Fourier methods for the perturbed harmonic oscillator in linear and nonlinear Schr\"odinger equations

We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with Fourier techniques since the system can be split into the kinetic and remaining part, and each part can be solved efficiently using Fast Fourier Transforms. To split the system into the quantum harmonic oscillator problem and the remaining part allows to get higher accuracies in many cases, but it requires to change between Hermite basis functions and the coordinate space, and this is not efficient for time-dependent frequencies or strong nonlinearities. We show how to build new methods which combine the advantages of using Fourier methods while solving the timedependent harmonic oscillator exactly (or with a high accuracy by using a Magnus integrator and an appropriate decomposition).Comment: 12 pages of RevTex4-1, 8 figures; substantially revised and extended versio

High order structure preserving explicit methods for solving linear-quadratic optimal control problems

[EN] We consider the numerical integration of linear-quadratic optimal control problems. This problem requires the solution of a boundary value problem: a non-autonomous matrix Riccati differential equation (RDE) with final conditions coupled with the state vector equation with initial conditions. The RDE has positive definite matrix solution and to numerically preserve this qualitative property we propose first to integrate this equation backward in time with a sufficiently accurate scheme. Then, this problem turns into an initial value problem, and we analyse splitting and Magnus integrators for the forward time integration which preserve the positive definite matrix solutions for the RDE. Duplicating the time as two new coordinates and using appropriate splitting methods, high order methods preserving the desired property can be obtained. The schemes make sequential computations and do not require the storrage of intermediate results, so the storage requirements are minimal. The proposed methods are also adapted for solving linear-quadratic N-player differential games. The performance of the splitting methods can be considerably improved if the system is a perturbation of an exactly solvable problem and the system is properly split. Some numerical examples illustrate the performance of the proposed methods.The author wishes to thank the University of California San Diego for its hospitality where part of this work was done. He also acknowledges the support of the Ministerio de Ciencia e Innovacion (Spain) under the coordinated project MTM2010-18246-C03. The author also acknowledges the suggestions by the referees to improve the presentation of this work.Blanes Zamora, S. (2015). High order structure preserving explicit methods for solving linear-quadratic optimal control problems. 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Math. 262, 223–233 (2014)Basar, T., Olsder, G.J.: Dynamic non cooperative game theory, 2nd Ed, SIAM, Philadelphhia (1999)Blanes, S., Casas, F.: On the necessity of negative coefficients for operator splitting schemes of order higher than two. Appl. Num. Math. 54, 23–37 (2005)Blanes, S., Casas, F., Farrés, A., Laskar, J., Makazaga, J., Murua, A.: New families of symplectic splitting methods for numerical integration in dynamical astronomy. Appl. Numer. Math. 68, 58–72 (2013)Blanes, S., Casas, F., Oteo, J.A., Ros, J.: The Magnus expansion and some of its applications. Phys. Rep. 470, 151–238 (2009)Blanes, S., Casas, F., Ros, J.: High order optimized geometric integrators for linear differential equations. BIT 42, 262–284 (2002)Blanes, S., Diele, F., Marangi, C., Ragni, S.: Splitting and composition methods for explicit time dependence in separable dynamical systems. J. Comput. Appl. Math. 235, 646–659 (2010)Blanes, S., Moan, P.C.: Practical symplectic partitioned Runge-Kutta and Runge-Kutta-Nystrm methods. J. Comput. Appl. Math. 142, 313–330 (2002)Blanes, S., Ponsoda, E.: Magnus integrators for solving linear-quadratic differential games. J. Comput. Appl. Math. 236, 3394–3408 (2012)Brif, C., Chakrabarti, R., Rabitz, H.: Control of quantum phenomena: past, present and future. New J. Phys. 12, 075008(68pp) (2010)Cruz, J.B., Chen, C.I.: Series Nash solution of two person non zero sum linear quadratic games. J. Optim. Theory Appl. 7, 240–257 (1971)Dieci, L., Eirola, T.: Positive definitness in the numerical solution of Riccati differential quations. Numer. Math. 67, 303–313 (1994)Engwerda, J.: LQ dynamic optimization and differential games. Wiley (2005)Hairer, E., Lubich, C., Wanner, G.: Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations (2nd edition). Springer Series in Computational Mathematics, 31. 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A rapid method for the in-field analysis of amphetamines employing the agilent bioanalyzer

This paper reports the first analysis of small molecules on the Agilent bio-analyser. The Bioanalyzer is a commercial lab-on-a-chip instrument designed for the analysis of DNA and proteins. We demonstrate that the instrument is suitable for analyses beyond its design specifications. Amphetamine, methamphetamine and pseudoephedrine were separated with a 50 mM borate and 50 mM sodium dodecyl sulfate (SDS) buffer at pH 9.66. The analytes were derivatised with fluorescein isothiocyanate (FITC) in 3 minutes with a heating block set at 90°C, reducing the typical time of 12 hours required for amine-labelling. Analytes were detected by LED-induced fluorescence (λ = 525 nm and λ = 470 nm). Furthermore, five amphetamine analogues were baseline separated within 1 minute. An average limit of detection of 0.6 mg mL -1 and limit of quantification of 2.2μ mg mL-1 were obtained for all analytes. These rapid analyses in conjunction with a fast and reliable derivatisation method with FITC demonstrate its potential use for the in-field analysis of samples of forensic significance. © 2011 The Royal Society of Chemistry

Influence of tank bottom surface on growth and welfare of Senegalese sole (Solea senegalensis)

Tank bottom surface is an important question to take into account in flatfish aquaculture considering the intimate contact that the fish have with it. The most usual materials in aquaculture tank surfaces are inert materials such as epoxy resins or plastics with null porosity, and cement that presents a high alkalinity, roughness and porosity. To improve the cement characteristics, silica fume admixture is usually added in construction industry. The aim of this study was to evaluate the effect of three types of tank bottom surfaces on growth and welfare over a Solea senegalensis population. Moreover, the degree of fin erosion, the appearance of skin lesions and malpigmentation patterns were also monitored. The bottom surfaces tested were plain cement (CE), the same plain cement blended with silica fume (10%) (SF) and epoxy coated surface (EP). Specific growth rate for each bottom surface were compared. The Image Processing Activity Index (IPAI) was used to evaluate the Senegalese sole welfare. Higher SGR and lower IPAI values were obtained in the surface of cement with silica fume, suggesting a higher welfare. The use of plain cement affected negatively the performance of fish, probably due to the high pH and alkalinity of the water in direct contact with fish skin. The null porosity of EP seems to be related to the main cause of higher activity level of fish kept on it outcoming in lower growth. Silica fume that is frequently use to improve the mechanical characteristics of plain cement, also provides benefits in terms of fish welfare.Postprint (author's final draft

Detection of gunshot residues using mass spectrometry

In recent years, forensic scientists have become increasingly interested in the detection and interpretation of organic gunshot residues (OGSR) due to the increasing use of lead- and heavy metal-free ammunition. This has also been prompted by the identification of gunshot residue- (GSR-) like particles in environmental and occupational samples. Various techniques have been investigated for their ability to detect OGSR. Mass spectrometry (MS) coupled to a chromatographic system is a powerful tool due to its high selectivity and sensitivity. Further, modern MS instruments can detect and identify a number of explosives and additives which may require different ionization techniques. Finally, MS has been applied to the analysis of both OGSR and inorganic gunshot residue (IGSR), although the "gold standard" for analysis is scanning electron microscopy with energy dispersive X-ray microscopy (SEM-EDX). This review presents an overview of the technical attributes of currently available MS and ionization techniques and their reported applications to GSR analysis. © 2014 Regina Verena Taudte et al

A portable explosive detector based on fluorescence quenching of pyrene deposited on coloured wax-printed μpADs

A new technique for the detection of explosives has been developed based on fluorescence quenching of pyrene on paper-based analytical devices (μPADs). Wax barriers were generated (150 °C, 5 min) using ten different colours. Magenta was found as the most suitable wax colour for the generation of the hydrophobic barriers with a nominal width of 120 μm resulting in fully functioning hydrophobic barriers. One microliter of 0.5 mg mL-1 pyrene dissolved in an 80 : 20 methanol-water solution was deposited on the hydrophobic circle (5 mm diameter) to produce the active microchip device. Under ultra-violet (UV) illumination, ten different organic explosives were detected using the μPAD, with limits of detection ranging from 100-600 ppm. A prototype of a portable battery operated instrument using a 3 W power UV light-emitting-diode (LED) (365 nm) and a photodiode sensor was also built and evaluated for the successful automatic detection of explosives and potential application for field-based screening. © 2013 The Royal Society of Chemistry

Strategy of microscopic parallelism for Bitplane Image Coding

Recent years have seen the upraising of a new type of processors strongly relying on the Single Instruction, Multiple Data (SIMD) architectural principle. The main idea behind SIMD computing is to apply a flow of instructions to multiple pieces of data in parallel and synchronously. This permits the execution of thousands of operations in parallel, achieving higher computational performance than with traditional Multiple Instruction, Multiple Data (MIMD) architectures. The level of parallelism required in SIMD computing can only be achieved in image coding systems via microscopic parallel strategies that code multiple coefficients in parallel. Until now, the only way to achieve microscopic parallelism in bitplane coding engines was by executing multiple coding passes in parallel. Such a strategy does not suit well SIMD computing because each thread executes different instructions. This paper introduces the first bitplane coding engine devised for the fine grain of parallelism required in SIMD computing. Its main insight is to allow parallel coefficient processing in a coding pass. Experimental tests show coding performance results similar to those of JPEG2000

Skin Tumors in Patients Aged 90 Years and Older

Background: The aging of the population in the developed world is an accepted fact. Consequently, the number of patients aged 90 years or over with cutaneous cancer will increase in coming years. Objective: The objective was to determine the nature of skin lesions amenable to dermatologic surgery in patients aged 90 years or more. Methods: We studied the clinical histories of 52 outpatients in their 90 s, who had had histopathologic studies made of their skin tumors when attended in the Hospital General de Alicante (Spain) between January 1999 and July 2002. We studied sex, age, type of tumor, site, associated disorders, regular medications, type of anesthesia, and type of treatment given. Results: The average age of the patients was 92.4 years. Thirty-six patients were women and 16 were men. Altogether the 52 patients had a total of 72 lesions. The most frequent diagnosis was basal cell carcinoma with 36 lesions, followed by 20 squamous cell carcinomas. The overall ratio of basal cell carcinoma to squamous cell carcinoma was 1.8. Patients had an average of 1.5 comorbid medical conditions and were taking an average of 2.3 regular medications. Conclusion: Dermatologists often attend patients aged 90 years or over with nonmelanoma skin cancer. The most important decision is as to what is the best management of these patients

Purification, characterization and molecular cloning of the major chitinase from Tenebrio molitor larval midgut

Insect chitinases are involved in degradation of chitin from the exoskeleton cuticle or from midgut peritrophic membrane during molts. cDNAs coding for insect cuticular and gut chitinases were cloned, but only chitinases from moulting fluid were purified and characterized. In this study the major digestive chitinase from T. molitor midgut (TmChi) was purified to homogeneity, characterized and sequenced after cDNA cloning. TmChi is secreted by midgut epithelial cells, has a molecular weight of 44 kDa and is unstable in the presence of midgut proteinases. TmChi shows strong substrate inhibition when acting on umbelliferyl-derivatives of chitobio- and chitotriosaccharides, but has normal Michaelis kinetics with the N-acetylglucosamine derivative as substrate. TmChi has very low activity against colloidal chitin, but effectively converts oligosaccharides to shorter fragments. The best substrate for TmChi is chitopentaose, with highest kcat/KM value. Sequence analysis and chemical modification experiments showed that the TmChi active site contains carboxylic groups and a tryptophane, which are known to be important for catalysis in family 18 chitinases. Modification with p-hidroximercuribenzoate of a cysteine residue, which is exposed after substrate binding, leads to complete inactivation of the enzyme. TmChi mRNA encodes a signal peptide plus a protein with 37 kDa and high similarity with other insect chitinases from family 18. Surprisingly, this gene does not encode the C-terminal Ser-Thr-rich connector and chitin-binding domain normally present in chitinases. The special features of TmChi probably result from its adaptation to digest chitin-rich food without damaging the peritrophic membrane. © 2006 Elsevier Ltd. All rights reserved

SiC JFET/P-MOSFET cascode for SSCB and inrush current limiter in 300V DC power systems

This work presents a solid-state distribution and protection switch based on the SiC JFET/P-MOSFET cascode structure. The concept is aimed for 300V applications, but it can be adapted easily to other voltages. Detailed circuit design and simulation is discussed, as well as the potential application in 300V bus voltage satellite