Time Rate Of Change Research Articles

Well-posedness and solution structure of dual-phase-lagging heat conduction

The dual-phase-lagging heat conduction equation is shown to be well-posed in a finite 1D region under Dirichlet, Neumann or Robin boundary conditions. Two solution structure theorems are developed for dual-phase-lagging heat conduction equations under linear boundary conditions. These theorems express contributions (to the temperature field) of the initial temperature distribution and the source term by that of the initial time-rate change of the temperature. This reveals the structure of the temperature field and considerably simplifies the development of solutions of dual-phase-lagging heat conduction equations.

Numerical Models for the Simulation of Flexible Artificial Heart Valves: Part II - Valve Studies

Using a coupled Lagrangian dynamic leaflet model and an unsteady potential flow solver the motion of a polyurethane type heart valve is simulated in the aortic position. The simulations incorporate two flow domains; the first comprises only the leaflets which are embedded within an unsteady flow of infinite expanse, and the second incorporates the influence of the aortic geometry via a conformal mapping. Simulations are performed for a cardiac output of 51itres/min and a beat period of 72 b.p.m. corresponding to a typical aortic pulse. Resulting valve motions are computed for various leaflet bending stiffnesses in both flow domains. In addition both the bending stress and strain and their time rate of change are evaluated. Valve motion displays the characteristic rapid opening, stable opening and slow closing phases as detailed in the literature. The computed stress values along the leaflet surface are of the order of those found experimentally.

A conceptual model for pancake-ice formation in a wave field

AbstractIt is well known that waves jostle frazil-ice crystals together, providing opportunities for them to compact into floes. The shape of these consolidated floes is nearly circular, hence the name: pancakes. From field and laboratory observations, the size of these pancakes seems to depend on the wavelength. Further aggregation of these individual pancakes produces the seasonal ice cover. Pancake-ice covers prevail in the marginal ice zone of the Southern Ocean and along the edges of many polar and subpolar seas. This theoretical paper describes conceptually the formation process of a pancake-ice cover in a wave field. The mechanisms that affect the evolution of the entire ice cover are discussed. Governing equations for the time-rate change of the floe diameter, its thickness and the thickness of the ice-cover are derived based on these mechanisms. Two criteria are proposed to determine the maximum floe size under a given wave condition, one based on bending and the other on stretching. Field and laboratory observations to date are discussed in view of this theory.

Constitutive equations and reciprocity

The differential equations that must be satisfied for most fields (physical variables) in geophysics are determined primarily by conservation equations which relate the divergence of the flux of the field, the field's time rate of change, and its sources and sinks. These conservation (or equilibrium) equations do not provide sufficient constraints to determine the fluxes and fields even when boundary conditions (both in space and time) are specified. To constrain the fields completely, it is necessary to introduce the properties of the media; that is, the constitutive equations. Because the conservation equations can be determined without considering the properties of the media, these equations are valid for the most general media; that is, heterogeneous, anisotropic, time-varying, non-linear, etc. media in which many field variables can interact or be coupled. When the fields can be described by ‘self-adjoint’ differential equations in space–time, these media exhibit reciprocity; that is, upon interchange of ‘sources’ and ‘detectors’, the same result is obtained. We show that viscoelastic, elastodynamic problems relating to generalized Kelvin–Voigt and generalized Maxwell media satisfy the conditions for reciprocity. In addition, we show that the introduction of tensor ‘densities’ (which relate the inertial-force density to the particle-acceleration, particle-velocity and particle-displacement vectors in the inertial force's constitutive equation) do not invalidate the reciprocity conditions. The two constitutive equations (the stress/strain and the inertial-force ones) lead to dispersion and attenuation in the propagation of the fields even though none of the material constants in the constitutive or conservation equations is complex (i.e. with real and imaginary parts). Complex material properties cannot exist in nature for actual materials or media; nor can the material constants or properties be functions of frequency. However, ‘apparent’ or ‘equivalent’ properties may be complex and functions of frequency if time-harmonic fields are assumed to exist.

Transient Polymer Flow Rate in Injection Mold Filling

Abstract An analytical and experimental study of the transient flow behavior of polymer melt in injection molding is presented. The polymer volume flow rate into a rectangular mold cavity during the filling stage was determined using the Reynold's transport theory. The analysis, which neglects melt elasticity, shows that the flow rate is transient during the initial filling of the cavity. Moreover, the cavity flow rate was found to depend on material compressibility and expansivity, total volume upstream of the gate as well as time rate of change of melt pressure and temperature. Experimental results obtained through direct flow visualization are in good agreement with the theory. The effect of gate size on the cavity flow rate was also examined. A small gate gives rise to a greater degree of melt compressibility in the runner system. The prediction of actual flow rates into the cavity not only enhances determination of the interrelationship of flow rate, morphology, and properties in injection molding but also aids in the avoidance of molding defects. The results of this study can be used to improve the accuracy of CAE analysis.

Numerical studies of the motion of spheroidal particles flowing with liquid metals through an electric sensing zone

A mathematical model has been developed to describe the motion of variously shaped and oriented spheroids entrained in liquid metals passing through a cylindrical electric sensing zone (ESZ) developed for liquid metals cleanliness analyzer (LiMCA) systems. The fluid velocity field within the ESZ was obtained by solving the Navier-Stokes equations, while the trajectories of particles within the ESZ were calculated using the equations of motion for particles. These incorporate forces resulting from drag, added mass, history, and electromagnetic and fluid acceleration balanced against the time rate of changes in a particle momentum. The effects of particle or inclusion shape and orientation were taken into account by including correction factors for drag (RD), added mass (MA), history (B), and electromagnetic force (EM). The numerical results show that particle trajectories are affected by the magnetic pressure number (RH), the Reynolds number (Re), the blockage ratio (k), and the particle-fluid density ratio (γ). In the axial direction, spheroidal particles travel further axially before hitting the wall as the fluid velocity (Re) increases. In the radial direction, the outwardly directed electromagnetic force on nonconducting spheroids increases with radial distance from the axis, with increasing electric current (RH) and with increasing size (k) of the particle. At low electric currents (low RH), the competition between the electromagnetic force and the radial fluid acceleration force in the entrance region is predicted to result in particle movements first toward the central axis, before outward motion toward the wall, but directly toward the wall at large currents (high RH). Spheroidal particles with symmetric axes perpendicular to the transverse axis of the ESZ move faster toward the sidewall as the particle aspect ratio (E) increases. The dominating increase in the added mass force over the increase in the electromagnetic force with decreasing E makes this effect much stronger for oblates (E 1). The stronger drag force on a prolate with its symmetric axis parallel to the axis of the ESZ makes it move slower toward the wall than a prolate with its axis of symmetry perpendicular to the axis of the ESZ. Low-inertia (low-γ) spheroidal particles move faster toward the sidewall than do heavier particles. This effect of γ is stronger for prolates than for oblates traversing with their symmetric axes perpendicular to the axis of the ESZ, owing to the decreased added mass effect as E increases, while the effect of γ becomes much stronger for a prolate traversing with its symmetric axis perpendicular rather than parallel to the axis of the ESZ, owing to its smaller added mass. The radial particle velocity when approaching the wall is predicted to decrease due to the wall effects. This model has been applied to the movement of spheroidal inclusions within the ESZ of a LiMCA system in molten aluminum, and it was proven from the theoretical point of view that LiMCA systems could be used in aluminum industries.

The Top With a Blunted Vertex Slipping With Light Friction at a High Rate of Spin

The problem of determining the motion of a top is a classic example of a complex analysis in analytical dynamics. Adding a blunt tip to the top and setting it spinning on a surface with sliding friction might be thought to render it intractable for simple analysis. However, if it is set in motion with a high rate of spin it is possible to find a simple approximate solution for the case of approximate steady precession. For this pseudo-steady motion it will be noted that the rate of diminution of the nutation will also be almost constant. Further, the ratio of these rates (latter over former) will be equal to the negative of the coefficient of friction for the top slipping on the surface. As a consequence the mass center of the top will tend to proceed around a steady circle above the plane. These results will first be observed by writing the full Lagrange’s equations for the problem and reducing them prior to integration by observing appropriate approximations by deleting relatively smaller terms. The above results will then follow directly. Further, the full Lagrange’s equations will be numerically integrated to show that the analytically developed approximate results are appropriate. Once these results are known, it is observed that a subsequent intuitive analysis based on time rate of change of angular momentum leads to the same results, if only the angular momentum about the spin axis is considered with other relevant assumptions. [S0021-8936(00)00203-8]

Calculation of Wellbore Pressures and Rate Distribution in Multilayered Reservoirs

Summary An analytic procedure in Laplace space is developed to calculate the wellbore pressure and rate distribution, and their time rate of change, in anisotropic multilayer formations with axial symmetry and interlayer crossflow, in the presence of skins and wellbore storage, for any number of layers, any number of intervals open to the formation, for wells of nonzero radius, for finite external radii, and for no flow at the outer boundaries. Numerically, the procedure appears to be robust and trouble free. A number of applications to which the procedure can meaningfully be used are identified, and some elements of the procedure are illustrated through two brief examples.

Two-phase flow through porous media in the fixed-contact-line regime.

The complete set of equations controlling immiscible two-phase flow through porous media are derived from first principles under the sole restriction that contact lines between the two fluids and the grain surfaces are not allowed to migrate irreversibly. Because rough grain surfaces have the ability to trap contact lines over significant ranges of capillary-pressure variation, such laws are of practical interest. As distinct from previous coarse-graining work, we explicitly allow for the stretching of the fluid interface, which results in considerable nonlinearity at the macroscopic scale. The laws are obtained through an asymptotic analysis and have several new features compared to the standard laws conventionally used in two-phase flow modeling. These include the need to (i) distinguish between measurable fluxes and the volume-averaged flow; (ii) allow for flow induced by the time rate of change of the capillary pressure; and (iii) include quadratic-force terms in the generalized Darcy laws when macroscopic-pressure diffusion is slow (as defined herein).

Self-consistent theory of large amplitude collective motion at finite excitation energy

We formulate a theory for the transfer of energy from collective degrees of freedom to internal degrees of freedom when the former belong to the adiabatic large-amplitude regime. The framework is that of an extended mean-field theory including dissipation, with the following salient features: (i) The Born-Oppenheimer approximation is extended to finite excitation energy by the introduction of the concept of thermal state, that is pure with respect to collective coordinates and a (square root of $a)$ density matrix with respect to internal coordinates. (ii) By assuming that these states form an approximate complete set for application of the Kerman-Klein method, the self-consistent theory of large amplitude collective motion is extended to finite excitation energy. (iii) The mean-field limit is taken, and further study is carried out in the basis of natural orbitals that diagonalizes the one-particle density matrix. In the approximation maintained uniformly in this work, the equations of motion for the orbitals are shown to be of Hamiltonian form; to these are conjoined the master equations for the time rate of change of the occupation numbers. The latter are studied in two extreme limits. In the collisionless limit, dissipation still arises from the response of the mean field to the collective motion (one-body friction). At the opposite extreme, collisions are assumed to be so effective as to force the system always to be in a state of local (constrained) equilibrium. (iv) We review a procedure by which the noncollective variables in the Hamiltonian may be eliminated, leading to equations of motion for the collective variables with dissipative terms that in general depend on the history of the system. The limit of instantaneous friction can be justified in an adiabatic approximation. (v) A decoupling procedure is developed for deriving the form of these equations of motion from the mean-field theory, with the ultimate aim of obtaining the macroscopic parameters that appear in the classical equations of motion for the collective variables. This procedure generalizes that developed in extensive previous work on large amplitude collective motion at zero temperature. (vi) Associating the dissipative equations of motion for the collective variables with one of the assumptions concerning the rates of change of the occupation numbers provides a description of the relaxation of a system initially perturbed from a state of dynamic equilibrium.

A comparison of inter-frame feature measures for robust object classification in sector scan sonar image sequences

This paper presents an investigation of the robustness of an inter-frame feature measure classifier for underwater sector scan sonar image sequences. In the initial stages the images are of either divers or remotely operated vehicles (ROV's). The inter-frame feature measures are derived from sequences of sonar scans to characterize the behavior of the objects over time. The classifier has been shown to produce error rates of 0%-2% using real nonnoisy images. The investigation looks at the robustness of the classifier with increased noise conditions and changes in the filtering of the images. It also identifies a set of features that are less susceptible to increased noise conditions and changes in the image filters. These features are the mean variance, and the variance of the rate of change in time of the intra-frame feature measures area, perimeter, compactness, maximum dimension and the first and second invariant moments of the objects. It is shown how the performance of the classifier can be improved. Success rates of up to 100% were obtained for a classifier trained under normal noise conditions, signal-to-noise ratio (SNR) around 9.5 dB, and a noisy test sequence of SNR 7.6 dB.

The slope of isentropes constituting a frontal zone

This paper investigates the use of the slope of isentropes as an objective indicator of the presenceof frontal zones in the atmosphere. It derives an equation for the change in time relative to thefront of the slope of isentropes and applies this equation to a specific case. It discusses theadvantages and disadvantages of this approach and compares it with the traditional approachbased on the horizontal temperature gradient. It appears that the use of the slope of isentropesto identify fronts brings out some features of frontal systems more clearly than the traditionaldefinition, especially cold fronts which lean forward toward the warm air. Three new frontogeneticterms appear in the equation governing the time rate of change of frontal intensity. In theparticular case studied here, these frontogenetic terms cannot be neglected, although they playonly a secondary rôle.

Effect of railgun electrodynamics on armature discard

An experiment was conducted to examine the role that electromagnetics plays during the sabot discard process. This investigation is less rigorous than an accuracy test but uses a number of performance indicators, including measured downrange magnetic fields, to quantify the effect on subprojectile performance. The test program consisted of two sets of shots with different armature current profiles. A muzzle switch, which closed prior to exit, was employed to tailor the current and armature acceleration profiles. The exit velocity was 1100 m/s for both profiles so as to maintain the same aerodynamic pressure loads during armature discard. The time rate of change of launcher and switch currents and launcher voltages were measured. In addition, the time rate of change of the armature magnetic field was measured downrange from the launcher. The residual magnetic field in the armature after exit produced no observable effect on the sabot discard process.

An Apparatus for Specific Heat Capacity Measurement by Thermal Radiation Calorimetry

Specific heat capacity measurements of disk-shaped specimens have been performed with an apparatus based on thermal radiation calorimetry. The specimen surfaces were irradiated by two fiat heaters in a vacuum chamber so that homogeneous temperature distribution within an insulating specimen was achieved. Homogeneity was confirmed by computer simulation based on the control-volume method. The values of specific heat capacity were obtained by measurement of the specimen temperature, the time rate change of the specimen temperature, and the radiant power from the heater for heating and cooling modes. The specific heat capacities of Ni metal, A12O3 ceramic, MgO ceramic, and A1N ceramic were measured in the temperature range from 220 to 500°C to confirm the validity of this calorimeter. The relative error involved in the measured values was estimated to be ±3%.

Quantum Vlasov equation and its Markov limit

The adiabatic particle number in mean field theory obeys a quantum Vlasov equation which is nonlocal in time. For weak, slowly varying electric fields this particle number can be identified with the single particle distribution function in phase space, and its time rate of change is the appropriate effective source term for the Boltzmann-Vlasov equation. By analyzing the evolution of the particle number we exhibit the time structure of the particle creation process in a constant electric field, and derive the local form of the source term due to pair creation. In order to capture the secular Schwinger creation rate, the source term requires an asymptotic expansion which is uniform in time, and whose longitudinal momentum dependence can be approximated by a delta function only on long time scales. The local Vlasov source term amounts to a kind of Markov limit of field theory, where information about quantum phase correlations in the created pairs is ignored and a reversible Hamiltonian evolution is replaced by an irreversible kinetic one. This replacement has a precise counterpart in the density matrix description, where it corresponds to disregarding the rapidly varying off-diagonal terms in the adiabatic number basis and treating the more slowly varying diagonal elements as the probabilities of creating pairs in a stochastic process. A numerical comparison between the quantum and local kinetic approaches to the dynamical backreaction problem shows remarkably good agreement, even in quite strong electric fields, over a large range of times.

Analysis of Solar Astrolabe Measurements during 20 Years

Recent observations of the Sun made between 1974 and 1995 at two observatories were examined to determine the constant and/or linear terms to the equinox and equator of the FK5 reference frame, the mean obliquity of the ecliptic, the mean longitude of the Sun, the mean eccentricity of the Earth's orbit, and the mean longitude of perihelion. The VSOP82 theory was used to reduce the data. The global solution of the weighted least-squares adjustment shows that the equinox of the FK5 requires a correction of +0072 ± 0005 at the mean epoch 1987.24. The FK5 and dynamical equinox agree closely at J2000.0 (-0040 ± 0020), but an anomalous negative secular variation with respect to the dynamical equinox was detected: -0881 ± 0116 century-1. The FK5 equator requires a correction of +0088 ± 0016, and there is no indication of a time rate of change. The corrections to the mean longitude of the Sun (-0020 ± 0010) and to the mean obliquity of the ecliptic (-0041 ± 0016) do appear to be statistically significant, although only marginally. The time rates of change for these quantities are not significant on the system to which the observations are referred. In spite of the short time span used in this analysis, the strong correlation between constant and linear terms was completely eliminated with the complete covering of the orbit by the data sets of both sites.

Predictability of Flashover by Zone Models

Two additional flashover inspection criteria were established from a recent study on identifying routes to chaos in a compartment fire. There, phase space diagrams on fire temperatures and their time rates of change were analyzed. The proposal was applied to study whether flashover can be predicted by a two-layer zone model. Two popular zone models ASET and CFAST were se lected. Compartments of different sizes and fires with different heat release rates were considered. Transient values of the fire temperatures and their time deriva tives were studied. It is concluded that in addition to the current flashover crite ria based on gas temperature near to the ceiling, heat flux at the floor level and flames coming out of the openings, the rate of change of fire temperature should be inspected.

A bond graph approach to the modeling of general multibody dynamic systems

A vector bond approach which effectively leads to a compact form of Hamiltonian bond graph structure and naturally to Hamilton’s equation of motion is proposed for the modeling of general multibody dynamic system. The methods for determining required bond graph elements are formulated in terms of kinematic influence coefficients. All moduli of transformers and their time rate of changes are found by pure vector (matrix) operations for the readiness for computer simulation of the resulting bond graph.

Modeling Road Racing Times of Competitive Recreational Runners Using Extreme Value Theory

Times of competitive recreational distance runners in a 10K road race can be modeled using extreme value theory. The derivative of the function fit to the times across age using this theory will express the rate of change in time per year that the runners are experiencing.

Exact analytic characteristic initial data for axisymmetric, non-rotating, vacuum spacetimes, with an application to the binary black hole problem

Bondi's approach to the construction of a coordinate system is used with a different choice of gauge, in accordance with which the radial coordinate r is an affine parameter, to cast the metric tensor into a form suitable for use with the Newman-Penrose null tetrad formalism. The choice of tetrad has the result that the equations and all the functions that appear in them are real-valued. A group classification of the Sachs equations in this gauge leads to a unique expression for the first of the five independent elements of the Weyl spinor, and to the corresponding exact solutions for two of the metric functions on an initial null hypersurface. A proof is presented that the result for constitutes the appropriate characteristic initial value function for all physically realistic axisymmetric, non-rotating vacuum spacetimes. Integration of the field equations on the axis of symmetry when an equatorial symmetry plane is also present, and on the equatorial plane itself when time rates of change can be neglected, shows that these data produce results consistent with Newton's laws and with the Schwarzschild solution in the appropriate limits. The solution on the axis of symmetry indicates that the Weyl curvature increases without limit between black holes as their separation decreases.