Biomedical subjects

Robert E Wyatt

Publications and source records attributed to Robert E Wyatt.

9 recordsLinked to original sources

PubMed2006

Computational method for the quantum Hamilton-Jacobi equation: bound states in one dimension.

An accurate computational method for the one-dimensional quantum Hamilton-Jacobi equation is presented. The Mobius propagation scheme, which can accurately pass through singularities, is used to numerically integrate the quantum Hamilton-Jacobi equation for the quantum momentum function. Bound state wave functions are then synthesized from the phase integral using the antithetic cancellation technique. Through this procedure, not only the quantum momentum functions but also the wave functions are accurately obtained. This computational approach is demonstrated through two solvable examples: the harmonic oscillator and the Morse potential. The excellent agreement between the computational and the exact analytical results shows that the method proposed here may be useful for solving similar quantum mechanical problems.

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PubMed2006

Multidimensional reactive scattering with quantum trajectories: dynamics with Morse vibrational modes.

The reactive scattering of a wave packet is studied by the quantum trajectory method for a model system with up to 25 Morse vibrational modes. The equations of motion are formulated in curvilinear reaction path coordinates with the restriction to a planar reaction path. Spatial derivatives are evaluated by the least squares method using contracted basis sets. Dynamical results, including trajectory evolution and time-dependent reaction probabilities, are presented and analyzed. For the case of one Morse vibrational mode, the results are in good agreement with those derived through direct numerical integration of the time-dependent Schrodinger equation.

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PubMed2006

Multidimensional reactive scattering with quantum trajectories: dynamics with 50-200 vibrational modes.

The dynamics of ensembles containing thousands of quantum trajectories are studied for multidimensional systems undergoing reactive scattering. The Hamiltonian and equations of motion are formulated in curvilinear reaction path coordinates, for the case of a planar (zero-torsion) reaction path. In order to enhance the computational efficiency, an improved least squares fitting procedure is introduced. This scheme involves contracted basis sets and the use of inner and outer stencils around points where fitting is performed. This method is applied to reactive systems with 50-200 harmonic vibrational modes which are coupled to motion along the reaction coordinate. Dynamical results, including trajectory evolution and time-dependent reaction probabilities, are presented and power law scaling of computation time with the number of vibrational modes is described.

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PubMed2006

Multidimensional reactive scattering with quantum trajectories.

Ensembles of quantum trajectories are evolved to study time-dependent reaction dynamics in multidimensional systems with up to 25 vibrational modes. The equations of motion are formulated in curvilinear reaction path coordinates and all coupling terms are retained, including those involving curvature of the reaction path. The model potential is a Gaussian barrier along the translational coordinate coupled to M vibrational modes. Spatial derivatives needed to propagate the trajectories are evaluated by least squares fitting in a contracted basis set. Stable propagation of the trajectory ensembles was carried out until complete bifurcation into reflected and reactive subensembles. The reaction probabilities were evaluated by Monte Carlo integration of the multidimensional smooth transmitted densities. Computational results, including trajectory plots and time-dependent reaction probabilities, are presented for M = 1, 5, and 25 vibrational modes.

Journal Article↗

PubMed2005

Multidimensional quantum trajectories: applications of the derivative propagation method.

In a previous publication [J. Chem. Phys. 118, 9911 (2003)], the derivative propagation method (DPM) was introduced as a novel numerical scheme for solving the quantum hydrodynamic equations of motion (QHEM) and computing the time evolution of quantum mechanical wave packets. These equations are a set of coupled, nonlinear partial differential equations governing the time evolution of the real-valued functions C and S in the complex action, S=C(r,t) + iS(r,t)/Planck's over 2pi, where Psi(r,t)=exp(S). Past numerical solutions to the QHEM were obtained via ensemble trajectory propagation, where the required first- and second-order spatial derivatives were evaluated using fitting techniques such as moving least squares. In the DPM, however, equations of motion are developed for the derivatives themselves, and a truncated set of these are integrated along quantum trajectories concurrently with the original QHEM equations for C and S. Using the DPM quantum effects can be included at various orders of approximation; no spatial fitting is involved; there is no basis set expansion; and single, uncoupled quantum trajectories can be propagated (in parallel) rather than in correlated ensembles. In this study, the DPM is extended from previous one-dimensional (1D) results to calculate transmission probabilities for 2D and 3D wave packet evolution on coupled Eckart barrier/harmonic oscillator surfaces. In the 2D problem, the DPM results are compared to standard numerical integration of the time-dependent Schrodinger equation. Also in this study, the practicality of implementing the DPM for systems with many more degrees of freedom is discussed.

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PubMed2004

Coping with the node problem in quantum hydrodynamics: the covering function method.

A conceptually simple approach, the covering function method (CFM), is developed to cope with the node problem in the hydrodynamic formulation of quantum mechanics. As nodes begin to form in a scattering wave packet (detected by a monitor function), a nodeless covering wave function is added to it yielding a total function that is also nodeless. Both local and global choices for the covering function are described. The total and covering functions are then propagated separately in the hydrodynamic picture. At a later time, the actual wave function is recovered from the two propagated functions. The results obtained for Eckart barrier scattering in one dimension are in excellent agreement with exact results, even for very long propagation times t=1.2 ps. The capability of the CFM is also demonstrated for multidimensional propagation of a vibrationally excited wave packet.

Biophysics↗

PubMed2004

Trajectory approach to dissipative quantum phase space dynamics: Application to barrier scattering.

The Caldeira-Leggett master equation, expressed in Lindblad form, has been used in the numerical study of the effect of a thermal environment on the dynamics of the scattering of a wave packet from a repulsive Eckart barrier. The dynamics are studied in terms of phase space trajectories associated with the distribution function, W(q,p,t). The equations of motion for the trajectories include quantum terms that introduce nonlocality into the motion, which imply that an ensemble of correlated trajectories needs to be propagated. However, use of the derivative propagation method (DPM) allows each trajectory to be propagated individually. This is achieved by deriving equations of motion for the partial derivatives of W(q,p,t) that appear in the master equation. The effects of dissipation on the trajectories are studied and results are shown for the transmission probability. On short time scales, decoherence is demonstrated by a swelling of trajectories into momentum space. For a nondissipative system, a comparison is made of the DPM with the "exact" transmission probability calculated from a fixed grid calculation.

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PubMed2003

Pediatric oligodendrogliomas: a study of molecular alterations on 1p and 19q using fluorescence in situ hybridization.

Oligodendrogliomas (OGs) are rare in children and have not been well characterized from a molecular viewpoint. In adults, losses on chromosomes 1p and/or 19q are common in "oligodendroglial" neoplasms and are highly associated with chemosensitivity and greater length of survival, especially in the anaplastic category. We have analyzed the 1p/19q status of pediatric OGs and compared it with similar alterations in adult OGs. Paraffin sections from 26 pediatric OGs (21 WHO Grade II OGs: 2 anaplastic oligodendrogliomas [AOGs]: and 3 mixed oligo-astrocytomas [MOA]) were retrieved. Fluorescence in situ hybridization (FISH) was performed using probes spanning the 1p32 and 19q13 regions. In tumors from children 0 to 9 years of age (n = 15), none had any deletions on 1p or 19q, but 2 had polysomies for 1p and/or 19q. All are alive and 4 have had recurrences. In tumors from children > 9 years, losses were identified on chromosomes 1p (5/11; 45%) and/or 19q (3/11; 27%), but to a much lesser extent than that observed in adult OGs. Tumors from 6 older patients also had polysomies for 1p and/or 19q. Although the majority of the older children are alive, 4 had recurrences. Curiously, 2 of the older children with AOGs had combined losses and polysomies on 1p and 19q, but responded poorly to treatment and died within a year. We conclude that alterations on 1p or 19q are infrequent in pediatric compared to adult OGs and are virtually absent in OGs presenting in the first decade of life. Compared to adults therefore, different genetic pathways are likely involved in the pathogenesis of most pediatric OGs. Genomic screening on a larger series is clearly indicated to delineate the unique molecular characteristics of these rare pediatric tumors.

Adolescent↗

PubMed2001

Quantum trajectory analysis of multimode subsystem-bath dynamics.

The dynamics of a swarm of quantum trajectories is investigated for systems involving the interaction of an active mode (the subsystem) with an M-mode harmonic reservoir (the bath). Equations of motion for the position, velocity, and action function for elements of the probability fluid are integrated in the Lagrangian (moving with the fluid) picture of quantum hydrodynamics. These fluid elements are coupled through the Bohm quantum potential and as a result evolve as a correlated ensemble. Wave function synthesis along the trajectories permits an exact description of the quantum dynamics for the evolving probability fluid. The approach is fully quantum mechanical and does not involve classical or semiclassical approximations. Computational results are presented for three systems involving the interaction on an active mode with M=1, 10, and 15 bath modes. These results include configuration space trajectory evolution, flux analysis of the evolving ensemble, wave function synthesis along trajectories, and energy partitioning along specific trajectories. These results demonstrate the feasibility of using a small number of quantum trajectories to obtain accurate quantum results on some types of open quantum systems that are not amenable to standard quantum approaches involving basis set expansions or Eulerian space-fixed grids.

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