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Register a new userQuantification of group chasing and escaping process
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Added by
Shigenori Matsumoto
Publication date
2012
fields
Physics
and research's language is
English
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We study a simple group chase and escape model by introducing new parameters with which configurations of chasing and escaping in groups are classified into three characteristic patterns. In particular, the parameters distinguish two essential configurations: a one-directional formation of chasers and escapees, and an escapee surrounded by chasers. In addition, pincer movements and aggregating processes of chasers and escapees are also quantified. Appearance of these configurations highlights efficiency of hunting during chasing and escaping.
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The existence of juxtaposed regions of distinct cultures in spite of the fact that peoples beliefs have a tendency to become more similar to each others as the individuals interact repeatedly is a puzzling phenomenon in the social sciences. Here we study an extreme version of the frequency-dependent bias model of social influence in which an individual adopts the opinion shared by the majority of the members of its extended neighborhood, which includes the individual itself. This is a variant of the majority-vote model in which the individual retains its opinion in case there is a tie among the neighbors opinions. We assume that the individuals are fixed in the sites of a square lattice of linear size $L$ and that they interact with their nearest neighbors only. Within a mean-field framework, we derive the equations of motion for the density of individuals adopting a particular opinion in the single-site and pair approximations. Although the single-site approximation predicts a single opinion domain that takes over the entire lattice, the pair approximation yields a qualitatively correct picture with the coexistence of different opinion domains and a strong dependence on the initial conditions. Extensive Monte Carlo simulations indicate the existence of a rich distribution of opinion domains or clusters, the number of which grows with $L^2$ whereas the size of the largest cluster grows with $ln L^2$. The analysis of the sizes of the opinion domains shows that they obey a power-law distribution for not too large sizes but that they are exponentially distributed in the limit of very large clusters. In addition, similarly to other well-known social influence model -- Axelrods model -- we found that these opinion domains are unstable to the effect of a thermal-like noise.
We present a new efficient transition pathway search method based on the least action principle and the Gaussian process regression method. Most pathway search methods developed so far rely on string representations, which approximate a transition pathway by a series of slowly varying replicas of a system. Since those methods require a large number of replica images, they are computationally expensive in general. Our approach employs the Gaussian process regression method, which takes the Bayesian inference on the shape of a given potential energy surface with a few observed data and Gaussian-shaped kernel functions. Based on the inferred potential, we find multiple low-action pathways by carrying out the action optimization based on the Action-CSA (Conformational space annealing). Here we demonstrate a drastic elevation of computing efficiency about five orders of magnitude for the system with the Muller-Brown potential. Further, for the sake of demonstrating its real-world capabilities, we apply our method to ab initio calculations on alanine dipeptide. The improved efficiency of GPAO makes it possible to identify multiple transition pathways of alanine dipeptide and calculate their transition probabilities with ab initio accuracy. We are confident that our GPAO method is a powerful approach to investigate the mechanisms of complex chemical reactions
This chapter discusses how the PLUMED plugin for molecular dynamics can be used to analyze and bias molecular dynamics trajectories. The chapter begins by introducing the notion of a collective variable and by then explaining how the free energy can be computed as a function of one or more collective variables. A number of practical issues mostly around periodic boundary conditions that arise when these types of calculations are performed using PLUMED are then discussed. Later parts of the chapter discuss how PLUMED can be used to perform enhanced sampling simulations that introduce simulation biases or multiple replicas of the system and Monte Carlo exchanges between these replicas. This section is then followed by a discussion on how free-energy surfaces and associated error bars can be extracted from such simulations by using weighted histogram and block averaging techniques.
The macroscopic behavior of many materials is complex and the end result of mechanisms that operate across a broad range of disparate scales. An imperfect knowledge of material behavior across scales is a source of epistemic uncertainty of the overall material behavior. However, assessing this uncertainty is difficult due to the complex nature of material response and the prohibitive computational cost of integral calculations. In this paper, we exploit the multiscale and hierarchical nature of material response to develop an approach to quantify the overall uncertainty of material response without the need for integral calculations. Specifically, we bound the uncertainty at each scale and then combine the partial uncertainties in a way that provides a bound on the overall or integral uncertainty. The bound provides a conservative estimate on the uncertainty. Importantly, this approach does not require integral calculations that are prohibitively expensive. We demonstrate the framework on the problem of ballistic impact of a polycrystalline magnesium plate. Magnesium and its alloys are of current interest as promising light-weight structural and protective materials. Finally, we remark that the approach can also be used to study the sensitivity of the overall response to particular mechanisms at lower scales in a materials-by-design approach.
Molecular dynamics (MD) simulations allow investigating the structural dynamics of biomolecular systems with unrivaled time and space resolution. However, in order to compensate for the inaccuracies of the utilized empirical force fields, it is becoming common to integrate MD simulations with experimental data obtained from ensemble measurements. We here review the approaches that can be used to combine MD and experiment under the guidance of the maximum entropy principle. We mostly focus on methods based on Lagrangian multipliers, either implemented as reweighting of existing simulations or through an on-the-fly optimization. We discuss how errors in the experimental data can be modeled and accounted for. Finally, we use simple model systems to illustrate the typical difficulties arising when applying these methods.
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