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The Naming Game (NG) describes the emergence of conventions and shared lexicons in a population of agents interacting in a pairwise fashion. In this work, we introduce a new yet simple speakers’ rule into a minimal Naming Game where the speaker is more likely to choose the successful word in her earlier history and to convey it to the hearer. We find that the convergence time decreases with the increasing weight of successful words, which indicates that preferential selection of successful words may accelerate the reaching of consensus.

Vapour–liquid equilibrium (VLE) data were measured for the ternary mixtures of water (1) + 2-propanol (2) + 1-butyl-3-methylimidazolium acetate ([bmim][OAc]) (3). Complete T, x and y data were obtained in a relatively wide range of ionic liquid (IL) mass fractions up to 0.8. The data were correlated by means of NRTL and eNRTL equations with satisfactory results. Using the eNRTL equation, the ternary VLE behaviour was also modelled through correlation of two data sets, in which the mole fraction of 2-propanol on IL-free basis is respectively at 0.1 and 0.98. In this way, the six data sets were reproduced satisfactorily, with root mean square deviations of 1.06 K for temperature and 0.0098 for vapour-phase mole fractions. Owing to the regular distribution of the experimental data, good agreement between experiment and calculation was graphically presented. Effect of the IL on the VLE behaviour of the volatile components was also illustrated.

An more reliable human upper respiratory tract model that consisted of an oropharynx and four generations of asymmetric tracheo-bronchial (TB) airways has been constructed to investigate the micro-particle deposition pattern and mass distribution in five lobes under steady inspiratory condition in former work by Huang and Zhang (2011) . In the present work, transient airflow patterns and particle deposition during both inspiratory and expiratory processes were numerically simulated in the realistic human upper respiratory tract model with 14 cartilaginous rings (CRs) in the tracheal tube. The present model was validated under steady inspiratory flow rates by comparing current results with the theoretical models and published experimental data. The transient deposition fraction was found to strongly depend on breathing flow rate and particle diameter but slightly on turbulence intensity. Particles were mainly distributed in the high axial speed zones and traveled basically following the secondary flow. “Hot spots” of deposition were found in the lower portion of mouth cavity and posterior wall of pharynx/larynx during inspiration, but transferred to upper portion of mouth and interior wall of pharynx/larynx during expiration. The deposition fraction in the trachea during expiration was found to be much higher than that during inspiration because of the stronger secondary flow.

A representative human upper respiratory tract (URT) with idealized oral region and asymmetric tracheobronchial (TB) airway has been modeled, and laminar-to-turbulent airflow for typical inhalation modes as well as micro-particle transport and deposition has been simulated using CFX10.0 software from Ansys Inc. on a personal computer. The asymmetric TB airway could not be replaced by an extended straight tube as outlet of the oral region while investigating the tracheal airflow field and particle deposition. Compared to an idealized oral airway with an extended straight tube, several differences could be noted: (i) The laryngeal jet extends further down the trachea and inclines towards the anterior wall; (ii) the turbulence level in trachea is less and decays more quickly; (iii) three recirculation zones are visible with intense adverse current after the glottis; (iv) deposition of small particles in trachea is reduced due to lower turbulence. Refined unstructured mesh with densified boundary layer mesh could be a proper substitute for the structured mesh in the human URT model with asymmetric TB airway. Based on the refined unstructured mesh, the physiological structure of uvula in the soft palate is properly simulated in the present human URT model.

A Green function-based analytic solution of pressure diffusive wave motion is introduced for investigating the transient pressure response in fluid saturated matrix-fracture media. One-dimensional solutions are presented for a time-harmonically forced problem with internal damping and are used to analyze the propagation and attenuation of pressure pulse in a semi-infinite spatial domain. The concise form of the solutions simplifies the calculation of pressure diffusion with arbitrary forcing functions at fixed boundaries. It indicates that the periodically forced function with internal damping has remarkable effects on pressure diffusion-wave motions. It is found that the characteristic delay-frequency separates the pressure diffusion-wave domain into matrix-dominated, transition, and fracture-dominated zones. The Green functions could physically predict any transient response of pressure fluctuations due to hydro-fracturing in geological reservoirs given proper physical parameters.

It is one of the fundamental problems in biology and social sciences how to maintain high levels of cooperation among selfish individuals. Theorists present an effective mechanism promoting cooperation by allowing for voluntary participation in public goods games. But Nash's theory predicts that no one can do better or worse than loners (players unwilling to join the public goods game) in the long run, and that the frequency of participants is independent of loners' payoff. In this paper, we introduce a degree of rationality and investigate the model by means of an approximate best response dynamics. Our research shows that the payoffs of the loners have a significant effect in anonymous voluntary public goods games by this introduction and that the dynamics will drive the system to a fixed point, which is different from the Nash equilibrium. In addition, we also qualitatively explain the existing experimental results.

It is well known that punishment has been considered to enhance cooperation based on empirical and theoretical studies. An important question arises over the existence of the "second-order" problems, which result from the interactions between individuals. In this paper, we propose strategy intervention as a new mechanism in spatial voluntary public goods game, in which individuals only know their own payoffs. By virtue of centralized institution, the defectors may reserve amounts of probabilities to contribute to the common pool with a certain amount of investments. The centralized institution is established costly by all the participants to enforce the intervention rather than peer punishment. We find that the number of cooperators (defectors) decreases (increases) with weak intervention, which contrasts our intuition. Loners vanish and cooperation emerges significantly, as the level of intervention reaches a threshold. We give an accurate range of intervention leading to full cooperation, and demonstrate that at partial cooperation state, proper intervention can remarkably increase income accumulations of individuals, between which there exists smaller income gap in contrast to typical models. We highlight the significance of intervention enforced by a higher authority for maintaining social stability.

Vapor−liquid equilibrium (VLE) data were measured for the ternary system water (1) + ethanol (2) + 1-butyl-3-methylimidazolium chloride ([bmim]Cl) (3). Complete T, x, and y data were obtained in a relatively wide range of ionic liquid (IL) mass fractions up to 0.8 and in a relatively complete composition range for the volatile binary pair. The nonrandom two-liquid (NRTL) equation was used for correlation and was revealed to be adequate for the ternary system in the experimental composition range. The ternary VLE behavior was also modeled by the correlation of two data sets, in which the ethanol mole fraction on IL-free basis is respectively at 0.1 and 0.98. In this way, the six data sets were reproduced satisfactorily, with root-mean-square deviations of 0.40 K for temperature and 0.0070 for vapor-phase mole fractions. Owing to the regular distribution of the experimental data, a good agreement between the experiment and the calculation was graphically presented. The effect of the IL on the VLE behavior o...

Vapor−liquid equilibrium (VLE) data were measured for the ternary system water (1) + ethanol (2) + 1-hexyl-3-methylimidazolium chloride ([hmim]Cl) (3) at p = 100 kPa. Six sets of complete T, x, y data were reported. While the mole fraction of ethanol on an ionic liquid (IL)-free basis was fixed, respectively, at 0.1, 0.2, 0.4, 0.6, 0.8, and 0.98, measurements were performed in a way in which the IL mass fraction varied from 0.8 to 0.1, in an interval of 0.1. The NRTL equation was used for correlation and was revealed as adequate for the ternary system in the experimental composition range. The quality of correlation appeared to be sensitive to the parameters used for water + ethanol. The ternary VLE behavior was also modeled by correlation of two data sets, in which the ethanol mole fraction on an IL-free basis is, respectively, at 0.1 and 0.98. In this way, the six data sets were reproduced satisfactorily, with root-mean-square deviations of 0.49 K for temperature and 0.0042 for vapor phase mole fraction...

Isobaric T, x, y data were reported for ternary systems of {water + 2-methyl-2-propanol (tert-butyl alcohol, TBA) + ionic liquid (IL)} at p = 100 kPa. When the mole fraction of TBA on IL-free basis was fixed at 0.95, measurements were performed at IL mass fractions from 0.6 down to 0.05, in a way of repeated synthesis. The vapor-phase compositions were obtained by analytical methods and the liquid-phase compositions were calculated with the aid of mass balances. Activity coefficients of water and TBA were obtained without the need of a thermodynamic model of the liquid-phase. Six ILs, composed of an anion chosen from [OAc]− or [Cl]−, and a cation from [emim]+, or [bmim]+, or [hmim]+, were studied. Relative volatility and activity coefficients were presented in relation with the IL mole fraction, showing the effect of the ILs on a molar basis. The effect of the ILs on relative volatility of TBA to water was depicted by the effect of anions and cations on, respectively, the activity coefficients of water and TBA. The results indicated that, among the six ILs studied, [emim][Cl] has the most significant effect on enhancement of the relative volatility, which reaches a value of 7.2 at an IL mass fraction of 0.58. Another IL, [emim][OAc], has also significant effect, with an appreciable value of 5.2 for the relative volatility when the IL mass fraction is 0.6. Considering the relatively low viscosity and melting point of [emim][OAc], it might be a favorable candidate as solvent for the separation of water and TBA by extractive distillation. Simultaneous correlation by the NRTL model was presented for both systems of (water + ethanol + IL) and (water + TBA + IL), using consistent binary parameters for water and IL.

For selection of ionic liquids (ILs) which can be potentially used as entrainers for separation of the azeotropic mixture of (water + ethanol) by extractive distillation, (vapor + liquid) equilibrium was measured for the ternary systems of (water + ethanol + an IL) using a previously proposed ebulliometer. The experimental measurement was performed at p = 100 kPa and in a way of continuous synthesis, in which analysis of liquid phase composition was avoided. While the mole fraction of ethanol calculated on IL-free basis, x 2 ′ , was kept almost unchanged at 0.95, isobaric T, x, y data were measured at different IL mass fractions. Activity coefficients, as well as relative volatilities, of the volatile components were obtained from the experimental data without the need of a thermodynamic model of the liquid phase. There were eight ILs in our investigation: 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4]), 1-ethyl-3-methylimidazolium tetrafluoroborate ([emim][BF4]), 1-butyl-3-methylimidazolium dicyanamide ([bmim][N(CN)2]), 1-ethyl-3-methylimidazolium dicyanamide ([emim][N(CN)2]), 1-butyl-3-methylimidazolium chloride ([bmim][Cl]), 1-ethyl-3-methylimidazolium chloride ([emim][Cl]), 1-butyl-3-methylimidazolium acetate ([bmim][OAc]), and 1-ethyl-3-methylimidazolium acetate ([emim][OAc]). The effect of the ILs on the relative volatility of the volatile components was depicted separately by their effect on the activity coefficients. The results indicated that, among the eight ILs studied, [emim][Cl] has the largest effect on enhancement of the relative volatility. Another IL, [emim][OAc], has also significant effect. Considering the relatively low viscosity and melting point of [emim][OAc], this IL might be favorable candidate as entrainer for potential industrial application.

Isobaric T, x, y data were measured for the quaternary system water + ethanol + ethyl acetate + 1-butyl-3-methylimidazolium acetate at low water mole fractions and at p = 100 kPa. By a procedure presented in this work for systems composed of three volatile components and a nonvolatile ionic liquid (IL), the vapor-phase compositions were obtained by analytical methods and the liquid-phase compositions were calculated with the aid of mass balances. Activity coefficients of the volatile components were obtained without the need of a thermodynamic model of the liquid phase. Enhancement of the relative volatilities by addition of the IL was related with the effect of the IL on the activity coefficients. With the addition of the IL, the activity coefficients of water and ethanol decreased, while the activity coefficient of ethyl acetate increased. The reversed effect of the IL on the activity coefficients resulted in a consistent effect on the relative volatility. At an IL mass fraction of 0.7, the relative vol...

A procedure for experimental evaluation of ionic liquids (ILs) as entrainers was proposed. For selection of ILs which can be potentially used for the separation of the azeotropic mixture of water and 2-propanol by extractive distillation, vapor–liquid equilibria were measured for ternary systems of water + 2-propanol + IL at 100 kPa. A previously presented ebulliometer was modified to improve the reliability of measurement of equilibrium temperature and vapor phase composition. A packed column was adopted in the place of the Cottrell pump tube to enhance the equilibration of temperature and compositions of the arising mixture of vapor and liquid. By use of the modified ebulliometer, the experimental measurement was performed in a way of continuous synthesis, in which analysis of liquid phase composition was avoided. While the mole fraction of 2-propanol calculated on IL-free basis, x ′ 2 , was kept almost unchanged at 0.95, isobaric T, x, y data were measured at different IL mass fractions. Activity coefficients of the volatile components as well as their relative volatility were obtained from the experimental data without the need of a thermodynamic model of the liquid phase. There were seven ILs in our investigation: 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4]), 1-ethyl-3-methylimidazolium tetrafluoroborate ([emim][BF4]), 1-butyl-3-methylimidazolium dicyanamide ([bmim][N(CN)2]), 1-ethyl-3-methylimidazolium dicyanamide ([emim][N(CN)2]), 1-butyl-3-methylimidazolium acetate ([bmim][OAc]), 1-ethyl-3-methylimidazolium acetate ([emim][OAc]), and 1-butyl-3-methylimidazolium chloride ([bmim][Cl]). Results showed that the activity coefficients are mainly decided by the anions and the interactions of the anions with water and 2-propanol are in the same order, namely [Cl]− ≈ [OAc]− > [N(CN)2]− > [BF4]−. The similarity in the interactions cancels in some extent the effect of the ILs. While the cation has relatively small effect on the activity coefficients, their interactions with water and 2-propanol show reversed orders, namely [emim]+ > [bmim]+ for interactions with water and [emim]+

Isobaric vapor−liquid equilibrium (VLE) data were measured for three ternary systems containing ionic liquids (ILs): water + 2-propanol + 1-ethyl-3-methylimidazolium tetrafluoroborate ([emim][BF4]), water + 1-propanol + [emim][BF4], and water + 1-propanol + 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4]). The measurements were performed at P = 100 kPa and at several constant IL mass fractions. Activity coefficients of the volatile components were obtained without the need of a thermodynamic model of the liquid phase. The effect of the ILs on the relative volatility of the volatile components was depicted separately by their effect on the activity coefficients. Results of the activity coefficients showed that [emim]+ has a stronger interaction with water than [bmim]+; however, it has a weaker interaction with 1-propanol or 2-propanol. Boiling temperature data were also measured at 100 kPa for the six binary systems containing ILs. Ternary VLE data were also calculated from binary NRTL paramete...

An ebulliometer has been designed for vapor−liquid equilibrium measurement of systems containing an ionic liquid (IL). The new design allows vapor phase sampling and analysis, while the liquid composition is calculated on the basis of synthetic quantities and with regard to vapor phase composition, quantity of vapor material, and vapor-to-liquid circulation ratio. T, x, y data are reported for the system water + 2-propanol + 1-butyl-3-methylimidazolium tetrafluoroborate at 100 kPa and ionic liquid mass fractions of 0.300, 0.500, and 0.700. The quasi-binary system water + 2-propanol presents a temperature minimum when IL mass fraction is kept constant at these three concentrations. Addition of the IL with mass fraction of 0.500 and 0.700 breaks the azeotrope. Activity coefficients are calculated from the experimental data for the volatile components in the IL-containing mixture. The activity coefficients are directly related to the relative volatility of the quasi-binary mixture and show rather complicated...

In this paper, the fluid field of a human oral airway model is gained though the simulation method. After computing the system in the stable condition, the deposition efficiencies of aerosols in different Stokes number are obtained and the trace of typical aerosols are figured.

Background Little information is available regarding the penetrance of 1q21.1 copy number variants (CNVs). In the present study, we explored the clinical significance of 1q21.1 microdeletion or microduplication. Methods In four families, chromosome karyotype was analyzed using G‐banding karyotype analysis technology. CNVs were detected using array‐comparative genomic hybridization (aCGH) and then a quantitative polymerase chain reaction (qPCR) was used to validate candidate CNVs. Sequence signature in the breakpoint region was analyzed using University of California Santa Cruz (UCSC) databases. Results Except for karyotype 45, XX, der (13, 14) (q10, q10) in the mother (I2) of family 2, the karyotype was normal in all other members of the four families. In the mother (I2) and fetus (II2) of family 1, in newborn (II1) of family 2 and in fetus (II1) of family 3, there was 1.22‐Mb heterozygous microdeletion in the chromosome 1q21.1q21.2 region. The child (II1) of family 4 had a 1.46‐Mb heterozygous microduplication in the chromosome 1q21.1q21.2 region. The results of the qPCR were consistent with that of aCGH. There was large number of low copy repeats (LCRs) in the breakpoint region found by analysis of the UCSC database, and multiple LCRs were matched with sequences in the chromosome 1 short‐arm region. Conclusions 1q21.1 microdeletion and microduplication exhibit a variety of clinical manifestations and the specificity of their clinical features is not high. The penetrance of the distal 1q21.1 microdeletion may be affected by other factors in the present study. In summary, we report the discovery of a new distal 1q21.1 microduplication, which enriches the CNV spectrum in the 1q21.1 region and is conducive to prenatal genetic counseling.

Reactions between chlorine disinfectants, dissolved organic matter, and other chemicals in water form a series of disinfection by-products (DBPs), including trihalomethanes (THMs) and haloacetic acids (HAAs), that are toxic and subject to increasingly stringent regulations. This paper explores effects on DBP formation produced by an alternative, non-chlorine-based secondary disinfectant comprised of silver and hydrogen peroxide (Ag+/H2O2) that is designed to provide long-lasting residual disinfection. Based on a series of laboratory experiments using simulated treatment and distribution systems, post-chlorination additions of the secondary disinfectant dramatically reduced the formation of halogenated DBPs. Five source waters were tested over a range of conditions, including various levels of chlorine dosing, bromine and organic carbon concentrations, pH and temperature. For surface and ground waters, DBP reductions at 24 h with the secondary disinfectant averaged 72±9% for THMs and 67±11% for HAAs after a 10-min chlorination period. The dramatic reduction in halogenated DBPs occurred for all tested source waters and all disinfection conditions. The likely mechanism is the reduction of chlorine to chloride by H2O2, which halts further reaction of chlorine with dissolved organic matter and other DBP precursors. Thus, H2O2 acts as a quenching agent, in addition to its residual disinfectant properties in combination with Ag+. This research shows a potential benefit of mixed disinfectants that provide a potentially viable option for controlling the formation of DBPs while maintaining effective disinfection.

High-speed countercurrent chromatography is a recently developed separation method that has been remarkably improved in both separating efficiency and separating time. In this paper, this advanced countercurrent chromatographic method was applied to the separation of lanthanides. In combination with the measurement of the partition coefficient of lanthanides, a suitable solvent system was chosen. The separation of a mixture containing trivalent lanthanides (Sm, Gd, Tb, Dy, Er and Yb) was performed with a two-phase solvent system consisting of 0.15 M di(2-ethylhexyl)phosphate in chloroform (lower phase) and hydrochloric acid (upper phase). As the rotational speed increased, the resolution of adjacent bands was enhanced. While the resolution first increased with increasing the flow-rate of the mobile phase, it reached a maximum at a flow-rate of 1 ml min −1 and then decreased with increasing the flow-rate of the mobile phase. This enhancement resulted from an increasing number of theoretical plates. Mutual separation of adjacent lanthanides was accomplished with sufficient resolution.

In this paper, we investigate the evolution of cooperation in the spatial prisoner's dilemma game by incorporating partner choice into the framework of evolutionary game theory. Our research shows that the introduction of partner choice can notably promote the cooperative behavior in the prisoner's dilemma game. All the players are more likely to play the game with cooperators, which makes it easier for cooperators to form alliances. In particular, the system will be dominated completely by cooperators in a comfortable environment (i.e., with lower survival cost) because the cooperators can get more benefits than the defectors in this case due to their good reputation. In addition, we have found that the sustenance of cooperators improves notably as well in the snowdrift game and the stag-hunt game due to this introduction.

Sedimentation in dilute suspensions of charged particles with thin double layers was investigated. The study covered sedimentation in polydisperse systems at a large Peclet number. The pair-distribution equation was solved by a regular perturbation method, and it was found that generally speaking the sedimentation coefficient deviates slightly from that at the infinitely large Peclet number except that the double layer was very thin. The results were found to possess much more diversities than the case of hard spheres.

A mechanism has been established for pressure diffusion waves in dual-porosity media. Pressure diffusion waves are heavily damped with relatively low velocities and short wavelengths. The characteristic frequency dominates the attenuation behavior of pressure diffusions and separates wave fields into two asymptotic regimes: relaxed and unrelaxed. Characteristic delay times control the pressure diffusion between the matrix and the fractures. The transition zones in wavelength and attenuation peak shift toward high frequencies when the characteristic delay time decreases. In contrast, the transition zones in both phase and group velocity shift toward low frequencies as the characteristic time of the delay increases. In a spatially dependent diffusivity field, the pressure diffusion waves in dual-porosity media obey an accumulation-depletion law.

The unsteady flow field past a two-dimensional permeable square cylinder was predicted by an updated CE/SE method. The periodic patterns of streamline and vortex shedding were obtained. The evolution of lift and drag coefficients were analysed. Results of 2D computations were compared with the experimental data. It found that the Reynolds number dominated the magnitude and frequency of the vorticity given porosity and Darcy number. It proved that the CE/SE method was an effective tool for predicting viscous flows in porous media.

We study how the presence of committed vaccinators, a small fraction of individuals who consistently hold the vaccinating strategy and are immune to influence, impact the vaccination dynamics in well-mixed and spatially structured populations. For this purpose, we develop an epidemiological game-theoretic model of a flu-like vaccination by integrating an epidemiological process into a simple agent-based model of adaptive learning, where individuals (except for those committed ones) use anecdotal evidence to estimate costs and benefits of vaccination. We show that the committed vaccinators, acting as "steadfast role models" in the populations, can efficiently avoid the clustering of susceptible individuals and stimulate other imitators to take vaccination, hence contributing to the promotion of vaccine uptake. We substantiate our findings by making comparative studies of our model on a full lattice and on a randomly diluted one. Our work is expected to provide valuable information for decision-making and design more effective disease-control strategy.

By incorporating ecological dynamics into evolutionary games, we introduce natural and unnatural death to the spatial prisoner's dilemma game in which individuals can play mixed strategies. This introduction can give a simple explanation for the emergence and abundance of cooperation in animal and human societies. We found that individuals are more likely to cooperate in a highly competitive environment. In addition, our simulation results suggest that the individuals would tend to cooperate when the temptation to defect is small.

In this paper, we have explored the relationship between carbon dioxide emissions and GDP growth both in US and China, and got some significant conclusions. The results showed that the total carbon dioxide emissions were large both in China and US, there are many differences between two countries. Although both the CO2 emissions growth and GDP growth of China were much higher than those of the US, the elasticity of CO2 growth with GDP growth showed the same conclusion. Fortunately, the trend of this dictator was declined in China in recent years. It means the Environmental policy was at work.

A fundamental question of human society is the evolution of cooperation. Many previous studies explored this question via setting spatial background, where players obtain their payoffs by playing game with their nearest neighbors. Another undoubted fact is that the environment plays an important role in the individual development. Inspired by these phenomena, we reconsider the definition of individual fitness which integrates the environment, denoted by the average payoff of all individual neighbors, with the traditional individual payoffs by introducing a selection parameter u . Tuning u equal to zero returns the traditional version, while increasing u bears the influence of environment. We find that considering the environment, i.e., integrating neighborhoods in the evaluation of fitness, promotes cooperation. If we enhance the value of u , the invasion of defection could be resisted better. We also provide quantitative explanations and complete phase diagrams presenting the influence of the environment on the evolution of cooperation. Finally, the universality of this mechanism is testified for different neighborhood sizes, different topology structures and different game models. Our work may shed light on the emergence and persistence of cooperation in our life.

In this paper, we have compared the feature of carbon dioxide emissions both in USA and China. Firstly, the total carbon dioxide emissions were large both in China and USA. Secondly, the per capita carbon dioxide emissions in USA are at a stable high level, while China's relatively low. Thirdly, as per capita carbon dioxide emissions index, the EKC of USA has already turn to the right, but China is still in the left side.

In this work, we introduce a degree of rationality to the public goods games in which players can determine whether or not to participate, and with it a new mechanism has been established. Existence of the bounded rationality would lead to a new equilibrium which differs from the Nash equilibrium and qualitatively explains the fundamental role of loners' payoff for maintaining cooperation. Meanwhile, it is shown how the potential strategy influences the players' decision. Finally, we explicitly demonstrate a rock-scissors-paper dynamics which is a consequence of this model.

A microscopic 1D analytical model was developed for describing pore pressure diffusion wave propagation in porous media. The pressure diffusion waves, being heavily damped, have relatively slow velocities and short wavelength, and do not exhibit square-law behavior. Investigation on permeability effect on attenuation dispersion and penetration depth indicates that the transition zone in attenuation and penetration depth peak shifts toward low frequency when permeability decreases. Controversially, the transition zone in phase velocity peak shifts toward high frequency when permeability decreases. The high frequency-dependent attenuation of low-frequency waves was well predicted by the pressure diffusion mechanism. At a mass interface, pressure diffusion waves obey an accumulation–depletion law, rather than the reflection–refraction law. Pressure diffusion waves are accelerated and amplified by a space-dependent diffusivity field.

Hardin’s “The Tragedy of the Commons” prophesies the inescapable collapse of many human enterprises. The emergence and abundance of cooperation in animal and human societies is a challenging puzzle to evolutionary theory. In this work, we introduce a new decision-making criterion into a voluntary public goods game with incomplete information and choose successful strategies according to previous payoffs for a certain strategy as well as the risk-averse benefit. We find that the interest rate of the common pool and the magnitude of memory have crucial effects on the average welfare of the population. The appropriate sense of individuals’ innovation also substantially influences the equilibrium strategies distribution in the long run.