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The likelihood that a mutant fixates in the wild population, i.e., fixation probability, has been intensively studied in evolutionary game theory, where individuals' fitness is frequency dependent. However, it is of limited interest when it takes long to take over. Thus the speed of evolution becomes an important issue. In general, it is still unclear how fixation times are affected by the population structure, although the fixation times have already been addressed in the well-mixed populations. Here we theoretically address this issue by pair approximation and diffusion approximation on regular graphs. It is shown (i) that under neutral selection, both unconditional and conditional fixation time are shortened by increasing the number of neighbors; (ii) that under weak selection, for the simplified prisoner's dilemma game, if benefit-to-cost ratio exceeds the degree of the graph, then the unconditional fixation time of a single cooperator is slower than that in the neutral case; and (iii) that under weak selection, for the conditional fixation time, limited neighbor size dilutes the counterintuitive stochastic slowdown which was found in well-mixed populations. Interestingly, we find that all of our results can be interpreted as that in the well-mixed population with a transformed payoff matrix. This interpretation is also valid for both death-birth and birth-death processes on graphs. This interpretation bridges the fixation time in the structured population and that in the well-mixed population. Thus it opens the avenue to investigate the challenging fixation time in structured populations by the known results in well-mixed populations. [ABSTRACT FROM AUTHOR]

Liquids are condensed matter in which atoms are strongly correlated in position and momentum. The atomic pair density function (PDF) is used often in describing such correlation. However, elucidation of many properties requires higher degrees of correlation than the pair correlation. For instance, viscosity depends upon the stress correlations in space and time. In this paper, we examine the cross correlation between the stress correlation at the atomic level and the PDF for two-dimensional liquids. We introduce the concept of the stress-resolved pair distribution function (SRPDF) that uses the sign of atomic-level stress as a selection rule to include particles from density correlations. The connection between SRPDFs and stress correlation function is explained through an approximation in which the shear stress is replaced by a pseudospin. We further assess the possibility of interpreting the long-range stress correlation as a consequence of short-range Ising-like pseudospin interactions. [ABSTRACT FROM AUTHOR]

The surface of expanded face-centered tetragonal antiferromagnetic Mn films of a few atomic monolayers thickness grown epitaxially on Co/Cu(001) was investigated at room temperature by scanning tunneling microscopy and scanning tunneling spectroscopy using a ferromagnetic ring-shaped bulk iron probe. We show that the main contribution to the contrast modulation observed as a function of Mn thickness in differential conductance maps is not due to spin-polarized tunneling from a layerwise antiferromagnetic spin alignment. Instead, it is mainly of electronic origin resulting from layer-dependent electronic properties of the Mn film, probably related to different levels of intermixing with Co atoms. On the atomic scale, the Mn surface demonstrates a geometrical reconstruction with a (12 × 2) periodicity in two orthogonal domains on the fourfold symmetric substrate with an apparent surface corrugation of up to 0.3 Å. Simultaneously recorded differential conductance maps show different textures in the two orthogonal domains, providing evidence for noncollinearity in the Mn surface spin structure. [ABSTRACT FROM AUTHOR]

In this paper we demonstrate the presence of anisotropic stress correlations in the simulated two-dimensional liquids. Whereas the temporal correlation of macroscopic shear stress is known to contribute to viscosity via the Green-Kubo formula, the general question regarding angular dependence of the spatial correlation among atomiclevel stresses in liquids without external shear has not been explored. We observed the apparent anisotropicity with well-defined symmetry which can be explained in terms of the elastic continuum theory by Eshelby. In addition, we found that the shear stress correlation is screened compared to the prediction by the elastic continuum theory, and the screening length depends on temperature and follows the power law, suggesting divergence around the glass transition temperature. The success of the Eshelby theory to explain the anisotropy of the stress correlations justifies the idea that the mismatch between the atom and its nearest neighbor cage produces the atomic-level stress as well as the long-range stress fields. [ABSTRACT FROM AUTHOR]

The in-plane shear (C) modes between neighbor layers of 2-4 layer graphenes (2-4LGs) and the corresponding 2-4 layer graphene scrolls (2-4LGSs) rolled up by 2-4LGs at edges are investigated by Raman scattering. In contrast to the result that only one C mode is observed in 3-4LGs, all the C modes of 3-4LGs are observed in 3-4LGSs, whose frequencies agree with the theoretical prediction by the force-constant and linear chain models. The results indicate that the C mode intensity of 2-4LGSs is resonantly enhanced by the electronic transition gaps of band structures of 2-4LGS structures at edges, which makes it possible to observe all the C modes. Indeed, for a simple assumption, the calculated band structures of twisted (n+n)LGs (n=2,3,4) show parallel conduction and valence bands and the corresponding Van Hove singularities in the joint density of states along Γ-M, Γ-K and/or K-M directions. The intensity resonance of the C modes provides direct evidence to explain how the band structure of few layer graphenes can be sensitive to local stacking configurations. This result can be extended to n layer graphene (n>4) for understanding the basic phonon and electronic properties of multilayer graphenes. This observation of all the C modes in graphene scrolls can be foreseen in other two-dimensional materials with similar scroll structures. [ABSTRACT FROM AUTHOR]

Magneto-optical Kerr effect measurements of epitaxial AFM/FM bilayers and FM/AFM/FM trilayers on Cu3Au(001), where "AFM" stands for a Ni25Mn75 antiferromagnetic layer, and "FM" for ferromagnetic layers that are either Ni or Ni/Co with out-of-plane or in-plane easy axis of magnetization, show that trilayers with collinear magnetization directions of both FM layers exhibit always a much lower exchange bias field Heb at a fixed temperature compared to bilayers of the same Ni25Mn75 thickness. At the same time, the blocking temperature for exchange bias Tb is strongly reduced. In trilayers with orthogonal easy axes of the two FM layers (in-plane and out-of-plane), in contrast, both Heb and Tb are nearly identical to that of the corresponding bilayers. Such a behavior can be explained by pinned magnetic moments inside the bulk of the AFM layer that coexist independently for orthogonal spin directions, but have to be equally shared between both interfaces in the case of collinear spin directions. This result thus also confirms a 3Q-like noncollinear spin structure of Ni25Mn75. [ABSTRACT FROM AUTHOR]

Globalization facilitates our communication with each other, while it magnifies problems such as overharvesting of natural resources and human-induced climate change. Thus people all over the world are involved in a global social dilemma which calls for worldwide cooperation to reduce the risks of these extreme events and disasters. A collective target (threshold) is required to prevent such events. Everyone may lose their wealth once their total individual contributions fail to reach the threshold. To this end, we establish a model of threshold public goods games in a group-structured population and investigate its evolutionary process. We study multilevel public goods games with defectors, local cooperators, and global cooperators and are primarily concerned with how the global cooperative behavior evolves. We find that, compared with the standard public goods games, the strategy of global cooperation accounts for a bigger proportion in the stationary distribution of threshold public goods games. On the other hand, the fixation time of the global cooperation strategy is greatly shortened with increase of the probability of disaster striking. Therefore, global risks induced by the threshold can effectively promote global cooperation in environmental investment and the reduction of greenhouse gas emissions. [ABSTRACT FROM AUTHOR]

Evolutionary game theory on dynamical networks has received much attention. Most of the work has been focused on 2 x 2 games such as prisoner's dilemma and snowdrift, with general n x n games seldom addressed. In particular, analytical methods are still lacking. Here we generalize the stochastic linking dynamics proposed by Wu, Zhou, Fu, Luo, Wang, and Traulsen [PLoS ONE5, e 11187 (2010)] to n x n games. We analytically obtain that the fast linking dynamics results in the replicator dynamics with a rescaled payoff matrix. In the rescaled matrix, intuitively, each entry is the product of the original entry and the average duration time of the corresponding link. This result is shown to be robust to a wide class of imitation processes. As applications, we show both analytically and numerically that the biodiversity, modeled as the stability of a zero-sum rock-paper-scissors game, cannot be altered by the fast linking dynamics. In addition, we show that the fast linking dynamics can stabilize tit-for-tat as an evolutionary stable strategy in the repeated prisoner's dilemma game provided the interaction between the identical strategies happens sufficiently often. Our method paves the way for an analytical study of the multiple-strategy coevolutionary dynamics. [ABSTRACT FROM AUTHOR]

Cooperators increase the fitness of others at a cost to themselves. Thus cooperation should not be favored by natural selection in a well-mixed population. It challenges the evolutionists since cooperation is widespread. Information spreading has been revealed to play a key role in the emergence of cooperation. Individuals, however, are typically assumed to be passive in the information spreading. Here we assume that individuals self-recommend themselves to those that are about to have new neighbors. Individuals with higher tendencies of self-recommendation are likely to have more neighbors. In this way, individuals are active to spread the information. We analytically obtain a critical cost-to-benefit ratio, below which cooperation emerges. It reveals quantitatively how eloquent cooperators have to be compared with defectors to ensure that cooperation takes over the population. It also indicates that individuals need to be open enough to the self-recommendation to enhance cooperation level. In addition, the critical cost-to-benefit ratio represents the viscosity of the population, measuring how close cooperators are to each other. Our results highlight the role self-recommendation plays in cooperation. [ABSTRACT FROM AUTHOR]

The de Gennes narrowing phenomenon is frequently observed by neutron or x-ray scattering measurements of the dynamics of complex systems, such as liquids, proteins, colloids, and polymers. The characteristic slowing down of dynamics in the vicinity of the maximum of the total scattering intensity is commonly attributed to enhanced cooperativity. In this Letter, we present an alternative view on its origin through the examination of the time-dependent pair correlation function, the van Hove correlation function, for a model liquid in two, three, and four dimensions. We find that the relaxation time increases monotonically with distance and the dependence on distance varies with dimension. We propose a heuristic explanation of this dependence based on a simple geometrical model. This finding sheds new light on the interpretation of the de Gennes narrowing phenomenon and the α-relaxation time. [ABSTRACT FROM AUTHOR]

The molecular rearrangements of most fluids under flow and deformation do not directly follow the macroscopic strain field. In this work, we describe a phenomenological method for characterizing such nonaffine deformation via the anisotropic pair distribution function (PDF). We demonstrate how the microscopic strain can be calculated in both simple shear and uniaxial extension, by perturbation expansion of anisotropic PDF in terms of real spherical harmonics. Our results, given in the real as well as the reciprocal space, can be applied in spectrum analysis of small-angle scattering experiments and nonequilibrium molecular dynamics simulations of soft matter under flow. [ABSTRACT FROM AUTHOR]

Combining ultrahigh sensitivity, spatial resolution, and the capability to resolve chemical information, tip-enhanced Raman spectroscopy (TERS) is a powerful tool to study molecules or nanoscale objects. Here we show that TERS can also be a powerful tool in studying two-dimensional materials. We have achieved a 109 Raman signal enhancement and a 0.5 nm spatial resolution using monolayer silicene on Ag(111) as a prototypical 2D material system. Because of the selective enhancement on Raman modes with vertical vibrational components in TERS, our experiment provides direct evidence of the origination of Raman modes in silicene. Furthermore, the ultrahigh sensitivity of TERS allows us to identify different vibrational properties of silicene phases, which differ only in the bucking direction of the Si-Si bonds. Local vibrational features from defects and domain boundaries in silicene can also be identified. [ABSTRACT FROM AUTHOR]

Epidemic control is of great importance for human society. Adjusting interacting partners is an effective individualized control strategy. Intuitively, it is done either by shortening the interaction time between susceptible and infected individuals or by increasing the opportunities for contact between susceptible individuals. Here, we provide a comparative study on these two control strategies by establishing an epidemic model with nonuniform stochastic interactions. It seems that the two strategies should be similar, since shortening the interaction time between susceptible and infected individuals somehow increases the chances for contact between susceptible individuals. However, analytical results indicate that the effectiveness of the former strategy sensitively depends on the infectious intensity and the combinations of different interaction rates, whereas the latter one is quite robust and efficient. Simulations are shown to verify our analytical predictions. Our work may shed light on the strategic choice of disease control. [ABSTRACT FROM AUTHOR]

It has been shown recently that taking into account strong, weak, electromagnetic, and gravitational interactions, and fulfilling the global charge neutrality of the system, a transition layer will happen between the core and crust of neutron stars, at the nuclear saturation density. We use relativistic mean field theory together with the Thomas-Fermi approximation to study the detailed structure of this transition layer and calculate its surface and Coulomb energy. We find that the surface tension is proportional to a power-law function of the baryon number density in the core bulk region. We also analyze the influence of the electron component and the gravitational field on the structure of the transition layer and the value of the surface tension, to compare and contrast with known phenomenological results in nuclear physics. Based on the above results we study the instability against Bohr-Wheeler surface deformations in the case of neutron stars obeying global charge neutrality. Assuming the core-crust transition at nuclear density pcore ≈ 2.7 × 1014 g cm-3, we find that the instability sets the upper limit to the crust density, pcritcrust ≈ 1.2 × 1014 g cm-3. This result implies a nonzero lower limit to the maximum electric field of the core-crust transition surface and makes inaccessible a limit of quasilocal charge neutrality in the limit pcrust = pcore. The general framework presented here can be also applied to study the stability of sharp phase transitions in hybrid stars as well as in strange stars, both bare and with outer crust. The results of this work open the way to a more general analysis of the stability of these transition surfaces, accounting for other effects such as gravitational binding, centrifugal repulsion, magnetic field induced by rotating electric field, and therefore magnetic dipole-dipole interactions. [ABSTRACT FROM AUTHOR]

Spanning trees provide crucial insight into the origin of fractality in fractal scale-free networks. In this paper, we present the number of spanning trees in a particular fractal scale-free lattice (network). We first study analytically the topological characteristics of the lattice and show that it is simultaneously scale-free, highly clustered, "large-world," fractal, and disassortative. Any previous model does not have all the properties as the studied one. Then, by using the renormalization group technique we derive analytically the number of spanning trees in the network under consideration, based on which we also determine the entropy for the spanning trees of the network. These results shed light on understanding the structural characteristics of and dynamical processes on scale-free networks with fractality. Moreover, our method and process for employing the decimation technique to enumerate spanning trees are general and can be easily extended to other deterministic media with self-similarity. [ABSTRACT FROM AUTHOR]

When subjected to flow, the structures of many soft-matter systems become anisotropic due to the symmetry breaking of the spatial arrangements of constituent particles at the microscopic level. At present, it is common practice to use various small-angle scattering techniques to explore flow-induced microstructural distortion. However, there has not been a thorough discussion in the literature on how a three-dimensional anisotropic structure can be faithfully reconstructed from two-dimensional small-angle scattering spectra. In this work, we address this issue rigorously from a mathematical perspective by using real spherical harmonic expansion analysis. We first show that, except for cases in which mechanical perturbation is sufficiently small, the existing small-angle scattering techniques generally do not provide complete information on structural distortion. This limitation is caused by the linear dependence of certain real spherical harmonic basis vectors on the flow-vorticity and flow-velocity gradient planes in the Couette shear cell. To circumvent the constraint imposed by this geometry, an alternative approach is proposed in which a parallel sliding plate shear cell is used with a central rotary axis along the flow direction. From the calculation of rotation of the reference frame, we demonstrate the feasibility of this experimental implementation for a fully resolved three-dimensional anisotropic structure via a case study of sheared polymers. [ABSTRACT FROM AUTHOR]

Spin structures of an exchange-coupled-bilayer system of expanded-face-centered-tetragonal (e-fct) Mn(001) ultrathin films grown on Co/Cu(001) were resolved by means of spin-polarized scanning-tunneling microscopy. With an in-plane spin-sensitive probe, a layered antiferromagnetic-spin ordering of Mn overlayers was evidenced directly. In addition, the spin frustration across the same Mn layer creating a narrow domain wall down to nanometer scale was also observed along the buried step of Co underlayers. According to the micromagnetic simulation, the step-induced domain-wall width is in agreement with the experimental results. Such in-plane layered antiferromagnetic-spin structures of e-fct Mn(001) provide uncompensated spins at the interface with Co underlayers and elucidate the mechanism of the corresponding exchange-bias field observed in the previous studies. [ABSTRACT FROM AUTHOR]

Whether, how, and to what extent solutions of Bjorken-expanding systems become insensitive to aspects of their initial conditions is of importance for heavy-ion collisions. Here we study 1+1D and phenomenologically relevant boost-invariant 3+1D systems in which initial conditions approach a universal attractor. In Israel-Stewart theory (IS) and kinetic theory where the universal attractor extends to arbitrarily early times, we show that all initial conditions approach the attractor at early times by a power law while their approach is exponential at late times. In these theories, the physical mechanisms of hydrodynamization operational at late times do not drive the approach to the attractor at early times, and the early-time attractor is reached prior to hydrodynamization. In marked contrast, the attractor in strongly coupled systems is realized concurrent with hydrodynamization. This qualitative difference may offer a basis for discriminating weakly and strongly coupled scenarios of heavy-ion collisions. [ABSTRACT FROM AUTHOR]

Even though viscosity is one of the fundamental properties of liquids, its microscopic origin is not fully understood. We determined the spatial and temporal correlation of molecular motions of water near room temperature and its temperature variation on a picosecond timescale and a subnanometer spatial scale, through high-resolution inelastic x-ray scattering measurement. The results, expressed in terms of the time-dependent pair correlation function called the Van Hove function, show that the timescale of the decay of the molecular correlation is directly related to the Maxwell relaxation time near room temperature, which is proportional to viscosity. This conclusion validates our earlier finding that the topological changes in atomic or molecular connectivity are the origin of viscosity in liquids. [ABSTRACT FROM AUTHOR]

We report on a systematic study of type-II Dirac fermions in a layered crystal of PdTe2. De Haas-van Alphen oscillations show a small Fermi-surface pocket with a cross section of 0.077nm-2 with a nontrivial Berry phase. First-principles calculation reveals that the nontrivial Berry phase originates from a hole pocket formed by the tilted Dirac cone. In addition, the band dispersion measured with angle-resolved photoemission spectroscopy is found to be consistent with that of a type-II Dirac cone dispersion. We propose that PdTe2 is an improved platform to host topological superconductors. [ABSTRACT FROM AUTHOR]