Dynamical Trapping Research Articles

Dynamical trapping and relaxation of scalar gravitational fields

We present a framework for nonlinearly coupled scalar–tensor theory of gravity to address both inflation and core-collapse supernova problems. The unified approach is based on a novel dynamical trapping and relaxation of scalar gravity in highly energetic regimes. The new model provides a viable alternative mechanism of inflation free from various issues known to affect previous proposals. Furthermore, it could be related to observable violent astronomical events, specifically by releasing a significant amount of additional gravitational energy during core-collapse supernovae. A recent experiment at CERN relevant for testing this new model is briefly outlined.

Dynamical black holes in2+1dimensions

We investigate the global structure of a recently discovered simple exact, non-stationary solution of topologically massive and new massive gravity with the asymptotic charges of an undeformed BTZ black hole. We establish the existence of a timelike singularity in the causal structure of the spacetime even in the absence of angular momentum. The dynamical trapping and event horizons are determined and we investigate the evolution of the outer horizon showing that it may increase or decrease with time, depending on the value of the mass parameter. Finally, we test two proposals for dynamical entropy on this solution, one of them depending on the Kodama vector. In addition we show that the Kodama vector leads to the correct entropy for all stationary black holes in 2+1 dimensions.

Publisher's Note: Dynamical trapping of colloids at the stagnation points of electro-osmotic vortices of the second kind [Phys. Rev. E87, 033005 (2013)

Publisher's Note: Dynamical trapping of colloids at the stagnation points of electro-osmotic vortices of the second kind [Phys. Rev. E<b>87</b>, 033005 (2013)

Dynamical trapping of colloids at the stagnation points of electro-osmotic vortices of the second kind

By applying a stepwise overlimiting voltage to a nanoslot system in equilibrium, it is possible to follow the time evolution of the electroconvective instability vortex array via the depletion dynamics or, alternatively, by following dielectrophoretically trapped particles at the stagnation points of each of the hydrodynamic vortex pairs. Particles are advected to the stagnation point by the hydrodynamics, where they are trapped by a short-range dielectrophoretic force. It is experimentally confirmed that the wavelength selection process occurs at the diffusive time scale and that the wavelength selection mechanism, started by the Rubinstein and Zaltzman electroconvective instability is eventually determined by the system lateral geometry and dictated by Dukhin's electro-osmosis of the second kind. The steady-state case was numerically studied by solving the fully coupled electroconvective problem, confirming that the vortex stagnation point is indeed of a converging type. The particle's planar (two-dimensional) equations of motion are solved after adding a dielectrophoretic force that accounts for quasi-three-dimensional effects. It is shown that this force can account for trapping at the nanoslot interface.

Spacetime near isolated and dynamical trapping horizons

We study the near-horizon spacetime for isolated and dynamical trapping horizons (equivalently marginally outer trapped tubes). The metric is expanded relative to an ingoing Gaussian null coordinate and the terms of that expansion are explicitly calculated to second order. For the spacelike case, knowledge of the intrinsic and extrinsic geometry of the (dynamical) horizon is sufficient to determine the near-horizon spacetime, while for the null case (an isolated horizon) more information is needed. In both cases spacetime is allowed to be of arbitrary dimension and the formalism accomodates both general relativity as well as more general field equations. The formalism is demonstrated for two applications. First, spacetime is considered near an isolated horizon and the construction is both checked against the Kerr-Newman solution and compared to the well-known near-horizon limit for stationary extremal black hole spacetimes. Second, spacetime is examined in the vicinity of a slowly evolving horizon and it is demonstrated that there is always an event horizon candidate in this region. The geometry and other properties of this null surface match those of the slowly evolving horizon to leading order and in this approximation the candidate evolves in a locally determined way. This generalizes known results for Vaidya as well as certain spacetimes known from studies of the fluid-gravity correspondence.

Localized modes in nonlinear photonic kagome nanoribbons

We examine localization of light in nonlinear (Kerr) kagome lattices in the shape of narrow strips of varying width. For the narrowest ribbon, the band structure features a flat band leading to linear dynamical trapping of an initially localized excitation. We also find a geometry-induced bistability of the nonlinear modes as the width of the strip is changed. A crossover from one to two dimensions localization behavior is observed as the width is increased, attaining two-dimensional behavior for relatively narrow ribbons.

Non-Gaussianity and dynamical trapping in locally activated random walks

We propose a minimal model of locally activated diffusion, in which the diffusion coefficient of a one-dimensional Brownian particle is modified in a prescribed way-either increased or decreased-upon each crossing of the origin. Such a local mobility decrease arises in the formation of atherosclerotic plaques due to diffusing macrophage cells accumulating lipid particles. We show that spatially localized mobility perturbations have remarkable consequences on diffusion at all scales, such as the emergence of a non-Gaussian multipeaked probability distribution and a dynamical transition to an absorbing static state. In the context of atherosclerosis, this dynamical transition can be viewed as a minimal mechanism that causes macrophages to aggregate in lipid-enriched regions and thereby to the formation of atherosclerotic plaques.

AN INTRODUCTION TO LOCAL BLACK HOLE HORIZONS IN THE 3+1 APPROACH TO GENERAL RELATIVITY

We present an introduction to dynamical trapping horizons as quasi-local models for black hole horizons, from the perspective of an Initial Value Problem approach to the construction of generic black hole spacetimes. We focus on the geometric and structural properties of these horizons aiming, as a main application, at the numerical evolution and analysis of black hole spacetimes in astrophysical scenarios. In this setting, we discuss their dual role as an a priori ingredient in certain formulations of Einstein equations and as an a posteriori tool for the diagnosis of dynamical black hole spacetimes. Complementary to the first-principles discussion of quasi-local horizon physics, we place an emphasis on the rigidity properties of these hypersurfaces and their role as privileged geometric probes into near-horizon strong-field spacetime dynamics.

Coverage effects in the adsorption of H2 on Pd(100) studied by ab initio molecular dynamics simulations

The interaction of hydrogen with palladium surfaces represents one of the model systems for the study of the adsorption and absorption at metal surfaces. Theoretical gas-surface dynamics studies have usually concentrated on the adsorption dynamics on clean surfaces. Only recently it has become possible, based on advances in the electronic structure codes and improvements in the computer power, to address the much more complex problem of the adsorption dynamics on precovered surfaces. Here, I present ab initio molecular dynamics (AIMD) simulations based on periodic density functional theory (DFT) calculations of the adsorption of H(2) on hydrogen-precovered Pd(100) for a broad variety of different hydrogen coverage structures. The stability of the adsorbate structures and the adsorption dynamics are analyzed in detail. Calculated sticking probabilities are larger than expected for pure site-blocking consistent with experimental results. It turns out that the adsorption dynamics on the strongly corrugated surfaces depends sensitively on the dynamic response of the substrate atoms upon the impact of the impinging H(2) molecules. In addition, for some structures the adsorption probability was evaluated as a function of the kinetic energy. Adsorbate structures corresponding to the same coverage but with different arrangements of the adsorbed atoms can lead to a qualitatively different dependence of the adsorption probability on the kinetic energy changing also the order of the preferred structures, as far as the adsorption is concerned, as a function of the kinetic energy. This indicates that dynamical effects such as steering and dynamical trapping play an important role in the adsorption on these precovered substrates.

AN INTRODUCTION TO LOCAL BLACK HOLE HORIZONS IN THE 3+1 APPROACH TO GENERAL RELATIVITY

We present an introduction to dynamical trapping horizons as quasi-local models for black hole horizons, from the perspective of an Initial Value Problem approach to the construction of generic black hole spacetimes. We focus on the geometric and structural properties of these horizons aiming, as a main application, at the numerical evolution and analysis of black hole spacetimes in astrophysical scenarios. In this setting, we discuss their dual role as an a priori ingredient in certain formulations of Einstein equations and as an a posteriori tool for the diagnosis of dynamical black hole spacetimes. Complementary to the first-principles discussion of quasi-local horizon physics, we place an emphasis on the rigidity properties of these hypersurfaces and their role as privileged geometric probes into near-horizon strong-field spacetime dynamics.

Dynamic trapping of light in modulated waveguide lattices

A discrete analogue of the dynamic (Kapitza) trapping effect, known for classical and quantum particles in rapidly oscillating potentials, is proposed for light waves in modulated graded-index waveguide lattices. In particular, it is shown that, while a graded-index potential in a nonmodulated waveguide lattice can confine light at either normal or Bragg angle incidence, periodic modulation of the potential in the longitudinal direction enables one to trap optical beams at both normal and Bragg incidence angles.

Dynamical horizon entropy and equilibrium thermodynamics of generalized gravity theories

We study the relation between the thermodynamics and field equations of generalized gravity theories on the dynamical trapping horizon with sphere symmetry. We assume the entropy of dynamical horizon as the Noether charge associated with the Kodama vector and point out that it satisfies the second law when a Gibbs equation holds. We generalize two kinds of Gibbs equations to Gauss-Bonnet gravity on any trapping horizon. Based on the quasi-local gravitational energy found recently for $f(R)$ gravity and scalar-tensor gravity in some special cases, we also build up the Gibbs equations, where the nonequilibrium entropy production, which is usually invoked to balance the energy conservation, is just absorbed into the modified Wald entropy in the FRW spacetime with slowly varying horizon. Moreover, the equilibrium thermodynamic identity remains valid for $f(R)$ gravity in a static spacetime. Our work provides an alternative treatment to reinterpret the nonequilibrium correction and supports the idea that the horizon thermodynamics is universal for generalized gravity theories.

Dynamical Slowing and trapping of light in coupled semiconductor laser arrays

We propose and analyze a new scheme for storing and releasing optical pulses comprising an array of weakly coupled semiconductor lasers. By activating and deactivating individual lasers in the array we are able to manipulate optical pulses, trap them for long periods and release them without noticeable distortion. In addition, the proposed scheme can also regenerate and reshape distorted pulses all-optically. Additional applications such as routing, pulse synchronization and true-time-delaying are also presented and discussed.

ENERGY AND ANGULAR MOMENTUM IN STRONG GRAVITATING SYSTEMS

A quasilocal framework of stationary and dynamical untrapped hypersurfaces is introduced to generalize the notions of energy and angular momentum of isolated and dynamical trapping horizons to general strong gravitating systems.

Dynamical trapping and chaotic scattering of the harmonically driven barrier

A detailed analysis of the classical nonlinear dynamics of a single driven square potential barrier with harmonically oscillating position is performed. The system exhibits dynamical trapping which is associated with the existence of a stable island in phase space. Due to the unstable periodic orbits of the KAM structure, the driven barrier is a chaotic scatterer and shows stickiness of scattering trajectories in the vicinity of the stable island. The transmission function of a suitably prepared ensemble yields results which are very similar to tunneling resonances in the quantum mechanical regime. However, the origin of these resonances is different in the classical regime.

Blocking of alkaline migration under ionizing irradiation in Cr-doped oxide glasses

Effects of ionizing irradiation on different chromium-doped silicate glass compositions have been studied using EPR and Raman spectroscopies. We observe first reduction processes of Cr3+ and Cr6+ ions correlated with the dose integrated inside the glass. With the doping content in theses glasses, we observe also by EPR spectroscopy a complete blocking of defects production under ionizing radiation for samples doped with more than 1mol% of Cr2O3. This result is explained by dynamical reversible trapping of the excitons produced during irradiation. Associated to the disappearance of defects produced by irradiation, a decrease of the glass structural changes are also detected by Raman spectroscopy at integrated doses higher than 109Gy.

Trapping horizons as inner boundary conditions for black hole spacetimes

We present a set of inner boundary conditions for the numerical construction of dynamical black hole spacetimes, when employing a $3+1$ constrained evolution scheme and an excision technique. These inner boundary conditions are heuristically motivated by the dynamical trapping horizon framework and are enforced in an elliptic subsystem of the full Einstein equation. In the stationary limit they reduce to existing isolated horizon boundary conditions. A characteristic analysis completes the discussion of inner boundary conditions for the radiative modes.

Diversity of close-in planets and the interactions with their host stars

AbstractShort period planets provide an exciting opportunity of constraining structural properties. Observations have revealed a diverse class of objects, including several at odds with aspects of conventional planet formation theories. Here we present several scenarios that may help in producing the observed diversity. For short period planets in particular, their proximity to their host stars suggests that star-planet interactions may play an important role in their orbital and structural evolution. We first show that the penetration of a non-synchronous stellar magnetic field into short period planets will provide a significant source of energy for planetary expansion and may help stall inward migration. In addition to magnetic dissipation, the intense irradiation from the host star will drive atmospheric flows, whose behaviour is strongly influenced by the opacity of the envelope. Finally, we explore the role of late stage planetesimal and embryo bombardment on the structure of gas-giant planets. Dynamical trapping during migration, followed by orbital destablization during the final stage of gas-giant growth, leads to a surge in the collision rate. Such collisions will lead to preferential core growth and inflated radii. All three of these processes, occurring late in the planetary formation process, will produce a large range in planetary properties and may account for the diversity we see today.

Origin of power-law distributions in deterministic walks: The influence of landscape geometry

We investigate the properties of a deterministic walk, whose locomotion rule is always to travel to the nearest site. Initially the sites are randomly distributed in a closed rectangular (ALxL) landscape and, once reached, they become unavailable for future visits. As expected, the walker step lengths present characteristic scales in one (L-->0) and two (AL approximately L) dimensions. However, we find scale invariance for an intermediate geometry, when the landscape is a thin striplike region. This result is induced geometrically by a dynamical trapping mechanism, leading to a power-law distribution for the step lengths. The relevance of our findings in broader contexts--of both deterministic and random walks--is also briefly discussed.

Isolated, slowly evolving, and dynamical trapping horizons: Geometry and mechanics from surface deformations

We study the geometry and dynamics of both isolated and dynamical trapping horizons by considering the allowed variations of their foliating two-surfaces. This provides a common framework that may be used to consider both their possible evolutions and their deformations as well as derive the well-known flux laws. Using this framework, we unify much of what is already known about these objects as well as derive some new results. In particular we characterize and study the ``almost isolated'' trapping horizons known as slowly evolving horizons. It is for these horizons that a dynamical first law holds and this is analogous and closely related to the Hawking-Hartle formula for event horizons.