Transformation optics with photonic band gap media

We introduce a class of optical media based on adiabatically modulated, dielectric-only, and potentially extremely low-loss, photonic crystals (PC). The media we describe represent a generalization of the eikonal limit of transformation optics (TO). The basis of the concept is the possibility to fit some equal frequency surfaces of certain PCs with elliptic surfaces, allowing them to mimic the dispersion relation of light in anisotropic effective media. PC cloaks and other TO devices operating at visible wavelengths can be constructed from optically transparent substances such as glasses, whose attenuation coefficient can be as small as 10 dB/km, suggesting the TO design methodology can be applied to the development of optical devices not limited by the losses inherent to metal-based, passive metamaterials.     

Noncontact optical tomography of turbid media

Optical tomography of turbid media has so far been limited by systems that require fixed geometries or measurements employing fibers. We present a system that records noncontact optical measurements from diffuse media of arbitrary shapes and retrieves the three-dimensional surface information of the diffuse medium. We further present a novel method of combining this composite data set and obtain accurate fluorescence reconstructions. This approach offers significant experimental simplicity and yields high-information-content datasets. The performance of this novel tomographic approach is demonstrated with experimental reconstructions of phantoms.     

Capacities as conformal quasi-invariants on pseudo-riemannian manifolds

A class of capacities is introduced on pseudo-riemannian manifolds. They arise as a natural counterpart of the well-known plane quasiconformal capacities and their higher dimensional analogues which have been studied extensively in the recent years by F.W. Gehring, R. Kühnau and others. The capacities in question are shown to be either conformal invariants or conformal quasi-invariants, and, in the latter case, exact bounds are established. We thus arrive at the notion of quasiconformal mappings of pseudo-riemannian manifolds, which correspond to the inhomogeneous media. These mappings are studied briefly and the physical interpretation of some of the capacities in question is also given.     

Read channel simulation based on microtrack and micromagnetic modeling for 1 Tb/in magnetic recording

Channel design for ultra-high-density perpendicular magnetic recording requires fast and precise modeling to generate readback signals corrupted by media noise. In this paper, we present a geometric-dependent approach to model random readback pulses, where a three-dimensional head and media combination for 1 Tb/in² density design is considered in the micromagnetic simulation. A systematic approach is developed to extract media noise statistics from micromagnetic modeling and generate readback pulses based on a fast microtrack model incorporating nonlinear effects. The feasibility of the proposed model is demonstrated through bit-error-rate (BER) simulation of a turbo equalization scheme over a low-density parity-check (LDPC) coded, general-partial-response (GPR) equalized perpendicular recording channel.     

Application of generalized complex modes to the calculation of the forced response of three-dimensional poroelastic materials

Finite element models based on Biot's {u,P} formulation for poroelastic materials are widely used to predict the behaviour of structures involving porous media. The numerical solution of such problems requires however important computational resources and the solution algorithms are not optimized. To improve the solution process, a modal approach based on an extension of the complex modes technique has been proposed recently and applied successfully to a simplified mono-dimensional problem. In this paper, this technique is investigated in the case of three-dimensional poroelastic problems. The technique is first recalled, then analytical proof of the stability of the model are given followed by considerations of numerical improvements of the method. An energetic interpretation of the generalized complex modes is then given and some numerical results are presented to illustrate the performance of the approach.     

Dynamics of Anderson localization in open 3D media

We develop a self-consistent theoretical approach to the dynamics of Anderson localization in open three-dimensional (3D) disordered media. The approach allows us to study time-dependent transmission and reflection, and the distribution of decay rates of quasimodes of 3D disordered slabs near the Anderson mobility edge.     

Cluster control of a distributed-parameter planar structure--middle authority control

This paper proposes a generalized active vibration control approach, "cluster control," that explicitly targets sets of structural modes with some common property. The approach falls into a category of MAC (middle authority control) between conventionally used LAC (low authority control) and HAC (high authority control), possessing the benefit of stability and control law simplicity analogous to LAC, while providing high control performance as well as some flexibility of control gain assignment similar to HAC. The structure of a cluster control system is outlined, showing that it is possible to control a target cluster without affecting the other clusters. A design procedure for the cluster control system is then proposed. Experimental results are also presented.     

QED in arbitrary linear media: Amplifying media

Recently, we have developed a unified approach to QED in arbitrary linearly responding media in equilibrium—media that give rise to absorption [Phys. Rev. A 75, 053813 (2007)]. In the present paper we show that, under appropriate conditions, the theory can be quite naturally generalized to amplifying media the effect of which is described within the framework of linear response theory. We discuss the limits of validity of the generalized theory and make contact with earlier quantization schemes suggested for the case of linearly and locally responding amplifying dielectric-type media. To illustrate the theory, we present the electromagnetic-field correlation functions that determine the Casimir force in the presence of amplifying media.     

Fast analytical approximation for arbitrary geometries in diffuse optical tomography

Diffuse optical tomography is a novel imaging technique that resolves and quantifies the optical properties of objects buried in turbid media. Typically, numerical solutions of the diffusion equation are employed to construct the tomographic problem when media of complex geometries are investigated. Numerical methods offer implementation simplicity but also significant computation burden, especially when large three-dimensional reconstructions are involved. We present an alternative method of performing tomography of diffuse media of arbitrary geometries by means of an analytical approach, the Kirchhoff approximation. We show that the method is extremely efficient in computation times and consider its potential as a real-time three-dimensional imaging tool.     

Three-dimensional vector radiative transfer in a semi-infinite, Rayleigh scattering medium exposed to spatially varying polarized radiation: generalized reflection matrix

Three-dimensional vector radiative transfer in a semi-infinite medium exposed to spatially varying, polarized radiation is studied. The problem is to determine the generalized reflection matrix for a multiple scattering medium characterized by a 4×4 scattering matrix. A double integral transform is used to convert the three-dimensional vector radiative transfer equation to a one-dimensional form, and a modified Ambarzumian's method is then applied to derive a nonlinear integral equation for the generalized reflection matrix. The spatially varying backscattered radiation for an arbitrarily polarized incident beam can be found from the generalized reflection matrix. For Rayleigh scattering and normal incidence and emergence, the generalized reflection matrix is shown to have five non-zero elements. Benchmark results for these five elements are presented and compared to asymptotic results. When the incident radiation is polarized, the vector approach used in this study correctly predicts three-dimensional behavior, while the scalar approach does not. When the incident radiation is unpolarized, both the vector and scalar approaches predict a two-dimensional distribution of the intensity, but the error in the scalar prediction can be as high as 20%.     

Transformation Optics: From Classic Theory and Applications to its New Branches

In the modern world, the ability to manipulate and control electromagnetic waves has greatly changed people's lives. Novel optical and electromagnetic phenomena and devices will lead to new scientific trends and techniques in the future. The exploration of new theories of optical design and new materials for optical engineering has attracted great attention in recent years. Transformation optics (TO) provides a new way to design optical devices with extraordinary predesigned functions such as invisibility cloaks and electromagnetic wormholes. As the development of artificial electromagnetic media (e.g. metamaterials and metasurfaces) progresses, many of these novel optical devices designed by TO have been experimentally demonstrated and used in specific applications. Starting from the basic theory of transformation optics, we review its applications, extensions, new branches and recent developments in this paper.     

Thermal stabilization of anomalies in inhomogeneous conducting structures

We study the thermal mechanism of suppression of the anomalies in the nonlinear characteristics of inhomogeneous media. A generalized expression for the effective nonlinear conductivity is derived that allows for heat transfer from hot regions. We study the nature of the divergences in two-and three-dimensional inhomogeneous structures as depending on the local parameters and the microgeometry of the system. Finally, we show that in the critical region the effective nonlinear conductivity may be much higher than the conductivity of the components. Zh. éksp. Teor. Fiz. 115, 1818–1832 (May 1999)     

Suppress Winfree turbulence by local forcing excitable systems

The occurrence of Winfree turbulence is currently regarded as one of the principal mechanisms underlying cardiac fibrillation. We develop a local stimulation method that suppresses Winfree turbulence in three-dimensional excitable media. We find that Winfree turbulence can be effectively suppressed by locally injecting periodic signals to only a very small subset (around some surface region) of total space sites. Our method for the first time demonstrates the effectiveness of local low-amplitude periodic excitations in suppressing turbulence in 3D excitable media and has fundamental improvements in efficiency, convenience, and turbulence suppression speed compared with previous strategies. Therefore, it has great potential for developing into a practical low-amplitude defibrillation approach.     

跨音速单转子压气机气动设计的优化

本文发展了一种提高跨音压气机效率的优化设计方法。该方法由快速叶片造型和网格生成、三维NS方程求解器和优化方法三部分组成。以绝热效率为设计目标,只选择两个参数-最大弯度和最大厚度相对位置沿叶高的分布为优化参数,成功设计了一个跨音单转子压气机。在此基础上,进一步考察了叶片端布周向弯曲对跨音单转子压气机性能的影响。     

Facts and Fictions About Anti deSitter Spacetimes¶with Local Quantum Matter

We present a nonlinear realization of E ₈₍₈₎ on a space of 57 dimensions, which is quasiconformal in the sense that it leaves invariant a suitably defined “light cone” in ℝ⁵⁷. This realization, which is related to the Freudenthal triple system associated with the unique exceptional Jordan algebra over the split octonions, contains previous conformal realizations of the lower rank exceptional Lie groups on generalized space times, and in particular a conformal realization of E ₇₍₇₎ on ℝ²⁷ which we exhibit explicitly. Possible applications of our results to supergravity and M-Theory are briefly mentioned. Received: 12 August 2000 / Accepted: 2 March 2001     

A discrete geometric approach to solving time independent Schrödinger equation

The time independent Schrödinger equation stems from quantum theory axioms as a partial differential equation. This work aims at providing a novel discrete geometric formulation of this equation in terms of integral variables associated with precise geometric elements of a pair of three-dimensional interlocked grids, one of them based on tetrahedra. We will deduce, in a purely geometric way, a computationally efficient discrete counterpart of the time independent Schrödinger equation in terms of a standard symmetric eigenvalue problem. Moreover boundary and interface conditions together with non homogeneity and anisotropy of the media involved are accounted for in a straightforward manner.This approach yields to a sensible computational advantage with respect to the finite element method, where a generalized eigenvalue problem has to be solved instead. Such a modeling tool can be used for analyzing a number of quantum phenomena in modern nano-structured devices, where the accounting of the real 3D geometry is a crucial issue.     

Simulation of polarization-sensitive optical coherence tomography images by a Monte Carlo method

We introduce a new Monte Carlo (MC) method for simulating optical coherence tomography (OCT) images of complex multilayered turbid scattering media. We demonstrate, for the first time of our knowledge, the use of a MC technique to imitate two-dimensional polarization-sensitive OCT images with nonplanar boundaries of layers in the medium like a human skin. The simulation of polarized low-coherent optical radiation is based on the vector approach generalized from the iterative procedure of the solution of Bethe-Saltpeter equation. The performances of the developed method are demonstrated both for conventional and polarization-sensitive OCT modalities.     

Towards Generative Design of Computationally Efficient Mathematical Models with Evolutionary Learning

In this paper, we describe the concept of generative design approach applied to the automated evolutionary learning of mathematical models in a computationally efficient way. To formalize the problems of models’ design and co-design, the generalized formulation of the modeling workflow is proposed. A parallelized evolutionary learning approach for the identification of model structure is described for the equation-based model and composite machine learning models. Moreover, the involvement of the performance models in the design process is analyzed. A set of experiments with various models and computational resources is conducted to verify different aspects of the proposed approach.     

Symplectic Geometry,Hopf Algebraic Structures of Classical and Quantum q-Deformations of SU(2) Algebra

By deforming the symplectic structure on S², we get the q-deformation of SU(2) algebra at classical level, SU_q,h→0(2), in a Hamiltonian approach. Furthermore, we construct a set of operators on the line bundle over the deformed symplectic manifo1d.S_q² such that they form SU_q,h→0(2) in Lie brackets and set up a nontrivial Hopf algebra with a parameter q only in such a classical Hamiltonian system. We also show that the deformations from S_q² to S_q² are a set of quasiconformal transformations. The quantization via geometric approach of the system gives rise to the quantum q-deformed algebra SU_q,h(2), wnich has a Hopf algebraic structure with two independent parameters q and h.