Transitions to Measure Synchronization in Coupled Hamiltonian Systems

Transitions to measure synchronization in two coupled $\phi ^{4}$ lattices are investigated based on numerical simulations. The relationship between measure synchronization (MS), phase locking and system's total energy is studied both for periodic and chaotic states. Two different scalings are discovered during the process to MS according to phase locking. Random walk like phase synchronization in chaotic measure synchronization is found, and phase locking interrupted by phase slips irregularly is also investigated. Meanwhile, related analysis is qualitative given to explain this phenomenon.Comment: 10 pages, 6 figure

Dynamics of multiply charged ions in intense laser fields

We numerically investigate the dynamics of multiply charged hydrogenic ions in near-optical linearly polarized laser fields with intensities of order 10^16 to 10^17 W/cm^2. Depending on the charge state Z of the ion the relation of strength between laser field and ionic core changes. We find around Z=12 typical multiphoton dynamics and for Z=3 tunneling behaviour, however with clear relativistic signatures. In first order in v/c the magnetic field component of the laser field induces a Z-dependent drift in the laser propagation direction and a substantial Z-dependent angular momentum with repect to the ionic core. While spin oscillations occur already in first order in v/c as described by the Pauli equation, spin induced forces via spin orbit coupling only appear in the parameter regime where (v/c)^2 corrections are significant. In this regime for Z=12 ions we show strong splittings of resonant spectral lines due to spin-orbit coupling and substantial corrections to the conventional Stark shift due to the relativistic mass shift while those to the Darwin term are shown to be small. For smaller charges or higher laser intensities, parts of the electronic wavepacket may tunnel through the potential barrier of the ionic core, and when recombining are shown to give rise to keV harmonics in the radiation spectrum. Some parts of the wavepacket do not recombine after ionisation and we find very energetic electrons in the weakly relativistic regime of above threshold ionization.Comment: submitte

Stray field and superconducting surface spin valve effect in La0.7_{0.7}Ca0.3_{0.3}MnO3_3/YBa2_2Cu3_3O7−δ_{7-\delta} bilayers

Electronic transport and magnetization measurements were performed on La$_{0.7}$Ca$_{0.3}$MnO$_3$/YBa$_2$Cu$_3$O$_{7-\delta}$ (LCMO/YBCO) bilayers below the superconducting transition temperature in order to study the interaction between magnetism and superconductivity. This study shows that a substantial number of weakly pinned vortices are induced in the YBCO layer by the large out-of-plane stray field in the domain walls. Their motion gives rise to large dissipation peaks at the coercive field. The angular dependent magnetoresistance (MR) data reveal the interaction between the stripe domain structure present in the LCMO layer and the vortices and anti-vortices induced in the YBCO layer by the out-of-plane stray field. In addition, this study shows that a superconducting surface spin valve effect is present in these bilayers as a result of the relative orientation between the magnetization at the LCMO/YBCO interface and the magnetization in the interior of the LCMO layer that can be tuned by the rotation of a small $H$. This latter finding will facilitate the development of superconductive magnetoresistive memory devices. These low-magnetic field MR data, furthermore, suggest that triplet superconductivity is induced in the LCMO layer, which is consistent with recent reports of triplet superconductivity in LCMO/YBCO/LCMO trilayers and LCMO/YBCO bilayers.Comment: 14 pages, 3 figure

Semantic modelling of learning objects and instruction

We introduce an ontology-based semantic modelling framework that addresses subject domain modelling, instruction modelling, and interoperability aspects in the development of complex reusable learning objects. Ontologies are knowledge representation frameworks, ideally suited to support knowledge-based modelling of these learning objects. We illustrate the benefits of semantic modelling for learning object assemblies within the context of standards such as SCORM Sequencing and Navigation and Learning Object Metadata

Universal scaling functions for bond percolation on planar random and square lattices with multiple percolating clusters

Percolation models with multiple percolating clusters have attracted much attention in recent years. Here we use Monte Carlo simulations to study bond percolation on $L_{1}\times L_{2}$ planar random lattices, duals of random lattices, and square lattices with free and periodic boundary conditions, in vertical and horizontal directions, respectively, and with various aspect ratio $L_{1}/L_{2}$. We calculate the probability for the appearance of $n$ percolating clusters, $W_{n},$ the percolating probabilities, $P$, the average fraction of lattice bonds (sites) in the percolating clusters, $_{n}$ ($_{n}$), and the probability distribution function for the fraction $c$ of lattice bonds (sites), in percolating clusters of subgraphs with $n$ percolating clusters, $f_{n}(c^{b})$ ($f_{n}(c^{s})$). Using a small number of nonuniversal metric factors, we find that $W_{n}$, $P$, $_{n}$ ($_{n}$), and $f_{n}(c^{b})$ ($f_{n}(c^{s})$) for random lattices, duals of random lattices, and square lattices have the same universal finite-size scaling functions. We also find that nonuniversal metric factors are independent of boundary conditions and aspect ratios.Comment: 15 pages, 11 figure

Quantum Brownian motion of multipartite systems and their entanglement dynamics

We solve the model of N quantum Brownian oscillators linearly coupled to an environment of quantum oscillators at finite temperature, with no extra assumptions about the structure of the system-environment coupling. Using a compact phase-space formalism, we give a rather quick and direct derivation of the master equation and its solutions for general spectral functions and arbitrary temperatures. Since our framework is intrinsically nonperturbative, we are able to analyze the entanglement dynamics of two oscillators coupled to a common scalar field in previously unexplored regimes, such as off resonance and strong coupling.Comment: 10 pages, 6 figure

Mapping functions and critical behavior of percolation on rectangular domains

The existence probability $E_p$ and the percolation probability $P$ of the bond percolation on rectangular domains with different aspect ratios $R$ are studied via the mapping functions between systems with different aspect ratios. The superscaling behavior of $E_p$ and $P$ for such systems with exponents $a$ and $b$, respectively, found by Watanabe, Yukawa, Ito, and Hu in [Phys. Rev. Lett. \textbf{93}, 190601 (2004)] can be understood from the lower order approximation of the mapping functions $f_R$ and $g_R$ for $E_p$ and $P$, respectively; the exponents $a$ and $b$ can be obtained from numerically determined mapping functions $f_R$ and $g_R$, respectively.Comment: 17 pages with 6 figure