Loading a Bose-Einstein Condensate onto an Optical Lattice: an Application of Optimal Control Theory to The Non Linear Schr\"odinger Equation

Using a set of general methods developed by Krotov [A. I. Konnov and V. A. Krotov, Automation and Remote Control, {\bf 60}, 1427 (1999)], we extend the capabilities of Optimal Control Theory to the Nonlinear Schr\"odinger Equation (NLSE). The paper begins with a general review of the Krotov approach to optimization. Although the linearized version of the method is sufficient for the linear Schr\"odinger equation, the full flexibility of the general method is required for treatment of the nonlinear Schr\"odinger equation. Formal equations for the optimization of the NLSE, as well as a concrete algorithm are presented. As an illustration, we consider a Bose-Einstein condensate initially at rest in a harmonic trap. A phase develops across the BEC when an optical lattice potential is turned on. The goal is to counter this effect and keep the phase flat by adjusting the trap strength. The problem is formulated in the language of Optimal Control Theory (OCT) and solved using the above methodology. To our knowledge, this is the first rigorous application of OCT to the Nonlinear Schr\"odinger equation, a capability that is bound to have numerous other applications.Comment: 11 pages, 4 figures, A reference added, Some typos correcte

Ultrafast Dynamics for Electron Photodetachment from Aqueous Hydroxide

Charge-transfer-to-solvent (CTTS) reactions of hydroxide induced by 200 nm monophotonic or 337 nm and 389 nm biphotonic excitation of this anion in aqueous solution have been studied by means of pump-probe ultrafast laser spectroscopy. Transient absorption kinetics of the hydrated electron, eaq-, have been observed, from a few hundred femtoseconds out to 600 ps, and studied as function of hydroxide concentration and temperature. The geminate decay kinetics are bimodal, with a fast exponential component (ca. 13 ps) and a slower power "tail" due to the diffusional escape of the electrons. For the biphotonic excitation, the extrapolated fraction of escaped electrons is 1.8 times higher than for the monophotonic 200 nm excitation (31% vs. 17.5% at 25 oC, respectively), due to the broadening of the electron distribution. The biphotonic electron detachment is very inefficient; the corresponding absorption coefficient at 400 nm is < 4 cm TW-1 M-1 (assuming unity quantum efficiency for the photodetachment). For [OH-] between 10 mM and 10 M, almost no concentration dependence of the time profiles of solvated electron kinetics was observed. At higher temperature, the escape fraction of the electrons increases with a slope of 3x10-3 K-1 and the recombination and diffusion-controlled dissociation of the close pairs become faster. Activation energies of 8.3 and 22.3 kJ/mol for these two processes were obtained. The semianalytical theory of Shushin for diffusion controlled reactions in the central force field was used to model the geminate dynamics. The implications of these results for photoionization of water are discussed.Comment: 44 pages, 9 figures; supplement: 4 pages, 7 figures; to be submitted to J. Chem. Phy

Relationships between Serotonin Transporter Binding in the Raphe Nuclei, Basal Ganglia, and Hippocampus with Clinical Symptoms in Cervical Dystonia:A [C]DASB Positron Emission Tomography Study

PurposeAlterations of the central serotonergic system have been implicated in the pathophysiology of dystonia. In this molecular imaging study, we assessed whether altered presynaptic serotonin transporter (SERT) binding contributes to the pathophysiology of cervical dystonia (CD), concerning both motor and non-motor symptoms (NMS).MethodsWe assessed the non-displaceable binding potential (BPND) using the selective SERT tracer [11C]DASB and positron emission tomography (PET) in 14 CD patients and 12 age- and gender-matched controls. Severity of motor symptoms was scored using the Toronto Western Spasmodic Torticollis Rating Scale and Clinical Global Impression jerks/tremor scale. NMS for depressive symptoms, anxiety, fatigue, and sleep disturbances were assessed with quantitative rating scales. The relationship between SERT binding and clinical patient characteristics was analyzed with the Spearman’s rho test and multiple regression.ResultsWhen comparing the CD patients with controls, no significant differences in BPND were found. Higher BPND in the dorsal raphe nucleus was statistically significantly correlated (p &lt; 0.001) with motor symptom severity (rs = 0.65), pain (rs = 0.73), and sleep disturbances (rs = 0.73), with motor symptom severity being the most important predictor of SERT binding. Furthermore, fatigue was negatively associated with the BPND in the medial raphe nucleus (rs = −0.61, p = 0.045), and sleep disorders were positively associated with the BPND in the caudate nucleus (rs = 0.58, p = 0.03) and the hippocampus (rs = 0.56, p = 0.02).ConclusionMotor symptoms, as well as pain, sleep disturbances, and fatigue in CD showed a significant relationship with SERT binding in the raphe nuclei. Moreover, fatigue showed a significant relationship with the medial raphe nucleus and sleep disorders with the caudate nucleus and hippocampus. These findings suggest that an altered serotonergic signaling in different brain areas in CD is related to different motor as well as NMS, which will further stimulate research on the role of serotonin in the pathogenesis of dystonia

Laser-initiated decomposition products of indocyanine green (ICG) and carbon black sensitized biological tissues

Organic dyes have found increasing use a s sensitizers in laser surgical procedures, due to their high optical absorbances. Little is known, however, about the nature of the degradation products formed when these dyes are irradiated with a laser. Previous work in our laboratories has shown that irradiation of polymeric and biological tissues with CO2 and Nd:YAG lasers produces a host of volatile and semivolatile by-products, some of which are known to be potential carcinogens. This work focuses on the identification of the chemical by-products formed by diode laser and Nd:YAG laser irradiation of indocyanine green (ICG) and carbon black based ink sensitized tissues, including bone, tendon and sheep\u27s teeth. Samples were mounted in a 0.5-L Pyrex sample chamber equipped with quartz optical windows, charcoal filtered air inlet and an outlet attached to an appropriate sample trap and a constant flow pump. By-products were analyzed by GC/MS and HPLC. Volatiles identified included benzene and formaldehyde. Semi-volatiles included traces of polycyclic aromatics, arising from the biological matrix and inks, as well as fragments of ICG and the carbon ink components. The significance of these results will be discussed, including the necessity of using appropriate evacuation devices when utilizing lasers for surgical procedures

Electron Photodetachment from Aqueous Anions. II. Ionic Strength Effect on Geminate Recombination Dynamics and Quantum Yield for Hydrated Electron

In concentrated solutions of NaClO4 and Na2SO4, the quantum yield for free electron generated by detachment from photoexcited anions (such as I-, OH-, ClO^4-, and [SO3]^2-) linearly decreases by 6-12% per 1 M ionic strength. In 9 M sodium perchlorate solution, this quantum yield decreases by roughly an order of magnitude. Ultrafast kinetic studies of 200 nm photon induced electron detachment from Br-, HO- and [SO3]^2- suggest that the prompt yield of thermalized electron does not change in these solutions; rather, the ionic strength effect originates in more efficient recombination of geminate pairs. Within the framework of the recently proposed mean force potential (MFP) model of charge separation dynamics in such photosystems, the observed changes are interpreted as an increase in the short-range attractive potential between the geminate partners. Association of sodium cation(s) with the electron and the parent anion is suggested as the most likely cause for the observed modification of the MFP. Electron thermalization kinetics suggest that the cation associated with the parent anion (by ion pairing and/or ionic atmosphere interaction) is passed to the detached electron in the course of the photoreaction. The precise atomic-level mechanism for the ionic strength effect is presently unclear; any further advance is likely to require the development of an adequate quantum molecular dynamics model.Comment: 40 pages, 10 figures + supplement 2 pages, 9 figures; will be submitted, in a modified form, to J. Phys. Chem

Supersymmetry on a Spatial Lattice

We construct a variety of supersymmetric gauge theories on a spatial lattice, including N=4 supersymmetric Yang-Mills theory in 3+1 dimensions. Exact lattice supersymmetry greatly reduces or eliminates the need for fine tuning to arrive at the desired continuum limit in these examples.Comment: Version 3: Text brought in line with published version (extended discussion of orbifolding

Generation of spatially coherent light at extreme ultraviolet wavelengths

Includes bibliographical references (page 378).We present spatial coherence measurements of extreme ultraviolet (EUV) light generated through the process of high-harmonic up-conversion of a femtosecond laser. With a phase-matched hollow-fiber geometry, the generated beam was found to exhibit essentially full spatial coherence. The coherence of this laser-like EUV source was shown by recording Gabor holograms of small objects. This work demonstrates the capability to perform EUV holography with a tabletop experimental setup. Such an EUV source, with low divergence and high spatial coherence, can be used for experiments involving high-precision metrology, inspection of optical components for EUV lithography, and microscopy and holography with nanometer resolution. Furthermore, the short time duration of the EUV radiation (a few femtoseconds) will enable EUV microscopy and holography to be performed with ultrahigh time resolution

Aeroelastic Response and Protection of Space Shuttle External Tank Cable Trays

Sections of the Space Shuttle External Tank Liquid Oxygen (LO2) and Liquid Hydrogen (LH2) cable trays are shielded from potentially damaging airloads with foam Protuberance Aerodynamic Load (PAL) Ramps. Flight standard design LO2 and LH2 cable tray sections were tested with and without PAL Ramp models in the United States Air Force Arnold Engineering Development Center s (AEDC) 16T transonic wind tunnel to obtain experimental data on the aeroelastic stability and response characteristics of the trays and as part of the larger effort to determine whether the PAL ramps can be safely modified or removed. Computational Fluid Dynamic simulations of the full-stack shuttle launch configuration were used to investigate the flow characeristics around and under the cable trays without the protective PAL ramps and to define maximum crossflow Mach numbers and dynamic pressures experienced during launch. These crossflow conditions were used to establish wind tunnel test conditions which also included conservative margins. For all of the conditions and configurations tested, no aeroelastic instabilities or unacceptable dynamic response levels were encountered and no visible structural damage was experienced by any of the tested cable tray sections. Based upon this aeroelastic characterization test, three potentially acceptable alternatives are available for the LO2 cable tray PAL Ramps: Mini-Ramps, Tray Fences, or No Ramps. All configurations were tested to maximum conditions, except the LH2 trays at -15 deg. crossflow angle. This exception is the only caveat preventing the proposal of acceptable alternative configurations for the LH2 trays as well. Structural assessment of all tray loads and tray response measurements from launches following the Shuttle Return To Flight with the existing PAL Ramps will determine the acceptability of these PAL Ramp alternatives

A new paediatric formulation of valaciclovir : development and bioequivalence assessment

Peer reviewedPostprin

Clinical, radiologic, pathologic, and molecular characteristics of long-term survivors of diffuse intrinsic pontine glioma (DIPG): a collaborative report from the International and European Society for Pediatric Oncology DIPG registries

Purpose Diffuse intrinsic pontine glioma (DIPG) is a brainstem malignancy with a median survival of &lt; 1 year. The International and European Society for Pediatric Oncology DIPG Registries collaborated to compare clinical, radiologic, and histomolecular characteristics between short-term survivors (STSs) and long-term survivors (LTSs). Materials and Methods Data abstracted from registry databases included patients from North America, Australia, Germany, Austria, Switzerland, the Netherlands, Italy, France, the United Kingdom, and Croatia. Results Among 1,130 pediatric and young adults with radiographically confirmed DIPG, 122 (11%) were excluded. Of the 1,008 remaining patients, 101 (10%) were LTSs (survival ≥ 2 years). Median survival time was 11 months (interquartile range, 7.5 to 16 months), and 1-, 2-, 3-, 4-, and 5-year survival rates were 42.3% (95% CI, 38.1% to 44.1%), 9.6% (95% CI, 7.8% to 11.3%), 4.3% (95% CI, 3.2% to 5.8%), 3.2% (95% CI, 2.4% to 4.6%), and 2.2% (95% CI, 1.4% to 3.4%), respectively. LTSs, compared with STSs, more commonly presented at age &lt; 3 or &gt; 10 years (11% v 3% and 33% v 23%, respectively; P &lt; .001) and with longer symptom duration ( P &lt; .001). STSs, compared with LTSs, more commonly presented with cranial nerve palsy (83% v 73%, respectively; P = .008), ring enhancement (38% v 23%, respectively; P = .007), necrosis (42% v 26%, respectively; P = .009), and extrapontine extension (92% v 86%, respectively; P = .04). LTSs more commonly received systemic therapy at diagnosis (88% v 75% for STSs; P = .005). Biopsies and autopsies were performed in 299 patients (30%) and 77 patients (10%), respectively; 181 tumors (48%) were molecularly characterized. LTSs were more likely to harbor a HIST1H3B mutation (odds ratio, 1.28; 95% CI, 1.1 to 1.5; P = .002). Conclusion We report clinical, radiologic, and molecular factors that correlate with survival in children and young adults with DIPG, which are important for risk stratification in future clinical trials