Spectral zeta functions of a 1D Schr\"odinger problem

We study the spectral zeta functions associated to the radial Schr\"odinger problem with potential V(x)=x^{2M}+alpha x^{M-1}+(lambda^2-1/4)/x^2. Using the quantum Wronskian equation, we provide results such as closed-form evaluations for some of the second zeta functions i.e. the sum over the inverse eigenvalues squared. Also we discuss how our results can be used to derive relationships and identities involving special functions, using a particular 5F_4 hypergeometric series as an example. Our work is then extended to a class of related PT-symmetric eigenvalue problems. Using the fused quantum Wronskian we give a simple method for calculating the related spectral zeta functions. This method has a number of applications including the use of the ODE/IM correspondence to compute the (vacuum) nonlocal integrals of motion G_n which appear in an associated integrable quantum field theory.Comment: 15 pages, version

Repeated games for eikonal equations, integral curvature flows and non-linear parabolic integro-differential equations

The main purpose of this paper is to approximate several non-local evolution equations by zero-sum repeated games in the spirit of the previous works of Kohn and the second author (2006 and 2009): general fully non-linear parabolic integro-differential equations on the one hand, and the integral curvature flow of an interface (Imbert, 2008) on the other hand. In order to do so, we start by constructing such a game for eikonal equations whose speed has a non-constant sign. This provides a (discrete) deterministic control interpretation of these evolution equations. In all our games, two players choose positions successively, and their final payoff is determined by their positions and additional parameters of choice. Because of the non-locality of the problems approximated, by contrast with local problems, their choices have to "collect" information far from their current position. For integral curvature flows, players choose hypersurfaces in the whole space and positions on these hypersurfaces. For parabolic integro-differential equations, players choose smooth functions on the whole space

Geometric approach to nonvariational singular elliptic equations

In this work we develop a systematic geometric approach to study fully nonlinear elliptic equations with singular absorption terms as well as their related free boundary problems. The magnitude of the singularity is measured by a negative parameter $(\gamma -1)$, for $0 < \gamma < 1$, which reflects on lack of smoothness for an existing solution along the singular interface between its positive and zero phases. We establish existence as well sharp regularity properties of solutions. We further prove that minimal solutions are non-degenerate and obtain fine geometric-measure properties of the free boundary $\mathfrak{F} = \partial \{u > 0 \}$. In particular we show sharp Hausdorff estimates which imply local finiteness of the perimeter of the region $\{u > 0 \}$ and $\mathcal{H}^{n-1}$ a.e. weak differentiability property of $\mathfrak{F}$.Comment: Paper from D. Araujo's Ph.D. thesis, distinguished at the 2013 Carlos Gutierrez prize for best thesis, Archive for Rational Mechanics and Analysis 201

Exact propagators for atom-laser interactions

A class of exact propagators describing the interaction of an $N$-level atom with a set of on-resonance $\delta$-lasers is obtained by means of the Laplace transform method. State-selective mirrors are described in the limit of strong lasers. The ladder, V and $\Lambda$ configurations for a three-level atom are discussed. For the two level case, the transient effects arising as result of the interaction between both a semi-infinite beam and a wavepacket with the on-resonance laser are examined.Comment: 13 pages, 6 figure

Mesoscopic structure and social aspects of human mobility

The individual movements of large numbers of people are important in many contexts, from urban planning to disease spreading. Datasets that capture human mobility are now available and many interesting features have been discovered, including the ultra-slow spatial growth of individual mobility. However, the detailed substructures and spatiotemporal flows of mobility - the sets and sequences of visited locations - have not been well studied. We show that individual mobility is dominated by small groups of frequently visited, dynamically close locations, forming primary "habitats" capturing typical daily activity, along with subsidiary habitats representing additional travel. These habitats do not correspond to typical contexts such as home or work. The temporal evolution of mobility within habitats, which constitutes most motion, is universal across habitats and exhibits scaling patterns both distinct from all previous observations and unpredicted by current models. The delay to enter subsidiary habitats is a primary factor in the spatiotemporal growth of human travel. Interestingly, habitats correlate with non-mobility dynamics such as communication activity, implying that habitats may influence processes such as information spreading and revealing new connections between human mobility and social networks.Comment: 7 pages, 5 figures (main text); 11 pages, 9 figures, 1 table (supporting information

Organic film thickness influence on the bias stress instability in Sexithiophene Field Effect Transistors

In this paper, the dynamics of bias stress phenomenon in Sexithiophene (T6) Field Effect Transistors (FETs) has been investigated. T6 FETs have been fabricated by vacuum depositing films with thickness from 10 nm to 130 nm on Si/SiO2 substrates. After the T6 film structural analysis by X-Ray diffraction and the FET electrical investigation focused on carrier mobility evaluation, bias stress instability parameters have been estimated and discussed in the context of existing models. By increasing the film thickness, a clear correlation between the stress parameters and the structural properties of the organic layer has been highlighted. Conversely, the mobility values result almost thickness independent

The effects of social service contact on teenagers in England

Objective: This study investigated outcomes of social service contact during teenage years. Method: Secondary analysis was conducted of the Longitudinal Survey of Young People in England (N = 15,770), using data on reported contact with social services resulting from teenagers’ behavior. Outcomes considered were educational achievement and aspiration, mental health, and locus of control. Inverse-probability-weighted regression adjustment was used to estimate the effect of social service contact. Results: There was no significant difference between those who received social service contact and those who did not for mental health outcome or aspiration to apply to university. Those with contact had lower odds of achieving good exam results or of being confident in university acceptance if sought. Results for locus of control were mixed. Conclusions: Attention is needed to the role of social services in supporting the education of young people in difficulty. Further research is needed on the outcomes of social services contact

Menopausal hormone therapy reduces the risk of fracture regardless of falls risk or baseline FRAX probability — Results from the Women’s Health Initiative hormone therapy trials

Summary In a combined analysis of 25,389 postmenopausal women aged 50–79 years, enrolled in the two Women’s Health Initiative hormone therapy trials, menopausal hormone therapy vs. placebo reduced the risk of fracture regardless of baseline FRAX fracture probability and falls history. Introduction The aim of this study was to determine if the anti-fracture efficacy of menopausal hormone therapy (MHT) differed by baseline falls history or fracture risk probability as estimated by FRAX, in a combined analysis of the two Women’s Health Initiative (WHI) hormone therapy trials. Methods A total of 25,389 postmenopausal women aged 50–79 years were randomized to receive MHT (n = 12,739) or matching placebo (n = 12,650). At baseline, questionnaires were used to collect information on falls history, within the last 12 months, and clinical risk factors. FRAX 10-year probability of major osteoporotic fracture (MOF) was calculated without BMD. Incident clinical fractures were verified using medical records. An extension of Poisson regression was used to investigate the relationship between treatment and fractures in (1) the whole cohort; (2) those with prior falls; and (3) those without prior falls. The effect of baseline FRAX probability on efficacy was investigated in the whole cohort. Results Over 4.3 ± 2.1 years (mean ± SD), MHT (vs. placebo) significantly reduced the risk of any clinical fracture (hazard ratio [HR] 0.72 [95% CI, 0.65–0.78]), MOF (HR 0.60 [95% CI, 0.53–0.69]), and hip fracture (0.66 [95% CI, 0.45–0.96]). Treatment was effective in reducing the risk of any clinical fracture, MOF, and hip fracture in women regardless of baseline FRAX MOF probability, with no evidence of an interaction between MHT and FRAX (p > 0.30). Similarly, there was no interaction (p > 0.30) between MHT and prior falls. Conclusion In the combined WHI trials, compared to placebo, MHT reduces fracture risk regardless of FRAX probability and falls history in postmenopausal women

Electron Impact Excitation Cross Sections for Hydrogen-Like Ions

We present cross sections for electron-impact-induced transitions n --> n' in hydrogen-like ions C 5+, Ne 9+, Al 12+, and Ar 17+. The cross sections are computed by Coulomb-Born with exchange and normalization (CBE) method for all transitions with n < n' < 7 and by convergent close-coupling (CCC) method for transitions with n 2s and 1s --> 2p are presented as well. The CCC and CBE cross sections agree to better than 10% with each other and with earlier close-coupling results (available for transition 1 --> 2 only). Analytical expression for n --> n' cross sections and semiempirical formulae are discussed.Comment: RevTeX, 5 pages, 13 PostScript figures, submitted to Phys. Rev.