Free Field Models Research Articles

Reliquefaction behavior of sand and response of pile group subjected to repeated shaking sequence using centrifuge model experiments

A series of centrifuge model experiments were performed in this study to investigate the sand reliquefaction behavior in free field and pile group models subjected to repeated shakings. Toyoura sand was used to prepare the model ground with 50 % relative density and experimented at 50g centrifugal acceleration. A 2 × 2 pile group model was used to examine the response of piles and its effect on sand reliquefaction during repeated shakings. A seismic sequence comprising foreshocks–mainshock–aftershocks–mainshock pattern was imparted to both free field and pile group models. In addition, an independent mainshock was imparted to a free field model and compared with the seismic sequence to examine the effect of foreshocks in triggering future liquefaction. Acceleration time response, excess pore pressure (EPP), ground subsidence, bending moment and lateral displacement of the pile group were measured. Significant de-amplification and unsymmetrical response with presence of shear-induced dilatancy spikes were observed in both free field and pile group models. Results from this study indicate that foreshocks and aftershocks are not sufficient to induce liquefaction. However, liquefaction and subsequent reliquefaction were recorded in both models during mainshocks. Pile group recorded smaller EPP response and subsidence compared to free field model. Higher magnitude of reliquefaction was induced even at moderate depths during the second mainshock at a quicker time. This was primarily associated with the increase in magnitude of anisotropy due to repeated generation and dissipation of pore water which results in decrease in resistance to further reliquefaction. Hardening induced around the vicinity of the pile group due to sand densification has resulted in smaller bending moment values during second mainshock compared to the first.

Krylov complexity in conformal field theory

Krylov complexity, or K-complexity for short, has recently emerged as a new probe of chaos in quantum systems. It is a measure of operator growth in Krylov space, which conjecturally bounds the operator growth measured by the out of time ordered correlator (OTOC). We study Krylov complexity in conformal field theories by considering arbitrary 2d CFTs, free field, and holographic models. We find that the bound on OTOC provided by Krylov complexity reduces to bound on chaos of Maldacena, Shenker, and Stanford. In all considered examples including free and rational CFTs Krylov complexity grows exponentially, in stark violation of the expectation that exponential growth signifies chaos.

Study on the influence of the seafloor soft soil layer on seismic ground motion

Abstract. In the complex medium system of the sea area, the overlying seawater and the surface soft soil have a significant impact on the seafloor ground motion, which brings great seismic risk to the safety of offshore-engineering structures. In this paper, four sets of typical free-field models are constructed and established, comprising a land model, land model with surface soft soil, sea model and sea model with surface soft soil. The dynamic finite-difference method is used to carry out two-dimensional seismic response analysis of a typical free field based on the input forms of P and SV waves. By comparing the seismic response analysis results of four groups of calculation models, the effects of overlying seawater and soft soil on the peak acceleration and acceleration response spectrum are studied. The results show that when an SV wave is input, the peak acceleration and response spectrum of the surface of soft soil on the surface and the seabed surface can be amplified, while the overlying seawater can significantly reduce the ground motion. When the P wave is used, the effect of overlying seawater and soft soil on the peak acceleration and response spectrum of the surface and seabed can be ignored. The peak acceleration decreases first and then increases from the bottom to the surface, and the difference of peak acceleration calculated by four free-field models is not obvious. The results show that the overlying seawater and the surface soft soil layer have little effect on the peak acceleration of ground motion below the surface.

Field Theory with Coordinate Dependent Noncommutativity

We discuss the formulation of classical field theoretical models on $n$-dimensional noncommutative space-time defined by a generic associative star product. A simple procedure for deriving conservation laws is presented and applied to field theories in noncommutative space-time to obtain local conservation laws (for the electric charge and for the energy-momentum tensor of free fields) and more generally an energy-momentum balance equation for interacting fields. For free field models an analogy with the damped harmonic oscillator in classical mechanics is pointed out, which allows us to get a physical understanding for the obtained conservation laws. To conclude, the formulation of field theories on curved noncommutative space is addressed.

Finite Element Seismic Analysis of Soil–Tunnel Interactions in Clay Soils

Seismic waves propagate from bedrock through the soil layers and during this propagation they pass different layers of soil and rock until they reach the soil surface. These waves can be amplified or damped by the soil layers. Underground structures response, like tunnels, is related to a number of factors such as soil type and earthquake frequency. In this paper the simulation of the models is done in two-dimensional plain strain system with finite element mesh generation which consists of soil–tunnel using frequency spectrum analysis. All analyses consist of three actual ground motion records with low, intermediate and high-frequency content. Two different clay soils (Normally or Lightly Over-Consolidate Clay and Heavily Over-Consolidate Clay) have been used in free field and models consist of cylindrical tunnel. In this study, the results of both free field (models without structure) and soil–tunnel analysis have been compared to show the effect of the tunnel on responses. Effect of soil–tunnel interaction in all earthquakes with different frequency content on-site response, amplification, acceleration response and stress and strain propagation in the tunnel’s perimeter are discussed. Based on the results of the analysis, acceleration frequency at different depths of models had different characteristics. Both clay soils amplified seismic waves on the soil surface in free filled models and the soil–structure interaction effects on the tunnel dynamic responses.

Experiments of multichannel least-square methods for sound field reproduction inside aircraft mock-up: Objective evaluations

Sound environment reproduction of various flight conditions in aircraft mock-ups is a valuable tool for the study, prediction, demonstration and jury testing of interior aircraft sound quality and annoyance. To provide a faithful reproduced sound environment, time, frequency and spatial characteristics should be preserved. Physical sound field reproduction methods for spatial sound reproduction are mandatory to immerse the listener׳s body in the proper sound fields so that localization cues are recreated at the listener׳s ears. Vehicle mock-ups pose specific problems for sound field reproduction. Confined spaces, needs for invisible sound sources and very specific acoustical environment make the use of open-loop sound field reproduction technologies such as wave field synthesis (based on free-field models of monopole sources) not ideal. In this paper, experiments in an aircraft mock-up with multichannel least-square methods and equalization are reported. The novelty is the actual implementation of sound field reproduction with 3180 transfer paths and trim panel reproduction sources in laboratory conditions with a synthetic target sound field. The paper presents objective evaluations of reproduced sound fields using various metrics as well as sound field extrapolation and sound field characterization.

THE RELATION BETWEEN SOLAR ERUPTION TOPOLOGIES AND OBSERVED FLARE FEATURES. II. DYNAMICAL EVOLUTION

ABSTRACT A long-established goal of solar physics is to build understanding of solar eruptions and develop flare and coronal mass ejection (CME) forecasting models. In this paper, we continue our investigation of nonlinear forces free field (NLFFF) models by comparing topological properties of the solutions to the evolution of the flare ribbons. In particular, we show that data-constrained NLFFF models of three erupting sigmoid regions (SOL2010-04-08, SOL2010-08-07, and SOL2012-05-12) built to reproduce the active region magnetic field in the pre-flare state can be rendered unstable and the subsequent sequence of unstable solutions produces quasi-separatrix layers that match the flare ribbon evolution as observed by SDO/AIA. We begin with a best-fit equilibrium model for the pre-flare active region. We then add axial flux to the flux rope in the model to move it across the stability boundary. At this point, the magnetofrictional code no longer converges to an equilibrium solution. The flux rope rises as the solutions are iterated. We interpret the sequence of magnetofrictional steps as an evolution of the active region as the flare/CME begins. The magnetic field solutions at different steps are compared with the flare ribbons. The results are fully consistent with the three-dimensional extension of the standard flare/CME model. Our ability to capture essential topological features of flaring active regions with a non-dynamic magnetofrictional code strongly suggests that the pre-flare, large-scale topological structures are preserved as the flux rope becomes unstable and lifts off.

Acoustic measurements and modeling of air-filled underwater resonator cavities

This project investigated the near-resonance acoustical properties of submerged air-filled resonator cavities intended for use in underwater noise abatement systems, exploring a potential alternative to encapsulated bubbles. The underwater resonator cavities are air-filled containers resembling Helmholtz resonators, inverted and submerged in water, creating a direct interface between the volume of air trapped inside the cavity and the surrounding water. Experiments were performed with a prototype resonator cavity in a closed water-filled laboratory tank operated in the long wavelength limit (under 500 Hz) and the resonance frequencies and Q-factors were measured for various air-fill volumes. A finite-element simulation was used to examine the behavior of the resonator cavities within the experimental tank apparatus, yielding good agreement with measurements. Finally, free-field models were also developed (a finite-element numerical model and a Helmholtz-resonator-based analytical model), both of which yielded good agreement with the tank measurements. The measurements and models presented here indicate that inexpensive and convenient sub-wavelength laboratory tank measurements, along with simple analytical models can be used to accurately design and verify the free-field behavior of low frequency underwater noise abatement resonators.

Modeling magnetic flux ropes in the solar atmosphere

Coronal flux ropes are highly sheared or twisted magnetic fields overlying polarity inversion lines on the solar photosphere. The formation of such flux ropes is briefly discussed. A coronal flux rope can be stable for many days and then suddenly lose equilibrium and erupt, producing a coronal mass ejection (CME). To understand what causes such eruptions, we need to determine the 3D magnetic structure of observed active regions prior to CMEs. This requires constructing nonlinear force free field models of active regions based on observed photospheric vector fields, Hα filaments, or coronal loop structures. We describe a new method for constructing models containing flux ropes.

Crosstalk cancellation in virtual acoustic imaging systems for multiple listeners

The perception of a virtual sound source is achieved by ensuring that the sound pressures at the ears of the listener are equivalent to those produced by the source at the virtual position. Theoretically, with only two loudspeakers for a single listener, virtual sources positioned anywhere in space can be presented provided that “crosstalk cancellation” can be achieved. The crosstalk cancellation problem is central to the problem of sound reproduction since an efficient crosstalk canceller gives one complete control over the sound field at a number of target positions. However, all crosstalk cancellation systems implemented so far have in practice produced virtual sources for only a single listener at a time. The design of crosstalk cancellers for multiple listeners involves a detailed study of the relative orientation of both sources and listeners. It is vital in any multiple listener system to first establish the conditioning of the potential geometrical arrangements of transducers and listeners by using simple free field models of the electro-acoustic transfer functions between transducers and ears. This gives an important link between the conditioning of the electro-acoustic transfer function matrix and the inverse filters for crosstalk cancellation. Optimal transducer arrangements for the efficient crosstalk canceller have been identified for the case of two listeners and these are evaluated here with time domain simulations.

QUANTUM ENERGY INEQUALITIES IN TWO-DIMENSIONAL CONFORMAL FIELD THEORY

Quantum energy inequalities (QEIs) are state-independent lower bounds on weighted averages of the stress-energy tensor, and have been established for several free quantum field models. We present rigorous QEI bounds for a class of interacting quantum fields, namely the unitary, positive energy conformal field theories (with stress-energy tensor) on two-dimensional Minkowski space. The QEI bound depends on the weight used to average the stress-energy tensor and the central charge(s) of the theory, but not on the quantum state. We give bounds for various situations: averaging along timelike, null and spacelike curves, as well as over a space-time volume. In addition, we consider boundary conformal field theories and more general "moving mirror" models. Our results hold for all theories obeying a minimal set of axioms which — as we show — are satisfied by all models built from unitary highest-weight representations of the Virasoro algebra. In particular, this includes all (unitary, positive energy) minimal models and rational conformal field theories. Our discussion of this issue collects together (and, in places, corrects) various results from the literature which do not appear to have been assembled in this form elsewhere.

Discrete-time quantum field theory and the deformed super-Virasoro algebra

We show that the deformations of Virasoro and super-Virasoro algebra, constructed earlier on an abstract mathematical background, emerge after Wick rotation, within an exact treatment of discrete-time free field models on a circle. The deformation parameter is e λ , where λ= τ/ ρ is the ratio of the discrete-time scale τ and the radius ρ of the compact space.

Classification of Subsystems for Local Nets¶with Trivial Superselection Structure

Let F be a local net of von Neumann algebras in four spacetime dimensions satisfying certain natural structural assumptions. We prove that if F has trivial superselection structure then every covariant, Haag-dual subsystem B is the fixed point net under a compact group action on one component in a suitable tensor product decomposition of F. Then we discuss some application of our result, including free field models and certain theories with at most countably many sectors.

Representation theory for a class of so( N)-extended superconformal operator algebras

We study the representation theory for a class of so( N)-extended superconformal operator algebras, which was originally proposed by Knizhnik. Our main result is a set of conditions for consistency and unitarity, which are formulated in terms of the labels (Δ; m 1, m 2…, m [ N 2 ] ) that characterize an irreducible highest weight module. We exploit the correspondence of level-1 so( N)-extended superconformal theories, which have c N = 1 2 N + 1 , with certain free-field models, to derive character formulas for all representations that are allowed at level 1.

On the simplicity of the even CAR algebra and free field models

An example of a local rings system where the quasilocal algebra is a simple countably generatedC*-algebra with unit is provided by the “local observables” for the free Fermi field.