Rate theory for correlated processes: Double-jumps in adatom diffusion

We study the rate of activated motion over multiple barriers, in particular the correlated double-jump of an adatom diffusing on a missing-row reconstructed Platinum (110) surface. We develop a Transition Path Theory, showing that the activation energy is given by the minimum-energy trajectory which succeeds in the double-jump. We explicitly calculate this trajectory within an effective-medium molecular dynamics simulation. A cusp in the acceptance region leads to a sqrt{T} prefactor for the activated rate of double-jumps. Theory and numerical results agree

Critical manifold of the kagome-lattice Potts model

Any two-dimensional infinite regular lattice G can be produced by tiling the plane with a finite subgraph B of G; we call B a basis of G. We introduce a two-parameter graph polynomial P_B(q,v) that depends on B and its embedding in G. The algebraic curve P_B(q,v) = 0 is shown to provide an approximation to the critical manifold of the q-state Potts model, with coupling v = exp(K)-1, defined on G. This curve predicts the phase diagram both in the ferromagnetic (v>0) and antiferromagnetic (v<0) regions. For larger bases B the approximations become increasingly accurate, and we conjecture that P_B(q,v) = 0 provides the exact critical manifold in the limit of infinite B. Furthermore, for some lattices G, or for the Ising model (q=2) on any G, P_B(q,v) factorises for any choice of B: the zero set of the recurrent factor then provides the exact critical manifold. In this sense, the computation of P_B(q,v) can be used to detect exact solvability of the Potts model on G. We illustrate the method for the square lattice, where the Potts model has been exactly solved, and the kagome lattice, where it has not. For the square lattice we correctly reproduce the known phase diagram, including the antiferromagnetic transition and the singularities in the Berker-Kadanoff phase. For the kagome lattice, taking the smallest basis with six edges we recover a well-known (but now refuted) conjecture of F.Y. Wu. Larger bases provide successive improvements on this formula, giving a natural extension of Wu's approach. The polynomial predictions are in excellent agreement with numerical computations. For v>0 the accuracy of the predicted critical coupling v_c is of the order 10^{-4} or 10^{-5} for the 6-edge basis, and improves to 10^{-6} or 10^{-7} for the largest basis studied (with 36 edges).Comment: 31 pages, 12 figure

Simulations of energetic beam deposition: from picoseconds to seconds

We present a new method for simulating crystal growth by energetic beam deposition. The method combines a Kinetic Monte-Carlo simulation for the thermal surface diffusion with a small scale molecular dynamics simulation of every single deposition event. We have implemented the method using the effective medium theory as a model potential for the atomic interactions, and present simulations for Ag/Ag(111) and Pt/Pt(111) for incoming energies up to 35 eV. The method is capable of following the growth of several monolayers at realistic growth rates of 1 monolayer per second, correctly accounting for both energy-induced atomic mobility and thermal surface diffusion. We find that the energy influences island and step densities and can induce layer-by-layer growth. We find an optimal energy for layer-by-layer growth (25 eV for Ag), which correlates with where the net impact-induced downward interlayer transport is at a maximum. A high step density is needed for energy induced layer-by-layer growth, hence the effect dies away at increased temperatures, where thermal surface diffusion reduces the step density. As part of the development of the method, we present molecular dynamics simulations of single atom-surface collisions on flat parts of the surface and near straight steps, we identify microscopic mechanisms by which the energy influences the growth, and we discuss the nature of the energy-induced atomic mobility

The Random-bond Potts model in the large-q limit

We study the critical behavior of the q-state Potts model with random ferromagnetic couplings. Working with the cluster representation the partition sum of the model in the large-q limit is dominated by a single graph, the fractal properties of which are related to the critical singularities of the random Potts model. The optimization problem of finding the dominant graph, is studied on the square lattice by simulated annealing and by a combinatorial algorithm. Critical exponents of the magnetization and the correlation length are estimated and conformal predictions are compared with numerical results.Comment: 7 pages, 6 figure

Sound velocity and absorption measurements under high pressure using picosecond ultrasonics in diamond anvil cell. Application to the stability study of AlPdMn

We report an innovative high pressure method combining the diamond anvil cell device with the technique of picosecond ultrasonics. Such an approach allows to accurately measure sound velocity and attenuation of solids and liquids under pressure of tens of GPa, overcoming all the drawbacks of traditional techniques. The power of this new experimental technique is demonstrated in studies of lattice dynamics, stability domain and relaxation process in a metallic sample, a perfect single-grain AlPdMn quasicrystal, and rare gas, neon and argon. Application to the study of defect-induced lattice stability in AlPdMn up to 30 GPa is proposed. The present work has potential for application in areas ranging from fundamental problems in physics of solid and liquid state, which in turn could be beneficial for various other scientific fields as Earth and planetary science or material research

Exact Potts Model Partition Functions for Strips of the Honeycomb Lattice

We present exact calculations of the Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature-like variable $v$ on $n$-vertex strip graphs $G$ of the honeycomb lattice for a variety of transverse widths equal to $L_y$ vertices and for arbitrarily great length, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These partition functions have the form $Z(G,q,v)=\sum_{j=1}^{N_{Z,G,\lambda}} c_{Z,G,j}(\lambda_{Z,G,j})^m$, where $m$ denotes the number of repeated subgraphs in the longitudinal direction. We give general formulas for $N_{Z,G,j}$ for arbitrary $L_y$. We also present plots of zeros of the partition function in the $q$ plane for various values of $v$ and in the $v$ plane for various values of $q$. Explicit results for partition functions are given in the text for $L_y=2,3$ (free) and $L_y=4$ (cylindrical), and plots of partition function zeros are given for $L_y$ up to 5 (free) and $L_y=6$ (cylindrical). Plots of the internal energy and specific heat per site for infinite-length strips are also presented.Comment: 39 pages, 34 eps figures, 3 sty file

Grand solar minima and maxima deduced from 10Be and 14C: magnetic dynamo configuration and polarity reversal

International audienceAims. This study aims to improve our understanding of the occurrence and origin of grand solar maxima and minima.Methods. We first investigate the statistics of peaks and dips simultaneously occurring in the solar modulation potentials reconstructed using the Greenland Ice Core Project (GRIP) 10Be and IntCal13 14C records for the overlapping time period spanning between ~1650 AD to 6600 BC. Based on the distribution of these events, we propose a method to identify grand minima and maxima periods. By using waiting time distribution analysis, we investigate the nature of grand minima and maxima periods identified based on the criteria as well as the variance and significance of the Hale cycle during these kinds of events throughout the Holocene epoch.Results. Analysis of grand minima and maxima events occurring simultaneously in the solar modulation potentials, reconstructed based on the 14C and the 10Be records, shows that the majority of events characterized by periods of moderate activity levels tend to last less than 50 years: grand maxima periods do not last longer than 100 years, while grand minima can persist slightly longer. The power and the variance of the 22-year Hale cycle increases during grand maxima and decreases during grand minima, compared to periods characterized by moderate activity levels.Conclusions. We present the first reconstruction of the occurrence of grand solar maxima and minima during the Holocene based on simultaneous changes in records of past solar variability derived from tree-ring 14C and ice-core 10Be, respectively. This robust determination of the occurrence of grand solar minima and maxima periods will enable systematic investigations of the influence of grand solar minima and maxima episodes on Earth’s climate

Multi-source hierarchical conditional random field model for feature fusion of remote sensing images and LiDAR data

Feature fusion of remote sensing images and LiDAR points cloud data, which have strong complementarity, can effectively play the advantages of multi-class features to provide more reliable information support for the remote sensing applications, such as object classification and recognition. In this paper, we introduce a novel multi-source hierarchical conditional random field (MSHCRF) model to fuse features extracted from remote sensing images and LiDAR data for image classification. Firstly, typical features are selected to obtain the interest regions from multi-source data, then MSHCRF model is constructed to exploit up the features, category compatibility of images and the category consistency of multi-source data based on the regions, and the outputs of the model represents the optimal results of the image classification. Competitive results demonstrate the precision and robustness of the proposed method