Positional Encoding by Robots with Non-Rigid Movements

Consider a set of autonomous computational entities, called \emph{robots}, operating inside a polygonal enclosure (possibly with holes), that have to perform some collaborative tasks. The boundary of the polygon obstructs both visibility and mobility of a robot. Since the polygon is initially unknown to the robots, the natural approach is to first explore and construct a map of the polygon. For this, the robots need an unlimited amount of persistent memory to store the snapshots taken from different points inside the polygon. However, it has been shown by Di Luna et al. [DISC 2017] that map construction can be done even by oblivious robots by employing a positional encoding strategy where a robot carefully positions itself inside the polygon to encode information in the binary representation of its distance from the closest polygon vertex. Of course, to execute this strategy, it is crucial for the robots to make accurate movements. In this paper, we address the question whether this technique can be implemented even when the movements of the robots are unpredictable in the sense that the robot can be stopped by the adversary during its movement before reaching its destination. However, there exists a constant $\delta > 0$, unknown to the robot, such that the robot can always reach its destination if it has to move by no more than $\delta$ amount. This model is known in literature as \emph{non-rigid} movement. We give a partial answer to the question in the affirmative by presenting a map construction algorithm for robots with non-rigid movement, but having $O(1)$ bits of persistent memory and ability to make circular moves

Trends in source gases

Source gases are defined as those gases that, by their breakdown, introduce into the stratosphere halogen, hydrogen, and nitrogen compounds that are important in stratospheric ozone destruction. Given here is an update of the existing concentration time series for chlorocarbons, nitrous oxide, and methane. Also reviewed is information on halogen containing species and the use of these data for establishing trends. Also reviewed is evidence on trends in trace gases that influence tropospheric chemistry and thus the tropospheric lifetimes of source gases, such as carbon dioxide, carbon monoxide, or nitrogen oxides. Much of the information is given in tabular form

Anisotropic Local Stress and Particle Hopping in a Deeply Supercooled Liquid

The origin of the microscopic motions that lead to stress relaxation in deeply supercooled liquid remains unclear. We show that in such a liquid the stress relaxation is locally anisotropic which can serve as the driving force for the hopping of the system on its free energy surface. However, not all hopping are equally effective in relaxing the local stress, suggesting that diffusion can decouple from viscosity even at local level. On the other hand, orientational relaxation is found to be always coupled to stress relaxation.Comment: 4 pages, 3 figure

Dynamical Heterogeneities Below the Glass Transition

We present molecular dynamics simulations of a binary Lennard-Jones mixture at temperatures below the kinetic glass transition. The ``mobility'' of a particle is characterized by the amplitude of its fluctuation around its average position. The 5% particles with the largest/smallest mean amplitude are thus defined as the relatively most mobile/immobile particles. We investigate for these 5% particles their spatial distribution and find them to be distributed very heterogeneously in that mobile as well as immobile particles form clusters. The reason for this dynamic heterogeneity is traced back to the fact that mobile/immobile particles are surrounded by fewer/more neighbors which form an effectively wider/narrower cage. The dependence of our results on the length of the simulation run indicates that individual particles have a characteristic mobility time scale, which can be approximated via the non-Gaussian parameter.Comment: revtex, 10 pages, 20 postscript figure

Dynamical heterogeneities in a supercooled Lennard-Jones liquid

We present the results of a large scale molecular dynamics computer simulation study in which we investigate whether a supercooled Lennard-Jones liquid exhibits dynamical heterogeneities. We evaluate the non-Gaussian parameter for the self part of the van Hove correlation function and use it to identify ``mobile'' particles. We find that these particles form clusters whose size grows with decreasing temperature. We also find that the relaxation time of the mobile particles is significantly shorter than that of the bulk, and that this difference increases with decreasing temperature.Comment: 8 pages of RevTex, 4 ps figure

String-like Clusters and Cooperative Motion in a Model Glass-Forming Liquid

A large-scale molecular dynamics simulation is performed on a glass-forming Lennard-Jones mixture to determine the nature of dynamical heterogeneities which arise in this model fragile liquid. We observe that the most mobile particles exhibit a cooperative motion in the form of string-like paths (``strings'') whose mean length and radius of gyration increase as the liquid is cooled. The length distribution of the strings is found to be similar to that expected for the equilibrium polymerization of linear polymer chains.Comment: 6 pages of RevTex, 6 postscript figures, uses epsf.st

Backward correlations and dynamic heterogeneities: a computer study of ion dynamics

We analyse the correlated back and forth dynamics and dynamic heterogeneities, i.e. the presence of fast and slow ions, for a lithium metasilicate system via computer simulations. For this purpose we define, in analogy to previous work in the field of glass transition, appropriate three-time correlation functions. They contain information about the dynamics during two successive time intervals. First we apply them to simple model systems in order to clarify their information content. Afterwards we use this formalism to analyse the lithium trajectories. A strong back-dragging effect is observed, which also fulfills the time-temperature superposition principle. Furthermore, it turns out that the back-dragging effect is long-ranged and exceeds the nearest neighbor position. In contrast, the strength of the dynamic heterogeneities does not fulfill the time-temperature superposition principle. The lower the temperature, the stronger the mobility difference between fast and slow ions. The results are then compared with the simple model systems considered here as well as with some lattice models of ion dynamics.Comment: 12 pages, 10 figure

Decoupling of diffusion from structural relaxation and spatial heterogeneity in a supercooled simple liquid

We report a molecular dynamics simulation of a supercooled simple monatomic glass-forming liquid. It is found that the onset of the supercooled regime results in formation of distinct domains of slow diffusion which are confined to the long-lived icosahedrally structured clusters associated with deeper minima in the energy landscape. As these domains, possessing a low-dimensional geometry, grow with cooling and percolate below $T_c$, the critical temperature of the mode coupling theory, a sharp slowing down of the structural relaxation relative to diffusion is observed. It is concluded that this latter anomaly cannot be accounted for by the spatial variation in atomic mobility; instead, we explain it as a direct result of the configuration-space constraints imposed by the transient structural correlations. We also conjecture that the observed tendency for low-dimensional clustering may be regarded as a possible mechanism of fragility.Comment: To be published in PR

Nanometer Scale Dielectric Fluctuations at the Glass Transition

Using non-contact scanning probe microscopy (SPM) techniques, dielectric properties were studied on 50 nanometer length scales in poly-vinyl-acetate (PVAc) films in the vicinity of the glass transition. Low frequency (1/f) noise observed in the measurements, was shown to arise from thermal fluctuations of the electric polarization. Anomalous variations observed in the noise spectrum provide direct evidence for cooperative nano-regions with heterogeneous kinetics. The cooperative length scale was determined. Heterogeneity was long-lived only well below the glass transition for faster than average processes.Comment: 4 pages, 4 embedded PS figures, RevTeX - To appear in Phys. Rev. Let