Making precise predictions of the Casimir force between metallic plates via a weighted Kramers-Kronig transform

The possibility of making precise predictions for the Casimir force is essential for the theoretical interpretation of current precision experiments on the thermal Casimir effect with metallic plates, especially for sub-micron separations. For this purpose it is necessary to estimate very accurately the dielectric function of a conductor along the imaginary frequency axis. This task is complicated in the case of ohmic conductors, because optical data do not usually extend to sufficiently low frequencies to permit an accurate evaluation of the standard Kramers-Kronig integral used to compute $\epsilon(i \xi)$. By making important improvements in the results of a previous paper by the author, it is shown that this difficulty can be resolved by considering suitable weighted dispersions relations, which strongly suppress the contribution of low frequencies. The weighted dispersion formulae presented in this paper permit to estimate accurately the dielectric function of ohmic conductors for imaginary frequencies, on the basis of optical data extending from the IR to the UV, with no need of uncontrolled data extrapolations towards zero frequency that are instead necessary with standard Kramers-Kronig relations. Applications to several sets of data for gold films are presented to demonstrate viability of the new dispersion formulae.Comment: 18 pages, 15 encapsulated figures. In the revised version important improvements have been made, which affect the main conclusions of the pape

Quartic double solids with ordinary singularities

We study the mixed Hodge structure on the third homology group of a threefold which is the double cover of projective three-space ramified over a quartic surface with a double conic. We deal with the Torelli problem for such threefolds.Comment: 14 pages, presented at the Conference Arnol'd 7

Linear stability of planar premixed flames: reactive Navier-Stokes equations with finite activation energy and arbitrary Lewis number

A numerical shooting method for performing linear stability analyses of travelling waves is described and applied to the problem of freely propagating planar premixed flames. Previous linear stability analyses of premixed flames either employ high activation temperature asymptotics or have been performed numerically with finite activation temperature, but either for unit Lewis numbers (which ignores thermal-diffusive effects) or in the limit of small heat release (which ignores hydrodynamic effects). In this paper the full reactive Navier-Stokes equations are used with arbitrary values of the parameters (activation temperature, Lewis number, heat of reaction, Prandtl number), for which both thermal-diffusive and hydrodynamic effects on the instability, and their interactions, are taken into account. Comparisons are made with previous asymptotic and numerical results. For Lewis numbers very close to or above unity, for which hydrodynamic effects caused by thermal expansion are the dominant destablizing mechanism, it is shown that slowly varying flame analyses give qualitatively good but quantitatively poor predictions, and also that the stability is insensitive to the activation temperature. However, for Lewis numbers sufficiently below unity for which thermal-diffusive effects play a major role, the stability of the flame becomes very sensitive to the activation temperature. Indeed, unphysically high activation temperatures are required for the high activation temperature analysis to give quantitatively good predictions at such low Lewis numbers. It is also shown that state-insensitive viscosity has a small destabilizing effect on the cellular instability at low Lewis numbers

Cohomogeneity one manifolds and selfmaps of nontrivial degree

We construct natural selfmaps of compact cohomgeneity one manifolds with finite Weyl group and compute their degrees and Lefschetz numbers. On manifolds with simple cohomology rings this yields in certain cases relations between the order of the Weyl group and the Euler characteristic of a principal orbit. We apply our construction to the compact Lie group SU(3) where we extend identity and transposition to an infinite family of selfmaps of every odd degree. The compositions of these selfmaps with the power maps realize all possible degrees of selfmaps of SU(3).Comment: v2, v3: minor improvement

Gauge Orbit Types for Theories with Classical Compact Gauge Group

We determine the orbit types of the action of the group of local gauge transformations on the space of connections in a principal bundle with structure group O(n), SO(n) or $Sp(n)$ over a closed, simply connected manifold of dimension 4. Complemented with earlier results on U(n) and SU(n) this completes the classification of the orbit types for all classical compact gauge groups over such space-time manifolds. On the way we derive the classification of principal bundles with structure group SO(n) over these manifolds and the Howe subgroups of SO(n).Comment: 57 page

Ignition of thermally sensitive explosives between a contact surface and a shock

The dynamics of ignition between a contact surface and a shock wave is investigated using a one-step reaction model with Arrhenius kinetics. Both large activation energy asymptotics and high-resolution finite activation energy numerical simulations are employed. Emphasis is on comparing and contrasting the solutions with those of the ignition process between a piston and a shock, considered previously. The large activation energy asymptotic solutions are found to be qualitatively different from the piston driven shock case, in that thermal runaway first occurs ahead of the contact surface, and both forward and backward moving reaction waves emerge. These waves take the form of quasi-steady weak detonations that may later transition into strong detonation waves. For the finite activation energies considered in the numerical simulations, the results are qualitatively different to the asymptotic predictions in that no backward weak detonation wave forms, and there is only a weak dependence of the evolutionary events on the acoustic impedance of the contact surface. The above conclusions are relevant to gas phase equation of state models. However, when a large polytropic index more representative of condensed phase explosives is used, the large activation energy asymptotic and finite activation energy numerical results are found to be in quantitative agreement

Clinical Correlates and Outcome of Major Depressive Disorder and Comorbid Migraine: A Report of the European Group for the Study of Resistant Depression

Background: The present multicenter study aimed at defining the clinical profile of patients with major depressive disorder (MDD) and comorbid migraine. Methods: Demographic and clinical information for 1410 MDD patients with vs without concurrent migraine were compared by descriptive statistics, analyses of covariance, and binary logistic regression analyses. Results: The point prevalence rate for comorbid migraine was 13.5% for female and 6.2% for male patients. MDD + migraine patients were significantly younger, heavier, more likely female, of non-Caucasian origin, outpatient, and suffering from asthma. The presence of MDD + migraine resulted in a significantly higher functional disability. First-line antidepressant treatment strategy revealed a trend towards agomelatine. Second-generation antipsychotics were significantly less often administered for augmentation treatment in migraineurs. Overall, MDD + migraine patients tended to respond worse to their pharmacotherapy. Conclusion: Treatment guidelines for comorbid depression and migraine are warranted to ensure optimal efficacy and avoid possible pitfalls in psychopharmacotherapy, including serotonin syndrome

Near-Surface Te+ 125 Spins with Millisecond Coherence Lifetime

Impurity spins in crystal matrices are promising components in quantum technologies, particularly if they can maintain their spin properties when close to surfaces and material interfaces. Here, we investigate an attractive candidate for microwave-domain applications, the spins of group-VI Te+125 donors implanted into natural Si at depths as shallow as 20 nm. We show that surface band bending can be used to ionize such near-surface Te to spin-active Te+ state, and that optical illumination can be used further to control the Te donor charge state. We examine spin activation yield, spin linewidth, and relaxation (T1) and coherence times (T2) and show how a zero-field 3.5 GHz "clock transition"extends spin coherence times to over 1 ms, which is about an order of magnitude longer than other near-surface spin systems

Sex-related effects in major depressive disorder: Results of the European Group for the Study of Resistant Depression

Background: Sex-related effects on the evolution and phenotype of major depressive disorder (MDD) were reported previously. Methods: This European multicenter cross-sectional study compared sociodemographic, clinical, and treatment patterns between males and females in a real-world sample of 1410 in- and outpatients with current MDD. Results: Male MDD patients (33.1%) were rather inpatients, suffered from moderate to high suicidality levels, received noradrenergic and specific serotonergic antidepressants (ADs) as first-line AD treatment, generally higher mean AD daily doses, and showed a trend towards a more frequent administration of add-on treatments. Female MDD patients (66.9%) were rather outpatients, experienced lower suicidality levels, comorbid thyroid dysfunction, migraine, asthma, and a trend towards earlier disease onset. Conclusions: The identified divergencies may contribute to the concept of male and female depressive syndromes and serve as predictors of disease severity and course, as they reflect phenomena that were repeatedly related to treatment-resistant depression (TRD). Especially the greater necessity of inpatient treatment and more complex psychopharmacotherapy in men may reflect increased therapeutic efforts undertaken to treat suicidality and to avoid TRD. Hence, considering sex may guide the diagnostic and treatment processes towards targeting challenging clinical manifestations including comorbidities and suicidality, and prevention of TRD and chronicity