John B. Delos

Semiclassical calculations of vibrational energy levels for nonseparable systems using the Birkhoff–Gustavson normal form

We present a semiclassical method of calculating vibrational energy levels for a system of nonseparable coupled oscillators. For a Hamiltonian written as a power series in which the leading terms are given by a sum of one‐dimensional harmonic oscillator Hamiltonians, the method involves transforming the original classical Hamiltonian via a succession of canonical transformations into a normal form which is a power series originally defined by Birkhoff and later generalized by Gustavson. Two cases are distinguished. If the harmonic oscillator frequencies in the unperturbed Hamiltonian are incommensurable, then the normal form is a power series whose terms are products of one‐dimensional harmonic oscillator Hamiltonians; if the frequencies in the unperturbed Hamiltonian are commensurable, then additional terms which cannot be written as products of one‐dimensional harmonic oscillator Hamiltonians enter into the normal form. Once the normal form is obtained, semiclassical quantization of action variables is ...

Diabatic and adiabatic representations for atomic collision processes

A consistent general definition of diabatic representations has not previously been given, even though many practical examples of such representations have been constructed for specific problems. Such a definition is provided in this paper. Beginning with a classical trajectory formulation, we describe the form and behavior of velocity‐dependent couplings in slow collisions, including the effects of electron‐translation factors (ETF’s). We compare the couplings arising from atomic representations and atomic ETF’s with those arising from molecular representations and ’’switching function’’ ETF’s. We show that a unique set of switching functions makes the two descriptions identical in their effects. We then show that an acceptable general definition of a diabatic representation is provided by the condition P+A=0, where P is the usual nonadiabatic coupling matrix and A represents corrections to it arising from electron translation factors (ETF’s). Two distinct types of diabatic representation result, dependi...

On the reactions of N2 with O

Unimolecular decomposition of N2O, quenching of O(1D) by N2, and vibrational relaxation of N2 in the presence of O(3P) are all believed to occur by the same curve crossing mechanism. This mechanism is examined making use of a complete theory of curve crossings that we have developed earlier. Good agreement with experiment is found for the unimolecular decomposition rate. The simple curve crossing mechanism does not explain the observed O(1D) quenching rate; this rate must be due to complex formation and/or additional crossings. At high temperatures, the calculated vibrational relaxation time is in good agreement with experiment, but at low temperatures there is a serious, unexplained discrepancy.

Cardiovascular oscillations at the bedside: early diagnosis of neonatal sepsis using heart rate characteristics monitoring

We have applied principles of statistical signal processing and nonlinear dynamics to analyze heart rate time series from premature newborn infants in order to assist in the early diagnosis of sepsis, a common and potentially deadly bacterial infection of the bloodstream. We began with the observation of reduced variability and transient decelerations in heart rate interval time series for hours up to days prior to clinical signs of illness. We find that measurements of standard deviation, sample asymmetry and sample entropy are highly related to imminent clinical illness. We developed multivariable statistical predictive models, and an interface to display the real-time results to clinicians. Using this approach, we have observed numerous cases in which incipient neonatal sepsis was diagnosed and treated without any clinical illness at all. This review focuses on the mathematical and statistical time series approaches used to detect these abnormal heart rate characteristics and present predictive monitoring information to the clinician.

A new algorithm for detecting central apnea in neonates

Apnea of prematurity is an important and common clinical problem, and is often the rate-limiting process in NICU discharge. Accurate detection of episodes of clinically important neonatal apnea using existing chest impedance (CI) monitoring is a clinical imperative. The technique relies on changes in impedance as the lungs fill with air, a high impedance substance. A potential confounder, however, is blood coursing through the heart. Thus, the cardiac signal during apnea might be mistaken for breathing. We report here a new filter to remove the cardiac signal from the CI that employs a novel resampling technique optimally suited to remove the heart rate signal, allowing improved apnea detection. We also develop an apnea detection method that employs the CI after cardiac filtering. The method has been applied to a large database of physiological signals, and we prove that, compared to the presently used monitors, the new method gives substantial improvement in apnea detection.

Mechanism of collisionally induced transitions among fine-structure levels: semiclassical calculations of alignment effects in the Na-He system

To gain insight into the mechanism of Na(3p)2P3/2→2P1/2 fine‐structure transitions induced by collision with He, we monitor the expectation values of the orbital‐ and spin‐angular momentum vectors, l and s, as a function of time along the trajectory, using a semiclassical formalism. In a typical collision, 〈s〉 remains nearly space‐fixed while 〈l〉 precesses about the rotating internuclear axis. Thus, in the interaction region, the projection of 〈l〉 onto the internuclear axis, 〈λ〉, remains nearly constant, and the molecular alignment of the orbital is preserved. We show how equations of motion for the classical analogues of these expectation values agree qualitatively with the quantum equations of motion. A qualitative comparison is also made with the Cs–He system for which the spin–orbit coupling is much stronger. We calculate cross sections for Na(2P3/2)+He→Na(2P1/2)+He as a function of the alignment of the excitation laser polarization with respect to the asymptotic relative velocity vector. For stationa...

Anemia, Apnea of Prematurity, and Blood Transfusions

OBJECTIVE To compare the frequency and severity of apneic events in very low birth weight (VLBW) infants before and after blood transfusions using continuous electronic waveform analysis. STUDY DESIGN We continuously collected waveform, heart rate, and oxygen saturation data from patients in all 45 neonatal intensive care unit beds at the University of Virginia for 120 weeks. Central apneas were detected using continuous computer processing of chest impedance, electrocardiographic, and oximetry signals. Apnea was defined as respiratory pauses of >10, >20, and >30 seconds when accompanied by bradycardia (<100 beats per minute) and hypoxemia (<80% oxyhemoglobin saturation as detected by pulse oximetry). Times of packed red blood cell transfusions were determined from bedside charts. Two cohorts were analyzed. In the transfusion cohort, waveforms were analyzed for 3 days before and after the transfusion for all VLBW infants who received a blood transfusion while also breathing spontaneously. Mean apnea rates for the previous 12 hours were quantified and differences for 12 hours before and after transfusion were compared. In the hematocrit cohort, 1453 hematocrit values from all VLBW infants admitted and breathing spontaneously during the time period were retrieved, and the association of hematocrit and apnea in the next 12 hours was tested using logistic regression. RESULTS Sixty-seven infants had 110 blood transfusions during times when complete monitoring data were available. Transfusion was associated with fewer computer-detected apneic events (P < .01). Probability of future apnea occurring within 12 hours increased with decreasing hematocrit values (P < .001). CONCLUSIONS Blood transfusions are associated with decreased apnea in VLBW infants, and apneas are less frequent at higher hematocrits.

Semiclassical calculation of energy levels for non-separable systems

Abstract A series expansion for a second isolating integral is calculated for a nonseparable system of two coupled oscillators. This integral, together with the hamiltonian, is used to calculate semi classical energy levels. The agreement with the exact quantum levels is sufficient to verity the validity of the method.

Accurate automated apnea analysis in preterm infants.

OBJECTIVE In 2006 the apnea of prematurity (AOP) consensus group identified inaccurate counting of apnea episodes as a major barrier to progress in AOP research. We compare nursing records of AOP to events detected by a clinically validated computer algorithm that detects apnea from standard bedside monitors. STUDY DESIGN Waveform, vital sign, and alarm data were collected continuously from all very low-birth-weight infants admitted over a 25-month period, analyzed for central apnea, bradycardia, and desaturation (ABD) events, and compared with nursing documentation collected from charts. Our algorithm defined apnea as > 10 seconds if accompanied by bradycardia and desaturation. RESULTS Of the 3,019 nurse-recorded events, only 68% had any algorithm-detected ABD event. Of the 5,275 algorithm-detected prolonged apnea events > 30 seconds, only 26% had nurse-recorded documentation within 1 hour. Monitor alarms sounded in only 74% of events of algorithm-detected prolonged apnea events > 10 seconds. There were 8,190,418 monitor alarms of any description throughout the neonatal intensive care unit during the 747 days analyzed, or one alarm every 2 to 3 minutes per nurse. CONCLUSION An automated computer algorithm for continuous ABD quantitation is a far more reliable tool than the medical record to address the important research questions identified by the 2006 AOP consensus group.

Periodic heart rate decelerations in premature infants.

The pacemaking system of the heart is complex; a healthy heart constantly integrates and responds to extracardiac signals, resulting in highly complex heart rate patterns with a great deal of variability. In the laboratory and in some pathological or age-related states, however, dynamics can show reduced complexity that is more readily described and modeled. Reduced heart rate complexity has both clinical and dynamical significance – it may provide warning of impending illness or clues about the dynamics of the hearts pacemaking system. In this paper, we describe simple and interesting heart rate dynamics that we have observed in premature human infants – reversible transitions to large-amplitude periodic oscillations – and we show that the appearance and disappearance of these periodic oscillations can be described by a simple mathematical model, a Hopf bifurcation.