This communication reports the effect of phosphorus (P) added in micro concentration range in steel on kinetics, mechanism and growth of passive film in contact of chloride contaminated concrete. Electrochemical impedance spectroscopy, direct-current polarization, mass loss and Raman spectroscopic techniques were used to arrive at the findings. The results showed that an intentional addition of P in steel (0.064%) makes it more prone to uniform and localized corrosion (about 1.1 and 1.7 times) than the steel having low phosphorus  exposed under wet/dry conditions in simulated pore solution added with chloride and in the absence of this ion. A similar effect is also noted for the rebars embedded in mortars. Identification of corrosion products formed on steel rebars surface by Raman spectroscopy reveals thermodynamically stable maghemite and goethite phases on the surface of low P content steel. Unstable phase of lepidocrocite is recorded on the surface of higher phosphorus steel rebars. The findings are discussed with experimental evidence and taking clues from the published literature to arrive at plausible mechanism for this behaviour. Very limited information on their role in changing the corrosion characteristics especially in concrete environments of the resultant micro alloyed steels are available in the literature8. It is more so for phosphorus added in steels. This element segregates in grain boundaries of steels causing brittleness and adversely affecting the fracture toughness5. In view of this the P content in steels is maintained at minimum level by some international standards9. Rebars embedded in concrete experience static and dynamic loadings during their service life. Some international standards for steels used to roll rebars therefore limit the maximum P content in chemistry of such steels. When weldability and enhanced ductility is required, rebars meeting ASTM A7069 standard is specified. ASTM A706 limits the phosphorus content to 0.035%. On the other hand, in USA and many other countries, ASTM A61510 is widely used and deals with the rebars for concrete reinforcement with no limitation on phosphorus content. The present research focuses on this type of rebars which has a much larger usage in the concrete construction industry.Many metallic and non-metallic elements namely carbon, sulphur, manganese, copper, vanadium, niobium, phosphorus etc. are added in steels in micro concentration ranges to achieve improvement in their properties. Literature survey reveals that researchers in the past had found that the added elements either improved2. Some rebar manufacturers in certain countries expecting the same effect add extra phosphorus in steels used to roll the rebars. The rebars rolled from the scrap steels also contain higher content of phosphorus. The de-phosphorization of scrap steels is an expensive process and difficult to achieve the acceptable limit of this element. In view of the above facts, it is important to know the effect of content of P in rebars on their resistance to corrosion exposed in chloride contaminated concrete environments. Literature search reveals that extra addition of P in steels generally have a deteriorating effect on their resistance to corrosion exposed in environments with high humidity and water content. Kim et al.11 reported an adverse effect of P alloying in mild steel on its corrosion resistance in a gas desulphurisation system and attributed it to the increased hydrogen evolution reaction. A similar effect was also reported by Uhlig12 and Cleary and Greene13. Windisch et al.14 found an adverse effect of this element added in steel and tested in a calcium nitrate solution. The authors attributed it to the destabilising effect of phosphate (generated by the ionisation of P from the corroding steel) on the semi-protective Fe3O4 film. Krautschick et al.15 reported the accelerating effect of P and attributed it to the formation of a negatively charged species Pδ- that accelerated the attack. P has exhibited an augmenting effect on the stress corrosion cracking of steels in different test media22.It is known that the higher content of P in steel improves the atmospheric corrosion resistance of structures fabricated from such steels23 on the other hand reported that higher content of phosphorus in steel rebars had no effect on their resistance to corrosion in concrete environments. These results indicate that the protective or deleterious effect of P in steel is determined by the nature of the environment, the pH, and the anionic and cationic components surrounding the steels. Considering the aforementioned findings and the fact that P in steels segregates at grain boundaries, which may have a distressing effect on the soundness of the embedded reinforcement bars, it was prudent to test whether extra addition of this element in steels affects the performance of rebars exposed in concrete environments. This communication incorporates the results of tests of two types of rebars rolled from microalloyed C-Mn steel: one with the practically negligible content of phosphorus (present as the tramp element) and the other one having an intentionally added higher P content produced by some reinforcement bar manufacturers and allowed by many international standards25.Balma et al.Two types of steels one with a high P content (HP) intentionally added by the rebar manufacturer and the other with low P content (LP) having the chemical composition presented in Table Both HP and LP steels were taken in the form of rebars of 16 mm diameter. After hot rolling, both the rebars were subjected to quenching and tempering treatments. Approximately 10–12% of their outer diameter was transformed into a tempered martensite rim. Appropriate lengths of the test specimens were cut by a diamond cutting machine from a single full-length rebar avoiding localized heating during the cutting.8. This involved mixing of 0.55 M KOH, 0.16 M NaOH, and 0.017 M Ca(OH)2 in distilled water, stirring on magnetic stirrer for two hours followed by filtration on filter paper to remove insoluble lime. The solution was stored in a high-density polyethylene (HDPE) plastic airtight container. The pH of the solution was 13.5.To assess the effect of chloride on the performance of rebars, 0.6 m chloride ion was added in the form of sodium chloride in SPSL.The SPSL was made as detailed in our previous publication26 and schematically depicted in Fig. The geometry, composition and method of preparation of mortars, size of embedded rebars and graphite rods were the same as described in authors’ previously published papersThree sets of mortars were prepared, each embedded with “HP” and “LP” rebars, as prescribed in ASTM –C192. After 24 h of casting the mortars were de-molded and cured for 28 days in a humidity chamber maintained at 95% RH and a 25 °C temperature.27. This involved cutting of 20 mm length of rebars samples, mounting them in acid/alkali resistant resins leaving one end of their cross sectional area (2 cm2) to be exposed in the test electrolytes. The cross sectional area of these samples was mirror polished. After swabbing with acetone and drying, the polished specimens were weighed on an electronic balance with an accuracy of 0.0001 g. Six specimens of each type of reinforcement bar were prepared. Subsequently, two drops of the test electrolyte with the aforementioned compositions were placed on each surface  was dropped onto the other three). This quantity of solution was enough to wet the bare cross section area of the test specimens. These specimens were then placed in a chamber for 78 h, where the relative humidity and temperature were controlled at 95% and 45 °C, respectively. After this period of exposure, the specimens were removed from the chamber. Then, two drops of the test electrolytes were again dropped onto the specimens, and they were returned to the chamber for another period of 78 h. After 156 h of exposure ((wet cycle), the specimens were removed from the chamber and kept in the laboratory environment for 156 h, where the temperature varied in the range of 25 ± 5 °C (dry cycle). This process of 312 h (13 days) was taken as one cycle. After the completion of each cycle, the aforementioned procedure of applying the test electrolyte, drying etc. was continued for seven cycles. After the completion of seven cycles , the rust on the surface of the tested specimens were cleaned in Clarke’s solution as detailed in ASTM G1-90 (re-approved 2010)28, and the corrosion losses were computed using the average weight-loss data of the three samples of each steel.These experiments were performed as described in the author’s past research2 was exposed in the test electrolyte. A calomel electrode fitted with Luggin capillary was positioned very close to the surface of the rebar samples. There after SPSL (without chloride addition) and SPSL added with chloride ions (0.6 M) was poured in three sets each of the test samples. The change in open circuit potential with time was measured connecting the wire leads of rebar samples and Calomel electrode with a potentiostat.Potential–time measurement tests were performed by exposing the appropriate area of samples in the test environments after de-scaling, abrading, and emery polishing of their surfaces. For this test each rebar 15 cm length were fitted in electrochemical cells shown in Fig. 2.The data were analysed by using a DC 105 software of M/S gamry instrument. Three sets of experiments were performed for each steel rebars and the two data close to each other were averaged and produced in the paper. The experiments were performed at 25 ± 1 °C.To assess the severity of uniform and localized corrosion of the two rebars exposed in chloride added and chloride free SPSL test electrolyte, the cyclic anodic polarization experiments were performed in the same cell Fig.  and soluThese experiments were conducted in the similar cells as detailed in Fig. 29 .The prepared mortars as described in “30.The EIS tests of rebars embedded in mortars were performed under wet condition of the mortars as described in our earlier publication31. An Almega Dispersive micro-Raman spectroscope equipped with the beam of an Nd:YAG  green laser with a wavelength of 532 nm was used. The laser was maintained at low power to avoid the transformation of corrosion products due to the heating effect. The locations of the specimens to be studied were focused through an Olympus microscope at a magnification of 50 × . The sample holder incorporated a motorised platform with a jockey to facilitate precise focusing and mapping at suitably specified portions of the specimens. The grating was 672 lines/mm, with a 25-µm pinhole. Prior to the analysis of the samples, the instrument was calibrated by using pure Si at the peak of 532 cm−1.Raman spectroscopy of the corrosion products collected from the test samples was performed as described in reference2O diagram predicts the formation of protective film of Fe3O4 on iron surface up to pH 14 . The simulated pore solution used in the present study is well below 1 N NaOH (0.55 M KOH + 0.16 M NaOH + 0.017 M Ca (OH)2 dissolved in 1 L of water) and pH of this solution was in the range of passive zone of the Pourbaix diagram (pH 13.5). The abnormally high rate of corrosion of the studied steel may be due to the leaching out of phosphorus from the studied steel rebars in the pore solution which facilitated the oxygen reduction reaction at the steel-test solution interface. Many organo-metallic P doped catalysts are reported to increase oxygen reduction reactions in alkaline solutions because of interaction of leached out P with alkali solutions34. P in alkaline solution disproportionate to phosphene (PH3) and sodium hydrogen phosphide (NaH2PO4)35. Phosphene is a known accelerator for the corrosion reactions36. Higher the leached out P at the interface (in case of HP) greater is the rate of corrosion.The corrosion rates of the two studied rebars based on mass loss after seven cycles of wet/dry treatments with SPSL (with and without chloride) were computed considering that uniform corrosion took place on their surfaces. The thickness losses of HP and LP rebars are recorded as histograms in Figs. The corrosion rate under the influence of the chloride-added pore solution was very high for both the steels as illustrated in Fig. Digital images of the surfaces of the rebars after seven cycles of wet/dry treatments (wetted with chloride added SPSL), after cleaning the rusts as described previously, are shown in Fig. Figure 37.The ionic adsorption on oxidized metal surfaces depends on their pHo  for the double layer formed at the corroding interface of LP and HP steel bars are found considerably higher for SPSL added with chloride than those for chloride free solutions (an indication of unstable film)  for low phosphorus (0.007%) rebar having copper content very close to the steel used in this study (0.37%). This is probably due to insufficient time given by the authors of reference46 to stabilize the passive film in SPSL (3 h). In our case the time allowed before starting of the cyclic polarization tests was 1700 h which is good enough to form stable passive film on the surface of exposed rebars29. It is further noted from the curves of Fig. In chloride added SPSL, both the steels suffered pitting attacks at different anodic potentials below the oxygen evolution potential, as indicated in Fig. ars Fig.  show thamax) for a corroding interface is greater for the LP than for the HP steel rebars, indicating that the passive film formed in 24 h on the surface of the LP rebar was more protective than that on the HP rebar. The log frequency–phase shift plots for the two steels shown in Fig. max) corresponding to the lowest studied frequency (10 mHz) was greater for LP than the HP steel rebar  corresponding to the lowest studied frequency (10 mHz) was greater , are significantly reduced compared with the corresponding tests performed in chloride-free SPSL  for the LP rebar at 192 h of exposure remained almost the same as that at 24 h, whereas it deteriorated considerably for the HP rebar with longer durations of exposure. Another notable feature at higher frequencies (1 to 100 kHz) for both the rebars is observed. The impedance values are higher than that noted for 24 h exposure  with phase shift Ɵ tending to 90°. However the experimental data also in this case could be fitted only after putting Warburg component in the simulated electrical circuit (discussed in the forthcoming paragraphs).To assess the performance of the two steels in chloride added SPSL, they were tested after the addition of 0.6 M chloride (added as sodium chloride) to the solution. The results of EIS tests performed after 24 h of exposure in this test electrolyte are presented in Fig. PSL Fig. a. Both tPSL Fig. b indicatPSL Fig. a, the Zmure Fig. a with HPo angle between the abscissa and ordinate axes. The plots for the second set of samples exposed in chloride added solutions on the other hand tend to form depressed semi circles. These characteristics of the plots are associated with a spread of relaxation times and represented by substituting a constant phase element (CPE) in place of pure capacitor in the equivalent electrical circuit47. The CPEs (constant phase elements) which are defined by frequency independent phase angles are used for the parameterization of impedance values including non-ideal behavior of double layer, charge transfer resistance, ionic adsorption or diffusion across the corroding interface and uncompensated resistance(electrolytic ionic resistance (R0) between the interface of the solution and the electrode surface). Many researchers in the past have used such circuits to extract impedance data for rebars corroding in concrete pore solutions51. CPE is an empirically derived parameter and mathematically expressed as52:−1sα. The value of α is greater than zero but less than 1. The value of α = 1 for the interface corresponds to its behaviour as pure capacitor. In view of the non-ideal capacitance behaviour of the corroding interface of the two studied rebars , charge transfer resistance (Rct) and CPE element) did not yield the satisfactory fitting results. In view of this another component , the Warburg diffusion element (Wd) was incorporated in this circuit, schematically shown in Fig. The impedance data plotted in Nyqist form  provide much important and valuable information about the corroding interface. In view of this the data of Figs. 2) which is an indication of standard deviation in the results are of the order of 10–3. Some researchers opine that the values of chi-square for a good fitting should be below 10–3. Many others including Macdonald56, Ren et al.57 and Zhao et al.58 on the other hand suggest that the chi-square factor is a subjective value which sometimes leads to biased parameter estimates and merely 10–3 criteria should not be a deciding factor for the reliability of the data. Since the fitting of the data using the simulated equivalent circuit of Fig. –5–10–7 were recorded we proceeded to extract the fitting of data from EIS experimental results.The results incorporated in this table show that the values of chi-square (Χd) is related to the impedance caused due to the diffusion of species from the solution-passive film interface to the passive film–metal interface60.As stated above the Warburg diffusion (W62. The Warburg impedance (Wd) does not provide any inkling whether it is due to the diffusion of oxygen, chloride or any other specie through the interface. The data for R0 (uncompensated resistance) recorded in Table 0 in addition to the solution resistance also incorporates the resistance caused by the surface film. At longer durations of exposure, the corrosion products formed on the surface of two steels added to the resistance. Further, as expected the chloride addition made the electrolyte more conducting which reduced the value of R0. A notable increase in R0 for the steels at 192 h of exposure in chloride added solution is attributed to the rust layer formed on their surface.This element in equivalent electrical circuit is a contentious issue and is reported to account for diffusion  processes, and is commonly used when the diffusion of species through the pores of the passive film or corrosion products controls the corrosion rate .The component is also related to ease of diffusion of species such as chloride and oxygen through the film formed at the interfacect) recorded in the above Table ct values recorded under all the test conditions. The addition of chloride to the test electrolyte significantly reduced the value for both the steels at shorter duration of exposure (in comparison to chloride free SCPL solution). After longer exposure (192 h) however, the values increased which is more pronounced for HP steel, it is attributed to the embedding of carbonate in rust layer making it more impervious. Since the rust was denser on HP steel the carbonate embedding effect was more visible than that on LP steel. The Warburg diffusion component (Wd) recorded in the Table 0 and Rct. Warburg impedance element (Wd) depends on the concentration of the active material and diffusion coefficient of oxidant and reluctant species, number of mobile electrons, angular frequency and is expressed by the equation63:The values of charge transfer resistance , it is expected that in SPSL oxygen is diffusing species and in other case (chloride added SPSL) it is chloride ion that diffuse through the surface film. The diffusion coefficient of chloride is reported to have considerably lower than that of oxygen in concrete environments  which is formed due to the existence of the electrical double layer  across the interface between the exposed metal and the corroding electrolyte. An increased value of Cdl is normally attributed to increase in surface area and roughness of the test electrode caused due to the progress of corrosion. The Cdl values for the corroding interfaces were computed from the extracted data of EIS plots, using the following equation67:Another important parameter for the corroding interfaces is double layer capacitance .max) at the lowest studied frequency (0.01 Hz) for the LP rebar was higher than that for the HP steel rebar  and longer durations (after 10 cycles) are presented in Figs. ar Figs. a and 21aar Figs. b. After 69. To minimize this effect the experiments were conducted keeping mortars in metal shield and spectra with minimum distortions were noted.The values for different components associated with reactions occurring at the interface of steel reinforcement bars embedded in mortars are presented in Table 0) after ten cycles of wet/dry treatments are noted to decrease vis-a-vis shorter duration test. This is attributed to the diffusion and accumulation of chloride in the concrete pore solution after longer durations of the exposure.These data plotted in Nyquist form exhibited a similar behaviour as recorded for SPSL solution i.e., forming straight line with about 45° angle between real and imaginary impedance axes (plots not showed).In view of this, the simulated equivalent electrical circuit as schematically presented in Fig. 0 (admittance) indicating an increased vulnerability of both the rebars with longer durations of wet/dry treatments. Under all the test conditions Rct values are higher and Y0 lower for LP than the HP steel, confirming the results of the other tests where LP steel rebar had an edge over the HP rebar. The increased Wd noted for the longer exposure (10 cycles) in comparison to shorter duration (2 cycles) test is probably due to lower diffusion coefficient of chloride  than oxygen which was dominant at shorter exposure test. Under all the test conditions the performance of the LP steel rebar is clearly better than that of the HP rebar also in mortar-embedded conditions.The charge transfer resistance for both the mortars embedded rebars was reduced after longer durations (10 cycles) of wet/dry treatments. An opposite trend is noted for Y75. The foregoing test results for the LP and HP rebars indicate that increasing the P content in steel rebars has deleterious effects on their resistance to corrosion in alkaline concrete pore solutions. This finding is contrary to the reported beneficial effects of higher contents of P in low-alloy steels exposed to dry industrial environments76.Phosphorus content in metals, alloys and coatings play very important role on corrosion, film formation, catalytic activity on reactions, microstructures and mechanical properties77. Phosphates are normally alkaline in nature, act as anodic inhibitor and facilitate the formation of a passive film on the steel surface78. This assertion is acceptable for corroding electrolytes where the moisture/water content at the corroding interface is low, such as steels exposed in an industrial dry atmosphere. However, it may not be valid for steels exposed in aqueous solutions. In solutions such as SPSL and mortars having plenty availability of moisture / water, the formed phosphate concentration is probably too low to impart passivation effects on the steel surface. It is to be noted that phosphate anions in concrete pore solution act as an anodic corrosion inhibitor79.The performance of such inhibitors is sensitive to their concentration in the test electrolytes and accelerate corrosion if present below a threshold concentration. In rebars steels the addition of P is maintained in the range of 0.06–0.08% to avoid other deleterious effects. This low concentration of P is inadequate to meet the threshold concentration for the passivation of steel surface. This argument gets support from the findings in reference80 where very high level of the addition of P (0.5% and above) in steel provided good protection to the surface of steel rebars exposed in simulated concrete pore solution.This contrast behaviour suggests that the reaction mechanism for the corrosion of steels with a high P content in an alkaline concrete pore solution differs from that in atmospheric environments. The corrosion resistance of metals is controlled by the protective nature of the passive film formed on their surfaces in a particular environment. The nature of the film is determined by the compositions of the test electrolytes; the bulk chemistry of the metals; the grain size of the metals; and the microstructure, non-metallic inclusions, and stability of the grain boundaries. The beneficial effect of P with Cu on the corrosion resistance of steels in industrial dry environment is attributed to the oxidation of P atoms of steel into phosphates by Cu ions and their co-precipitation with rust during the process of corrosion79. A bulk concentration of 0.013% of P in steels was reported to reduce the ferrite grain boundary cohesive energy by 10%82. An increased concentration of P in steels is known to have adverse effects on the integrity of the grain boundaries82. The cohesive energy of a grain boundary is defined as the energy needed to separate the two adjacent grains to form free surfaces. The bulk concentration of P in the HP steel rebar is significantly higher (0.064%) than the aforementioned reported value (0.013%)82. Theoretical calculations and experimental evidence suggest that the electronic charge transfer between the segregated atoms and the host metal atoms was responsible for this loss of cohesiveness of the grain boundaries81. The segregated metal atoms  are more electronegative than the host atoms (Fe). The charge transfer from the latter atoms to the former atoms reduces the number of electrons that can participate in metal–metal bonds that hold the grain boundaries together. Abundant experimental evidences indicate that grain boundaries with poor cohesion cause different types of metallic failures, including intergranular corrosion and stress-assisted corrosion87. The higher rate of corrosion of HP steel rebars in concrete environments may be attributed to the P present in a concentration range causing segregation and reduction in the cohesiveness of ferrite grain boundaries and ultimately leading to accelerated rate of corrosion. However, this degradation effect is absent in LP steel owing to the lower P content.In addition to the above mechanism the increased corrosion rate of HP steel appears to be associated with the inherent tendency of P to segregate in ferrite grain boundaries of steels causing accelerated ionisation of Fe atoms from the lattice. Alloying of P in steels affects their properties in different ways depending on the concentration. A high concentration of P in Fe can cause segregation at ferrite grain boundaries leading to their reduced cohesion, whereas a lower content leads to the formation of a solid solution with Fe without grain boundary segregation12. The maghemite and goethite phases of Fe rust present on the surface of LP steel rebars are thermodynamically more stable than the lepidocrocite phase of rust present on the surface of HP steel bars. Astable phase of rust is strongly bonded to the steel surface, has sound morphologies, and provides a tortuous path for the diffusion of moisture, oxygen and chloride ions at the metal surface It appears that the higher content of phosphorus in HP discouraged the transformation of thermodynamically weaker lepidocrocite in to stable forms of maghemite and goethite phases of rust. The leached out P from HP which transforms into phosphide and phosphene in alkaline environments36 probably impeded the transformation of lepidocrocite in to maghemite and goethite. This is probably the reason why the LP steel rebar had a lower rate of corrosion during the wet/dry cycle than the HP steel rebars  has deleterious effect on the stability of the steel-pore solution interface vis-a-vis lower P content (< 0.016%).The localized corrosion in higher P content steel (HP)is significantly high than the normal P containing steel (LP).Cyclic polarization indicates that in the presence of chloride ions (0.6 M) the passive film formed on the surface of both the steels is deteriorated leading to lowering of break down potential of HP than the LP steel. However, in absence of chloride ions both the steels were immune to localized corrosion. EIS studies also corroborate the findings of weight loss and polarization techniques confirming that the HP steel was more vulnerable to corrosion than the LP steel rebars. The diffusion coefficient for Cl and O


This paper focuses on the problem of intelligent evacuation route planning for emergencies, including natural and human resource disasters and epidemic disasters, such as the COVID-19 pandemic. The goal of this study was to quickly generate an evacuation route for a community for victims to be evacuated to safe areas as soon as possible. The evacuation route planning problem needs to determine appropriate routes and allocate a specific number of victims to each route. This paper formulates the problem as a maximum flow problem and proposes a binary search algorithm based on a maximum flow algorithm, which is an intelligent optimization evacuation route planning algorithm for the community. Furthermore, the formulation is a nonlinear optimization problem because each route’s suggested evacuation time is a convex nonlinear function of the number of victims assigned to that route. Finally, numerical examples and Matlab simulations demonstrate not only the algorithm’s effectiveness, but also that the algorithm has low complexity and high precision. The study’s findings offer a practical solution for nonlinear models of evacuation route planning, which will be widely used in human society and robot path planning schemes. Evacuation is a key task in the emergency management response stage. For any public safety incident, especially in the global prevention and control of COVID-19, the evacuation of victims and potential victims from the victim site to a safe area has become a top priority . AccordiThe purpose of an evacuation plan is to establish procedures for orderly and coordinated evacuation routes for a community. This can be applied to different types of emergencies that may require evacuation from homes to shelters or quarantined areas. For natural and human resource disaster emergencies such as typhoons, floods, volcanoes, tsunamis, tornadoes, and home fires, evacuation plans can be applied to evacuate people from homes to shelters. For epidemic disasters, such as COVID-19, the proposed plan can be applied to evacuate affected people from homes to quarantined areas in a timely manner. For different communities, it is essential to identify the common hazards that may occur and identify appropriate evacuation routes.Regional evacuation refers to the process of moving people from a dangerous area to a safe area within a certain period. The study of regional evacuation involves the division of evacuation areas, the estimation of evacuation traffic needs, and the formulation of evacuation plans ,5,6. ComEmergency evacuation research first appeared in the 1960s in the form of proposing and discussing the concept and framework of emergency evacuation . Later, In this paper, the research on emergency evacuation path planning is based on the macromodel algorithm. A nonlinear model is established, and a polynomial time approximation algorithm is given, assuming no crossover between different paths and considering the nonlinear relationship between crowd density and evacuation speed. The main contributions of the paper are as follows. (1) We consider the evacuated people as a group and formulate the problem as an optimization model. (2) We assume no mutual influence between any two roads; the traffic conditions on one road do not affect those of another. The approximation algorithm based on network flow is provided to solve the model. (3) We theoretically analyze the complexity of the proposed algorithm, and simulation experiments prove the algorithm’s effectiveness.Macromodel research can study the model and algorithm of evacuation path planning. A good evacuation path planning model and algorithm can give a better evacuation planning scheme to effectively shorten the evacuation time. Hamacher  presenteV contains source point sources, endpoint sinks, and a medium point set. Every arc From the point of view of solving methods and algorithms of the macro evacuation model, it can be divided into a polynomial algorithm based on linear programming to solve the optimal evacuation scheme and various heuristic algorithms based on nonlinear programming ,13,14,15endpoint . Burkardendpoint  presenteendpoint  gave a pendpoint .In addition to the dynamic network flow method, many studies use classical network flow methods, such as the algorithm of the least short circuit, least cost flow, and maximum flow to solve the evacuation path optimization problem. Dunn and Newton  used theIn summary, most researchers describe the evacuation problem as a network flow graph The nonlinear programming of the evacuation problem mainly considers the nonlinear relationship between crowd density and evacuation speed. At present, there is no polynomial algorithm for solving the nonlinear programming of evacuation problems, only a variety of heuristic algorithms. Pursals  considerAs mentioned before, there are two types of methods for solving the evacuation problem in the literature. One is to model the problem as nonlinear programming and design a heuristic algorithm to solve it. The other is to model the problem as a network flow problem. The first type of method generally obtains an approximate solution, and the approximation ratio is not guaranteed. The advantage of the second method is that the evacuation problem is transformed into a classic network flow problem, and can be solved by using the mature polynomial network flow algorithm, which is convenient and effective. In this paper, we adopted the second method, and the nonlinear evacuation time with respect to the crowd density is considered in the model.The problem is how to transfer everyone that needs to be evacuated to designated shelters as soon as possible within the limited traffic network . There iM communities to N shelters, as shown in To sum up, this problem can be described as evacuating the population of i. j. i and shelter j. The sets I and the shelter set J, respectively. There is an edge connection between vertex i and shelter j.It is assumed that there is no mutual influence between any two roads; the traffic conditions on a road do not affect those of another. The problem can be described by bipartite graph t, vertex set When When I and J, the set of arcs whose time required for a single person i to j transfer to the network is less than the parameter t is incorporated into the network. That is, if In the arc between The network flow graph is constructed on the bipartite graph t; then, it constitutes a network flow graph with all parameters known. The maximum flow problem is a classical network flow problem. One may refer to Schrijver , T/2, and calculate the maximum flow under this time limit. Then, according to the calculation results, the binary search method is used to search step by step, and the optimal evacuation time is gradually reduced to a small temporal interval. When the length of the interval is less than a certain small number t with high precision, and correspondingly obtain a specific evacuation plan under the evacuation time t.When the problem is described as the network flow graph in chrijver  for furtt on the network flow graph as the decision variable and a sufficiently large constant T as the initial value. By searching for the optimal evacuation time An approximate algorithm for this problem is given for the network flow graph. It should be emphasized that the algorithm proposed below does not directly calculate the number of people allocated to each path to minimize the evacuation time, but takes the parameter Theorem 1.The accuracy of Algorithm 1 can be Algorithm 1: Binary search algorithm based on network flowProof of Theorem 1.k iterations is the global optimum. Assume that the time interval of the KTH iteration is Suppose that the evacuation time on each path is a convex function of the number of evacuees allocated on the path ; that isThus, the accuracy of Algorithm 1 is: Theorem 2.The complexity of Algorithm 1 is:Proof of Theorem 2. For each iteration in Algorithm 1, the length of the interval of The complexity of the labeling algorithm is n3+n4 , so the T, it is assumed that after k iterations of the algorithm, precision of parameter t can be achieved as Starting from the initial value k is:When the number of iterations n is the number of vertices on the directed graph G, the complexity of Algorithm 1 can be obtained as:As □In this paper, a nonlinear model is established, and a polynomial time approximation algorithm is given, assuming no crossover between different paths and considering the nonlinear relationship between crowd density and evacuation speed. The complexity and accuracy of the algorithm are proved by theory, and the method’s effectiveness is verified by an example. The classical evacuation model only needs to satisfy the capacity limitation of road and shelter, but the relationship between evacuation time and evacuation number is a nonlinear convex function . The innCompared to the existing network flow algorithm that generally can only solve the linear programming problem, we consider the nonlinear evacuation time with respect to the crowd density in the model, and first formulate the problem as a nonlinear network flow model. It is a binary search model based on the classical maximum flow algorithm  and the accuracy ratio is guaranteed to be within a pre-defined number . The existing methods in the literature either are unable to guarantee the accuracy ratio or are unable to deal with the nonlinear function in the model.Theoretically, this research proves the accuracy of the algorithm to be within any pre-defined small number in Theorem 1, and we also prove the complexity of the algorithm is polynomial in Theorem 2. These two theorems have shown the algorithm has high accuracy and polonomial computational complexity.Take the earthquake evacuation of the local community as an example. There are 16 buildings in this community; and there are three exits, namely, the north gate, the main entrance, and the south gate, as shown in There are seven open shelters on Financial Street, and the capacity of each shelter is shown in v is the crowd evacuation speed and 2. Formula (1) is converted into a functional relationship between time and crowd number:The functional relationship between evacuation speed and density adopts the functional relationship between evacuation speed and crowd density proposed by Pursals , as foll2 and 3.5 person/m2 to the destination, as shown in The inverse function of Algorithm 1 was simulated using Matlab software. The algorithm’s accuracy was set to be less than 0.05%, i.e., The total evacuation time and algorithm accuracy are shown in The results show that the accuracy of the optimal target value obtained by the algorithm reached 0.0005 over 13 iterative operations. The total evacuation time was around 24.92 min. The upper bound and lower bound in the 13th iteration had a gap of 0.041%. This indicates that the optimal evacuation time located in between the upper and lower bounds must be within 0.04% deviation from the optimal value, which is lower than the predefined accuracy level of 0.005. Finally, the network flow diagram obtained is shown in In this empirical study of the Fenghuiyuan community, we used Algorithm 1 and obtained the routing results in seconds. The accuracy of the obtained evacuation results reached 0.05%. The theoretical and practical results show that the algorithm has four advantages. Firstly, the algorithm is simple, intuitive, and easy to implement in programming languages. Secondly, an effective method for solving nonlinear evacuation problems is provided, with high precision, low complexity, and fast calculation speed. Thirdly, no matter how complex the specific nonlinear function relationship between the number of evacuated people and the evacuation time, as long as the function is invertible, the algorithm can be used to solve it. Therefore, the scope of application is wide. Fourthly, the precision is high, and precision of any preset value can be achieved.The results in This paper studied the nonlinear model construction of intelligent route planning in community evacuation. The nonlinear model reflects the nonlinear relationship between the evacuation time and the number of people evacuated; that is, as the number of people increases, the evacuation speed will slow down, and the evacuation time will increase. In order to solve the nonlinear model of evacuation route planning in the community evacuation problem, we proposed a binary search method based on the maximum flow algorithm within the network flow method to solve the nonlinear model. Finally, we empirically studied Fenghuiyuan community’s earthquake evacuation. Our proposed algorithm provides efficient and highly accurate results.In a nutshell, the algorithm designed in this paper provides an ingenious idea for solving evacuation problems, especially nonlinear evacuation problems. Avoiding starting from the problem itself, the algorithm starts indirectly, taking the evacuation time as the solution variable. By searching for the optimal evacuation time step by step, the maximum flow algorithm finds the number of evacuees allocated on each path under the determined evacuation time.However, the proposed algorithm has some limitations. It is currently only applicable for the situation where there is no intersection between the evacuation paths. For the situation where the roads intersect, the complexity of the model and algorithm will be increased. Therefore, in cases of more complex road conditions, the algorithm needs to be further expanded and further analyzed.


The introduction of the EU Unfair Terms in Consumer Contracts Directive in the legal system of Cyprus was the first instrument specifically dealing with the problems that arise with standard form contracts and the issue of consent. However, the Directive only generated caselaw approximately twenty years after its adoption, whereas the principle-based approach of the test for unfairness  was interpreted in the common law notion of absence of dishonesty. Hence, Cypriot courts interpreted good faith as “honesty in fact”. Under this interpretation, it seems that both procedural and substantive unfairness are not captured under the test. It is understood that whereas the statute codifying the contract law of Cyprus has incorporated the [civil law] will theory of contracts, no tools for the invalidation and scrutiny of terms that may be deemed unfair were provided. The statute placed considerable emphasis on procedural fairness, however, Cypriot courts seemed unwilling to adapt their approach and deal with the problems that standard form contracting poses, failing also to follow the developments in the UK. Thus, even after the adoption of EU consumer law directives, Cypriot courts show an unwillingness to scrutinize the parties’ initial allocation of risk, even though such allocation was done in a standardized manner by one party. Despite the mixed character of the legal system, consumer law directives and the introduction of content control can be seen as legal irritants. The most impactful EU legislative measure upon the common law of contract is the Directive on Unfair Terms in Consumer Contracts (Directive 93/13)4L’Estrange v Graucob, where it was held that where a document containing contractual terms was signed, then, in the absence of fraud, misrepresentation and non est factum, the party cannot claim that he or she has not read the document and is, therefore, bound by such terms.9Contract law in Cyprus is based on the common law principle that contracts are commonly formed by offer and acceptance. A principle underpinning contract law in Cyprus provides that where written agreements exist, those agreements are the basis to deduce and derive the intentions of the parties.This paper firstly introduces the legal system of Cyprus, presenting its unique nature as a mixed legal system in which common law and civil law contend for supremacy. Secondly, the paper proceeds with a brief analysis of contract law in Cyprus which is codified in the Contracts’ Law (Cap. 149), a transplant of the Indian Contract Act of 1872. The importance of the English common law in the development of the law of contract in Cyprus is mentioned, emphasizing the unwillingness, however, to follow the discussions in England and Wales as to the role of a duty of good faith in the common law of contract. A comparative analysis of the way content control of terms has been performed in the two jurisdictions, namely, England  and Cyprus is performed. It will be seen that a functional equivalent of the content control of standard form contracts found in the English common law is not to be found under Cyprus contract law. The paper presents the tension between European law, particularly Directive 93/13, and the common law of contract before examining the interpretation that the Cypriot courts have given to the requirement of good faith found within the directive and reaching conclusions as to the role of good faith (and interpretation of it) within the common law of contract regime in Cyprus.In order to have a better understanding of the greater context it is worth mentioning that the legal system of Cyprus is a mixed legal system that, as Symeon Symeonides correctly points out, owes the origin and survival of its “diverse elements […] to its troubled political history” Unlike other common law jurisdictions where more settled approaches to good faith can be seen Hogg, , Cyprus The impact of EU derivative law is just beginning to be felt in contractual practice and caselaw, mainly through Directive 93/13. Despite its early adoption, prior to accession, the Directive has only recently started to exert influence. Courts altered their approach in a minimal number of cases and scrutinized terms in consumer contracts. As Hatzimihail highlights, effective consumer protection is still in its early stages (c) of the Courts of Justice Law provides that the applicable law in Cyprus is the common law and the principles of equity;37The primary differences between the Indian Contract Act and the Contracts’ Law (Cap. 149) are technical: certain explanations were moved into the main text, illustrations have been removed and specific performance is provided for in Cyprus contract law .As a response to the failure to comply with the consumer protection directives, the legislature has passed a new statute for the consolidation, modernization and codification of consumer law in Cyprus, Law 112(I)/2021. Among its most important provisions is Article 63 establishing a private right of action, thus giving the consumer the right to file an action before a competent court for compensation and/or withdrawal from the contract and/or for reduction of the price. A rule of interpretation for all written terms is also adopted, providing that such written terms shall be formulated in a clear and intelligible manner and in case of doubt the meaning most favorable to the consumer shall prevail  v Kimonos (Κίµωνος),93The Unfair Contract Terms in Consumer Contracts Law (Law 93(I)/96) transposed the directive The interpretation of contractual terms by Cypriot courts is done with limited interference, allocating the risks based on the initial contractual stipulation following the four corners rule.95ex officio control of unfairness that is provided under the protective regime of the Directive, is more closely oriented towards the civil law understanding regarding the supervisory powers of courts. In a great number of cases before Cypriot courts, consumers did not specifically point out the exact terms of the contract that they deemed unfair, despite claiming such unfairness. The courts, however, in such scenarios could request further clarifications by the litigating parties, in order to perform their role under the Directive which requires courts to raise out of their own motion issues of unfairness of terms.96The limited interference of courts in the interpretation of written terms, even though such terms were written unilaterally, reflects the limited supervisory powers of the courts in the common law of contract in contrast to the civil law where a contract gives rise to obligation, the enforcement of which is out of the hands of the parties and into the supervisory powers of the courts de Moor . The ex non est factum.As mentioned above, Sect. 10 of the Contracts’ Law provides that all agreements are contracts if they are made by the free consent of the parties competent to contract for a lawful consideration and for a lawful object, but two or more persons are said to consent when they agree upon the same thing in the same sense (meeting of the wills).Lloyds Bank Ltd v Bundy.In particular, the undue influence defense was seen as potentially relevant to decide on the transaction’s unconscionability Tofaris, , howeverdictum by Lord Bingham in Director General of Fair Trading v First National Bank plc,dictum, however, Cypriot courts did not elaborate further to point out that this interpretation goes against the interpretation of good faith given by the Supreme Court of Cyprus as an absence of dishonesty.A number of Cypriot decisions referred to the Maria Nicolaou (Μαρία Νικολάου) v Ellinas Finance LTD,Lower courts have repeatedly held that if the signature on the agreement is not disputed, the consumers are estopped from raising an issue of unfair contract terms; an interpretation which is more in line with the common law of contract.Euroinvestment & Finance v Schiza (Σχίζα),I.S.G. Developers Limited, S. Yurmanov v Bank of Cyprus Public Company Ltd (Τράπεζας Κύπρου Δηµόσια Εταιρεία Λτδ),At the same time, Cypriot courts tend to examine the unfairness of the contractual term without regard to the status of the contractual party as a consumer or business. For example, in In cases before Cypriot courts, debtors have argued that the bank had an obligation to make sure that the borrowers received sufficient legal advice before signing the loan agreement or guarantee.121Section 73(3) of the Contracts Law has been utilized as a defense to compensate for the loss that came as a result of the bank not selling the shares under an investment project financing contract.non est factum (not my deed). The defense of non est factum can be utilized by persons whose objective inability to understand the purpose of the particular document they are signing is due to blindness, illiteracy or some other disability. However, in Saunders v Anglia Building Society,non est factum.125In the same vein, debtors use the defense of non est factum to succeed, reasonable care must have been exercised as to the circumstances that have led the person pleading to sign the particular document.The Cyprus Development Bank LTD v Krini Evangelou Kyriacou,Bank of Cyprus v Theophanous,non est factum; however, the court emphasized that in the facts of the case, the defendant knew that he was signing as a guarantor despite the fact that the document which he was signing was empty. Had he exercised reasonable care to ensure that the document was sufficiently completed before signing, he could have had a successful plea for non est factum. The non est factum defense is often accompanied by a claim of unfairness of contract terms under Directive 93/13. The courts examine the knowledge background of the person raising the defense in order to ascertain whether a contractual term is unfair.As a second precondition in order for a plea of In a recent judgment of first instance,133The District Court of Nicosia simply copies the text used by the Director for the Consumer Protection Service that states that the non-transparency of terms disturbs the contractual equilibrium in contravention of the principle of good faith. Be that as it may, this indicates the influence that sectorial regulators may have in the reception of continental interpretations of the good faith requirement of Directive 93/13. The Director for the Consumer Protection Service, in a number of decisions, has used jurisprudence from Greece and Germany in interpreting Directive 93/13.non est factum and/or misrepresentation  only when the element of consent to it is totally lacking.The principle-based approach found in Directive 93/13 as well as the caselaw of the CJEU reflect an understanding which is closely aligned to the continental handling of standard form contracting. Although it could undoubtedly be argued that the EU conception of fairness in contracts is highly instrumental de Moor  it is clThus, the absence of similar statutory developments meant that judicial discretion in contractual matters was limited, with the courts having little interest in interfering in the terms of the contract. This has resulted in a discomfort by the courts about the power to interfere in such terms conferred on them under EU law. However, interpreting the terms of the contract via Directive 93/13 has become the cornerstone of consumer policy in the Union. With the increased focus on ensuring the effectiveness of Directive 93/13 as well as Directive 2005/29 on unfair commercial practices, it is expected that the approach of the courts will change, something that has gradually started to take place.


The Covid‐19 pandemic posed new issues about vaccination and contagious diseases that had not been the focus of public policy debate in the United States since the tuberculosis pandemic of the late 19th century and the early 20th century. Using a national address‐based probability sample of American adults in 2020 and a structural equation model, this analysis seeks to understand the role of education, age, gender, race, education, partisanship, religious fundamentalism, biological literacy, and understanding of the coronavirus to predict individual intention concerning taking the Covid‐19 vaccine. Given the substantial changes in the United States since the tuberculosis pandemic, it is important to understand the factors that drive acceptance and hesitancy about Covid‐19 vaccination. We find that education, biological literacy, and understanding of the coronavirus were strong positive predictors of willingness to be vaccinated and religious fundamentalism and conservative partisanship were strong negative predictors of intent to vaccinate. These results should be encouraging to the scientific community. ACMAssociation for Computing MachineryCHIComputer‐Human InteractionCFAconfirmatory factor analysisICPSRInter‐university Consortium for Political ResearchLISRELlinear structural relationsSEMstructural equation modelTEtotal effect1The Covid‐19 pandemic was the most serious public health crisis in the lifetime of most American adults. Although effective vaccines were developed and made available about 12 months after the onset of the pandemic, a significant portion of American adults declined or resisted vaccination. It is important to understand the factors that are associated with vaccine acceptance, resistance, or hesitancy.The Covid‐19 pandemic differed in several ways from previous pandemics. In the 18th and 19th centuries, tuberculosis killed approximately one in seven adults and the cause of the disease was not known. Early in the 20th century, scientists discovered that tuberculosis was caused by a bacterium, but it was not until the development of effective antibiotics during and after the Second World War that widespread treatment became possible. In recent decades, a new antibiotic‐resistant strain of tuberculosis developed and the World Health Organization had made its control one of their top priorities. For most of the years prior to the development of effective pharmaceutical treatments, tuberculosis patients were sent to sanatoriums, often against their will, to prevent the spread of tuberculosis.The polio pandemic in the 1940’s and 1950’s in the United States followed a similar pattern. The cause of polio was unknown for several years. President Franklin Roosevelt had polio as a young man and was crippled for the remainder of his life. President Roosevelt and other concerned citizens and leaders created a national organization – the March of Dimes – to collect small gifts from children and adults to be used to find the cause and a cure of polio. Given this history of national concern and the unknown cause of the disease, the discovery of a vaccine by Jonas Salk in 1955 was a source of national relief. President Eisenhower and Elvis Pressley were vaccinated publicly and there was a strong demand for polio vaccinations by adults for themselves and for their children. There was no partisan resistance to the polio vaccine.In the context of the previous experience of Americans with contagious and deadly diseases, the partisan polarization of attitudes toward Covid‐19 and Covid‐19 vaccinations is unusual and requires some explanation. The purpose of this analysis is to utilize a pair of national surveys of a probability‐sample of American adults to identify, measure, and analyze the factors associated with a positive intent to be vaccinated against Covid‐19 and a hesitancy toward or rejection of a Covid‐19 vaccination.22.1This analysis will utilize data from a national two‐wave probability sample of American adults selected and administered by Ameri‐Speak, a service of the National Opinion Research Center. An initial survey was collected in February and March of 2020, near the onset of the Covid‐19 pandemic. A second wave was collected from the same respondents in November and December of 2020 – a year into the pandemic. A total of 3141 completions were obtained in the first wave and 2737 of the same respondents were obtained in the second cycle – a retention rate of 87.1%. Respondents in both waves were offered the choice of an online survey or a telephone survey and were free to select the method most comfortable to each individual. The data from these surveys have been deposited in the Inter‐university Consortium for Political and Social Research (ICPSR) and are being processed for public use.2.2Our measure of each respondent's attitude toward Covid‐19 vaccination is based on a question asking each respondent:definitely take itprobably take ittake it only if required for my job or by lawrefuse to take itnot sure what I would doIf a tested and effective vaccine were to become available, would you:vaccination intent.These responses were recoded into a five‐category ordinal variable: 1) Refuse, (2) Only if required, (3) Not sure, (4) Probably, or (5) Definitely. Using a national address‐based probability sample, 49% of American adults indicated in November and December 2020 that they would definitely or probably seek a Covid‐19 vaccination as soon as a safe and effective vaccine became available  in each of 19 countries,Even though 59% of European respondents did not expect the availability of a vaccine by the end of the year, 74% of Europeans indicated in September 2020 that they would take the Covid‐19 vaccination if it were available. Significantly lower values were noted for France, Russia, Hungary, and Poland.It is useful to recall that the Pfizer and Moderna Covid‐19 vaccines were developed during 2020 and that clinical trials were completed just before the end of calendar 2020. The Food and Drug Administration gave the two vaccines an Emergency Use Authorization in the U.S. in mid‐December 2020. The second wave of our 2020 survey was conducted in November and December of 2020 with a small number of completions collected in January and early February 2021. Our question about the willingness of respondents to take a Covid‐19 vaccine asked about respondents’ willingness to take a “tested and effective vaccine” when it became available without specifying a date. This measure is a good indicator of the predisposition to take a Covid‐19 vaccine apart from any subsequent discussions about the efficacy of any specific vaccine.33.1We begin with a review of three exogenous variables acquired at birth: age, race, and gender.Older respondents were significantly more likely to express a definite or probable willingness to be vaccinated for Covid‐19 than younger adults  to determine the relative influence of each variable, taking into account the chronological and logical relationships among the predictor variables.Data about European countries shows that a higher proportion of men were willing to get vaccinated than women, and it is largest among men above the age of 55. Males who were unwilling to get vaccinated tended to be younger with the largest share of 12% among the 18–24‐year old.3.2A second important set of predictors of a predisposition in favor of vaccination for Covid‐19 involves each respondent's education, general biological literacy, and level of understanding of viruses generally and the coronavirus specifically. There is a large literature demonstrating that when complex science policy issues become the subject of politicized debate, the level of education and understanding become important tools to help a citizen make sense of discussions and debates involving those issues.Our 2020 surveys found that the level of educational attainment was positively related to a receptive attitude toward vaccination for Covid‐19  found to constitute a unidimensional scale. The CFA factor score was converted into a 0‐to‐100 index. A dichotomous version of this index  indicates that it is a very strong predictor of a positive predisposition toward vaccination against the coronavirus, accounting for 54% of the variation in vaccination attitude  using LISREL.The variables are arranged from left to right in an approximate chronological or logical order and influence is presumed to flow from left to right. When two or more variables occur or operate simultaneously, they are placed in the same column, giving them a common left to right location. If one variable is correlated or associated with another variable at a significant level, the two variables are connected with by a path. If two variables are not significantly correlated or associated, the two variables are not connected by a path. Each path has an arrow head on one end, indicating the direction that influence is presumed to flow.The strength of the relationship between two related variables is indicated by a path coefficient. Path coefficients vary from −1.0 to +1.0 and may be thought of as a partial correlation coefficient. These path coefficients are interesting and numerous in a large model, but we want to know analytically how much total influence each independent variable has on our outcome variable. To estimate the total effect of each variable in the model on the outcome variable, we can multiply all of the coefficients in each pathway from a given independent variable to our outcome variable and sum all of the paths that connect the two variables.An example may be helpful. If we want to estimate the total effect of coronavirus understanding on vaccination attitude, we can calculate the total effect attributable to the path from CVKnow to TrustExperts to CVVaxAttitude 0.65 × 0.14 = 0.091). There is a second direct  path from CVKnow to CVVaxAttitude (0.33). This residual path reflects the amount of adjustment needed to reflect the known relationship between CVKnow and CVVaxAttitude. The sum of the two paths is 0.42, which is the total effect shown in the table of total effects in Figure 4 = 0.091For analytic purposes, we want to know the total effects (TE) of each of the independent variables in the model. An examination of the total effects table indicates that coronavirus understanding is the strongest single predictor of vaccination attitude (TE = 0.42). Biological literacy is the second strongest predictor (TE = 0.32). Exposure to college science courses (TE = 0.27), the level of educational attainment (TE = 0.22), respondent age (TE = −0.21), and ideological partisanship (TE = 0.21) are moderately strong predictors of a positive attitude toward taking a Covid‐19 vaccine. Religious fundamentalism (TE = −0.17) and female gender (TE = −0.18) had a negative influence on attitude toward Covid‐19 vaccination. It appears that education, biological literacy, and coronavirus understanding are the primary drivers of a positive attitude toward Covid‐19 vaccination.γ = 0.18), our SEM indicates that the frequency of Covid‐19 information acquisition did not have a significant marginal influence on vaccination attitudes once the preceding independent variables were taken into account. Similarly, neither the level of trust in broadcast news nor the level of trust in online and social media sources has a significant marginal influence of vaccination attitude once the preceding independent variables are taken into account. The level of trust in expertise did have a marginal positive influence on vaccination attitude (TE = 0.14), indicating that trust in experts was more than a reflection of age, education, biological literacy, and other variables formed earlier in life.The model provides some useful insights into the relationship between the several independent variables in our model. Although the bivariate relationship between the amount of Covid‐related information sought and acquired displayed a modest positive relationship . Religious fundamentalism in strongly related to identification as a Conservative Republican (TE = 0.45). Although the structure of these relationships is complex, it is a good empirical description of the current structure of these factors.Looking at the full landscape of relevant factors over the life course, our model describes a complex network of life course influences that predict individual intent to take the Covid‐19 vaccine. Education and biological literacy are important baseline influences and will become even stronger influences in the decades ahead. The uniquely American requirement of a full year of science courses during a baccalaureate program in the United States provides a critically important exposure to college science courses, which fosters both biological literacy during the adult years and provides the tools to acquire and utilize current information from traditional media and online sources – more often websites than social media – to enhance an individual's understanding of an emerging public policy issue like the coronavirus pandemic. It is not a simple system, but it appears to work reasonably well.These results should be encouraging to the scientific community. Apart from our research, many of us engage in extensive efforts to improve the biological literacy of undergraduates and graduate students. Some scientists engage in public outreach efforts formally or informally. Our finding that a substantial proportion of American adults value expertise and utilize it in making personal and public policy judgments indicates that these efforts have produced useful changes in American society and politics. The importance of coronavirus understanding in making a vaccination decision is even stronger evidence of the short‐term influence of expertise. Few American adults would have heard of a coronavirus as an undergraduate and it was almost non‐existent in media prior to the onset of the pandemic. The acquisition of information about the coronavirus and Covid‐19 had to occur in the year prior to our interviews and surveys, indicating that respondents with a high score on the Index of Coronavirus Understanding would have had to acquire almost all of that information and make sense of it with the first year of the pandemic. This kind of learning would not be possible with some prior experience in college science courses – especially biological science courses – and some level of prior interest in understanding science and technology. Collectively, these results indicate that our substantial and continuing investment in scientific and biological education pays dividends in critical situations.jondmiller@umich.edu. Mark S. Ackerman is a Professor jointly appointed in the School of Information and the Department of Electrical Engineering and Computer Science in the College of Engineering at the University of Michigan, Ann Arbor. He is also the GH Mead Collegiate Professor of Human‐Computer Interaction. Mark is a member of the CHI Academy (HCI fellow) and an ACM Fellow. He publishes widely in collaborative information access, misinformation, and health information from a socio‐technical perspective. Email: ackerm@umich.edu. Belén Laspra Pérez is Assistant Professor of Logic and Philosophy of Science at the Department of Philosophy at the University of Oviedo (Spain). Her current research interests are in scientific literacy, culture of science, and public understanding of science. Email: lasprabelen@uniovi.es. Carmelo Polino is an Assistant Professor in the Department of Philosophy at the University of Oviedo (Spain), and a researcher at Centro Redes . He holds a PhD in Social Studies of Science, and his main research interests are public understanding of science, STS studies, philosophy of science, and sociology of science communication. Email: polinocarmelo@uniovi.es. Jordan Huffaker is a PhD student in Computer Science and Engineering at the University of Michigan, Ann Arbor. His area of research is social computing. Email: jhuffak@umich.edu.Jon D. Miller is Director of the International Center for the Advancement of Scientific Literacy in the Institute for Social Research at the University of Michigan and is a Research Scientist Emeritus. He is a political scientist who has studied the development and use of scientific literacy because of its critical role in the functioning of democratic societies in the 21st century. He is a fellow of the American Association for the Advancement of Science. Email: The authors report that there are no competing interests to declare.


Alligator mississippiensis, and to explore the functional bases of coordinated movements between the lower earflap and lower eyelid in this species. This anatomical system was examined using a combination of fresh dissection, histology, and micro‐CT analyses applied to post‐embryonic specimens. The rostral margin of the lower earflap is tightly bound to a block of dense connective tissue herein termed the orbitalauricular chord. The orbitalauricular chord is anatomically distinct from both a ligament and a tendon. The dorsal surface of the orbitalauricular chord is attached to a slip of the levator palpebra, while the ventral surface is attached to a slip of the depressor palpebra. These attachments produce a simple mechanism for the elevation and depression of the lower earflap, and thus the opening and closing of the meatal aperture. The caudal surface of the orbitalauricular chord has connective tissue links to the rostral margin of the lower earflap. The morphology of the orbitalauricular chord appears to explain both the mechanics of the lower earflap and the functional coupling between the lower eyelid and lower earflap.One of the distinctive features of the Crocodylia is the presence of a superficial meatal chamber the aperture of which is regulated by two earflaps. The movements of the upper earflap have been detailed by multiple workers, however, the mechanics of the lower earflap remain unresolved. The present study was undertaken to document the mechanics of the lower earflap in the American alligator,  The orbitalauricular chord is a specialized segment of dense irregular connective tissue that functionally links the lower eyelid and lower earflaps of the American alligator (Alligator mississippiensis). For reasons detailed below, hereafter the structure dubbed “Ypsilon” by Shute and Bellairs  , three were juveniles , two were sub‐adults , and three were adults . The specimens were either purchased commercially or obtained through the courtesy of the Louisiana Department of Wildlife and Fisheries. These specimens were all used for a study on spinal and vertebral morphometrics in Alligator  or a dissecting microscope (Leica M80) using the IC80HD digital camera (Leica).The heads of the nbf‐preserved specimens were transferred to 70% ethanol for storage. Each specimen was placed in RDO Rapid Decalcifier for 24–48 h, then dehydrated through an ethanol series prior to paraffin embedding. Complete serial transverse, sagittal, and frontal sections were cut (at 10 μm) through the region of the orbitalauricular chord. Sections were stained with Hematoxylin and Eosin, Masson's trichrome stain, Phosphotungstic Acid Hematoxylin (PTAH) stain, and Picrosirius Red. Microscopic anatomy was documented using a DM 4000B microscope (Leica Microsystems Inc.).The head of one of the juvenile specimens was pre‐treated in Lugol's solution and then scanned at the University of Texas High‐Resolution X‐ray CT Facility using a custom‐built North Star Imaging scanner in volume mode. The X‐ray source was set to 130 kV and 0.14 mA with an aluminum foil pre‐filter. A total of 3600 projections were acquired over 360 degrees of rotation, at 1 frame per second with no frame averaging and no detector binning. A beam‐hardening correction of 0.25 was applied; the resulting slices measured 1979x1979 pixels and had a voxel resolution of 9.65 microns. The resulting DICOM images were examined, and a 3‐D reconstruction was performed, using Dragonfly (Object Research Systems).33.1Alligator mississippiensis has three mobile eyelids; an upper eyelid , a lower eyelid, and an internal eyelid (nictitating membrane) which retracts into the rostral‐ventral portion of the orbit  jugal bone, the dorsal  frontal bone, and the nearly vertical postorbital bone that fuses to the frontal and jugal  as it courses ventrally. The dorsal portion of the Oc is nearly stellate Figure ; a caudaThe Oc is composed of dense irregular connective tissue. The surface of the Oc can be indistinct at times, given the integration with surrounding tissue . The surrounding loose connective tissue frequently abutted the surface of the Oc in a way that suggested possible adherence Figure . Larger 3.3The orbitalauricular chord is located in an anatomical space defined rostrally by the caudal and inferior surfaces of the eye, and caudally by the postorbital bone and the rostral surface of the jaw adductors Figure . The ven3.4Dorsally the Oc has two well‐developed attachments. The dorsocaudal surface of the Oc is bound to the rostral margin of the lower earflap Figures , 7b, 8, 3.5Alligator mississippiensis, and perhaps all crocodylians, the reflex elevation of the lower eyelid is linked with the elevation of the lower earflap  found, as the present study did, that the “medial arm” described by Shute and Bellairs   was not Shute and Bellairs   postulatThe present study used the term “chord” to refer to this mass of dense irregular connective tissue. The term “ligament” seems a poor choice since these collagen fibers neither interconnect two bones, span a joint, nor show a common orientation Figures  and 5. ANone of the sections cut through the Oc, whether from hatchling or adult specimens, had chondrocytes or any evidence of chondrification or ossification. Most of the connections with the Oc involved dense regular connective tissue; essentially the same tissue and tissue density, just a different organization. This proved to be problematic in that while the micro‐CT images generated as part of this study could distinguish the Oc from the adjacent postorbital process, they were not adequate to resolve the precise borders of the Oc (see Figure A. mississippiensis (Lessner & Holliday, Though not the focus of the present contribution, it is interesting to speculate on the evolutionary origin of the Oc. The meatal chamber, and the associated earflaps, appear to be a regular feature of Crocodyliforms (Montefeltro et al., BAY designed this study and drafted the original version of the manuscript. All of the authors participated in the anatomical analysis and assisted in the editing/preparation of the final manuscript.The authors declare that they have no conflicts of interest.Video S1Click here for additional data file.Video S2Click here for additional data file.


In this paper, a novel planar and wideband metal-only retroreflector is proposed that efficiently reflects the obliquely incident electromagnetic wave along its incident direction in omnidirectional angle range. The means of omnidirectional is the capability of retroreflectivity in all azimuth angles  The retroreflector can be used in two major fields; civil and military. In civil field, this can be used for navigation safety (aviation and marine), RF identification (RFID), satellite communication, and automotive collision avoidance. The mechanism of navigation safety is that in response to a signal from a friendly interrogating unit, it is desirable that the reflected wave is scattered monostatically back to the interrogator at a specified frequency corresponding to the target. Since the target is moving, the angular direction of the signal entering the target is variable, and so the retroreflector structure must operate in a wide angular range and at a certain frequency. RFID refers to a wireless system comprised of two components: tags and readers. The reader is a device that has one or more antennas that emits electromagnetic interrogation signals and receives identifying signals back from the tags attached to objects. Thus the tag must be a retroreflector structure and since tagged objects can be placed in different positions relative to the reader, the tag structure needs to be a retroreflector with a wide angular range. In addition, since the identifying signals are different digital data, the tag needs to have wide frequency bandwidth as well. In satellite communication, retroreflector structures are placed on satellites and used as a transponder, similar to navigation safety applications. In automotive collision avoidance systems, a signal is sent from one automotive to the surroundings, and if there are other automobiles around it, it is desirable that the reflected wave from the surrounding automobiles is scattered monostatically back to the main automotive. In this application also since the automobiles are moving, the angular direction of the signal entering the surrounding automobiles is variable, and so the retroreflector structure must operate in a wide angular range and at a certain frequency.A retroreflector is a device that reflects light along its incident direction over a continuous range of incident anglesIn military field, the retroreflector structures can be used for stealth and deception applications. In the field of stealth applications, sometimes there are small vehicles that have a small RCS and it is desirable that it can be detected by friendly radars but not by hostile radars. In these cases, it is desirable to use frequency-limited retroreflector structures mounted on small vehicles. Then the target will be detectable within the frequency range of a friendly radar while at other frequencies appears invisible. In this case, also, since the small vehicle can be moving, the radiated electromagnetic wave by the radar impinges on the target from different angles, and therefore requires a retroreflector structure with wide angular range and at a certain frequency. In deception applications, high RCS fake objects are required to be easily detected as targets by hostile radars. These fake objects are called decoys. Because the radiated wave by hostile radars can impinge on the decoys from different angular directions, in this case also retroreflector structures with wide angular range are needed.2. In addition, in some applications (such as RFID) a wide frequency bandwidth is also needed.In these applications, the general characteristics which are preferred for the retroreflector would be the ability for a wide-angle of incidence, the handling of both TE- and TM-polarized waves, high efficiency, low-profile, lightweight, low loss, low cost, and fabrication simplicity3 in 1927 and was used in advertising signs and then road marking4. The invented structure comprised of a plano-convex lens and a concave reflector arranged behind the plane rear surface of the lens. The mechanism is that the convex lens converges the incident beam onto the concave reflector and the reflector bounces the beam back along the incident direction. The first detailed study for cat’s eye retroreflectors was done by Beer and Marjaniemi in 1966, which was about wavefront error and construction tolerances5. Then the first analysis of the cat’s eye retroreflector was done by Snyder in 1975 using the paraxial ray matrix approach6. Finally, in 2017, Arbabi et al. proposed1 a planar near-infrared cat’s eye retroreflector composed of two layers of silicon nanoposts with a normal incidence efficiency of 78% and a large half-power field of view of 60° (± 30°).To the best of our knowledge, the first structure with retroreflectivity property was cat’s eye in the optics domain that was invented by Murray7 in 1943. A corner reflector consisting of two or three electrically conductive surfaces which are mounted crosswise (at an angle of exactly 90 degrees) and causes the incoming electromagnetic waves are backscattered by multiple reflections accurately in that direction from which they come. Theoretical and experimental works show that the corner reflector provides half-power retroreflection in the range of ± 20°9. The main disadvantage of the corner reflector is that the structure is large and takes up a lot of space.Historically, the next retroreflector structure is corner reflector that was proposed by Spencer and Duboc10 in 1944, a retroreflector structure using the Luneburg lens was invited by Kelleher11 in 1958 in which a Luneburg lens is partially covered by a metalized cap. This structure can facilitate half-power retroreflection across a wide angular range of about ± 50°9. However, it is limited by its large size, heavy weight, and relatively expensive fabrication.With the advent and development of dielectric lenses such as Luneburg lens introduced by Luneburg12. It consists of pairs of antenna elements equally spaced from the array center with equal-length or multiple wavelength difference transmission lines. The arrangement of the array causes a reversal of this phase progression for the outgoing signal, causing it to retro-reflect back in the same direction. With the advent of microstrips and striplines, the planar Van Atta array retroreflectors also were established that a wide angular bandwidth of over ± 30° half-power retroreflection has also been demonstrated13. However, the Van Atta structure has a few drawbacks, such as the transmission line network used has losses, which degrade the efficiency of the overall structure; and the transmission line network structure becomes very complex as the array size increases. This makes Van Atta array impractical for aperture lengths of several wavelengths and beyond.The next retroreflector structure is Van Atta array that was invented in 1959 by Van Atta14. In this paper, a novel planar, metal-only, and wideband retroreflector with omnidirectional angular range in microwave frequency is designed. The proposed structure is inspired by the theory of cat's eye retroreflector, which is implemented using transmitarray structures. The transmitarray structure is designed based on the generalized multifocal beam scanning approach in such a way that it focuses the incident wave with different incident angles on a flat plane and the direction of focused waves is almost perpendicular to the flat plane. In this case, by placing a metal plate which coincides with this focused beam plane, the whole structure behaves as an effective planar retroreflector with wide-angle operation range.Due to the applications of the retroreflector mentioned at the beginning of this section, the need for a flat, low-cost, and wideband retroreflector in the microwave frequency range with a wide continuous angular range is strongly felt. To the best of our knowledge, only one retroreflector in microwave domain with non-planar overall structure is presented, which has 3 dB RCS level for the incident angles from − 30° to 30° at 10 GHz and only for TM polarizationThe structure of the lens is designed to concentrate the incident wave with different incident angles to different locations but on a flat surface, and the reflective structure is a spatially varying phase gradient metasurface, which is placed in the location of the focal plane and is designed in such a way that the focused waves reflect back along the direction of focus. The illustration of this type of planar cat’s eye retroreflector is shown in Fig. The structure of the lens is designed to concentrate the incident wave with different incident angles on a flat surface so that the direction of the focused waves is approximately perpendicular to the focal plane and a flat metal plate is placed in the location of the focal plane. The illustration of this type of planar cat’s eye retroreflector is shown in Fig. The basic theory that this work inspired by it is the theory of cat’s eye retroreflectors. A conventional cat’s eye retroreflector is shown in Fig. 15. An approach17 is proposed for beam scanning called multifocal approach with feed displacement that the quadrufocal case is shown in Fig. xz-plane goes from focal point 1 to focal point 2, the beam moves from mode A to mode B and it focuses quite well nearby and between the two focal points16. The same apply to the two focal points in the yz-plane. Therefore, according to the reciprocity theorem, planar waves that propagate to the transmitarray antenna at angles In this paper, the second method is followed. The lens structure in cat’s eye retroreflector is implemented with transmitarray structures. Transmitarray antennas are typically composed of one or several focal sources illuminating a planar arrangement of sub-wavelength phase-shifting unit cells designed to define a predetermined phase distribution across the aperture and therefore a predetermined radiation characteristic in far-field or near-field18 a wideband metal-only unit cell is proposed that is composed of a square ring within which there are two sets of parallel stubs in front of each other. The square ring and parallel stubs create a notch at zero and a controllable frequency, respectively. Therefore a passband with low slope phase shift response between these two notches is created which leads to a wideband transmitarray. But this unit cell has single linear polarization that makes it unable to support both TE and TM polarizations. Here this unit cell is modified so that four similar stubs are placed within all four sides of the square ring as shown in Fig. 19, a unit cell of four identical layers, separated by quarter-wavelength air gaps, can achieve a full transmission phase range of 360° for transmission magnitudes equal to or better than − 1 dB.The first step in the design of a transmitarray structure is to select the appropriate unit cell. By changing one parameter of the unit cell over a wide frequency band, the transmission magnitude should remain close to 0 dB and the transmission phase should cover from 0 to The optimal values of the fixed geometrical parameters are presented in Table The diagram of the transmission magnitude and phase shift of the unit cell versus different values of 21 in which x- and y-boundaries were set to “unit cell” to model an infinite array of that unit cell. In this case, the mutual coupling between unit cells is also included in the simulation results. At the z-boundaries, two floquet ports are set up on both sides of the unit cell and the first two floquet modes that their polarizations are along the y-axis (TE(0.0)) and the x-axis ) are excited. It is usually assumed that these floquet modes are normally incident on all elements. But in retroreflector structures, the elements are also illuminated by oblique incidence angles. Thus, it is worthy to present the behavior of the proposed unit cell under oblique incidence. Figure The results shown in Fig. 16:mnth element, mnth element, and BDF = 0.9009 are usually considered17.The second step in the design of a transmitarray structure is to determine the phase of the elements. As mentioned in the previous section, the phase of the elements is obtained based on the multi-focal approach. It is well known that the elements phase in reflectarray and transmitarray antennas depending on the location of the feed and the direction of the scanned beam is obtained using the following equationentclass1pt{minimaTo have retroreflectivity in all azimuth directions entclass1pt{minimaP is the periodicity of the unit cell.To maintain the overall symmetry of the structure with respect to the azimuth angle, the overall shape of the transmitarray structure is considered as a circle. Here the diameter of the circle is selected 21 full-wave software using the unit cell mentioned in Fig. The structure of the transmitarray simulated in CST STUDIOF/D value. This parameter affects the spatial coordinate of focused spots. Therefore, first, the effect of changing this parameter on the focused spot locations for different incident angles is investigated. To do this, for four values of z value.The last step in the design of a transmitarray structure is to select the appropriate F/D, the focused beam angle, as well as the amplitude of the electric field at the focused spots, are obtained for different incident angles and for different values of F/D. The first one is done by placing a circular metal strip beneath the transmitarray structure at the focused spot location for a specific incident angle. By changing the slope of this metal strip, the angle for which the maximum monostatic RCS is obtained is extracted, which is equal to the angle of focused waves for a certain incident angle. The amplitude of the electric field at the focused spots indicates the ability of the transmitarray structure to concentrate the beam and is obtained by simulating the transmitarray structure alone in CST STUDIO21. The values of angle F/D values, are given in Table F/D, the smaller the focused waves angle relative to the vertical axis for different incident angles, but also the smaller the amplitude of the electric field at the focused spots for different incident angles.Now to more accurately determine the value of z-axis and the minimum amplitude of the electric field at the focused spots. Therefore, according to Fig. F/D is selected 0.3. The electric field distribution on x–z plane for the designed transmitarray structure with F/D = 0.3 which is illuminated by a plane wave with different incident angles is shown in Fig. From the above discussions, it is concluded that there should be a compromise between the range of changes of the focused spot location along 21 is shown in Fig. 20, a quantity is presented to measure the RCS enhancement of a retroreflector. This quantity called The proposed retroreflector structure that is simulated in CST softwareTo verify the omnidirectional property of the proposed retroreflector, the simulation results of the monostatic RCS diagram versus elevation incident angle for five different azimuth angles at frequency 9 GHz and for TE polarization are drawn in Fig. The 3D scattering pattern for the designed retroreflector structure which is illuminated by a plane wave with different incident angles, is shown in Fig. To validate the proposed retroreflector with simulation results, one prototype is fabricated as shown in Fig. 14 is illustrated in Table To better determine the characteristics of our work, a comparison between our work and referenceIn this paper, a novel planar and wideband metal-only retroreflector was proposed that covers omnidirectional incident angle range. The proposed structure is inspired by the theory of cat's eye retroreflector in which a symmetrical transmitarray structure with beam scanning capability act as a concave lens and a metal plate act as a mirror. The transmitarray structure is designed based on the generalized multifocal beam scanning approach in such a way that it focuses the incident wave with different incident angles on a flat plane and the direction of focused waves is almost perpendicular to the flat plane. In this case, by placing a metal plate which coincides with this focused beam plane, the whole structure behaves as an effective planar retroreflector with wide-angle operation range. One prototype of the proposed retroreflector was fabricated and tested. The results of measurement show an omnidirectional retroreflectivity with half-power (3-dB RCS level) elevation field of view of 60° (− 30° to 30°) in the frequency range of 8.5–10 GHz (approximately 17%) for both TE and TM polarization.