Van De Vyver Research Articles

A new phase-fitted modified Runge–Kutta pair for the numerical solution of the radial Schrödinger equation

A new embedded pair of phase-fitted explicit modified Runge–Kutta (RK) methods for the numerical integration of the radial Schrödinger equation is presented in this paper. The two component methods in the pair have algebraic order five and four, respectively. The new fifth-order method is shown to have the phase-lag constant of one order higher than that in Van de Vyver’s RK5(4) pair (Van de Vyver (2006) [5]) when the fitting frequency is close to the real frequency. The numerical results in the integration of the radial Schrödinger equation are reported showing the higher efficiency of the new fifth-order modified RK method and the new modified RK5(4) pair compared to some highly efficient methods in the recent literature.

Abdominal mycobacterial infection in HIV - Invited Comment

No Abstract

CRP and toxic granulation; reply by Dr Van de Vyver

CRP and toxic granulation; reply by Dr Van de Vyver

Construction of Intensity–Duration–Frequency (IDF) curves for precipitation at Lubumbashi, Congo, under the hypothesis of inadequate data

Intensity–Duration–Frequency (IDF) curves for precipitation constitute a probabilistic tool and have proven useful in water resources management. In particular, IDF curves for precipitation enable questions on the extreme character of precipitation to be answered. The construction of IDF curves for precipitation is difficult or impossible in tropical areas due to the lack of long-term extreme precipitation data. A technique is proposed to overcome this shortcoming by combining limited high-frequency information on rainfall extremes with long-term daily rainfall information. It may be regarded as an extension of Koutsoyiannis' approach. Using this technique, IDF curves for precipitation are produced for Lubumbashi in Congo. Citation Van de Vyver, H. & Demarée, G. R. (2010) Construction of Intensity–Duration–Frequency (IDF) curves for precipitation at Lubumbashi, Congo, under the hypothesis of inadequate data. Hydrol. Sci. J. 55(4), 555–564.

On high order symmetric and symplectic trigonometrically fitted Runge-Kutta methods with an even number of stages

The existence and construction of symplectic 2s-stage variable coefficients Runge-Kutta (RK) methods that integrate exactly IVPs whose solution is a trigonometrical polynomial of order s with a given frequency ω is considered. The resulting methods, that can be considered as trigonometrical collocation methods, are fully implicit, symmetric and symplectic RK methods with variable nodes and coefficients that are even functions of ν=ωh (h is the step size), and for ω→0 they tend to the conventional RK Gauss methods. The present analysis extends previous results on two-stage symplectic exponentially fitted integrators of Van de Vyver (Comput. Phys. Commun. 174: 255–262, 2006) and Calvo et al. (J. Comput. Appl. Math. 218: 421–434, 2008) to symmetric and symplectic trigonometrically fitted methods of high order. The algebraic order of the trigonometrically fitted symmetric and symplectic 2s-stage methods is shown to be 4s like in conventional RK Gauss methods. Finally, some numerical experiments with oscillatory Hamiltonian systems are presented.

‘To the adornment and honour of the city’: the mathematics course of the Flemish Jesuits in the seventeenth century

In 1980 Omer van de Vyver drew attention to the existence of a Jesuit ‘school of mathematics’ in the Flemish province. However, in recent years historians of science have constructed a more refined picture of Jesuit science and Jesuit scientific teaching in the different colleges scattered around Europe. A reappraisal of the specific conditions and underlying motives of the inauguration of the mathematics course in the Flemish province shows that this course cannot be reduced to a mere copy of Clavius's Academy in Rome. Nor can the course be considered to be a straightforward implementation of the Ratio studiorum. Rather, the foundation and organization of the Flemish course of mathematics responded to characteristic contextual impulses.1 1 This work was done with the support of a scholarship from the Vlaams-Nederlands Comité voor Nederlanse Taal en Cultuur (VNC). This is a revised version of the paper I read to a colloquium in Antwerp, organized by the Koninklijke Zuid-Nederlandse Maatschappij voor Taal- en Letterkunde en Geschiedenis and published in Dutch in the proceedings of that colloquium.

Sixth-order symmetric and symplectic exponentially fitted modified Runge–Kutta methods of Gauss type

The construction of symmetric and symplectic exponentially fitted modified Runge–Kutta (RK) methods for the numerical integration of Hamiltonian systems with oscillatory solutions is considered. In a previous paper [H. Van de Vyver, A fourth order symplectic exponentially fitted integrator, Comput. Phys. Comm. 176 (2006) 255–262] a two-stage fourth-order symplectic exponentially fitted modified RK method has been proposed. Here, two three-stage symmetric and symplectic exponentially fitted integrators of Gauss type, either with fixed nodes or variable nodes, are derived. The algebraic order of the new integrators is also analyzed, obtaining that they possess sixth-order as the classical three-stage RK Gauss method. Numerical experiments with some oscillatory problems are presented to show that the new methods are more efficient than other symplectic RK Gauss codes proposed in the scientific literature.

Structure preservation of exponentially fitted Runge–Kutta methods

The preservation of some structure properties of the flow of differential systems by numerical exponentially fitted Runge–Kutta (EFRK) methods is considered. A complete characterisation of EFRK methods that preserve linear or quadratic invariants is given and, following the approach of Bochev and Scovel [On quadratic invariants and symplectic structure, BIT 34 (1994) 337–345], the sufficient conditions on symplecticity of EFRK methods derived by Van de Vyver [A fourth-order symplectic exponentially fitted integrator, Comput. Phys. Comm. 174 (2006) 255–262] are obtained. Further, a family of symplectic EFRK two-stage methods with order four has been derived. It includes the symplectic EFRK method proposed by Van de Vyver as well as a collocation method at variable nodes that can be considered as the natural collocation extension of the classical RK Gauss method. Finally, the results of some numerical experiments are presented to compare the relative merits of several fitted and nonfitted fourth-order methods in the integration of oscillatory systems.

Phase-fitted and amplification-fitted two-step hybrid methods for [formula omitted

This paper provides a theoretical framework for a new type of phase-fitted and amplification-fitted two-step hybrid (FTSH) methods which is introduced by the author in [H. Van de Vyver, A phase-fitted and amplification-fitted explicit two-step hybrid method for second-order periodic initial value problems, Internat. J. Modern Phys. C 17 (2006) 663–675]. The methods constitute a modification of dissipative two-step hybrid methods in the sense that two free parameters are added to eliminate the phase-lag and the amplification error. The methods are useful only when a good estimate of the frequency of the problem is known in advance. The parameters depend on the product of the estimated frequency and the stepsize. The algebraic order, zero-stability, stability and phase properties are examined. The theory is illustrated with sixth-order explicit FTSH methods. Numerical results carried out on an assortment of test problems show the relevance of the theory.

A fourth-order symplectic exponentially fitted integrator

A numerical method for ordinary differential equations is called symplectic if, when applied to Hamiltonian problems, it preserves the symplectic structure in phase space, thus reproducing the main qualitative property of solutions of Hamiltonian systems. In a previous paper [G. Vanden Berghe, M. Van Daele, H. Van de Vyver, Exponential fitted Runge–Kutta methods of collocation type: fixed or variable knot points?, J. Comput. Appl. Math. 159 (2003) 217–239] some exponentially fitted RK methods of collocation type are proposed. In particular, three different versions of fourth-order exponentially fitted Gauss methods are described. It is well known that classical Gauss methods are symplectic. In contrast, the exponentially fitted versions given in [G. Vanden Berghe, M. Van Daele, H. Van de Vyver, Exponential fitted Runge–Kutta methods of collocation type: fixed or variable knot points?, J. Comput. Appl. Math. 159 (2003) 217–239] do not share this property. This paper deals with the construction of a fourth-order symplectic exponentially fitted modified Gauss method. The RK method is modified in the sense that two free parameters are added to the Buthcher tableau in order to retain symplecticity.

Lead, renal disease and hypertension

Lead, renal disease and hypertension

Commonwealth Catholicism: A History of the Catholic Church in Virginia (review)

Commonwealth Catholicism:A History of the Catholic Church in Virginia. By Gerald P Fogarty, S.J. (Notre Dame, Indiana: University of Notre Dame Press. 2001. Pp. xxix, 687. $34.95.) In this authoritative narrative the author has left no stone unturned in his effort to describe a remarkable development that covered some four hundred years. It begins with the ill-fated efforts of Spanish Jesuits to establish a mission near the York River in 1570. It ends with the appointment of Walter E Sullivan as Richmond's eleventh bishop in 1974. The movement of the Brents from Maryland to northern Virginia is cited as a milestone. Their home on Aquia Creek would in 1930 be memorialized with a large crucifix and plaque. There annual pilgrimages would be held, often favored by the Marine Band from Quantico, as a reminder of the longevity of the Catholic presence in Virginia. John Carroll's visits to his Brent relatives is duly noted before the author takes us to the first unhappy attempt to make Virginia a diocese. In 1820, in an effort to quell trusteeism in Norfolk, Patrick Kelly of Ireland was named first bishop of the Diocese of Richmond, which encompassed the State of Virginia. As a result of the vehement opposition to this appointment on the part of Archbishop Ambrose Marechal of Baltimore, who was not consuited, Kelly left Virginia in 1822 without even having seen his see city. From then until 1840 the archbishops of Baltimore were, in effect, also the bishops of Richmond. The nine bishops of Richmond after 1840 were Richard Vincent Whelan (1840-1850), John McGill (1850-1872), James Gibbons (1872-1877), John Joseph Keane (1878-1888), Augustine van de Vyver (1889-1911), Denis O'Connell (1912-1926), Andrew Brennan (1926-1945), Peter L. Ireton (1945-1958), and John J. Russell (1958-1973). Four of the nine were born in Baltimore (Whelan, Gibbons, Ireton, and Russell), two in Ireland (Keane and O'Connell), two in Pennsylvania (McGill and Brennan), and one in Belgium (van de Vyver). Three (Gibbons, Keane, and O'Connell), who had attempted to apply the accommodating style of Virginia Catholicism on a national level (p. 190), were the leaders of the Americanizers in the turbulent decade and a half at the end of the nineteenth century so well rehearsed by the historians of American Catholicism. Despite certain affinities the bishops of Richmond differed markedly in temperament and tactics. None was a carbon copy of his predecessor. By and large the bishops of Richmond were liberal-minded, at least ecumenical. Beginning with McGill all were attentive to the needs of their AfricanAmerican charges. Russell was outstanding in his promotion of civil rights; integration came to the diocese on the eve of Brown vs. Board of Education. From the diocesan clergy came three of the most progressive bishops in the South in near-contemporary times: Vincent Waters of Raleigh, Ernest Unterkoefier of Charleston, and Carroll Dozier of Memphis. …

Chronic Lead Nephropathy with Excessive Body Lead Burden

Journal of Occupational HealthVolume 42, Issue 5 p. 260-262 Case StudyFree Access Chronic Lead Nephropathy with Excessive Body Lead Burden Hyun-Cheol Ahn, Hyun-Cheol Ahn Department of Preventive Medicine and Institute of Industrial Medicine, School of Medicine, Soonchunhyang UniversitySearch for more papers by this authorKyu-Yoon Hwang, Kyu-Yoon Hwang Department of Preventive Medicine and Institute of Industrial Medicine, School of Medicine, Soonchunhyang UniversitySearch for more papers by this authorSae-Yong Hong, Sae-Yong Hong Department of Internal Medicine, Soonchunhyang Hospital, Republic of KoreaSearch for more papers by this authorDong-Ho Yang, Dong-Ho Yang Department of Internal Medicine, Soonchunhyang Hospital, Republic of KoreaSearch for more papers by this authorByung-Kook Lee, Byung-Kook Lee Department of Preventive Medicine and Institute of Industrial Medicine, School of Medicine, Soonchunhyang UniversitySearch for more papers by this authorAndrew C. Todd, Andrew C. Todd Department of Community and Preventive Medicine, Mount Sinai Medical Center, New York, USASearch for more papers by this author Hyun-Cheol Ahn, Hyun-Cheol Ahn Department of Preventive Medicine and Institute of Industrial Medicine, School of Medicine, Soonchunhyang UniversitySearch for more papers by this authorKyu-Yoon Hwang, Kyu-Yoon Hwang Department of Preventive Medicine and Institute of Industrial Medicine, School of Medicine, Soonchunhyang UniversitySearch for more papers by this authorSae-Yong Hong, Sae-Yong Hong Department of Internal Medicine, Soonchunhyang Hospital, Republic of KoreaSearch for more papers by this authorDong-Ho Yang, Dong-Ho Yang Department of Internal Medicine, Soonchunhyang Hospital, Republic of KoreaSearch for more papers by this authorByung-Kook Lee, Byung-Kook Lee Department of Preventive Medicine and Institute of Industrial Medicine, School of Medicine, Soonchunhyang UniversitySearch for more papers by this authorAndrew C. Todd, Andrew C. Todd Department of Community and Preventive Medicine, Mount Sinai Medical Center, New York, USASearch for more papers by this author First published: 07 April 2006 https://doi.org/10.1539/joh.42.260 Correspondence to; B.-K. Lee, Department of Preventive Medicine and Institute of Industrial Medicine, School of Medicine, Soonchunhyang University, 23-20 Bongtnyung-Dong, Chunan, Chungnam 330-100, Republic of Korea AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. References Todd AC, McNeill FE, Palethorpe JE, et al. In vivo X-ray fluorescence of lead in bone using K X-ray excitation with 109Cd sources: Radiation dosimetry study. Environ Res 1992; 57: 117– 132. Schwartz BS, Stewart WF, Todd AC, Links JM. Predictors of DMSA-chelatable lead levels and bone lead levels in organolead manufacturing workers. Occup Environ Med 1999; 56: 22– 29. Nuyts GD, Daelemans RA, Jorens PG, Elseviers MM, Van de Vyver FL, DeBore ME. Does lead play a role in the development of chronic renal disease? Nephrol Dial Transplant 1991; 6: 307– 315. Lilis R, Fischbein A, Valcincas JA, Blumberg W, Selikoff IJ. Kidney function and lead: relationship in several occupational groups with different levels of exposure. Am J Ind Med 1980; 1: 405– 412. Morgan JM, Hartley MW, Miller RE. Nephropathy in chronic lead poisoning. Arch Intern Med 1966; 118: 17– 29. Hu H, Pepper L, Goldman R. Effect of repeated occupational exposure to lead, cessation of exposure, and chelation on levels of lead in bone. Am J Ind Med 1991; 20: 723– 735. Wielopolski L, Ellis KJ, Vaswani AN, et al. In vivo bone lead measurements: a rapid monitoring method for cumulative lead exposure. Am J Ind Med 1986; 9: 221– 226. Wedeen RR Mallik DK, Batuman V. Detection and treatment of occupational lead nephropathy. Arch Intern Med 1979; 139: 53– 57. Bautman V, Wedeen RP, Bogden JD, Balestra DJ, Jones K, Schidlovsky G. Reducing bone lead content by chelation treatment in chronic lead poisoning: An in vivo X-ray fluorescence and bone biopsy study. Environ Res 1989; 48: 70– 75. Volume42, Issue5September 2000Pages 260-262 ReferencesRelatedInformation

Video and Electron Microscopy of Particle Feeding in Sandwich Cultures of the Hexactinellid Sponge, Rhabdocalyptus dawsoni

Cultured fragments of the hexactinellid sponge, Rhabdocalyptus dawsoni, were observed feeding on 1.0 Jm latex beads. Using contrast-enhanced video microscopy of live cultures, the events preceding, during, and after phagocytosis were observed. Particle ingestion occurred almost exclusively in flagellated areas where the water currents generated by the flagella of collar bodies could trap and hold particles against sponge tissue. Transmission electron microscopy of cultures fixed after feeding on latex beads showed that collar bodies themselves do not participate in particle phagocytosis. Rather, it is the primary and, probably, the secondary reticula of the trabecular reticulum in the flagellated chamber wall which effect phagocytosis. The intact sponge's tissue organization appears admirably suited for particle capture, and these sponges are likely to be, at least in part, particle feeders in their natural habitat. Additional key words: Hexactinellida, Porifera, filter feeding, culture The Hexactinellida (Porifera, subphylum Symplasma) is an enigmatic marine sponge group which has received little attention in the past due to their seclusion in deep waters. However, recent advances exploiting the few shallow-water species available for study have begun to reveal various aspects of their tissue organization, cell biology, and feeding (e.g. Reiswig & Mehl 1991; Boury-Esnault & Vacelet 1994; Leys 1995; Leys & Mackie 1997). Feeding studies have been pursued using two species: Oopsacas minuta TOPSENT 1927, a Mediterranean cave species (Perez 1996), and Rhabdocalyptus dawsoni (LAMBE 1892) a Northeast Pacific fjord species (Wyeth et al. 1996). Investigation of sponge feeding has focused on demosponges (Porifera, subphylum Cellularia), which has established them as non-specific particle feeders. Particles are extracted from water pumped through the body wall by choanocytes. Most tissues of the demosponge body wall have been implicated in particle phagocytosis. In addition to choanocytes, whose collar microvilli strain the current driven by the flagella, exopinacocytes of the dermal surface and endopinacocytes of the incurrent canals have been shown to engulf particles (Schmidt 1970; Diaz 1979; Willenz & Van de Vyver 1982; Imsiecke 1993). Furthermore, investigations of pumping rates (e.g., Reiswig 1971), a E-mail: rwyeth@u.washington.edu feeding and clearance efficiencies (e.g., Reiswig 1975a; Frost 1980), and the demosponge pump design (Larsen & Riisg'ard 1994) have also been conducted. The assumption that hexactinellid and demosponge feeding are the same should not be made a priori, since the two groups differ in the details of tissue organization and structure. In hexactinellids, the dermal membrane, trabeculae of the body wall, and flagellated chamber walls are all formed by the syncytial trabecular reticulum (Mackie & Singla 1983; Reiswig & Mehl 1991; Leys 1999). The hexactinellid aquiferous system consists of broad, expansive incurrent and excurrent canals bounded by a network of trabeculae (Schulze 1887; Ijima 1904; Leys 1999), unlike the smaller diameter canals, bounded by endopinacocytes, found in the demosponges used for feeding studies (Schmidt 1970; Diaz 1979; Imsiecke 1993). The large and oblong hexactinellid flagellated chambers, 60 (Jm or more in maximal dimension, are serviced by proportionately far more prosopyles (Schulze 1887; Ijima 1904; Reiswig & Mehl 1991; Leys 1999) than the smaller (30 Im in diameter) spherical chambers in demosponges used in feeding studies (Reiswig 1975b; Diaz 1979; de Vos et al. 1991). In hexactinellids, the trabecular reticulum branches to create a double reticulum in the chamber wall. The primary reticulum forms the wall of the chamber and encloses the bases of collar bodies. Inside the chamber, the secondary reticulum, offset from the primary, fills the gaps between This content downloaded from 207.46.13.176 on Mon, 20 Jun 2016 07:22:20 UTC All use subject to http://about.jstor.org/terms Hexactinellid sponge feeding collars inside the chamber (Reiswig 1979; Reiswig & Mehl 1991; Boury-Esnault & Vacelet 1994; Leys 1999). Hexactinellid collar bodies, although bearing similar collars of microvilli, are more widely spaced than demosponge choanocytes, are enucleate, and form part of a partially connected network within the flagellated chamber walls (Reiswig 1979; Mackie & Singla 1983; Leys 1999). Furthermore, the 20 tim flagella in hexactinellids are roughly 2-3 times the length of their associated collars (Reiswig 1979; Reiswig & Mehl 1991; Boury-Esnault & Vacelet 1994), considerably smaller than the equivalent ratio in demosponges which may have 45 pLm flagella, 4-6 times the collar length (see Larsen & Riisgard 1994). Although individually none of these structural differences leaps out as a reason to suspect substantial differences between hexactinellid and demosponge feeding, when considered together it is quite possible they could lead to considerable differences in the details of feeding

Van de Vyver, P. J. W., et al. Surgical orthodontic and prosthetic correction in patients with cleft lip, jaw, and palate. (Dutch)

Van de Vyver, P. J. W., et al. Surgical orthodontic and prosthetic correction in patients with cleft lip, jaw, and palate. (Dutch)

De "wiskundeschool" van de Vlaamse jezuïeten in de eerste helft van de zeventiende eeuw

In 1980 Father Omer Van de Vyver drew attention to the existence of aJesuit "school of mathematics" in the Flemish province of the Jesuit order. Inrecent years historians of science have constructed a more refined picture ofJesuit science and Jesuit scientific teaching in the different colleges scatteredaround Europe. A reappraisal of the specific conditions and underlyingmotives of the inauguration of the mathematics course in the Flemish provinceshows that this course cannot be reduced to a mere copy of Clavius's Academyin Rome. Nor can the course be considered to be a straightforward implementationof the Ratio Studiorum. The foundation and organisation of the Flemishcourse of mathematics rather responded to characteristic contextual impulses.