Uniform asymptotic stability for perturbed neutral delay differential equations

One-dimensional perturbed neutral delay differential equations of the form (x(t)−P(t,x(t−τ)))′=f(t,x_t)+g(t,x_t) are considered assuming that f satisfies −v(t)M(φ)?f(t,φ)?v(t)M(−φ), where M(φ)=max{0,max_s∈[−r,0]φ(s)}. A typical result is the following: if ‖g(t,φ)‖?w(t)‖φ‖ and , then the zero solution is uniformly asymptotically stable providing that the zero solution of the corresponding equation without perturbation (x(t)−P(t,x(t−τ)))′=f(t,x_t) is uniformly asymptotically stable. Some known results associated with this equation are extended and improved.     

Computation of multiple eigenvalues of infinite tridiagonal matrices

In this paper, it is first given as a necessary and sufficient condition that infinite matrices of a certain type have double eigenvalues. The computation of such double eigenvalues is enabled by the Newton method of two variables. The three-term recurrence relations obtained from its eigenvalue problem (EVP) subsume the well-known relations of (A) the zeros of ; (B) the zeros of ; (C) the EVP of the Mathieu differential equation; and (D) the EVP of the spheroidal wave equation. The results of experiments are shown for the three cases (A)-(C) for the computation of their ``double pairs'.

     

Characterization of the signature of subwavelength variation from far-field irradiance

The dynamic signature of the subwavelength variation of a slit is shown to be determinable from far-field irradiance with a precision of better than 1 nm. One can increase the efficiency of measurement of the subwavelength's signature by adjusting the detection width over which the subwavelength variation is detected. The subwavelength variation of a rectangular aperture was also examined to show the general feasibility.     

Analysis of performance optimization in supercontinuum sources

We have determined the cause of performance variation as a function of system parameters in supercontinuum (SC) sources in a normal-dispersion fiber by numerically analyzing the noise evolution of the SC. High-order nonlinearity was considered in such an analysis for the first time to our knowledge. We found that the evolution of noise along the SC fiber has two stages: First, the noise is governed by dispersion, which is different from that of the signal, whereas self-steeping leads to an asymmetric noise distribution across the spectrum. Second, four-wave mixing generates new noise components, whereas Raman scattering augments the asymmetry. We evaluated the qualities of the spectrally sliced pulses at several stages to verify the analysis and found an asymmetric profile of the sliced-pulses' quality versus frequency.     

Microfluidic sensor based on integrated optical hollow waveguides

A simple integrated optical refractometric sensor based on hollow-core antiresonant reflecting optical waveguides is proposed. The sensor uses the antiresonant reflecting guidance mechanism and permits one to measure the refractive index of a liquid filling the core by simply monitoring the transmitted spectrum. The device has been made with standard silicon technology, and the experimental results confirm numerical simulations performed in one- and two-dimensional geometry. The sensor exhibits a linear response over a wide measurement range (1.3330-1.4450) and a resolution of 9 x 10(-4) and requires a small analyte volume.     

Computerized quantification of carotid artery stenosis using MRA axial images

Currently, the North American symptomatic carotid endarterectomy trial, European carotid surgery trial, and common carotid method are used to measure the carotid stenosis for determining candidates for carotid endarterectomy using the projection angiography from different modalities such as digital subtraction angiography, rotational angiography, computed tomography angiography and magnetic resonance angiography. A new computerized carotid stenosis measuring system was developed using MR angiography axial image to overcome the drawbacks of conventional carotid stenosis measuring methods, to reduce the variability of inter-observer and intra-observer. The gray-level thresholding is one of the most popular and efficient methods for image segmentation. We segmented the carotid artery and lumen from three-dimensional time-of-flight MRA axial images using gray-level thresholding technique. Using the measured intima-media thickness value of common carotid artery for each case, we separated carotid artery wall from the segmented carotid artery region. After that, the regions of segmented carotid without artery wall were divided into region of blood flow and plaque. The calculation of carotid stenosis degree was performed as follows: carotid stenosis grading = (area measure of plaque/area measure of blood flow region and plaque) * 100%. No previous study has developed the carotid stenosis measuring method using MRA axial image. The new computerized stenosis measuring system has advantage over conventional caliper measuring methods; it will not only greatly increase the speed of stenosis measuring but also reduce the variability between readers. It should also reduce the variability between different institutions.     

A density-functional study for the liquid-vapor coexistence curve of nitrogen fluid

We have used a density-functional theory based on the interaction site model to predict the liquid-vapor coexistence curve of nitrogen fluid. The pressure and chemical potential were calculated from thermodynamic integrations. The different paths of thermodynamic integration provide slightly different predictions for the liquid-vapor coexistence curve. However, these critical points and coexistence curves evaluated by the theory are in qualitative agreement with the experimental data. The theoretical coexistence curves scaled to critical constants agree with the experimental data quantitatively.     

Performance of optical fibers for transmission of high-peak-power XeCl excimer laser pulses

The simple and efficient fiber delivery of 5-ns pulses from a XeCl excimer laser operating at a wavelength of 308 nm is demonstrated. The coupling scheme uses all of the output energy of the XeCl excimer laser and benefits from a simple and easy-to-adjust fiber coupling. Experiments on the 308-nm fiber delivery for more than 2.5 million laser pulses of 8-ns pulse width (FWHM) and up to 8-mJ stabilized pulse energy are performed. The long-time pulsed UV laser transmission is found to be different for individual samples of optical fibers that perform very similarly in low-intensity UV light applications. For applications with strict demands on the long-time stability, a critical evaluation of the fiber performance with the 308-nm laser under operating conditions is necessary. Measurements between 1 and 200 Hz show a negligible dependence of the fiber delivery performance on the repetition rate of the transmitted laser pulses. PACS 42.55.Lt; 42.81.Cn; 07.69.Vg     

Power of entanglement in quantum communication

A communication channel is a physical system that transfers information from one place to another. Examples of communication channels include wires, optical fibers, and chains of spins that propagate spin waves through a medium. This Letter shows that the power-limited communication capacity of a multimode optical fiber or a set of parallel spin chains can be enhanced by introducing nonlinear couplings between the modes or chains. In particular, M coupled, entangled modes can send M bits in the same time it takes a single mode to send a single bit, and in the same time it takes M uncoupled, unentangled modes to send sqrt[M] bits.     

Definition and properties of ideal amorphous solids

It is proposed that two ideal amorphous structures, type I and type II, based on maximally random jammed packing of spheres of equal size, form a distinct class of ideal amorphous solids. The ideal amorphous structures contain wide variations in local density, limited by the condition of solidity. Four distinct characteristics, based on statistical geometry and topology, are shown to define this class. Voronoi tessellations carried out on simulated cells of random packed spheres and amorphous polymers give a broad distribution of individual volumes, skewed, with a tail at the high volume end.