Adiabatic motion of a neutral spinning particle in an inhomogeneous magnetic field

The motion of a neutral particle with a magnetic moment in an inhomogeneous magnetic field is considered. This situation, occurring, for example, in a Stern-Gerlach experiment, is investigated from classical and semiclassical points of view. It is assumed that the magnetic field is strong or slowly varying in space, i.e., that adiabatic conditions hold. To the classical model, a systematic Lie-transform perturbation technique is applied up to second order in the adiabatic-expansion parameter. The averaged classical Hamiltonian contains not only terms representing fictitious electric and magnetic fields but also an additional velocity-dependent potential. The Hamiltonian of the quantum-mechanical system is diagonalized by means of a systematic WKB analysis for coupled wave equations up to second order in the adiabaticity parameter, which is coupled to Planck’s constant. An exact term-by-term correspondence with the averaged classical Hamiltonian is established, thus confirming the relevance of the additional velocity-dependent second-order contribution

Decay Rate of Triaxially-Deformed Proton Emitters

The decay rate of a triaxially-deformed proton emitter is calculated in a particle-rotor model, which is based on a deformed Woods-Saxon potential and includes a deformed spin-orbit interaction. The wave function of the $I=7/2^{-}$ ground state of the deformed proton emitter $^{141}$Ho is obtained in the adiabatic limit, and a Green's function technique is used to calculate the decay rate and branching ratio to the first excited 2$^{+}$ state of the daughter nucleus. Only for values of the triaxial angle $\gamma$ $<5^{\circ}$ is good agreement obtained for both the total decay rate and the 2$^{+}$ branching ratio.Comment: 19 pages, 4 figure

Global Superdiffusion of Weak Chaos

A class of kicked rotors is introduced, exhibiting accelerator-mode islands (AIs) and {\em global} superdiffusion for {\em arbitrarily weak} chaos. The corresponding standard maps are shown to be exactly related to generalized web maps taken modulo an ``oblique cylinder''. Then, in a case that the web-map orbit structure is periodic in the phase plane, the AIs are essentially {\em normal} web islands folded back into the cylinder. As a consequence, chaotic orbits sticking around the AI boundary are accelerated {\em only} when they traverse tiny {\em ``acceleration spots''}. This leads to chaotic flights having a quasiregular {\em steplike} structure. The global weak-chaos superdiffusion is thus basically different in nature from the strong-chaos one in the usual standard and web maps.Comment: REVTEX, 4 Figures: fig1.jpg, fig2.ps, fig3.ps, fig4.p

The Theory of the Interleaving Distance on Multidimensional Persistence Modules

In 2009, Chazal et al. introduced $\epsilon$-interleavings of persistence modules. $\epsilon$-interleavings induce a pseudometric $d_I$ on (isomorphism classes of) persistence modules, the interleaving distance. The definitions of $\epsilon$-interleavings and $d_I$ generalize readily to multidimensional persistence modules. In this paper, we develop the theory of multidimensional interleavings, with a view towards applications to topological data analysis. We present four main results. First, we show that on 1-D persistence modules, $d_I$ is equal to the bottleneck distance $d_B$. This result, which first appeared in an earlier preprint of this paper, has since appeared in several other places, and is now known as the isometry theorem. Second, we present a characterization of the $\epsilon$-interleaving relation on multidimensional persistence modules. This expresses transparently the sense in which two $\epsilon$-interleaved modules are algebraically similar. Third, using this characterization, we show that when we define our persistence modules over a prime field, $d_I$ satisfies a universality property. This universality result is the central result of the paper. It says that $d_I$ satisfies a stability property generalizing one which $d_B$ is known to satisfy, and that in addition, if $d$ is any other pseudometric on multidimensional persistence modules satisfying the same stability property, then $d\leq d_I$. We also show that a variant of this universality result holds for $d_B$, over arbitrary fields. Finally, we show that $d_I$ restricts to a metric on isomorphism classes of finitely presented multidimensional persistence modules.Comment: Major revision; exposition improved throughout. To appear in Foundations of Computational Mathematics. 36 page

Diabetes Mellitus in HIV-Infected Patients Receiving Antiretroviral Therapy

Background. There is little in the literature on HIV and diabetes mellitus (DM) in sub-Saharan Africa. Objective. To assess the characteristics of HIV and DM in patients receiving antiretroviral therapy (ART) in Botswana. Methods. A retrospective case-control study was conducted at 4 sites. Each HIV-infected patient with DM (n=48) was matched with 2 HIV-infected controls (n=108) by age (±2 years) and sex. Primary analysis was conditional logistic regression to estimate univariate odds and 95% confidence intervals (CIs) for each characteristic. Results. There was no significant association between co-morbid diseases, tuberculosis, hypertension or cancer and risk of diabetes. DM patients were more likely to have higher pre-ART weight (odds ratio (OR) 1.09; 95% CI 1.04 - 1.14). HIV-infected adults \u3e70 kg were significantly more likely to have DM (OR 12.30; 95% CI 1.40 - 107.98). Participants receiving efavirenz (OR 4.58; 95% CI 1.44 - 14.57) or protease inhibitor therapy (OR 20.7; 95% CI 1.79 - 240.02) were more likely to have DM. Neither mean pre-ART CD4 cell count (OR 1.0; 95% CI 0.99 - 1.01) nor pre-ART viral load \u3e100 000 copies/ml (OR 0.71; 95% CI 0.21 - 2.43) were associated with a significant risk of diabetes. Conclusions. These findings suggest a complex interrelation among traditional host factors and treatment-related metabolic changes in the pathogenesis of DM inpatients receiving ART. Notably, pre-ART weight, particularly if \u3e70 kg, is associated with the diagnosis of diabetes in HIV-infected patients in Botswana

Novel Biomarkers of Physical Activity Maintenance in Midlife Women: Preliminary Investigation

The precision health initiative is leading the discovery of novel biomarkers as important indicators of biological processes or responses to behavior, such as physical activity. Neural biomarkers identified by magnetic resonance imaging (MRI) hold promise to inform future research, and ultimately, for transfer to the clinical setting to optimize health outcomes. This study investigated resting-state and functional brain biomarkers between midlife women who were maintaining physical activity in accordance with the current national guidelines and previously acquired age-matched sedentary controls. Approval was obtained from the Human Subjects Committee. Participants included nondiabetic, healthy weight to overweight (body mass index 19–29.9 kg/m2) women (n = 12) aged 40–64 years. Control group data were used from participants enrolled in our previous functional MRI study and baseline resting-state MRI data from a subset of sedentary (week) midlife women who were enrolled in a 9-month exercise intervention conducted in our imaging center. Differential activation of the inferior frontal gyrus (IFG) and greater connectivity with the dorsolateral prefrontal cortex (dlPFC) was identified between physically active women and sedentary controls. After correcting for multiple comparisons, these differences in biomarkers of physical activity maintenance did not reach statistical significance. Preliminary evidence in this small sample suggests that neural biomarkers of physical activity maintenance involve activations in the brain region associated with areas involved in implementing goal-directed behavior. Specifically, activation of the IFG and connectivity with the dlPFC is identified as a neural biomarker to explain and predict long-term physical activity maintenance for healthy aging. Future studies should evaluate these biomarker links with relevant clinical correlations

Validation of frequency and mode extraction calculations from time-domain simulations of accelerator cavities

The recently developed frequency extraction algorithm [G.R. Werner and J.R. Cary, J. Comp. Phys. 227, 5200 (2008)] that enables a simple FDTD algorithm to be transformed into an efficient eigenmode solver is applied to a realistic accelerator cavity modeled with embedded boundaries and Richardson extrapolation. Previously, the frequency extraction method was shown to be capable of distinguishing M degenerate modes by running M different simulations and to permit mode extraction with minimal post-processing effort that only requires solving a small eigenvalue problem. Realistic calculations for an accelerator cavity are presented in this work to establish the validity of the method for realistic modeling scenarios and to illustrate the complexities of the computational validation process. The method is found to be able to extract the frequencies with error that is less than a part in 10^5. The corrected experimental and computed values differ by about one parts in 10^$, which is accounted for (in largest part) by machining errors. The extraction of frequencies and modes from accelerator cavities provides engineers and physicists an understanding of potential cavity performance as it depends on shape without incurring manufacture and measurement costs

Small denominators, frequency operators, and Lie transforms for nearly integrable quantum spin systems

Based on the previously proposed notions of action operators and of quantum integrability, frequency operators are introduced in a fully quantum-mechanical setting. They are conceptually useful because another formulation can be given to unitary perturbation theory. When worked out for quantum spin systems, this variant is found to be formally equivalent to canonical perturbation theory applied to nearly integrable systems consisting of classical spins. In particular, it becomes possible to locate the quantum-mechanical operator-valued equivalent of the frequency denominators that may cause divergence of the classical perturbation series. The results that are established here link the concept of quantum-mechanical integrability to a technical question, namely, the behavior of specific perturbation series

SIMULATION AND ANALYSIS OF MICROWAVE TRANSMISSION THROUGH ANELECTRON CLOUD, A COMPARISON OF RESULTS

Simulation studies for transmission of microwaves through electron clouds show good agreement with analytic results. The electron cloud produces a shift in phase of the microwave. Experimental observation of this phenomena would lead to a useful diagnostic tool for accessing the local density of electron clouds in an accelerator. These experiments are being carried out at the CERN SPS and the PEP-II LER at SLAC and is proposed to be done at the Fermilab main injector. In this study, a brief analysis of the phase shift is provided and the results are compared with that obtained from simulations

Single-stage plasma-based correlated energy spread compensation for ultrahigh 6D brightness electron beams

Plasma photocathode wakefield acceleration combines energy gains of tens of GeV m−1 with generation of ultralow emittance electron bunches, and opens a path towards 5D-brightness orders of magnitude larger than state-of-the-art. This holds great promise for compact accelerator building blocks and advanced light sources. However, an intrinsic by-product of the enormous electric field gradients inherent to plasma accelerators is substantial correlated energy spread—an obstacle for key applications such as free-electron-lasers. Here we show that by releasing an additional tailored escort electron beam at a later phase of the acceleration, when the witness bunch is relativistically stable, the plasma wave can be locally overloaded without compromising the witness bunch normalized emittance. This reverses the effective accelerating gradient, and counter-rotates the accumulated negative longitudinal phase space chirp of the witness bunch. Thereby, the energy spread is reduced by an order of magnitude, thus enabling the production of ultrahigh 6D-brightness beams