The numerical integration of relative equilibrium solutions. The nonlinear Schrodinger equation

We analyse different error propagation mechanisms for conservativeand nonconservative time-integrators of nonlinear Schrödingerequations. We use a geometric approach based on interpretingwaves as relative equilibria.     

General form of the equation of motion of a charged particle

The most general form of the equation of motion of a charged particle is derived. The equation allows for an arbitrary self-field and is consistent with energy-momentum conservation, angular momentum conservation and the Dirac mass renormalization.     

Transfinite ordinals as axiom number symbols for unification of quantum and electromagnetic wave functions

The mapping of axioms into transfinite number fields provides a method whereby axioms and the magnitudes of experimental values can be distinguished in a clear manner. This procedure is shown also to result in a logical interpretation for the presence of exponential forms and for their imaginary arguments.     

Synthesis of potential antimalarials

A series of quinoline derivatives containing a 2-thienyl ring in the 2-position and CO₂H, CH₂OH, CHO, CH(OH)CN, CH(OH)CO₂H, CO₂C₂H₅, COCH[N(C₂H₅)₂]CO₂C₂H₅, COCH₂N(C₂H₅)₂, COCH₃, substituents in the 4-position was synthesized. Both intermediate and target compounds were tested for antimalarial activity. A second series with a 5-bromo-2-thienyl group in the 2-position and CHOHCH₂N(C₂H₅)₂, CHOHCH₂N(CH₂)₆, and CHOHCH₂N(CH₂C₆H₅)₂ substituents in the 4-position was also prepared, it was found that, although these quinoline methanols were moderately active antimalarials, they exhibited a high degree of phototoxicity. A third series of compounds with 2-alkyl substituents (methyl, t-butyl) was also synthesized, and these were found to combine a modest degree of antimalarial activity with low phototoxicity. Several novel synthetic routes to the above compounds were developed and are detailed.     

Photon rest frames and null geodesics

A stationary spatial model for electromagnetic waves has the useful feature that it provides a means for characterizing discrete field distributions. Such a distribution may then be mapped to spherical particlelike entities, so that it then corresponds to a particle (photon) in its own rest frame.     

Charge ordering and elastic constants in Fe3-xZnx xO4

We present the temperature dependence of elastic modes of Fe_3-xZn_xO₄ with x = 0, x = 0.02 and x = 0.032. The c₄₄ shear modes show a pronounced softening which can be normalized to a common behavior for all these substances. We can explain the softening with a bilinear coupling of the elastic strain to an order parameter linked to charge ordering processes. The other elastic modes (c₁₁, c₁₂ and the bulk modulus) do not show any softening. We present a symmetry analysis for the charge ordering model. Received 27 April 1999     

Structure analysis of discotic,sanidic and ferroelectric crystals and liquid crystals using electron microscopy

Three types of liquid-crystalline materials with specific molecular structures were investigated using electron diffraction and high resolution imaging. Discotic and smectic liquid crystals were compared with the crystalline state. The superstructure of the sanidic liquid crystals showed effects in the line profiles and contour plots of the electron diffraction patterns.     

Average entropy dissipation in irreversible mesoscopic processes

The Clausius inequality is rectified to obtain expressions for the entropy produced as the result of irreversible work and/or heat exchanges. These are combined with the Jarzynski equality and its generalizations to explicitly relate mean (as opposed to transient) entropy dissipation to experimental or simulation observables. The results are extended to nonisothermal processes which begin and end at nonequilibrium steady states, leading to a new exact expression and positive lower bound for the resulting average entropy dissipation. The Carnot engine emerges as a limiting case of a family of irreversible processes arising from an interface between materials at different temperatures, whose mapping onto reversible and irreversible molecular extension experiments is discussed.     

The rectified second law of thermodynamics

Equilibrium thermodynamics is combined with Jarzynski's irreversible work theorem to quantify the excess entropy produced by irreversible processes. The resulting rectified form of the second law parallels the first law, in the sense that it facilitates the experimental measurement of excess entropy changes resulting from irreversible work and heat exchanges, just as the first law quantifies energy changes produced by either reversible or irreversible work and heat exchanges. The general form of the rectified second law is further applied to a broad class of quasi-static irreverisble (QSI) processes, for which all of the thermodynamic functions of both the system and surroundings remain continuously well-defined, thus facilitating excess entropy measurements by integrating exact differential functions along QSI paths. The results are illustrated by calculating the mechanical and thermal excess entropy produced by the irreversible unfolding of an RNA molecule.     

Integral resource capacity planning for inpatient care services based on bed census predictions by hour

The design and operations of inpatient care facilities are typically largely historically shaped. A better match with the changing environment is often possible, and even inevitable due to the pressure on hospital budgets. Effectively organizing inpatient care requires simultaneous consideration of several interrelated planning issues. Also, coordination with upstream departments like the operating theatre and the emergency department is much-needed. We present a generic analytical approach to predict bed census on nursing wards by hour, as a function of the Master Surgical Schedule and arrival patterns of emergency patients. Along these predictions, insight is gained on the impact of strategic (ie, case mix, care unit size, care unit partitioning), tactical (ie, allocation of operating room time, misplacement rules), and operational decisions (ie, time of admission/discharge). The method is used in the Academic Medical Center Amsterdam as a decision-support tool in a complete redesign of the inpatient care operations.