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PubMed2006

Comparison of longitudinal phenotypes based on number and timing of assessments: a systematic comparison of trajectory approaches II.

The popularity of trajectory-based research to characterize developmental courses of alcohol (and other drug) involvement is growing rapidly. Given the increasing use of these methods, there is a need to identify methodological factors that affect course shape and prevalence. Using growth mixture models, the authors characterized the developmental course of 2 indices of alcohol involvement, alcohol use disorder and frequency of heavy drinking, with a prospective sample of 489 young adults (Year 1 age = 18.52; 55% female; 51% with family history of alcoholism) assessed 6 times over 11 years. Then, the authors explored the extent to which trajectory models that eliminated an assessment (at the beginning, middle, or end of the study interval) were similar to the full 6-wave model. Although classifications showed relatively high concordance, trajectory shape and predicted prevalences varied. Misclassification was associated with methodological factors such as probability of class membership and missing data. Findings suggest that researchers thoughtfully consider the nature of the phenomena being studied and the developmental period of interest when designing prospective studies.

Adolescent↗
PubMed2003

Distributional assumptions of growth mixture models: implications for overextraction of latent trajectory classes.

Growth mixture models are often used to determine if subgroups exist within the population that follow qualitatively distinct developmental trajectories. However, statistical theory developed for finite normal mixture models suggests that latent trajectory classes can be estimated even in the absence of population heterogeneity if the distribution of the repeated measures is nonnormal. By drawing on this theory, this article demonstrates that multiple trajectory classes can be estimated and appear optimal for nonnormal data even when only 1 group exists in the population. Further, the within-class parameter estimates obtained from these models are largely uninterpretable. Significant predictive relationships may be obscured or spurious relationships identified. The implications of these results for applied research are highlighted, and future directions for quantitative developments are suggested.

Group Processes↗
PubMed2000

Re-thinking stroke rehabilitation: the Corbin and Strauss chronic illness trajectory framework.

Re-thinking stroke rehabilitation: the Corbin and Strauss chronic illness trajectory framework The dramatic effects of a stroke can have far-reaching implications for patients and carers. Effective recovery involves a considerable array of coping strategies that facilitate and promote engagement in the social world. Their development is a long-term process that requires considerable effort, motivation and enterprise on the part of patients and their families. Traditional approaches to the provision of stroke rehabilitation services, however, appear to be underpinned by frameworks that are short-term in outlook. As a consequence, nursing interventions often focus on the progression of the patient through the care system, rather than on facilitating future recovery. Much of the work of stroke recovery is consequently done by patients and their families at home, with little provision of ongoing professional help and advice. This paper explores the application of the Corbin and Strauss Chronic Illness Trajectory Framework for stroke. In particular, the major concepts of the framework are applied to a vignette derived from a longitudinal study of patients' experiences of recovery. The trajectory framework is shown to be a useful structure that has the potential to enhance the appropriateness of nursing interventions for stroke patients. However, the validity of the framework can only be established through its application and evaluation in clinical practice. The purpose of this paper is to contribute to a debate that encourages consideration of the framework's utility for nurses to enhance the stroke rehabilitation experience.

Activities of Daily Living↗
PubMed1999

The shape of field emitters and the ion trajectories in three-dimensional atom probes

The lateral resolution of three-dimensional atom probes is mainly controlled by the aberrations of the ion trajectories near the specimen surface. For the first time, a simulation program has been developed to reconstruct the ion trajectories near a sharp hemispherical electrode defined at the atomic scale. Surface atoms submitted to the highest field were removed one by one. The consecutive gradual change of the surface topology was taken into account in the calculation of ion trajectories. As the tip was 'field evaporated', the initial spherical shape of the emitter was observed to transform gradually into a polygonal shape. When the tip reached its equilibrium shape, the field distribution at the tip surface was found to be much more uniform compared to the initial distribution. The calculated distribution of ion impacts on the detector exhibits the presence of depleted zones both at the centre of low index poles and along <001> zone axes. These predictions are in excellent agreement with experiments.

Journal Article↗
PubMed2001

Trabecular trajectory in the articular processes of the human fourth cervical vertebra.

The articular processes (AP) of the neural arch have been implicated in weight transmission through the cervical spine. To analyse the mechanism of weight transmission in the AP, we studied the direction of forces within it, in particular, the pattern of trabecular trajectories. Twenty-two AP from C4 vertebrae were studied in anatomical sections, and corresponding photoelastic models from selected sections were constructed and analysed. Anatomical and photoelastic findings show the subarticular spongiosa of the superior articular process (SAP) to be orthogonally arranged with vertical and oblique trabeculae in the direction of compressive forces and additional trabeculae always oriented perpendicular to the former. Vertical and oblique trabeculae are divided into rostral, middle and posterior groups. Rostral and middle trabeculae end in the anterior wall of the SAP and the transitional zone with the pedicle. Posterior trabeculae end in the subarticular spongiosa of the inferior articular process (IAP). The findings relating to trabecular trajectories in the SAP differ from previous descriptions and instead suggest that a part of the weight forces distributed within the AP transmit to the subchondral zone of the IAP. Knowledge of the trajectorial architecture of the AP may contribute to refining finite element analytical models for investigating its weight-bearing function.

Adult↗
PubMedDate not supplied

Symptom trajectories in psychotic episodes.

Whereas the cross-sectional structure of schizophrenic symptoms has been studied extensively, little is known about the development of symptoms during acute episodes. In this study, symptom trajectories of 46 schizophrenia spectrum patients were examined based on daily observation during an average treatment period of 104 days. A novel time series approach was used to identify initial phases of response and other descriptive features of the trajectories. The results yielded five dynamical factors: (1) overall level of positive symptoms, (2) duration of nonspecific response, (3) slope of response in all symptom domains, (4) enduring negative symptoms, and (5) duration of response regarding psychoticity. Compared to patients with an acute schizophrenia-like psychotic disorder, schizophrenia and schizoaffective disorder patients ranked higher in factor 4 (enduring negative symptoms). They tended towards a lower level of positive symptoms and showed a less prominent response to treatment. The examination of a subsample of 19 patients with relapse indicated a prolonged duration of initial treatment response regarding psychoticity. The results support the validity of this approach for the description of symptom trajectories.

Acute Disease↗
PubMed2004

Army ants algorithm for rare event sampling of delocalized nonadiabatic transitions by trajectory surface hopping and the estimation of sampling errors by the bootstrap method.

The most widely used algorithm for Monte Carlo sampling of electronic transitions in trajectory surface hopping (TSH) calculations is the so-called anteater algorithm, which is inefficient for sampling low-probability nonadiabatic events. We present a new sampling scheme (called the army ants algorithm) for carrying out TSH calculations that is applicable to systems with any strength of coupling. The army ants algorithm is a form of rare event sampling whose efficiency is controlled by an input parameter. By choosing a suitable value of the input parameter the army ants algorithm can be reduced to the anteater algorithm (which is efficient for strongly coupled cases), and by optimizing the parameter the army ants algorithm may be efficiently applied to systems with low-probability events. To demonstrate the efficiency of the army ants algorithm, we performed atom-diatom scattering calculations on a model system involving weakly coupled electronic states. Fully converged quantum mechanical calculations were performed, and the probabilities for nonadiabatic reaction and nonreactive deexcitation (quenching) were found to be on the order of 10(-8). For such low-probability events the anteater sampling scheme requires a large number of trajectories ( approximately 10(10)) to obtain good statistics and converged semiclassical results. In contrast by using the new army ants algorithm converged results were obtained by running 10(5) trajectories. Furthermore, the results were found to be in excellent agreement with the quantum mechanical results. Sampling errors were estimated using the bootstrap method, which is validated for use with the army ants algorithm.

Journal Article↗
PubMed2004

Non-Born-Oppenheimer trajectories with self-consistent decay of mixing.

A semiclassical trajectory method, called the self-consistent decay of mixing (SCDM) method, is presented for the treatment of electronically nonadiabatic dynamics. The SCDM method is a modification of the semiclassical Ehrenfest (SE) method (also called the semiclassical time-dependent self-consistent-field method) that solves the problem of unphysical mixed final states by including decay-of-mixing terms in the equations for the evolution of the electronic state populations. These terms generate a force, called the decoherent force (or dephasing force), that drives the electronic component of each trajectory toward a pure state. Results for several mixed quantum-classical methods, in particular the SCDM, SE, and natural-decay-of-mixing methods and several trajectory surface hopping methods, are compared to the results of accurate quantum mechanical calculations for 12 cases involving five different fully dimensional triatomic model systems. The SCDM method is found to be the most accurate of the methods tested. The method should be useful for the simulation of photochemical reactions.

Journal Article↗
PubMed1995

Unstable evolution of pointwise trajectory solutions to chaotic maps.

Simple chaotic maps are used to illustrate the inherent instability of trajectory solutions to the Frobenius-Perron equation. This is demonstrated by the difference in the behavior of delta-function solutions and of extended densities. Extended densities evolve asymptotically and irreversibly into invariant measures on stationary attractors. Pointwise trajectories chaotically roam over these attractors forever. Periodic Gaussian distributions on the unit interval are used to provide insight. Viewing evolving densities as ensembles of unstable pointwise trajectories gives densities a stochastic interpretation. (c) 1995 American Institute of Physics.

Journal Article↗
PubMed2004

Rovibrational distributions of HF in the photodissociation of vinyl fluoride at 193 nm: a direct MP2 quasiclassical trajectory study.

Quasiclassical trajectory calculations were performed to calculate rovibrational distributions of the nascent HF fragment in the photodissociation of vinyl fluoride at 193 nm. The trajectories were initiated at the transition states of the four-center (4C) and three-center (3C) HF elimination channels, using a microcanonical, quasiclassical normal-mode sampling. In general, the calculated distributions are in reasonably good agreement with experiment. In particular, the trajectory distributions show bimodal character, although not as pronounced as that observed experimentally. The calculations predict that the 3C and 4C distributions are rather similar to each other, which suggests that the low-J and high-J components of the rotational distributions cannot be specifically assigned to each of these channels.

Journal Article↗
PubMed2005

Quantum trajectories in elastic atom-surface scattering: threshold and selective adsorption resonances.

The elastic resonant scattering of He atoms off the Cu(117) surface is fully described with the formalism of quantum trajectories provided by Bohmian mechanics. Within this theory of quantum motion, the concept of trapping is widely studied and discussed. Classically, atoms undergo impulsive collisions with the surface, and then the trapped motion takes place covering at least two consecutive unit cells. However, from a Bohmian viewpoint, atom trajectories can smoothly adjust to the equipotential energy surface profile in a sort of sliding motion; thus the trapping process could eventually occur within one single unit cell. In particular, both threshold and selective adsorption resonances are explained by means of this quantum trapping considering different space and time scales. Furthermore, a mapping between each region of the (initial) incoming plane wave and the different parts of the diffraction and resonance patterns can be easily established, an important issue only provided by a quantum trajectory formalism.

Journal Article↗
PubMed2005

Determination of photophysical parameters from photon arrival time trajectories in single molecule fluorescence spectroscopy.

Triplet blinking is a phenomenon observed commonly in single molecule fluorescence spectroscopy. At high to moderate excitation intensities one can distinguish bright (on) and dark (off) periods in the fluorescence intensity trajectory caused by sojourns into the nonemissive triplet state. In this work, we focus on triplet blinking of an immobilized molecule in the low excitation regime, where a threshold between on and off intensity levels cannot be set, and, therefore, a standard on/off analysis of fluorescence intensity trajectories is not possible. In the low excitation regime triplet blinking parameters can be recovered from photon arrival time trajectories, i.e., records of individual photon arrival time. We use computer-generated data to compare the recovery of the triplet blinking parameters from the intensity correlation function (ICF) and the histogram of interarrival time. We have found that the ICF offers a better statistics for the recovery of the triplet blinking parameters.

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.

Journal Article↗
PubMed2005

Quasiperiodic trajectories in the unimolecular dissociation of ethyl radicals by time-frequency analysis.

Direct classical trajectory calculations for ethyl radical, C2H5, at the HCTH147@6-31 +G**/6-31G** level of theory support the experimental observation that the dissociation of highly excited ethyl radicals to ethylene and and a hydrogen atom can occur much more slowly than predicted by statistical rate theories. Only 78% of the trajectories of ethyl radicals prepared in a microcanonical ensemble with 120-kcal/mol excitation energy above the zero-point energy and zero total angular momentum dissociate to form C2H4 + H. The remaining hot ground-state ethyl radicals have a lifetime of >>2 ps, during which a time-frequency analysis finds them trapped for extended periods of time in long-lived quasiperiodic trajectories.

Journal Article↗
PubMed2005

Chemical reaction dynamics of Rydberg atoms with neutral molecules: a comparison of molecular-beam and classical trajectory results for the H(n)+D2-->HD+D(n') reaction.

Recent molecular-beam experiments have probed the dynamics of the Rydberg-atom reaction, H(n)+D2-->HD+D(n) at low collision energies. It was discovered that the rotationally resolved product distribution was remarkably similar to a much more limited data set obtained at a single scattering angle for the ion-molecule reaction H++D2-->D++HD. The equivalence of these two problems would be consistent with the Fermi-independent-collider model (electron acting as a spectator) and would provide an important new avenue for the study of ion-molecule reactions. In this work, we employ a classical trajectory calculation on the ion-molecule reaction to facilitate a more extensive comparison between the two systems. The trajectory simulations tend to confirm the equivalence of the ion+molecule dynamics to that for the Rydberg-atom+molecule system. The theory reproduces the close relationship of the two experimental observations made previously. However, some differences between the Rydberg-atom experiments and the trajectory simulations are seen when comparisons are made to a broader data set. In particular, the angular distribution of the differential cross section exhibits more asymmetry in the experiment than in the theory. The potential breakdown of the classical model is discussed. The role of the "spectator" Rydberg electron is addressed and several crucial issues for future theoretical work are brought out.

Journal Article↗
PubMed2006

Use of a single trajectory to study product energy partitioning in unimolecular dissociation: mass effects for halogenated alkanes.

A single trajectory (ST) direct dynamics approach is compared with quasiclassical trajectory (QCT) direct dynamics calculations for determining product energy partitioning in unimolecular dissociation. Three comparisons are made by simulating C(2)H(5)F-->HF + C(2)H(4) product energy partitioning for the MP26-31G(*) and MP26-311 + + G(**) potential energy surfaces (PESs) and using the MP26-31G(*) PES for C(2)H(5)F dissociation as a model to simulate CHCl(2)CCl(3)-->HCl + C(2)Cl(4) dissociation and its product energy partitioning. The trajectories are initiated at the transition state with fixed energy in reaction-coordinate translation E(t) (double dagger). The QCT simulations have zero-point energy (ZPE) in the vibrational modes orthogonal to the reaction coordinate, while there is no ZPE for the STs. A semiquantitative agreement is obtained between the ST and QCT average percent product energy partitionings. The ST approach is used to study mass effects for product energy partitioning in HX(X = F or Cl) elimination from halogenated alkanes by using the MP26-31G(*) PES for C(2)H(5)F dissociation and varying the masses of the C, H, and F atoms. There is, at most, only a small mass effect for partitioning of energy to HX vibration and rotation. In contrast, there are substantial mass effects for partitioning to relative translation and the polyatomic product's vibration and rotation. If the center of mass of the polyatomic product is located away from the C atom from which HX recoils, the polyatomic has substantial rotation energy. Polyatomic products, with heavy atoms such as Cl atoms replacing the H atoms, receive substantial vibration energy that is primarily transferred to the wag-bend motions. For E(t) (double dagger) of 1.0 kcalmol, the ST calculations give average percent partitionings to relative translation, polyatomic vibration, polyatomic rotation, HX vibration, and HX rotation of 74.9%, 6.8%, 1.5%, 14.4%, and 2.4% for C(2)H(5)F dissociation and 39.7%, 38.1%, 0.2%, 16.1%, and 5.9% for a model of CHCl(2)CCl(3) dissociation.

Journal Article↗
PubMed2006

Ab initio and direct quasiclassical-trajectory study of the Cl + CH4-->HCl + CH3 reaction.

We present an electronic structure and dynamics study of the Cl + CH(4)--> HCl + CH(3) reaction. We have characterized the stationary points of the ground-state potential-energy surface using various electronic structure methods and basis sets. Our best calculations, CCSD(T) extrapolated to the complete basis-set limit based on geometries and harmonic frequencies obtained at the CCSD(T)/aug-cc-pvtz level, are in agreement with the experimental reaction energy and indirect measurements of the barrier height. Using ab initio information, we have reparametrized a semiempirical Hamiltonian so that the predictions of the improved Hamiltonian agree with the higher-level calculations in various regions of the potential-energy surface. This improved semiempirical Hamiltonian is then used to propagate quasiclassical trajectories and characterize the reaction dynamics. The good agreement of the calculated HCl rotational and angular distributions with the experiment indicates that reparametrizing semiempirical Hamiltonians is a promising approach to derive accurate potential-energy surfaces for polyatomic reactions. However, excessive energy leakage from the initial vibrational energy of the CH(4) molecule to the reaction coordinate in the trajectory calculations calls into question the suitability of the standard quasiclassical-trajectory method to describe energy partitioning in polyatomic reactions.

Journal Article↗
PubMed2006

Quasiclassical trajectory study of O(1D) + N2O --> NO + NO: classification of reaction paths and vibrational distribution.

Quasiclassical trajectory calculations for the planar reaction of O(1D) + N2O --> NO + NO are performed on a newly constructed ab initio potential energy surface. In spite of the reduced dimension approximation, the agreement between the computational and experimental results is largely satisfactory, especially on the similar amount of excitation of the two kinds of NO products found by Akagi et al. [J. Chem. Phys. 111, 115 (1999)]. Analyzing the initial condition dependence of the trajectories, we find that the trajectories of this reaction can be classified into four reaction paths, which correspond to respective areas in the space of initial condition. In one of the four paths, a long-lived stable complex is formed in the course of reaction, whereas the other three paths have direct mechanism. Contradictory to conventional understanding of the chemical reaction dynamics, the direct paths show more efficient energy exchange between the NO stretching modes than that with a long-lived intermediate. This indicates that the vibrational mode coupling along the short-lived paths is considerably stronger than expected.

Journal Article↗