM and PFM images typical scan parameters were as follows: between 1 and 2 Hz scan speed, 0.1–0.2 V deflection setpoint and 20–40 gain factor. PFM images of Figs. All room temperature scanning probe microscopy experiments were preformed using an Asylum Research (Oxford Instruments) Cypher AFM system (Asylum Research Cypher ES) equipped with the environmental scanner. The measurements were carried out in a temperature controlled 306 ± 0.1 K) environmental chamber under a small continuous N K envirots stiff 0 N/m conTop Cr/Au (thicknesses: 5/20 nm) electrodes with different sizes between 80 nm and 5 μm were deposited using electron-beam lithography (Raith EBPG5000) and metal evaporation (Alliance-Concept EVA 760) together with lift-off techniques.−9 mbar) Cryo-SFM, manufactured by Omicron Nanotechnology (currently Scienta Omicron). Conductive diamond coated probes (NaDiaProbes) with a nominal spring constant of 5 ± 1 N/m were used in order to minimize tip degradation during multiple scans. All cryogenic PFM and cAFM scans shown in the present work were done using the same probe.The measurements at cryogenic temperatures down to 4 K were done using an UHV .Numerical simulations of domain walls in the ferroelectric thin film are based on the minimization of the Ginzburg-Landau-Devonshire free-energy functional32 given in the first square brackets. The second term is the polarization gradient energy33. Third and fourth terms represent the electrostatic energy, accounting also the screening effects34. The last two terms correspond to the elastic energy. The electrostatic potential and strain tensor are denoted as φ and uij respectively. The value of the vacuum permittivity ε0 is 8.85 × 10−12 CV−1m−1 and the value of the background dielectric constant εb is 1035. The numerical values of the Ginzburg-Landau expansion coefficients aijk, gradient energy coefficients Gijkl, elastic stiffness tensor Cijkl and tensor of electrostrictive coefficients Qijkl are given below.Functional  compriseρbound = −∇ ⋅ Ptot, is provided by the non-uniform distribution of the total polarization in the bent 90°-DWs, which includes the spontaneous and field-induced parts: Ptot = P + (εb − 1) ∇ φ. Here ε0 is the vacuum dielectric permittivity and εb ≈ 10 is the background dielectric constant of non-polar ions35. The density of the uncompensated free charges is given by the linearized Thomas-Fermi equation δ can be estimated36 through the Bohr radius a0 = 0.053 nm and the concentration of carriers n0 ≈ 1020 m3 as The electrostatic properties of the system are described by the Poisson equation, φ and the elastic strains uij is found from the respective electrostatic (with screening) and elastic equations:The distribution of the electrostatic potential 0.1Ti0.9)O3 at room temperature37 are as follows: a1 = −0.1618 × 105 C2m2N, a11 = 0.3883 × 109 C−4m6N, a12 = 0.6357 × 109 C−4m6N, a111 = 0.2518 × 109 C−6m10N, a112 = 0.8099 × 109 C−6m10N, a123 = −4.3588 × 109 C−6m10N . The values of the electrostrictive tensor coefficients are: Q1111 = 0.085 C−2m4, Q1122 = −0.0251 C−2m4, Q1212 = 0.0328 C−2m437. Components of the elastic stiffness are: C1111 = 1.7 × 1011 m−2N, C1122 = 0.76 × 1011 m−2N, C1212 = 0.83 × 1011 m2N. The gradient energy coefficients39 are: G1111 = 2.77 × 10−10 C−2m4N, G1122 = 0, G1212 = 1.38 × 10−10 bC−2m4N.The coefficients of the Ginzburg-Landau expansion for Pb(Zrγ is a time-scale parameter which is taken to be equal unity. The non-linear part of the equations is accompanied by two linear systems of equations defined by the screened Poisson Eq. (The non-linear differential relaxation equation is used to find the minima of the free energy :4\documeentclass1pt{minimasson Eq. .40. Two- and three-dimensional rectangular computational regions are represented by structured triangular and tetrahedral finite element meshes, respectively, that were created with the 3D mesh generator gmsh41. The solutions for P, φ and uij was sought in the functional space of piece-wise linear polynomials.The phase-field simulations were conducted with the help of the FEniCS software packageφbot = 0 and φtop = 1 × 10−6 V at the top side. The application of the tip was simulated by imposition of the Dirichlet boundary condition φ = −6 V in the circular area of the tip application and zero everywhere else at the top side of the computational region. Substrate-induced strain is taken into account by imposition of the Dirichlet boundary conditions on components of the displacement vector u at the bottom surface of the thin film, ux = u0x/Lx and uy = u0y/Ly, where u0 = 0.35% is the strain value, Lx = 500 nm and Ly = 500 nm are in-plane geometrical dimensions of thin film for the 3D case (as in Fig. Lx = 150 nm for the 2D case (as in Fig. P and φ are constrained with periodic boundary conditions in the x and y directions.The initial quenching from the paraelectric state was conducted with the imposition of Dirichlet boundary conditions at the bottom side of the computational region 42. The initial condition for polarization at the first-time step is a random distribution of the polarization vector components in the range of −10−6 to 10−6 Cm−2. Newton method with line search is used to solve the non-linear system arising from Eq. (44.The approximation of the time derivative on the left-hand side of Eq.  is accomfrom Eq. , the genFurther information on research design is available in the Supplementary InformationPeer Review FileLasing Reporting Summary


The cable-stayed suspension bridge is one type of bridge that has been increasingly applied to bridge engineering, especially in cross-sea projects. However, the complex combined system of this type of bridge makes it quite difficult for researchers to make a quick decision of the parameter values during the design stage. The Hellinger–Reissner method is applied here to analyze the deformation and force of the structural members in the bridge. The advantage of this method is that the solving of deformation and force is independent of each other, which would enhance the accuracy of the final results. Different load conditions are also considered in the analysis. The results from the present method are compared with test results and finite element analysis, and show good agreements. It implies that the Hellinger–Reissner is a comparatively more efficient method to help designers choose the key parameters for cable-stayed suspension bridges.  The cable-stayed suspension bridge is a combination of the cable-stayed system and the suspension system . The strThere has been a large amount of research work on cable-stayed bridges and suspension bridges, including analyses of static, dynamic, linear, and nonlinear behaviors ,13,14,15The cable-stayed suspension bridges are still not as commonly constructed as cable-stayed bridges or suspension bridges. One of the major reasons is that there are interactions within the cable-stayed system and the suspension system in the design stage ,16,20. AThe Hellinger–Reissner variational principle is introduced here for the design of the cable-stayed suspension bridge. There are several parts included in the formulations of the Hellinger–Reissner functional ,28. The (1)A symmetrical three-span cable-stayed suspension bridge with two pylons is taken as an example to analyze this type of bridge, as shown in (2)t1. Meanwhile, for the stay cables connecting the pylon and girder in the main span, the forces in the stay cables are equivalent to the uniformly distributed load t2 acting on the girder and t2T acting on the pylon. Similarly, in the side span, the forces in the stay cables are changed into a uniformly distributed load t3 acting on the girder and t3T acting on the pylon.The hangers and stay cables are distributed uniformly along the girder of the suspension and girder of the cable-stayed part, respectively. According to the membrane analogy, the force effects of the hangers and cables could be equivalent to those of a membrane between the catenary and girder. The rationality of this step is also supported by the results of a previous study . As show(3)q and concentrated load P, as shown in q and concentrated load P are considered in the following calculation.The live load caused by traffic and walking people could be replaced by a distributed load and concentrated load for static analysis. Meanwhile, the dead load of the bridge could also be equivalent to a uniformly distributed load. According to the superimposition principle, the load on the bridge can be assumed to be a combination of the distributed load (4)The axial force and deformation of either the main beam or pylon are neglected. Hence, the corresponding terms of the strain energy are also neglected. The effect of the shear force of the main beam and pylon is also not considered here. The strain energy of the auxiliary pier is neglected.The cable-stayed suspension bridge is a composite of many complex structural members. The following assumptions are suggested for the analysis in the conceptual design stage: (1)Trial functions of force and deformation should be proposed first with the coefficients to be solved. In this stage, the engineer is required to have the basic knowledge about how the structural members would deform with the load.(2)The trial functions are then applied to the Hellinger–Reissner principle to obtain the expression of the functional.(3)Partial differential equations for individual coefficients are obtained.(4)The deformation compatibility conditions are introduced to obtain the following equations.(5)By combining the equations from Step 3 and Step 4, the expressions of the coefficients are obtained by solving the equation sets.(6)By employing the expressions of the coefficients in the trial functions of force and deformation, the force and deformation expressions are obtained.With the mechanic model of the cable-stayed suspension system, the Hellinger–Reissner method was adopted to analyze the cable-stayed suspension bridge. The steps for data processing are as follows:(1)Force functions:M1 uses the linear function hypotheses. Function M1 is divided into two parts, M11 and M12, to fit the force distribution with the support from the pylon and auxiliary pier. The hypothesis of the bending moment trial function of the cable-stayed part from 0 to L1 is named M11. The second part, L1–Lc, is named M12. During the early design stage, engineers focus more on the forces and deformations in several vital cross-sectional areas. Higher-order functions would make the computing results more accurate but would make the computing procedures more complicated. Hence, the trial function of the bending moment of the cable-stayed part M2.(2)Deformation function:The suspension part uses a quadratic equation as the hypothesis of the bending moment function, w1 and that of the suspension part w2 both used quartic functions. Meanwhile, the deformation function w1 is a composite of two piecewise functions w11 and w12, corresponding to the force functions M11 and M12, respectively. The piecewise function w12 adopts the same function formation as w11 based on the coordinate translation.To simplify the computing procedures, deformation hypotheses are provided under the local coordinate system. The deformation function of the cable-stayed part (1)L1, as shown in L1 in the local coordinate system, the deformation and force assumptions are described as follows:For the cable-stayed part from 0 to b1, b2, e1, and e2 are the coefficients to be solved. The hypotheses of the trial functions for the deformation and force of the girder are as follows:(2)L1 to Lc in the global coordinate system, as shown in L3. The deformation and force expressions are as follows:For the cable-stayed part from e3 and e4 are the coefficients to be solved. where (3)Lc to (Lc+Ls) in the global coordinate system, as shown in Ls in the local coordinate system, the deformation and force expressions are as follows:For the suspension part from L3 equals (Lc−L1), which is the distance from the auxiliary pier or the support of the pylon to the first hanger that does not cross the stay cables, and a1–a3 and e5–e6 are the coefficients to be solved. where w2|x=0 = w12|xL=3, (dw2/dx)|x=0 = (dw12/dx)|xL=3, and (d2w2/dx2)|x=0 = (d2w12/dx2)|xL=3.Meanwhile, the continuous conditions should be satisfied because of the piecewise functions adopted in the deformation functions. The continuous conditions are described as a1, a2, and a3: Which gives the following solution of b1 and b2, are to be solved. Hence, only two coefficients, M11|xL= 1 = M12|x0= and M12|xL= 3 = M2|x0=.The piecewise functions of the force should also satisfy the continuous conditions e4 and e6 are solved and eliminated by this step, which gives the following expressions for e4 and e6: e4 = e1L1 + e2, e4 = e1L1 + e2 + e3L3 – (e5Ls2)/4.The coefficients In summary, the expression of the girder part in the Hellinger–Reissner principle is as follows:R1–R16 are listed in The simplified formation of the equation could be expressed as:c1, c2, e7, and e8 are the coefficients to be solved. The pylon subjected to an external load is similar to a cantilever. The deformation uses a quartic function, while the force in the pylon is in the form of a quadratic function, which is as follows:U1 to U7 are described in Hence, the flexural strain energy of the two pylons in the Hellinger–Reissner principle is expressed as:The tensile strain energy of the main cable is considered here, while the flexural strain energy of the main cable is neglected. The main cable was divided into two parts during the computing procedures: the main cable crossing the main span and the main cable crossing the side span. The parts were individually investigated.f is the main cable sag and Lm is the length of the main span.The main cable crossing the main span was assumed to be a parabola. The shape of this part is described by the following expression in a local coordinate system in which the ‘0′ in the abscissa starts from the left pylon:Hy(x) = M(x), where H is the horizontal component of the load in the main cable, q is the distributed load on the simply-supported beam, M is the bending moment distribution along the beam, α in α = (L1 + L2 − Lb)/Lm = Lcs/Lm, where Lcs is the horizontal distance from the pylon to the first left hanger. The shape of the main cable is similar to the deformation of a simply supported beam subjected to a load , as showHence, the bending moment for a simply supported beam with the same span can be calculated as:t1, as shown in q0 and q1 in q0= t1 and q1= 0, respectively, according to which the horizontal component of the force in the main cable can be computed as:When there is a live load on the girder, the main cable is subjected to the vertical membrane tension stress H here should be derived by multiplying H by a reduction factor (1 − 4α2). Consequently, the expression in the Hellinger–Reissner principle for the main cable crossing the midspan part is as follows:Compared with suspension bridges, the horizontal component ut=3h4c1+2h3c2.The elongation of the main cable of the side-span part is dependent on the displacement of the pylon top. The displacement of the top of the pylon is expressed as Emc is the Young’s modulus of the main cable, Amc is the cross-sectional area of the main cable, n is the ratio of the main cable sag to the span, which is calculated as n = f/Lm, Fmc is the axial force in the main cable of the side-span part, Δ is the elongation of the main cable, and φ is the angle between the girder and the main cable in the side span.The strain energy of the main cable corresponding to the left- and right-side span parts can be expressed asG1 to G4 are listed in Hence, by combining Equations (19) and (20), the total strain energy of the main cable in the Hellinger–Reissner principle can be described as:t1 caused by the hangers on the girder, (3) the membrane tensile load t1 from the hangers on the main cable, (4) the membrane tensile loads t2 and t3 from the stay cables on the girder, and (5) the membrane tensile loads t2T and t3T from the stay cables on the pylons. To simplify the computing procedures, an analysis of the work done by the external load was carried out in the global coordinate system. According to the simplified mechanical model shown in (1)Effects of live load on girder:q and P in The live loads on the bridge could be the different combinations of q. The potential energy of the external load is expressed as:In the case of the first type of load combination, the entire bridge is loaded with a uniformly distributed load q. Hence, the potential energy by the external load can be expressed as:In the second case of load combination, only the main span of the bridge is loaded with a uniformly distributed load q on the girder corresponding to the suspension part of the bridge. The expression of potential energy by the external load is:The third type of load condition is the uniformly distributed load P can be added to the abovementioned expressions, Equations (22)–(24), if the concentrated load is considered: Q11, Q12, Q21, Q22, Q31, Q32, Qp1, and Qp2 are shown in The following term of the effect caused by the concentrated load (2)t1 on girder:Effect of membrane tension Lx is equal to (L1 + L2), and D1 and D2 are listed in The work done by the hanger membrane tension on the girder is negative, assuming that the positive displacement of the girder is vertically downward and the membrane tension on the girder is vertically upward.(3)t1 on main cable:Effect of membrane tension f. The main cable under the load maintains a parabolic shape. Hence, the expression for the shape of the main cable after deformation is expressed as:The displacement at the midspan of the main cable is Δf1 is the deformation of the main cable caused by the displacement of the pylon top, Δf2 is the deformation of the main cable caused by the elongation of the main cable itself, and Δlmc is the amount of elongation of the main cable, expressed as:f = Δf1 + Δf2.The deformation of the main cable at midspan under the live load is related to the deformation of the pylon top and elongation of the main cable. The two parts of the deformation are independent of each other. The effects of these two parts on the deformation of the main cable were derived by Chai et al. :(28)Δf12t1 on the main cable is:D3 to D5 are shown in The expression of the work done by membrane tension (4)t2 and t3 on girder:Effects of membrane tensions t2 and t3 on the girder is similar to that of the hanger membrane tension on the girder and main cable. Hence, the expression for the effects of t2 and t3 on the girder can be expressed as:D6 to D9 are shown in The calculation of the effects of stay cable membrane tensions (5)t2T and t3T on the pylon:Effects of membrane tensions θ is the stay cable inclination angle, as shown in d1 is the space between the stay cables on the girder, d2 is the space between the stay cables on the pylon, and the relationship between the three factors is cot(θ) = d1/d2 if the stay cables are parallel to each other. It can be observed from t2T and t3T on the pylon is expressed as:hc1 and hc2 are the heights of the beginning and end points of the stay cables anchored on the pylon, which are equal to h1 and h, respectively, as shown in D10 to D13 are shown in The stay cable membrane tensions are uniformly distributed along the pylon. The work done by the membrane tensions qiπ is the work done by the ith type of load condition on the girder.iξ is the ith element in the vector ξHR, and ξHR is expressed as:According to each part of the potential energy explained above, the total potential energy of the system can be obtained as:HRK and F could be expressed as: To sum up, Equation (37) can be transformed into the following matrix equation:t1, t2, and t3. However, solutions for the coefficients have not yet been obtained at this step. Hence, deformation compatibility conditions shown in The expressions for the coefficients can be obtained by solving Equation (38), but as a function of The first deformation compatibility condition in (1)Side span:The other deformation compatibility condition shown in (2)Main span:x0 is the location on the abscissa of the stay cable anchored at the girder, and γ is the inclination angle of the stay cable, which is equal to θ when the stay cables are parallel to each other. If the sag effect of the stay cables is considered, the Young’s modulus of the stay cables can be adjusted or reduced according to the Ernst equation [where equation  if the iThe membrane tension can be solved using Equations (39)–(41). Based on this, the solutions for the deformation of the structure members can be presented. To carry out the verification of the presented method, the results from the finite element analysis and test are both compared with the presented H-R method. First, a cable-stayed suspension bridge with a 263 + 800 + 263 m span is introduced here ,19. The Researchers ,19 have The key parameters of the structural members are listed in P = 250 N on the midspan and a distributed load q = 125 N/m along the suspension part. P = 250 N on the midspan and a distributed load q = 125 N/m along the main span.The midspan deflection and the displacement of the top of the pylon were investigated using both tests and the finite element analysis by Du  and WangThe comparison results are then shown in For the top displacement of the pylon in Lm is equal to twice the summation of ‘a’, ‘b’, ‘c’, and ‘d’. The side span Lb is equal to the summation of ‘d’, ‘c’, and ‘e’.The impact of the sag-to-span ratio on the deformation of the combined cable-stayed suspension bridge was then investigated. Jin et al.  providedDetailed values are listed in gΔL from the two methods are almost the same for models A, D, and E, as shown in As illustrated in pΔL, is shown in The fitting of the top displacement of the pylon, The Hellinger–Reissner variational principle is introduced here to investigate the structural behavior of the combined cable-stayed suspension bridge. The procedures of the application of Hellinger–Reissner variational principle in the analysis of cable-stayed suspension bridge is described in detail, which consist of the hypotheses of the deformation, the hypotheses of the force expressions for the structural members, along with the boundary compatibility conditions to build the matrix equation. By solving the matrix equation, the coefficients of the deformation and force expressions are derived directly. The main works are described as follows:(1) One case of the cable-stayed suspension bridge was analyzed and compared with finite element analysis and test results, and the comparisons showed good agreement. This means that the results from the Hellinger–Reissner method satisfy the requirements of the conceptual design stage. (2) Parametric discussion including the sag-to-span ratio of the bridge was conducted, showing that the agreement between the Hellinger–Reissner results and the finite element analysis increases as the sag-to-span ratio goes up within the appropriate range. (3) The Hellinger–Reissner method is efficient in solving the deformation and force of the members of bridges with a combined system. It could be used as a quick solution to help designers make decisions in the early design stage. Besides, it could also be used to verify the finite element analysis to reduce human errors. This article provides methodology for the early design stage of the combined cable-stayed suspension bridge. However, this methodology could be extended to some complicated problems during the state of serviceability, e.g., dynamic behavior, geometric nonlinearities of the suspension cables, and torsional effects. These problems could not be neglected when the bridge is in service state.


This study explored the quality of hypoallergenic wheat (’O-free’) developed in Korea and optimized the basic ingredients and processing conditions for making ‘O-free’ bread using response surface methodology. Water and yeast amounts and mixing and fermentation times were selected as factors, and each factor’s tested range was set by a central composite design using Design Experts: water 52–60 g, yeast 1.5–4.5 g, mixing time 2.5–5 min, and fermentation time 50–70 min. Bread height, volume, and firmness were analyzed to determine bread quality. Flour quality analysis showed that ‘O-free’ flour’s gluten strength was weak. ‘O-free’ flour exhibited inferior bread-making performance compared to representative bread flour. Water and yeast amounts and mixing time, except for fermentation time, affected bread quality significantly. The interaction between yeast and fermentation also affected bread quality significantly. The optimized condition for making bread using ‘O-free’ flour is 60 g of water, 2.6 g of yeast, 2.5 min of mixing time, and 70.0 min of fermentation time. In conclusion, ‘O-free’ flour with the changed gluten composition showed poor gluten strength and bread-making performance. However, modifying the formulation of the basic ingredients and processing conditions could significantly improve the production of high-quality hypoallergenic bread. Wheat is a highly adaptable and widely distributed cereal grain with high nutritional value globally, providing approximately 21% of food calories and 20% of the protein people need. Approximately 35–40% of the world’s population consumes wheat as their staple food. Wheat consumption in Korea is approximately 2 million tons per year and the per capita annual consumption of 34.2 kg [Approximately 15% and 80–85% of wheat is composed of protein and gluten protein, respectively ,7. CompaGluten is an essential structural building protein widely used to fortify low-protein flour to produce excellent baked goods. It forms a gluten network structure through interchain and intermolecular disulfide bonds, providing dough with viscoelasticity, good gas retention, and good crumb structure for the resulting baked products ,14,15. TThis study explored the effect of changes in the gluten composition of low-allergy wheat ‘O-free’ flour on flour quality and bread-making performance. Commercial bread flour and the ‘Baekkang’ (Korean domestic wheat cultivar for bread making) flour were used as the control group and compared with ‘O-free’ flour. Using response surface methodology (RSM), the basic ingredients and processing conditions were optimized for producing high-quality bread. Four factors were selected based on the central composite design for optimization: water amount and yeast amount as ingredients, mixing and fermentation time as processing conditions. Each factor was tested at two levels, including the center points. Bread quality was analyzed based on bread height, volume, and texture.The ‘O-free’  flour and ‘Baekkang’ flour (designated as bread flour A: BF-A) were supplied from the National Institute of Crop Science in Korea, and a commercial bread flour (designated as bread flour B: BF-B)  was purchased at a local market. The protein content of the ‘O-free’ flour, BF-A, and BF-B was 11.5, 13.2, and 14.0% (14% mb), respectively. Ingredients for baking bread were also purchased from a local market. All chemicals were reagent grade for testing the solvent retention capacity (SRC) and sodium dodecyl sulfate (SDS) sedimentation volume. w/w) sodium carbonate, 5% (w/w) lactic acid, and 50% (w/w) sucrose were used as the solvents. The flour suspension (5 g flour and 25 g of each solution) in a conical tube was dispersed and hydrated for 20 min and centrifuged at 1000× g for 15 min . After removing the supernatant, the tube was inverted for 10 min. The SRC was calculated based on the weight of the tube with the pellet.The SRC analysis was conducted according to the Method 56-11.02  to evaluThe SDS sedimentation volume of the flour samples was measured using the method described by Axford et al. . The floThe dough characteristics of flour were evaluated using Method 54-40.02 . A flourThe bread was prepared using a slightly modified Method 10-10.03 . As showThe fermented dough was baked at 215 °C for 18 min in an oven . The baked bread was cooled and removed from the pan. Moisture loss during baking was calculated based on the recorded dough and bread weights. In addition, dough height before and after fermentation and bread height were measured.Dough heights before and after fermentation and bread height were measured using a caliper . The degree of expansion of the dough was calculated from the change in dough height. The bread volume was measured according to a slight modification of Method 10-05.01 [The Design Expert 10  program was used for the experimental plan based on a central composite design using response surface methodology. Based on a preliminary study using a factorial design, water, yeast, mixing time, and fermentation time were selected as factors. It is also well known that water and mixing time are essential for developing gluten, and yeast and fermentation time are important for leavening bread dough. p < 0.05. The Design Expert program was used to analyze the data from the experiments designed using RSM. According to the analysis of variance, adequate models were developed by identifying significant contributing factors and fitting response surface reduced quadratic models, and 3D plots were obtained. The optimum conditions for the amount of water and yeast and mixing and fermentation time were determined by setting the maximum bread volume and height and minimum bread firmness.Analysis of variance (ANOVA) and Tukey’s honestly significant difference (HSD) test  were used to analyze data and average comparisons between samples at w/w) exhibited good solvent compatibility with the xylan backbone of wheat flour arabinoxylans, and the swelling of the arabinoxylan network can be exaggerated in the solution, which can predict the arabinoxylan contribution of the flour [The SRC results of the flour samples are shown in he flour ,26. Ram he flour  demonstrThe SDS sedimentation volume is based on the swelling of gluten in the SDS/lactic acid solution. It can be used to obtain a semi-quantitative estimate of the gluten content . The SDSConsumer expectations of products are generally determined through sensory evaluations . The sofThe fermented dough height and bread height are shown in The volume of bread made with ‘O-free’ flour is shown in The firmness of bread made with ‘O-free’ flour was 3.1–17.1 N . The bre2) ranging from 0.807 to 0.963 and insignificant lack of fit except for bread firmness due to a somewhat larger standard deviation of data than other responses. However, bread firmness is an important bread quality parameter in the industrial aspect and was selected for optimizing ingredient and processing conditions in the study.Among the checked adequate models, the Design Expert program suggested the quadratic model when fitting the data for all responses. However, the lack of fit for the responses except for bread volume was significant, suggesting improving adequacy by developing a reduced quadratic model. The ANOVA results for the reduced quadratic models are listed in p < 0.05) for each response were identified. Fermented dough height was significantly affected by all four factors and the interactions between water and yeast and yeast and fermentation time. Bread height was significantly affected by water, yeast, mixing time, and the interaction between yeast and fermentation time. Bread volume was significantly affected by water and mixing time. Based on the developed models, significant model terms (As dough ferments, yeast decomposes simple sugars and generates carbon dioxide and ethanol, which increases dough volume. As the bread dough is baked in the oven, more carbon dioxide is released, and the ethanol evaporates and turns into bubbles, causing the bread to expand. If the flour lacks gluten, air bubbles in the bread dough are lost, resulting in denser crumbs . An adequate amount of water can improve the viscoelasticity of the dough and help the gluten network become firmer so that the bread expands to a larger volume. However, insufficient or excessive water affects the interaction between the ingredients in the dough . ‘O-freeWater and the interaction between yeast and fermentation time significantly influenced bread firmness. Several studies have shown that soft bread had high moisture content and volume ,37,43, sA three-dimensional diagram of each bread quality parameter is shown in Among the four factors set up in the experiment, fermentation time itself had no significant effect on the representative attributes of bread quality, such as bread volume, height, and firmness. However, the interaction between yeast and fermentation affected bread quality significantly. Furthermore, the water, yeast, and mixing time appeared to affect the quality. As the major quality parameter of bread, the maximum value of bread height and volume and the minimum value of bread firmness were set to identify the optimum conditions based on desirability. The optimized conditions were as follows: 60 g of water, 2.6 g of yeast, 2.5 min mixing time, and 70 min fermentation time. To validate the predicted value, one of the optimized solutions suggested by the Design Expert program was used to prepare bread and compare it with bread made at the center point . The breAs an allergy-reducing wheat variety, ‘O-free,’ developed by traditional breeding at the National Institute of Crop Science in Korea, lacks omega-gliadin. The effect of ‘O-free’ wheat flour on the qualitative characteristics of gluten protein and bread-making performance was explored. In addition, to improve the bread-making performance of ‘O-free’ flour, the basic ingredient formula and processing conditions were optimized using a response surface methodology. The lactic acid SRC value and SDS sedimentation volume of ‘O-free’ flour were significantly lower than those of the control bread flour samples, suggesting weaker gluten strength. The mixograms also showed a weak dough strength of ‘O-free’ flour as the bandwidth was reduced significantly after the mixing peak of the dough made from ‘O-free’ flour. Bread made with ‘O-free’ flour had significantly smaller height and volume and greater firmness than bread made with control wheat flour samples. The results suggested that the bread-making performance of ‘O-free’ flour was not excellent. The reduced quadratic model for each response was adequate and significant for fitting data. The significant model terms were the amount of water, yeast, mixing time, and interaction between yeast and fermentation. The optimized ingredient formula and process conditions were 60 g of water, 2.6 g of yeast, 2.5 min of mixing time, and 70.0 min of fermentation time, significantly improving the bread-making performance of ‘O-free’ flour. In conclusion, although the bread-making performance of ‘O-free’ flour itself was inferior, it could be significantly improved by optimizing the basic ingredient formula and process conditions.


Plasmodium falciparum, has dedicated an unusually large proportion of its genome to molecular chaperones, with a disproportionately high number of JDPs (PfJDPs) of 49 members. Interestingly, just under half of the PfJDPs are exported into the host cell during the asexual stage of the life cycle, when the malaria parasite invades mature red blood cells. Recent evidence suggests that these PfJDPs may be functionalizing both host and parasite Hsp70s within the infected red blood cell, and thereby driving the renovation of the host cell towards pathological ends. PfJDPs have been found to localize to the host cytosol, mobile structures within the host cytosol , the host plasma membrane, and specialized structures associated with malaria pathology such as the knobs. A number of these exported PfJDPs are essential, and there is growing experimental evidence that they are important for the survival and pathogenesis of the malaria parasite. This review critiques our understanding of the important role these exported PfJDPs play at the host-parasite interface.The heat shock protein 40 (Hsp40) family, also called J domain proteins (JDPs), regulate their Hsp70 partners by ensuring that they are engaging the right substrate at the right time and in the right location within the cell. A number of JDPs can serve as co-chaperone for a particular Hsp70, and so one generally finds many more JDPs than Hsp70s in the cell. In humans there are 13 Hsp70s and 49 JDPs. The human malaria parasite,  Plasmodium falciparum, invades the cells of its human host, enabling it to evade the immune system and ultimately harness the cellular machinery to propagate itself and cause severe pathology. Surrounded by a self-created parasitophorous vacuole (PV) within human erythrocytes, the malaria parasite renovates the host cell by exporting over 400 parasite proteins, including a number of heat shock proteins, which oversee protein folding as molecular chaperones and co-chaperones , are localized to almost every compartment of the infected erythrocyte, with arguably the greatest number of exported members of any protein family , leading to the proposal that they may be involved in the trafficking of this major virulence factor  domain , three of which contain the ) domain . Four ex) domain  also con) domain . All of ) domain . PHIST p) domain . Therefo) domain . RESA as) domain , and its) domain . The MEC) domain ; and MES) domain . However) domain . PF10_03) domain , while i) domain . Apart fVery few small molecule inhibitors have been identified that bind specifically to JDPs  functionally associate with PfHsp70-x , and are


Epoxy resin plasticity and damage was studied from molecular dynamic simulations and interpreted by the help of constitutive modelling. For the latter, we suggested a physically motivated approach that aims at interpolating two well-defined limiting cases; namely, pulling at the vanishing strain rate and very rapid deformation; here, taken as 50% of the speed of sound of the material. In turn, to consider 0.1–10-m/s-scale deformation rates, we employed a simple relaxation model featuring exponential stress decay with a relaxation time of 1.5 ns. As benchmarks, deformation and strain reversal runs were performed by molecular dynamic simulations using two different strain rates. Our analyses show the importance of molecular rearrangements within the epoxy network loops for rationalizing the strain-rate dependence of plasticity and residual stress upon strain reversal. To this end, our constitutive model reasonably reproduced experimental data of elastic and visco-elastic epoxy deformation, along with the maximum stress experienced before fracturing. Moreover, we show the importance of introducing damage elements for mimicking the mechanical behavior of epoxy resins. Epoxy resins and their composites with fibers and particles have become indispensable construction materials for a continuously growing range of industrial applications. These range from using reinforced polymers in lightweight, mechanically resilient devices to use as versatile repair materials ,2,3. DueWhile we are still in the beginning stage of this endeavor, molecular simulation approaches recently showed significant advances in elaborating realistic models of crosslinked polymers, such as epoxy resins. Pioneering studies dating back to more than ten years ago reasonably reproduced elastic moduli and bulk density, albeit reaching hardly more than 70% of crosslinking in the underlying network models ,8,9. On At length scales larger than ~5 nm, epoxy resins display structural homogeneity and thus isotropic elasticity behavior. In turn, anisotropic behavior is observed upon deformation beyond the yielding point. Visco-elastic modes and plastic deformation behavior account for manifold processes in the polymer. These may span from twisting and sliding of individual loops within intact networks of covalently linked epoxy moieties to bond-reorganization and finally the dissociation of covalent bonds . Thus, iBased on reactive atomic interaction models, we recently enabled molecular dynamic simulations to study thousands of molecule-sized simulation cells of bisphenol-F-diglycidyl-ether, BFDGE, epoxy monomers and 4,6-diethyl-2-methylbenzene-1,3-diamine, DETDA, and linkers . AlthougFrom the perspective of epoxy resin application as a building part, re-occurring loading and unloading is of immense importance. In this regard, a plethora of approaches has been published. Recent studies have focused on the constitutive modelling of thermosetting polymers regarding temperature-dependent and visco-elastic effects ,15, as wConstitutive models of material deformation take use of intuitive mechanical elements to describe the loading and relaxation behavior. For this, simplified basic elements, such as Hookean springs, St. Venant, and Newtonian elements have been combined into a network of serial/parallel arrangements ,20. The In this study, we aimed at the formulation of an irreducible set of mechanical elements to describe the cyclic testing of epoxy resins. For this, we revisited our earlier work on EPON-DEDTA resin deformation and fracture  and exteThe standards for the mechanical testing were adopted from our earlier study described in detail in . In briel0 = 8.4-nm-long dimensions. Elongation s of this model thus referred to a technical strain of ε = s/l0. For the limiting case of a vanishing strain rate The two stress–strain profiles used as inputs in our constitutive modelling are shown in er study . Thereinain rate . maxσ = 185 MPa  the change in momentary stress from elongation/strain reversal by Δs and (ii) the stress relaxation according to the damping term. Thus,The constitutive model was thus implemented as a set of differential equations that were numerically integrated. For this, robust numerical accuracy was found for a time step of Δimmediate response of the material to increments of the deformation Δs as ideally elastic. In turn, the time-dependence of the momentarystress σ(t) was given by the first-order kinetics of its decay towards the quasi-static limit. The latter depended on the overall deformation s. Accordingly, we assumed the 8 and 109 s−1, respectively. To benchmark the constitutive modelling of tensile deformation/strain reversal cycles, we took use of our previously elaborated simulation system featuring a 3D periodic bulk model of epoxy resin . Thus, as > 10 nm. On one side, this may have been related to our rather simple damage model, which suggests a linear decline of the elastic constants after pulling beyond crits. However, our constitutive model also relied on a rather strong simplification of time-dependent relaxation.Our constitutive model was first applied to tensile testing and epoxy fracture runs using different strain rates in line with previous molecular dynamic runs . The lats up to various elongations smax was performed, followed by a full reversal to s = 0. For this, smax was chosen as 2, 8, 20, and 100% of the size l0 = 8.4 nm of the pristine epoxy model. This selection of maximal deformation smax < scrit was chosen in such a way that our epoxy system remained in the plastic deformation regime. In other terms, the damage model used for describing cavitation and fracture did not apply, and the cyclic deformation runs instead put a focus on the visco-elastic relaxation and plastic behavior.To further elucidate this issue, the constitutive model was applied to a series of tensile testing and strain reversal runs. In parallel setups, deformation smax and s = 0 (hence imposing a full cycle of σ(s = 0) as observed after a full reversal of the deformation is provided in The stress profiles for two sets of cyclic deformation runs are illustrated in While the agreement of the constitutive model and molecular dynamic data appeared promising for the last stage of deformation reversal, we found larger discrepancies for the onset of the reversal runs. This led to a quite drastic mismatch in predicting the ‘relaxed state’; that is, the residual deformation after reversing to zero stress, namely A(s), taken as normal to the elongation s. This was contrasted to the cross-section A0 of the pristine model. In A(s) – A0)/A0 is indicated. While our epoxy models experienced tapering during deformation, upon full reversal runs of s = 10 nm when experiencing ultimate stress [e stress . Our conrmsd) of the molecular simulation systems during cyclic deformation. These are indicated for s = 0 and s = A more local picture of plastic deformation may be derived from the root-mean-square-deviation  to restore the pristine system. We suggest this as the molecular scale mechanism of plasticity.In more general terms, the overall manifold of possible atomic arrangements was related to a very complex energy landscape of high dimensionality. This featured manifold minima and, in line with the amorphous nature of the epoxy network, we suggest many of these energy minima were equivalent to that of the molecular system before deformation. Consequently, alternative network arrangements may have represented stable configurations that did not experience driving forces  free relaxation at 1 atm and 300 K of the snapshots from cyclic deformation by −1 taken for σs=0 showed an exponential relaxation of s(t), in favor of the non-zero residual deformation s(t→∞) = 4.8 and 5.2 nm, respectively.To underpin this picture, we performed additional molecular dynamic runs (i) at the constant σs=0 = 0 for vanishing deformation rates. Consequently, we propose that a physics-driven approach to better account for plasticity could avoid additional damping and Hookean mechanical elements. Instead, we advocate for the development of a model that can describe an offset ∆plastics to elongation s because of plastic deformation. We attempted to formulate this in analogy to the damage model for ∆damages that we suggested in Equation (1); however, we found only unsatisfactory changes in the predicted stress profiles. Therefore, more than the simple linear model that we tested in the present study is required, and we leave this issue for future research. Such developments can improve the description of the strong change of momentary stress during the initial stage of visco-elastic deformation and at the beginning of the reversal runs.These findings contradicted the constitutive model that predicts The bridging of length and time scales from the MD simulations (micro to meso) to experiments  represented an immense challenge. The presented constitutive models reached the macro scale, but also showed the need of improvements for assessing the time scales inherent to common material testing experiments. Our constitutive model was formulated as a minimalistic, irreducible set of well-defined mechanical elements. A comparison with the momentary stress profiles from molecular-dynamic-reference simulation runs revealed some shortcomings in the predictive modelling at its current stage. From a mathematical viewpoint, the use of more mechanical elements has enabled more accurate fitting ,26,27,28From discriminating different aspects of the momentary stress profiles, we identified the description of residual deformation after cyclic tensile testing as a fundamental problem to constitutive modelling. The widely used approach of introducing further damping elements may improve the mathematical reproduction for a given range of strain rates, but it cannot fix the misconception identified for the limiting case of the vanishing speed of deformation. The presented constitutive model was nevertheless quite helpful for the interpretation of our molecular dynamic runs. While the elastic and visco-elastic aspects of epoxy deformation and relaxation are well described by mechanical elements, the difference of the predicted stress diagrams regarding the molecular dynamics data may be directly attributed to the role of plasticity. In other terms, we suggest such a comparison as a quantification of the contributions from viscous and residual modes, providing at least some guidance to tackle the immense complexity of the extended structural reorganization of the epoxy network observed from molecular dynamic simulations.While the present study focused on pure epoxy resins, the elaborated modelling and simulation approaches appeared quite transferrable. Provided that reference molecular dynamic runs are available, the described designing of constitutive models can also qualify for polymer composites involving particles and fiber components. This would allow the rationalization of reinforced polymers by comparing the individual mechanical elements. To this end, we suggest the present study as a reference point and envisage composite analyses for future studies.


Talaromyces stipitatus was previously reported to produce a similar polyester, talapolyester G. The complete genome sequence and the development of bioinformatics tools have enabled the discovery of the biosynthetic potential of this microorganism. Here, a putative biosynthetic gene cluster (BGC) of the polyesters encoding a highly reducing polyketide synthase (HR-PKS) and nonreducing polyketide synthase (NR-PKS), a cytochrome P450 and a regulator, was identified. Although talapolyester G does not require an oxidative step for its biosynthesis, further investigation into the secondary metabolite production of T. stipitatus resulted in isolating two new metabolites called talarodioxadione and talarooxime, in addition to three known compounds, namely 6-hydroxymellein, 15G256α and transtorine that have never been reported from this organism. Interestingly, the biosynthesis of the cyclic polyester 15G256α requires hydroxylation of an inactive methyl group and thus could be a product of the identified gene cluster. The two compounds, talarooxime and transtorine, are probably the catabolic metabolites of tryptophan through the kynurenine pathway. Tryptophan metabolism exists in almost all organisms and has been of interest to many researchers. The biosynthesis of the new oxime is proposed to involve two subsequent N-hydroxylation of 2-aminoacetophenone.Polyesters containing 2,4-dihydroxy-6-(2-hydroxypropyl)benzoate and 3-hydroxybutyrate moieties have been isolated from many fungal species.  Talaromyces produces a broad spectrum of bioactive natural products of interest to many scientists - and [2-13C]-labelled acetate into the structure of a macrocyclic polylactone menisporopsin A, which confirmed the polyketide origin of such a fungal polyester +, .Talarodioxadione 5: colorless crystals, IR (neat): vmax 3402, 2970, 2880, 2742, 2359, 1652, 1525, 1451, 1451, 1281, 765 cm−1; 1H-NMR  δ (ppm) = 9.72 , 9.29 , 7.66 , 6.93 , 6.84 , 6.75 , 2.09 ; 13C NMR  δ (ppm) = 168.9, 147.8, 126.4, 124.6, 122.3, 118.9, 115.9, 23.6. HR-ESI-MS at m/z 152.07061 [M + H]+ .Talarooxime 2, 3, 4 and 6 agreed with the literature. Furthermore, 1D and 2D-NMR spectra of all metabolites are presented in the The NMR data of the metabolites T. stipitatus non-redundant protein sequence database. The algorithm parameters were as follows: the substitution matrix used was BLOSUM62, gap opening penalty 11, gap extension penalty 1, expectation value  10−10, and compositional matrix adjust method +, . Additional confirmation was obtained from the isotopic distribution (ID), which matched the simulated ID of the proposed molecular formula. The 1H and 13C-NMR chemical shifts of compound 1 were similar to that reported for the fungal polyesters  6.37 and 6.19, which indicated the presence of a tetra-substituted benzene ring, whereas the 3-hydroxybutyrate moieties were recognized from the presence of two oxygenated methine protons at δH (ppm) 5.30 and 5.20, two methylenes at δH (ppm) 3.66, 2.86, and 2.49 (2H overlapped), and two methyl groups resonated as duplets at δH 1.68 and 1.03. One dimensional Nuclear Overhauser Effect Spectroscopy (1D-NOESY) spectra were indicative of the correlation between the aromatic proton H-5 and the aliphatic protons Ha,b-7. Other 1H-1H space couplings were detected between H-7/H8, H-7/H9, H-8/H-9, H-11/H12, H-12/H13, and H-11/H-13. The 13C-NMR spectrum showed 14 carbons assigned based on Heteronuclear Single Quantum Coherence (HSQC) and Heteronuclear Multiple Bond Connectivity (HMBC) analyses. The HMBC spectral data suggested the cyclic structure of 1. A Key HMBC 1H-13C long rang correlation was detected between H-12/C-14. More correlations supported the predicted structure of 1 were observed from H-3 to C1/ C-2/C-5, from H-5 to C-1/C-3/C-4/C-7, from Hab-7 to C-5/C-6/C-8, from H-9 to C-7/C-8, from Hab-11 to C-10/C-12/C-13, from H-12 to C-14, and from H-13 to C-10/C-11/C-12 . The NMR experiments were performed in DMSO-6d to enable the detection of exchangeable protons. Two broad singles of the two hydroxyl groups appeared at δH (ppm) 9.72 and 9.29, whereas the four aromatic protons resonated at δH (ppm) 7.66 (dd), 6.93 (td), 6.84 (dd) and 6.75 (td). 1D-NOESY experiment helped assign the configuration of 5. Clear NOESY correlations between the hydroxyl groups and the aromatic protons were observed, suggesting trans-conformation around the external double bonds : H-3/C-3 (122.3), H-4/C-4 (118.9), H-5/C-5 (124.6), H-6/C-6 (115.9) and H-8/C-8 (23.6). The designation of C-1, C-2 and C-7 were deduced from the HMBC spectrum at δc (ppm) 147.8, 126.4 and 168.9, respectively, as the 1H-13C correlations were detected from N-OH to C-1/C-2/C-6, from -CH3 to C-7, and from C-OH to C-2/C-3. Talarooxime le bonds . 13C-NMRT. stipitatus consist of 2,4-dihydroxy-6-(2-hydroxypropyl)benzoate and 3-hydroxybutyrate subunits, which were predicted to derive from an HR-PKS and NR-PKS homologous to Men1 and Men2. Indeed, protein Blast searches using the amino acid sequence of Men1 against the T. stipitatus protein database revealed a highly homologous HR-PKS (XP_002488696) at the top hit with 59% identity and 73% similarity, which is over twice higher similarity than the second top hit. The Men2 query showed an NR-PKS (XP_002488697) that shares a significant similarity, with 67% identity and 80% similarity compared to the second top hit  and a regulator protein (tpeD) (The polyesters isolated from  top hit . Interesn (tpeD) .980XXXSXXXXP989 and E1169XXXQ1173, indicating the replacement of Asp with Glu which may not be enough as indicative for non-functional DH0 domain [1945AVG1948 motif, suggesting the inactive ER0 domain [The conserved domain analysis of TpeA and TpeB was performed using the SMART protein domain analysis tool. Both enzymes showed similar domain architecture to Men1 and Men2, respectively . TpeA co0 domain ,29. Howe0 domain . In addi0 domain . TpeB has a typical fungal NR-PKS domains, including a starter-unit acyltransferase (SAT), ketosynthase KS, MAT, product template (PT), tandem ACP doublet and thioesterase (TE)  32,33,3,333,34. 6 as a derailment product. This polyketide was also produced by transformants of A. oryzae expressing men1 and men2. Similarly to the biosynthetic steps of ascotrichalactone A, the polyesterification process maybe occurs when additional molecules of 3-hydroxybutyryl are transferred to the NR-PKS [1, whereas the ethyl esterification of talapolyester G 2 perhaps happens spontaneously . The acceptance of 3-hydroxybutyryl by the NR-PKS (TpeB) would initiate further elongation and cyclization, catalyzed by KS and PT, respectively, to form 2,4-dihydroxy-6-(2-hydroxyn-propyl)benzoyl-S-ACP intermediate. The TE domain could catalyze lactonization at this step to yield 6-hydroxymellein e NR-PKS . Followianeously a. Accumu2 domains. Although the low-resolution small-angle X-ray scattering (SAXS) model of Men2 ACP1-ACP2-TE showed a great flexibility beads-on-a-string configuration, there was no interaction between ACP and TE domain was detected [1-ACP2) from prodigiosin biosynthesis revealed two distinct conformers, bent and extended. In addition, an interaction between the ACP domains and the ACP cross-liker has also been observed, which may suggest the importance of the linker sequence in the biosynthetic programming of NR-PKS [The mechanism of esterification is ambiguous. It was hypothesized that esterification and cyclolactonization are catalyzed by the TE domain as the reduced diketide intermediate 3-hydroxybutyryl is passed to the TE for the first esterification reaction with the 2,4-dihydroxy-6-(2-hydroxyn-propyl)benzoyl-S-ACP subunit and further esterification reactions happen through interactions between TE and ACPdetected ,37. Anotf NR-PKS . Conceivf NR-PKS .2 does not require an oxidative step, the existence of other polyesters was predicted. The investigation led to identifying the macrocyclic polyester 15G256α, which was also produced by other filamentous fungi, Hypoxylon oceanicum LL-15G256 [Talaromyces flavus [T. stipitatus polyesters as the P450 (TpeC) is the best candidate for catalyzing this oxidative step , TpeB (NR-PKS), TpeC (P450) and TpeD (regulator) required for the biosynthesis of 15G256α. The presented result may allow for domain swap experiments to greater understand the mechanism and programming that govern the iterative esterification process. In addition, tryptophan metabolism exists in almost all organisms and has been of interest to many researchers. Therefore, the characterization of talarooxime may help identify and understand such a metabolite’s effect on human health.The fungal polyesters containing 2,4-dihydroxy-6-(2-hydroxypropyl)benzoate and 3-hydroxybutyrate moieties are interesting polyketides due to their potential biological activities and unusual biosynthesis. The shared production of some polyesters by many filamentous fungi suggests programmed esterification catalyzed by dedicated HR-PKS and NR-PKS. The fungus


For robot swarm applications, accurate positioning is one of the most important requirements for avoiding collisions and keeping formations and cooperation between individuals. However, in some worst cases, the GNSS  signals are weak due to the crowd being in a swarm or blocked by a forest, mountains, and high buildings in the environment. Thus, relative localization is an indispensable way to provide position information for the swarm. In this paper, we review the status and development of relative localization. It is first assessed that relative localization to obtain spatio-temporal relationships between individuals is necessary to achieve the stable operation of the group. After analyzing typical relative localization systems and algorithms from the perspective of functionality and practicality, this paper concludes that the UWB-based (ultra wideband) system is suitable for the relative localization of robots in large-scale applications. Finally, after analyzing the current challenges in the field of fully distributed localization for robotic swarms, a complete mechanism encompassing the relative localization process and the relationship between local and global localization that can be a possible direction for future research is proposed. Failure of a single individual does not significantly affect the biological swarm performance.2.Individual simplicityIndividuals within a swarm do not have a strong ability to accomplish the swarm’s tasks alone. Due to their simplicity, individuals accomplish complex tasks with each other through cooperative behavior with spatio-temporal relationships.3.ScalabilityWhen the number of individuals in a swarm increases, the control mechanism is still effective. The relative relationships within a swarm can be maintained steadily. The characteristics displayed by a swarm depend on the ability of individuals within the swarm to obtain the relative position of those around them.Biological swarms in nature realize complex group behaviors in the form of distributed control and self-organization under the interaction between adjacent individuals and the environment through simple autonomous decision-making rules and local sensing communication . A bioloDue to the limitations of endurance, sensing and load capacity, the robot’s ability to perform tasks alone is restricted. With the complex changes of task demands, people turn their attention to robot swarms, hoping that they can break through the limitations of individual and complete more complex tasks through group cooperation. Inspired by biological swarms, robot research has been developing in decision-making planning, communication networking, formation control, conflict resolution and other aspects . KushleyLocalization can be divided into GNSS-based positioning and relative localization according to whether absolute location information can be obtained ,6. BioloWith the development of technology, the accuracy of GNSS-based positioning has been continuously improved. The localization precision of GNSS using RTK  technology reaches the centimeter level ,8. HowevResearch on relative localization technology has been developed for decades . At presAccording to our investigation, although necessary, there is currently a lack of reviews of the relative localization method of robot swarms. An existing survey in ,23,24 foThis work examines and describes a number of features of relative localization systems that are appropriate for robot swarms.This work analyzes and evaluates typical positioning systems in terms of measurement frequency, positioning mode, and weight energy consumption, with the goal of meeting the application requirements of large-scale, high dynamic networking, and flexible mobility of robot swarms. According to our findings, UWB has the potential to be used in large-scale robotic swarm applications.This work considers the challenges that need to be met when the relative localization technology is applied to large-scale robot swarms.For a large number of robot swarms, a fully distributed relative localization method and its essential technologies are explored in this study, which can realize local and global localization.Based on the EBSE (evidence-based software engineering) method in , this paThe rest of this article is shown below. This section introduces and discusses the current development of relative localization technology. First, typical sensors such as Bluetooth, Wi-Fi, RFID (radio frequency identification), UWB, visible and infrared devices are introduced. At the same time, the basic principles of several classic positioning algorithms are introduced. After that, this paper compares and analyzes the advantages and disadvantages of various technologies in typical applications, and summarizes the relative localization technologies that can be applied to large-scale robot swarms.We use sensors to get raw measurement information. Typical sensor devices that can be used for relative localization include Bluetooth, Wi-Fi, RFID, UWB, lidar, RGB camera, infrared camera, etc.Bluetooth works in the 2.4 GHz ISM  band, with fast signal attenuation and weak penetration. When adjacent devices communicate, RSS  can be used to obtain distance information , and an Wi-Fi works in the ISM band of 2.4 G/5 GHz, and the signal range of Wi-Fi 4 can reach 250 m . SimilarRFID has LF , HF , UHF  and SHF  frequency bands . The effUWB devices operate in the 250–750 MHz, 3244–4742 MHz, and 5944–10,234 MHz frequency bands . They trLidar  uses 905Similar to lidar, RGB cameras  are usedInfrared cameras use 850 nm infrared light to illuminate objects and receive reflected images. A typical infrared camera indoor positioning system is a motion capture system [There are many kinds of relative localization algorithms , but theRSSRF-based communication technology can provide signal strength information , which iTOA Similar to RSS, TOA  calculatAOA AOA  obtains TDOA TDOA  uses tagSLAM SLAM  helps roMulti-Camera Target Identification and Location AlgorithmThe multi-camera target identification and localization algorithm determines the three-dimensional location of the target by capturing the two-dimensional position with a minimum of two cameras. The motion capture system uses an infrared camera array to solve the coordinates of the placed reflective marker points with sub-millimeter error. This algorithm centralizes the data from fixed nodes and consumes large computational resources. It is highly influenced by the environment, and the system cannot be used when the marker points are obscured.To visually demonstrate the positioning algorithm introduced in this section, the measurement data required by the positioning algorithm, the basic process of measurement, required conditions and typical platforms are sorted out, as shown in According to the positioning mode, this paper divides the positioning system into an “anchor-tag” mechanism and a full distribution mechanism.The mechanism has anchors with known positions pre-installed in the scene (whether the anchor moves or not). The tag initiates measurement communication with the anchor, and the position of the tag relative to the anchor is solved by an algorithm. Typical positioning systems using this mechanism are based on Bluetooth, Wi-Fi, RFID, UWB, infrared cameras, etc.BluetoothObreja and Vulpe  studied Wi-FiRubina et al.  proposedu et al.  proposedu et al.  used macu et al. . The sysRFIDZhang et al.  proposedUWBChen et al.  optimizeInfrared CameraMotion capture systems locate a moving reflective marker ball by a fixed infrared camera array ,64. The In this mode, there is no limit to the anchors in the scene, and centralized calculation is not required. By accepting external information or active detection, the position of the agent relative to the map can be calculated, which can be called a complete distribution mode. Methods of measurement using this mode include UWB, lidar and RGB cameras.UWBCao et al.  designedLidarLu et al.  proposedRGB CameraZhang et al.  aimed toSensors with the Characteristics of Being Lightweight, Having Low Power Consumption, and Being Low-costThe sensors for relative measurement are lightweight, have low power consumption, and have low cost . These fFully Distributed Localization Mechanism with RobustnessThe relative localization mechanism should be adapted to the dynamic topology between nodes . The numObtaining Positioning Information in a Very Short TimeRelative localization, as the fundamental access control loop of navigation , enablesIn an emergency task scenario, a robot swarm should have the characteristics of the micro-miniaturization of the platform, low power consumption/lightweight load and limited energy, etc. The swarm has hierarchical relationship in communication and management, and the space-time relationship between individuals changes rapidly, so it must have the ability of mutual perception and collision avoidance . SeveralIn a crowded dynamic environment, three aspects need to be considered for the application of micro-robots in large groups. First, it is important to focus on the power consumption, sensing distance, weight, and cost of sensors. Second, the localization mechanism should be considered in terms of the localization mode and cooperation method. Third, it is important to pay attention to the measurement frequency and localization solving delay in the update frequency.A single UWB node ,70 weighRGB cameras ,50 weighLidar  weighs nWe summarized UWB, RGB camera and lidar in terms of equipment parameters and capabilities, as shown in According to our literature review, Fontana and Gunderson  first prWith the extensive application of UAVs, the demand for positioning is increasing. Aiming at the indoor application environment, researchers have studied the methods of improving the relative localization accuracy and frequency of a single UAV and multiple UAVs. Tiemann et al.  mounted UAVs are mostly used in outdoor environments, and many studies have researched relative localization in outdoor environments. Steup et al.  set UWB To improve the accuracy of the UWB positioning system, Hol et al.  proposedWith the research of multi-sensor fusion state estimation, the research of UWB measurement system and sensor characteristics is also carried out simultaneously. To improve the measurement accuracy of the positioning chip, Sidorenko et al.  proposedA summary of the above UWB positioning systems is givenin n increases. In a completely connected manner, the robot conducts one-to-one ranging interactions Q times, with the ranging time being Robots need to recognize which vehicles are around them, in which direction, and how far away they are in both indoor and outdoor environments. The robot has no pre-positioned anchors to rely on in a dynamic environment. The localization mode of anchor-tag cannot satisfy the swarm application research, and the distributed relative localization oriented to fully peer nodes must be explored. As a result, the robot’s position information can only be solved using UWB ranging information. Due to the pulse communication characteristics of UWB , it is dCurrently, there is a lack of a positioning mechanism, i.e., a complete set of processes including “initialization, local measurement, decomposition, local positioning information update, and global positioning information update”. The literature  investigSwarms require collective robustness , and theIn the existing studies, there are 6 or 7 robots based on UWB relative localization ,83. HoweWe propose an implementable solution to the challenges of applying relative localization technology to large-scale robotic swarms.The positioning mechanism of robot swarms should be built from individual nodes, which have modules of initialization, adjacency inquiry, local positioning and global positioning, and can be executed sequentially as shown on the left side of In order to prevent communication congestion, we need to allocate channel resources reasonably and adopt polling multiple access technology. The polling mechanism can either allocate time slots for nodes using TDMA synchronously  or asyncTo adapt to the dynamic changes in the system, the adjacency node list needs to be updated periodically according to the rules.UWB has the best measurement range, and the positioning accuracy of nodes beyond the range is reduced . We seleThe nodes are polled for measurements based on the initialized rules. The measurement method used needs to balance time with packet loss during measurement.The nodes are distributed to solve the relative position by distance measurement information. To reduce the error caused by relative moving position in the measurement process, methods such as shortening the distance measurement time to shorten the time slot length , a minimIt is necessary to construct some connection points between locals to complete coordinate transformation between local and global graphic calculation. Local coordinate systems are unified into global coordinate systems through mutual transformation. In this process, overlapping connection points must exist between adjacent locals . TherefoIn this paper, the relative positioning technologies for large robot swarm are analyzed and summarized. Firstly, the existing measurement systems of different sensors and typical positioning algorithms are discussed. After that, two different localization systems are examined: anchor-tag and complete distribution. According to our examination, se summarize several characteristics of relative localization technologies suitable for robot swarms. This paper analyses the typical positioning system from the measurement frequency, positioning mode, weight energy consumption and other aspects. Based on our analysis, we conclude that UWB has the potential for large-scale robotic swarm applications.In particular, we sort out and summarize the current situation of indoor and outdoor applications and the integration and improvement of UWB relative positioning technology according to development. We then analyze the challenges that will be encountered with relative positioning technology as the number of robot swarms increases. Finally, a more detailed fully distributed relative localization mechanism that can be implemented and its key techniques are discussed for swarms with a large number of robots in grouped networks, which can achieve local and global localization and provide some promising directions for future research.