Displacive To Order-Disorder Two-Step Phase Transition Model For Para-Ferroelectric Transition

Two-step phase transition model, displacive to order-disorder, is proposed. The driving forces for these two transitions are fundamentally different. The displacive phase transition is one type of the structural phase transitions. We clearly define the structural phase transition as the symmetry broking of the unit cell and the electric dipole starts to form in the unit cell. Then the dipole-dipole interaction takes place as soon as the dipoles in unit cells are formed. We believe that the dipole-dipole interaction may cause an order-disorder phase transition following the displacive phase transition. Both structural and order-disorder phase transition can be first-order or second-order or in between. We found that the structural transition temperatures can be lower or equal or higher than the order-disorder transition temperature. The para-ferroelectric phase transition is the combination of the displacive and order-disorder phase transitions. It generates a variety of transition configurations along with confusions. In this paper, we discuss all these configurations using our displacive to order-disorder two-step phase transition model and clarified all the confusions.

High Order Multi-Moment Constrained Finite Volume Method. Part I: Basic Formulation

A new high-order finite volume method based on local reconstruction is presented in this paper. The method, so-called the multi-moment constrained finite volume (MCV) method, uses the point values defined within single cell at equally spaced points as the model variables (or unknowns). The time evolution equations used to update the unknowns are derived from a set of constraint conditions imposed on multi kinds of moments, i.e. the cell-averaged value and the point-wise value of the state variable and its derivatives. The finite volume constraint on the cell-average guarantees the numerical conservativeness of the method. Most constraint conditions are imposed on the cell boundaries, where the numerical flux and its derivatives are solved as general Riemann problems. A multi-moment constrained Lagrange interpolation reconstruction for the demanded order of accuracy is constructed over single cell and converts the evolution equations of the moments to those of the unknowns. The presented method provides a general framework to construct efficient schemes of high orders. The basic formulations for hyperbolic conservation laws in 1- and 2D structured grids are detailed with the numerical results of widely used benchmark tests. (C) 2009 Elsevier Inc. All rights reserved.

The stochastic exit problem for dynamical systems

The problem of "exit against a flow" for dynamical systems subject to small Gaussian white noise excitation is studied. Here the word "flow" refers to the behavior in phase space of the unperturbed system's state variables. "Exit against a flow" occurs if a perturbation causes the phase point to leave a phase space region within which it would normally be confined. In particular, there are two components of the problem of exit against a flow:

i) the mean exit time

ii) the phase-space distribution of exit locations.

When the noise perturbing the dynamical systems is small, the solution of each component of the problem of exit against a flow is, in general, the solution of a singularly perturbed, degenerate elliptic-parabolic boundary value problem.

Singular perturbation techniques are used to express the asymptotic solution in terms of an unknown parameter. The unknown parameter is determined using the solution of the adjoint boundary value problem.

The problem of exit against a flow for several dynamical systems of physical interest is considered, and the mean exit times and distributions of exit positions are calculated. The systems are then simulated numerically, using Monte Carlo techniques, in order to determine the validity of the asymptotic solutions.

Ejection of energetic photoelectrons in laser-induced autoionisation: effects of high-order ionisation processes

Resonant interaction of an autoionising state with a strong laser field is considered and effects of second-order ionisation processes are investigated. The authors show that these processes play a very important role in laser-induced autoionisation (LIA). They drastically affect the lowest-order peaks in the photoelectron spectrum. In addition to these peaks, high-order peaks due to ejection of energetic photoelectrons appear. For the laser intensities of current interest, second-order peaks are much stronger than the original ones, an important result that, they believe, can be observed experimentally. Moreover, `peak switching', a general feature of above-threshold ionisation, is also manifest in the electron spectrum of LIA.

Dense, efficient chip-to-chip communication at the extremes of computing

The scalability of CMOS technology has driven computation into a diverse range of applications across the power consumption, performance and size spectra. Communication is a necessary adjunct to computation, and whether this is to push data from node-to-node in a high-performance computing cluster or from the receiver of wireless link to a neural stimulator in a biomedical implant, interconnect can take up a significant portion of the overall system power budget. Although a single interconnect methodology cannot address such a broad range of systems efficiently, there are a number of key design concepts that enable good interconnect design in the age of highly-scaled CMOS: an emphasis on highly-digital approaches to solving ‘analog’ problems, hardware sharing between links as well as between different functions (such as equalization and synchronization) in the same link, and adaptive hardware that changes its operating parameters to mitigate not only variation in the fabrication of the link, but also link conditions that change over time. These concepts are demonstrated through the use of two design examples, at the extremes of the power and performance spectra.

A novel all-digital clock and data recovery technique for high-performance, high density interconnect has been developed. Two independently adjustable clock phases are generated from a delay line calibrated to 2 UI. One clock phase is placed in the middle of the eye to recover the data, while the other is swept across the delay line. The samples produced by the two clocks are compared to generate eye information, which is used to determine the best phase for data recovery. The functions of the two clocks are swapped after the data phase is updated; this ping-pong action allows an infinite delay range without the use of a PLL or DLL. The scheme's generalized sampling and retiming architecture is used in a sharing technique that saves power and area in high-density interconnect. The eye information generated is also useful for tuning an adaptive equalizer, circumventing the need for dedicated adaptation hardware.

On the other side of the performance/power spectra, a capacitive proximity interconnect has been developed to support 3D integration of biomedical implants. In order to integrate more functionality while staying within size limits, implant electronics can be embedded onto a foldable parylene (‘origami’) substrate. Many of the ICs in an origami implant will be placed face-to-face with each other, so wireless proximity interconnect can be used to increase communication density while decreasing implant size, as well as facilitate a modular approach to implant design, where pre-fabricated parylene-and-IC modules are assembled together on-demand to make custom implants. Such an interconnect needs to be able to sense and adapt to changes in alignment. The proposed array uses a TDC-like structure to realize both communication and alignment sensing within the same set of plates, increasing communication density and eliminating the need to infer link quality from a separate alignment block. In order to distinguish the communication plates from the nearby ground plane, a stimulus is applied to the transmitter plate, which is rectified at the receiver to bias a delay generation block. This delay is in turn converted into a digital word using a TDC, providing alignment information.

Constrained high-order statistical blind deconvolution of spectral data

A constrained high-order statistical algorithm is proposed to blindly deconvolute the measured spectral data and estimate the response function of the instruments simultaneously. In this algorithm, no prior-knowledge is necessary except a proper length of the unit-impulse response. This length can be easily set to be the width of the narrowest spectral line by observing the measured data. The feasibility of this method has been demonstrated experimentally by the measured Raman and absorption spectral data.

Ghosts of order on the frontier of chaos

What kinds of motion can occur in classical mechanics? We address this question by looking at the structures traced out by trajectories in phase space; the most orderly, completely integrable systems are characterized by phase trajectories confined to low-dimensional, invariant tori. The KAM theory examines what happens to the tori when an integrable system is subjected to a small perturbation and finds that, for small enough perturbations, most of them survive.

The KAM theory is mute about the disrupted tori, but, for two-dimensional systems, Aubry and Mather discovered an astonishing picture: the broken tori are replaced by "cantori," tattered, Cantor-set remnants of the original invariant curves. We seek to extend Aubry and Mather's picture to higher dimensional systems and report two kinds of studies; both concern perturbations of a completely integrable, four-dimensional symplectic map. In the first study we compute some numerical approximations to Birkhoff periodic orbits; sequences of such orbits should approximate any higher dimensional analogs of the cantori. In the second study we prove converse KAM theorems; that is, we use a combination of analytic arguments and rigorous, machine-assisted computations to find perturbations so large that no KAM tori survive. We are able to show that the last few of our Birkhoff orbits exist in a regime where there are no tori.

Fine interference fringes formed in high-order harmonic spectra generated by infrared driving laser pulses

We experimentally investigate the high-order harmonic generation in argon gas using a driving laser pulse at a center wavelength of 1240 nm. High-contrast fine interference fringes could be observed in the harmonic spectra near the propagation axis, which is attributed to the interference between long and short quantum paths. We also systematically examine the variation of the interference fringe pattern with increasing energy of the driving pulse and with different phase-matching conditions.

Laser intensity dependence of high-order harmonic generation from aligned CO2 molecules

We investigate experimentally the high-order harmonic generation from aligned CO2 molecules and demonstrate that the modulation inversion of the harmonic yield with respect to molecular alignment can be altered dramatically by fine-tuning the intensity of the driving laser pulse for harmonic generation. The results can be modeled by employing the strong field approximation including a ground state depletion factor. The laser intensity is thus proved to be a parameter that can control the high-harmonic emission from aligned molecules.

Spectral evolution of angularly resolved third-order harmonic generation by infrared femtosecond laser-pulse filamentation in air

We experimentally investigate the evolution of an angularly resolved spectrum of third harmonic generated by infrared femtosecond laser pulse filamentation in air. We show that at low pump intensity, phase matching between the fundamental and third-harmonic waves dominates the nonlinear optical effect and induces a ring structure of the third-harmonic beam, whereas at high pump intensity, the dispersion properties of air begin to affect the angular spectrum, leading to the formation of a nonlinear X wave at third harmonic.

A new high-order Fourier continuation-based elasticity solver for complex three-dimensional geometries

This thesis presents a new approach for the numerical solution of three-dimensional problems in elastodynamics. The new methodology, which is based on a recently introduced Fourier continuation (FC) algorithm for the solution of Partial Differential Equations on the basis of accurate Fourier expansions of possibly non-periodic functions, enables fast, high-order solutions of the time-dependent elastic wave equation in a nearly dispersionless manner, and it requires use of CFL constraints that scale only linearly with spatial discretizations. A new FC operator is introduced to treat Neumann and traction boundary conditions, and a block-decomposed (sub-patch) overset strategy is presented for implementation of general, complex geometries in distributed-memory parallel computing environments. Our treatment of the elastic wave equation, which is formulated as a complex system of variable-coefficient PDEs that includes possibly heterogeneous and spatially varying material constants, represents the first fully-realized three-dimensional extension of FC-based solvers to date. Challenges for three-dimensional elastodynamics simulations such as treatment of corners and edges in three-dimensional geometries, the existence of variable coefficients arising from physical configurations and/or use of curvilinear coordinate systems and treatment of boundary conditions, are all addressed. The broad applicability of our new FC elasticity solver is demonstrated through application to realistic problems concerning seismic wave motion on three-dimensional topographies as well as applications to non-destructive evaluation where, for the first time, we present three-dimensional simulations for comparison to experimental studies of guided-wave scattering by through-thickness holes in thin plates.