Stability of microstretch fluid motions

Criteria of stability of the unsteady motion of incompressible microstretch fluid in an arbitrary time-dependent domain are obtained using a general energy method introduced by Serrin. It is shown that the original motion is stable in the mean if either of the two sets of numbers ($\text{?}{}_1$,$\text{?}{}_2$,$\text{?}{}_3$) or ($\text{σ}{}_1$, $\text{σ}{}_2$,$\text{σ}{}_3$) consists of positive numbers only. These numbers are expressible in terms of the various Reynolds numbers of the original motion. The theorems giving the stability criteria are universal in the sense that they do not depend on the geometry of the domain or the actual distribution of the flow field quantities. The decay of energy of the flow in a rigid and fixed container as well as a theorem on the uniqueness of steady flows are deduced.     

Station-keeping of moored vessels by reliability-based optimization

Floating marine structures are frequently kept in position by means of mooring lines in addition to a thruster system. Various types of control schemes for the thruster system are first investigated based on a simplified response model. In particular, the role of structural reliability criteria applied to the mooring system is investigated. Subsequently, a more refined control algorithm based on such reliability criteria is introduced. The performance of this control system is demonstrated by numerical simulations.     

Trapping of water waves by moored bodies

Certain types of floating bodies are known to support trapped modes, with oscillatory fluid motion near the body and no energy radiation in the far field. Previous work has considered either fixed bodies, where the boundary conditions are homogeneous, or bodies which are freely floating and moving without any exciting force. For a fixed body the existence of a trapped mode implies that there is no unique solution of the boundary-value problem for the velocity potential with a prescribed body motion. For a free body which supports a trapped mode, the solution of the coupled problem for the motions of the fluid and body does not have a unique solution. A more general case is considered here, of a body with a linear restoring force such as an elastic mooring. The limiting cases of a fixed and free body correspond to infinite or zero values of the corresponding spring constant. A variety of body shapes are found including cylinders in two dimensions and axisymmetric bodies in three dimensions, which illustrate this more general case of trapping and provide a connection between the fixed and free cases.     

Stability of penethamate,a benzylpenicillin ester prodrug,in oily vehicles

Penethamate (PNT) is an ester prodrug of benzylpenicillin which is marketed as dry powder for reconstitution with aqueous vehicle prior to injection. The purpose of this paper was to investigate the chemical stability of PNT in oily formulations to provide a basis for a ready-to-use (RTU) oil-based PNT formulation. The chemical stability of PNT solutions and suspensions in light liquid paraffin (LP), medium chain triglyceride (MIG), ethyl oleate (EO) and sunflower oil (SO) was investigated at 30?°C. Solid state stability of PNT powder and stability of PNT in EO suspensions with different moisture contents were also evaluated. The solubility of PNT in the oils was in order SO?>?EO?>?MIG?>?LP. Degradation of PNT was rapid in oily solutions and less than 10% remained after 7–15 days. Stability of PNT decreased with increase in moisture content in ethyl oleate suspensions. PNT was stable over four weeks in the solid state. Hydrolysis, due to moisture in the oil formulation is not the only degradation mechanism. PNT stability (% drug remaining) in oily suspensions after 3.5 months was in the order LP (96.2%)?>?MIG (95.4%)?>?EO (94.1%)?>?SO (86%). A shelf-life of up to 5.5 years at 30?°C may be achieved for PNT suspension in these oils.     

Stability analysis of an explicit finite element scheme for plane wave motions in elastic solids

 Expressions for critical timesteps are provided for an explicit finite element method for plane elastodynamic problems in isotropic, linear elastic solids. Both 4-node and 8-node quadrilateral elements are considered. The method involves solving for the eigenvalues directly from the eigenvalue problem at the element level. The characteristic polynomial is of order 8 for 4-node elements and 16 for 8-node elements. Due to the complexity of these equations, direct solution of these polynomials had not been attempted previously. The commonly used critical time-step estimates in the literature were obtained by reducing the characteristic equation for 4-node elements to a second-order equation involving only the normal strain modes of deformation. Furthermore, the results appear to be valid only for lumped-mass 4-node elements. In this paper, the characteristic equations are solved directly for the eigenvalues using <ty>Mathematica<ty> and critical time-step estimates are provided for both lumped and consistent mass matrix formulations. For lumped-mass method, both full and reduced integration are considered. In each case, the natural modes of deformation are obtained and it is shown that when Poisson's ratio is below a certain transition value, either shear-mode or hourglass mode of deformation dominates depending on the formulation. And when Poisson's ratio is above the transition value, in all the cases, the uniform normal strain mode dominates. Consequently, depending on Poisson's ratio the critical time-step also assumes two different expressions. The approach used in this work also has a definite pedagogical merit as the same approach is used in obtaining time-step estimates for simpler problems such as rod and beam elements. Received: 8 January 2002 / Accepted: 12 July 2002 The support of NSF under grant number DMI-9820880 is gratefully acknowledged.     

Efficient vector outcrossing analysis of the excursion of a moored vessel

Extreme value prediction of combined first- and second-order motions of a moored floating structure has remained topical for years. Many researchers have applied the Kac–Siegert technique to derive the statistical distribution of the non-Gaussian responses. Almost exclusively, the previous studies have focused on a single-degree-of-freedom system, with the understanding that for any linear dynamical system, one may decouple a specific mode of interest from other degrees-of-freedom. The design philosophy is to assess the allowable limit of each individual motion separately. This paper presents an efficient method for predicting the extreme lateral excursion based on the vector sum of the surge and sway offsets. To this end, the vector outcrossing rate from a prescribed watch-circle is calculated. The joint probability density of the surge and sway responses is approximated using the Nataf transformation. The outcrossing rates thus estimated are found to agree well with those directly extracted from Monte Carlo simulation.     

Classification of human motions

Stages in the development of the classification for human motions are reviewed from the 17th century up to the present day, with special emphasis on the discrete events approach to the classification of human motions as advocated by the Gilbreths. It is put forward that this approach is inappropriate both from the psychological and the physiological view point; while at the same time it is emphasized that, although the therblig approach contributed significantly to the understanding of human motions and skills, nevertheless it may be more harmful than beneficial in the long run. The additive properties of the discrete events approach to the analysis of human motions are considered. Results of the investigations reported here suggest that, in the performance of repetitive tasks of the nature described here, the therblig times of the task are independent units within a work cycle, when analysed by means of 100 cycles. Thus, the times are additive in the mathematical sense, but when the same task is repeated only once, or a very few times, and analysed by single cycles, the therblig times form an integrated part of the entire work cycle and, therefore, their times are not additive in the mathematical sense.     

Diffraction of water waves by a moored,horizontal, flat plate

Summary A Norwegian research group has investigated the feasibility of constructing a system of underwater structures which would act like a lens and focus water waves prior to harnessing their energy. In the present work we consider modelling one of these structures by a horizontal, flat plate which is moored to the seabed. The water is assumed to be incompressible and inviscid and two-dimensional, linear, irrotational theory is used. Solutions to the scattering and radiation potentials are obtained by the method of matched eigenfunction expansions. Comparisons are made with various approximate solutions and results are presented illustrating the effect of varying the mooring stiffness in the cables on both the responses of the plate and the far-field wave motion.     

Dynamics of four-wheel-steering vehicles

In this paper we present an optimised 3 degrees-of-freedom non-linear dynamic model of a four-wheel-steering (4WS) vehicle. As variables, we retain the lateral velocity V, the rolling velocity p and yaw velocity r. The front steer angle δ_f and rear steer angle δ_r are considered to be linear functions of the steering wheel angle θ_s and of dθ_s/dt, the proportionality parameters being k _1f, k _2f for δ_f and k _1r, k _2r for δ_r. The parameters k _1f, k _2f, k _1r, k _2r are optimised by use of the BOX mathematical algorithm. In a first optimisation loop we minimise the sideslip angle β of the vehicle and in a second optimisation loop we assure, that the resultant (taken in the centre of gravity of the vehicle) of all the transversal forces F _y applied on the wheels of the vehicle (reaction forces contained in the road plane), give a component F _yx along the longitudinal axis of the vehicle, that takes a non negative value. This assures, that the motor of the vehicle will not waste fuel to overcome resistance forces originating from the steering system of the vehicle. A numerical application is also presented for a 4WS vehicle negotiating a curve at constant velocity. The results are compared to those obtained by two models frequently used in the literature. The comparison testifies on the superiority of our model for the application presented here.     

Partitioning in situ total spectral absorption by use of moored spectral absorption-attenuation meters

High-temporal-resolution spectral absorption data were acquired by use of one bottom-mounted (~68-m) and three moored spectral absorption and attenuation meters (ac-9 meters at 14, 37, and 52 m) on the Middle Atlantic Bight continental shelf during the fall 1996 period of the Coastal Mixing and Optics experiment. We employed a previously published spectral absorption model with the data to partition total absorption into absorption by water, phytoplankton, detritus, and gelbstoff (dissolved matter). We validated the model by comparing its results against coincident in vivo absorption coefficients derived from discrete bottle samples. Correlations between modeled and in vivo spectra range from 0.873 to 0.998. We optimized these correlations to determine the model parameters. These parameters could not be determined solely from the moored ac-9 results. Therefore a separate set of absorption measurements (from discrete bottle samples) was necessary to permit values for the model parameters to be determined. Model results allow us to separate particulate and dissolved components of absorption and to examine the temporal variability and the vertical distributions and concentrations of each component, given the total absorption in the water column.     

Kinematics of four-wheel-steering vehicles

In this paper, we review some aspects of the kinematical theory of four-wheel-steering (4WS) vehicles and present some new results and conclusions that we came across during our research on the subject. In a first paragraph, we compare the turning radius of two-wheel-steering (2WS) and 4WS vehicles and draw some interesting conclusions on the manoeuvring ability of either of them. In a second paragraph, we present a general kinematical analysis of 4WS vehicles by considering either the simplified two-wheel (bicycle) model or the more complete four-wheel model. In this analysis, we assume the sideslip angles of the wheels as non-negligible and we derive the general formulae relating the steering angles of the wheels to the geometrical data of the vehicle. By taking as zero the steering angles of the rear wheels, we derive from the above relations the well-known formulae of Ackermann–Jeantaux that are valid for 2WS vehicles.     

The kaleidoscope ocean

Oceanic plant life is dominated by the microscopic phytoplankton. Regardless of the scale at which they are observed, they display striking heterogeneity in their distribution. At their most dramatic they paint colorful swathes across whole seas. A short history of observations of phytoplankton 'patchiness' is presented, illustrated with some of the many ideas put forward to explain it. Focus is then turned to the mesoscale, covering scales of roughly 1-500 km. It is argued that the spatial variability seen in phytoplankton at these scales gives important information on the biogeochemistry of the ocean. In particular, interplay between the physical circulation and biological processes results in constantly shifting patterns that are strongly related to changes induced in phytoplankton production. It is thought that this physical influence may play a major role in controlling the rate at which new plant material (primary production) is generated in much of the world's oceans. Major questions yet to be addressed are also discussed including the difficulty of quantifying processes on the very limit of what we can model or observe and how these processes may change in response to and exert a feedback on future climate change.     

Universal stability of thermo-magneto-micropolar fluid motions

Criteria for universal stability of the unsteady motion of an incompressible, electrically conducting linear micropolar fluid with heat transfer in the presence of an arbitrary magnetic field, and in an arbitrary time dependent domain are established. The model of the micropolar fluid employed is essentially the one proposed by Eringen. The interaction between the flow field and the magnetic field is manifested through the Lorentz force and the coupling between the flow and temperature field arises through the Boussinesq equation of state.The stability method employed is an energy technique due to James Serrin. Certain uniqueness theorems for the unsteady and steady flows of thermo-magneto-micropolar fluid are also established.The theorems established for the stability and uniqueness are universal in the sense that they may be applied to any geometry of bound domains and any distribution of the basic field variables.     

Universal stability of magneto-micropolar fluid motions

Criteria for universal stability of the unsteady motion of an incompressible, electrically conducting linear micropolar fluid, i.e. with rigid microinclusions, in the presence of an arbitrary magnetic field, and in an arbitrary bounded time dependent domain are established. The model of the micropolar fluid employed is essentially the one proposed by Eringen. The interaction between the flow field and the magnetic field is manifested through the body force and body couple. Relativistic, Hall, and temperature effects are neglected. The stability method employed is an energy technique due to James Serrin. Certain uniqueness theorems for the unsteady and steady flows of magneto-micropolar fluid are also established.The theorems established for the stability and uniqueness are universal in the sense that they may be applied to any geometry of bounded domains and any distribution of the basic field variables. The present problem finds application in MHD generators with neutral fluid seedings in the form of rigid microinclusions.     

The radial motions of elastic shells

The equations of motion governing the behaviour of thin elastic shells, cylindrical or spherical, under the action of uniform time-dependent normal tractions acting upon the curved surfaces, are obtained. The material of the shells is taken to be uniform, isotropic and hyperelastic but the form of the strain-energy function is unspecified. It is supposed that the internal structure of the material imposes a constraint upon the principal stretches within the shell and the effect of certain special constraints is examined in detail.     

一种海底应答器绝对位置的精确校准方法

应答器越来越多地应用于各种水下作业，而其绝对位置的校准是工作的前提。在深海下由于声速的不均匀性，声线会发生弯曲。海底应答器绝对位置的校准需要进行声线弯曲修正。给出了一种深海条件下含声线弯曲修正的海底应答器绝对位置精确校准的方法。深海试验结果验证了该算法的有效性以及进行声线修正的必要性。     

Orbital motions in 3He-A

Orbital motions in ³He-A in very low magnetic field and driven by heat flow are studied using crossed detecting zero-sound fields. A precessional type of motion of the % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GabmiBayaajaaaaa!3C6D!\[\hat l\] field is frequently observed, though a rich variety of phenomena are also observed. There is no evidence for phase slip due to motion of nonsingular vortices along the surface. Motion of the % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GabmiBayaajaaaaa!3C6D!\[\hat l\] field following sudden parallel magnetic field turn-off is also observed above a threshold field change which is related to coherent dipolar energy. The time scale for these % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GabmiBayaajaaaaa!3C6D!\[\hat l\]-field changes is, however, a factor of about 10² larger than expected for the formation of composite solitons.Work supported by the U.S. Department of Energy under contract EY-76-S-03-0034, P.A. 143.     

On-orbit vicarious calibration of ocean color sensors using an ocean surface reflectance model

Recent advances in global biogeochemical research demonstrate a critical need for long-term ocean color satellite data records of consistent high quality. To achieve that quality, spaceborne instruments require on-orbit vicarious calibration, where the integrated instrument and atmospheric correction system is adjusted using in situ normalized water-leaving radiances, such as those collected by the marine optical buoy (MOBY). Unfortunately, well-characterized time-series of in situ data are scarce for many historical satellite missions, in particular, the NASA coastal zone color scanner (CZCS) and the ocean color and temperature scanner (OCTS). Ocean surface reflectance models (ORMs) accurately reproduce spectra observed in clear marine waters, using only chlorophyll a (C(a)) as input, a measurement for which long-term in situ time series exist. Before recalibrating CZCS and OCTS using modeled radiances, however, we evaluate the approach with the Sea-viewing Wide-Field-of-view Sensor (SeaWiFS). Using annual C(a) climatologies as input into an ORM, we derive SeaWiFS vicarious gains that differ from the operational MOBY gains by less than +/-0.9% spectrally. In the context of generating decadal C(a) climate data records, we quantify the downstream effects of using these modeled gains by generating satellite-to-in situ data product validation statistics for comparison with the operational SeaWiFS results. Finally, we apply these methods to the CZCS and OCTS ocean color time series.