bluuebunny/crossref_metadata_2025 huggingface dataset:
Hua's Lemma and Simultaneous Diagonal Equations
Authors: Brüdern Jörg , Wooley Trevor D.
Published: October 2003

This paper concerns systems of r homogeneous diagonal equations of degree k in s variables, with integer coefficients. Subject to a suitable non‐singularity condition, it is shown that the expected asymptotic formula holds for the number of such systems inside a box [−P, P]s, provided only that s > (3r + 1)2k−2. By way of comparison, classical methods based on the use of Hua's lemma would establish a similar conclusion, provided instead that s > r2k.
On the Gauss–Bonnet Formula in Riemann–Finsler Geometry
Authors: Lackey Brad
Published: October 2003

Using Chern's method of transgression, the Euler class of a compact orientable Riemann–Finsler space is represented by polynomials in the connection and curvature matrices of a torsion‐free connection. When using the Chern connection (and hence the Christoffel–Levi–Civita connection in the Riemannian case), this result extends the Gauss–Bonnet formula of Bao and Chern to Finsler spaces whose indicatrices need not have constant volume.
Bifurcation from Simple Eigenvalues and Eigenvalues of Geometric Multiplicity One
Authors: Dancer E. N.
Published: October 2003

A counterexample has been constructed to show that a conjectured global solution structure for bifurcation of non‐trivial solutions from a simple eigenvalue of the linearization at zero really can occur. In addition, new results and counterexamples have been obtained for bifurcation from an eigenvalue of geometric multiplicity 1 and odd algebraic multiplicity. 2000 Mathematics Subject Classification 58E07, 47J15, 37G10.
FREE GROUPS OF OUTER COMMUTATOR VARIETIES OF GROUPS
Authors: GROVES DANIEL P.
Published: October 2003

If F is a free group, 1 < i [les ] j [les ] 2i and
i [les ] k [les ] i + j + 1 then
F/[γj(F), γi(F),
γk(F)] is residually nilpotent and torsion-free. This result is extended to
1 < i [les ] j [les ] 2i and i [les ] k [les ] 2i + 2j.
It is proved that the analogous Lie rings, L/[Lj,
Li, Lk] where L is a free Lie ring,
are torsion-free. Candidates are found for torsion in L/[Lj,
Li, Lk] whenever k is the least of
{i, j, k}, and the existence of torsion in L/[Lj,
Li, Lk] is proved when
i, j, k [les ] 5 and k is the least of {i, j, k}.
Autoduality of the Compactified Jacobian
Authors: Esteves Eduardo , Gagné Mathieu , Kleiman Steven
Published: October 2003

The following autoduality theorem is proved for an integral projective curve C in any characteristic. Given an invertible sheaf L of degree 1, form the corresponding Abel map AL:C→, which maps C into its compactified Jacobian, and form its pullback map , which carries the connected component of 0 in the Picard scheme back to the Jacobian. If C has, at worst, points of multiplicity 2, then is an isomorphism, and forming it commutes with specializing C.

Much of the work in the paper is valid, more generally, for a family of curves with, at worst, points of embedding dimension 2. In this case, the determinant of cohomology is used to construct a right inverse to . Then a scheme‐theoretic version of the theorem of the cube is proved, generalizing Mumford's, and it is used to prove that is independent of the choice of L. Finally, the autoduality theorem is proved. The presentation scheme is used to achieve an induction on the difference between the arithmetic and geometric genera; here, special properties of points of multiplicity 2 are used.
Involvement of Calmodulin in Glucagon‐Like Peptide 1(7‐36) Amide‐Induced Inhibition of the ATP‐Sensitive K+ Channel in Mouse Pancreatic β‐Cells
Authors: Ding W. G. , Kitasato H. , Matsuura H.
Published: October 2003

The present investigation was designed to examine whether calmodulin is involved in the inhibition of the ATP‐sensitive K+ (KATP) channel by glucagon‐like peptide 1(7‐36) amide (GLP‐1) in mouse pancreatic β‐cells. Membrane potential, single channel and whole‐cell currents through the KATP channels, and intracellular free Ca2+ concentration ([Ca2+]i) were measured in single mouse pancreatic β‐cells. Whole‐cell patch‐clamp experiments with amphotericin‐perforated patches revealed that membrane conductance at around the resting potential is predominantly supplied by the KATP channels in mouse pancreatic β‐cells. The addition of 20 nM GLP‐1 in the presence of 5 mM glucose significantly reduced the membrane KATP conductance, accompanied by membrane depolarization and the generation of electrical activity. A calmodulin inhibitor N‐(6‐aminohexyl)‐5‐chloro‐1‐naphthalenesulphonamide (W‐7, 20 μM) completely reversed the inhibitory actions of GLP‐1 on the membrane KATP conductance and resultant membrane depolarization. Cell‐attached patch recordings confirmed the inhibition of the KATP channel activity by 20 nM GLP‐1 and its restoration by 20 μM W‐7 or 10 μM calmidazolium at the single channel level. Bath application of 20 μM W‐7 also consistently abolished the GLP‐1‐evoked increase in [Ca2+]i in the presence of 5 mM glucose. These results strongly suggest that the mechanisms by which GLP‐1 inhibits the KATP channel activity accompanied by the initiation of electrical activity in mouse pancreatic β‐cells include a calmodulin‐dependent mechanism in addition to the well‐documented activation of the cyclic AMP‐protein kinase A system.
Desensitisation of the Oxytocin Receptor and other G‐Protein Coupled Receptors in the Human Myometrium
Authors: Plested C. Paul , Bernal Andrés López
Published: October 2003

G‐protein coupled receptors (GPCRs) are key to maintaining uterine quiescence and inducing phasic contractions at term. However, the biochemical mechanisms whereby uterine GPCRs are desensitised and re‐sensitised during these physiological conditions are unknown. For example, the number of oxytocin receptors (OTRs) on uterine myocytes decrease significantly after the addition of oxytocin. Therefore, further understanding of the desensitisation/re‐sensitisation of the OTR and other uterine GPCRs during pregnancy may provide a target for more efficient tocolytic drugs and more selective ways to modulate uterine activity. Here, we briefly review some of the mechanisms that may be involved during OTR and other GPCR desensitisation.
The Effects of Pregnancy and Maternal Nutrition on the Maternal Renin‐Angiotensin System in Sheep
Authors: Dandrea J. , Cooper S. , Ramsay M. M. , Keller‐Woods M. , Pipkin F. Broughton , Symonds M. E. , Stephenson T.
Published: October 2003

Physiological changes occurring in the mother during pregnancy can determine the outcome of pregnancy in terms of birthweight and neonatal viability. Maternal adaptations include plasma volume expansion linked to enhanced activity of the renin‐angiotensin system (RAS). The present study was designed to determine whether these changes occur very early in gestation, and the extent to which maternal nutrient restriction may compromise the maternal RAS. Using sheep, we have investigated the effects of pregnancy per se, maternal nutrient restriction and later restoration of maternal diet on maternal body weight, plasma volume and plasma renin concentration (PRC), and angiotensinogen (Aogen) and arginine vasopressin (AVP) concentration. During the period of placental growth (i.e. 28‐80 days gestation) ewes were fed either a nutrient‐restricted (NR) diet or were well fed (WF). NR ewes consumed between 3.2 and 3.8 MJ day−1 of metabolisable energy (ME) which is close to 60% of requirements taking into account the ME required for both ewe maintenance and growth of the conceptus in order to produce a 4.5 kg lamb at term. WF ewes consumed 150% of ME requirements. Restoration of maternal diet between 80 and 140 days gestation (i.e. fed to satiety and consuming between 8 and 10.9 MJ day−1, which is close to 150% of ME requirements) followed previous nutrient restriction. Between pre‐conception and 28 days gestation, plasma volume increased in conjunction with a decline in PRC and Aogen concentration. During the period of nutrient restriction ewe body weight did not increase and plasma volume was lower in NR than WF ewes. During this time there was no effect of maternal nutrition on PRC; however, Aogen concentration was lower in the NR group. From 80 days gestation following the rise in food intake for previously NR ewes, greater increases in ewe body weight, plasma volume and PRC occurred up to term compared with ewes that were well fed throughout gestation. Plasma AVP concentration was not significantly affected by either maternal nutrition or gestational age. In conclusion, the stimulus of moderately severe maternal nutrient restriction evoked smaller rises in maternal weight, plasma volume and Aogen concentration than occurred in ewes that were well fed throughout gestation. Following the restoration of maternal diet after 80 days gestation, PRC gradually rose to peak at term. These adaptations in the maternal RAS during the critical period of placental growth may have long‐term effects on fetal development.
Anatomy of Primary Afferents and Projection Neurones in the Rat Spinal Dorsal Horn with Particular Emphasis on Substance P and the Neurokinin 1 Receptor
Authors: Todd A. J.
Published: October 2003

The dorsal horn of the spinal cord plays an important role in transmitting information from nociceptive primary afferent neurones to the brain; however, our knowledge of its neuronal and synaptic organisation is still limited. Nociceptive afferents terminate mainly in laminae I and II and some of these contain substance P. Many projection neurones are located in lamina I and these send axons to various parts of the brain, including the caudal ventrolateral medulla (CVLM), parabrachial area, periaqueductal grey matter and thalamus. The neurokinin 1 (NK1) receptor on which substance P acts is expressed by certain neurones in the dorsal horn, including approximately 80% of lamina I projection neurones. There is also a population of large NK1 receptor‐immunoreactive neurones with cell bodies in laminae III and IV which project to the CVLM and parabrachial area. It has been shown that the lamina III/IV NK1 receptor‐immunoreactive projection neurones are densely and selectively innervated by substance P‐containing primary afferent neurones, and there is evidence that these afferents also target lamina I projection neurones with the receptor. Both types of neurone are innervated by descending serotoninergic axons from the medullary raphe nuclei. The lamina III/IV neurones also receive numerous synapses from axons of local inhibitory interneurones which contain GABA and neuropeptide Y, and again this input shows some specificity since post‐synaptic dorsal column neurones which also have cell bodies in laminae III and IV receive few contacts from neuropeptide Y‐containing axons. These observations indicate that there are specific patterns of synaptic connectivity within the spinal dorsal horn.
Changes in Human Muscle Transverse Relaxation Following Short‐Term Creatine Supplementation
Authors: Saab George , Marsh Greg D. , Casselman Mark A. , Thompson R. Terry
Published: October 2003

The rapid increase in body mass that often occurs following creatine (Cr) supplementation is believed to be due to intracellular water retention. The purpose of this study was to determine whether Cr consumption alters the magnetic resonance (MR) transverse relaxation (T2) distribution of skeletal muscle. Transverse relaxation can be used to model water compartments within a cell or tissue. In this double‐blind study, subjects were asked to supplement their normal diet with creatine monohydrate (20 g day−1 for 5 days) mixed with a grape drink (Creatine group, n= 7), or the grape drink alone (Placebo group, n= 8). Phosphorous MR spectroscopy was used to determine the effectiveness of the supplementation protocol. Subjects that responded to the Cr supplementation (i.e. showed a > 5% increase in the ratio of the levels of phosphocreatine (PCr) and ATP) were placed in the Creatine group. Both proton MR imaging and spectroscopy were used to acquire T2 data, at 1.89 T, from the flexor digitorum profundus muscle of each subject before and after supplementation. Following the supplementation period, the Creatine group showed a gain in body mass (1.2 ± 0.8 kg, P < 0.05, mean ± S.D.), and an increase in PCr/ATP ratio (23.8 ± 16.4%, P < 0.001). Neither group showed any changes in intracellular pH or T2 calculated from MR images. However, the spectroscopy data revealed at least three components (> 5 ms) at approximately 20, 40 and 125 ms in both groups. Only in the Creatine group was there an increase in the apparent proton concentration of the two shorter components combined (+5.0 ± 4.7%, P < 0.05). According to the cellular water compartment model, the changes observed in the shorter T2 components are consistent with an increase in intracellular water.
Changes in Cerebral Blood Flow During and After 48 H of Both Isocapnic and Poikilocapnic Hypoxia in Humans
Authors: Poulin Marc J. , Fatemian Marzieh , Tansley John G. , O'Connor David F. , Robbins Peter A.
Published: October 2003

During acclimatization to the hypoxia of altitude, the cerebral circulation is exposed to arterial hypoxia and hypocapnia, two stimuli with opposing influences on cerebral blood flow (CBF). In order to understand the resultant changes in CBF, this study examined the responses of CBF during a period of constant mild hypoxia both with and without concomitant regulation of arterial PCO2. Nine subjects were each exposed to two protocols in a purpose‐built chamber: (1) 48 h of isocapnic hypoxia (Protocol I), where end‐tidal PO2 (PET,O2) was held at 60 Torr and end‐tidal PCO2 (PET,CO2) at the subject's resting value prior to experimentation; and (2) 48 h of poikilocapnic hypoxia (Protocol P), where PET,O2 was held at 60 Torr and PET,CO2 was uncontrolled. Transcranial Doppler ultrasound was used to assess CBF. At 24 h intervals during and after the hypoxic exposure CBF was measured and the sensitivity of CBF to acute variations in PO2 and PCO2 was determined. During Protocol P, PET,CO2 decreased by 13% (P < 0.001) and CBF decreased by 6% (P < 0.05), whereas during Protocol I, PET,CO2 and CBF remained unchanged. The sensitivity of CBF to acute variations in PO2 and PCO2 increased by 103% (P < 0.001) and 28% (P < 0.01), respectively, over the 48 h period of hypoxia. These changes did not differ between protocols. In conclusion, CBF decreases during mild poikilocapnic hypoxia, indicating that there is a predominant effect on CBF of the associated arterial hypocapnia. This fall occurs despite increases in the sensitivity of CBF to acute variations in PO2/PCO2 arising directly from the hypoxic exposure.
Mitochondrial Diseases ‐ An Expanding Spectrum of Disorders and Affected Genes
Authors: von Kleist‐Retzow Jürgen‐Christoph , Schauseil‐Zipf Ulrike , Michalk Dietrich V. , Kunz Wolfram S.
Published: October 2003

Mitochondrial diseases are a heterogeneous group of disorders caused by the impairment of the mitochondrial oxidative phosphorylation system which have been associated with various mutations of the mitochondrial DNA (mtDNA) and nuclear gene mutations. The clinical phenotypes are very diverse and the spectrum is still expanding. This review gives an overview of the principal clinical phenotypes and the molecular genetic basis of mitochondrial disorders identified so far.
Different Metabolic Properties of Mitochondrial Oxidative Phosphorylation in Different Cell Types ‐ Important Implications for Mitochondrial Cytopathies
Authors: Kunz Wolfram S.
Published: October 2003

The metabolic and functional diversity of animal mitochondria caused by different mitochondrial compositions due to tissue‐specific mitochondrial pathways and tissue‐specific differences in expression of isoforms of subunits of enzymes participating in oxidative phosphorylation will be reviewed here. Applying the concept of metabolic control analysis, the relevance of this diversity for the explanation of tissue‐specific effects observed in mitochondrial diseases with homoplasmic mitochondrial DNA mutations and nuclear‐encoded respiratory chain defects is discussed.
Coincidence of Boobnov-Galerkin and Closed-Form Solutions in an Applied Mechanics Problem
Authors: Elishakoff I. , Zingales M.
Published: October 2003

It is shown that the utilization of the Filonenko-Borodich set of functions, as the comparison functions in the Boobnov-Galerkin method leads to the result that coincides with the closed-form solution for the clamped-clamped uniform beam under uniformly distributed load. It is hoped that this remarkable, direct coincidence could be used in graduate courses and books on mechanics of solids.
Equilibrium and Belt-Pulley Vibration Coupling in Serpentine Belt Drives
Authors: Kong L. , Parker R. G.
Published: October 2003

Serpentine belt drives with spring-loaded tensioners are now widely used in the automotive industry. Experimental measurements show that linear system vibration coupling exists between the pulley rotations and the transverse span deflections. Former models that treat the belt as a string and neglect the belt bending stiffness cannot explain this coupling phenomenon. In this paper, a new serpentine belt system model incorporating the belt bending stiffness is established. The finite belt bending stiffness causes nontrivial transverse span equilibria, in contrast to string models with straight span equilibria. Nontrivial span equilibria cause linear span-pulley coupling, and the degree of coupling is determined by the equilibrium curvatures. A computational method based on boundary value problem solvers is developed to obtain the numerically exact solution of the nonlinear equilibrium equations. An approximate analytical solution of closed-form is also obtained for the case of small bending stiffness. Based on these solutions, the effects of design variables on the equilibrium deflections and span-pulley coupling are investigated.
Capturing the Pinch-Off of Liquid Jets by the Level Set Method
Authors: Pan Y. , Suga K.
Published: October 2003

Full three-dimensional dynamic simulations of forced liquid jets flowing into and pinching off in ambient of another liquid were performed by using the level set method for tracking the interface between the immiscible materials. The simulations were performed for jets with viscosity ratios between the inner and outer fluids of 0.17 and 1.7. The jets were forced at Strouhal number of 4.0. The Reynolds, Froud, and Bond numbers based on the conditions at the nozzle exit were 34–35, 0.2, and 6.1, for both cases. The numerical results are compared with the data from the experiment made by Longmire et al. (2001). The comparisons were made for (1) flow images of one complete pinch-off cycle and (2) the axial and radial profiles of the instantaneous velocities around the region of jet disintegration. The feasibility and accuracy of using the level set method in multiphase problems involving interface breakup/coalescence is explored and accessed by simulating such relatively low speed, low density-ratio two-phase flows. Although the level set method is quite promising, due to the surface tension model, it requires very fine grid resolution (the Weber number based on the grid spacing is smaller than 10−2) even for capturing the laminar surface phenomena.
On the Water-Entry-Induced Cavity Closure for a Wide Range of Entry Speeds
Authors: Lee M.
Published: October 2003

One of the important research areas in the water-entry problem is the cavity dynamics. A theoretical analysis is presented to predict the dynamics of water-entry cavity up to the first cavity closure, which is generated by a solid body entering a semi-inifinite free surface of water at a wide range of entry speed. Two types of cavity closure, which are surface closure and the deep closure, depending on the magnitude of ambient atmosphere pressure and entry speed are described by the proposed theory. The time of surface closure at the relatively low-speed entry regime is estimated and compared with published experimental data. Currently no experimental data are available for the high-speed entry case.
Effects of Seal Geometry on Dynamic Impeller Fluid Forces and Moments
Authors: Yoshida Yoshiki , Tsujimoto Yoshinobu , Morimoto Goh , Nishida Hiroki , Morii Shigeki
Published: October 2003

This paper reports an experimental investigation of the rotordynamic fluid force and moment on a centrifugal impeller with three types of wear-ring seals; i.e., a face seal and two types of toothed seals. The impeller is equipped with a vaneless diffuser. Rotordynamic fluid forces and moments on the impeller in whirling motion were measured directly by using four-axis force sensor. Unsteady pressures were measured at several locations in the diffuser. It was found that, (1) at low flow rate, the fluid force and fluid force moment become maximum at a certain whirling speed caused by a coupling between the whirl motion and vaneless diffuser rotating stall and (2) the seal geometry with axial seal affects the direction of the coupled fluid force relative to the direction of eccentricity through the change in the unsteady leakage flow due to the whirl.
Out-of-Plane Motion Effects in Microscopic Particle Image Velocimetry
Authors: Olsen Michael G. , Bourdon Chris J.
Published: October 2003

In microscopic particle image velocimetry (microPIV) experiments, the entire volume of a flowfield is illuminated, resulting in all of the particles in the field of view contributing to the image. Unlike in light-sheet PIV, where the depth of the measurement volume is simply the thickness of the laser sheet, in microPIV, the measurement volume depth is a function of the image forming optics of the microscope. In a flowfield with out-of-plane motion, the measurement volume (called the depth of correlation) is also a function of the magnitude of the out-of-plane motion within the measurement volume. Equations are presented describing the depth of correlation and its dependence on out-of-plane motion. The consequences of this dependence and suggestions for limiting its significance are also presented. Another result of the out-of-plane motion is that the height of the PIV signal peak in the correlation plane will decrease. Because the height of the noise peaks will not be affected by the out-of-plane motion, this could lead to erroneous velocity measurements. An equation is introduced that describes the effect of the out-of-plane motion on the signal peak height, and its implications are discussed. Finally, the derived analytical equations are compared to results calculated using synthetic PIV images, and the agreement between the two is seen to be excellent.
A Cavity Wake Model Based on the Viscous/Inviscid Interaction Approach and Its Application to Nonsymmetric Cavity Flows in Inducers
Authors: Semenov Yury , Tsujimoto Yoshinobu
Published: October 2003

A cavity wake model based on the flow interaction between the viscous wake behind the cavity and external inviscid cavity flow is proposed. The conditions of interaction between viscous and inviscid flows make it possible to obtain a unique solution of the problem. The viscous wake model is formulated within the theory of boundary layers. The problem for the external inviscid flow is considered in both nonlinear and linear formulation. The developed cavity wake model provides reasonable agreement with experimental data for cavitation performance and cavitation compliance over a wide range of cavitation numbers from cavitation inception to the super cavity flow. The cavity model is applied to predict nonsymmetric flows in inducers with two and more blades. The regions of nonsymmetric cavity flow are compared with those in experiments. It is found that the local head decrease of an inducer might be caused by the nonsymmetric cavity patterns. The predicted regions of a steady nonsymmetric cavity flow correlate with the region of cavitation instability observed in experiments.
Behavior of Radial Incompressible Flow in Pneumatic Dimensional Control Systems
Authors: Roy G. , Vo-Ngoc D. , Nguyen D. N. , Florent P.
Published: October 2003

The application of pneumatic metrology to control dimensional accuracy on machined parts is based on the measurement of gas flow resistance through a restricted section formed by a jet orifice placed at a small distance away from a machined surface. The backpressure, which is sensed and indicated by a pressure gauge, is calibrated to measure dimensional variations. It has been found that in some typical industrial applications, the nozzles are subject to fouling, e.g., dirt and oil deposits accumulate on their frontal areas, thus requiring more frequent calibration of the apparatus for reliable service. In this paper, a numerical and experimental analysis of the flow behavior in the region between an injection nozzle and a flat surface is presented. The analysis is based on the steady-state axisymmetric flow of an incompressible fluid. The governing equations, coupled with the appropriate boundary conditions, are solved using the SIMPLER algorithm. Results have shown that for the standard nozzle geometry used in industrial applications, an annular low-pressure separated flow area was found to exist near the frontal surface of the nozzle. The existence of this area is believed to be the cause of the nozzle fouling problem. A study of various alternate nozzle geometries has shown that this low-pressure recirculation area can be eliminated quite readily. Well-designed chamfered, rounded, and reduced frontal area nozzles have all reduced or eliminated the separated recirculation flow area. It has been noted, however, that rounded nozzles may adversely cause a reduction in apparatus sensitivity.
Influence of Three-Dimensional Roughness on Pressure-Driven Flow Through Microchannels
Authors: Hu Yandong , Werner Carsten , Li Dongqing
Published: October 2003

Surface roughness is present in most of the microfluidic devices due to the microfabrication techniques or particle adhesion. It is highly desirable to understand the roughness effect on microscale flow. In this study, we developed a three-dimensional finite-volume-based numerical model to simulate pressure-driven liquid flow in microchannels with rectangular prism rough elements on the surfaces. Both symmetrical and asymmetric roughness element arrangements were considered, and the influence of the roughness on pressure drop was examined. The three-dimensional numerical solution shows significant effects of surface roughness in terms of the rough elements’ height, size, spacing, and the channel height on both the velocity distribution and the pressure drop. The compression-expansion flow around the three-dimensional roughness elements and the flow blockage caused by the roughness in the microchannel were discussed. An expression of the relative channel height reduction due to roughness effect was presented.
A Displacement Equivalence-Based Damage Model for Brittle Materials—Part I: Theory
Authors: Soh C. K. , Liu Y. , Yang Y. , Dong Y.
Published: October 2003

In this paper, a displacement equivalence-based damage model for brittle materials is proposed. A new damage deactivation criterion, which depends on both the stress and strain states of the materials, is adopted. Based on the concept of effective stress, the virtual undamaged configuration is introduced, and the assumption of displacement equivalence is proposed to correlate the damaged and the virtual undamaged configurations. Then, an additional crack-opening-induced normal deformation is introduced, and the three-dimensional (3D) effect of these opened cracks is also considered. The evolution rule of damage is deduced using the Onsager relations, which also ensure that the second law of thermodynamics is satisfied.
Response Power Spectrum of Multi-Degree-of-Freedom Nonlinear Systems by a Galerkin Technique
Authors: Failla G. , Spanos P. D. , Di Paola M.
Published: October 2003

This paper deals with the estimation of spectral properties of randomly excited multi-degree-of-freedom (MDOF) nonlinear vibrating systems. Each component of the vector of the stationary system response is expanded into a trigonometric Fourier series over an adequately long interval T. The unknown Fourier coefficients of individual samples of the response process are treated by harmonic balance, which leads to a set of nonlinear equations that are solved by Newton’s method. For polynomial nonlinearities of cubic order, exact solutions are developed to compute the Fourier coefficients of the nonlinear terms, including those involved in the Jacobian matrix associated with the implementation of Newton’s method. The proposed technique is also applicable for arbitrary nonlinearities via a cubicization procedure over the interval T. Upon determining the Fourier coefficients, estimates of the response power spectral density matrix are constructed by averaging their squared moduli over the samples ensemble. Examples of application prove the reliability of the technique by comparison with digital simulation data.
Dynamic Analysis of a Mode I Propagating Crack Subjected to a Concentrated Load
Authors: Chung Y.-L. , Chen M.-R.
Published: October 2003

This work investigates the phenomenon of mode I central crack propagating with a constant speed subjected to a concentrated load on the crack surfaces. This problem is not a self-similar problem. However, the method of self-similar potential (SSP) in conjunction with superposition can be successfully applied if the time delay and the origin shift are considered. After the complete solution is obtained, attention is stressed on the dynamic stress intensity factors (DSIFs). Analytical results indicate that the DSIF equals the static stress intensity factor if the crack-tip speed is very slow and equal to zero if the crack-tip velocity approaches the Rayleigh-wave speed. However, the dynamic effect becomes obvious only if the crack-tip speed is 0.4 times faster than the S-wave speed. Moreover, the combination of SSP method and the superposition scheme can be applied to the expanding uniformly distributed load acting on a portion of the crack surfaces.
The Application of Lagrange Equations to Mechanical Systems With Mass Explicitly Dependent on Position
Authors: Pesce C. P.
Published: October 2003

The derivation and application of the Lagrange equations of motion to systems with mass varying explicitly with position are discussed. Two perspectives can be followed: systems with a material type of source, attached to particles continuously gaining or losing mass, and systems for which the variation of mass is of a nonlinear control volume type, mass trespassing a control surface. This is the case if, for some theoretical or practical reason, a partition into subsystems is considered. An important class of problems in which the extended Lagrange equations turn to be useful emerges from “hydromechanics,” whenever a finite number of generalized coordinates can be used, under the concept of the added mass tensor. A particular and interesting one is addressed in the present paper: the classical hydrodynamic impact of a rigid body against a liquid free surface.
The Inlet Flow Structure of a Centrifugal Compressor Stage and Its Influence on the Compressor Performance
Authors: Engeda Abraham , Kim Yunbae , Aungier Ronald , Direnzi Gregory
Published: October 2003

The performance of centrifugal compressors can be seriously degraded by inlet flow distortions that result from an unsatisfactory inlet configuration. In this present work, the flow is numerically simulated and the flow details are analyzed and discussed in order to understand the performance behavior of the compressor exposed to different inlet configurations. In a previous work, complementary to this present work, experimental tests were carried out for the comparison of a centrifugal compressor stage performance with two different inlet configurations: one of which was a straight pipe with constant cross-sectional area and the other a 90-deg curved pipe with nozzle shape. The comparative test results indicated significant compressor stage performance difference between the two different inlet configurations. Steady-state compressor stage simulation including the impeller and diffuser with three different inlets has been carried out to investigate the influence of each inlet type on the compressor performance. The three different inlet systems included a proposed and improved inlet model. The flow from the bend inlet is not axisymmetric in the circumferential and radial distortion, thus the diffuser and the impeller are modeled with fully 360-deg passages.
Frictional Performance of U-Type Wavy Tubes
Authors: Chen Ing Youn , Lai Yee Kang , Wang Chi-Chuan
Published: October 2003

Measurements of the pressure drops for water flowing in small diameter tubes having U-type wavy configuration are presented. The inner diameters of the test copper tubes D are 3.43, 5.07, and 8.29 mm, whereas the curvature ratios 2R/D and spacer length L/D span from 3.75 to 7.87 and 1.93 to 7.0, respectively. The test range of the Reynolds number for water is about 200<Re<18000. The measured pressure loss in U-type wavy tube includes the loss in U-bends and the loss caused by the distorted flow in the downstream straight tube. Thus, an equivalent friction factor, fB, is then defined. For both laminar and turbulent flow the bend friction factor increases with the decrease of dimensionless curvature ratio and spacer length. The test results indicate that the recent reported correlations by Popiel and Wojkowiak (2000) and Wojkowiak (2000) do not accurately predict the data. A simple friction factor equation is developed based on the experimental data with characterizing parameters like curvature ratio and spacer length, new Dean number, and the Reynolds number. A good agreement with a mean standard deviation of 5.6% is observed between the proposed correlation and the existing data, which includes the test results of this study and those from Popiel and Wojtkowiak (2000).
A New Approach for Reduced Order Modeling of Mechanical Systems Using Vibration Measurements
Authors: Lus¸ H. , De Angelis M. , Betti R.
Published: October 2003

This study investigates the possibilities of obtaining reduced order mass-damping-stiffness models of mechanical systems using state space realizations identified via dynamic tests. It is shown that even when the system is insufficiently instrumented with sensors and actuators, it is still possible to create physically meaningful reduced order mass-damping-stiffness models that incorporate measured and unmeasured degrees of freedom. It is further discussed that certain assumptions, such as having a diagonal mass matrix or having classical damping in the system, allow one to develop alternative reduced order representations with different physical interpretations. The theoretical presentation is supplemented by a numerical example that illustrates the applications of the formulations developed herein.
Nonintegrability of an Infinite-Degree-of-Freedom Model for Unforced and Undamped, Straight Beams
Authors: Yagasaki K.
Published: October 2003

We study a mathematical model for unforced and undamped, initially straight beams. This system is governed by an integro-partial differential equation, and its energy is conserved: It is an infinite-degree-of-freedom Hamiltonian system. We can derive “exact” finite-degree-of-freedom mode truncations for it. Using the differential Galois theory for Hamiltonian systems, we prove that any two or more modal truncations for the model are nonintegrable in the following sense: The Hamiltonian systems do not have the same number of “meromorphic” first complex integrals which are independent and in involution, as the number of their degrees of freedom, when they are regarded as Hamiltonian systems with complex time and coordinates. This also means the nonintegrability of the infinite-degree-of-freedom model for the beams. We present numerical simulation results and observe that chaotic motions occur as in typical nonintegrable Hamiltonian systems.
A Unified Characteristic Theory for Plastic Plane Stress and Strain Problems
Authors: Zhang Y.-Q. , Hao H. , Yu M.-H.
Published: October 2003

Based on the unified strength criterion, a characteristic theory for solving the plastic plane stress and plane strain problems of an ideal rigid-plastic body is established in this paper, which can be adapted for a wide variety of materials. Through this new theory, a suitable characteristic method for material of interest can be obtained and the relations among different sorts of characteristic methods can be revealed. Those characteristic methods on the basis of different strength criteria, such as Tresca, von Mises, Mohr-Coulomb, twin shear (TS) and generalized twin shear (GTS), are the special cases (Tresca, Mohr-Coulomb, TS, and GTS) or linear approximation (von Mises) of the proposed theory. Moreover, a series of new characteristic methods can be easily derived from it. Using the proposed theory, the influence of yield criterion on the limit analysis is analyzed. Two examples are given to illustrate the application of this theory.
Resolving Turbulent Wakes
Authors: Jordan Stephen A.
Published: October 2003

Resolving the turbulent statistics of bluff-body wakes is a challenging task. Frequently, the streamwise grid point spacing approaching the vortex exit boundary is sacrificed to gain near full resolution of the turbulent scales neighboring the body surface. This choice favors the solution strategies of direct numerical and large-eddy simulations (DNS and LES) that house spectral-like resolving characteristics with inherent dissipation. Herein, two differencing stencils are tested for approximating four forms of the convective derivative in the DNS and LES formulations for incompressible flows. The wake spectral characteristics and conventional parameters are computed for Reynolds numbers Re=200 (laminar wake) and Re=3900. These tests demonstrated reliable stability and spectral-like accuracy of compact fifth-order upwinding for the advective derivative and fourth-order cell-centered Pade´ (with fourth-order upwinding interpolation) for the Arakawa form of the convective derivative. Specifically, observations of the DNS computations suggest that best results of the wake properties are acquired when the inertial subrange of the spectral energy is fully resolved at the grid-scale level. The LES solutions degraded dramatically only when the fifth-order upwind stencil resolved the spanwise periodic turbulence. Although the dynamic subgrid-scale model showed strong participation on the instantaneous level, its spectral contributions were negligible regardless of the chosen grid-scale scheme.
Integral Solution for the Mean Flow Profiles of Turbulent Jets, Plumes, and Wakes
Authors: Agrawal Amit , Prasad Ajay K.
Published: October 2003

Integral methods are used to derive similarity solutions for several quantities of interest including the cross-stream velocity, Reynolds stress, the dominant turbulent kinetic energy production term, and eddy diffusivities of momentum and heat for axisymmetric and planar turbulent jets, plumes, and wakes. A universal constant is evaluated for axisymmetric and planar plumes. The cross-stream velocity profiles show that jets and axisymmetric plumes experience an outflow near the axis and an inflow far away from it. The outflow is attributed to the decay of the centerline velocity with downstream distance, and the extent and magnitude of outflow correlates with the streamwise decay of the centerline velocity. It is also shown that the entrainment velocity should not in general be equated to the product of the entrainment coefficient and the centerline velocity. It is found that, due to similar governing equations, profiles for jets and plumes are qualitatively similar. Our results show that the derived quantities are strong functions of streamwise and cross-stream positions, in contrast to previous approaches that assumed constant (in the cross-stream direction) eddy viscosity and thermal diffusivity. The turbulent Prandtl number is approximately equal to unity which matches the value quoted in the literature.
Nonlinear Free Flexural Vibration of Oval Rings
Authors: Ganapathi M. , Patel B. P. , Makhecha D. P.
Published: October 2003

In this article, the nonlinear free vibration characteristics of isotropic oval rings are analyzed using a shear flexible cubic B-spline curved beam element. The amplitude-frequency relationships are estimated from the response history. The participation of various modes in the total response is highlighted.
On Corrosion-Induced Creep and the Shedding of Oxide Pest From Metal Plates
Authors: Marshall D. L. , Taylor M. E. , Ivshin Y. , Diderrich G. , Pence T. J.
Published: October 2003

We consider a boundary value problem for a flat plate of an originally ductile metal that is subject to surface corrosion. Corrosion is modeled with the aid of two mobile interfaces. The leading interface is an oxidation front where volumetric expansion generates stress. This interface is initially present, with its location taken as prescribed. The trailing interface is a failure front associated with the shedding of oxide pest. This interface is not initially present, rather it first appears at some finite time into the process, and is determined via a stress-based failure criterion. The problem is reduced to a set of ordinary differential equations whose form changes depending on whether or not shedding has initiated. Numerical treatment shows a substantial increase in creep rate due to oxide shedding.
Lund’s Tilting Pad Journal Bearing Pad Assembly Method
Authors: Nicholas John C.
Published: October 2003

This paper summarizes the development during the last 50 years of tilting pad journal bearing analysis and design. The major impetus of this development was a landmark paper published by Jørgen Lund in 1964, “Spring and Damping Coefficients for the Tilting-Pad Journal Bearing.” His paper contained the first widely published dynamic coefficients for tilting pad bearings along with his pad assembly method equations. In the 38 years since Lund’s publication, many other authors have written tilting pad journal bearing codes, the first of which were based on Lund’s assembly method. These assembly method codes were utilized for many years to analyze and design tilting pad bearings for improved rotordynamic performance. During this time, some key design tools were developed utilizing Lund’s method. Other authors have written newer codes which solve the energy and elasticity equations iteratively with the pressure equation, including pad degrees of freedom. With the simple addition of a turbulence correction and heat balance, many designers continue to utilize Lund’s method, shunning the more modern codes.
Lund’s Elliptic Orbit Forced Response Analysis: The Keystone of Modern Rotating Machinery Analysis
Authors: Kirk R. Gordon
Published: October 2003

A total understanding of rotating machinery vibration analysis requires evaluation of critical speed placement, forced response sensitivity to imbalance, linear onset of instability prediction and full non-linear response analysis. Of these four areas of analysis, only the first three are applied as a basic design tool in modern turbo-machinery analysis. The prediction of multi-mass flexible rotor steady-state elliptic orbit response, including bearing damping and support flexibility, has been and remains in this author’s opinion, to be the basic workhorse and keystone of machinery design. This has now been true for over 35 years. The person responsible for developing this basic method of analysis has been a longtime friend of many engineers worldwide. This paper is written to acknowledge this contribution, one of many in fact, made by Jørgen W. Lund and is presented in memory of his life’s work at this occasion of honoring his contributions to our profession. A short section on the methods and understanding gained from the basic analysis will be presented. Finally, some personal reflections will be given concerning Jørgen Lund.
Lund’s Contribution to Rotor Stability: The Indispensable and Fundamental Basis of Modern Compressor Design
Authors: Gunter Edgar J.
Published: October 2003

In the early design of compressors and turbines, it was of importance to locate the rotor critical speeds so as to insure that a turbo rotor would not be operating at a critical speed. As compressor and turbine design became more sophisticated, a more detailed analysis of the rotor damped critical speeds and rotor log decrements was necessary. With compressors and turbines operating at higher speeds, under high power levels, and at multiples of the first critical speed, the problem of stability or self-excited whirling is of paramount importance. The onset of self-excited motion may lead to large amplitudes of motion with possible destructions of the rotor or the inability of the compressor to operate at peak power levels. Encountering this phenomenon with a compressor on an off-shore oil platform can mean millions of dollars of lost production. Self-excited whirling can be caused by fluid-film bearings, seals, Alford-type cross-coupling forces, or internal shaft friction, to name a few of the excitation mechanisms. The problem of computing the approximate values of the rotor log decrement under full speed and loading conditions requires the solution of a complex eigenvalue problem. The computation of the rotor complex roots is an order of magnitude more difficult than the problem of undamped critical speed calculations. J. W. Lund presented the first practical numerical procedure for computing turbo-rotor log decrements. The mathematical transfer matrix method pioneered by Lund has allowed industry to develop and stabilize a vast array of rotating machinery leading to the savings to industry of millions of dollars. Without the procedures of Lund, for example, it would not have been possible to resolve stability problems encountered with both the hydrogen and oxygen space shuttle pumps. This paper briefly presents some of the attributes of the Lund stability procedure and its unique characteristics.
Jørgen W. Lund: Theories Versus Tests, Part 1: Balancing and Response of Flexible Rotors
Authors: Tonnesen Jørgen
Published: October 2003

The contribution of the late Professor Jørgen W. Lund in the field of rotor dynamics and fluid film bearings is presented in a condensed form with the emphasis on the experimental work and results that confirm and support many of Dr. Lund’s theories and analyses. Part 1(A) covers the subject of rotor balancing by the influence method and Part 1(B) the unbalance response of a flexible rotor. In Part 2(A), experiments on instability and the influence of unbalance on whirl frequency are discussed for two rotors supported in cylindrical bearings. In Part 2(B), experiments using a cylindrical, two-axial groove journal bearing over a range of loads and speeds are reviewed.
Inertia Effects in Squeeze-Film Damper Bearings Generated by Circumferential Oil Supply Groove
Authors: Lund Jørgen W. , Myllerup Claus M. , Hartmann Henning
Published: October 2003

The dynamic properties of an industrial Squeeze-Film Damper (SFD) bearing design are described using the well-known perturbation approach, where the reaction forces induced by small movements away from the position of equilibrium are expanded into a Taylor series in terms of displacement, velocity, and acceleration. Although generally negligible, the acceleration term can become significant in SFD bearings when inertia effects in the damper lands are enhanced by the flow in a central circumferential oil supply groove. By using a bulk flow approximation in the oil supply groove an explicit expression is derived for the acceleration term. Experimental results confirm the significance of the oil supply groove geometry and appear to validate the bulk flow approximation.