Poles and zeros of the scattering matrix associated to defect modes

We analyze electromagnetic waves propagation in one-dimensional periodic media with single or periodic defects. The study is made both from the point of view of the modes and of the diffraction problem. We provide an explicit dispersion equation for the numerical calculation of the modes, and we establish a connection between modes and poles and zeros of the scattering matrix.Comment: 6 pages (Revtex), no figure

Acoustic properties of colloidal crystals

We present a systematic study of the frequency band structure of acoustic waves in crystals consisting of nonoverlapping solid spheres in a fluid. We consider colloidal crystals consisting of polystyrene spheres in water, and an opal consisting of close-packed silica spheres in air. The opal exhibits an omnidirectional frequency gap of considerable width; the colloidal crystals do not. The physical origin of the bands are discussed for each case in some detail. We present also results on the transmittance of finite slabs of the above crystals.Comment: 7 pages, 9 figures, prb approve

Factors Associated with Ulcer Healing and Quality of Life in Patients with Diabetic Foot Ulcer

A prospective nonrandomized cohort study on consecutive diabetic patients with foot ulcer was undertaken to assess the factors associated with the healing process or limb salvage and evaluate the impact of their treatment on their quality of life. Quality of life was evaluated using Diabetic Foot Ulcer Scale–Short Form (DFS-SF) questionnaire before and after treatment. A total of 103 diabetic patients with ulcer (mean age 69.7 ± 9.6 years, 77% male) were treated and followed up for 12 months. Ulcer healing, minor amputation, and major amputation rates were 41%, 41%, and 18%, respectively, while the mortality rate was 18%. Ulcer healing was associated with University of Texas wound grade 1 and the Study of Infections in Diabetic feet comparing Efficacy, Safety and Tolerability of Ertapenem versus Piperacillin/Tazobactam trial’s diabetic foot infection wound score. Limb loss was associated with nonpalpable popliteal artery, longer in-hospital stay, and delay until referral. Quality of life was improved in all domains of DFS-SF (P < .0001) throughout the cohort of our patients regardless of their outcome, and no outcome (healing, minor amputation, or major amputation) was superior to other. Significant improvement was observed in all domains of hygiene self-management after consultation during the follow-up period

Radiative energy transfer in disordered photonic crystals

The difficulty of description of the radiative transfer in disordered photonic crystals arises from the necessity to consider on the equal footing the wave scattering by periodic modulations of the dielectric function and by its random inhomogeneities. We resolve this difficulty by approaching this problem from the standpoint of the general multiple scattering theory in media with arbitrary regular profile of the dielectric function. We use the general asymptotic solution of the Bethe-Salpeter equation in order to show that for a sufficiently weak disorder the diffusion limit in disordered photonic crystals is presented by incoherent superpositions of the modes of the ideal structure with weights inversely proportional to the respective group velocities. The radiative transfer and the diffusion equations are derived as a relaxation of long-scale deviations from this limiting distribution. In particular, it is shown that in general the diffusion is anisotropic unless the crystal has sufficiently rich symmetry, say, the square lattice in 2D or the cubic lattice in 3D. In this case, the diffusion is isotropic and only in this case the effect of the disorder can be characterized by the single mean-free-path depending on frequency.Comment: 27 pages, 4 figure

Symmetry characterization of eigenstates in opal-based photonic crystals

The complete symmetry characterization of eigenstates in bare opal systems is obtained by means of group theory. This symmetry assignment has allowed us to identify several bands that cannot couple with an incident external plane wave. Our prediction is supported by layer-KKR calculations, which are also performed: the coupling coefficients between bulk modes and externally excited field tend to zero when symmetry properties mismatch.Comment: 7 pages, 5 figures, submitted to Physical Review

Scattering of elastic waves by periodic arrays of spherical bodies

We develop a formalism for the calculation of the frequency band structure of a phononic crystal consisting of non-overlapping elastic spheres, characterized by Lam\'e coefficients which may be complex and frequency dependent, arranged periodically in a host medium with different mass density and Lam\'e coefficients. We view the crystal as a sequence of planes of spheres, parallel to and having the two dimensional periodicity of a given crystallographic plane, and obtain the complex band structure of the infinite crystal associated with this plane. The method allows one to calculate, also, the transmission, reflection, and absorption coefficients for an elastic wave (longitudinal or transverse) incident, at any angle, on a slab of the crystal of finite thickness. We demonstrate the efficiency of the method by applying it to a specific example.Comment: 19 pages, 5 figures, Phys. Rev. B (in press

Ultrafast Nonlinear Optical Response of Strongly Correlated Systems: Dynamics in the Quantum Hall Effect Regime

We present a theoretical formulation of the coherent ultrafast nonlinear optical response of a strongly correlated system and discuss an example where the Coulomb correlations dominate. We separate out the correlated contributions to the third-order nonlinear polarization, and identify non-Markovian dephasing effects coming from the non-instantaneous interactions and propagation in time of the collective excitations of the many-body system. We discuss the signatures, in the time and frequency dependence of the four-wave-mixing (FWM) spectrum, of the inter-Landau level magnetoplasmon (MP) excitations of the two-dimensional electron gas (2DEG) in a perpendicular magnetic field. We predict a resonant enhancement of the lowest Landau level (LL) FWM signal, a strong non-Markovian dephasing of the next LL magnetoexciton (X), a symmetric FWM temporal profile, and strong oscillations as function of time delay, of quantum kinetic origin. We show that the correlation effects can be controlled experimentally by tuning the central frequency of the optical excitation between the two lowest LLs.Comment: 21 pages, 10 figure

Second asymptomatic carotid surgery trial (ACST-2): a randomised comparison of carotid artery stenting versus carotid endarterectomy

Background: Among asymptomatic patients with severe carotid artery stenosis but no recent stroke or transient cerebral ischaemia, either carotid artery stenting (CAS) or carotid endarterectomy (CEA) can restore patency and reduce long-term stroke risks. However, from recent national registry data, each option causes about 1% procedural risk of disabling stroke or death. Comparison of their long-term protective effects requires large-scale randomised evidence. Methods: ACST-2 is an international multicentre randomised trial of CAS versus CEA among asymptomatic patients with severe stenosis thought to require intervention, interpreted with all other relevant trials. Patients were eligible if they had severe unilateral or bilateral carotid artery stenosis and both doctor and patient agreed that a carotid procedure should be undertaken, but they were substantially uncertain which one to choose. Patients were randomly allocated to CAS or CEA and followed up at 1 month and then annually, for a mean 5 years. Procedural events were those within 30 days of the intervention. Intention-to-treat analyses are provided. Analyses including procedural hazards use tabular methods. Analyses and meta-analyses of non-procedural strokes use Kaplan-Meier and log-rank methods. The trial is registered with the ISRCTN registry, ISRCTN21144362. Findings: Between Jan 15, 2008, and Dec 31, 2020, 3625 patients in 130 centres were randomly allocated, 1811 to CAS and 1814 to CEA, with good compliance, good medical therapy and a mean 5 years of follow-up. Overall, 1% had disabling stroke or death procedurally (15 allocated to CAS and 18 to CEA) and 2% had non-disabling procedural stroke (48 allocated to CAS and 29 to CEA). Kaplan-Meier estimates of 5-year non-procedural stroke were 2·5% in each group for fatal or disabling stroke, and 5·3% with CAS versus 4·5% with CEA for any stroke (rate ratio [RR] 1·16, 95% CI 0·86–1·57; p=0·33). Combining RRs for any non-procedural stroke in all CAS versus CEA trials, the RR was similar in symptomatic and asymptomatic patients (overall RR 1·11, 95% CI 0·91–1·32; p=0·21). Interpretation: Serious complications are similarly uncommon after competent CAS and CEA, and the long-term effects of these two carotid artery procedures on fatal or disabling stroke are comparable. Funding: UK Medical Research Council and Health Technology Assessment Programme