Periodic homogenization with an interface

We consider a diffusion process with coefficients that are periodic outside of an 'interface region' of finite thickness. The question investigated in the articles [1,2] is the limiting long time / large scale behaviour of such a process under diffusive rescaling. It is clear that outside of the interface, the limiting process must behave like Brownian motion, with diffusion matrices given by the standard theory of homogenization. The interesting behaviour therefore occurs on the interface. Our main result is that the limiting process is a semimartingale whose bounded variation part is proportional to the local time spent on the interface. We also exhibit an explicit way of identifying its parameters in terms of the coefficients of the original diffusion. Our method of proof relies on the framework provided by Freidlin and Wentzell for diffusion processes on a graph in order to identify the generator of the limiting process.Comment: ISAAC 09 conference proceeding

Some topics in homogenization

This thesis is mainly concerned with solving a new type of periodic homogenization problem. A solution of removing the Diophantine hypothesis on the homogenization problem where the interface sits at an irrational angle to the period is attempted but is not yet complete. As an aside an oscillator problem is analyzed using the corrector based approach of homogenization

Some topics in homogenization

This thesis is mainly concerned with solving a new type of periodic homogenization problem. A solution of removing the Diophantine hypothesis on the homogenization problem where the interface sits at an irrational angle to the period is attempted but is not yet complete. As an aside an oscillator problem is analyzed using the corrector based approach of homogenization.EThOS - Electronic Theses Online ServiceUniversity of WarwickGBUnited Kingdo

Some topics in homogenization

This thesis is mainly concerned with solving a new type of periodic homogenization problem. A solution of removing the Diophantine hypothesis on the homogenization problem where the interface sits at an irrational angle to the period is attempted but is not yet complete. As an aside an oscillator problem is analyzed using the corrector based approach of homogenization.EThOS - Electronic Theses Online ServiceUniversity of WarwickGBUnited Kingdo

Observation of the dynamic Jahn-Teller effect in the excited states of nitrogen-vacancy centers in diamond

The optical transition linewidth and emission polarization of single nitrogen-vacancy (NV) centers are measured from 5 K to room temperature. Inter-excited state population relaxation is shown to broaden the zero-phonon line and both the relaxation and linewidth are found to follow a T^5 dependence for T up to 100 K. This dependence indicates that the dynamic Jahn-Teller effect is the dominant dephasing mechanism for the NV optical transitions at low temperatures

A comparison of optical and radar measurements of mesospheric winds and tides

Optical measurements of mesospheric winds by Fabry‐Perot spectrometers, FPSs, at Mawson, 67.6°S 62.9°E, and Davis, 68.6°S 78.0°E, Antarctica are compared with similar measurements obtained using a spaced‐antenna MF radar at Davis. The FPSs observed the OH emission. Different analysis procedures, used to determine the mean wind, and amplitude and phase of the semidiurnal tide, have been compared. At these latitudes the diurnal tide is weak and the semi‐diurnal tide, although highly variable in amplitude, is usually the dominant periodicity. When comparing the amplitude and phase of the semidiurnal tide good agreement is obtained between measurements by the two instruments

DAS28(3)CRP is a reliable measure of disease activity in pregnant women with rheumatoid arthritis

OBJECTIVES: The disease activity of rheumatoid arthritis (RA) in pregnancy is most commonly assessed with the modified Disease Activity Score (DAS)-28, the DAS28(3)CRP. However, the performance of the DAS28(3)CRP in pregnancy has not been compared to musculoskeletal ultrasound (MSK-US) as a gold standard. We performed a prospective pilot study to test the hypothesis that pregnancy-related factors limit the reliability of the DAS28(3)CRP. METHODS: Pregnant women with RA were recruited from an Obstetric Rheumatology clinic and assessed during pregnancy (second (T2) and third (T3) trimesters) and postpartum with DAS28(3)CRP and MSK-US scores, with quantification of power Doppler (PD) signal in small joints (hands and feet). Age-matched non-pregnant women with RA underwent equivalent assessments. PD scores were calculated as mean scores of all joints scanned. RESULTS: We recruited 27 pregnant and 20 non-pregnant women with RA. DAS28(3)CRP was sensitive and specific for active RA in pregnancy and postpartum as defined by positive PD signal, but not in non-pregnancy. There were significant correlations between DAS28(3)CRP and PD scores throughout pregnancy (T2, r=0.82 (95% CI [0.42, 0.95], p<0.01); T3, r=0.68 (95% CI [0.38, 0.86], p<0.01)) and postpartum, r=0.84 (95% CI [0.60, 0.94], p<0.01), while this correlation in non-pregnancy was weaker (r=0.47 (95% CI [0, 0.77], p<0.05). CONCLUSIONS: This pilot study found that DAS28(3)CRP is a reliable measure of disease activity in pregnant women with RA. Based on these data, pregnancy does not appear to confound clinical evaluation of the tender and/or swollen joint counts