Mid-range adiabatic wireless energy transfer via a mediator coil

A technique for efficient mid-range wireless energy transfer between two coils via a mediator coil is proposed. By varying the coil frequencies three resonances are created: emitter-mediator (EM), mediator-receiver (MR) and emitter-receiver (ER). If the frequency sweeps are adiabatic and such that the ER resonance precedes the MR resonance, the energy flows sequentially along the chain emitter-mediator-receiver. If the MR resonance precedes the ER resonance, then the energy flows directly from the emitter to the receiver via the ER resonance; then the losses from the mediator are suppressed. This technique is robust to noise, resonant constraints and external interferences

Asymptotic constant-factor approximation algorithm for the Traveling Salesperson Problem for Dubins' vehicle

This article proposes the first known algorithm that achieves a constant-factor approximation of the minimum length tour for a Dubins' vehicle through $n$ points on the plane. By Dubins' vehicle, we mean a vehicle constrained to move at constant speed along paths with bounded curvature without reversing direction. For this version of the classic Traveling Salesperson Problem, our algorithm closes the gap between previously established lower and upper bounds; the achievable performance is of order $n^{2/3}$

Internal Diffusion-Limited Aggregation: Parallel Algorithms and Complexity

The computational complexity of internal diffusion-limited aggregation (DLA) is examined from both a theoretical and a practical point of view. We show that for two or more dimensions, the problem of predicting the cluster from a given set of paths is complete for the complexity class CC, the subset of P characterized by circuits composed of comparator gates. CC-completeness is believed to imply that, in the worst case, growing a cluster of size n requires polynomial time in n even on a parallel computer. A parallel relaxation algorithm is presented that uses the fact that clusters are nearly spherical to guess the cluster from a given set of paths, and then corrects defects in the guessed cluster through a non-local annihilation process. The parallel running time of the relaxation algorithm for two-dimensional internal DLA is studied by simulating it on a serial computer. The numerical results are compatible with a running time that is either polylogarithmic in n or a small power of n. Thus the computational resources needed to grow large clusters are significantly less on average than the worst-case analysis would suggest. For a parallel machine with k processors, we show that random clusters in d dimensions can be generated in O((n/k + log k) n^{2/d}) steps. This is a significant speedup over explicit sequential simulation, which takes O(n^{1+2/d}) time on average. Finally, we show that in one dimension internal DLA can be predicted in O(log n) parallel time, and so is in the complexity class NC

Can local single-pass methods solve any stationary Hamilton-Jacobi-Bellman equation?

The use of local single-pass methods (like, e.g., the Fast Marching method) has become popular in the solution of some Hamilton-Jacobi equations. The prototype of these equations is the eikonal equation, for which the methods can be applied saving CPU time and possibly memory allocation. Then, some natural questions arise: can local single-pass methods solve any Hamilton-Jacobi equation? If not, where the limit should be set? This paper tries to answer these questions. In order to give a complete picture, we present an overview of some fast methods available in literature and we briefly analyze their main features. We also introduce some numerical tools and provide several numerical tests which are intended to exhibit the limitations of the methods. We show that the construction of a local single-pass method for general Hamilton-Jacobi equations is very hard, if not impossible. Nevertheless, some special classes of problems can be actually solved, making local single-pass methods very useful from the practical point of view.Comment: 19 page

Population aging through survival of the fit and stable

Motivated by the wide range of known self-replicating systems, some far from genetics, we study a system composed by individuals having an internal dynamics with many possible states that are partially stable, with varying mutation rates. Individuals reproduce and die with a rate that is a property of each state, not necessarily related to its stability, and the offspring is born on the parent's state. The total population is limited by resources or space, as for example in a chemostat or a Petri dish. Our aim is to show that mutation rate and fitness become more correlated, \emph{even if they are completely uncorrelated for an isolated individual}, underlining the fact that the interaction induced by limitation of resources is by itself efficient for generating collective effects

Probing Vortex Unbinding via Dipole Fluctuations

We develop a numerical method for detecting a vortex unbinding transition in a two-dimensional system by measuring large scale fluctuations in the total vortex dipole moment ${\vec P}$ of the system. These are characterized by a quantity $\cal F$ which measures the number of configurations in a simulation for which the either $P_x$ or $P_y$ is half the system size. It is shown that $\cal F$ tends to a non-vanishing constant for large system sizes in the unbound phase, and vanishes in the bound phase. The method is applied to the XY model both in the absence and presence of a magnetic field. In the latter case, the system size dependence of $\cal F$ suggests that there exist three distinct phases, one unbound vortex phase, a logarithmically bound phase, and a linearly bound phase.Comment: 6 pages, 2 figure

Multicanonical Methods vs. Molecular Dynamics vs. Monte Carlo: Comparison for Lennard-Jones Glasses

We applied a multicanonical algorithm (entropic sampling) to a two-dimensional and a three-dimensional Lennard-Jones system with quasicrystalline and glassy ground states. Focusing on the ability of the algorithm to locate low lying energy states, we compared the results of the multicanonical simulations with standard Monte Carlo simulated annealing and molecular dynamics methods. We find slight benefits to using entropic sampling in small systems (less than 80 particles), which disappear with larger systems. This is disappointing as the multicanonical methods are designed to surmount energy barriers to relaxation. We analyze this failure theoretically, and show (1) the multicanonical method is reduced in the thermodynamic limit (large systems) to an effective Monte Carlo simulated annealing with a random temperature vs. time, and (2) the multicanonical method gets trapped by unphysical entropy barriers in the same metastable states whose energy barriers trap the traditional quenches. The performance of Monte Carlo and molecular dynamics quenches were remarkably similar.Comment: 12 pages, 6 figures, REVTEX, epsf.st

On the out of equilibrium order parameters in long-range spin-glases

We show that the dynamical order parameters can be reexpressed in terms of the distribution of the staggered auto-correlation and response functions. We calculate these distributions for the out of equilibrium dynamics of the Sherrington-Kirpatrick model at long times. The results suggest that the landscape this model visits at different long times in an out of equilibrium relaxation process is, in a sense, self-similar. Furthermore, there is a similarity between the landscape seen out of equilibrium at long times and the equilibrium landscape. The calculation is greatly simplified by making use of the superspace notation in the dynamical approach. This notation also highlights the rather mysterious formal connection between the dynamical and replica approaches.Comment: 25 pages, Univ. di Roma I preprint #1049 (we replaced the file by the RevTex file, figures available upon request