Nonrigid Systems Research Articles

Detection of a perfect conductor with an airborne electromagnetic system: The Gemini Field Test

The cores of high-grade nickel and copper sulphides appear as “perfect conductors” to most electromagnetic (EM) and airborne electromagnetic (AEM) systems, because they have bulk electrical conductivities of the order of [Formula: see text]. The EM response of these highly conductive cores is essentially undetectable with off-time measurements or when using nonrigid towed-bird systems. Compact AEM systems with accurate primary field bucking and on-time or in-phase measurements are sensitive to perfect conductors, but are incapable of detecting deep targets. Using a GPS system to define geometry, calculations suggest that it should be easy for an AEM system to detect “perfect conductors” provided the receiver was several hundred meters distant from the transmitter. A twin (Gemini) aircraft test was undertaken to test this concept in 2005. The field test successfully demonstrated detection of very conductive targets. Errors associated with geometric changes were better than 0.5% of the primary field at 400 m separation, allowing detection and characterization of the 30 Hz, in-phase response of small and extended conductors. The test shows that a 200 × 100 m very-strongly conductive thin-sheet target would be detectable to depths of 200 m below surface using off-the-shelf technology. Larger conductors would be detectable at greater depths.

Operators of physical quantities of nonrigid molecular systems with continuous axial symmetry groups

The construction of the effective operators of physical quantities is considered for nonrigid molecular systems whose geometrical symmetry of internal dynamics is determined by continuous axial groups. The construction is based on the methods of a symmetry group chain.

Classification of the states of nonrigid molecular systems with continuous axial symmetry groups

Construction of the stationary state classification is considered for nonrigid molecular systems whose geometrical symmetry of internal dynamics is determined by continuous axial groups. The construction is based on the methods of symmetry group chains.

Depletion interactions in binary mixtures of repulsive colloids

Acceptance ratio method, which has been used to calculate the depletion potential in binary hard-sphere mixtures, is extended to the computation of the depletion potential of non-rigid particle systems. The repulsive part of the Lennard-Jones pair potential is used as the direct pair potential between the non-rigid particles. The depletion potential between two big spheres immersed in a suspension of small spheres is determined with the acceptance ratio method through the application of Monte Carlo simulation. In order to check the validity of this method, our results are compared with those obtained by the Asakura-Oosawa approximation, and by Varial expansion approach, and by molecular dynamics simulation. The total effective potential and the depth of its potential well are computed for various softness parameters of the direct pair potential.

The differentiable manifold model of quantum-chemical reaction networks

The methods of general and differential topology (topology ≈ “rubber geometry”) are particularly suitable for the quantum-mechanical description of nonrigid molecular systems. The concept of nuclear configuration space 3NR is replaced by a metric space M and subsequently by a topological space (M, TC) where points of nuclear geometries, as fundamental entities, are replaced by open sets. These open sets provide a quantum-mechanical description of molecular structures, reaction mechanisms, and reaction networks. Exploiting the special properties of the metric of M, the topological space (M, TC) can be provided with a differentiable manifold structure. This differentiable manifold is proposed as a common basis for both local and global analysis of reacting molecular systems.

Double relaxation phenomena of associated binary polar liquid mixture in non-polar solvent under high frequency electric field

Double relaxation times τ 2 and τ 1 due to whole molecular rotation and the flexible parts of the binary polar liquid mixture ( jk) 3-bromoaniline and 1-propanol dissolved in non-polar solvent ( i) benzene were estimated in terms of measured real χ ′ i j k , imaginary χ ″ i j k parts of complex high frequency orientational susceptibility χ i j k * and χ 0 ijk which is real at 20, 30, 40 and 47 °C experimental temperatures for 0.0, 0.25, 0.50,0.75 and 1.00 mole fractions x j 's of 1-propanol under 9.1 GHz electric field. The slopes ω( τ 2 + τ 1) and intercepts ω 2 τ 2 τ 1 of the analytical straight line equations used to estimate τ 2 and τ 1 were derived from Bergmann's equation [U. Saha, S.K. Sit, R.C. Basak, S. Acharyya, J. Phys. D: Appl. Phys. 27 (1994) 596] based on two Debye type dispersion model of binary polar mixture. The systems 3-bromoaniline in C 6H 6 and 1-propanol in C 6H 6 show τ 2 and τ 1 only at 47 °C temperature like 3-bromoaniline + 1-propanol in C 6H 6 at 20 and 47 °C temperatures for 0.25 and 0.50 mole fractions x j 's of 1-propanol. The binary polar mixture for x j = 0.75 of 1-propanol is an exception exhibiting double relaxation times at all the experimental temperatures. The relative contributions c 1 and c 2 due to τ 1 and τ 2 for eight non-rigid systems were calculated from Fröhlich's equation as well as graphical plots of χ ′ i j k / χ 0 i j k − w j k and χ ″ i j k / χ 0 i j k − w j k curve at w j k → 0 . c 1 and c 2 are positive for Fröhlich's method whereas most of the c 2's are negative for graphical method. The dipole moments μ 2 and μ 1 for all the systems are calculated from slopes β of χ ′ i j k − w j k curve at w j k → 0 and compared with the measured μ’s due to τ’s from ratio of slopes of χ ″ i j k − w j k and χ ′ i j k − w j k curves at w j k → 0 as well as χ ″ i j k − χ ′ i j k linear curves and reported μ’s due to Higasi's most probable τ. The reported and measured τ’s and μ’s agree with the most probable τ 0 = τ 1 τ 2 and μ 1's of the eight system like τ 2's and μ 2's of the rest twelve systems. This indicates that double relaxation phenomena yield average τ and μ for binary polar mixture under GHz electric field. The associational behavior of the polar molecules are inferred from the theoretical dipole moments μ theo's in terms of bond angles and bond moments of the substituent polar groups to exhibit solute–solute or solute–solvent molecular association arising out of inductive, mesomeric and electromeric effects of polar groups in them. The associative natures are ascertained from convex or concave shape of τ jk or μ jk – x j curves and μ jk – T curves respectively under different state of molecular environment. The thermodynamic energy parameters are calculated from Eyring's rate theory to know the molecular dynamics of the systems in order to establish the fact that the binary polar mixture obeys the Debye–Smyth relaxation mechanism.

Frequency Response Analysis for Rolling-Bearing Damage Diagnosis

This paper deals with a new diagnosis method for detecting bearing faults (BFs) based on frequency response analysis. For non-rigid multi-mass systems with dominant mechanical resonance frequencies, the frequency response has to be calculated during the commissioning of the plant for reasons of safety and controlling. This task can be achieved by measuring two control variables of the drive which are both affected by BFs. This paper proposes that the measurement of the frequency response is a suitable strategy for detecting incipient BFs. In doing so, a two-channel analysis method for bearing damage diagnosis without additional sensors is developed. Deviations from the frequency response of the healthy state serve as indicators for a present BF. As the measurement of the two signals can be carried out during normal operation of the plant, online BF diagnosis is achieved. For the investigated two-inertia system, single-point bearing defects on the inner and outer raceways of rolling bearings and generalized roughness faults are within the scope of this paper.

Application of the instanton method for analyzing tunneling splitting spectra of nonrigid molecular systems: II. Excited states

For nonrigid molecules with two equivalent minima on their potential energy surface, expressions are obtained in terms of the instanton method for the calculation of the magnitude of the tunneling splitting of vibrational levels with the number n≥0 both in the harmonic approximation and taking into account the anharmonic corrections ∼ ℏ2. Using comparative calculations of the lowest spectral region of the tunneling splitting of the NH3 molecule as an example, it is shown that, even in the harmonic approximation, the calculation accuracy of the instanton method is as good as that of the standard Wentzel-Kramers-Brillouin method. When the anharmonic corrections to the energy levels are taken into account, the accuracy of description of the tunneling splittings of the vibration-inversion spectrum of molecules of the NH3 type in terms of the instanton method increases almost to the level of quantitative agreement with experimental data.

Anterior Single Rod Instrumentation for Thoracolumbar Adolescent Idiopathic Scoliosis With And Without the Use of Structural Interbody Support

A radiographic and clinical outcomes analysis of 41 patients treated for thoracolumbar adolescent idiopathic scoliosis utilizing a single anterior rigid rod construct. To evaluate the necessity of structural interbody support to improve primary curve correction and preserve or augment lordosis when used in conjunction with a single anterior rigid rod construct, to identify parameters that predict horizontalization of the lowest instrumented vertebra, adjacent disc angulation, and distal uninstrumented vertebrae, and to assess patient satisfaction following surgery. Instrumentation-induced kyphosis has been a concern with nonrigid anterior systems used in the past for the treatment of scoliosis. Interbody structural support has been recommended to maintain appropriate sagittal profile when anterior systems are utilized. It has also been suggested that the use of structural interbody support creates a fulcrum to increase curve correction when compression is applied to the convexity of the deformity. However, the necessity of interbody structural support when used in conjunction with a rigid anterior system has not been previously evaluated in patients with adolescent idiopathic scoliosis. Forty-one patients mean age 15.9 years (range 12.1-18.6 years) with thoracolumbar adolescent idiopathic scoliosis underwent anterior spinal fusion using a single 6.0 to 6.5 mm solid rod construct between June 1995 and August 1999 performed by the senior author (T.G.L.). Four additional patients with thoracolumbar curves with similar anterior instrumentation over the same time period were lost to follow-up or had incomplete records and were not included in the study. Structural interbody support was used in 21 patients and packed morselized autograft alone was used in 20 patients. The patients in the group with packed morselized bone alone generally underwent surgery earlier in the series before the author began using structural interbody support on a regular basis. Each patient had a minimum follow-up of 3 years. Preoperative, initial, and most recent (>3 years) follow-up radiographs were reviewed to determine in each group Cobb angle measurements, flexibility of primary, secondary, and fractional curves, apical and end vertebral translation, lowest instrumented vertebral and caudal disc angulation, global coronal and sagittal balance, and sagittal Cobb measurements in both instrumented levels as well as lumbar lordosis (T12-S1). In addition, the SRS outcomes instrument was completed by 38 of 41 patients. The mean preoperative primary curve in patients with structural support was 47 degrees (Group II) and 45 degrees in patients without structural support (Group I). Mean curve correction was to 13 degrees in Groups I and II. One patient in Group II became slightly more unbalanced at final follow-up; otherwise all were improved after surgery. Sagittal measurements over instrumented segments as well as total lumbar lordosis (T12-S1) was maintained between preoperative and final postoperative values in both groups. Similarly, in both groups, when horizontalization of the distal end instrumented vertebra was achieved on the preoperative reverse side-bending radiograph, more normal relationships were achieved between instrumented and distal noninstrumented segments (adjacent disc angulation and fractional lumbar curve) at final follow-up (P <or= 0.01). Patients in both groups were equally pleased with their clinical outcomes based on the SRS outcomes instrument. The use of interbody structural support does not appear to be necessary to maintain an appropriate sagittal profile or to maximize coronal curve correction when a rigid rod construct with packed morselized bone is used for the treatment of thoracolumbar adolescent idiopathic scoliosis. Parameters predicting horizontalization of the lower instrumented vertebra and uninstrumented segments below the construct were identified, which, if achieved, should predict an optimal long-term outcome. Clinical outcomes were very good in both groups.

Flexible monomer formulation for non-rigid systems

In this Letter, the general and rigorous approach for deriving adiabatically constrained kinetic energy operators of Gatti et al. is reformulated and simplified. Emphasis is placed on weakly bound systems such as van der Waals polymers, molecules bound to a surface or located inside a rare gas matrix since an adiabatic approximation might turn out to be very relevant for them. This allows us to recast the flexible adiabatic monomer formulation into that for the rigid case.

Microfluidic diffusion diluter: bulging of PDMS microchannels under pressure-driven flow*

The bulging of microfluidic systems during pressure-driven flow is potentially a major consideration for polydimethylsiloxane (PDMS)-based devices. Microchannel cross-sectional areas can change drastically as a function of flow rate and downstream microchannel position. Such geometrical flexibility leads to difficulties in predicting convective/diffusive transport for these systems. We have previously introduced a non-dimensional parameter, κ, for characterizing convection and diffusion behavior for pressure-driven flow in rigid all-glass systems. This paper describes a modification of that concept for application to non-rigid systems, which is accomplished by incorporating an experimental step to account for the bulging in PDMS/glass microsystems. Specifically, an experimental measurement of channel height by fluorescence microscopy is combined with the aforementioned theory to characterize convective/diffusive behavior at a single location in the device. This allowed the parameter κ to be determined at that point and applied to predict fluid flow in the subsequent portion of the PDMS microsystem. This procedure was applied to a PDMS/glass microfluidic diffusion dilution (μDD) device designed for generating concentration gradients. Theoretically predicted and experimentally measured distributions of concentrations within the microsystem matched well.

Application of the instanton method for analyzing tunneling splitting spectra of nonrigid molecular systems

General formalism and basic ideas of the instanton method are described. The potentialities of the method are demonstrated by calculating the tunneling splitting of the ground vibrational level for nonrigid molecules with two and three equivalent minima on their potential-energy surface. Some advantages of the application of the instanton method as compared to the well-known semiclassical approximation for describing the spectra of tunneling splitting of a nonrigid molecular system are proved.

Nonrigid systems: mechanical and thermodynamic aspects

The motion of a uniform chain has been used to exemplify systems with variable mass. The discussion is usually confinedto the dynamical aspects of the problem or to other derivationsthat use energy-conserving methods. Here this type of problem isre-examined by considering the chain as a closed one-dimensionalmotion, showing that the concept of centre of mass can beparticularly useful in this kind of multi-particle system. It issimilarly instructive to analyse the work-energy processes fromthe viewpoint of the first law of thermodynamics.

Dynamical body frames, orientation-shape variables and canonical spin bases for the nonrelativistic N-body problem

After the separation of the center-of-mass motion, a new privileged class of canonical Darboux bases is proposed for the nonrelativistic N-body problem by exploiting a geometrical and group theoretical approach to the definition of body frame for deformable bodies. This basis is adapted to the rotation group SO(3), whose canonical realization is associated with a symmetry Hamiltonian left action. The analysis of the SO(3) coadjoint orbits contained in the N-body phase space implies the existence of a spin frame for the N-body system. Then, the existence of appropriate nonsymmetry Hamiltonian right actions for nonrigid systems leads to the construction of an N-dependent discrete number of dynamical body frames for the N-body system, hence to the associated notions of dynamical and measurable orientation and shape variables, angular velocity, rotational and vibrational configurations. For N=3 the dynamical body frame turns out to be unique and our approach reproduces the xxzz gauge of the gauge theory associated with the orientation-shape SO(3) principal bundle approach of Littlejohn and Reinsch. For N⩾4 our description is different, since the dynamical body frames turn out to be momentum dependent. The resulting Darboux bases for N⩾4 are connected to the coupling of the spins of particle clusters rather than the coupling of the centers of mass (based on Jacobi relative normal coordinates). One of the advantages of the spin coupling is that, unlike the center-of-mass coupling, it admits a relativistic generalization.

Peculiarities of NMR spectra of heterospin complexes

Experimental investigation and theoretical simulation of the unusual phenomenon of multiple broadening and narrowing of NMR signals due to the temperature variation of a solution of the stereochemically non-rigid heterospin Ni2+ complex with stable nitroxide were performed. The investigation of the temperature dependence of the NMR signals of stereochemically non-rigid heterospin systems can be used for choosing conditions for growing heterospin single crystals containing molecules in a definite conformation.

Isomerism and Vibrational Spectra of Alkali Metal Perrhenates: Ab Initio CISD+Q Calculations

The equilibrium geometric parameters, isomerization energies, force fields, vibrational frequencies and intensities in the IR spectra of MReO4 molecules (M = Li, Na, K) are calculated by the configuration interaction method including all singly and doubly excited configurations with Davidson's correction for quartic excitations in expanded basis sets using effective relativistic core potentials. The calculations indicate that the chemical bonds between the metal atoms and the ReO4 anion group are highly polar. It is found that the MReO4 molecule has two isomers. The basic isomer with C2v symmetry has bidentate b coordination of the M+ cation to the ReO 4 - anion. The excited isomer is of C3v symmetry and corresponds to monodentate m coordination of M+. The low relative energies of the m isomers (17-29 kJ/mole) and the low energy barriers to the intramolecular m→b rearrangements (5-11 kJ/mole) indicate that MReO4 molecules are structurally nonrigid systems where the M–XO4 chemical bonds are “polytopic.” The results of calculations are compared with the available literature data on the structure and vibrational spectra of MReO4 molecules.

On chirality measures and chirality properties

It is shown that chiral zeroes are integral to all pseudoscalar functions, and that these functions, and thus the chirality properties that are described by them, are therefore normally unsuitable as chirality measures. The multidimensional nature of chirality properties is explored. Chirality measures for nonrigid objects and stochastic systems are discussed. It is shown that if the chirality of a nonrigid object is described as a time average of the chirality measures of its instant configurations, this time average is nonzero not only for chiral but also for achiral molecules. This paradox can be resolved if chirality measures are properly applied to nonrigid objects.Key words: chirality, chiral zeroes, chirality measures, chirality properties.

Fluid-structure interaction in non-rigid pipeline systems

Fluid-structure interaction in non-rigid pipeline systems is modelled by water hammer theory for the fluid coupled with beam theory for the pipe. Two different beam theories and two different solution methods in the time domain are studied and compared. In the first method, the fluid equations are solved by the method of characteristics and the pipe equations are solved by the finite element method in combination with a direct time integration scheme. In the second method, all basic equations (fluid and pipe) are solved by the method of characteristics. The solution methods are applied to a straight pipeline system subjected to axial and lateral impact loads and to a one-elbow pipeline system subjected to a rapid valve closure. In comparing the beam theories, the effects of rotatory inertia and shear deformation for practical pipe geometries and loading conditions are investigated. The significance of fluid-structure interaction is demonstrated. The fluid-structure interaction computer code flustrin, developed by delft hydraulics and which solves the acoustic equations using the method of characteristics (fluid) and the finite element method (structure), enables the user to determine dynamic fluid pressures, structural stresses and displacements in a liquid filled pipeline system under transient conditions. To validate flustrin, experiments are performed in a large scale 3D test facility consisting of a steel pipeline system suspended by wires. Pressure surges are generated by a fast acting shut-off valve. Dynamic pressures, structural displacements and strains (in total 70 signals) are measured under well determined initial and boundary conditions. The experiments are simulated with flustrin. The agreement between experiments and simulations is shown to be good: frequencies, amplitudes and wave phenomena are well predicted by the numerical simulations. It is demonstrated that the results obtained from a classical uncoupled water hammer computation, would render completely unreliable and useless results.

Nonrigid systems in chemistry: A unified view

Nonrigid systems in chemistry: A unified view

Nonrigid systems in chemistry: A unified view

Nonrigid systems in chemistry: A unified view