Harmonic Surface Research Articles

Modeling, analysis, and visualization of left ventricle shape and motion by hierarchical decomposition

This paper presents an approach to the modeling, analysis, and visualization of left ventricle motion and deformation. The authors' modeling of left ventricle shape and motion as a hierarchical representation enables them to develop a promising noninvasive technique for monitoring heart dynamics where both image analysis and image synthesis are involved. The proposed hierarchical motion model of left ventricle is constructed by combining several existing simple models and is able to capture major motion and deformation components of the left ventricle. The hierarchical decomposition characterizes the left ventricle motion and deformation in a coarse-to-fine fashion and leads to computationally efficient estimation algorithms. The authors estimate the global rigid motion of the left ventricle by establishing a time-varying object-centered coordinate system. The global deformations of the left ventricle are obtained by fitting the given data to superquadric modeling primitives. The local deformations are estimated by a tensor-description approach that is based on the locally deformable surface obtained by constructing spherical harmonic local surface from the residues of global shape estimation. The authors also describe in this paper methods of image synthesis and dynamic animation for visualizing the estimated results of the time-varying left ventricle shape, motion, and deformations. These animation results are consistent with the apparent motion pattern of the left ventricle and therefore show the success of the authors' hierarchical decomposition based approach.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A Harmonically Excited Elastic Half-Plane Containing a Rigid Flat Inclusion

The plane strain problem for an elastic half-plane containing a rigid flat inclusion and subjected to a concentrated harmonic surface load is considered. The problem is reduced to a system of singular integral equations, with the differences in interface stresses between the inclusion and the matrix as the unknown functions. With the potential applications to problems in fracture mechanics and the non-destructive testing and evaluation in mind, the main results presented are the modes I and II stress intensity factors and the components of the displacement vector on the surface.

Observation of a harmonic two-phonon vibration in a deformed nucleus

We report on the observation of a rotational band in 232Th built on a 4 + state at 1414 KeV, which shows all characteristics expected for the band head of a pure K π =4 + two-phonon γγ-vibrational band: The excitation energy is about twice that of the γ-band head, all observed decays lead to the γ-band, and the B(E2) values between the two bands have the appropriate strength expected for a harmonic surface vibration.

Wave scattering over uneven depth using the mild-slope equation

This paper examines the scattering of a train of small-amplitude harmonic surface waves on water by one-dimensional topography, using the mild-slope equation. The associated boundary value problem is converted into a pair of integral equations whose solutions are approximated by variational techniques, which also supply error bounds. Excellent approximations to the reflection and transmission coefficients and to the free surface shape are produced with only 2- or 3-dimensional trial spaces, by choosing these spaces to be problem dependent. The bed profiles considered include localised humps and taluds which join two horizontal planes at different depths.

(n,3s) Rydberg spectra of diethyl ether, diisopropyl ether, and methyl vinyl ether: Analysis of the torsional motion

Two-photon resonance mass resolved excitation spectra are obtained for diethyl ether-h10, diethyl ether-d10, diisopropyl either, and methyl vinyl ether cooled in a supersonic jet expansion. The spectra are assigned as due to 2p3s←(2p)2 Rydberg excitations: significant progressions in a low energy vibrational mode are observed for both diethyl and diisopropyl ethers, but not for methyl vinyl ether. The transition energies for the vibronic progressions are modeled by a double well potential function of polynomial form truncated at the quartic term. The transition intensities for the progressions are calculated based on a Franck–Condon analysis of the excited state potential surface and a harmonic ground state surface. Calculations identify the progression forming mode as the antigeared torsion of the C–O–C–C dihedral angles. Excitation of diethyl ether from its ground electronic state to its 2p3s Rydberg state leads to changes in the dihedral angles (τ1, τ2) from ±180° to ±157°. Similar electronic excitation of diisopropyl ether yields changes in (τ1,τ2) from ±157° in the ground state to ±146° in the Rydberg state. The torsional displacement active in the 2p3s←(2p)2 oxygen Rydberg transition is suggested to arise from the interaction between the diffuse 3s electron and the β-methyl groups on both diethyl and diisopropyl ethers.

Excitation of guided elastic wave modes in hollow cylinders by applied surface tractions

The problem of the generation of guided elastic wave modes in infinite hollow circular cylinders by loading applied to the boundaries of the cylinder, apart from being an interesting problem in itself, has important applications in the field of nondestructive evaluation. Hollow cylinders are commonly used in the nuclear industry in heat exchangers and hence must be inspected for defects regularly to ensure continued safe operation. An exact, closed-form solution is given for the amplitude with which any propagating waveguide mode is generated due to the application of prescribed (time harmonic) surface tractions. Instead of using classical integral transform techniques to solve the problem, the normal mode expansion technique is used. In this technique, analogous to the expansion of a function in terms of an orthogonal (and complete) set of functions, the fields generated in the cylinder due to the application of the surface loading are expanded in terms of the normal modes of the cylinder. The general results are then specialized to loading configurations of practical importance in nondestructive testing.

Theory of dynamic absorption spectroscopy of nonstationary states. 4. Application to 12-fs resonant impulsive Raman spectroscopy of bacteriorhodopsin

A time-dependent theory for femtosecond dynamic absorption spectroscopy is used to describe the creation and observation of molecular ground-state vibrational coherence through the resonance impulsive stimulated Raman mechanism. Model calculations show that the oscillatory absorption signal that arises from this ground-state coherence is maximized for a limited range of pulse lengths and that there is a complex relationship between the probe wavelength and the strength of the spectral oscillations. The generalized time-dependent linear susceptibility of the nonstationary system created by the impulsive pump pulse is defined and used to discuss the strong dependence of the measured signals on the properties of the probe pulse. Finally, calculations are presented to analyze the high-frequency oscillations ({approximately}20-fs period) recently observed in the transient absorption spectra of light-adapted bacteriorhodopsin (BR{sub 568}) following excitation with a 12-fs optical pulse. At the probe wavelengths used in this experiment, the contribution of stimulated emission is negligible at long times because of the extremely rapid excited-state isomerization; as a result, the spectral oscillations observed after this time are due to the impulsive excitation of coherent vibrations in the ground state. The transient response observed for BR{sub 568} is calculated using a 29-mode harmonic potential surface derived from amore » prior resonance Raman intensity analysis. Both the oscillatory signals and their dependence on the probe wavelength are satisfactorily reproduced. 68 refs., 11 figs.« less

Useful results for the determination of excited state geometries from resonance Raman spectra: Application to inorganic complexes

The time-dependent formulation of Raman scattering is used to derive simple expressions for fundamental and overtone intensities that depend on potential energy features in the Franck–Condon region and the homogeneous damping constant due to the bath modes. From the Raman excitation profiles, the dependence of the full width at half-maximum on the damping constant is calculated. The results are applied to the rich resonance Raman spectra and Raman excitation profiles of transition metal complexes, in particular, Cs3[Re2OCl10] and Cs4[W2OCl10], to determine the magnitude of the geometric changes occurring upon excitation of the molecule from the ground to the excited electronic state. For each compound, the multidimensional harmonic potential surface and damping constant derived for the excited electronic state are then used to simulate the observed Raman excitation profiles and resonance Raman spectrum.

Linear and non-linear optical studies of mono- and multilayer Langmuir-Blodgett films of N-docosanoyl para-nitroaniline

Abstract Second harmonic generation (SHG) and surface plasmon studies have been carried out on mono- and multilayer Langmuir-Blodgett (LB) films of an amphiphile containing a small chromophore (N-docosanoyl-4-nitroaniline). A quadratic variation in the second harmonic intensity was observed for Y-type multilayers (film thickness above 4 bilayers), but for the thinner films (film thickness less than 4 bilayers) the enhancement of the SHG intensity does not follow the quadratic dependence. The results indicate that the non-linear chromophores lie almost flat on the plane of the substrate with orientation preference in the dopping direction. The SHG behavior and the second-order non-linearity of the LB films are compared with those of 2-docosylamino-5-nitropyridine and N-docosyl-4-nitroaniline which also have a chromophore of similar size.

Dilational viscoelasticity of fluid interfaces: The diffusion model for transient processes

The functional form of the surface dilational modulus is determined by considering the subsurface concentration changes produced by the diffusion process consequent to a non-periodic (rectangular step) perturbation of surface area (local equilibrium between surface and subsurface is assumed). The mathematical treatment is intended to present a straightforward demonstration that the same (unique) physical quantity, i.e. the dilational modulus, governs both harmonic and transient surface processes. The results definitely show that this modulus is an intrinsic physical property of a diffusive system, independent of the type of surface disturbance (within the linearity approximation).

An elastic half-space containing a flat inclusion under a harmonic surface load

The plane strain problem for an elastic half-space containing a flat inclusion is considered. It is assumed that the medium is subjected to a harmonic surface load of given frequency. The inclusion is approximated by an inextensible or an elastic membrane. The problem is reduced to a complex integral equation with the interfacial shear stress as the unknown function. In addition to the interfacial shear and the stress intensity factors, the components of the displacement vector on the free boundary are calculated. The results provide a limited contribution to the assembly of inverse solutions that are needed in non-destructive testing and evaluation studies.

Solutions positives et mesure harmonique pour des opérateurs paraboliques dans des ouverts «lipschitziens»

Let L be a parabolic operator on R n+1 written in divergence form and with Lipschitz coefficients relatively to an adapted metric. We compare, near the boundary, the relative behavior of positive L-solutions on a Lipschitz domain. We first establish a so-called weak boundary Harnack principle. We then establish a uniform Harnack principle for certain particular positive L-solutions. This principle then allows us to prove another strong boundary Harnack principle for certain pairs of positive L-solutions. Then, we can generalize to L-operators some of J. T. Kemper results: we characterize the Martin boundary for “Lipschitz” domains and we show that the positive L-solutions on such domains admit non tangential limits except for a negligible set with respect to harmonic measure. Finally, in the last part, and for slightly more regular domains, we establish the equivalence between harmonic measure, adjoint harmonic measure and surface measure thus developing some results of J. M. Wu and R. Kaufman.

An iterative method to evaluate the impedance matrix of finite-size foundation

A new approach used in the finite element method to calculate the impedance matrix of rock (or soil) foundation, is presented. First, an iterative technique is developed to solve the complex-valued equations of motion for the foundation subjected to a harmonic surface force. The proposed technique can be used to calculate the complex-valued displacement response of the foundation in an adjacent area near a certain exciting frequency. Second, the complex-valued static substructure method is introduced to the procedure for solving the equations of motion. The method of combining the complex-valued static substructure method with the iterative technique is presented to reduce the computational effort needed in the procedure. The effectiveness of these new calculation techniques is demonstrated by numerical examples.

Langevin modes of macromolecules: Applications to crambin and DNA hexamers

Langevin modes describe the behavior of atoms moving on a harmonic potential surface subject to viscous damping described by a classical Langevin equation. We present applications to the protein crambin and to the DNA duplex d(CpGpCpGpCpG)2 and its complex with ethidium. Our friction matrix is weighted according to surface area exposed to solvent, and results are reported for various values of the solvent viscosity and models for hydrodynamic interactions. Even for relatively small solvent friction (eta = 0.3 cp) a substantial number of modes are overdamped, and time correlation functions decay smoothly without the oscillations characteristic of gas-phase calculations. Perturbation theory starting from the gas-phase modes is accurate for many low-frequency modes (which are overdamped in the presence of solvent), but fails badly for higher modes. For correlation functions of interest to fluorescence depolarization or nmr relaxation, the plateau values are insensitive to solvent viscosity, but the relaxation times are not. The advantages and limitations of this analysis of macromolecular motions are discussed.

Characterization of ion trapping motion in the dual cell ion cyclotron resonance spectrometer: experimental and theoretical studies

Ions produced in one cell of a dual cell Fourier transform-ion cyclotron resonance mass spectrometer are partitioned by temporarily grounding the conductance limit separating mass two cells. Theoretical predictions for transfer behavior were produced by used of Runge—Kutta integration and an elliptical function method to calculate ion motion during the transfer period. Comparison between the experimental and theoretical results indicates that ion transfer between cells is occurring on a more harmonic potential surface than expected. These results suggest that only ions formed near the center of the source cell can be effectively transferred and/or detected.

Theoretical analysis of resonance Raman spectra from the blue copper protein azurin

Using a time domain methodology, we have simulated low-temperature resonance Raman data from the blue copper protein azurin in an effort to determine an effective harmonic potential surface (relative to the ground-state geometry and normal coordinates) for the 600-nm transition of the blue copper active site. We find that utilization of overtone and combination intensities greatly facilitates the extraction of reliable parameter values. We are able in this manner to obtain accurate results for the linear displacements of the excited-state surface.

Surface Waves for Material Characterization

Analyses are presented for the propagation of harmonic surface waves on a transversely isotropic layer rigidly bonded to a transversely isotropic substrate of different material. The layer-substrate system is also assumed to be in contact with a liquid and inviscid space. The propagation takes place along an axis of symmetry of both the layer and the substrate. Exact closed-form solutions for the characteristic dispersion relations are presented. Numerical results are presented for material combinations of three classes of centrifugally cast stainless steel material. Results clearly demonstrate the influence of the layer thickness on the propagation speed and, hence, provide a means of material characterization.

Earthquake‐Induced Shear Stresses in Soils

Closed-form expressions for the earthquake-induced shear stress magnitude in soils and its phase shift with respect to the ground acceleration are presented. They are expressed as functions of the depth, the damping ratio of the soil, and the thickness of the resonant layer. In the development of these expressions the soil was treated as a viscoelastic material with a horizontal surface and harmonic surface displacement. The natural frequency is determined by assuming that a known depth of soil is in resonance. The shear stress induced in the soil by the earthquake is then evaluated from the governing equation of motion and expressed in complex form. As in the simplified method of evaluating soil liquefaction potential, the magnitude of the shear stress is presented as the product of the rigid-body shear stress and a stress-reduction coefficient. By doing this an analytic expression for the stress-reduction coefficient is derived.

Absolute calibration of interferometric systems for detection and measurement of surface acoustic waves

A calibration method for interferometric systems is shown to produce a minimum wave amplitude to which these systems may be calibrated in the measurement of harmonic surface acoustic waves. The calibration limit is ~3 orders of magnitude larger than the theoretical detection limit. The method proposed allows experimental determination of the detection limit of these systems. The calibration of a fiber-optic heterodyne interferometer is demonstrated, and the experimentally derived detection limit for the interferometer is shown to be 5.5 x 10(-15) m for unity detection bandwidth. This limit is obtained for a mirrored specimen with 0.14 mW of laser power incident on the optical detector.

Classical dynamics of t r a n s-diimide: Intramolecular vibrational relaxation involving an active torsion

The classical dynamics of vibrationally excited trans-diimide (N2H2) were studied, focusing on the interaction of the torsion with the local NNH bends and NH stretches. Energy flow to and from the torsion is facilitated by nonlinear resonances between the NH stretch and a bend-torsion combination mode, as has been found for other types of vibrational motions. The significant frequency ratios for such combination resonances have been predicted by a simple, analytic model and verified using a local harmonic oscillator potential surface. Several of these resonances were observed for trans-diimide. Since the dominant couplings are primarily kinetic, these resonances should also be important in the torsional vibrational dynamics of other molecules.