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PubMed2002

Reversible maps in two-degrees of freedom Hamiltonian systems.

It has been shown that a sub-class of two-degrees of freedom Hamiltonian systems possesses a reversing symmetry discovered by Birkhoff in the restricted problem of three bodies. This mixed space-time reversing symmetry, which is different from the classical time reversal symmetry, can be shared by time-reversible as well as time-irreversible systems. Examples of time-irreversible systems which possess this reversing symmetry are the restricted problem of three bodies as shown by Birkhoff in 1915, and a special case of the motion of a rigid body with a fixed point discussed in this paper. If a Hamiltonian system possesses this Birkhoff reversing symmetry, then there exists a surface of section for which the corresponding Poincare map is Birkhoff-reversible. The Birkhoff-reversibility of this map may be used to study its global dynamics such as the locations and the distribution of the stable and unstable periodic points, the distribution of stable and chaotic regions, and the identification of the scattering regions. (c) 2002 American Institute of Physics.

Journal Article↗
PubMed1991

Heat transfer between two degrees of freedom.

A particularly simple chaotic nonequilibrium open system with two Cartesian degrees of freedom, characterized by two distinct temperatures T(x) and T(y), is introduced. The two temperatures are maintained by Nose-Hoover canonical-ensemble thermostats. Both the equilibrium (no net heat transfer) and nonequilibrium (dissipative) Lyapunov spectra are characterized for this simple system.

Journal Article↗
PubMed1999

Diffusion and scaling in escapes from two-degrees-of-freedom Hamiltonian systems.

This paper summarizes an investigation of the statistical properties of orbits escaping from three different two-degrees-of-freedom Hamiltonian systems which exhibit global stochasticity. Each time-independent H=H(0)+ varepsilon H('), with H(0) an integrable Hamiltonian and varepsilon H(') a nonintegrable correction, not necessarily small. Despite possessing very different symmetries, ensembles of orbits in all three potentials exhibit similar behavior. For varepsilon below a critical varepsilon (0), escapes are impossible energetically. For somewhat higher values, escape is allowed energetically but still many orbits never escape. The escape probability P computed for an arbitrary orbit ensemble decays toward zero exponentially. At or near a critical value varepsilon (1)> varepsilon (0) there is a rather abrupt qualitative change in behavior. Above varepsilon (1), P typically exhibits (1) an initial rapid evolution toward a nonzero P(0)( varepsilon ), the value of which is independent of the detailed choice of initial conditions, followed by (2) a much slower subsequent decay toward zero which, in at least one case, is well fit by a power law P(t) proportional, variant t(-&mgr;), with &mgr; approximately 0.35-0.40. In all three cases, P(0) and the time T required to converge toward P(0) scale as powers of varepsilon - varepsilon (1), i.e., P(0) proportional, variant ( varepsilon - varepsilon (1))(alpha) and T proportional, variant ( varepsilon - varepsilon (1))(beta), and T also scales in the linear size r of the region sampled for initial conditions, i.e., T proportional, variant r(-delta). To within statistical uncertainties, the best fit values of the critical exponents alpha, beta, and delta appear to be the same for all three potentials, namely alpha approximately 0.5, beta approximately 0.4, and delta approximately 0.1, and satisfy alpha-beta-delta approximately 0. The transitional behavior observed near varepsilon (1) is attributed to the breakdown of some especially significant KAM tori or cantori. The power law behavior at late times is interpreted as reflecting intrinsic diffusion of chaotic orbits through cantori surrounding islands of regular orbits. (c) 1999 American Institute of Physics.

Journal Article↗
PubMed2004

Altered inertial response of generic degrees of freedom.

A method to alter the inertial response of generic degrees of freedom is presented. A Hamiltonian acts on the inertial response of a set of independent configurational observables by the introduction of a kinetic bias. The method finds its natural application in reducing the spreading of arbitrary modes in a complex system. The resulting compressed spectrum allows a more efficient sampling of configurational space.

Journal Article↗
PubMed2005

Simulation of electronic and geometric degrees of freedom using a kink-based path integral formulation: application to molecular systems.

A kink-based path integral method, previously applied to atomic systems, is modified and used to study molecular systems. The method allows the simultaneous evolution of atomic and electronic degrees of freedom. The results for CH4, NH3, and H2O demonstrate this method to be accurate for both geometries and energies. A comparison with density functional theory (DFT) and second-order Moller-Plesset (MP2) level calculations show the path integral approach to produce energies in close agreement with MP2 energies and geometries in close agreement with both DFT and MP2 results.

Journal Article↗
PubMed2005

Laser cooling of vibrational degrees of freedom of a molecular system.

We consider the cooling of vibrational degrees of freedom in a photoinduced excited electronic state of a model molecular system. For the various parameters of the potential surfaces of the ground and excited electronic states and depending on the excitation frequency of a single-mode laser light, the average energy or average vibrational temperature of the excited state passes through a minimum. The amount of cooling is quantified in terms of the overlap integral between the ground and excited electronic states of the molecule. We have given an approach to calculate the Franck-Condon factor for a multimode displaced-distorted-rotated oscillator surface of the molecular system. This is subsequently used to study the effect of displacement, distortion, and Duschinsky rotation on the vibrational cooling in the excited state. The absorption spectra and also the average energy or the effective temperature of the excited electronic state are studied for the above model molecular system. Considering the non-Condon effect for the symmetry-forbidden transitions, we have discussed the absorption spectra and average temperature in the excited-state vibrational manifold.

Journal Article↗
PubMed2006

Multistate multimode vibronic dynamics: entanglement of electronic and vibrational degrees of freedom in the benzene radical cation.

An earlier theoretical treatment of multimode and multistate vibronic coupling in the benzene radical cation [Koppel et al., J. Chem. Phys. 117, 2657 (2002)] is extended to investigate also the behavior of the nuclear degrees of freedom and to include additional electronic states. The five lowest doublet electronic states are considered which have been shown earlier to be all interconnected through a series of conical intersections of their potential-energy surfaces. In the most extensive calculations, they are all included simultaneously in the quantum dynamical calculations performed, which represent a system of unprecedented complexity treated in this way. The results are compared with various reduced-dimensionality treatments (i.e., employing reduced vibrational and electronic function spaces). The different temporal behavior of the various electronic populations is emphasized and traced to the different locations of the various seams of conical intersections: due to the coherent oscillations of the time-dependent wave packet this leads to an oscillatory behavior in some cases and to monotonous behavior in others. A seemingly irreversible behavior of the system dynamics in this strictly microscopic treatment is confirmed. The importance of this benchmark system to highlight complex, entangled multimode, and multistate vibronic dynamics is pointed out.

Journal Article↗
PubMed2006

Herman-Kluk semiclassical dynamics in action-angle representation: new approaches to mapping quantum degrees of freedom.

A general approach to mapping a discrete quantum mechanical problem by a continuous Hamiltonian is presented. The method is based on the representation of the quantum number by a continuous action variable that extends from -infinity to infinity. The projection of this Hilbert space onto the set of integer quantum numbers reduces the Hamiltonian to a discrete matrix of interest. The theory allows the application of the semiclassical methods to discrete quantum mechanical problems and, in particular, to problems where quantum Hamiltonians are coupled to continuous degrees of freedom. The Herman Kluk semiclassical propagation is used to calculate the nonadiabatic dynamics for a model avoided crossing system. The results demonstrate several advantages of the new theory compared to the existing mapping approaches.

Journal Article↗
PubMed2006

A full dimensional, nine-degree-of-freedom, time-dependent quantum dynamics study for the H2+C2H reaction.

A full dimensional, nine-degree-of-freedom (9DOF), time-dependent quantum dynamics wave packet approach is presented for the study of the H2+C2H-->H+C2H2 reaction system. This is the first full dimensional quantum dynamics study for a diatom-triatom reaction system. The effects of the initial vibrational and rotational excitations of the reactants on the reactivity of this reaction are investigated. This study shows that vibrational excitations of H2 enhance the reactivity; whereas, the vibrational excitations of C2H only have a small effect on the reaction probability. In addition, the bending excitations of C2H, compared to the ground state reaction probability, hinder the reactivity. Comparison of the ground state reaction probabilities of the 9DOF and 8DOF shows the reaction probability from the full dimensional calculation is larger, with more prominent resonance features.

Journal Article↗
PubMed2000

Measurement of the dimensions and abutment rotational freedom of gold-machined 3i UCLA-type abutments in the as-received condition, after casting with a noble metal alloy and porcelain firing.

STATEMENT OF PROBLEM: Laboratory processing of implant-supported prostheses may alter the surface of the abutment in contact with the implant head and thus the interface fit. PURPOSE: This study assessed changes at the implant interface of gold-machined UCLA abutments after casting and porcelain baking in the case of single-tooth restorations. MATERIAL AND METHODS: The depth (d) and width (w) of the hexagonal portion of the abutment, the apical diameter (D) of the abutment, and the abutment rotational freedom (R) were assessed for 30 gold-machined UCLA abutments before casting procedures (time 0), after casting with a noble metal alloy (time 1), and after the addition of porcelain (time 2) to detect any eventual fitting change in the abutments on the top of the implant hexagon. RESULTS: No significant differences relative to all study parameters (d, w, D, and R) were observed between times 0, 1, and 2 (P=.576). CONCLUSION: The results of this investigation suggest that, if all laboratory steps are observed carefully, changes at the implant interface of gold-machined UCLA abutments do not occur.

Analysis of Variance↗
PubMed1998

Structure of cysteine- and glycine-rich protein CRP2. Backbone dynamics reveal motional freedom and independent spatial orientation of the lim domains.

Members of the cysteine- and glycine-rich protein family (CRP1, CRP2, and CRP3) contain two zinc-binding LIM domains, LIM1 (amino-terminal) and LIM2 (carboxyl-terminal), and are implicated in diverse cellular processes linked to differentiation, growth control, and pathogenesis. Here we report the solution structure of full-length recombinant quail CRP2 as determined by multi-dimensional triple-resonance NMR spectroscopy. The structural analysis revealed that the global fold of the two LIM domains in the context of the full-length protein is identical to the recently determined solution structures of the isolated individual LIM domains of quail CRP2. There is no preference in relative spatial orientation of the two domains. This supports the view that the two LIM domains are independent structural and presumably functional modules of CRP proteins. This is also reflected by the dynamic properties of CRP2 probed by 15N relaxation values (T1, T2, and nuclear Overhauser effect). A model-free analysis revealed local variations in mobility along the backbone of the two LIM domains in the native protein, similar to those observed for the isolated domains. Interestingly, fast and slow motions observed in the 58-amino acid linker region between the two LIM domains endow extensive motional freedom to CRP2. The dynamic analysis indicates independent backbone mobility of the two LIM domains and rules out correlated LIM domain motion in full-length CRP2. The finding that the LIM domains in a protein encompassing multiple LIM motifs are structurally and dynamically independent from each other supports the notion that these proteins may function as adaptor molecules arranging two or more protein constituents into a macromolecular complex.

Amino Acid Sequence↗
PubMed2000

Advantages of rhythmic movements at resonance: minimal active degrees of freedom, minimal noise, and maximal predictability.

Using time delay embedding, the authors applied phase space reconstruction to the time series of rhythmic movements of a hand-held pendulum. Subjects (N = 6) produced the manual oscillations about the wrist at the pendulum's resonant frequency and at a higher and a lower frequency. The number of active degrees of freedom required to capture the dynamics of the rhythmic behavior was 3 for the resonant frequency and 4 for each of the nonresonant frequencies. The residual high-dimensional noise was similarly lowest for the resonant frequency. Whereas 33% and 20%, respectively, of the vectors in the phase spaces of the dynamics higher and lower than resonance were unpredictable, only 12% were unpredictable at resonance. Finally, the predictability of the evolving dynamics extended farther into the future for oscillations at the resonant frequency. At resonance, the prediction horizon was 5 times farther than the prediction horizon for the higher than resonance behavior and 2.5 times farther than that for the lower than resonance behavior. The results suggest that, in pendular oscillations of a limb or limb segment, attunement of the central nervous system to the resonant frequency minimizes the variables to be controlled and maximizes the predictability of the rhythmic movement's chaotic dynamics.

Forecasting↗
PubMed1999

To Switch or Not to Switch: Recruitment of Degrees of Freedom Stabilizes Biological Coordination.

Recruitment and suppression processes were studied in the swinging-pendulum paradigm (cf. P. N. Kugler & M. T. Turvey, 1987). The authors pursued the hypothesis that active recruitment of previously unmeasured degrees of freedom serves to stabilize an antiphase bimanual coordination pattern and thereby obviates the need for pattern switching from an antiphase to an in-phase coordination pattern, a key prediction of the H. Haken, J. A. S. Kelso, and H. Bunz (1985) model. In Experiment 1, 7 subjects swung single hand-held pendulums in time with an auditory metronome whose frequency increased. Pendulum motion changed from planar (2D) to elliptical (3D), and forearm motion (produced by elbow flexion-extension) was recruited with increasing movement rate for cycling frequencies typically above the pendulum's eigenfrequency. In Experiment 2, 7 subjects swung paired pendulums in either an in-phase or an antiphase coordinative mode as movement rate was increased. With the systematic increase in movement rate, the authors attempted to induce transitions from the antiphase to the in-phase coordinative pattern, with loss of stability the key mechanism of pattern change. Transitions from the antiphase to the in-phase coordinative mode were not observed. Pattern stability, as defined by the variability of the phase relation between the pendulums, was affected only a little by increasing movement rate. As in the single-pendulum case, pendulum motion changed from planar to elliptical, and forearm motion was recruited with increasing cycling frequency. Those results reveal a richer dynamics than previously observed in the pendulum paradigm and support the hypothesis that recruitment processes stabilize coordination in biomechanically redundant systems, thereby reducing the need for pattern switching.

Journal Article↗
PubMed1989

Distances as degrees of freedom.

Tertiary contact distance information of varying resolution for large biological molecules abounds in the literature. The results provided herein develop a framework by which information of this type can be used to reduce the allowable configuration space of a macromolecule. The approach combines graph theory and distance geometry. Large molecules are represented as simple, undirected graphs, with atoms, or groups, as vertices, and distances between them as edges. It is shown that determination of the exact structure of a molecule in three dimensions only requires the specification of all the distances in a single tetrahedron, and four distances to every other atom. This is 4N-10 distances which is a subset of the total N(N-1)/2 unique distances in a molecule consisting of N atoms. This requirement for only 4N-10 distances has serious implications for distance geometry implementations in which all N(N-1)/2 distances are specified by bounded random numbers. Such distance matrices represent overspecified systems which when solved lead to non-obvious distribution of any error caused by inherent contradictions in the input data. It is also shown that numerous valid subsets of 4N-10 distances can be constructed. It is thus possible to tailor a subset of distances using all known distances as degrees of freedom, and thereby reduce the configuration space of the molecule. Simple algebraic relationships are derived that relate sets of distances, and complicated rotations are avoided. These relationships are used to construct minimum, complete sets of distances necessary to specify the exact structure of the entire molecule in three dimensions from incomplete distance information, and to identify sets of inconsistent distances. The method is illustrated for the flexible structural types present in large ribosomal RNAs: 1.) A five-membered ring; 2.) a chemically bonded chain with its ends in contact (i.e., a hairpin loop); 3.) the spatial orientation of two separate molecules, and; 4.) an RNA helix that can have variation in individual base pairs, giving rise to global deviation from standardized helical forms.

Base Composition↗
PubMed2001

Robotics in endoscopic surgery: can mechanical manipulators provide a more simple solution for the problem of limited degrees of freedom?

Robotic manipulators for endoscopic surgery have been developed on an experimental basis from the early 1990s and are now in clinical use. The main motivation to apply robotics technology to endoscopic surgery is to re-establish six degrees of freedom (DoF) of motion at the tip of the instrument. The cost–benefit ratio of these devices is still unclear. Although the products offered today are based on excellent technology and show a high functionality, most hospitals still hesitate to invest in robotic manipulators for fiscal reasons. For a significant number of procedures, especially in non-microsurgical disciplines, the functionality offered by robotic manipulators is not required, although the procedures would profit from instrumentation with 6 DoF. Mechanical manipulators with 6 DoF, but without computerised control, may be the right solution for these procedures. We have developed a workplace solution for endoscopic surgery that involves mechanical instrument-guiding systems and manipulators that offer 6 DoF, but use a significantly simplified technology at low cost. Further studies will need to show whether these mechanical manipulators answer the needs of the surgeon and offer an affordable alternative to robotic manipulators in surgical areas where microsurgical manipulations are not dominant.

Journal Article↗
PubMed2004

Mechanical manipulator for intuitive control of endoscopic instruments with seven degrees of freedom.

Performing complex tasks such as vascular anastomosis in minimally invasive surgery (MIS) is demanding due to a disturbed hand-eye co-ordination, the application of non-ergonomic instruments with limited number of degrees of freedom (DOFs) and a lack of three-dimensional perception. Robotic tele-manipulatory systems enhance surgical dexterity by providing up to seven DOFs. They allow the surgeon to operate in an ergonomically favourable position with more intuitive manipulation of the instruments. Robotic systems, however, are very bulky, expensive and do not provide any force feedback from the tissue. The aim of our study is to develop a simple mechanical manipulator for MIS. The Minimally Invasive Manipulator (MIM) is a purely mechanical device. When manipulating the handle of the MIM, the surgeon's wrist and grasping movements, which are essential for suturing, are directly transmitted to the deflectable instrument tip in seven DOFs. It gives the surgeon direct control of the instrument tip. First phantom experience indicates that the system functions properly. The MIM provides force feedback to improve safety. A set of MIMs seems to be an economical and compact alternative to robotic systems and will offer more surgeons the capability to perform complex MIS and to shorten their learning curve.

Journal Article↗
PubMed2006

Efficacy of stereoscopic visualization and six degrees of freedom interaction in preoperative planning of total hip replacement.

The aim of this study was to assess the accuracy of a six-degrees-of-freedom application for pre-operative planning of total hip replacement in a virtual reality (VR) environment. A test was performed estimating the system inherent accuracy. The users can move objects in the VR environment with an intrinsic accuracy almost four orders of magnitude greater than the object dimension. A second unambiguous and relevant task was defined to assess the accuracy achievable with the interface in a specific planning task. The results were compared with those obtained with 2D interfaces for both the stem and the cup component. The RMSE was assumed as an indicator of the achievable accuracy. The accuracy of the immersive interface was comparable with that achievable with a standard mouse - monitor interface. The users were consistent using the VR interface, confirming the high usability of the new interface and the steep learning curve of users unfamiliar with the new environment. This study has demonstrated that the application of VR environment for pre-operative planning of total hip replacement may help to shorten the duration of the positioning and to yield consistent results even with first-time users.

Arthroplasty, Replacement, Hip↗
PubMed2005

Gastroenteritis in US Marines during Operation Iraqi Freedom.

BACKGROUND: Approximately 83,000 US Marines participated in the opening phase of Operation Iraqi Freedom in Spring 2003. A Navy Preventive Medicine laboratory was set up in Ad Diwaniyah, Iraq, to provide clinical diagnostic support for Marine medical units during a period of repositioning in south-central Iraq. METHODS: Specimen collection boxes were sent to >30 primary care medical stations handling 500-900 personnel each. The laboratory had capability to detect many different disease agents, especially those causing febrile illness. Diarrheal stool diagnostic evaluation included plating and biochemical identification, antigen serologic testing, fluorescent antibody antigen detection, disk diffusion antimicrobial susceptibility testing, enzyme immunoassay, and reverse-transcriptase polymerase chain reaction for norovirus (NV). Confirmation and sequencing work for NV was done at Cincinnati Children's Hospital Medical Center (Ohio). RESULTS: By far the most common reason for infectious disease sick call visits was gastrointestinal illness; no other symptoms had equivalent impact. An enteropathogen was detected in 57 (44%) of 129 stool samples, with NV detected in 30 stool samples (23%) obtained from 14 different battalion or similar-sized units; next in frequency were Shigella flexneri and Shigella sonnei, which were isolated from 26 stool samples (20%) obtained from 15 units. Sequencing the NV RNA polymerase gene demonstrated that NV strains represented 7 genetic clusters, including 2 strains from genogroup I and 5 from genogroup II. Ciprofloxacin was effective in vitro against most bacterial agents, but neither doxycyline (which was taken daily as the antimalarial prophylaxis dose) nor trimethoprim-sulfamethoxazole were effective. CONCLUSIONS: Multiple strains of Shigella species and NV predominated, probably because they do not require a large inoculum to cause infection. Otherwise, personnel remained free of infectious illness during this phase of the conflict, because other infectious agents were rare or absent.

Anti-Bacterial Agents↗