Time Rate Of Change Research Articles

Temperature distribution in a tungsten electrothermal atomizer

Temperature distribution in the tube surface of a tungsten electrothermal atomizer (WETA-82) has been studied both theoretically and experimentally; also, the temperature distribution in the gas inside the atomizer has been studied theoretically. A theoretical model of the temperature distribution in the tube surface and in the gas inside the atomizer is proposed. It is considered that thermal radiation to the surroundings and beat conduction towards the water-cooled electrode supports are the only paths for heat loss, and electrical resistive heating and conduction from adjacent nodes are the only sources of heat gain. The time rate of change in temperature of the atomizer is expressed in the form of a differential equation. A finite-difference form of the differential equation is used in a computer program to calculate the temperature at each time step. Optical pyrometry was used to determine the surface temperature of the tube atomizer. The model predicts that an increase in the heating rate of the tube atomizer will slightly decrease the temperature gradient over the tube circumference; however, unambiguous observation of this decrease could not be made in the sequentially measured temperature difference between two selected point using optical pyrometry. Variation in the hydrogen content of the hydrogen-argon mixture purge gas did not have a significant effect on the temperature gradient of the tungsten tube surface. The results of this study have indicated possible improvements in the atomizer design with a view to making the temperature distribution over the circumference of the tube atomizer more uniform.

Flow Acceleration and Mountain Drag*

Abstract Dynamic explanations of mountain drag usually invoke viscous effects and/or wave momentum flux by either Rossby or internal gravity waves. This paper explores an alternative mechanism in terms of the unsteadiness of the incident flow. The reaction to acceleration (local time rate of change) of the flow put a stationary obstacle can manifest itself as a contribution to the drag on the flow. A simple model provides an estimate of this acceleration reaction in a geophysically relevant context. The shallow-water flow of a periodic current around a right-circular cylinder is determined for subinertial periods and arbitrary rotational Froude number. The results of this prototype calculation support the hypothesis that acceleration reaction may provide a substantial contribution to the mountain drag exerted by mesoscale and synoptic-scale obstacles.

Application of Bond Graphs to Thermofluid Processes and Systems

Over the past few years a study was focused on the development of bond graphs for thermofluid processes and systems using the true power variables of temperature and time rate of change of entropy. This paper summarizes results of the study. Discussion begins with the study of a simple case of single phase incompressible fluid flow and ends with a completely general case of multiphase, variable density flow. Variations in density require introduction of the momentum equation to the bond graph. Inclusion of entropy as a state variable necessitates the use of Gibb’s equation and its representation by means of bond graphs. This paper presents these formulations and representations, and compares dynamic results predicted by bond graphs with those of classical approaches.

Reply by Authors to B. Etkin and G. D'Eleuterio

ONES and DeLaurier1 have undertaken a difficult task in developing methods for estimating the aerodynamic forces on aerostats and airships. We trust that their results will be of practical utility to workers in this field. However, the portion of their paper that deals with the modeling of forces in unsteady flow has errors in the theory that users should be aware of. In particular, Eq. (45) of the paper is wrong. It reads w= W+Py-Qx-Pv + Qu (1) In fact, w is defined correctly in Eq. (14) of Ref. 1, and its time rate of change w (for a quasirigid vehicle with y = x~Q) is iv= W+Py-Qx (2) This follows clearly and simply from the definitions of the quantities in Eq. (14); w is nothing other than the component, along the z-body axis, of the inertial velocity of the center of the panel (slice). The authors arrive at their incorrect equation (45) by a convoluted and erroneous argument following Eq. (40). The source of the error appears to be an invalid statement in Eq. (41). The vector r cannot be both as in Eq. (14) and in Eq. (41); according to the definition of r preceding Eq. (14), r is constant in the body-fixed frame, so that r = 0, whereas in Eq. (41) rVO. The incorrect value of w is then substituted into Eq. (38), which is the strip-theory application of an exact theoretical result. An erroneous expression for the dZ7 force component is then obtained in Eq. (46). It should read dZ7 = - 3' ( W+ Py - Qx) - k(Qu + k^Pv (3)

On theories of rotating convection zones

It is shown that the time rate of change (brought about by the turbulent convective motions) in the angular momentum of a thin spherical shell of radius r is such as to increase the angular velocity of the lower part (τΩ<SUB>0</SUB> &gt; 1; τ is the dominant eddy's lifetime) of the solar convection zone (SCZ) and to decrease the angular velocity of the upper part (τΩ<SUB>0</SUB> &lt; 1). A tentative model of rotation in the SCZ is proposed: (1) the (τΩ<SUB>0</SUB> &gt; 1)-region is in weaker differential rotation than the surface and not constrained by the Taylor-Proudman theorem, (2) the observed solar differential rotation at the surface is then generated as the SCZ relaxes from the (τΩ<SUB>0</SUB> &gt; 1)-state in the lower part to the (τΩ<SUB>0</SUB> &lt; 1)-state at the surface. In the upper and lower layers of the SCZ, angular-momentum conservation between the turbulent motions and viscous stresses leads to an angular velocity increasing inward.

A Non-Invasive Index of Leg Arterial Perfusion Pressure During Walking, Derived From Cutaneous Toe Temperature

This article describes and evaluates a non-invasive technique for continuous monitoring of hemodynamic changes in the legs during walking. The method involves monitoring of cutaneous toe temperature. In six normal subjects we have shown that, during exercise under carefully controlled conditions, a unique steady-state toe temperature exists for any given leg arterial perfusion pressure, when perfusion pressure is varied by means of an external occluding ankle cuff. Further, we have demonstrated a strong correlation between this external ankle cuff pressure and the time rate of changes of toe temperature during the test-period following occlusion. Correlation coefficients, r1, were between -1 and -0.88 (mean -0.95; standard deviation +/- 0.03) for big toe and between -1 and -0.87 (mean -0.94; standard deviation +/- 0.03) for third toe. We conclude that during walking the time profile of toe temperature changes is a useful index of changes in leg perfusion pressure. Therefore, toe temperature may be used to study the dynamics of leg arterial circulation in atherosclerotic occlusive diseases.

Negative capacitance bus terminator for improving the switching speed of a microcomputer databus

The data transfer speed of a microcomputer bus can be improved by adding an active circuit to the bus. This active circuit amplifies the bus voltage and feeds back to the bus a current which is proportional to the time rate of change of the bus voltage. This circuit effectively adds a negative capacitance to the bus. The practical capacitance canceling capability is limited by the propagation delay time of the operational amplifier in the active circuit. The theory of microcomputer bus structures with negative capacitance including effects of amplifier delay is presented. Typically, an operational amplifier with propagation delay less than one tenth of the bus time constant is required to achieve significant (factor of 2) bus speed improvement. High performance operational amplifiers were used to construct a working model of the negative capacitance bus terminator. The experimental results agree well with the theory.

An experimental investigation of two dimensional flame-vortex interactions

Experiments have been performed to study the interaction between a flame and a single vortex impulsively generated by the flame. The objectives are to investigate the amplitude of the cylindrically diverging acoustic wave produced by the interaction and to develop a quantitative approach to determine the degree of violence of the flame-vortex interaction. With the Reynolds number, defined as the ratio of the strength of the vortex to the kinematic viscosity of the unburned gas, characterizing the unburned gas flow condition quantitatively, the acoustic pressure Δ p(t) generated by the interaction has been measured at distances 1.5, 1.75 and 2.0 meters away from the interaction zone using a microcomputer-based data acquisition system and a storage oscilloscope. The dimensionless time rate of change in the heat addition rate, Q( t ), of the flame-vortex interaction, is deduced from the acoustic pressure data via the line source equation in linear acoustic theory. The Fast Fourier Transform has been used to perform the analysis. For the thirty experiments performed, the amplitudes of Q( t ) and Δ p(t) have been found to be dependent on Re, burning speed and two dimensionless geometric parameters. The results show that Q max increases with Re when the geometric parameters are fixed. An empirical logarithmic equation has been obtained to describe the variation of Q max for Re between 10 5 and 4.5×10 5 . The maximum Δ p max recorded was 72 mbar at 1.5 m from the interaction zone. The increase in the “violence” of the interaction has been found to be associated with an increase in the heat addition rate during the period of flame-vortex interaction.

The principles of continuum mechanics applied to transport processes and deformation in plant tissue

The principles of continuum mechanics provide a consistent framework for the derivation of mathematical statements describing transport and deformation in a continuous medium. In this manuscript we formulate mathematical expressions for the transport of water and solute along the direction of deformation in plant tissue. Mathematical expressions for the local tissue deformation are also obtained and are expressed in terms of the displacement velocities and axial strain. These derivations are based upon the explicit consideration of the tissue as a mathematical continuum composed of a cell wall matrix, water, and solute phases. The principles of mass conservation for each component phase are employed to construct individual continuity equations for the matrix, water, and solute phases respectively. The differential equation for the flow of water in tissue is found by combining the continuity equations for both the water and cell wall phases with the axial derivative of the constitutive relationship relating the motion of the water with respect to the cell wall matrix. The partial differential equation for solute flow in deforming tissue is found by combining the continuity statements for the solute and the cell wall phases with the axial derivative of the constitutive relationship for solute motion with respect to cell wall matrix. The mathematical description of tissue deformation is found from the balance of linear momentum. Momentum balance for plant tissue states that the time rate of change of momentum of the cell wall phase equals the forces acting on the matrix expressed as the axial gradients of mechanical stress and osmotic potential, respectively. This expression is then combined with the axial derivative of constitutive relations found from a generalized form of Hooke's law and the Boyle-Van't Hoff relationship. The resulting description of deformation is formed as a system of coupled, quasi-linear, first-order, partial differential equations for the local tissue displacement velocities and the longitudinal tissue strain. The deformation equations describe either elastic or plastic one dimensional tissue expansion or contraction. The overall mathematical statements of transport processes and deformation in plant tissue is given by four differential equations coupled through the gradient of the tissue displacement velocities which describe the local shrinking or swelling of the tissue. This coupling provides the explicit connection between the local tissue deformation and the instantaneous water potential and solute concentration of the tissue.

A numerical model of the time‐dependent wintertime circulation of the New York Bight

The time‐dependent flow in the New York Bight from March 7 to April 30, 1975, is calculated from approximations to the barotropic vorticity equation subject to forcing by winds observed at the John F. Kennedy airport and by an upstream flow across the Long Island shelf. Comparisons of major axis velocities to observations throughout the bight show reasonable agreement. There is also considerable model skill in the prediction of alongshore variations in the major axis velocity with relatively low absolute errors. In general, associated with northeastward winds are northeastward shelf flows and upvalley currents in the Hudson Shelf Valley (HSV). Downvalley flows in the HSV occur when the northeastward wind abates and the flow on the shelf turns southwestward. The mechanism responsible for the behavior of the valley flow appears to be topographic steering with moderation due to bottom friction. The time rate of change of relative vorticity does not appear to have large net effect over the duration of an event Consequently, steady state models represent well the dynamics for an event‐averaged flow. Discrepancies between model results and observation suggest that there is indeed a southwestward pressure gradient force operating in the New York Bight, and an adiabatic pressure condition offshore may be an over simplification that need be removed.

The relation between various coupling schemes for calculating nonradiative multiphonon transition rates

In an earlier paper (see ibid., vol.15, p.L381, 1982) the author gave a simple proof that the static, adiabatic and intermediate coupling schemes give the same nonradiative multiphonon transition rates to leading order in the off-diagonal part of the electron-phonon interaction. In that proof, the time dependence in the interaction picture of the matrices describing the transformation from one representation to another was neglected using a heuristic argument. In this paper it is shown explicitly that this time dependence can be neglected, hence firmly establishing the earlier result. The equivalence between the various coupling schemes is also established for the time rate of change of a general observable; for example the charge density. The present work is discussed in relation to the recent papers by Peuker et al. (1982) and by Wagner (1982). In particular it is shown that there is no contradiction between the present work and that due to Wagner. It is also shown that Wagner's alternative adiabatic base is none other than the base defined by Condon electronic wavefunctions and displaced lattice oscillators and that this result holds independently of the strength of the off-diagonal part of the electron-phonon interaction.

Design and fabrication of a simple, versatile cryomicroscopy stage

A new cell freezing stage for cryomicroscopy is described with the intention of providing information adequate to enable easy duplication by other investigators. The stage is designed to be constructed from commonly available stock materials and to be fabricated with a minimal investment of time using simple techniques with standard machine tools. Provisions are made both for convective cooling with a chilled refrigerant gas and for heating with a transparent electrical resistance coating applied to a glass plate on which the specimen is mounted. The specimen temperature and its time rate of change can be regulated independently by continuously adjusting the balance between the cooling and heating fluxes. A temperature controller may be interfaced to the stage to regulate the specimen temperature automatically according to a preprogrammed protocol. Thermal performance capabilities of the stage satisfy most general cryomicroscopy requirements. Cooling and warming rates can be effected up to several hundred degrees Kelvin per minute across a temperature range in excess of 120 to 375 K. Thermal gradients within the viewing aperature of the stage are kept small by creating a tortuous convective flow path for the refrigerant fluid.

Optimal initial conditions for eastern roll high jump

In mathematical models of athletic performance the competitor is often viewed as a state determined dynamic system, whose states are the positions, orientations and their first time derivatives of as many body segments as are deemed necessary to adequately describe the motion. The time rates of change of the states depend on the states themselves and on certain inputs ū(t) (generally muscle torques), which the competitor specifies at all times throughout the event.

'Proper time' and the Dirac equation

In the theory of the Dirac equation in quantum mechanics, the Dirac matrix beta is taken to connect 'proper time' and coordinate time rates of change of operators. The usual Heisenberg equation for the coordinate time rate of change of an operator then leads to a Heisenberg-like equation for its proper time rate (the 'Hamiltonian' being analogous to the generator of proper time translations in classical mechanics). Certain terms have to be set to zero by the use of the Dirac equation, and this is here justified. The equivalence of the formalisms under these conditions is shown and the method entitles us to derive some well known results for the Dirac equation in a comparatively effortless manner. The present work justifies methods introduced by H.C. Corben (1961).

Statistical acceleration of electrons by lower-hybrid turbulence

The statistical acceleration of electrons along an ambient magnetic field by large-amplitude lower-hybrid turbulence is discussed. Perturbations driven by a crossfield current and propagating nearly perpendicular to the applied magnetic field are considered. It is assumed that the instability saturates rapidly and that the fluctuating electric field is predominantly electrostatic. This work is not concerned with the detailed saturation mechanism, but rather with what happens to the electrons after the turbulence has saturated. If the turbulence is characterized by a spectrum of small parallel wavenumbers, such that the parallel phase velocity of the waves is greater than the electron thermal velocity, then the turbulence can only accelerate electrons moving with large velocities along the magnetic field. The qusai-linear diffusion equation is solved using a Green's function technique, assuming a power law spectral energy density. The time evolution of an initial Maxwellian distribution is given and the time rate of change of the mean electron energy is calculated for various cases.

HEMP Field Penetration into an Ideal Shelter without a Floor through a Lossy Earth

EMP hardening of existing ground based facilities by shielding the facility principally from above has been investigated. This study supports the following conclusions: 1) Wall extensions provide an added measure of protection for EMP hardening. 2) The soils with high conductivity shield best. 3) The angle of arrival of the EMP is relatively unimportant. 4) Finite length shelters (all real shelters) can allow significant energy to penetrate, and 5) Finite length shelters allow large magnetic fields to penetrate the shelter although the coupling mechanism (dH/dt, the time rate of change in the magnetic field) is considerably reduced (factor of u 50).

A Dynamic Leontief Modeling Approach to Management for Optimal Utilization in Water Resources Systems

A quantitative framework to the problem of management for optimal utilization in water resources systems is developed using a dynamic Leontief modeling approach. The framework is comprised of a supply-demand disequilibrium model which allows for excess demand or supply to exist at any time. A linear control regulator formulation is undertaken in which the weighted difference between the time rate of change of actual water levels and the excess water demand is used as the control instrument. Application to the River Nile system is performed using the presently available data bank information. Several computer experiments illustrate the validity of the modeling approach and its suitability as a planning tool.

Gauge-invariant non-relativistic limit of an electron in a time-dependent electromagnetic field

The Dirac equation for a charged particle in a time-dependent electromagnetic field is reduced to the Pauli equation in the non-relativistic limit by making a time-dependent Foldy-Wouthuysen transformation in a completely gauge-invariant way. In a time-dependent field, the expectation value of the Hamiltonian is dependent on the gauge, and so it cannot be the energy. The energy is obtained by taking the expectation value of the energy operator, the time rate of change of which is the average of the quantum mechanical power operator. The Hamiltonian formulation of a charged particle in a time-dependent external electromagnetic field is satisfactory when this distinction between the Hamiltonian, which describes the time evolution of the system, and the energy operator, which is gauge invariant, is made.

High-energy proton-hydrogen-atom excitation multipole moments

Proton-hydrogen-atom excitation angle-integrated multiple moments are calculated within a classical trajectory approximation for the relative proton-proton motion, but with full coupling of basis states centred on both protons. For the excitation channels the authors find that the dipole moment within the n=2 states is very sensitive to final-state interactions between the degenerate excited states. The dipole moment is similar in magnitude to the dipole moment induced in electron-hydrogen excitation but the sign is opposite. In this case the electron is more often on the down-beam side of the target proton. The time rate of change of the dipole moment for excitation to n=2 is similar in magnitude and the same sign (negative) as in electron-hydrogen excitation.

Estimation of corona current beneath thunderclouds

The intense electric field beneath a thunderstorm often produces corona discharge from bushes and trees. The average steady state corona current per unit horizontal area, Jc, is approximately proportional to the time rate of change of the electric field at the ground when the value of the field changes sign following a lightning flash. This paper derives this relationship and proposes that the contribution of corona discharge to the charge budget of a thunderstorm be evaluated from measurements of the electric field at many sites below a thunderstorm rather than from direct measurement of the corona current.